physics and mechanics of soil liquefaction : proceedings of the international workshop on the...

PHYSICS A N D M ECHANICS OF SOIL LIQUEFACTION

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PROCEEDINGS OF THE INTERNATIONAL WORKSHOP ON THE PHYSICS AND MECHANICS OF SOIL LIQUEFACTION/ BALTIM O R E/M A RY LAN D/USA /10-11 SEPTEMBER 1998

Physics and Mechanics of Soil LiquefactionEdited by

Poul V. LadeThe Johns Hopkins University, Baltimore, Maryland, USA

Jerry A.YamamuroClarkson University, Potsdam, New York, USA

A. A. B ALKEM A / ROTTERDAM / BROOKFIELD / 1 9 9 9

The texts of the various papers in this volume were set individually by typists under the supervision of each of the authors concerned.

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ISBN 90 5809 038 8 © 1999 A.A.Balkema, Rotterdam Printed in the Netherlands

Physics and Mechanics of Soil Liquefaction, Lade & Yamamuro (eds) © 1999 Balkema, Rotterdam, ISBN 90 5809 038 8

Table o f contents

Preface IX

1 The mechanism of instability

Instability of granular materials PVLade

Static liquefaction of very loose Hostun RF sand: Experiments and modelling T.Doanh, E.Ihraim, Ph.Duhujet, R.Matiotti ¿c I.Herle

The mechanism controlling static liquefaction and cyclic strength of sand L B. Ibsen

Advances in the effective stress approach to liquefaction behavior G.M. Norris

3

17

29

41

2 Effect of soil gradation on liquefactionStatic and cyclic liquefaction of silty sands 55J A Yamamuro, K.M. Covert & PVLade

Role of intergrain contacts, friction, and interactions on undrained response of granular mixes ClS. Thevanayagam

Triggering and post-liquefaction strength issues in fine-grained soils 79J.PKoester

Developments in gravelly soil liquefaction and dynamic behavior 91M D. Evans & K. M. Rollins

3 Factors affecting liquefaction susceptibilityFundamental factors affecting liquefaction susceptibility of sands YPVaid ¿c S.Sivathayalan

Elastic deformation properties of sands containing fines during liquefaction y. Koseki, N Maeshiro, I. Urano & T Sato

105

121

Constitutive issues in soil liquefactionS.Sture

Influence of confining stress on liquefaction resistance M E. Hynes & R. S. Olsen

Pore water pressure in limit analysis calculationsR. L. Michalowski

145

153

133

4 Soil fabric and its effect on liquefactionComparison of tests on undisturbed and reconstituted silt and silty sand R.Dyvik & K.H0eg

Quantitative characterization of microstructure evolution J,D.Frost, D.-JJang, C.-CChen & J.-Y.Park

Undisturbed sampling of loose sand using in-situ ground freezing D.C.Sego, B. A Hofmann, RK. Robertson & C.E.Wride (Fear)

159

169

179

5 Methods of characterizing liquefaction potentialThe critical state line and its application to soil liquefaction 195K.Been

Comments on the determination of the undrained steady state strength of sandy soils 205G. Castro

A methodology to evaluate the susceptibility of soils for liquefaction flow failures 213J.-M. Konrad

A critical state view of liquefaction 221M.GJefferies

Influence of grain-size characteristics in determining the liquefaction potential of a soil 237deposit by the energy methodJ. L Figueroa, A 5. Saada, M. D. Rokoff & L Liang

6 Methods of characterizing post-liquefaction deformationExperimental measurement of the residual strength of particulate materialsS. L Kramer, M. B. Byers & C. H Wang

Void redistribution in sand following earthquake loading R.W Boulanger

Liquefaction constitutive modelA-WElgamal, E.Parra, ZYang, R.Dobry & M.Zeghal

7 Centrifuge studies of liquefactionSeveral important issues related to liquefaction study using centrifuge modeling X.Zeng

249

261

269

283

VI

Investigations on the behavior of liquefying soils R. K Ledbetter, R. S. Steedman & G. D. Butler

Modeling liquefaction in centrifuges H. -Y. Ko & M M Dewoolkar

307

295

8 Field studies of liquefactionPhysics and mechanics of liquefaction from field records and experience TLYoud

In situ liquefaction resistance of sands S.Prakash & TGuo

Initial development of an impulse piezovibrocone for liquefaction evaluation J. A Schneider, RW. Moyne, TLH endren & C.M.Wise

325

335

341

List of participants

Author index

355

361

VII

Physics and Mechanics of Soil Liquefaction, Lade & Yamamuro (eds) © 1999 Baikema, Rotterdam, ISBN 90 5809 038 8

Preface

Soil liquefaction has been one of the most active and visible areas of research in geotechnical engineering over the past 30 years. Soil instability has caused spectacular and costly failures in terms of loss of human lives and destruction of property. Severe damage was induced by soil liquefaction during three recent, major earthquakes, the Loma Prieta earthquake in October 1989, the Northridge earthquake in January 1994 and the Hyogoken-Nanbu (Kobe) earthquake in January 1995. Despite progress in experimental and analytical research, observations have indicated that soil liquefaction is not completely understood.

An International Workshop on the Physics and Mechanics of Soil Liquefaction was organized to provide a forum where hands-on experimentalists in the field of liquefaction could meet under relatively informal conditions to review current knowledge and to exchange ideas and results of research in the area of soil instability and liquefaction. While many aspects of soil liquefaction deserve attention, the workshop concentrated on understanding the fundamental physics of the liquefaction phenomenon occurring under static and cyclic loading and on the mechanics by which the observed phenomenon may be modeled. A fundamental understanding of the liquefaction process is necessary to improve criteria and methods for prediction of the collapse of saturated soils, to enhance the triggering analysis, to develop mitigation measures, to evaluate the effectiveness of practical remedial techniques, and to ultimately improve the current design recommendations. Each invited participant was expected to contribute a paper, which represents, in the opinion of the author, the current state-of-the-ait in his/her focus area in experimental liquefaction research. The contributions are organized in eight sections:

1. The mechanism of instability;2. Effect of soil gradation on liquefaction;3. Eactors affecting liquefaction susceptibility;4. Soil fabric and its effect on liquefaction;5. Methods of characterizing liquefaction potential;6. Methods of characterizing post-liquefaction deformation;7. Centrifuge studies of liquefaction;8. Field studies of liquefaction.The workshop was sponsored by the Siting and Geotechnical Systems/Earthquake Hazard Mitiga

tion Program of the National Science Foundation under Grant No. CMS-9814023 to The Johns Hopkins University. The support and encouragement of the program director. Dr Clifford J.Astill, are much appreciated. The members of the Steering Committee for the Workshop were, in addition to the editors of the proceedings, Mary Ellen Hynes (Waterways Experiment Station, Vicksburg, MS), Y.P.Vaid (University of British Columbia, Vancouver), and Stein Sture (University of Colorado, Boulder, CO). Grateful appreciation is expressed for the support and help with organizing the workshop.

RVLade J. A. Yamamuro

November 1998

IX

1 The mechanism o f instability

Physics and Mechanics of Soil Liquefaction, LadeS. Yamamuro (eds) © 1999 Balkema, Rotterdam, ISBN 90 5809 038 8

Instability o f granular materials

RVLadeThe Johns Hopkins University, Baltimore, Md., USA

ABSTRACT: Experimental observations form the background for studies o f the conditions for instability of granular materials that exhibit nonassociated plastic flow. Triaxial tests on sand were performed to study the regions o f stable and unstable behavior. The variables were the sign o f the second work increment (positive or negative), the volumetric strain behavior (compression or dilation), the drainage condition (drained or undrained) and the degree o f saturation (fully or partly saturated). For saturated soil that tend to compress, undrained conditions may lead to instability if the state o f stress is located in the region between the instability line and the failure surface. Thus, granular materials may become unstable inside the failure surface, but instability is not synonymous with failure. The proposed analysis method for static instability o f slopes involves the state o f stress in the ground and the region o f potential instability. A trigger mechanism is required to initiate instability.

1 INTRODUCTION

Instability is a phenomenon that can occur in granular materials exhibiting nonassociated plastic flow. Instability is defined as the inability o f a material to carry or sustain a given load, resulting in large strains that eventually lead to failure. Collapse o f shallow submarine slopes and slopes o f tailings dams or hydraulic fill dams may be attributed to soil instability. Instability in saturated, cohesionless soils is a phenomenon in which catastrophic consequences similar to those following failure are encountered well within the established effective stress failure surface. Events triggering instability can be small in magnitude, such as seismic events, wave action, vibrations from machinery, or the result o f consolidation or volumetric creep.

Two criteria for failure in soils are commonly employed in interpretation o f results o f triaxial tests: (1) Failure occurs when the stress difference reaches a limiting value, ( a i -a 3)max, and (2) Failure occurs when the effective principal stress ratio reaches a limiting value, (aiVa3’)max- The two conditions are reached simultaneously in drained tests. The confusion as to the definition o f failure arises in interpretation o f undrained tests on loose sands and sensitive clays in which the pore pressures increase monotonically during shear. For these types o f soils the maximum stress difference is reached before the maximum effective stress ratio. The choice o f failure criterion vary with the purpose for which the strength

is to be used. Typically, (a i -a 3)max is employed in total stress analyses, and (aiVa3’)max is used in effective stress analyses. These issues have been discussed at length by e.g., Bjerrum and Simons (1960), Seed et al. (I960), and Whitman (1960).

The condition o f maximum stress difference does not correspond to a true failure condition, but rather to a condition of minimum stress difference at which instability may develop inside the true failure surface. This condition was studied in detail by Kramer and Seed (1988). Stress states can be reached above the minimum stress difference condition described by (a i -a 3)max and instability can be induced anywhere between the (a i~ a 3)max- condition and the true failure surface described by (a i’/a 3’)max- Thus, instability is not synonymous with failure.

Current design methods in geotechnical engineering practice are based on either total stress analyses or effective stress analyses. When soil instability is encountered, total stress analyses tend to be too conservative, because the total strength may underestimate the true strength o f the soil. For undrained conditions, effective stress analyses can significantly overestimate the resistance o f cohesionless soil to instability type failures. While soil instability is practically located between the two types o f analysis methods, the mechanics involved in this phenomenon is not captured correctly by stability procedures describing shear failure, such as those involved in conventional slope stability methods. Instability may eventually lead -to

liquefaction and flow slides. In fact, instability is a requirement for subsequent liquefaction, and preventing liquefaction necessitates prevention of instability. Thus, analysis o f liquefaction susceptibility should be an analysis o f susceptiblity to instability.

Presented here is a review o f the mechanics of instability, and the experimentally determined conditions for which granular materials are stable, conditionally unstable, and unconditionally unstable are presented. The location o f the region o f potential instability and its determination are discussed, and the factors that control instability are presented. Analysis procedures for static instability o f shallow submarine slopes and nearly fully saturated slopes representing tailings dams or hydraulic fill dams are reviewed. Such slopes can become unstable due to small disturbances, although conventional stability analyses indicate that they should remain stable.

FAILURE SURFACE IN COMPRESSION

Fig.l Pattern of yield surfaces for isotropic soils, and stress path for conventional triaxial compression test (BC).

2 STABILITY POSTULATES

Experimental evidence from tests on several types of soils have clearly indicated that the use o f conventional associated flow rules results in prediction o f too large volumetric expansion. To characterize the volume change correctly, it is necessary to employ a nonassociated flow rule. The plastic potential surfaces do therefore not coincide with the yield surfaces, but the two families o f surfaces cross each other.

The application o f nonassociated plastic flow rules for soil have resulted in questions regarding uniqueness and stability o f such materials. The stability postulate for time-independent materials due to Drucker (1951, 1956, 1959) is satisfied provided that associated plastic flow is employed in construction o f constitutive models involving convex, plastic yield surfaces. Hill's stability condition (Bishop and Hill, 1951; Hill, 1958) is expressed in terms o f total strain increments (elastic and plastic), and it extends the condition for stability a little beyond that due to Drucker. Theoretical considerations have suggested that they are not necessary conditions for stability (Mroz, 1963; Mandel, 1964).

The stability postulate formulated by Drucker is suitable for solid metals which exhibit associated flow. According to this postulate, stability requires that the second increment o f plastic work is positive or zero:

d^Wp = à i j - ^ j > 0 (1)

work are always associated with the stable, ascending part o f the stress-strain relationship, whereas negative values are associated with the unstable, descending part o f the stress-strain curve obtained after peak failure.

According to Hill's condition stability should be maintained as long as

• (¿ÿ + 4 ) = • «ÿ + d i j - é ^ j > 0 (2)

in which dy is the increment o f stress and is the resulting increment in plastic strain. For metals, positive values o f the second increment o f plastic

in which ¿iy and ¿y are the total and elastic strain increments, respectively. Hill's stability condition guarantees stability a little beyond the condition given by Drucker.

3 CONSEQUENCES OF NONASSOCIATED FLOW

A typical pattern o f yield surfaces for an isotropic soil is shown on the triaxial plane in Fig. 1. In three dimensions these yield surfaces are shaped as asymmetric tear drops. For an isotropic material the yield surfaces intersect the hydrostatic axis in a perpendicular manner, they bend smoothly backwards towards the origin, and cross the failure surface at sharp angles as indicated in Fig. 1.

Plastic potential surfaces have similar shapes as yield surfaces, but for nonassociated flow the two families o f surfaces cross each other. Experimental evidence for frictional materials indicates that the plastic potential surfaces have more pointed ends and they resemble cigars with asymmetric cross-sections. A typical plastic potential surface is shown at point A in Fig. 1.

The shaded wedge between the yield surface and the plastic potential surface defines a region in which Inequality (1) is not fulfilled for a material with

nonassociated flow. Since a stress increment vector from point A located inside the wedge and the plastic strain increment vector form an obtuse angle, the scalar product o f these two vectors (see Inequality (1)) is negative. According to Drucker’s stability postulate the sand may exhibit unstable behavior if the stress point lies adjacent to a region (e.g. the shaded region in Fig. 1) into which a stress probe would violate Inequality (1). However, experiments show that the sand is perfectly stable at stress points where the normal to the yield surface points in the outward direction o f the hydrostatic axis. For this condition the deviator stress can be safely increased to produce further plastic shear strains (workhardening). In other words, the sand can sustain higher loads and behave in an inelastic manner without undergoing any instability or collapse.

Potential instability occurs in regions where the yield surface opens up in the outward direction of the hydrostatic axis. This allows plastic strains (loading) to occur while the stresses are decreasing. Here loading occurs inside the failure surface and instability may develop in the form o f inability to sustain the current deviator stresses.

Fig. 1 shows the stress path for a conventional triaxial compression test performed at constant confining pressure. As the specimen is loaded from B to C the inclination o f the yield surface changes. At low deviator stresses near point B, the yield surface is inclined towards the outwards direction o f the hydrostatic axis. As loading proceeds, the inclination o f the yield surface changes gradually and becomes inclined towards the origin as failure is approached at point C. It is in this region o f high deviator stresses where the yield surface is inclined toward the origin that instability may occur.

Fig. 2 shows a schematic illustration o f the region in which Inequality (1) is not fulfilled for a dilating material with nonassociated flow. The region is shaped as a wedge between the current yield surface f and the plastic potential surface g corresponding to the current stress point. This wedge shaped region is located within a larger region bounded by lines corresponding to (aiVa3’) == const, and =const, as indicated on Fig. 2. All stresses, including the stress difference (ai-aa), are decreasing within the wedge between f and g, but the stress ratio (a i’/a 3’) is increasing in this region. By performing triaxial tests with stress paths located in this region, experimental evidence regarding the instability o f materials with nonassociated flow can be obtained.

It is important to recognize that the material behavior obtained for stress paths within the shaded wedge in Fig. 2 corresponds to work-hardening with positive plastic work, dWp, and outward motion o f the yield surface. Although the stresses in any direction within the wedge are decreasing, failure has not been reached and softening o f the material is therefore not occurring.

Fig. 2 Wedge-shaped region o f stress paths with decreasing stresses in which soils with nonassociated flow may be unstable during hardening inside the yield surface.

4 NONASSOCIATED FLOW IN GRANULAR SOILS

4.1 Drained Conditions

To demonstrate that nonassociated plastic flow is obtained for granular materials, the results o f a drained triaxial test on fine silica sand are shown in Fig. 3. This test was performed with a stress path inside the failure surface involving primary loading (hardening) with decreasing stress difference (cri-a3) and decreasing confining pressure g -. If stresses and strain increments are plotted on the same diagram, as in Fig. 3(b), the direction o f the plastic strain increment vector is uniquely determined from the state o f stress, and it is independent o f the stress path leading to this state o f stress as shown by Poorooshasb et al. (1966) and Lade and Duncan (1976). The stress path with decreasing stresses, shown in Fig. 3(b), is so steep as to form an obtuse angle (p -a = 110°) with the direction o f the plastic strain increment vector. Thus, the inequality in (1) is violated.

The fact that plastic yielding is occurring along the stress path with decreasing stresses is seen from the stress-strain curve in Fig. 3(a). Section BC on the stress path is labeled similarly on the stress-strain curve which indicates large plastic strains between B and C. Since the yield surface is being pushed out, it must be steeper than the stress path direction BC. If it were less steep, so as for example to be perpendicular to the plastic strain increment vector

(Ti (kg/cm2) f a i l u r e LINE

Fig. 3 (a) Stress-strain and volume change curves, and (b) stress path and plastic strain increment vectors for test on fine sand.

thereby indicating associated flow, then point C would be inside the yield surface passing through point B corresponding to unloading from B to C. This would contradict the large plastic strains shown in Fig. 3(a). Consequently, the yield surface must be steeper than stress path BC, and nonassociated plastic flow is therefore clearly indicated.

4.2 Undrained Conditions

To study the region of potential instability in stress space and to investigate the occurrence o f nonassociated flow under undrained conditions, a typical effective stress path observed in an undrained test performed with high confining pressure is shown in Fig. 4. Strain increments are superimposed on the stress diagram to allow analyses o f strain increment vector directions and to derive the directions o f the plastic potential surfaces g. These surfaces are by definition perpendicular to the plastic strain increment vector directions.

For undrained tests the total volumetric strain is zero corresponding to the total strain increment vector being perpendicular to the hydrostatic axis everywhere along the effective stress path. This is shown in Fig. 4. This figure also shows that volumetric compression is characterized by a strain increment vector pointing away from the origin o f the stress space.

The stress-strain relation corresponding to the effective stress path in Fig. 4 shows that plastic strains are produced everywhere along the undrained stress path. The yield surface must therefore be pushed out, and this requires it to be inclined relative

STRAIN INCREMENT VECTOR DIRECTIONS:

’ ^ 3' * ^3Fig. 4 Evaluation o f relative inclinations o f yield (f)

and plastic potential (g) surfaces along undrained effective stress path.

to the effective stress path as indicated in Fig. 4.The direction o f the elastic portion o f the total

strain increment vector in the triaxial plane depends on the value o f Poisson’s ratio, v. For v = 0 the elastic strain increment vector is parallel to the stress increment vector which is tangential to the stress path on the triaxial plane shown in Fig. 4. For v =

0.5, the elastic strain increment vector is perpendicular to the hydrostatic axis corresponding to no elastic volume change. For values o f Poisson's ratio between zero and 0.5 the elastic strain increment vector will be between the two extreme positions. With no loss o f generality, it will be assumed in the following that the elastic strain increment vector is parallel to the stress increment vector, i.e., corresponding to v = 0.

Three points o f interest are indicated along the undrained effective stress path in Fig. 4. The elastic portion o f the total strain increment vector is pointed in the current direction o f the effective stress path. The length and direction o f the plastic strain increment vector is obtained by vectorial subtraction o f the elastic from the total strain increment vector. It is clear that only the directions o f the elastic and the total strain increment vectors are known, and that the derived direction o f the plastic strain increment vector depends on the assumed relative magnitudes o f the elastic and total strain increments. However, as will be seen, it can be shown that nonassociated flow prevails at points B and C independent o f the assumed magnitudes o f strains.

At point A the length o f the elastic vector is chosen so as to show that nonassociated flow could occur. In fact, in the absence o f actual experimental determination o f the elastic and plastic strain magnitudes, it is not possible to argue whether the plastic flow is associated or nonassociated, i.e., whether the yield and plastic potential surfaces are identical or not. However, this is o f no importance to the study o f instability presented here. Whether associated flow or nonassociated flow is observed at point A, stability is obtained everywhere along the effective stress path from the hydrostatic axis up to point B. Along this portion o f the stress path the load can be maintained constant or increased without any observable instability.

Nonassociated flow is clearly obtained at points B and C. For the limiting case where the elastic strain increments become negligible the plastic strain increment vectors become perpendicular to the hydrostatic axis. Since the yield surfaces must be inclined relative to the effective stress paths as shown, nonassociated flow is clearly demonstrated to occur at points B and C.

Note that the plastic strain increment vector in Fig. 4 indicate that plastic volumetric compression occurs while the total volumetric strain is zero.

5 BEHAVIOR UNDER DRAINED CONDITIONS

In order to expose the potential instabilities in soil behavior that might occur for the stress paths in the prefailure region described earlier (see Fig. 2), it is necessary to perform triaxial tests under stress control. A series o f drained tests similar to that shown in Fig. 3 was therefore performed under stress control (Lade et al. 1987). In fact, the test shown in Fig. 3 is one of these tests. Seven experiments were performed. They all exhibited plastic dilation, and they all clearly showed nonassociated flow. When the sand specimens were exposed to stress paths in the region o f potential instability (d * < 0) , nonewas observed, i.e. run-away instability was not encountered. The tall cylindrical specimens with lubricated ends deformed as perfect right cylinders with no developing shear bands, no bulging or shearing in a nonuniform manner, or any other signs o f instability. Little but negligible creep was present in the sand specimens. Thus, stable behavior was observed in the region in which Drucker's stability postulate was violated.

Regardless o f the ability to define yield surfaces from experiments, the fact remains that negative values o f d Wp are obtained from direct experimental measurements. The fact that the specimens remained stable implies that the behavior is not strain softening, i.e. the peak strength has not been exceeded. Therefore, to model this behavior through any type o f normality would require a serious departure from plasticity theory.

In order to investigate whether the type o f volume change (dilation or compression) was important for stability o f granular soils, a second series o f tests was perfonned on sand that compressed during shear (Lade and Pradel, 1990). Drained tests with stress paths within the shaded wedge shown in Fig. 2 were performed on loose sand that exhibited compression during shear. Although Drucker’s stability condition was violated inside the failure surface, none o f the specimens showed any signs o f run-away instability.

The results o f these two series o f triaxial compression tests demonstrated that drained conditions produced stable behavior irrespective o f (1) the sign o f the second increment o f work (2) the sign o f the volumetric strain (dilation or compression), and (3) the sign and direction o f the increments in stress components. Thus, under fully controlled conditions such as those prevailing for drained conditions, unstable run-away situations cannot occur. These results therefore clearly show that Drucker's stability postulate is not a necessary condition for stability.

Several series o f triaxial compression tests were performed to study stability and instability in granular materials. The details o f these experiments are given by Lade et al. (1987, 1988), and by Lade and Pradel (1990).

6 BEHAVIOR UNDER UNDRAINED CONDITIONS

6.1 Fully Saturated Soil

On the other hand, fully saturated soils that tend to compress during shear may become unstable inside the failure surface and this may lead to liquefaction. A series o f stress controlled tests was performed on granular soil that tended to compress during shear (Lade et al. 1988). The specimens were exposed to stress paths within the shaded wedge shown in Fig.2. Fig. 5 shows the actual stress paths followed in these tests, and Fig. 6 shows the observed stress-strain, volume change, and pore pressure development in one o f the tests. In each test the saturated specimen was first loaded under drained conditions to a preselected stress level S (expressed as the ratio o f the current to the maximum stress difference at a given confining pressure). The drainage valve was then closed and instability developed in each specimen due to increasing pore pressures, i.e., the specimens could not sustain the applied load. The tendency for volumetric creep, however small it may be, caused the pore pressure to increase under undrained conditions, providing the small perturbation which rendered the material unstable. However, the large strains observed along the unstable stress paths could not be caused by creep or viscous flow as shown by Lade et al. (1988).

The effective stress paths shown in Fig. 5 were within the shaded wedge in Fig. 2, the specimens

exhibited nonassociated flow and plastic volumetric compression (although the total volumetric strain was zero), and instability was obtained in all cases in the hardening regime inside the failure surface.

6.2 Partly Saturated Soil

Stress paths with only one particular direction is obtained from undrained tests on fully saturated soils at each particular stress state, as shown in Fig. 5. In order to study the soil behavior for other stress path directions under undrained conditions, a series o f tests, similar to those described above, was performed on specimens with decreasing degree o f saturation (Lade and Pradel, 1990). By purposely introducing a controlled amount o f compressible air into the specimens, the undrained effective stress paths could be pointed in different directions within the shaded wedge in Fig. 2. The specimens in both tests, in which the effective stress paths were inside the shaded wedge, exhibited unstable behavior. The stress path in a third test was above the shaded wedge because the amount o f air introduced in the specimen was greater than critical. In this test the specimen was perfectly stable.

It is clear from these experiments that a change in drainage conditions for a fully or nearly fully

Fig. 6Fig. 5 Effective stress paths for stress-controlled

triaxial compression tests on loose Sacramento River sand.

Stress-strain, volume change, and pore pressure relations in stress-controlled triaxial compression test on loose Sacramento River sand.

saturated soil can activate unstable behavior. This may occur due to static or dynamic disturbances such as experienced in static flow failures o f tailings dams or in liquefaction o f granular materials during earthquakes.

The results o f the experimental investigations reviewed above showed that run-away instability can only be obtained for (1) negative values o f the second work increment, (2) undrained conditions, (3) fully or almost fully saturated specimens, and (4) granular materials that tend to compress. For these conditions the pore pressure is not controlled, but is able to develop freely to produce a run-away, unstable situation. All other combinations o f the second work increment, volumetric strain behavior, drainage conditions, and degrees o f saturation resulted m stable soil behavior.

7 INSTABILITY OF DILATING GRANULAR MATERIALS

In a discussion o f previously published experimental results reported above, Peters (1991) suggested that even dilating sand may become unstable: If a rate o f volumetric expansion were imposed on an element o f granular material and this rate exceeded the rate of expansion exhibited by the material, then the effective confining pressure would decrease and the element would become unable to sustain the current, applied shear stress. According to the definition, the material element would become unstable. Thus, a

rate o f volume change (whether positive, zero, or negative) imposed on a material element could cause it to become unstable depending on the rate o f volume change exhibited by the soil itself (compression or dilation). In order to study this hypothesis experimentally, a series o f triaxial compression tests was performed with appropriate test conditions. Fig. 7 shows the stress-strain relations, pore pressure development, and effective stress path for a test on dilating fine silica sand. These results are typical for all tests, and they confirm the suggestion that even dilating sand may become unstable (Lade et al. 1993).

The portion o f the stress path o f interest in the present study is that from point B to point C in Fig. 7. All stresses, as well as the vertical stress difference, are decreasing along this second branch. The strain increments produced along this branch correspond to dilation o f the sand. Superimposed on the triaxial plane in Fig. 7(c) are the strain increment vectors at points B and C. These correspond to essentially plastic strains since the elastic contributions are small compared to the plastic strains, as seen on Fig. 7(a). At failure, the elastic strains are zero since no increments in stress occur near peak failure. These strain increment vectors, which are almost parallel, are by definition perpendicular to the respective plastic potential surfaces (g) indicated at points B and C in Fig. 7(c).

It is clear that the stress increment vectors, which are tangential to the effective stress path, form both obtuse and acute angles, 0, with the corresponding

Fig. 7 (a) Stress-strain and volume change behavior, (b) pore pressures, and (c) effective stress path and plastic strain increment vector directions observed in stress controlled triaxial compression test on dilating fine silica sand.

strain increment directions. Thus, the second increment o f plastic work in Inequality (1) is both positive and negative from point B to point C. However, each specimen behaved in an unstable manner, i.e. it was unable to sustain the current stress difference along the entire length o f the prefailure stress path BC regardless o f the sign o f the second increment o f plastic work.

8 CONDITIONS FOR STABILITY ANDINSTABILITY

If instability is defined as a condition for which the current, applied shear stress cannot be sustained for perturbations in the state o f stress, then compressive as well as dilative materials may be considered to be unstable in the region where the yield surface opens up in the outward direction o f the hydrostatic axis. In this region, plastic strains can be produced under decreasing stresses. For undrained conditions and compressive material, the instability is selfsustaining and unconditional, i.e. it is not dependent on conditions outside the soil element. For drained conditions, the instability is conditional, i.e. the decrease in load carrying capability depends on the reduction in effective confining pressure. This reduction may occur as a decrease in total confining pressure or as an increase in pore pressure caused by injection o f water into the soil element.

Figures 8 and 9 show schematic diagrams o f the conditions for stability and instability o f compressing and dilating granular materials. The shear stress is represented by the stress deviator invariant and the mean normal stress is indicated by the stress invariant h . The generic yield surfaces, f, and plastic potential surfaces, g, cross each other at points (A) where the yield surfaces open up in the outward direction o f the hydrostatic axis. Stability is obtained when is constant or increases, whereas instability occurs w hen /2 decreases.

The signs o f the second increment o f work, d} Wp can be negative in the region o f stability, whereas ( f Wp can be positive in the region o f instability for dilating material. These observations suggest that the conditions o f Drucker and Hill provide neither necessary nor sufficient conditions for stability o f granular (frictional) materials.

9 LOCATION OF INSTABILITY LINE

It is the fact that loading o f a compressible soil (resulting in large plastic strains) can occur under decreasing stresses that leads to unstable behavior under undrained conditions. Loose, fine sands and silts have sufficiently low permeabilities that small disturbances in load or even small amounts o f

Unconditional for Undrained with S > S„„ (AV = 0)

Fig. 8 Schematic diagram o f conditions for stability and instability o f compressing granular material.

Conditional for Drained (AV ^ 0)

Unconditional is not Possible

I,

Fig. 9 Schematic diagram o f conditions for stability and instability o f dilating granular material.

Top o f E ffective Stress Path

Top o f Y ield Surface

^ Y ield Surface

Fig. 10 Location o f instability line for loose sand.

volumetric creep may temporarily produce undrained conditions in such soils, and instability o f the soil mass follows. As long as the soil remains drained, it will remain stable in the region o f potential instability.

When the condition o f instability is reached, the soil may not be able to sustain the current stress state. This state corresponds to the top o f the tear drop shaped yield surface as shown schematically on the p'-q diagram in Fig. 10. Following this top point the soil can deform plastically under decreasing stresses. The top o f the undrained effective stress

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Fig. 11 Schematic diagram o f location o f instability line in p’-q diagram.

path, corresponding to (gi -Gs )max , occurs slightly after but very close to the top o f the yield surface. Fig. 11 shows a schematic p'-q diagram in which the line connecting the tops o f a series o f effective stress paths from undrained tests provides the lower limit o f the region o f potential instability. Experiments show that this line is straight. Since it goes through the top points o f the yield surfaces which evolve from the origin o f the stress diagram, the instability line also intersects the stress origin.

A region o f temporary instability is located in the upper part o f the dilatancy zone, as shown in Fig. 11. It is a region where instability may initially occur, but conditions allow the soil to dilate after the initial instability, thus causing the soil to become stable again. The approximate upper limit o f the temporary instability region may be obtained from the intersection o f the instability line and the total strength envelope. For very loose soils the total strength envelope intersects the stress origin, and the region o f potential instability reaches down to the origin o f the stress diagram.

10 EFFECTS OF TIME ON INSTABILITY

The experiments performed to study the influence of time effects on instability o f granular materials were conducted at high pressures. Time effects are most pronounced at high pressures where crushing of grains contributes substantially to the overall deformation o f the granular material, whether dependent on time or not.

10.1 Effects of Strain Rate

To study the effect o f strain rate on the location of the instability line, Yamamuro and Lade (1993) performed undrained triaxial compression tests on dense Cambria sand at high pressures and with strain rates varying from a lower value o f 0.0042 %/min to the highest value o f 0.74 %/min. While the soil

behavior was clearly affected by the different strain rates, the effect on the location o f the instability line appeared to be negligible. Since both effective confining pressure and maximum deviator stress increased with increasing strain rate, all points corresponding to maximum deviator stress on the effective stress paths fell on essentially the same instability line regardless o f strain rate. The axial strains to the instability line were very small, but increased with increasing strain rate from 1.84 to 2.38 %.

10.2 Effects of Drained Creep

Pure creep may be observed in laboratory tests under drained conditions and constant effective stresses. These are typically present following primary consolidation in conventional uniaxial consolidation tests (often referred to as secondary compression) and in triaxial compression tests. The secondary compression observed in consolidation tests causes a stiffening o f the soil expressed as an increased quasi-preconsolidation pressure. In order to produce further consolidation (beyond elastic compression) the stress state must exceed the quasipreconsolidation pressure or the yield pressure. The increase in yield pressure depends on the time the soil is resting under the current pressure. Thus, it appears that the soil becomes stiffer with time or age.

This aging effect occurs for any soil at any state o f stress inside the failure surface. As the creep deformation occurs, the yield point is pushed out and can be reached by "reloading" beyond the previous maximum stresses. To demonstrate this effect as well as the consequent movement o f the point o f instability for a granular material, series o f triaxial compression tests were performed on loose Sacramento River sand (Lade 1994).

For a state of stress above the instability line, stability may be improved as a result o f movement of the plastic yield surface which occurs with time due to creep. This is demonstrated by the experiments shown in Fig. 12. All specimens, consisting o f loose Sacramento River sand, were first loaded to the same state o f stress under stress control and then allowed to creep under drained conditions for various periods o f time. The state o f stress was located above the instability line for loose Sacramento River sand.

Following loading, the specimens were allowed to creep under drained conditions for 0, 2, 20, 200, and 1690 minutes, respectively. The drainage valve was then closed, and the specimens were further loaded under stress control to study the yield surface location and the subsequent unstable behavior.

Fig. 12(a) shows the stress-strain behavior during loading and drained creep followed by the stress-strain behavior during subsequent undrained loading. Volumetric compression occurred during

11

drained creep (Fig. 12(a)), while pore pressures develop during undrained loading (Fig. 12(b)). The effective stress paths are shown on the triaxial plane in Fig. 12(c). The diagram in Fig. 12(a) shows that the undrained loading initially resulted in elastic "reloading." Both Figs. 12(a) and (c) indicate that the yield points move out with increasing amounts o f creep, and instability occurs under the stress controlled loading after the yield surface has been crossed. Thus, the effect o f creep is to move the yield surface out and to stabilize the soil, i.e. increasing amounts o f creep require increasingly high stress differences to render the sand unstable.

11 EFFECT OF OVERCONSOLIDATION

The effect o f drained creep is to push the yield surface out and consequently to make the sand more stable. Similarly, it may be seen that the effect o f overconsolidation is to push the yield surface out and to enlarge the region o f stable soil behavior in the vicinity o f the current stress point, as indicated on the schematic diagram in Fig. 13. Once the yield surface has been pushed out, and the current stress has been reduced, i.e. the soil has been overconsolidated, as exemplified in Fig. 13, then much higher stresses are required to exceed the outermost yield surface established during overconsolidation. Therefore, static liquefaction is inhibited in overconsolidated deposits for which plastic deformations do not occur until the yield surface has been exceeded.

12 INSTABILITY OF SATURATED SLOPES

Instability and failure are two different behavior aspects o f granular soils that exhibit nonassociated flow. Although both involve reduction in shear strength and consequently may lead to catastrophic events such as gross collapse o f earth structures, they are not synonymous. In fact, instability and failure

(b) pore pressures, and (c) effective stress paths in triaxial plane for five creep and instability tests on loose Sacramento River sand at = 51.5 kg/cm^ (5,050 kPa).

Fig. 13 Effect o f overconsolidation on region o f potential instability.

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are different in nature, and they require different types o f analyses. Failure analysis involves comparison o f current shear stresses on a potential failure surface with the shear strength available on that surface. Analysis o f instability requires determination o f the current effective stress states in the slope and recognition o f their locations relative to the instability line. Instability can potentially be triggered in any region o f the slope in which the stress states are above the instability line.

A method o f analysis o f instability was developed (Lade 1992) and employed to show that the large submarine slope failures that occurred in loose, fine sand and silt deposits in the fjords within a small area in the middle o f Norway (Andresen and Bjerrum 1967, Bjerrum 1971) clearly had the potential ftir instability. These slides happened in deposits with gentle slopes o f 3-15®. Bjerrum (1971) reports that “these slides have been surrounded by considerable mystery as they frequently occur in slopes which, according to conventional stability analysis, should be stable beyond any doubt.” The method was also used for analysis o f the static instability o f the submarine Nerlerk berm in the Beaufort Sea (Lade 1993). The analysis procedure can only indicate the potential for collapse. A trigger is required to initiate the actual collapse. A review of mechanisms that may act as trigger for slope instability was presented by Lade (1993).

The method o f analysis was also applied to a slope representing a tailings slope or a spoil heap consisting o f loose granular materials with permeabilities near those o f fine sands and silts to demonstrate that it may become unstable under essentially static loading conditions (Lade 1994). Such slopes are often not engineered, but simply created by dumping material in a loose state.

The slope shown in Fig. 14 has an inclination of horizontal: vertical = 2:1 (inclination angle = 26.6°), a height o f H = 45.7 m, and effective strength parameters o f c' = 0 and (j)’ = 30®. The soil in the slope is assumed to have a void ratio of 0.89 and a dry density o f 13.75 kN/m^ It is also assumed to be nearly saturated, say due to rain water infiltration, with a degree o f saturation o f 97%, and the total density is therefore 18.2 kN/m^ Only vertical water flow inside the slope is assumed and the pore water pressure is therefore dissipated as the water infiltrates the slope.

Conventional slope stability methods indicate that the most critical failure surface for a cohesionless slope is parallel to the slope surface. Thus, an infinite slope stability analysis o f a slope with vertical seepage produces

tantana

tan 30° tan 26.6° = 1.15 (3)

indicating that the slope should be stable.To determine whether the slope can become

unstable, it is necessary to compare the states o f stress in the slope with those required to produce unstable behavior. Conventional slope stability analyses methods may be employed to evaluate the state o f stress to an approximate degree. This approach has been used to determine the consolidation stress states in slopes (e.g. Lowe and Karafiath, 1960).

Spencer's slope stability method (1967) was employed to determine the approximate effective stress state along five circular slip surfaces as seen in Fig. 14. Since none o f these circles are critical, they all produce factors o f safety above unity, and the stress states can be calculated along each slip surface. Because the calculation procedure requires the factor o f safety to be constant along a given circle, the computed stress states are located on a straight line given by

T = -c'+cr'-tan^'

= c| -f-tan< rf (4)

For a cohesionless slope c ' = c = 0, and the straight line goes through the origin o f the x -a diagram. Fig. 15 indicates the stress states obtained from the five circles shown in Fig. 14. Some o f the stress states reach up into the region o f potential instability.

Fig. 14 Example slope with circular slip surfaces for analysis o f static state o f stress.

Fig. 15 Stress states along circular slip surfaces reach into region o f potential instability.

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whose lower limits are described by = 19 and 'imxJpa = 0.50, the latter indicating the approximate lower limit o f the temporary instability region. Thus, the slope is potentially unstable according to the concepts presented here.

To obtain the region within the slope in which the stresses reach values that are in the area o f potential instability in Fig. 15, the stress states (calculated at the middle o f each slice) have been plotted in Fig. 16(a). This diagram shows values o f Ipa versus the horizontal distance from the toe. The stress states for which

> T irnxJpa and t/(j' > tan (j)\ (5)

methods cannot be used to produce a factor o f safety. A slope with a large region o f potentially unstable soil is perfectly stable as long as the soil remains drained. But the moment the soil becomes undrained, it becomes unstable, and the volume o f unstable

are within the region o f potential instability. The range o f stresses for which these inequalities are fulfilled is then transferred to the respective circles in Fig. 16(b), and a region o f potential instability may be identified within the slope. The reliability o f this method for determination o f the stress state in a slope was studied by Lade (1992).

According to this analysis procedure, whose results are shown in Fig. 16(b), a region is present in which instability may be induced under essentially static loading conditions, e.g. due to increasing stresses caused by the weight o f additional rain water. Once a local zone o f instability has been created, the resulting pore pressure buildup will propagate and enlarge the unstable region in the slope. The instability initiated in the potentially unstable region is selfsustaining, i.e. the material is not dependent on any further outside perturbations, and it consequently exhibits unconditional, run-away instability.

The material in the sloping surface above the unstable region is in a dilating mode, and initially it does not exhibit unstable behavior, i.e. it forms a rigid crust on top o f the unstable region. As the pore pressure builds up in the underlying unstable region, water penetrates into the dilating material, increases the pore pressure, and eventually causes the dilating material to become unstable as well. Thus, the initially stable crust is conditionally unstable, i.e. its instability is dependent on the continued supply o f pore water from the underlying unstable region. Therefore, a progressively larger volume o f unstable soil will be engaged, and the slope will fail by static liquefaction. This mechanism is in agreement with “Mechanism C” o f the Committee o f Earthquake Engineering (1985), whose diagram in Fig. 17 shows a zone with high pore pressures, similar to that on Fig. 16, and outward flow o f water from the unstable region. The outward flow may also result in cracking o f the overlying soil “allowing sand to be carried upward into the cracks” (Comm, o f Earthquake Engrg. 1985).

Note that instability is not produced along a particular slip surface, but rather in a volume o f soil within the slope, and classical slope stability

Fig. 16 (a) Detailed analysis o f stress state relative to instability line, and (b) determination of region of potential instability in slope.

E F F E C T I V E S TR E S S E S R E D U C E D ; C RACKING

S A N D L O O S E N E D SAND W IT HBY O U T W A R D HIGH PORE P RE S SU R EFLOW

Fig. 17 “Example o f a potential situation for mechanism C failure resulting from spreading o f pore pressure and global volume changes” (after Committee on Earthquake Engineering 1985).

14

S h a l lo w te n s io n crac ks

■ G r o u n d w a te r s u rfa c e "□ A

Z o n e o f in itia l liq u e fa c t io n

(a) S ta r t o f liq u e fa c t io n

P rogressive te n s io n c ra c k in g

P rogressive l iq u e fa c t io n

(b ) P rogressive liq u e fa c t io n

F in a l scarp w h e re l iq u e fa c t io n stops

S h a l lo w z o n e o f lo w c o n fin in g pressure n o t s u s c e p tib le to liq u e fa c t io n

S an d mass in v o lv e d in progress ive liq u e fa c t io n e x te n d s to a l im ite d d e p th b e lo w fin a l e q u il ib r iu m slope

(c) S e c tio n th ro u g h s lid e area a f te r fa i lu re

(V e r t ic a l scale a b o u t 2 X h o r iz o n ta l scale)

Fig. 18 “Liquefaction in loose sand adjacent to a waterfront” (after Casagrande 1975, as reported by Holtz and Kovacs 1981).

For saturated specimens that tend to compress, undrained conditions lead to effective stress paths directed into the region o f potential instability, and instability is observed provided the yield surface opens up in the outward direction o f the hydrostatic axis. Thus, granular materials may become unstable inside the failure surface if the state o f stress is located or moves into the region o f potential instability between the instability line and the failure surface for the material. Instability is not synonymous with failure, although both may lead to catastrophic events. The experimentally determined conditions for which granular materials are stable, conditionally unstable, and unconditionally unstable are discussed, and the location o f the region o f potential instability and its determination are reviewed.

Analysis procedures for static instability o f shallow submarine slopes and nearly fully saturated slopes representing tailings dams or hydraulic fill dams are reviewed. It is shown that conventional slope stability methods, which describe shear failure, do not capture the mechanics o f instability and possible liquefaction. The proposed analysis method is based on the location o f the region o f potential instability and the state o f stress in the ground. In addition, a trigger mechanism is required to initiate instability.

material will spread beyond the boundaries indicated on Fig. 16(b).

The analysis procedure and the mode o f slope failure considered here is in close agreement with the mechanics, the geometry, and the sequence o f events in static liquefaction o f a slope presented by Casagrande (1975) and shown in Fig. 18. Following initial liquefaction inside a zone similar to that in Fig. 16(b), Casagrande explains that “liquefaction can progress backward and a large volume o f sand may flow into the river, leaving behind a slope surface with a very flat angle that reflects the low strength o f the liquefied sand.”

13 CONCLUSION

With background in the stability conditions proposed by Drucker and by Hill, the stability o f granular materials which exhibit nonassociated plastic flow has been investigated on the basis o f experimental observations. Triaxial tests on fully and partly saturated specimens o f sand have been performed under drained and undrained conditions to study the regions o f stable and unstable behavior. The variables in these studies were the sign o f the second work increment (positive or negative), the volumetric strain behavior (compression or dilation), the drainage condition (drained or undrained) and the degree o f saturation (fully or partly saturated).

ACKNOWLEDGMENTS

Much o f the work presented above was sponsored by the Air Force Office o f Scientific Research, USAF, under Grant Numbers 910117 and F49620-94-1-0032. Grateful appreciation is expressed for this support.

REFERENCES

Andresen, A., and Bjerrum, L. 1967 Slides in subagueous slopes in loose sand and silt. NGI Publication 81.

Bishop, J.F.W., and Hill, R. 1951 A Theory o f the Plastic Distortion o f a Polycrystalline Aggregate Under Combined Stresses. Philosophical Magazine, 42(327):414-427.

Bjerrum, L. 1971 Subagueous slope failures in norwegian fjords. NGI Publication 88.

Bjerrum, L., and Simons, N.E. 1960 Comparison o f shear strength characteristics o f normally consolidated clays. Proc. ASCE Res. Conf., Boulder, Colorado, 711-726.

Casagrande, A, 1975 Liquefaction and cyclic deformation o f sands, a critical review. Proc. 5th Panam. Conf. SMFE, Buenos Aires, 80-133.

Committee on Earthquake Engineering (1985) Liquefaction o f soils during earthquakes. Report to the National Research Council, National

15

Academy Press, Washington, D.C.Drucker, D.C. 1951 A More Fundamental Approach

to Stress-Strain Relations. First Congress of Applied Mechanics, 487-491.

Drucker, D.C. 1956 On Uniqueness in the Theory of Plasticity. Quarterly Appl Math., 14:35-42.

Drucker, D.C. 1959 A Definition o f Stable Inelastic Material. J. Appl Mech. 26:101-106.

Hill, R. 1958 A General Theory o f Uniqueness and Stability in Elasto-Plastic Solids. J. Mech. Phys Solids, 6:236-249.

Holtz, R.D., and Kovacs, W.D. 19S\ An Introduction to Geotechnical Engineering, Prentice-Hall, Inc. Englewood Cliffs, New Jersey.

Kramer, S.L., and Seed, H.B. 1988 Initiation o f soil liquefaction under static loading conditions. J. Geotech. Engr., ASCE ,114(4):412-430.

Lade, P.V. 1992 Static Instability and Liquefaction o f Loose Fine Sandy Slopes. J. Geotech. Engrg., ASCE, 118(1):51-71.

Lade, P.V. 1993 Initiation o f static instability in the submarine Nerlerk berm. Can. Geotech. J., 30: 895-904.

Lade, P.V. 1994 Instability Analysis for Tailings Slopes. 13th Int. Conf. Soil Mech. Found Engrg., 1649-1652.

Lade, P.V. 1994 Creep Effects on Static and Cyclic Instability o f Granular Soils. J. Geotech. Engrg., ASCE, 120(2):404-419.

Lade, P.V. and Duncan, J.M. (1976). "Stress-path dependent behavior o f cohesionless soil." J. Geot. Engrg. Div., ASCE 102(GT1), 51-68.

Lade, P.V., Nelson, R.B., and Ito, Y.M. 1987 Nonassociated flow and stability o f granular materials. J. Engrg. Mech., ASCE, 113(9): 1302-1318.

Lade, P.V., Nelson, R.B., and Ito, Y.M. 1988 Instability o f granular materials with nonassociated flow. J. Engrg. Mech., ASCE, 114(12):2173-2191.

Lade, P.V., and Pradel, D. 1990 Instability and plastic flow o f soils, I: Experimental observations. J. Engrg. Mech., ASCE, 116(ll):2532-2550.

Lade, P.V., Bopp, P.A., and Peters. J.F. 1993 Instability o f dilating sand. Mech. o f Mat., 16: 249-264.

Lowe, J., Ill, and Karafiath, L. 1960 Effect o f anisotropic consolidation on the undrained shear strength o f compacted clays. Proc. ASCE Res. Conf, Boulder, Colorado, 837-858.

Mandel, J. (1964). "Conditions de stabilite et postulat de Drucker". Proc. lUTAM Symp. Rheology and Soil Mech., Grenoble, France, 58-68 (in French).

Mroz, Z. (1963). "Non-associated flow laws in plasticity." J. de Mechanique, 2, 21-42.

Peters, J.F. 1991 "Discussion o f Instability of granular materials with nonassociated flow." J. Engrg. Mech., ASCE, 117, 934-936.

Poorooshasb, H.B., Holubec, I., Sherboume, A.N. 1966 Yielding and flow o f sand in triaxial compression: Part I. Can. Geot. J., 3:179-190.

Seed, H.B., Mitchell, J.K. and Chan, C.K. 1960 The strength o f compacted cohesive soils, Proc. ASCE Research Conf, Boulder, Colorado 877-964.

Spencer, E. 1967 A method o f analysis o f the stability o f embankments assuming parallel inter-slice forces. Geotechnique, 17(1): 11-26.

Whitman, R.V. 1960 Some considerations and data regarding the shear strength o f clays, Proc. ASCE Research Conf, Boulder, Colorado 581-614.

Yamamuro, J.A., and Lade, P.V. 1993 Effects o f Strain Rate on Instability o f Granular Soils. Geotech. Test. J., ASTM, 16:304-313.

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Static liquefaction o f very loose Hostun RF sand: Experiments and modelling

T. Doanh & E. Ibraim - Laboratoire Géomatériaux, Ecole Nationale des Travaux Publics de l’Etat, Vaulx-en-Velin, Erance

Ph.Dubujet - Ecole Centrale de Lyon, Erance

R. Matiotti - Milan University of Technology, Italy

I. Herle - Czech Academy of Sciences, Czech Republic

ABSTRACT; This paper highlights some new experimental results of the undrained behaviour of very loose Hostun sand and examines the possibilities offered by recent constitutive equations to model the static liquefaction phenomenon. The undrained behaviour of normally and lightly overconsolidated sand samples subjected to different initial anisotropic consolidation levels in triaxial compression and extension is described. The initial anisotropic consolidation strongly influences the instability concept, but the effective stress ratio increment stabilizes asymptotically. The systematic evaluation of the experimental errors assesses the nonuniqueness of the steady state of deformation within the double-side confidence limits. The performances and limitations of several recent constitutive equations to simulate the experimental data with emphasis to the extension domain from an anisotropic stress state are evaluated.

1 INTRODUCTION

Following the pioneer works of Castro (1969) and Casagrande (1975), an increasing number of experimental works in the geotechnical literature has been devoted to static liquefaction over the last three decades, particularly in recent years. This particular phenomenon can be observed in classical triaxial undrained compression and extension tests on loose to very loose saturated sand.

The main factors affecting the static liquefaction, such as the initial void ratio, the loading modes, the initial deviatoric stress state, the fines contents ... are studied by various workers, Kramer et al. (1988), Canou et al. (1991), di Frisco et al. (1995), Lade et al. (1998)... among others. Many attempts are introduced to characterize this phenomenon, for example the concept of state parameters. Been et al. (1985), the collapse surface, Sladen et al. (1985), the undrained instability line. Lade et al. (1988), or the minimum undrained strength framework, Konrad (1990).

Static liquefaction presents new challenges to constitutive modelling. Different theoretical approaches have been proposed to simulate the undrained behaviour of isotropic samples: standard and non-associated elastoplasticity models, Sladen et al. (1989), Saittaet al. (1992), Matiotti et al. (1995), or non-linear incremental constitutive equations, Darve (1994). The undrained instability domain is explored by Molenkamp (1991), explicitly determined by Dubujet et al. (1997), and the unconditioned instability region explained by Imposimato et al. (1998).

This paper describes in the first part the observed undrained behaviour of very loose isotropic and anisotropic Hostun RF sand during monotonic compression and extension triaxial tests. The influences of the initial anisotropic consolidation are examined considering the instability concept. The effects of complex stress loading, of recent stress history are subsequently analyzed. The controversial issue of the non-uniqueness of the steady state of deformation is also addressed. In the last part this paper proposes a comprehensive evaluation of recent advanced models to predict some delicate aspects of the static liquefaction phenomenon.

2 EXPERIMENTAL OBSERVATIONS

Hostun sand RF specimens, in very loose conditions, were tested under undrained monotonic compression and extension using a fully instrumented and computer controlled apparatus. All cylindrical short samples, 70 mm in height and 70 mm in diameter, were prepared by a modified most tamping and undercompaction method at a same initial void ratio eo- At fabrication state, eo was around 1.00. The minimum and maximum void ratio of Hostun RF sand (emax = 1.041, emin = 0.648) and other properties can be found at Flavigny et al. (1990).

Samples were subjected to various initial isotropic or anisotropic consolidations along constant effectivestress ratio paths K = aV/a'a before undrainedshearing, where and a'a are the effective radial and axial stress. Different consolidation ratios ranging

17

Effective mean pressure kPa Axial strain %

Figure 1. (a) Complete stress paths, (b) Stress-strain behaviour of isotropic samples.

Figure 1. (c) Normalized pore pressure at small strains, (d) Stress-strain behaviour at small strains.

from 1.00 (isotropic stress state) to 0.35 (highly anisotropic) were used. It is noted that all tests were sheared in strain-controlled mode and the usual anti- frictional system was not used due to the small axial strain at deviatoric stress peak. Complete details of testing procedure, equipment are given by Ibraim (1998).

The undrained instability of this experimental work is already reported in Doanh et al. (1997); the effects of recent stress history on the static liquefaction in Doanh et al. (1998), and the description of the minimum undrained strength at Steady State of Deformation (SSD) is given in Ibraim et al. (1997).

2.1 Static liquefaction characteristics.

The stress-strain undrained behaviour of very loose Hostun sand is characterized by a sharp drop of deviatoric stress after a peak reaching rapidly at the beginning of the undrained test, for example in figure lb in a series of undrained tests on isotropic samples. The axial strain at peak is lower than 0.5 % for isotropic samples (vertical arrows in figure Id) and an order of magnitude smaller for higher anisotropic consolidation level, figure 2d.

This characteristic is followed by a steady state in which the minimum undrained strength remains constant under a large range of axial strain, as shown in figure lb. The static liquefaction, defines usually

as the vanishing of the effective mean pressure p ' under monotonic undrained conditions, is never reached, even with the smallest confining pressure p'c of this study. It is possible that loose sand samples will liquefy at smaller confining pressure or with lower relative density, as reported by Yamamuro et al. (1998). In this study, a stress reversal at large strains is needed to liquefy all sand samples.

The nearly symmetric shapes of the effective stress paths in figure la show a close surface pointing toward the origin of the q/p' axes, and a perpendicular intersection with the isotropic axis. When normalized by the p 'c before undrained shearing, these effective stress paths vary in a quasi homothetic way. A closer look of the normalized pore pressure at small strains in figure Ic reveals the initial dilatancy phase of the extension test to obtain the continuity of the soil response from compression to extension through a regular pattern. The sharp asymmetric shape of the effective stress paths on isotropic Toyoura sand is reported by Hyodo et al. (1994).

Many of the above characteristics remain valid for anisotropic samples (partial static liquefaction, deviatoric stress peak at low strains, normalized behaviour, continuity of effective stress paths, ...) with some important differences.

Figure 2 gives the typical undrained behaviour of anisotropic sand with a close look at small strains.

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Effective mean pressure kPa

Figure 2. (a) Complete stress paths, (b) Stress-strain behaviour of anisotropic samples, K = 0.50.

The initial anisotropic consolidation level K of this series is 0.50. This high consolidation level situated above the deviatone stress peak of previous isotropic samples is chosen to check the validity of the instability concept (next section). A sharper drop of deviatone stress after a small peak is obtained for all anisotropic samples. The most striking change concerns the effective stress paths. Their shapes are always geometrically similar, but more elongated and strongly asymmetric about the consolidation axis.

As the initial consolidation level increases, the non-perpendicularity with the consolidation line becomes more evident, suggesting the development of an anisotropic structure of the sample at the end of the consolidation phase, figure 2a. Meanwhile, the continuity of the effective stress paths at the beginning of the undrained shearing remains.

As noted before, complete liquefaction is often obtained through a stress reversal at large strains for all samples. Figure 3 shows the results of two anisotropic samples of the series K=0.66. Point E (E') indicates the end of the monotonie undrained phase. A large stress reversal EFG in extension liquefies the first sample already sheared in compression, point F, and the reversal in compression E'F'G' leaves the second nearly in a full liquefaction state, point F'.

Figure 2. (c) Normalized pore pressure at small strains, (d) Stress-strain behaviour at small strains of anisotropic samples, K = 0.50.

Mean effective stress (kPa)

Figure 3. Complete liquefaction on anisotropic samples, K=0.66, after a stress reversal at large strains.

2.2 Instability concept.

Complete effective stress paths in the q/p' plane of several tests' series with different initial anisotropic consolidation are shown in figure 4. In compression as well as in extension, the effective stress peaks for different confining pressures on isotropic samples may be fitted by two straight lines passing through the origin of the q/p' axes. These peak lines, noted ic

19

and ie, identified as instability lines, Lade et al.(1988), have different slopes in compression (rjpeak

= 0.64) and in extension (-0.41). The mobilized frictional angle at peak (|)peak is about 18°6 in compression and 12°7 in extension. These values are well below the ultimate frictional angle ( ss at steady state condition, about 33°7 in compression and 30°0 in extension.

The Lade instability lines can still be defined for anisotropic samples. For instance, the instability lines of anisotropic samples at K = 0.66, not far away from isotropic axe, are very close to that obtained from isotropic samples. The instability lines kac and kae have a slope of 0.62 and -0.43. To avoid clumsy figures, only the instability lines of each series are reported, and not the individual peak position of each effective stress path.

Large initial anisotropic consolidation level at K=0.50 produces new instability lines with higher slope of 0.83 (line kbc) against 0.64 (line ic) that means 5° between these frictional angles at peak in compression; and -0.50 (line kbe) against -0.41 (line ie) or about 3° of difference. The slope of the instability lines depends on the initial anisotropic consolidation level K, therefore, the Lade instability concept is not intrinsic as is the failure envelope.

The compression tests of highest consolidation level at K=0.35 give a non-negligible undrained compressive strength and confirm the dependency of the instability lines on the consolidation level. The positive instability line kcc at K=0.35 has a slope of1.23 and produces a small undrained compressivestrength increment Aqu = 0.50 kPa, or a difference of 14° with the frictional angle at peak in isotropic samples. The compressive strength increment Aqu indicates the difference between the deviator stress at peak qpeak and the deviator stress at the end of the consolidation line qc- In contrast, the negative instability line kce has a slope of only about -0.15 or - 4°4, which is much lower than that of the instability line of isotropic samples. Therefore, positive

Figure 5. Asymptotic stabilization of effective stress ratio increment at peak.

anisotropic consolidation always produces a greater slope of the instability line in the q/p' plane in compression but a reverse trend may occur on the extension side.

Figure 5 gives another interpretation of the compression stress ratio at peak, explaining the previous apparent contradiction of the observed deviatone stress peak, when plotting the effective stress ratio increment against the anisotropicconsolidation level. The stress ratio increment Òr],indicating the difference between T|peak and r|c, decreases continuously as the slope of the consolidation line increases. This asymptotic stabilization behaviour can be modeled with a three- parameter exponential function.

The same analysis regarding the absolute effective stress ratio increment of the triaxial extension testscan apply. The decay of the 5ri in extension can also be approximated by the same mathematical expression. The asymptotic stabilization effect suggested in some experiments arises when the axial strain at the end of the consolidation exceeds a certain threshold. This dependence of the axial strain generated during the initial consolidation is still an open question.

Figure 4. Instability lines in compression and extension of anisotropic samples.

Figure 6. Repeatability of stress strain behaviour on isotropic samples.

20

Figure 7: Steady state of deformation of Hostun RF sand in compression (a), and extension (b)

21

2.3 Minimum undrained strength.

To account for the sample variabilities, a series of repetitive CIU tests on isotropic samples under the same conditions (same relative density, same initial confining pressure, same preparation method) was performed. Figure 6 gives the observed stress-strain behaviour with a fairly good reproducibility and a greater confidence in obtaining the minimum undrained strength.

Figures 7a, b show for all compression and extension tests the relationship between the void ratio after consolidation and the effective mean pressure p'c at the initial state (at the beginning of the monotonie undrained shearing, hollow square) and at the final state at SSD (solid square). The vertical bars represent the individual 70% double-side confidence limits for the void ratio of each test, and the horizontal bars represent the same double-side confidence limits for the effective mean pressure p \ The usual Poisson distribution is assumed for both confidence intervals of e and p \ These confidence limits indicate the relative uncertainty of the observed behaviour at steady state of deformation. They show the statistically probable range of the SSD for the void ratio and the effective mean stress that could be interpreted from the same test data.

The experimental results shown in this figure

p'/p;,Figure 8. Normalized stress paths on anisotropic samples (K=0.66) in compression.

Figure 9. Normalized stress paths on anisotropic samples (K=0.35) in compression.

corroborate the earlier results of Konrad (1990,1991), Megachou (1993) from triaxial compression tests on the same Hostun RF sand. The existence of two parallel lines at SSD (full lines) can be identified separately beyond all doubt within the observed double-side confidence limits. Konrad calls the upper line the UF line (upper flow), representing the upper hmit of steady state strength, and the lower line the LF line (lower flow) as the lower hmit of steady state strength.

The steady state line is not unique and the characteristics at SSD are not solely related to the void ratio at the beginning of undrained shearing.

It is noted that these parallel lines are almost identical in compression as well as in extension with a slope of about 0.72. Referring to these two figures, one logical question arises: what are the necessary conditions for a sand sample to reach the SSD at the UF line, at the LF line or between the two? The stateparameter \}/i, introduced by Been et al. (1985), and refined by Konrad (1990), taking into account the presence of the UF line, was a useful tool in estimating the undrained shear strength of loose isotropic sands. Later, Konrad (1993) developped a conceptual framework associated with triggering envelope (previously known as instability line) in the normalized stress plane for isotropic sands. Meanwhile, this framework was unable to explain the difference of tests KA-C2 and KC-C2 having a same state parameter but different initial anisotropic consolidation level. Test KA-C2 has a minimum undrained strength close to point LF whereas that of test KC-C2 is defined by point UF.

A refined version of this framework is proposed, Doanh et al. (1999), introducing the asymptotic stabilization property of the effective stress ratio increment. This dependence of the stress conditions on the normalized mean effective peak stress permits explicitly the evolution and the identification of the idealized piecewise linear relationship between the undrained strength ratio and normalized mean effective peak stress, materialized by 3 peak boundary points on the triggering envelope. In this refined framework, the normalized stress path of test KA-C2 crosses the triggering envelope around point p i in figure 8, thus its stress path ends at point LF. Higher initial consolidation level moves the triggering envelope close to the steady state line and shifts the peak boundary points toward the origin. The intersection of the normalized stress path of test KC- C2 is situated between the two intermediate peak boundary points, therefore its undrained strength corresponds to an intermediate point between UF and LF, figure 9.

In the realm of very loose sand behaviour, this refined framework can predict fairly well the undrained strength of anisotropic sands but leaves many unsolved questions: what are the reasons of the non-uniqueness of the steady state? What are the physical meanings of these parallel lines? A simple and clear explanation of the non-uniqueness needs to be found, thereby, it is beyond the scope of this paper.

22

Figure 10a. Complete effective stress path for a complex stress history.

Figure 11. Compressive undrained strength under different approaching stress paths.

Mean effective pressure kPa

Figure 10b. Effects of complex stress history on instability concept.


Figure 12. Effective stress path for normally and lightly overconsolidated anisotropic samples.

2.4 Complex stress loading.

In section 2.2, the asymptotic stabilization of the stress ratio increment was noted to explain the small but noticeable mobilized frictional angle at peak of largest anisotropic stress state. The same very flat peak and partial static liquefaction are still observed for sand samples subjected to a complex stress loading.

In figure 10a, isotropic loose samples, point B, were preloaded in drained condition up to point C, then unloaded to the previous isotropic stress state, and sheared in undrained condition in the opposite direction (compression / extension). The effective stress paths climb up unexpectedly the failure envelope like a dense sand; and as noted before, only a stress reversal at large strains can liquefy them. The stress deviatoric peaks, point D and D', are clearly defined in the enlarged portion in figure 1 0 b, but it is far below the instability lines defined on virgin isotropic samples. This unusual behaviour can be explained partly by the void ratio reduction before the undrained shearing and partly by the effects of induced anisotropy due to complex stress loading, as suggested by Lanier et al. (1993).

2.5 Recent stress history.

Following the dramatic influence of preloading on the subsequent undrained behaviour of very loose sand, the effects of recent stress history are investigated u sin g d ifferen t ap p roach ing effec tive stress paths passing through the same anisotropic stress state.

Test I-C2.3 in figure 11 follows the conventional CIU test on isotropic samples. The initial confining pressure was estimated to produce an effective stress path passing through the point A. Test SI was isotropically consolidated and sheared in drained condition of classical CID test up to point A, then undrained test was performed. Up to point A, the slope of the CDD part is not constant, because of two different axial strain rates used to test the viscous effect of the soil behaviour. This effect is not considered in this paper. Test KA-C2 was anisotropically consolidated at K = 0.66, and sheared in undrained condition beginning from point A. Tests KA-C2, OCR=1.5 and KA-C2, OCR=2.0 have the same initial anisotropic consolidation level as test KA- C2, but different OCR value.

The experimental results in figure 12 show that the recent stress history has a major influence on the subsequent undrained stress-strain behaviour.

23

Effective mean pressure kPa Axial strain %

Figure 13. (a) Complete stress paths, (b) Stress-strain behaviour of isotropic samples.

Figure 13. (c) Stress-strain behaviour at small strains, (d) Pore pressure generation of isotropic samples.

Qualitatively, similar results are obtained. But quantitatively, they are very different. Recent stress memory affects both the initial stiffness and the shape of the effective stress path from the undrained loading or unloading, particularly in the range of small stra in s . T he u n d ra in ed s tre ss-s tra in b e h av io u rs are highly non-linear. The magnitude of the deviatoric stress peak depends on the most recent stress history.

At large anisotropic stress state imposed by the first drained stage of test SI, which is above the deviatoric stress peak of the stress path I-C2.3, loose samples simply collapse under undrained conditions; whereas independently of the consolidation history of the stress path KA-C2, there always exists a mobilized undrained compressive strength increment. The usual and enhanced deviatoric stress peaks of overconsolidated samples can be explained using the viscous property of sand, Tatsuoka et al. (1997).

The partial static liquefaction always appears at large strains, irrespective to recent stress history, and to loading modes. The instability concept is still defined on lightly overconsolidated samples, as previously remarked by di Prisco et al. (1995). The effective stress paths obtained are now strongly asymmetric about the anisotropic consolidation axis, comparing to that of isotropic samples. Their protuberances are much more pronounced in compression, even for small overconsolidation ratio, and the continuity of the stress paths at the beginning of the undrained stage is lost.

3 MODELS EVALUATION

The previous experimental observations present some new challenges for constitutive modelling. Table 1 groups together these relevant observations into a co m p reh en siv e ch eck lis t to facilita te the com parison .

Can recent models simulate the static liquefaction of isotropic samples (feature 1 ), the undrained behaviour in compression from an anisotropic stress state (f2) in extension (f3) especially the effective stress path, and after higher anisotropic consolidation generating large amount of axial strain (f7)? Can the smooth transition of the effective stress paths from compression to extension (f5) and that of the pore pressure generation (f6 ) be predicted? How to explain the unexpected partial static liquefaction (f4), the dramatic effects of complex stress preloading (f8 ) or the non-uniqueness of the steady state (f ll)? How to determine analytically the instability lines (flO) and the associated asymptotic stabilization effect (f9)7

The theoretical analysis of the undrained instability is already proposed by Dubujet et al. (1997) using an elastoplastic model; the performances and limitations of two recent elastoplastic models are analysed in Doanh et al. (1997); and a new version of hypoplastic is evaluated by Herle et al. (1999a).

Two advanced non-associated elastoplastic and one recent hypoplastic models are evaluated against the static liquefaction phenomenon of loose sand. The first two, named Lyon and Milan models, are very

24

Axial strain %

Figure 14. (a) Complete stress paths, (b) Stress-strain behaviour of anisotropic samples for hypoplastic model.

Hypoplasticity K=0.66

-1 -0.5 0 0 .5 1Axial strain %

Figure 14. (c) Stress-strain behaviour at small strains, (d) Pore pressure generation of anisotropic samples for hypoplastic model.

similar within the elastoplastic framework. They are characterized by a combination of isotropic and kinematic hardening mechanism, with some new evolution functions for the latter.

Detailed description of these models, as well as the procedure for identification of model parameters from conventional triaxial tests, can be found in Cambou et al. (1988), di Frisco et al. (1993). The evaluated version of hypoplastic model is recently published by von Wolffersdorff (1996). Unlike elastoplastic models, hypoplastic has no decomposition of deformation into elastic and plastic components, no explicit formulation of yield surface and flow rule. Moreover, all the material constants can be determined from standard index tests, Herle et al. (1999b).

Very good agreement is obtained between the experimental data and the theoretical simulations of all models in the case of isotropic samples, with some flaws concerning the hypoplastic simulations of the effective stress paths and the pore pressure generation in extension. This result is expected for elastoplastic models since some tests are used to identify the model parameters.

A typical comparison of anisotropic sand samples with initial consolidation level K=0.66 is shown in figure 13 for elastoplastic models and in figure 14 for hypoplastic model. The final mean effective pressure of all experiments at the end of the anisotropic consolidation stage is 200 kPa.

Surprisingly, many important features of the undrained behaviour are correctly simulated, since none of the tests were used for model identification. Successively, figures 13&14a, b, c, d give the complete stress paths, the satisfactory simulation of the well-known drop of the deviatoric stress, the deviatoric stress peak at small strains and the continuity of the soil response at the beginning of the undrained tests, particularly the small drop of the pore pressure at the beginning of the extension test.

These figures also emphasize many shortcomings of the theoretical simulations. As expected, all elastoplastic models predict inevitably the complete static liquefaction, since the void ratio reduction during the anisotropic consolidation was completely ignored. On the contrary, the hypoplastic model shows the slow decay of the stress-strain curve and offers a possible first explanation of the partial static liquefaction, by formulating the void ratios of asymptotic states introduced by Gudehus (1996). The wrong start of the effective stress path is already recognized in the earlier development of hypoplastic models. However, this observed stress path is followed by dense sand under very large confining pressure, Yamamuro et al. (1998).

All models reproduce quite well the effective stress paths in compression, but large discrepancies occur in extension with unrealistic effective stress paths and inconsistent curvature, especially for hypoplastic model. Using elastoplastic vocabulary, hypoplastic

25

Figure 15a. Influence of the non-linearity of the elasticity on the stability domain, in the case of Lyon model.


Figure 16. Effective stress paths in extension after a preloading in compression on isotropic sample.

150

Oh Failure line

100 K

75 -

50

25 -

0 ^

/¡ r/ f

' Characteristic line

Stress path for undrained _ triaxial test

/Instability domain

Table 1. Checklist of static liquefaction verification. Features Lyon Milan Hypo

0 100 200 300F (kPa)

Figure 15b. Instability domain for dense sand, linear elasticity (n=0 ).

models simply lack an "elastic" component leading to a discontinuity of the soil response. Numerical predictions of higher anisotropic consolidation level are very similar. Simply put, the same problems are acutely repeated.

Lyon model formulated analytically the instability domain with strongly dependent of the non-linearity parameter of elasticity. Figure 15a shows the nearly straight line (n=0.6) of Hostun RF sand. The temporary instabilities observed on dense sand. Lade(1988), can be explained in figure 15b with linear elasticity (n=0 ).

Hypoplastic model also defined explicitly the instability line. Unfortunately, the deviatoric stress peaks of both models are independent of the initial anisotropic consolidation level. Only Milan model, taking the advantages of the strain hardening approach, and the accumulations of the plastic deformations, can describe qualitatively the asymptotic stabilization property.

The case of complex stress history suggests the density dependent of the model parameters, as implemented by hypoplastic model. Meanwhile, it can not describe the drastic reduction of the deviatoric stress peak, since the peak is independent of stress history. As usual, the two elastoplastic models

1 Isotropic state, Com&Ext2 Anisotropic state. Com.3 Anisotropic state. Ext.4 Partial static liquefaction5 Continuous stress paths6 Continuous response7 Large anisotropic state8 Complex stress history9 Stress history dependent10 Instability domain, ana.11 Non-uniqueness of SSD

v/

v/

v/

%/n/n/

x/

v/

liquefy the preloaded samples in extension, leaving the unexpected dilatancy behaviour unsatisfactory simulated, figure 16. Hypoplastic model, even with the explicit void ratio dependent of the material constants, leaves this behaviour unsimulated.

This complex stress loading illustrates qualitatively the limitations of the stress-hardening approach of Lyon model and the advantages of the strainhardening plasticity used by Milan model.

Table 1 summarizes the checklist when comparing the theoretical simulations with the experimental results of the undrained behaviour of loose sand. Symbol "Com" indicates triaxial compression test, "Com" extension test, and "ana" analytically determined.

As shown in the above checklist, recent advanced models simulate quite well many aspects of the undrained behaviour of very loose sand. Nevertheless, at least two advanced models fail to recognize the partial static liquefaction, and have unrealistic effective stress paths in extension from large anisotropic stress state. It seems that anisotropic elasticity should be adopted instead of the usual isotropic one, to correct this flaw of elastoplasticity framework. Predictions of the stress paths of a loose

26

sample in extension from a large anisotropic state or from an isotropic state after a preloading in compression or in extension present a real difficulty in constitutive modelling.

Despite these limitations, the theoretical simulations present an overall good agreement in several aspects of the observed behaviour, and demonstrate the interest of their use.

4 CONCLUSIONS

This paper has presented the experimental results of undrained compression and extension triaxial tests on very loose Hostun sand samples subjected to different initial anisotropic consolidation levels. Three advanced constitutive equations are evaluated through a comprehensive program. The following conclusions can be formulated:

1- Monotonie undrained compression and extension tests produce partial static liquefaction on isotropic and anisotropic sand samples. Static liquefaction can be reached after a subsequent stress reversal at large strains. The stress-strain behaviour is characterized by a sharp peak at small strains, following by a gradual post-peak reduction to a minimum undrained strength at large strains. Smooth transition from compression to extension of effective stress path and of pore pressure generation is observed.

2- Lade’s instability concept is generalized in compression and extension on normally consolidated and lightly overconsolidated samples shearing from an anisotropic stress state. This concept is strongly influenced by the initial anisotropic consolidation, the complex stress loading and the recent stress history. Asymptotic stabilization of effective stress ratio increment is obtained.

3- Konrad’s conceptual framework is corroborated and extended to predict the undrained steady state strength of anisotropic sand. Systematic evaluation of the experimental errors assesses the existence of two parallel lines UF and LF of the steady state of deformation, independently of the initial confining pressure, of the loading modes and of the initial anisotropic consolidation levels.

4- Many important features of the undrained behaviour of very loose sand are correctly simulated by several recent constitutive equations. The instability region can be analytically formulated. This evaluation emphasizes the advantages of using kinematic hardening mechanism to simulate the static liquefaction phenomenon and reveals many shortcomings of the theoretical simulations on the extension domain.

ACKNOWLEDGMENT

Part of the present work was developed within the ALERT Geomaterial program of the European Community.

REFERENCES

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Cambou, B., Jafari, K. 1988. Modèle de comportement des sols non cohérents. Revue française de Géotechnique. (44), 43-55.

Canon, J., Thorel, L. et De Laure, E. 1991. “Influence d’un déviateur de contrainte initial sur les caractéristiques ds liquéfaction statique du sable”, X ECSMFE, Firenze. Vol.I, 49-52;

Casagrande A. 1975. Liquefaction and cyclic deformation of sands: a critical review. N°88. Havard Soil Mechanics Series Havard University, Cambridge.

Castro, G. 1969. Liquefaction of sands. Harvard soil mechanics series, Harvard University, Cambridge.

Darve, F. 1994. Stability and uniqueness in geomaterials constitutive modelling. Localisation and bifurcation theory for soils and rock, R. Chambón Editor. 43-55.

di Prisco, C., Nova, R., Lanier, J. 1993. A mixed isotropic kinematic hardening constitutive law for sand. Modem approaches in plasticity. D. Kolymbas Editor. 83-124.

di Prisco, C., Matiotti, R, Nova R. 1995. Theorical investigation of the undrained stability of shallow submerged slopes. Geotechnique . 45(3), 479-496.

Doanh, T., Ibraim, E. 1998. Effects o f recent stress history on the static liquefaction of loose Hostun RF sand. 11th Euro. Conf. on Earthquake Engineering. Paris, (in press).

Doanh, T., Ibraim, E. 1999. Minimum undrained strength of very loose Hostun RF sand in triaxial compression and extension, (submitted).

Doanh, T., Ibraim, E., Dubujet, Ph., Matiotti, R. 1997. Static liquefaction: Performances and limitations o f two advanced elastoplasticity models. Numog VI. Montreal. Canada. G.N. Pande, S. Pietruszczak Eds, Balkema Publi. 279-282.

Doanh, T., Ibraim, E., Matiotti, R. 1997. Undrained instability of very loose Hostun sand in triaxial compression and extension. Part 1: Experimentalobservations. / of Cohesive-Frictional Materials, 2(1), 47- 70.

Dubujet, Ph., Doanh, T. 1997. Undrained instability of very loose Hostun sand in triaxial compression and extension. Part 2: Theoretical analysis using an elastoplasticity model.J. of Cohesive-Frictional Materials, 2(1), 71-92.

Flavigny E., Desrues J., PalayerB. 1990. Le sable Hostun RF.Revue Française de Géotechnique. 53, 67-69.

Gudehus, G. 1986. A comprehensive constitutive equation for granular materials . Soils and Fomdations. 36(1), 1-12.

Herle I., Doanh, T. 1999a. Verification of hypoplastic constitutive equation with static liquefaction of loose Hostun RF sand. 2nd Int. Symp. Prefailure deformation Torino. Italy, (submitted).

Herle I., Gudehus, G. 1999b. Determination o f parameters of a hypoplastic constitutive model from grain properties. J. of Cohesive-Frictional Materials, (submitted).

Hyodo M., Tanimizu H., Noriyuki Y., Murata H. 1994. Undrained cyclic and monotic triaxial behaviour of saturated loose sand. Soils and Foundations. 34(1), 19-32.

Ibraim E. 1998. Différents aspects du compórteme A des sables à partir d'essais triaxiaux: des petites déformations à la liquéfaction statique. PhD Thesis. INSA-ENTPE. France.

Ibraim. E., Doanh, T. 1997. Minimum undrained strength of anisotropically consolidated loose Hostun RF sand. IS on deformation and progressive failure in geomechanics. Nagoya. Japan. 623-628.^

27

Imposimato, S., Nova R. 1998. An investigation on the uniqueness of the incremental response o f elastoplastic models for virgin sands. J. of Cohesive-Frictional Materials, 3(1), 65-88.

Konrad, J.M. 1990. Minimum undrained strength versus steady state strength o f sand. J. Geotech. Engrg., ASCE, 116(6); 948-963.

Konrad, J.M., Flavigny E., Megachou M. 1991. Comportement non drainé du sable d'Hostun lâche. Revue française de Géotechnique. (54), 53-63.

Konrad, J.M. 1993. Undrained response of loosely compacted sands during monotonie and cyclic compression tests. Géotechnique, 43:1, 69-89.

Kramer, S. L. et Seed, H. B. 1988. Initiation of Soil Liquefaction Under Static Loading Conditions, Journal of Geotechnical Engineering.\\4{ 4), 412-430.

Lade, P.V., Nelson, R.B., Ito, Y.M. 1988. Instability of granular materials with nonassociated flow. J. Engrg. Mech. ASCE. 114(12), 2173-2191.

Lade, P.V, Yamamuro, J.A.. 1998. Effects of nonplastic fines on static liquefaction of sands. Canadian Geotechnical Journal, 34(6): 918-928.

Lanier, J., di Prisco, C., Nova, R. 1993. Etude expérimentale et analyse théorique de I'anisotropie induite du sable Hostun. Revue française de Géotechnique. (57), 59-74.

Matiotti, R., Ibraim, E., Doanh, T. 1995. Undrained behaviour of very loose RF sand in compression and extension tests. Numog V. Pande and Pietruszczak Editor. 119-124.

Megachou, M. 1993. Stabilité des sables lâches; essais et modélisations. PhD Thesis. Université J. Fourier. Grenoble. France.

Molenkamp, F. 1991. Material instability for drained and undrained behaviour. Part2: combined uniform deformation and shear-band generation. Int. J. for Num. Ana. Met. in Geomechanics 15(2), 73-83.

Sa'itta, A., Canou, J., Dupla, J.C, Dormieux, L.. 1992. Application of a generalized elastoplastic model to simulation of sand behaviour. Numog IV. Pande and Pietruszczak Editor. 119-124.

Sladen, J.A., D'Hollander, R.D., Krahn, J. 1985. The liquefaction of sand, a collapse surface approach. Canadian Geotechnical Journal, 22(4); 564-578.

Sladen, J.A., Oswell, J. M. 1989. The behaviour of very loose sand in triaxial compression test. Canadian Geotechnical Journal, 26(1); 103-113.

Tatsuoka, F., Jardine, R.J., Lo Presti, D., Di Benedetto, H., Kodaka, T.. 1997. Characterizing the pre-failure deformation properties o f geomaterials. XIVICSMFE.

Von Wolffersdorff 1996. A hypoplastic relation for granular materials with a predefined limit state surface. J. of Cohesive-Frictional Materials, 1(3), 251-271.

Yamamuro, J.A., Lade, P.V. 1998. Static liquefaction of very loose sands. Canadian Geotechnical Journal, 34(6): 905- 917.

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The mechanism controlling static liquefaction and cyclic strength o f sand

L.B. IbsenAalborg University, Denmark

ABSTRACT: Liquefaction and the cyclic strength of sand in undrained condition are strongly attached to the mechanisms observed in static tests. The cyclic failure condition, such as Cyclic Liquefaction and Cyclic Mobility is only part of the complex mechanism, which has to be determined in order to describe the development of stress and strain in cyclic tests. The key to explain and quantify the soil response is to understand the role of the volume changes and to be able to model these correctly. It is shown that the volume changes in soil subjected to static and cyclic loading are controlled by the characteristic line. Experiments have been performed to study the factors that influence the location of the characteristic line in drained and undrained tests for various types of sand and various types of loading. The relation of the characteristic line to other features of static, cyclic soil behaviour is explained and illustrated with experimental data.

I INTRODUCTION

Liquefaction and the cyclic strength of sand in undrained conditions are strongly attached to the mechanisms observed in static tests. The cyclic failure condition, such as Cyclic Liquefaction and Cyclic Mobility is only part of the complex mechanism, which has to be determined in order to describe the development of stress and strain in cyclic tests. The paper will describe a number of new characteristic phenomena of dense sand subjected to cyclic loading, which have been observed in triaxial tests using specimens with equal height and diameter. Experiments have been performed to study the factors that influence and control the fatigue which leads to Static and Cyclic Liquefaction. These experiments have shown that it is the volume changes that is the key player for understanding the behaviour of soils whether under drained or undrained conditions. Volume changes can be compressive or expansive in nature. Expansive or dilative volume changes are most pronounced for dense sands at low confining pressures and high stress levels approaching failure. The transition from compressive behaviour observed at lower stress levels to dilative behaviour at high stress levels occurs along a straight line through the origin of the stress space. For drained tests, this line is referred to as the Characteristic line.

In elasto-plasticity models the Characteristic line, evaluated from p = const tests, corresponds to the point on the plastic potential surface where the

plastic strain increment vector is perpendicular to the /?'- axis or the hydrostatic axis. This state is therefore comparable to the similar point on the yield surface at which the normal is perpendicular to the hydrostatic axis. This indicates the point at which sand may become unstable, as explained in detail elsewhere (Lade 1995j. Thus, the Characteristic line plays a similarly important role for the plastic potential surface as the instability line plays for the yield surface. Both lines are shown on the diagram in Figure 1. The behaviour of soils, static or cyclic is greatly influenced by and can be explained in view of the relative locations of these two lines. For sands the two lines are distinctly separate, while for normally consolidated, insensitive clays the two lines coincide, and they also coincide with the critical state or ultimate state line.

Figure 1. Characteristic and instability lines.

29

Triaxial cell

Generatoreg-tape recorder

Figure 2. The principle of the Danish triaxial apparatus. It is fully automatic and run by a computer. The triaxial is constructed in agreement with the principles described in (Jacobsen, M. 1970)

2 EXPERIMENTAL METHODS

The tests performed in connection which this paper were conventional static CD-tests, CU-tests,CUu=o-tests, and cyclic CU-tests. The cyclic tests were performed as undrained tests with pore pressure measurements. The CUu=o-tests were carried out by measuring the volume change and controlling the cell pressure in such a way that = 0 throughout the test. In this way the undrained condition is ensured and the effective stress path is followed throughout the test.

2.1 Testing equipment and procedures

To ensure homogeneous stress and strain conditions, the tests presented here were performed on cylindrical specimens with a height and diameter equal to 70 mm. Fully lubricated ends were employed on all test specimens. The lubricated ends consisted of latex rubber disks of 0.3 mm thickness placed onto the caps and bases of the specimen over a thin layer of vacuum grease. The tests were performed in a newly developed version of the Danish Triaxial Apparatus in which control of stress path, measurement, and data analysis is automated (Ibsen 1994). The apparatus is outlined in Figure 2.

The static triaxial specimen was loaded by a mechanically controlled piston, while the cyclic test is loaded by a hydraulic piston. The tests were performed with constant deformation rate of 4 % per hour. The measuring systems in the two apparatuses were identical and consisted of electronic load, pressure, and deformation transducers. The working principles of the triaxial cell are similar to those described by Jacobsen (1970).

2.2 Sand used

The study described in this paper is based on tests performed on two uniform sands: Aalborg University sand No. 1 and Lund sand No 0. The index properties for these sands are shown in Table 1.

Table 1. Index Properties.

Property Aalborg University sand No 1

Lund sand NoO

dso mm 0.14 0.4Cu 1.78 1.7ds 2.65 2.65max 0 . 8 6 0.82

emin 0.55 0.55

2.3 Specimen preparation and saturation

The test specimens were prepared by a pluvial deposition and carefully saturated in total vacuum (approx. -98 kPa). This causes all specimens to be pre-consolidated to approximated 100 kPa during the preparation process. This technique ensures homogeneous and totally saturated specimens. The triaxial test series was performed on isotropically consolidated specimens with relative densities as shown in Table 2. The test results are reported by Ibsen, L.B (1993), Ibsen, L.B. and Bpdker, L (1994), Jacobsen, F.R. and Simonsen, J (1994), and Ibsen and Jacobsen (1996).

Table 2. Relative densities for sand specimens in static triaxial tests.

_______________________ Relative densitiesAalborg University 0.10, 0.51, 0.80, 1.00sand No. 1Lund 0 .48 ,0 .78 ,0 .93 , 1.00sand No. 0 _____

30

Figure 3. Diagram illustrating the development of stress-strain behaviour in drained triaxial compression tests on dense sand and specimens with equal height and diameter.

3 THE CHARACTERISTIC STATE

3.1 Definition of characteristic state

Figure 3 shows the results of four drained triaxial compression tests with the same initial density. The effective stress path is shown in Figure 3.a on a Cambridge diagram. The tests are performed with different initial mean normal pressures p ', which are held constant throughout each test. Laboratory tests on several sands, (Lade and Ibsen 1997, Ibsen and Lade 1998) have shown that a characteristic threshold exists in granular materials which is defined as the stress state where the volume change goes from contraction to dilation. On the £i -Sv curve. Figure3.C, the characteristic threshold is marked by open circles at the point where the specimen has minimum volume. The stress state characterised by

q[¡) where Ó£ylÓE\ = 0 is defined and described as the Characteristic State. Characteristic states occur at the transition from contraction to dilation, and these states are located on a line, the Characteristic Line cl, through the stress origin. The slope of the Characteristic line may be described by an angle, (p,i, (Ibsen and Lade 1998).

Contraction and dilation can be caused by application of shear stresses as well as by changes in the mean normal stress. In the constant p ’-test the increment Sp' is zero and the measured volumetric strains are caused entirely by shear stresses. Since there is no change of p ', there in no elastic volumetric strain and the volume change is purely plastic. In elastoplasticity models the characteristic state, evaluated from p' = const, tests, therefore corresponds to the point on the plastic potential surface where the plastic strain increment vector is perpendicular to the p'- axis or the hydrostatic axis, as shown in Figure 1. The characteristic line represents the trace of this point in the stress space and divides it into two subspaces in which the stress combinations lead to different deformation mechanisms.

Below the characteristic line the stress combinations lead to contraction, i.e. Ssv > 0 .Above the line the stress combinations lead to dilation, i.e. Sev < 0 .

Below the characteristic line the resistance to deformation is governed by sliding friction due to microscopic interlocking depending upon surface roughness of the particles or interlocking friction between particles. The resistance is due to pure friction and the characteristic state describes an intrinsic parameter, which defines a characteristic angel (p for a given sand. This angle is independent of the relative density h , as shown in (Lade and Ibsen 1997, Ibsen and Lade 1998).

3.2 Interlocking capacity

Luong (1982) defined the characteristic state in a similar manner, as described above, based on conventional triaxial compression tests. In conventional triaxial tests, where the confining pressure is constant, the stress path corresponds to Sq'ISp' - 3. Luong’s characteristic state will in the following be refereed to as the Interlocking Capacity State of the sand.

The volumetric strain curves from three triaxial tests on Aalborg University sand No. 1 conducted with different stress paths are shown in Figure 4. The tests were all performed on specimens with Id =1 . 0 0 and consolidated to a mean normal stress of p' = 200 kPa before shearing.

In the constant p'-itsi the volumetric strains are caused entirely by shear stresses. The test shows shear-induced contraction in the beginning, and it is possible to define a characteristic state, as shown in Figure 4. As expected, the contraction^ becomes more pronounced as the stress ratio Sq'/Sp' decreases, and there are distinct differences between the characteristic states obtained from different stress paths. In Figure 5 the characteristic state and the interlocking capacity states, evaluated from the

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p' = const. qVp's3 qVp'=2

Figure 4. Volumetric curves obtained by stress path tests on Aalborg University sand No. 1. Id = 1.00. Isotropic consolidated to p ’= 200 kPa before shearing.

q' [kPa]

Figure 5. Stress paths employed in triaxial compression tests on Aalborg University sand No 1, /d = 1.00

test with the stress path Sq'/Sp' = 3 Sq'/Sp' = 2 , are compared. The figure shows, that the interlocking capacity states are located above the characteristic line and the values increase with decreasing stress path. For different stress paths, the increment in /?', produces both an elastic and plastic volumetric strain increment. The plastic volumetric strain is defined by the particular combination of stresses at the particular point where the characteristic line is reached, and not by the stress path followed. Whereas, the elastic volumetric strain is a function of the stress path followed. The distinction between the characteristic and interlocking capacity state is the elastic volumetric strain increment included in the interlocking capacity state. The interlocking capacity state is therefore stress path dependent and not useful as an intrinsic parameter in elasto-plasticity models.

3.3 Comparison of phase transformation and characteristic stress states

The phase transformation stress state plays a similar role for undrained tests as the characteristic stress state plays for drained tests. Figure 6 shows a schematic illustration of the stress state at which phase transformation occurs along an effective stress path from an undrained test. It is the point at which “the stress path turns its direction in p’- q’ space” (Ishi- hara et al. 1975J, i.e. the point where the effective stress path has a “knee” and the effective mean normal stress reaches a minimum value

Whereas the “knee” described above does not clearly define the location of the phase transformation point, the most consistent definition is one that is independent of the stress path. The phase transformation state is therefore best defined as the point at which the effective stress path has a vertical tangent.

Figure 6 . Schematic diagram of phase transformation state in undrained triaxial compression tests on sand, a) Conventional total stress path Sq'/Sp' = 3 , b) Total stress path p = const.

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A t th is p o in t o f th e u n d ra in e d tes t, the in crem en t Sp’ b e co m es zero , an d th e e la s tic v o lu m etric stra in in crem en t, Se , is th e re fo re a lso zero . C o n seq u en tly , the p las tic v o lu m e tric s tra in in crem en t, Ssv, is a lso zero . T h is d e fin itio n th eo re tic a lly m ak es the c h ara c teris tic and p h a se tran s fo rm a tio n sta tes iden tica l, (Ibsen and L ad e 1998).

3 .4 C o m p ariso n o f c ritica l s ta te and ch arac te ris ticstress sta tes

D iffe re n t v e rs io n s o f th e co n d itio n s th a t c o n stitu te critica l sta te hav e b een p re sen te d in the lite ra tu re (C asag ran d e 1940, S eed and L ee 1967). T h ese are illu s tra te d in F ig u re 7 to g e th e r w ith th e d e fin itio n o f the c h a ra c te ris tic s ta te , (Ib sen and L ad e 1998).

A c co rd in g to C a sa g ran d e (1 9 4 0 ), c ritica l s ta te is reach ed u n d e r d ra in e d co n d itio n s w hen the vo id ra tio and the n o rm al and sh ea r s tre sses rem a in c o n stan t u n d e r c o n tin u e d sh earin g . In sands, c ritica l s ta te ty p ica lly o ccu rs a fte r p e ak fa ilu re at large stra in s , as illu s tra te d in fig u re 7. R e ac h in g critica l s ta te u n d e r u n d ra in e d c o n d itio n s w o u ld req u ire tha t the p o re p re ssu re and the e ffe c tiv e s tresses rem ain co n stan t a t la rg e stra in s.

S eed and L ee (19 6 7 ) d e fin e d c ritica l sta te as the co m b in a tio n o f v o id ra tio , a fte r c o n so lid a tio n , and co n fin in g p re ssu re th a t p ro d u c es ze ro to ta l vo lum e ch an g e at p eak fa ilu re u n d e r d ra in e d c o n d itio n s, as a lso illu s tra te d in F ig u re 7. T h e c ritica l sta te line o b ta in ed a cc o rd in g to S eed and L e e ’s d efin itio n is d iffe ren t fro m th a t o b ta in e d at la rge stra in s, e sp e c ia lly fo r low v o id ra tio s and h ig h co n fin in g p re s sures. T o d ay the te rm c ritica l s ta te refers to the C a sa g ra n d e ’s d e fin e d critica l sta te .

T he ch a ra c te ris tic sta te and the c ritica l sta te are very s im ila r, as d isc u sse d by (L u o n g 1982). F o r loose sand and san d at h igh c o n fin in g pressu re ,

= 0 is reach ed at the critica l sta te . T he c ritica l s ta te is th e re fo re the sam e as the charac te ris tic sta te , and it o ccu rs at fa ilu re fo r sand th a t co m p resses d u ring shear. F o r d e n se san d o r san d at low co n fin in g p ressu re , the c h a ra c te ris tic sta te is reach ed at sm all stra in m ag n itu d es , as in d ica ted in F ig u re 7, w hile the critica l sta te is re ac h ed at la rge stra in s. T he e ffec t o f p o st-p eak sh ea r b a n d in g in d ra in e d triax ia l co m p re ssion tes ts on den se , m ed iu m and even loose sands and n o n u n ifo rm ity o f sp ec im en g eo m etry at large axial stra in s, all a ffec t the overa ll d e te rm in a tio n o f C a sa g ran d e ’s c ritica l sta te . In a d d itio n , ev alu atin g ex p erim en ta l re su lts to d e te rm in e w hen c ritica l sta te occu rs is d iffic u lt, b e ca u se ra re ly do the stress and v o lu m e ch an g e ten d e n c ie s in a sp e c im en rem ain co n stan t fo r very long . C o n tra ry to th is , th e ch a ra c teris tic sta te is d e fin e d p re -p e a k u n d e r u n ifo rm stress and stra in c o n d itio n . T h e sta te is w e ll d e fined , and

F ig u re 7. C o m p ariso n o f p h a se tran s fo rm a tio n and ch ara c te ris tic stress sta tes.

4>cl =0

- Drained stress path for triaxial compression test with p' = Constant

Characteristic line, 6 ^ = 0

F ig u re 8. V aria tio n o f d ra in e d sh e a r s tren g th e n v e lo p e fo r sand w ith m ean n o rm al p re ssu re .

the ev a lu a tin g o f the e x p e rim e n ta l re su lts to d e te rm in e w hen the c h ara c te ris tic s ta te o c cu rs is easy. C o m p ared to the critica l sta te , th e c h a ra c te ris tic s ta te is m u ch m o re su itab le as an in tr in s ic p a ra m e te r in e la s to -p las tic ity m odels.

4 C H A R A C T E R IS T IC S T A T E A N D S T A T IC S A N D B E H A V IO U R

4.1 D ra in ed sh ear s tren g th o f san d

T h e typ ica l v aria tion o f d ra in e d sh e a r s tren g th o f san d w ith m ean e ffec tiv e s tress is i llu s tra te d sc h e m atica lly in F igu re 8. F o r a san d w ith a g iv en in itia l den sity , the p eak fric tio n an g le c o n sis ts o f tw o c o m p o n en ts . O ne fro m the b asic fr ic tio n b e tw een sand

p a rtic le s m o d ifie d fo r c o n tr ib u tio n s fro m re a rra n g e m en t o f p a rtic le s at c o n s ta n t v o lum e. T h e re su ltin g fric tio n an g le is re fe rre d to as th e c h arac te ris tic fr ic tion ang le (pd.

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The second component derives from the dilation of the sand during shear. The dilation is suppressed at higher pressures due to crushing, and the resulting strength component therefore reduces to zero at very high pressures. Thus, a curved failure surface is observed. In this subspace, situated between the failure envelope and the characteristic line, the resistance to deformation is governed by interlocking dis- rupture. The individual particles are plucked from their interlocking seats and made to slide over/around the adjacent particles leading to large dilative volumetric changes. The resistance to the deformation and thereby the size of the subspace is strongly dependent on the initial sand density. It requires more energy for the grains in a dense sand to move the adjacent particles, than for the grains in a loose sand. The subspace does not exist in a very loose sand where no dilation occurs and in this case the failure envelope will be identical to the characteristic line. Experiments on sands have shown that both the contribution from dilation and the range of confining pressures in which dilation occurs reduce with decreasing relative density, as shown schematically in Figure 9.

4.2 Undrained shear strength of sand

The three schematic stress paths shown in Figure. 10 represent the three types of undrained behaviour typically observed for clean sands, (Yamamuro and Lade 1997).

Results of four conventional undrained triaxial tests performed at low pressure are shown in Figure 11. During undrained shear at low pressure, the pore pressure increases at first in order to prevent the sand from contraction, i.e. Su > 0 . When the deviator stress approaches the characteristic state Sp' -► 0. The test in Figure 11, indicates that the stress states where Sp^O are located on the characteristic line. If q' is increases further, the effective stress path is located in the subspace which is characterised by dilation. In order to prevent dilation, the pore pressure generation becomes negative, i.e. Su<0, as shown in Figure 11.a. This directs the stress path to the right towards higher effective confining pressures, causing the stress difference to increase continuously towards the point where the characteristic line and the drained failure envelope merge and become identical, as shown in Figure 10. At that point, failure develops. Figure 11.a shows that the effective stress path approaches a common stress path asymptotically, defined by the stress stage marked with open squares. This common stress path is identical with the stress path defined by the stress states where ZJey = 0 , marked by open squares in figure 3.

Figure 9. Variation of drained shear strength envelope for sand with relative density.

This common stress path is normally considered to be the undrained failure envelope. In figure 11 .b it is shown that the common stress path does not represent any failure in the sand, and tests covering a interval from 5 to 2000 kPa do not reveal any maximum at the performance curves. The sand behaviour is entirely stable until the point is reached, where the characteristic line and the drained failure envelope become identical

If the effective stress paths are studied in detail, it is observed that the stress state corresponding to maximum pore water pressure Wmax occurs slightly later than the characteristic stress state, as indicated in Figure 6 .a. If the tests are performed as undrained test, where the total stress path TSP p is constant, it is observed that the stress state corresponding to maximum pore water pressure Wmax is identical with the characteristic stress state, as shown in Figure 6 .b. Along the effective stress path in Figure 6 .b, the elastic and plastic volumetric strains have to compensate for each other, i.e. = Since there is no change in the mean normal stress p ’ , there is

Figure 10. Schematic stress paths of undrained soil behaviour.

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Figure 11. Results of four undrained tests performed on Lund sand No. with Id= 0.78.

no elastic volumetric strain either, i.e. there is no change in the amount of elastic strain energy stored in the soil. The stress state corresponding to maximum pore water pressure Wmax is therefore identical with the characteristic stress state.

In the conventional undrained compression test, see figure 6 .a, the total stress path corresponds to SqISp = 3 and additional elastic energy is stored in the soil. The elastic volumetric strain is identical with what was observed in the drained tests under the effective stress path Sq'ISp' = 3 . The stress state corresponding to maximum pore water pressure Wmax , is therefore identical with the interlocking capacity of the soil. For an arbitrary total stress path, different from constant p, the interlocking capacity controls the stress point where the maximum pore water pressure Wmax occurs. This stress point is therefore also stress path dependent.

The middle stress path in Figure. 10, indicates a more contractive behaviour pattern experienced at medium high confining pressures. The distance between the instability line and the eharacteristic line, is so large that the effective stress path is able to “wrap around” the top of the plastic yield surface. Then loading can occur while all stresses are decreasing (Lade 1992). The undrained sand behaviour along this declining portion of the effective stress path is unstable in the sense that the sand cannot sustain the current stress difference. However, as the effective stress path crosses the characteristic line, the suppressed dilation produces negative pore pressure increments, and the effective stress path is consequently directed towards higher effective confining pressures and higher stress differences. This stable behaviour continues until the point where the characteristic line and the drained failure envelope merge is reached. Thus, temporary instability is observed in the middle ranges of confining pressure (Yamamuro and Lade 1997). Note that the point where the characteristic line and the drained failure

envelope become identical does not coincide, because the void ratio after consolidation decreases with increasing confining pressure causing the failure envelope to grow, as shown in figure 10. The end points will therefore be slightly different for tests consolidated to difference confining pressures.

The third effective stress path at the highest confining pressure in Figure 10 indicates large contractive tendencies resulting in continuously increasing pore pressures. The effective stress path reaches a peak at the instability line, after which it declines until the characteristic line is reached. The characteristic line is reached at a stress level where the characteristic line and the drained failure envelope are identical. In this case the effective confining pressure is so high that there is no tendency for dilation. Past the point of maximum stress difference, the undrained sand becomes unstable (Lade et al. 1988, Lade 1993, Yamamuro and Lade 1997). This unstable behaviour continues until the point where the characteristic line and the drained failure envelope merge is reached. The stress difference and the mean stress stabilises, but failure develops completely.

4.3 Static liquefaction

The term static liquefaction is used for the condition described by 0-3 = 0 and cji - 0-3 = 0. Static liquefaction can only develop in very loose sand at low confining pressure. In this situation, the third effective stress path in figure 10 is observed. As a consequence of the applied confining pressures, a small subspace, where the soil dilate will always exist. The point where the characteristic line and the drained failure envelope merge will always exist. The declining stress will therefore stabilise before the static liquefaction is reached. An accelerator is needed to overcome this point in order to develop static liquefaction. The accelerator is the additional

35

■ Cyc. no.2 A C y c . no.10 ► Cyc. no.31 I Cyc. no.2 Cyc. no.40 • Cyc. no.312

I Cyc. no.1 > Cyc. no.1285_ I Cyc. no.1 • Cyc. no. 1285

Figure 12. Outline of the phenomena observed in cyclic triaxial tests, a) cyclic liquefaction, b) pore pressure buildup, c) stabilisation, d) instant stabilisation.

elastic energy stored in the soil, i.e. the difference between the characteristic and the interlocking capacity, as described above. The elastic energy is both material and stress path dependent. It’s potential is relative small and it can only accelerate the declining stresses so static liquefaction is developed at very low confining pressures, as shown by (Yama- muro and Lade 1997).

5 THE CHARACTERISTIC STATE AND CYCLIC LOADING

Liquefaction is more likely to occur under cyclic loading than during static loading. In the case of undrained cyclic loading the stress variation can develop cyclic liquefaction even at very dense densities. The cyclic failure condition, such as cyclic liquefaction (Seed and Lee 1966) and Cyclic Mobility (Casagrande 1971) is only part of the complex mechanism, which has to be determined in order to describe the development of stress and strain in cyclic tests. Experiments have been performed to study the factors that influence and control the fatigue which leads to Cyclic Liquefaction. (Ibsen1993). The observed stress paths, can be divided in

four typical stress paths, as shown in Figure 12. Two typical stress path in which positive pore pressures are generated. The phenomena named Pore Pressure Buildup or Cyclic Liquefaction can be observed. These stress paths are shown in Figure 12a) and 1 2 b), and two typical stress paths in which negative pore pressures are generated. The phenomena named Stabilization or Instant Stabilization can be observed. These stress paths are shown in Figure 1 2 c) and 1 2 d). These four typical stress paths will be shown to be controlled by the characteristic state.

5.1 Drained cyclic loading

In Figure 13 cycling sequences are carried out at different deviator stress levels under drained conditions and at constant confinement, = 2 0 0 kPa. Each cycling sequence consists of 2 0 cycles with an amplitude of 100 kPa. The diagram shows very clearly that the contracting behaviour of the soil is obtained when the mean deviator stress level is lower than the characteristic level at the interlocking capacity state. The dilation behaviour of the soil during load cycling is evident when the mean deviator stress level becomes higher than the characteristic threshold, q \i.

36

- ‘i-uu - t u w

F ig u re 13 C y c lic lo ad in g u n d e r c o n stan t co n fin in g p ressu re 200 k P a p e rfo rm ed on F o u n ta in b le au san d Id = 0 .6 4 (d a ta fro m L u o n g 1982).

5 .2 U n d ra in ed cy clic lo ad in g

S im ila r to the d ra in e d cyclic tes t in F ig u re 13, and w ith the e x p e rien c e fro m the sta tic tes t in m ind , the in te rlo ck in g c ap ac ity sta te c o u ld then be ex p ec ted to con tro l p o re p re ssu re in the so il d u rin g c o n v en tio n a l u n d ra in ed cy clic lo ad ing . H o w ev er, the ch an g es in the e ffe c tiv e s tre ss p a th due to cyclic lo ad in g are c o m p o sed o f the p o re p re ssu re p ro d u ced du rin g the lo ad in g p a rt o f th e cy cle and the ch an g es in the po re p re ssu re d u rin g the u n lo ad in g p a rt o f the cycle. In Ibsen (1994) the in te rlo ck in g cap acity sta te w as show n on ly to co n tro l the ch an g es in the pore p re ssu re d u rin g th e lo ad in g p a rt o f the cycle. T here fo re , the in te rlo ck in g cap ac ity sta te is no t able to co n tro l the s tress h a rd en in g /so fte n in g o f the soil d u ring a c o m p le te cycle .

It is a ssu m e d th a t a s tress sta te ex is ts , w here the p o sitiv e and n e g a tiv e p o re p re ssu res gen era ted d u ring a lo ad in g cycle n e u tra lise each o ther. T h e stress sta te is d e fin e d a.s Z(5u = 0 d u rin g a cycle. T h e stress sta te is d e sc rib e d as th e Cyclic Stable State. E ach tim e the m ean d e v ia to r s tress level is low er than the cyclic s tab le s ta te p o sitiv e p o re p re ssu re w ill be g en e ra ted and n eg a tiv e p o re p re ssu re is g enera ted each tim e the m ean d e v ia to r s tress level b eco m es h igher. A s a c o n se q u en c e th e cyclic lo ad in g leads the m ean norm al stress to w a rd s the cy clic s tab le sta te in each test, as sh o w n in fig u re 14, and w hen the cyclic sta-

F ig u re 14. T h e e ffec tiv e stress p a th o f n ine cyclic tes t is show n. T he tes t is p e rfo rm e d on L u n d N o. 0 w ith Id = 0 .78 and on sp ec im en s w ith eq u a l h e ig h t and d iam eter. N is the n u m b er o f cy cles ad d ed to the tes t an d the a rro w d esc rib es th e ch an g es in the e ffec tiv e m ean stress.

b le s ta te has been re ac h ed the m ean no rm al stress does n o t ch an g e and th e cyclic lo ad in g w ill no t lead to fu rth e r h a rd en in g o r so ften in g o f the soil.

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Figure 15 Observed phenomena explaned by the cyclic fatigue theory for sand

5.3 The cyclic fatigue theory for sand

The drained stress state {p's, q's), present before the cyclic loading is added to the test, controls the variation of the effective mean stress. If the anisotropic mean stress level is situated below the characteristic line CL, the increase in pore pressure during the loading part of one cycle is greater than the reduction during the unloading part. The cyclic loading will then lead to pore pressure buildup and the effective normal stress will decrease , as shown in Figure 15. a) and 15. b.

F a ilu re can tak e p lace , if the m in im u m stress level after a number of cycles exceeds the characteristic line in extension CL'. The pore pressure generation du will then go from Su > 0 i o twice during each cycle and the equilibrium of the stable state cannot be created. After the minimum stress level

has exceeded the characteristic line in extension CL, the drained failure envelope will be reached during the subsequent cycle. Cyclic Liquefaction as defined by Casagrande (1971) will be observed if the maximum stress level q'^^^dming the subsequent cycle reaches the drained failure envelope in compression. Necking, which is a phenomenon similar to Cyclic Liquefaction and defined by Casagrande (1971) will be observed if q' ^ reaches the drained failure envelope in extension. This failure mechanism is outlined in Figure 15 a). If the cyclic stable state is developed during the cyclic loading no failure will occur and the phenomenon Pore Pressure Buildup will be observed, as shown in figure 15. b). According to the figure no further changes in the

mean normal stress will be observed while adding further cycles.

If the anisotropic mean stress level is situated above the stable line CSL, the cyclic loading will generate negative pore pressure. Similar to the phenomenon Pore Pressure Buildup the cyclic stable state can be developed during the negative pore pressure generation and the phenomenon Stabilization will be observed, as shown in Figure 15.c). If the amplitude of the cyclic load is so large that the stress variation during the first half cycle follows the common stress path, the mean stress level changes from being situated above the cyclic stable line to being situated below, as shown in Figure 15.d). After the first half cycle, where considerably negative pore pressure is generated, the cyclic loading will generate positive pore pressure due to the fact that the mean normal stress state is situated below the stable line. The phenomenon which is described as Instant Stabilization will be observed. Similar to Pore Pressure Buildup failure can take place, if the minimum stress level q' ^ after a number of cycles exceeds the characteristic line in extension CL', otherwise the Stable State will develop.

6 CONCLUSIONS

Studying the basic sand behaviour in triaxial tests under uniform conditions, similar responses of the sand due to static and cyclic loading have been discovered. The static and cyclic responses of sand can

38

be explained with help of the characteristic state, and the strength of sand under undrained conditions is found to be controlled by the drained failure condition for both static and cyclic loading.

In this paper, the characteristic state is redefined as the stress state where Ssy becomes zero for the first time in a constant p' test. Further, the phase transformation state is defined as the state where becomes zero for the first time. As a consequence, the characteristic and phase transformation lines become identical. These definitions are mutually consistent, and they may therefore be useful in controlling the plastic potential function for description of plastic volume changes of soils.

In comparison, the characteristic angle defined by Luong (1982) is not an intrinsic parameter, independent of stress path, and it not useful for development of elasto-plasticity models.

Performing cyclic triaxial tests on specimens, which ensure homogeneous stress and strain distribution throughout the test, the existence of a cyclic stable state is found. The cyclic stable state is shown to have a considerable influence on the development of the effective stress variations during cyclic loading. The cyclic stable state represents an ideal stress state, where the positive and negative pore pressures generated during a loading cycle neutralise each other, and the mean normal stress is shown not to change, when the stable state is reached, and further loading will not lead to any stress hardening or softening of the soil. The cyclic stable state is an intrinsic parameter, which is found to be independent of the amplitude of the cyclic load.

The cyclic stable state is shown to divide the stress space into two subspaces, where the cyclic loading will generate positive or negative pore pressures, respectively. Especially the new phenomena Stabilization and Instant Stabilization observed in connection with the development of negative pore pressure are of great interest.

7 REFERENCES

Casagrande, A. 1971. On Liquefaction phenomena. Geotechnique, September, 1971 XXI(3), 197-202.

Guzmann, A. A. et al. 1988. Undrained moriotonic and cyclic strength of sand. Journal of the Geotechnical Engineering Division ASCE, 114(10), 1089-1118.

Ibsen, L.B. 1994. The stable state in cyclic triaxial testing on sand. Soil Dynamics and Earthquake Engineering IS, 63-72.

Ibsen, L.B 1993 Poretryksopbygning i sand. (Pore perssures in sand). Ph.D Thesis. Soil Mechanic Laboratory, Aalborg University, Denmark , Jan. 1993.

Ibsen, L.B. and Bpdker, L. 1994. Baskarp Sand No. 75. Data Report 9301, Soil Mechanics Laboratory, Aalborg University, Denmark.

Ibsen, L.B and Lade P.V. 1998. The Role of the Characteristic Line in Static Soil Behavior. 4 ” Workshop on Localisation and Bifurcaton Theory

for Soils and Rocks, A. A Balkema.Ibsen. L.B. and Jakobsen, F.R. 1996. Lund Sand No.

0, Data Report 8401, 8402, 8801 & 8901, Soil Mechanics Laboratory, Aalborg University, Denmark.

Ishihara, K., Tatsuoka, F. and Yasuda. S. 1975. Undrained deformation and liquefaction of sand under cyclic stresses. Soils and Foundations, 15(l),29-44.

Jacobsen, M. 1970. New Oedometer and Triaxial Apparatus for Firm Soil. DGI Bulletin No. 27.

Jakobsen, F.R. and Simonsen, J. 1994 Horizontal resistance of dynamically loaded piles, (in Danish). MSc. Thesis. Aalborg University.

Lade, P.V. 1992. Static Instability and Liquefaction of loose fine sandy slopes. Journal of Geotechnical Engineering, ASCE, 118( 1), 51-71.

Lade, P.V. 1993. Initiation of static instability in the submarine Nerlerk berm, Canadian Geotechnical Journal, 30(6) ,895-904.

Lade, P.V. 1994. Instability and Liquefaction of granular materials. Computers and Geotechnics,16, 123-151.

Lade,P.V. 1995. Instability of sand in the prefailure hardening regime. Proc. First conf on pre-failure Deformation Characteristics of Geomaterials, 2:837-854.

Lade P.V, Nelson,R.B., and Ito,Y.M (1988). Instability of granular materials with nonassociated flow. Journal of Engineering Mechanics, ASCE, 114(12),2173-2191.

Lade P.V and Ibsen L.B 1997. A Study of the Phase Transformation and the Characteristic Lines of Sand Behavior. Deformation and Progressive failure in Geomechanics. IS-NAGOYA '97. Pergamon Press, 353-358.

Lade, P.V. and Prabucki, M.-J. 1995. Softening and preshearing effects in sand. Soils and Foundations,35(4), 93-104.

Luong, M.P. 1982. Stress-strain aspects of cohesionless soils under cyclic and transient loading. International Symposium on Soil under Cyclic and transient Loading, A. A Balkema, Rotterdam, 3 15-324.

Seed, H.B. and Lee, K.L. (1967).Undrained strength characteristics of choesionless so\\,Journal of Soil Mechanics and Foundations Division, ASCE, 93(6), 333-360.

Yamamuro J.A. and Lade P.V. 1997. Static liquefaction of very loose sand. Canadian Geotechnical Journal 34, 905 - 917.

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Advances in the effective stress approach to liquefaction behavior

G.M. NorrisDepartment of Civil Engineering, University of Nevada, Reno, Nev., USA

ABSTRACT

An effective stress method for the evaluation o f the undrained stress-strain-stress path behavior o f loose sands based on drained triaxial test response is presented here. Understanding peak undrained resistance and residual strength in terms o f characteristics o f rebounded (i.e. overconsolidated) standard drained test response proves extremely useful. This approach works for both triaxial compression and extension tests and shows that these undrained paths control or bound the undrained cyclic triaxial test stress path. Hooke’s Law posed in terms o f drained test confining and deviatoric stress response can be used to demonstrate why the extension test resistance o f a loose sand measures less than the undrained compression peak resistance and residual strength. The characterization works for both contractive (i.e. steady-state or complete liquefaction) and dilative (i.e. quasi steady-state or limited liquefaction) behavior. Formulation o f the standard drained test stress-strain and volume change response based on confining pressure, OCR, peak friction angle, void ratio, uniformity coefficient, and particle shape allows the direct assessment o f undrained behavior (compression and possibly, in the future, extension and simple shear response) based upon the same variables. Such undrained response characterization from drained test formulation has direct application to a number o f practical problems.

1 INTRODUCTION

Norris et al. (1997a) have demonstrated on both angular and rounded loose clean sands that they can establish the undrained stress-strain curve and the undrained effective path from drained rebounded (overconsolidated) test stress-strain and volume change curves. They show that the residual strength and, separately (Norris et al. 1997b), the undrained peak resistance are artifacts o f the drained response curves. Blackett (1997) has shown that the same methodology works on loose and dense mine tailings (i.e. silty sand, 23% nonplastic fines) material. While such work was originally carried out for triaxial compression behavior. Palmer (1997) established that the same undrained to drained relationship holds true under triaxial extension response and that the effective stress path for the undrained cyclic triaxial test is bounded by the undrained monotonic triaxial compression and extension paths. Norris et al. (1998) demonstrated

that Hooke’s Law can be rewritten in terms o f the triaxial test deviatoric stress and effective confimng pressure components. They show by equation that, for an isotropic material, the undrained extension resistance o f a loose sand is lower than its undrained compression counterpart. Ashour and Norris (1998a) demonstrated that analytical formulation o f the drained axial compression test stress-strain and volume change behavior (a function o f confining pressure, OCR, peak friction angle, void ratio/relative density, uniformity coefficient, and particle shape) can be employed to successfiilly evaluate the corresponding undrained triaxial compression behavior. Such constructed undrained response can, in turn, be implemented with various practical applications, e g. the response o f a laterally loaded pile or pile group in sand under undrained conditions (Ashour and Norris 1998b). This paper summarizes the findings from these studies undertaken by researchers at the University o f Nevada, Reno.

41

roFi

gure

1

Isot

ropi

c co

nsol

idat

ion

(to

e. a

t O3J

and

rebo

und

from

e. a

t O3 J

res

pons

e

Ente

r wi

th

Figu

re 2

Dra

ined

str

ess-

stra

in (o

j -

8j)

and

vol

ume

chan

ge (C

v.^i

) cu

rves

(so

lid li

ne)

of re

boun

ded

(i.e.

ove

rcon

solid

ated

, O

CR

= o

^JOj

) sam

ples

with

sup

erpo

sed

undr

aine

d re

spon

se (

dash

ed li

ne)

Figu

re 3

U

ndra

ined

eff

ecti

ve s

tres

s pa

th (

ESP

) for

isot

ropi

cally

con

solid

ated

und

raln

ed te

st

UNDRAINED BEHAVIOR DRAINED TEST RESPONSE

FROM

Undrained triaxial test response can be established from drained test (i.e. effective stress behavior) provided the appropriate framework or formulation is employed. The undrained test stress-strain curve and effective stress path o f a sample isotropically consolidated to a confining pressure 0 3 at a void ratio e (Fig. 1) can be established from drained tests consolidated to the same e,. at 0 3 . Such drained test samples are then isotropically rebounded (points 1 , 2, 3, etc. in Fig. 1) to successively lower O3 values before being sheared. The resulting drained test stress-strain and volume change curves (Fig. 2) are used in conjunction with the isotropic rebound curve (Fig. 1) to establish the undrained stress-strain response (dashed line in Fig. 2) and effective stress path (Fig. 3).

Note that the vertical axis o f Figure 1 can be taken as either void ratio, e, or volumetric strain, i.e.

= Ae/( 1 + Co ). The volumetric strain in isotropic rebound, is taken from e at

With the availability o f the aforementioned rebounded (overconsolidated) drained test results, the undrained shear response can be constructed in the fashion described in the following few sentences.

In the consolidated undrained test, the application o f a deviatoric stress (o^) causes a porewater pressure buildup ( Au^) which results in a reduced effective confining pressure, O3 = 0 3 . - Au , and an associated volumetric strain ( £v,i8o), the same as recorded in the drained test response o f Figure 1. However, volume change and volumetric strain must be zero in an undrained test as shown, for example, by the vertical arrow from point 4 in Figure 1. Therefore, there must be compressive component due to Oj, or equal and opposite to £ ¿,0. Entering the drained test volume change curves (Fig.2 ) at £v,shear ^ ‘ oue moves horizontally until the curve for the associated 0 3 (= - Au^) isreached and then vertically to assess the associated £id and Oj (from the drained shear curve at O3). The corresponding effective stress path coordinate (p’,q) in Figure 3 is then p' = O3 + 0 ^ / 2 and q = oJ2. Therefore, with isotropically consolidated rebounded drained tests available for different O3 , one can assume a O3 (and, therefore, Au , = 0 3 - O3 ), find £v ijo (from the response o f Fig. 1), enter the £y - Ci drained shear curves (Fig. 2) at andfind £id,0 d and (p',q) as described above.

The difference in the current approach from true undrained behavior is that £ ^ ¡,0 and £ ,hear occur sequentially in the drained rebounded tests while

they occur simultaneously and mask each other in the undrained test. By contrast, there have been numerous unsuccessful attempts over the years to reproduce undrained behavior by performing a so- called “constant volume” test in which the investigator tries to simultaneously change 0 3 and o to keep £ = 0. The author has found that very small fluctuations from £ = 0 cause cumulative errors that make such an approach unsatisfactory.

The drained axial strain for Figure 2 (really £1 instead o f £j as it is labeled) comprises only part o f the total or undrained strain £1 . Just like the volumetric strain, the undrained, or total axial strain has two components, one due to shear, or deviator stress Oj (i.e. CiJ and the other due to the change in confining pressure (Ao3 = - Au^) or /3(assuming isotropic response). Since £^¿,0 is expansive, the undrained axial strain £j (=/3 ) represents a smaller compressive value than £1 . However, such a distinction becomes significant only at low values o f £ij (in the vicinity o f the undrained peak resistance, e g. point 2 in Fig. 2).

Figures 4, 5, and 6 show the undrained stress- strain curves and effective stress paths (ESPs) for triaxial tests (three each) on a subrounded Nevada sand (void ratios e . o f 0.82 and 0.92 for Series 1 and 2 respectively) and a subangular lone sand (e . ^0.91). The open circles represent the predicted undrained response assessed from the drained tests.

Figure 7 depicts the rebounded drained (i.e. effective stress) stress-strain curves for Nevada sand Series 1 used to establish the predicted behavior indicated in Figure 4. Figure 8 shows the corresponding consolidated-rebounded volumetric strain response. (Note that £^¿,0 in rebound is the difference in the value on the rebound curve from 1.14% ) From the open circles in the o - 8 1 curves o f Figure 7, one can see that the peak undrained resistance, occurs at a stress level, SL (=d,upeak/ df)» well below the drained or effective stress

failure (Odf) o f 345 kPa for the associated confining pressure (a3 „pg3iJ o f 150 kPa. Only beyond the post peak minimum (the quasi steady-state condition) for limited liquefaction in Series 1 tests on Nevada sand and the tests on lone sand does the material reach the Mohr Coulomb failure envelope (see the ESPs o f Figs. 4 and 6 ). For the complete liquefaction that occurs in the Series 2 tests on Nevada sand, the effective stress failure condition is reached only at the residual strength condition (Fig. 5), which, in this case, is virtually zero. Therefore, the undrained peak resistance is not strictly an effective stress (Mohr Coulomb) failure condition. Note also from Figure 7 that the "strain softening" o f the undrained

43

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/B

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sur<

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ln 0

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,, I 0

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00

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00

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00

4

00

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00

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100

20

0

30

0

400

50

0

P'

(kP

a)

P'

(kP

a)

Figu

re 4

U

ndra

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str

ess-

stra

in c

urve

and

eff

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tres

s pa

th,

Fig

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5 U

ndra

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str

ess-

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in c

urve

and

eff

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tres

s pa

th,

Nev

ada

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, S

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(e, =

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, a 3

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evad

a sa

nd,

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ies

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c =

0.9

4, a

3c =

400

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a)

stress strain curve is an artifact o f the drop in the confining pressure and the switch from one drained or effective stress-strain curve to a lower one.

Figure 9 shows the collection o f rebounded drained stress-strain curves for Nevada Series 1 tests (Fig. 7), each normalized by its drained strength (o^f) so that the vertical axis is a scale o f the stress level, SL (= o jo ^ . If, for the following discussion, one considers that, instead o f the spread seen in Figure 9, a single SL versus drained axial strain (ejd) curve results [see Fig. 10(a)], the corresponding peak undrained resistance o f Figure 10c can be characterized as the maximum o f the product o f an increasing drained stress level (SL) times a decreasing confining pressure (0 3 ) with increasing axial strain (Cj ) times a constant [tan^(45 + (|)/2)-l]. In other words.

SL a . (1)

where

= o'l - O3 = o ’3tan^ | 4 5 + - o'j (2 a)<l>

tann 4 5 + ^ 1 -1

SO that

= SL 0*3

o^ = SL o'yA ;

tani 45 + -1f)

(2 b)

(3a)

A = tan |45 + y (3b)

As shown in Figure 7b, where the dilatancy rate or slope (deydei)f is the same for all o f the rebounded tests, the same drained friction angle, (|), results provided that the constant volume fiiction angle, (1) , doesn't change with decreasing confining pressure. Therefore, o f Equation 3 varies with SL and O3

for a constant <|) (and, therefore, a constant value of A) as shown schematically in Figure 10.

3 LÍNDRAINED PEAK RESISTANCE, RESIDUAL STRENGTH, AND THE QUASISTEADY-STATE CONDITION AS A FUNCTION OF DRAINED CURVE CHARACTERISTICS

It is shown elsewhere (Norris et al. 1997b) that the undrained peak resistance (point 2 in both Figs. 2 and 3) corresponds to a specific point A o f the drained shear test response replotted as SL vs. shear as shown in Figure 11. While there are a family o f such curves (similar to the family o f SL vs. curves shown in Fig. 9), the particular curve where v, shear 0 ^ equal but opposite to for O3

specific to that rebounded curve (i.e. = 0 forundrained behavior), constitutes the drained or effective stress condition that signifies the undrained peak resistance (i.e. o¿ o f point 2 o f Fig. 2).

In a similar manner, note that the complete liquefaction shown in Figure 5 requires that the corresponding drained rebounded volume change curves (not shown) all reach their maximum compressive volumetric strain in shear and then become horizontal (deydCj = 0). The particular curve where equals for the 0 3 o f thatcurve signifies the residual strength condition. Since dcydCj = 0 , the drained strength (0 , ), which is two times the residual strength (i.e. = 2 S ),corresponds to (t)cv

By contrast. Figures 4 and 6 reflect limited liquefaction or the attainment o f a quasi steady-state condition where the ESP turns around and moves up the Mohr Coulomb failure envelope. As seen in Figure 7, the quasi steady-state condition occurs when the 8 - 8 path passes through the bottom (8vmax)of a drained volume change curve. In Figure 7 this corresponds to an imagined curve of approximately 62 kPa confining pressure, between the 60 and 65 kPa curves shown. The quasi steady- state condition requires that this value o f be equal and opposite to the value for the 0 3

pressure o f that curve. A steady-state condition does not develop because the volume change curves show a dilatant recovery beyond the maximum compressive strain (8^ ^ . Note that there are two points (one before and one after 8 ) intersected on the 65, 75 and 1 0 0 kPa curves. The stress-strain points after the postpeak minimum correspond to the points on the ESP o f Figure 4 moving up the failure envelope. While the postpeak minimum corresponds to a based on 4 ) (because dc^dc^ = 0 at 8 ,n,ax). it is at a SL < 1 in relation to o f based on the ^ o f the Mohr Coulomb envelope for the slope o f the dilatant part o f the volume change curves. One

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(kP

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6 U

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str

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in c

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eff

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tres

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th,

lone

san

d (e

c =

0.9

1, o

3c =

800

kP

a)

60

0

50

0 I

__

,--

40

0 I

/

.....---

-·· ,...

. 0

I I/

--------

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30

0

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:::~

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0 5

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0.4

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>

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-0.8

-1.2

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I 15

€1 (%

)

15

€1

(%)

.. ..

.._

..

250

····

~...

....

.._

20

0

··----

150

'I'" 20

20

~ 1~i

5

0

"~ =

25

kPa

I 25

3

0

"J=

25

kPa

50

6

5

75

1

00

150

20

0

25

0

25

3

0

Fig

ure

7 D

rain

ed s

tres

s-st

rain

(ad

-e 1

) an

d vo

lum

e ch

ange

(ev

_e,)

re

spon

se d

urin

11; s

hear

, S

erie

s 1,

Nev

ada

sand

can establish the postpeak minimum condition directly by comparing o f the volume change curve with 8 ¿.o for the value o f that curve. Thequasi steady-state condition occurs at the O3 value where and the corresponding o valueequals the postpeak minimum resistance.

4 DRAINED TEST FORMULATION

While it may seem that construction of the undrained triaxial compression response requires a significant number o f drained rebounded tests, since the rebounded volume change curves have the same form [in particular, the same dilatant failure slope, (deyd8 i)f], one can undertake a few good tests and interpolate/extrapolate the position o f the 0 ^ - 8 1 and 8 . - 8 1 curves for other pressures.

Alternatively, it was recognized that the shape of the 8^ o - O3 - 8 1 and 8 - 8 curves might be expressed as functions o f the state conditions and properties o f the sand. Ashour and Norris (1998a) have undertaken to develop such relationships where the parameters involved are each a possible function o f confining pressure (0 3 J, OCR ( = ), peakfiiction angle ((|>), void ratio (e) or relative density (Df), uniformity coefficient (CJ and particle shape (p). At present these expressions would seem to be reasonably accurate for clean sands even without specific consideration o f the sand’s fabric. The - 8 1 relationship is expected to be reasonably accurate for silty sands since the user should specify the 850

value (8 jd at SL = 0.50) and the pressure (0 3 J at which it was obtained. (A chart o f 850 as a fimction of e and C„ at 0 3 = 42 kPa is available if the user has no specific test data to use.) However, the 8 - 81

relationship should, at present, be restricted to clean sands since the compressibility o f silty sands has not adequately been accounted for in the relationship employed for the volume change curves.

Validation o f the use o f the drained test formulation to establish the undrained stress-strain curve and ESP for seven sands is presented elsewhere (Ashour and Norris 1998a). (A greater number o f comparisons along with suggested improvements to the characterization are sought.) This same formulation has been used in the Strain Wedge (SW) model program to assess laterally loaded pile and pile group response in sands under undrained conditions. Since the SW model program (and its “p-y” curve construction) relies on the triaxial compression stress-strain behavior o f the surrounding soil, such drained to undrained test formulation has direct application in this venue

(Ashour and Norris 1998b). The author likewise expects to incorporate such undrained formulation in vertical pile side shear or “t-z” response and pile tip ‘‘q-z” response in sand in an effort to improve seismic foundation analysis. At the same time, finite element programs that have trouble modeling a strain softening or dilative undrained stress-strain curve might well be able to accomplish the same result by adopting the characterization that the - 8 1 curve is a product o f SL vs. 8 ^ (a hyperbolic shaped curve) times O3 vs. 8 ij (a combination o f 8^ , - 0 3 and 8y - 8 1 relationships) and constant A (see Eq. 3 and Fig. 10).

5 SELTY SAND TESTS

While Blackett (1997) has shown that construction o f the undrained response from drained triaxial compression tests is equally valid when applied to loose and dense nonplastic silty sand mine tailings materials (23% fines), the greater compressibility o f such silty materials adds a certain complexity. As mentioned earlier, more documented drained rebounded tests on silty sands and nonplastic silts o f various percentage fines are needed to improve the drained formulation o f the volume change curves. Furthermore, it may be necessary to reload the isotropic rebound curve to more accurately evaluate the response beyond the postpeak minimum resistance since such a flexible material might experience a noticeable cyclic volume reduction. For the more rigid clean sands, the assumption that the reload 8 - 0 3 curve is identical to the originalisotropic rebound curve is sufficiently accurate. In turn, it may be necessary to undertake a drained rebounded shear test and a separate rebounded/ reloaded test to the same final 0 3 value and use the first to assess undrained response up to the postpeak minimum and the second for response beyond the postpeak minimum. Much more research on silty sands is needed.

6 UNDRAINED TRIAXIAL EXTENSION BEHAVIOR AND ITS EFFECT ON CYCLIC RESPONSE

Palmer (1997) has shown that undrained triaxial extension (i.e. lateral compression or axial extension) behavior can be constructed from drained triaxial extension (i.e. lateral compression) tests as shown for lone sand in Figure 12. The procedure is identical to that discussed in section 2 . Note the

47

~

0.0.---~-----------------------------------.

0.3

. 1

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53

~>

0.6

.64

8

.680

.6

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.7

15

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...:.J

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0.9

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....,-

~ .........

... ~!!

:l

0 50

20

0 25

0 30

0 35

0 10

0 40

0 15

0 (J~

(kP

a)

Fig

ure

8 Is

otro

pic

cons

olid

atio

n (t

o ec

= 0

.82

at 4

00 k

Pa)

and

re

boun

d re

spon

se,

Seri

es 1

, Nev

ada

sand

0.2

0.0+-------~------~------~------~------~~

0 5

10

15

E

(%)

I

20

25

Fig

ure

9 S

tres

s le

vel

(SL

) vs

. £

1 , S

erie

s I,

Nev

ada

sand

SL

al

, t

e:l

03

c

oj

b)

I (I

od

ad

m SL

a; [t

an

2 ( 4

5

+

ojl/

2) -

l]

\,

T'

,

cons

t cl

<I

Fig

ure

10

Rel

atio

nshi

p o

f a)

drai

ned

stre

ss l

evel

(S

L ),

b) d

ecre

asin

g co

nfin

ing

pres

sure

(a~)

that

lead

s to

c)

the

undr

aine

d pe

ak r

esis

tanc

e

SL

l j l ~

l l ; ~ l/ B

HA

~ mA

o~~~~~~~~~~~~~

0.0

1.

2 2

.4

1.5

l.B

2.

1 0

.3

0.6

0.9

E

<•I

V

Fig

ure

11

Dra

ined

str

ess

leve

l (S

L)

vs.

volu

me

chan

ge (E

v,sh

car)

much lower extension resistance as compared to the compression resistance pictured in Figure 6 for the same 0 3 and e .. In Figure 13, the undrained ESP in extension (plotted, as it should be, below the horizontal axis) is shown in conjunction with the three undrained axial compression test ESPs from Figure 4 for Nevada Series 1 tests. As with the loose lone sand, note the much lower peak (point 3 vs. point 1) and residual (point 4 vs. quasi steady- state point 2 ) stresses in extension as compared to compression behavior. Superimposed on Figure 13 is an isotropically consolidated undrained cyclic triaxial test ESP which, as can be seen, is constrained by the extension ESP rather than the compression path.

7 HOOKE’S LAW CHARACTERIZATION

The fact that the undrained peak resistance and residual strength is higher in the compression than extension stress state in loose (i.e. contractive) sands can readily be shown in terms o f Hooke’s Law. Writing Hooke’s Law for major principal strains (e) in terms o f applied effective stresses (o').

(5b)

where deviatone stresses o i and 0 ^ 2 are the same difference between effective or total stresses, i.e.

(6 a)

(6 b)

Substituting Equation 5 into Equation 4 yields the following modified equations.

* 32 v*)— (7a)

- 2 v*)— (7b)

^ 3- 2 v - ) ^E ’

(7c)

- V -E E E

^2 03= - V — -j- --- - V —

E E E

(4a)

(4b)

a , a ,8 (1 - 2 v ) ^ (1 - 2 v ) ^

t, Ej

1 - 2 v* (7d)

_ (1 - 2v;i(o , + Oj + a,)

(4c)

(4d)

where E = Young's modulus, v = Poisson's ratio, and volumetric strain, 8 (= AV/VJ represents the sum o f 8 1 , 8 2, and 8 3 . However, consider instead that stress o[ and O2 are

Oi = o . + o^ (5a)

Note the introduction o f the star symbol (*) to distinguish possible differences between the drained Young's and Poisson's values (E and v) for deviatone stresses and those associated with confining pressure (E* and v*).

If one considers the strains during the shear loading portion of the triaxial test, then oj in Equation 7 should be changed to A0 3 . Of course, in the consolidated drained test, A0 3 equals zero; while, in the consolidated undrained test, A0 3 would be (aj - 0 3 ^ or -Auj. For the traditional axial compression test, would also be zero and Equation 7 would then become

Aoje, = . ( 1 - 2 v-)—

E E '(8 a)

49

200

I7S

150

l:U

lOO 7S

"'""'

STR

ESS

/ST

RA

IN C

UR

VE

U

ndra

ined

Lal

ual C

ompr

essio

n

Fig

ure

12

Und

rain

ed s

tres

s-st

rain

cur

ve a

nd e

ffec

tive

str

ess

path

in e

xten

sion

, lon

e sa

nd (e

c =

0.9

1, a

3c =

800

kPa

)

"• L

CIA

E (e

xten

sion

)

AC

ILE

(com

pres

sion

)

cr,,g

20

01

-

180

Seri

es 1

C

ycli

c T

est

N, =

20

cycl

es

160

140

120

~~~ 1

q =

crd

/2

60

40

20

0 so

10

0 IS

O

··~

Und

rJS

.

200

2SO

30

0 JS

O

400

p' =

cr' 3

+ c

rd /

2

Fig

ure

13

Und

rain

ed e

ffec

tive

str

ess

path

s in

com

pres

sion

and

kPa

exte

nsio

n an

d th

e ef

fect

ive

stre

ss p

ath

of a

n is

otro

pica

lly

cons

olid

ated

und

rain

ed c

ycli

c tr

iaxi

al te

st,

Ser

ies

1, N

evad

a sa

nd 4S

O

Cj = - V — î- + (1 - 2v*)-Ao,

(8 b)

d, A0 3e, = - V — !- + (1 - 2v‘)— i (8c)

. 3 OE E '

8 . = ( 1 - 2 v ) - ^ + 3 ^ — ^Ao3 (8 d)

8 = 8 + 8Atar 1

undoubtedly due to greater horizontal stiffness caused by the compaction o f his samples and the fact that his material was more compressible than clean sand.

Originally it was hoped that the above Hooke’s Law relationships might be used to construct drained lateral compression response from drained axial compression tests and thus undrained compression, extension and even simple shear behavior from drained axial compression response. While Palmer (1997) has achieved a certain level o f success, it has been at the expense o f dealing with anisotropy and how it varies with SL and OCR. Needless to say, the drained formulation discussed in section 4 reflects compression behavior and more research is needed to extend it to extension behavior.

8 ^ = (1 - 2 v ) ^

3(1 - 2v*)a ’(8 e)

Note that, during undrained shear, 8 = 0 from which 8y shear ^ ’ v,iso Likcwisc, note thato^ /£

represents the drained axial strain, 8 (A 0 3 = 0 ), and the undrained value, 8 , equals -i- ( 1 - 2 v*)(Ao3/E*) or 8 + By inspection ofEquation 8 a, one can see that the undrained response contains the same effective stress component due to shear (i.e. the first term) as the rebounded drained test where A0 3 = 0 .

Instead, when considering the undrained lateral compression test = o^ j, recognize from

Equation 7d that there would be two components of (1 - 2v)o^ /£ to 8y shear Equation 8 d. Therefore,

for the same condition o f 8 = 0 , 8 iso the drop o f A0 3 would need to be greater; and, consequently, the lower O3 would yield reduced peak and residual resistances.

Of course, if the material were very dilative (v exceeds 0.5 in Eqs. 7d and 8 e, 8 shear becomes negative; and 8 ¿so and Aaj both become positive), then the extension resistance (from Eq. 7 where

will exceed the compression resistance

(from Eq. 8 ).The above analysis assumes isotropic material

properties (Young’s modulus and Poisson’s ratio) which is not necessarily realistic. Blackett performed undrained extension tests on his silty mine tailings sand and obtained about the same resistance as the undrained compression tests. This was

8 CONCLUSIONS

The establishment o f undrained stress-strain and stress path behavior from drained tests based on a framework o f effective stress understanding provides a straightforward and simple explanation for undrained response. It is much easier to envision and perform a limited number o f drained tests to see what effect a change in state or soil properties will cause relative to drained and, therefore, undrained behavior than it is to undertake a multitude of undrained tests in a “black box” fashion. Furthermore, it should be much easier to establish a database in terms o f drained tests than undrained tests.

Undrained response is truly a function o f volume change behavior and the factors that affect it such as density and stress state, mode o f deformation (compression, extension or simple shear) and soil properties (including fabric). The current approach provides specific conditions for the development o f undrained peak and residual (or quasi steady-state) stresses, encourages drained formulation as a means to investigate undrained response in a number o f practical applications, and uses simple Hooke’s Law expressions to relate undrained compression, extension and hopefully, in the near future, simple shear response.

The research undertaken to date provides a certain level o f capability. It needs to be expanded to more accurately characterize silty sands and the effect o f anisotropy (which differs with different methods o f sample preparation or fabric) on extension and, thereby, simple shear response in comparison to undrained compression behavior.

51

9 ACKNOWLEDGMENTS

The U S. Army CoqDS o f Engineers under the supervision o f Richard Ledbetter supported this research throughout Phases I through IV. The National Science Foundation provided matching support for Phase I. We gratefully acknowledge such financial assistance.

A number o f investigators undertook different aspects o f the collective work: Zia Zafir, Raghu Madhu, Robert Valceschini, Mohamed Ashour, Frank Blackett, Jeffrey Palmer, Tung Nguyen and Sherif Elfass. Their work made this overview possible.

REFERENCES

Ashour, M. & Norris, G. 1998a. Formulation o f undrained behavior o f saturated sands from drained rebounded response. Geotechnical Special Publication. Geotechnical Earthquake Engineering and Soil Dynamics III: Seattle, Washington. Vol. 1. ASCE. 75:361-372.

Ashour, M. & Norris G. 1998b. Undrained laterally loaded pile response in sand. Geotechnical Special Publication. Geotechnical Earthquake Engineering and Soil Dynamics III: Seattle, Washington. Vol. 2. ASCE. 75:1356-1367.

Blackett, F. 1997. Liquefaction and residual strength of a silty sand mine tailings from drained triaxial tests. MS Thesis. University o f Nevada. Reno.

Norris, G.M. et al. 1997a. Liquefaction and residual strength o f sands from drained triaxial tests. J. G eotech nica l and G eoenvironm ental Engineering. ASCE. Vol. 123. 3:220-228.

Norris, G.M. et al. 1997b. Peak undrained resistance o f loose sands. Transportation Research Record. TRB. 1569:65-76.

Norris, G.M. et al. 1998. An effective stress understand ing o f liq u efa c tio n beh av ior . Environmental and Engineering Geoscience. AEG/GSA. Vol. IV. 1:93-101.

Palmer J. 1997. Drained and undrained lateral compression response from drained axial compression tests. PhD Thesis. University o f Nevada. Reno.

52

2 Effect of soil gradation on liquefaction


Static and cyclic liquefaction o f silty sands

Jerry A. YamamuroClarkson University, Potsdam, NY., USA

Kelly M. CovertKlepper, Hahn and Hyatt, Syracuse, NY, USA

Poul V. LadeThe Johns Hopkins University, Baltimore, Md., USA

A B STR A C T; R esults o f an ex p erim en ta l p rog ram on silty sands are presented . D ra in ed and undra ined triaxial com pression tests, d ra in ed /u n d ra in ed instab ility tests under load contro l, and undra ined cyclic triaxial com pression tests w ere perfo rm ed . U nconven tional behav ior w as observed w ith varia tions in confin ing pressure. C om plete static liquefaction o ccu rred at low pressures, w hile increased stability w as observed at higher pressures. Increasing fines co n ten t increased the liquefaction potential. R esults are analyzed using steady state concepts indicating som e n o n-un ique aspects to the steady state line.

1 IN T R O D U C T IO N 2 E X PE R IM E N T A L M E T H O D S A N D SA N D

Silty sands are the m ost com m on type o f soil involved in both static and earth q u ak e -in d u ced liquefaction . This conclusion is based upon an ex tensive review of the literature (Y am am uro and L ad e 1998), w here docum ented h isto ric cases o f bo th static and earthquake liquefaction have b een exam ined . D espite this, m ost liquefaction research is p erfo rm ed on clean sands w ith the assum ption that the b eh av io r o f silty sands is sim ilar to that o f c lean sands. R ecent laboratory experim ental research (Lade and Y am am uro 1997, Y am am uro and L ade 1997b, Zlatovic and Ish ihara 1997, Y am am uro and Lade 1997b, 1998) indicates that sands deposited with significant silt con ten t are m uch m ore liquefiab le than clean sands. T hese new find ings, ind ica ting the im portance o f silt con ten t, have po ten tial im plications for liquefaction o f level g round , hydrau lic fills, and earth dam s, in w hich the silt co n ten t m ay be quite high. In addition , there m ay also be im plications based on this w ork w ith re sp ec t to in-situ testing m ethods used to estim ate liq u efac tio n potential. S tandard penetrom eter and cone penetrom eter liquefaction evaluation techn iques cu rren tly treat higher silt con ten t as a m itiga ting facto r in liquefaction potential (see e.g. Seed et al. 1985, R obertson and C am panella 1985).

Presented in this paper are experim en ta l results of drained and undrained triax ial com pression tests, instability tests under load con tro l, and undrained cyclic triaxial com pression tests. The observed behav io r is analyzed using steady state concepts.

D rained and undra ined tests w ere conducted on silty sands in triaxial com pression w ith initial confin ing pressu res up to 1,500 kP a w ith cy lindrica l specim ens 97 m m in d iam eter by 97 m m in height. E xperim ents w ere also conducted w ith in itial confin ing pressures at or above 2,000 kPa u tiliz ing a h igh pressure triaxial cell w ith cy lindrical specim ens 71 m m in d iam eter and 71 m m in height. L u brica ted end p latens were em ployed in all testing to avo id end friction and obtain un ifo rm strains. C orrections to axial stresses were m ade fo r p iston uplift, p iston friction and m em brane stiffness; the effects o f buoyancy o f the cap, soil, and piston w ere also included in the calculations.

The loose silty sand specim ens were produced b\ dry funnel deposition as described below , and correc tions to height and void ratio were m ade for se ttlem ent during saturation . T hese w ere based upon direct m easurem ent o f the axial and volum etric deform ations during sa tu ration . A xial deform ations w ere m easured as soon as the triaxial cell u as assem bled. V olum etric changes during saturation w ere detem iined by m easu ring the quantity of water draw n into the triaxial cell from a calib ra ted burette To determ ine the am ount o f volum e change that occurred during triaxial cell assem bly , the cell was assem bled and d isassem bled around a dry specim en, and the volum e m easured before and after each siaee.

The volum e during assem bly o f the triaxial cell w as determ ined to be insignificant.

Saturation was perfo rm ed by purging the specim en with carbon d ioxide before add ing de-aired water. A

55

GRAIN SIZE (mm)

Fig. 1 Grain size distributions for Nevada sand

minimum of 100 kPa back pressure was used to ensure complete saturation. A minimum B-value of0 .9 9 w a s obtained for all specimens. All test specimens were isotropically consolidated to their desired consolidation pressure before shearing. Shearing commenced as soon as possible to prevent creep from affecting the test results.

Nevada sand was used for all tests presented. The gradations of the base sands are shown in Fig. 1. The base sand designations indicate their gradation. For example, Nevada 50/200 denotes Nevada sand graded between the 50 and 200 sieve sizes. The base sands were combined with varying amounts of non-plastic Nevada fines (gradation shown on the insert in Fig. 1) depending on the test series. Nevada sand and Nevada fines both have a specific gravity of 2.68. The maximum and minimum void ratios for the various combinations of base sands and silt are presented by Lade and Yamamuro 1997. These values were used in the relative density computations. The methods employed to obtain these values are described in detail by Lade et al. (1998).All specimens used in the experimental program on Nevada sand were deposited by the dry funnel deposition method. This was performed by placing dry sand into a funnel with a small tube attached to the spout. The tube was placed at the bottom of the specimen split-mold. The tube was slowly raised from the bottom of the cylindrical mold, such that the silty sand was deposited without any drop height. This provided the loosest possible density. Denser specimens were achieved by gently tapping on the mold in a symmetrical pattern, as necessary. A complete discussion of the experimental methods and equipment is provided by Yamamuro and Lade (1997b).

The reasons for using dry deposition are:

1. Dry funnel deposition provides very low depositional energy into the specimen. This is

necessary to mimic alluvial deposits in creating a loose, compressible specimen.

2. Ongoing research at Clarkson University involving depositional methods such as slurry (Kuerbis et al.1988) or water pluviation (Ishihara 1993) result in minimum densities (e.g. relative densities between 70 and 90 percent) that appear to be unreasonably high for silty sands. This occurs especially in triaxial specimens that are formed under isotropic conditions. The specimen tends to collapse upon the application of an isotropic holding pressure. One-dimensional compression specimens appear to maintain minimum initial densities better (25 to 40 percent).

3. Water pluviation does not yield a homogeneous specimen with silty sands.

4. Higher B-values indicate better saturation for dry deposition specimens when using CO2 with back pressure than specimens prepared using wet methods.

3 EXPERIMENTAL RESULTS UNDER MONOTONIC LOADING

3.1 Undrained triaxial compression tests

Static liquefaction is referred to the condition described by

0 and C\ - C3 = 0 (3.1)

The physical response of the specimen to the occurrence of complete static liquefaction varied depending on gradation and density. Many times static liquefaction was observed with the entire specimen participating. Since all tests were conducted under deformation control, this type of behavior was typified by the specimen suddenly slumping vertically downward more than one centimeter. At other times, static liquefaction was accompanied by a less dramatic response. The specimen would not exhibit a sudden large deformation, but would continue to accept shearing at zero load and zero effective confining pressure. Specimens that responded in this manner were typically sheared out to very large strains with no apparent change in the stress conditions. Most likely a portion of the specimen had liquefied and accumulated the applied deformation in the liquefied portion. This, combined with the confinement provided by the latex rubber membrane surrounding the specimen, was apparently enough to prevent the specimen from slumping. Large wrinkles in the specimen membrane would form in all cases in which complete static liquefaction was achievéd.

56

p' = Effective Mean Normal Stress (kPa) P =1 ,0 0 0 2 ,0 0 0 3 ,0 0 0 4 ,0 0 0 5 ,0 0 0 6 ,0 0 0

Effective M ean Normal Stress (kPa)

Fig. 2 U n d ra in ed tests from 25 to 200 kPa

undrained triaxial com pression tests on N evada sand w ith 7 percen t fines con ten t at an initial re lative density o f 30 p ercen t w ere conducted at initial con fin ing pressures rang ing from 25 kPa to 6,000 kPa. The specim ens w ere sheared to large strains to obtain steady state conditions. S teady state is achieved w hen the pore p ressures becom e constan t under continued shearing at large axial strains. T he results of these undra ined tests are show n in Figs. 2(a) and 2(b) for initial con fin ing pressures from 25 to 200 kPa, and in Figs. 3(a) and 3(b) for in itial co n fin in g pressures from 500 to 6 ,000 kPa.

Figs. 2(a) and 3(a) show the undra ined effective

stress paths in p '-q d iag ram s. F igs. 2(b) and 3(b) show the stress d ifference vs. ax ia l strain relations. T he e ffec tive stress paths and stress-stra in curves ch aracte ris tica lly indicate: a) an in itial peak at low strains (1 to 2 pe rcen t); b) a low po in t in the stress d ifference at m odera te stra ins (4 to 8 percent), w hich has been called the quasi-steady state (A larcon-G uzm an et al. 1988, Ish ihara 1993); and c) an increase to a m ax im um stress d ifference obtained at large axial strains, w hich is referred to as steady state. The quasi-steady state (Q SS) is defined as the poin t w here con tractive behav ior changes to d ila tive behav ior, and this occurs at the point of phase transform ation and it co rresponds to the m inim um stress d ifference. S teady state occurs at large axial

Fig. 3 U ndrained tests from 500 to 6,0(X) kPa

strains w here the capacity o f the specim en to dilate is essen tia lly exhausted.

‘R ev erse ’ behav ior is observed for the tests perfo rm ed at low confin ing pressures, as show n in Figs. 2(a) and 2(b). T he undra ined test perform ed w ith an initial confin ing pressure o f 25 kPa com plete ly liquefied to zero effec tive stress. As the initial confin ing pressure is increased , the silty sand actually becom es m ore stable. T his is indicated by increasing values o f the m in im um stress d ifference ob tained at Q SS relative to the stress d ifference at the in itial peak. T his represents ‘rev erse ’ sand behavior, because sands norm ally exh ib it the opposite trend of increasing instability w ith increasing confin ing pressure. The reverse trend o f increasing stability con tinues w ith increasing confin ing pressure until the test conducted at an in itial con fin ing pressure of 4 ,000 kPa, as show n in F igs. 3(a) and 3(b). This test exh ib its nearly com plete stability , since there is a lm ost no drop in the stress d ifference after the initial peak.

S im ilar trends w ere repo rted by Y am am uro and Lade (1997b) for N evada sand w ith o ther percen tages o f tines. The test perform ed w ith an initial confin ing pressure o f 6 ,000 kPa show s a sligh tly larger decrease in stress d ifference be tw een the initial peak and the QSS point ind ica ting that it is less stable than the test conducted at 4 ,000 kPa. T hus, a change in the trend of increasing stability that w as consisten tly exhibited at low confin ing p ressu res also occurs at h igher confin ing pressures.

57

2CO

0) " E3 6

Axial Strain (%)Fig. 4 D ra in ed tests fro m 25 to 1,000 kP a

3.2 D ra ined triax ial com press ion tests

Seven d ra in ed triax ial co m p ress io n tests on N evada sand w ith 7 p e rcen t fines co n ten t w ere perform ed on specim ens w ith an initial re la tive density o f 30 percen t at con fin ing p ressu res rang ing from 25 kP a to 1,000 kPa. T he spec im ens w ere sheared to large strains to obtain steady sta te co nd itions in the sand. S teady state was ach ieved w hen the vo lum etric strains becam e constan t un d e r con tinued shearing at large axial strains. T he effec tive stress ra tio ( a , 703 ') vs. axial strain re la tions and the vo lum etric strain vs. axial strain re la tions are show n in F igs. 4(a) and 4(b), respectively. It is c lear that steady state conditions w ere only ach ieved at very large axial strains. The M ohr-C ou iom b secan t friction angles are show n in the insert in Fig. 4(a). T hey indicate an unusual behavior pattern . A norm al friction angle d istribution w ould have the h ighest value at the low est confin ing pressure, because d ila tancy is g reatest at low p ressures. H ow ever, for loose silty sands the friction angle is low at the low est initial con fin ing pressure (25 kPa). T h is is due to the very large contractive vo lum etric s tra in at th is confin ing pressure. T hus, it appears tha t the h igh com pressib ility slightly suppresses the d ra ined friction angle. N ote that the vo lum etric stra ins are a lm ost the sam e for confin ing p ressu res o f 25, 50 and 100 kPa. T h is m ay explain the o bserved tendency for increasing d ilatancy with

increasing confin ing pressu res observed in the co rrespond ing undra ined tests. T hese characteristics of unusual d ra ined b ehav io r o f silty sands are sim ilar to those described by Y am am uro and Lade (1997b) for N ev ad a sand w ith o th er percen tages o f fines and for O ttaw a sand.

4 E F F E C T O F N O N -P L A S T IC FIN ES C O N TE N T O N ST A T IC L IQ U E F A C T IO N B E H A V IO R

Specim ens from three d ifferen t base sands were p repared w ith various am ounts a N evada silt at their loosest possib le densities. T hese specim ens were tested for the e ffec t o f the fines con ten t on the undra ined behav io r in triax ial com pression . The e ffec t o f fines on N evada 50 /200 sand is show n on Fig. 5a and 5b and the e ffec t on N evada 50/80 sand is show n on Fig. 6 a and 6 b. Figs. 5a and 6 a show the effec tive stress pa ths on the C am bridge p' - q diagram , w hile F igs. 5b and 6 b show the corresponding stress-stra in curves. T he relative densities after conso lida tion , vo id ratios after conso lida tion and fines con ten t are show n in the legends o f Figs. 5a and 6 a. T he N ev ad a 50 /200 sand is ob serv ed to undergo static liquefaction at all fines con ten ts. Fig. 6 a show s that as the fines con ten t increases, the effec tive stress paths are dep ressed w ith a low er m ax im um value o f stress d ifference. Fig. 6 b show s that increased fines content results in the sand liquefy ing at low er values o f axial strain . Thus, it is o b served that the po ten tial for static liquefaction increases as the fines con ten t increases, even though the re la tive and absolu te densities increase. T his o bservation is inconsisten t w ith norm al soil behav ior, w hich suggests that the soil should exh ib it m ore d ila tan t b ehav io r as density increases.

T he N evada 50 /80 sand w as chosen to ascertain the effec t o f a s ign ifican tly m ore un ifo rm gradation in the base sand, as co m pared w ith the N evada 50/200 sand gradation . T he sand b etw een the Nos. 80 and 200 sieves w as rem oved from the N evada 50/200 gradation to create the m ore un ifo rm 50/80 gradation. The test w ith zero fines con ten t does not exhibit static liquefaction type o f behav io r as the N evada 50/200 sand d id w ith zero fines con ten t (Fig. 5). Therefore, it m ay be inferred that the sand betw een the Nos. 80 and 2 0 0 sieve sizes m ay have a sim ilar effect as the fines them selves. The role o f the finer fraction is apparently not ju s t lim ited to the m ateria l passing the No. 200 sieve size. As w ith the tests on N evada 50/200 sand, increasing the fines co n ten t in the N evada 50/80 sand results in increasing liquefaction potential and com plete static liquefaction . T h is occurs even though the rela tive and abso lu te densities increase. T his m ay im ply that the void ra tio and the relative density are not fully adequate m easures o f liquefaction potential for this type o f soil.

58

COCL

C 40 0 0

30Q0 20 0W 10

IICT ,

P =b 10 20 30 40 50 60

Effective Mean Normal Stress(kPa) p‘ = Effective Mean Normal Stress (kPa)

Fig. 5 Effect of fines content on Nevada 50/200 Fig. 6 Effect of fines content on Nevada 50/80

5 STATIC LIQUEFACTION ENVELOPE FOR NEVADA 50/200 SAND

The Nevada 50/200 sand was used in extensive testing to determine its behavior over the entire range of fines content, void ratios and confining pressures. Undrained tests were performed at specific fines contents at different relative densities to determine the void ratio at which static liquefaction would no longer occur. These undrained tests were performed with an initial confining pressure of 25 kPa, since liquefaction was found to be most prevalent at low pressures in either very loose clean sands or loose silty sands (Yamamuro and Lade 1997). The switch from complete liquefaction to stable behavior occurs over small changes in relative density. Similar results have been reported by Castro (1969). Results of tests with fines contents of 20, 50 and 100 percent and different values of relative density in addition to those presented here have been reported by Lade and Yamamuro 1997.

A large number of undrained tests have been conducted on Nevada 50/200 sand with widely varying densities, confining pressures, and fines contents. The static liquefaction envelope deduced from these tests is shown in Fig. 7 as an overlay on the maximum and minimum void ratio plot for Nevada 50/200 sand. Each test is represented by a point on Fig. 7 and located by the void ratio after consolidation and the fines content. A solid circle marks the point if

static liquefaction occurred and a solid diamond is used if either temporary liquefaction or stable behavior was exhibited. The division between these two conditions, i.e. the static liquefaction envelope is a uniquely defined line that runs through the diagram. This envelope indicates that the limiting void ratio for static liquefaction initially decreases with increasing fines content to a value of 30 to 40 percent fines. Normal soil behavior would suggest that increasing the soil density, and therefore decreasing the void ratio, should provide greater resistance to liquefaction. However, Fig. 7 shows that even though the density increases in the range up to 30-40 percent fines, the

Fig. 7 Static liquefaction envelope with respect to void ratio after consolidation

5 9

static liquefaction p o ten tia l in creases w ith increasing fines content. C learly the vo id ra tio does no t cap ture the varia tion in sta tic liq u efac tio n po ten tial for d ifferen t g radations as a ffec ted by the fines content.

The static liquefac tion en v elo p e re la ted to relative density is show n in F ig. 8 . A s can be observed , the m axim um relative density at w h ich static liquefaction can occu r increases rap id ly as the fines con ten t increases up to a m ax im u m value, and it rem ains constan t at high fines con ten t. S ince the relative density varies w idely w ith fines co n ten t a long the static liquefaction en v elo p e , it is a lso c lear that re lative density is no t a good in d ic a to r o f liquefaction potential in silty sands. At h igh fines con ten ts, the soil behavior is a lm ost to tally con tro lled by the behavior of the fines, because in this range, the coarser particles are com pletely separa ted by the fines.

6 B E H A V IO R IN D IF F E R E N T ST R E SS R E G IM ES

The gradation and initial density o f N evada sand was specifically se lec ted to p rov ide the w idest variation in undrained b eh av io r over the range o f confin ing pressures availab le for testing. Fig. 9 show s a log-log d iagram of tw o separa te stress d ifference ratios on the vertical axis vs. the in itial con fin ing pressure on the horizontal axis. T he purpose o f the tw o stress d ifference ratios is to illustra te and define the boundaries be tw een the observed types o f undrained behavior exh ib ited by loose silty sands. The q(qss)/q(peak) ra tio is the stress d ifference at the quasi-steady state cond ition (Q SS) d iv ided by the stress d ifference at the initial peak. T his ratiom easures the stab ility o f the soil in a particu lar test. A value o f zero ind ica tes com plete liquefaction [q(qss) = 0 ], and a value o f un ity indicates com pletely stable behav ior [q(qss) = q (peak)]. T h is ratio , show n in Fig. 9 , c learly ind ica tes tha t as the con fin ing pressure is

FINES CONTENT (%)Fig. 8 S ta tic liq u efac tio n e n v e lo p e w ith respect to

relative density .

Initial Confining Pressure (kPa)

Fig. 9 Silty sand b eh av io r in d ifferen t stress regim es (N evada 50 /200 w / 1% fines)

increased, the stab ility o f the soil increases, because the value indicates a con tinuously increasing trend. T he test perform ed at an initial confin ing pressure of 25 kPa possessed the least stability (com plete liquefaction w ith q (qss)/q (peak ) = 0 ), w hile the test conducted at 4 ,000 kP a ind ica tes the greatest stability [q(qss)/q(peak) = 0 .995]. N ote that the test conducted at 6 ,000 kPa ind ica tes a sligh t drop in the stress difference ratio from the test at 4 ,000 kPa.

The second line in F ig . 9 represen ts the q (peak)/q (ss) ratio. It is co m p rised o f the stressd ifference at the initial peak d iv id ed by the stressd ifference at the steady sta te cond ition . T h is ratiom easures the proxim ity o f the spec im en to com plete instability (e.g. w hen the u n d ra in ed post-peak residual strength is alw ays low er than the initial peak). Low values of this ratio occu r at low er pressures, and they indicate that the stress d iffe ren ce at the initial peak is m uch low er than at the steady state . A t high confin ing pressures a value o f unity w ou ld ind ica te that the initial peak is equal to the steady state. T his point w ould represen t the low er con fin ing pressureboundary o f instability . A t con fin ing pressures beyond this value, the ra tio q (peak )/q (ss) > 1, and com plete instability w ill o ccu r under undra ined conditions. A best fit s tra ig h t line on the log-log d iagram in Fig. 9 crosses q (p eak )/q (ss) = 1 at a confin ing pressure o f ap p ro x im ate ly 13,000 kPa. T herefore, this is the ap p ro x im ate low er con fin ing pressure boundary for co m p le te instability .

T hus, there are five d is tinc tly d ifferen t patterns o f behav ior identified for silty sands (N evada sand w ith 7 percen t fines at 30 p e rcen t re la tive density) associated w ith d ifferen t p re ssu re reg im es as show n at the top o f Fig. 9. S ta rting from the low est pressure region, they are:

1. Liquefaction Region - T h is reg ion occurs at low confin ing pressures w here the p ronounced

60

con tractiveness o f silty sands causes com plete liquefaction . O bserva tions o f sta tic and earthquake induced liquefaction even ts co n firm this aspect, in that rarely does liquefaction ex ten d to g rea t depths.

2. Temporary Liquefaction Region - T his region encom passes a very large c o n fin in g pressure range. The ch ie f characteris tic o f th is reg ion is that the stability o f the soil increases w ith increasing confin ing pressure. It is h y p o th es ized that the m echan ism o f con tractive vo lum etric b eh av io r in th is region is associated principally w ith partic le rearrangem ent occurring during conso lida tion .

3. Stable Region - T h is is a reg ion w here the undram ed stress path o f the soil does not exhibit a drop in the stress d ifferen ce (no quasi-steady state point). T he boundaries o f th is reg io n appear to be relatively narrow , som ew here b e tw een the 4 ,000 and6.000 kPa for this pa rticu la r sand and density .

4. Temporary Instability Region - T h is region is characterized by decreasing stab ility w ith increasing confin ing pressure. T hus, the sand returns to conventional soil behav ior. T he 6,000 kPa test appears to be in the low er end o f this region. This region occupies a large con fin ing pressure range.

5. Instability Region - T his region is characterized by effec tive stress pa ths w hose initial peak stress d ifference is the m ax im um ob ta ined in the test. The straight line fit in Fig. 9 indicates this region has an approxim ate low er con fin ing pressure boundary of13.000 kPa. T his is the stress region that is generally associated w ith liquefaction , but the stress m agnitudes are clearly too great to be com parab le to those present in the ground at real liquefaction sites. Therefore, liquefaction should be investiga ted at low pressures in loose silty sands. E xperim en ta l ev idence (Lade and Y am am uro 1996, L ade et al. 1996, Y am am uro and Lade 1997b) suggests that the m echanism of con tractive behav ior in the tem porary instability region and the in stab ility reg ion is associated with particle crushing occurring at h igher stresses. The characteristics and b oundaries o f the tem porary instability region and the instab ility region are also d iscussed by Y am am uro and Lade (1997a).

7 ST E A D Y ST A T E L IN E S

7.1 SS L ine from T ests P erfo rm ed from the Sam e Isotropic C om pression L ine

The steady state po in ts w ere ob tained from the drained and undrained tests on N ev ad a sand w ith 7 percent

fines and plo tted on the steady state d iagram show n in Fig. 10. The iso trop ic com press ion line is show n in this d iagram for reference . T hese specim ens w ere all c rea ted w ith the sam e in itial density , and the variations in void ratio are so lely due to the iso tropic com pression to d ifferen t conso lida tion pressures. Fig. 10 show s that the d ra in ed and undra ined SS lines appear to coincide b e tw een the p ressures o f 2 0 0 and1,000 kPa. H ow ever, at low er p ressures the tw o lines diverge. This is due to the fact that the drained tests are sheared to large stra ins w here the soil d ilates significantly to ach ieve steady state, as show n in Fig. 4(b). The drained SS line consequently m oves upw ard from the isotropic co m p ress io n line at low confin ing pressures. H ow ever, du rin g the in itial portions o f the drained tests in Fig. 4 (b), the sand exhibits very con tractive characteris tics . T he resu lting high com pressib ility at low axial strains produces liquefaction w hen the sand is sheared under undrained conditions at low co n fin in g pressures. The undrained SS line therefore m oves far to the left for these in itially low confin ing pressures. The test perform ed at an in itial confin ing p ressu re o f 25 kP a m oves from the

isotropic com pression line to a zero value o f effec tive confin ing pressure, but for c larity it is show n at the left vertical axis at a non-zero value on the ho rizon tal log scale. Z ero e ffec tive co n fin in g p ressu re and consequent liquefaction resu lted befo re the tendency for d ila tion occurring at large stra in s co u ld reverse the trend and produce g reater e ffec tiv e confin ing pressures (negative pore pressures). It w as show n that increasing the confin ing p ressu re p roduces a m ore stable specim en , and thus, liquefac tion does not occur at h igher confin ing p ressures as defined by Eq. 3.1.

The quasi-steady state line (Q S S) is a lso p lo tted in Fig. 10. The QSS line is loca ted to the left o f the SS line, and it indicates the sam e trends as the SS line. D epending on the density , in itial co n fin in g pressure, and silt con ten t it has been show n that co m p le te static

0 .8 2 N eva d a 5 0 /2 0 0 w / 7 % Finese = 0 .7 7 9 ± 0 .0 0 2 D r = 3 0 %

0 .8

/Static liquefaction d D ra ined line

0 .7 8 ^ U ndrainedS teady-sta t >

0 .7 6Q uasi-S teady

^ line

state line \0 .7 4 SS

L e a k / qss -quasi-steady-sta te0 .7 2 ■q Z ' ^ X g s s y / peak - in itia l peak

SS - steady-state

n 71 strain ^

. ii im l___1 1 j-a.q.i.mil___0.01 0.1 1 10 100 1,000

Effective Confining Pressure (kPa)

Fig. 10 SSL from a single iso trop ic com press ion line

61

liquefaction can occu r at initial re la tive densities up to 60 percen t and at re la tive ly high pressures.

7 .2 N on-un ique SS lines from tests p e rfo rm e d from d ifferen t iso trop ic com press ion lines

Fig. 10 show ed that the steady state lines ob tained from d ra ined and undra ined tests on silty sands co incide at h igher pressures, bu t they do no t co incide at low pressures w hen the tests are p e rfo rm ed on specim ens w ith the sam e initial density and sheared from a sing le iso trop ic co m p ress io n line. Fig. 11 show s the steady state and q u asi-s tead y state conditions from u n dra ined tests on N ev ad a sand with 6 percen t fines con ten t at initial re la tive densities o f 12, 22 and 31 p ercen t (Y am am uro and L ade 1997b). Thus, shearing w as in itia ted from d iffe ren t iso tropic com pression lines in these tests.

It is firs t ob serv ed from Fig . 11 th a t the SS lines ob tained from the th ree d ifferen t densities are not unique. The quasi-steady state lines also do not co incide. H ow ever, both sets o f lines are approx im ate ly parallel to each other. The trends observed in Fig. 10 are also indicated in Fig. 11. At low confin ing pressures silty sands exh ib it com plete static liquefaction , w hile increasing the confin ing pressure stab ilizes the sand.

H ow ever, the m ost su rp rising observation from Fig. 11 is that static liquefaction occurred in a specim en w ith an initial re lative density o f 22 percent, w hile it d id not occur in three specim ens w ith initial re lative density o f only 12 percent. The void ratio after conso lida tion in these three specim ens w ere also h igher than in the specim en that liquefied. In o ther w ords, a specim en w ith g reater density w as observed to liquefy at low er p ressures than looser specim ens at

0 "cO01

0.1 10 1,000 100,001Effective Confining Pressure (kPa)

Fig. 11 N on-un ique SSL 's from d ifferen t iso tropic com pression lines

h igher pressures. This is because silty sands exhibit g rea ter com pressib ility at low confin ing pressures, and th is resu lts in ‘rev erse ’ stress-stra in behavior. This perm its liquefaction to o ccu r at low p ressures, w hile increasing stability is ach ieved w ith increasing confin ing pressure.

In com parison, the analysis associated w ith the steady state diagram and SS line inherently assum es that instability and subsequen t liquefaction is p roduced at h igher con fin ing pressures. T herefore, a norm ally behaving sand w ould require a h igher confin ing pressure to liquefy , and thus, the SS line m oves to the right w ith increasing density . In silty sands, w hich exh ib it ‘re v e rse ’ behavior, liquefaction can occur at h igher densities with d ifferent com binations o f low er con fin ing pressures. T hese observations lead to the conclusion that the void ratio and the steady state d iagram do not uniquely describe the liquefaction behav ior o f loose silty sands.

8 H Y P O T H E S IZ E D M E C H A N IS M C A U S IN G ’R E V E R S E ’ B E H A V IO R

One of the s ign ifican t ch aracte ris tics o f the observed ‘rev erse ’ behav io r o f silty sands is that liquefaction is m ost p revalen t at low pressures. Increased confin ing pressures enhance stability . T h is has not alw ays been observed in experim en ts on silty sands (K uerbis, et al. 1988, P itm an et al. 1994). H ow ever, c lean sands alm ost a lw ays exh ib it ‘n o rm a l’ soil behav ior. W hy do silty sands deposited w ith low input energy behave in this m anner? It has been show n (L ade et al. 1998) that w hen c lean sand is m ixed w ith increasing am ounts o f non-plastic fines, the m in im u m and m axim um void ratios as w ell as the range o f void ratios change, and highly unstab le and co m p ress ib le partic le structures are fo rm ed w hen gently d eposited into loose configura tions (Y am am uro and L ade 1997b, L ade and Y am am uro 1997). T h is partic le struc tu re is show n in the schem atic d raw ings in F ig . 12. Fig. 12(a) show s a silty sand deposited w ith very low input energy into a loose state. The void spaces betw een the larger grains are relatively unoccupied , and the larger grains, w hich will m ake up the load bearing skeleton , are held slightly apart by sm aller silt partic les near the contact points. F ig . 12(b) show s how the app lied shear and norm al stresses affect this unstab le partic le structure. The silt pa rtic les that w ere separa ting the larger grains are fo rced into the void spaces. In itia lly , this collapse creates large con tractive vo lum etric strain .

These attribu tes m atch the observed behav ior as indicated by the vo lum etric stra ins in Fig. 4(b). A large am oun t o f con trac tive vo lum etric strain occurs at low p ressu res, and it is also ob se rv ed that the vo lum etric stra ins assoc ia ted w ith the co llapse is

62

nearly identical be tw een 25 and 100 kPa, indicating that the co llapse is easily triggered . T erzaghi (1956) hypo thesized a 'm eta -stab le ' soil structure to explain static liquefaction in subm arine slopes com posed of silty sands.

T he partic le struc tu re show n in Fig. 12 also exp la ins w hy silty sands exh ib it increasing dilatancy w ith increasing co nfin ing pressure under undrained conditions. O nce the initial co llapse has occurred and the silt particles have been pushed into the void spaces, the larger load bearing grains m ove into better con tact resu lting in increased d ila tan t tendencies (or increasing stab ility ) as the confin ing pressure is increased . T h is e ffec t counterbalances the norm ally observed tendency fo r increased am ounts of con traction w ith increasing confin ing pressures.

O ngoing research into the behav ior o f silty sands ind icates that the m ost liquefiab le base sands are unifo rm ly graded , because these allow adequate void space to accep t silt partic les during collapse. At lower silt con ten ts, the vo id space betw een load bearing gra ins w ill not be en tirely filled w ith silt particles. S ince the silt pa rtic les in the void spaces are not part of the load bearing skeleton , they have very little in fluence on the m echan ical behav ior o f the silty sand excep t to increase the bulk density o f the sand. D uring shearing , the silt particles ju s t roll freely a round in the void spaces. Thus, large changes in density can occu r w ithou t sign ifican t effects on the liquefaction b eh av io r o f the soil. L ade and Y am am uro (1997) o bserved that silty sands liquefied statically at m uch h igher re la tive densities (up to 60 percent) and abso lu te densities than have been reported for clean sands. T herefo re, re la tive and absolu te densities do not prov ide adequa te ind ications o f liquefaction resistance for silty sands.

C lean sands do not develop the particle structure d iscussed above. W hen c lean sands are deposited, even in a loose state, there are enough solid contacts

betw een grains tha t the sand w ill exhibit dilatant characteris tics at low pressures. Thus, clean sands are characte rized by ‘n o rm a l’ soil behavior.

9 B E H A V IO R U N D E R C Y C L IC LO A D IN G

U nder m ono ton ic load ing loose silty sands appear to be h igh ly liquefiab le . E arthquakes induce cyclic load ing into the soil deposits. T herefore, testing under cyclic load ing w as p erfo rm ed to evaluate its behavior w ith respec t to the o b served m onoton ic behavior.

T w o cyclic triax ial com press ion tests are presented that characte rizes the cyclic behav io r o f very loose silty sands. A fte r iso trop ica lly conso lidating the specim ens to 125 and 325 kPa, respectively , a deviator stress w as app lied un d e r d ra ined conditions to give the specim ens a stress ratio (a"^ /a \ ) o f 1.4. At that point the spec im ens w ere tu rned into an undra ined condition and cyclic load ing w as app lied at a cyclic stress ratio o f app rox im ate ly 0.05 at a frequency o f 0.1 Hz.

The e ffec tive stress pa ths and the stress strain curves are show n in F igs. 13 and 14, respective ly , for the test w ith an initial c o n fin in g p ressu re o f 125 kPa and they are show n in Figs. 15 and 16 fo r the test w ith 325 kPa initial con fin ing p ressu re . M ono ton ic tests are also show n in the figu res fo r com parison . The specim ens exh ib it h igh ly liquefiab le characteris tics , since they b ecom e u n stab le a fte r only tw o and three cycles o f loading, respective ly .

The conso lida tion stress ra tio w as chosen such that the am plitude o f the cyclic d ev ia to r stress w ould push the effec tive stress path up to app rox im ate ly the sam e stress state as that o f the m ono to n ic test. W hen the tw o d ifferen t stress pa ths jo in , they possess a com m on yield surface. A s can be observed , the tw o d ifferen t undrained effec tive stress paths fo llow each o ther very

(a) SILTY-SAND AS

DEPO SITED

L A R G E V O L U M E R E D U C T IO N

- L A R G E G R A IN S M O V E IN T O C O N T A C T

IN C R E A S IN G D ILA TA N C Y

( b ) S ILTY-SAND CO M PR ESSED A ND SHEA RED

Fig. 12 H y p o th esized p artic le s truc tu re explain ing observed b ehav io r

Fig.

p' = Effective Mean Normal Stress (kPa)

13 E ffec tive stress pa th fo r cyclic triax ial test at 125 kP a in itia l c o n fin in g p ressu re

63

Fig. 14 S tress s tra in cu rve fo r cyclic triax ial test at 125 kP a in itia l co n fin in g p ressu re

p' = Effective M ean Norm al Stress (kPa)

Fig. 15 E ffec tive stress path for cyclic triaxial test at 325 kPa initial con fin ing pressure

p‘ = Effective M ean Norm al Stress (kPa)

Fig. 17 E ffective stress pa th fo r cyclic triax ial test at 225 kPa initial co n fin in g pressure , but w ith low er co n so lid a tio n stress ratio.

used to define stable and unstab le stress states. T hese stress states can be u sed to p red ic t the undrained behav ior o f silty sands specim ens undergo ing cyclic loading. This is d em o n stra ted by a th ird cyclic triaxial test conso lida ted to a stress ratio o f 1.3 and with a cyclic stress ratio o f 0.05 as show n in Fig. 17. The stress state at the p o in t w hen the specim en is turned undra ined is at a low er re la tive location with the instability line than the o ther tw o tests show n in Figs. 13 and 15. T h is requ ires m ore load ing cycles (5) to initiate unstable behav io r. H ow ever, it can be seen that the instability line ob tained from the m onotonic

test accurately cap tu res the p o in t at w hich the cyclic test becom es unstable .

Fig. 16 S tress strain curve for cyclic triaxial test at 325 kP a in itia l confin ing pressure

closely in both tests. In fact, the instability line defined by the m ono ton ie tests is equally applicable to the cyclic tests in these tests. T herefore, in loose silty sands instab ility concep ts , based upon m onotonie undra ined tests, (Y am am uro and Lade 1997a) can be

10 C O N C L U SIO N S

E xperim ental resu lts from u n d ra in ed and dra ined m onotonic and cyclic triax ia l com press ion tests on specim ens co m p o sed o f loose N ev ad a 50 /200 sand w ith various am ounts o f silt have been presented . Som e conclusions th a t can be m ade are:

1. C om plete static liq u e fac tio n occu rs at low pressures in m onotonic undra ined tests. Increasing stability is observed as con fin ing p ressu res are increased up to high confin ing pressures. T h is is 'reverse ' from norm al soil behavior.

2. M onoton ie d ra ined tests show h igh ly con tractive volum e change ch aracte ris tics at low pressures. The M ohr-C ou lom b fric tion ang le is sup p ressed at low pressure, because o f the high level o f con tractiveness.

3. Increasing fines c o n ten t increases the static liquefaction potential.

64

4. A large n u m b er o f tests on N ev ad a 50 /200 sand indicate that sta tic liq u e fac tio n can occu r up to 60 percent relative density .

5. U ndra ined tests p e rfo rm ed at a w ide range of confin ing pressures on silty sands appear to indicate that there are 5 d iffe ren t p a tte rn s o f behav ior: static liquefaction , tem porary liq u efac tio n , stable , tem porary instability , and instability .

6 . U ndrained and d ra in ed tests on silty sands indicate that the steady state Hne is unique w hen sheared from a single iso tropic conso lida tion line. H ow ever, the steady state line m ay be non-un ique if sheared from separate isotropic conso lida tion lines.

7. A hypothesized partic le structure m ay be causing the 'reverse' soil b ehav io r that is characterized by volum etric con trac tion at low pressures and increasing d ilatancy w ith increasing confin ing pressure.

8 . U ndrained cyclic triax ial tests indicate that the instability line, w hich separates unstable and stable stress regim es, is va lid fo r cyclic loading conditions. The instability line is derived from m onotonie undrained tests.

11 A C K N O W L E D G M E N T S

T he studies p resen ted here w ere supported by the N ational S cience Foundation under grant No. C M S-9701467 and the A ir Force O ffice o f Scientific R esearch under g ran t N o. F49620-94-0032 . G rateful appreciation is ex p ressed for this support.

12 R E FE R E N C E S

C astro, G. 1969. L iquefac tion o f sands. Ph.D . Thesis, H arvard U niversity , C am bridge , M assachusetts.

Ishihara, K. 1993. L iquefaction and flow failure during earthquakes. Geotechnique, London, England, 43(3), 351-415.

K uerbis, R., N egussey , D., and V aid, Y.P. 1988. E ffect o f g radation and fines con ten t on the undrained response o f sand. In H ydraulic Fill Structures. G eo tech n ica l Special Publication No. 21, A m erican Society o f C ivil Engineers. Edited by D.J.A . Van Z yl and S.G . V ick, 330-345.

Lade, P.V ., and Y am am uro , J.A . 1996. U ndrained sand behav io r in ax isym m etric tests at high pressures. Journal of Geotechnical Engineering, A SC E, 122(2), 120-129.

Lade, P.V., and Y am am uro , J.A ., and B opp, P.A. 1996. S ign ificance o f partic le crushing in granular m aterials. Journal of Geotechnical Engineering, A SC E, 122(4), 309-316 .

Lade, P.V ., L iggio , C .D ., and Y am am uro, J.A. 1998. E ffects of n o n-p las tic fines on m in im um and m axim um void ra tios o f sand, accepted for publish ing by Geotechnical Testing Journal, A STM .

Lade, P.V. and Y am am uro , J.A . 1997. E ffects of non-plastic fines on static liquefaction o f sands. Canadian Geotechnical Journal, 34, 905-917.

Pitm an, T .D ., R obertson, P.K . and Sego, D .C . 1994. Influence o f fines on the co llapse o f loose sands. C anadian G eotechnica l Jou rnal. 31, 728-739.

R obertson, P.K. and C am p an ella , R .G . 1985. L iquefaction potential o f sands using the CPT. Journal of Geotechnical Engineering, A SC E, 111(3), 384-403.

Seed, H .B ., T okim atsu , K., H arder, L .F ., and C hung, R .M . 1985. Influence o f SP T P rocedures in Soil L iquefaction R esistance E valuations. Journal of Geotechnical Engineering, A SC E, 111(2), 1425-1445.

T erzhag i, K. 1956. V arieties o f subm arine slope failures. In Proceed ings o f the E igh th T exas C onference on Soil M ech an ics and Foundation E ngineering . U niversity o f T exas, A ustin , 41 pp.

Y am am uro, J.A . and Lade, P.V . 1997a. Instability of g ranu lar m aterials at high p ressu res. Soils and Foundations, JG S, 37(1), 41-52 .

Y am am uro, J.A . and L ade, P .V . 1997b. Static liquefaction o f very loose sands. Canadian Geotechnical Journal, 34, 918-928 .

Y am am uro, J.A . and L ade, P .V . 1998. E xperim ents and m odeling o f silty sands suscep tib le to static liquefaction , accepted by fo r pub lish ing by Mechanics of Cohesive-Frictional Materials.

Z latovic , S. and Ish ihara, K. 1997. N orm alized behav ior o f very loose non-p las tic soils: effects o f fabric. Soils and Foundations, JG S , 37(4), 47-56.

65


Role o f intergrain contacts, friction, and interactions on undrained response of granular mixes

S.ThevanayagamDepartment of Civil, Structural and Environmental Engineering, State University of New York, Buffalo, NY., USA

A B S T R A C T : A sim p le an aly sis o f a tw o -s ized partic le sys tem w ith large size d isp a rity (e.g . san d an d silt) is p re sen te d to h ig h lig h t the re la tiv e ro les o f in te rg ra in co n tac ts and in te rac tio n s b e tw ee n the fin e r and co a rse r g ra in s on the u n d ra in e d b e h av io r , s tren g th , and frag ility o f g ra n u la r m ix es. In te rg ra n u la r (Cs) and in te rfin e (Cf) v o id ra tio s are in d ices to q u a lita tiv e ly desc rib e the beh av io r. T h e a n tic ip a ted b e h a v io r is c a teg o riz ed in to five su b g ro u p s . T h e a n tic ip a te d s tre ss-s tra in b eh av io r, co llap se p o ten tia l, and steady sta te s tren g th b e h a v io r fo r each g ro u p is fu rth e r c h a ra c te riz ed in term s o f the b e h av io r o f e ith e r the host c o a rse r g ra in o r the f in e r g ra in m ed iu m . E x ce p tio n s are a lso id en tified . T he th resh o ld fin er g ra in c o n ten ts and th re sh o ld in te rg ran u la r v o id ra tio s d e lin e a tin g the tran s itio n b o u n d arie s b e tw een these su b g ro u p s are p re sen ted . T h is is e x p e rim e n ta lly ev a lu a ted . T h e re su lts p ro v id e a m ech an is tic u n d e rstan d in g o f p o ss ib le m ic ro sc o p ic m ec h an ism s th a t a ffec t the liq u e fac tio n an d p o s t- liq u e fa c tio n resp o n se o f m an m ade and n a tu ra l d e p o sits o f s ilty san d s, san d y silts and g rav e ly so ils. It can a lso be u sed to d ev elo p g u idelines fo r in te rp re ta tio n o f in s itu and lab o ra to ry b e h av io r o f su ch so ils and liq u e fac tio n m itig a tio n design . Ju d ic io u s cau tio n is c a lled fo r w h en th is is e x tra p o la ted to w ell g ra d ed o r lay e red soils.

1 IN T R O D U C T IO N

O b serv a tio n s fro m re ce n t e a rth q u ak e case h isto ries (S eed & H a rd e r 1990, JG S 1996) ind ica te that n a tu ra l so ils and m an m ad e fills th a t co n ta in a m ix o f san d s and fin e r-g ra in s (in so m e cases g ravel) are o ften frag ile ev en w h en m ed iu m den se to dense. T h ey do liq u e fy and cau se late ra l spreads. K n o w le d g e g a in e d fro m p ast th ree d ecades o f re sea rch on c le an san d s d o es n o t d irec tly transla te to such so ils. M an y co rre c tiv e p ro c ed u re s have been p ro p o se d to ch a ra c te riz e the ex p ec te d b eh av io r o f silty so ils b a se d on g lo b al o b se rv a tio n s o f fie ld case h is to rie s (S eed et al. 1983, S eed 1987, Seed & H a rd e r 1990, R o b e rtso n & W rid e 1997, S tark & M esri 1992). T h e re is c o n ce rn w h e th e r and how fin er g ra in s a ffec t the u n d ra in e d b e h av io r o f such (silty ) so ils (K u erb is e t al. 1988, C h an g 1990, C h a m e au & S u tte re r 1994, P itm a n et al. 1994, V aid 1994, K o este r 1994, T h ev a n ay a g a m et al. 1996a, Z la to v ic & Ish ih a ra 1997). T he m ech an ism s c o n tr ib u tin g to liq u e fac tio n an d large de fo rm a tio n in su ch so ils are c o m p le x . It d e se rv e s a g rea ter d e ta iled s tudy and u n d e rs tan d in g o f the so il m icro stru ctu re

and the c o n trib u tio n s o f so il p a rtic le s o f d iffe ren t sizes to its m ech an ica l resp o n se .

A ctiv e p a rtic ip a tio n o r lac k th e re o f by d iffe re n t types and sizes o f p a rtic le s w ith in th e so il m atrix in the tran sfe r o f in te r-p artic le fo rces fro m o n e an o th e r d ic ta te s the s tre ss-s tra in b e h av io r an d the re s is tan ce it can o ffe r u n d e r d iffe ren t lo ad in g c o n d itio n s . T he s tre ss-s tra in b eh av io r is a ffec ted by a c ritica l c o m b in a tio n o f intergranular and interfine contacts and in te rac tio n s thereo f. S u ch e ffec ts m u st be d e lin ea ted in d ealin g w ith silty san d s an d sandy silts in u n d e rs tan d in g the m ec h an ism s c o n tr ib u tin g to liq u e fac tio n and p o s t- liq u e fac tio n frag ility .

T h e p resen t p ap er fo cu ses on a simple tw o -s iz ed p a rtic le m ix (F ig .l) and in fe rs p o ss ib le ro les o f in te rg ran u la r and in te rf in e c o n ta c ts on its m ech an ica l response . F o r s im p lic ity , in te rg ran u la r (es) (K enny 1977, M itch e ll 1993) an d in te rfin e (ef) vo id ra tio s (F ig .2 , T h ev a n ay a g a m 1998) are u sed as ind ices to rep resen t th e re la tiv e fric tio n a l co n trib u tio n s at the in te rg ran u la r and in te rfin e g ra in co n tac t levels.

67

(a) Fully confined fines

(confined fines)fc

I Il i 1 - fc >

(c le a n c o a rs e r g ra in s )

ci

fc<FC,h/100 fc<FC,h/100 fc<FC,h/U>0

(Case-i)

(b) Fully dispersed coarser grains

(d) Fully layered

(Case-ii)

(f) Partial separation

(Case-iv)

(Case-iii)

N otes: e= G lo b a l V o id R atio ; F C th= threshold fines co n ten t (% )

Fig. 1 Intergranular and Interfine Matrix Phase Diagram

Si l ty S a n d P h a s e D i a g r a m

F i n e r - g r a i n - s k e l e t o n C o a r s e r - g r a i n - s k e le ton P h a s e D i a g r a m

T o t a l V 0 i d s A p p a r e n t V o i d s 1e e

F in e r -g ra m S o lid sfc !

fc i l i l i i s

f c = F C / 1 0 0

A p p a r e n t V o i d s

e + fc

1- f cF C = F i n e s c o n t e n t ( % )

e = g l o b a l v o i d r a t i o e , = i n t e r f i n e v o i d r a t i o e^= i n t e r g r a n u l a r v o i d ra t i o

e , =fc 1 -fc

Fig. 2 Intergranular Phase Diagram and Apparent Void Ratios

6 8

2 CONCEPTUAL FRAMEWORK

2.1 Soil Microstructure

The different ways by which microstructure in a granular mix can be constituted dictate its stress- strain response. Among infinite variations, four extreme limiting categories of microstructure are as follows. (1) Fig.la: the fines are fully contained within the intergranular (coarser grain) void spaces with no contribution whatsoever in supporting the coarser grain skeleton. (2) Fig. lb: the coarser grains are dispersed in the finer grain matrix. (3) Figs.lc-d: the coarser and finer grains constitute a fully layered system where the coarser grain layers have no fines contained in them and vice versa, and (4) Figs.le-f: a part and partial layering (partial separation of coarser grains by the finer grains) and confinement are prevalent. The figures la, c, e and f are more relevant at low finer grains content (FC). Figs, lb and d are relevant at high FC. The case of fully layered soils (Figs.lc-d) is not discussed further.

2.2 Threshold & Limiting Fines Content FCjh & FCi

Transition from Fig.la to Fig.lb occurs naturally with an increase in FC beyond a threshold value (FCth). The category shown in Fig.la is possible only if: (1) the size of the finer grains is much smaller than the possible minimum pore opening size in the coarser grain skeleton. For spherical particles this implies that D/d>6.5 (Fig.3) where d and D^sizes of finer and coarser grains, respectively, and (2) the intergranular voids are not completely filled with the fines (FC<FCth). From a conceptual standpoint FCth is expected to occur when ef decreases below enm.HP (Thevanayagam 1998b):

lOOe, \00e\ + e ,+

-% ( 1 )max. HF

where emax.uF = the maximum void ratio of the pure silt beyond which it has no appreciable strength. The rationale is that, as ef reaches below emax.uF, the finer grains are packed close enough so that direct finer- grain-to-finer-grain friction becomes active.

Up to FC=FCth the finer grains can, but not necessarily, remain within the intergranular voids. When the coarser granular skeleton is dense whether or not some of the fines fall between the coarser grain contacts or remain fully confined within the intergranular voids does not significantly affect the stress-strain response. When the coarser-granular skeleton is loose the presence of fines between the coarser-grain contacts may make a signifieant difference facilitating a general tendency for instability upon shearing.

For this reason, at FC<FCth, the granular mix is sub grouped into three categories: (i) case-i (Fig.la), (ii) case-ii (Fig.le), and (iii) case-iii (Fig.If). The logical point of departure for case-iii would be when the coarser grain skeleton becomes unstable due to dislocation of only a few finer grains located between the coarser grain contacts. For spherical particles this occurs when the average eoarser grains center-to-center spacing just exceeds D (s=l). The corresponding threshold

(e,)r/,=— 1=0.91 (2)

For other particle shapes this may be conveniently set at es = emax.ns [the max. void ratio of purely coarser grain soil].

When FC>FCth the finer grains begin to play a rather important role. The coarser grains begin to disperse (Fig. lb) and provide a sort of reinforcement effect until they are separated sufficiently apart when FC exceeds a limiting fines content FCi. The FCi is approximately given by (Thevanayagam 1998b):

FQ>100 1-n{\+e)

6 s'%=\00

—1(3)

where s=l-Fa/Rd, Rd=D/d=size disparity ratio, and a=10. The magnitude of a may be partly attributed to the observations of Roscoe (1970) that the zone of influence of shear is about ten times the particle diameter.

Beyond FCi the behavior is entirely governed by the finer grains. The soils in the transition zone (FCth<FC<FCi) and at FC>FCi are conveniently sub grouped into case-iv-2 and iv-1, respectively.

The Eqs.1-3 offer a simple means to infer important characteristics of poorly graded silty soils. The transition and limiting fines contents are dependent on Rd, global void ratio, other grain characteristics, and plasticity of fines. For example, for Rd=34 (soil used in this study), FCth and FCj corresponding to e=0.67 are less than about 37% and greater than about 60%, respectively.

The anticipated roles of coarser and finer grains are summarized in Table 1. Fig.4 depicts the locations on the various cases in e versus FC plot and the associated limiting minimum and maximum global void ratios. Clean sand may not be stable at or near es=emax,Hs and they belong to case-i. Silty soils can be constituted over the entire spectrum of cases i to iv. The stress-strain behavior and fragility of such mixes are expected to be different in each case.

69

d « D/6.5

Fig. 3 Fully Confined Fines

20 40 60Fines Content {%)

80 100

F ig. 4 Intergranular - S o il C lassifica tion D iagram

Fig. 5 Intergranular Matrix - Experimental Program - Specimen Locations

70

Table 1: Granular M ix ClassificationCase FC Roles o f coarser-grains and fìner-grains

FC<FC,h s* nui.x.HS ej>e,ncLX.HF Finer grains are inactive (or secondary) in the transfer of inter particle forces. They may largely play the role of "filler" of intergranular voids. The mechanical behavior is affected primarily by the coarser grain contacts.

la

e, near

enuLxMSFiner grains may be supporting the coarser-grain skeleton that is otherwise unstable. They act as a load transter vehicle between "some" of the coarse-grain particles in the soil-matrix while the remainder of the fines play the role of "filler" of voids. _________________ _

le

e.s>e,nax.HS Finer grains may play an active role of "separator" between a significant number of coarse-grain contacts and therefore begin to affect the strength characteristics.______

iv-2 FCth<FC< FC, ef<e,„a,.HF The fines may carry the contact and shear forces while the coarser grains may act as reinforcing elements embedded within the finer grain matrix.

lb

iv-1 FC>FC, Ss» ma.xm et<e,na.x.HF The fines may carry the contact and shear lorces while the coarser grains are fully dispersed.

lb

Notes; e,j_____________ ___________ ___________ ---------------------- --——j— —lax.Hs, Cmax.HF = maximuiTi void ratio of the coarser grains and finer grain media, respectively. (Thevanayagam 1998a)

3 UNDRAINED BEHAVIOR

The expected behavior of silty and/or gravely soils remains contentious in the literature. A few inferences may be made referring to the differences in the internal makeup in each case( Fig.l and 4).

Dilation is a consequence of the basic law of physics that two objects cannot occupy the same space at the same time. Collapse is the consequence of loss of proper contacts and ensuing instability (even momentarily as time marches forward). Dilation following initial collapse is due to initiation of participation of particles that were not very active in the force chain (or reactivation of the same particles due to different geometrical arrangement that facilitates the development of a more stable force chain). Dilation and collapse are two sides of the same coin. This leads to the phase transition phenomenon.

3.1 Role of coarser and finer grains

Do the fines enhance or reduce collapse potential? The answer is both. Fines can be beneficial and/or adverse. It depends on the intergranular matrix of the mix.

The adverse effect stems from the fines that separate some of the coarser grain contacts. They contribute creation of larger intergranular voids. This condition invariably occurs when the mix is loose (typically es>(es)th) in terms of eg. During ensuing shear, these finer grains can fall into the large pore openings and contribute to (or facilitate) the collapse of the coarser grain skeleton.

The beneficial effect comes from the fines that are already within the intergranular pore space. At the same es, an increase in FC is somewhat similar

to filling more of the physical space in the intergranular voids. The space available for a coarser grain particle to fall into, in the event the conditions for instability develop, is reduced. The degree of collapse is reduced. Furthermore, once the coarser grains fail into this space the fines that are already present in the intergranular voids may begin to actively participate in the force chain and could initiate a subsequent dilation process, even if the soil may be initially fragile. Therefore the finer grains can reduce the collapse potential and offer some resistance to further flow deformation following the initial collapse. At the same es a soil mix with the larger fines content would be less collapsible.

Therefore, ai the same confining stress, one may expect, comparatively, a very loose clean sand to be collapsible whereas a silty sand at the same es to be less collapsible or even dilative. This is most likely to be observed in case-ii. In case-i, the presence of fines may only have a secondary effect. If Cs is large (case-iii; sufficient number of intergranular contacts separated by the fines), the effect of fines can become fully adverse. The soil tends to be more fragile. However, even in case-iii, at the same es, an increase in FC is expected to reduce the degree of fragility.

For Case-iv, the soil behavior may be governed by either the finer grains (case-iv-1) or by the finer grains and the reinforcement effect from the coarser grain inclusions (case-iv-2). If a comparison is made at the same ef, sandy silt with higher sands content is expected to show higher strength and lower collapse potential than sandy silt at low sands content.

Based on the above framework, the anticipated trend in undrained behavior can be comparatively forecast for granular mixes prepared by the same

71

1.2

1.0

0.8

^ 0 .6o5

0.4

0.2

(a) • i Initial Conf. stress= lOOkPa |

* • • •i OSO ■1 A

■

OS 15 Vi ▼ AOS25 1

! OS40▼

>k ^ Sb1 ■‘ aw x >

X ;OS60

: *OS 100

1.0

0.9

•2 0.8aQC

'o>13 0.6 o

O 0.5

0.4

0.3

(a)

OSO-100

OSO-400

OS15-100

OS15-400T

OS25-100

OS25-400

Initial Conf. stress= 100 & 400 kPa

1 10 100 1000 Steady State Strength (kPa)

T V

▼ ^V

1 10 100Steady State Strength (kPa)

1000

Steady State Strength (kPa)

1.4

’o

1.0

0.6

Initial Coni', .stress^ lOOkPa

IOS40

OS60 I •i OS 100 1

iOS40 belong.s to case-iv-2 |OS60 belong.s to case-iv-l/iv-2 boundary O.S 100 beloiuts to case-iv-1


1000

Fig. 6 L arge S tra in U n d ra in ed S h ea r S tren g th :(a) G lo b a l V o id R a tio , (b) In te rg ra n u la r V o id R atio , and (c) In te rfin e V o id R atio

Steady State Strength (kPa)1.8

CO . .X 1.4■o‘o

s iZ1.0

0.6

! ! .) Initial Conf. stress=: l0 0 & 4 0 0 k P a 1 (C)

OS40-100

OS40-400 it!

1 X 1- I i-i

OS60-1001 i><]

-1H lii

OS60-400 11

X X .i ' *

H- lit

¡OSIOO-IOO x V X * m

1 • • • ^ 111

OS 100-400OS40 belongs to ca.se-iv -2 XOS60 belongs to case-iv - l/iv-2 boundary Ao s 1 0 0 belongs to case-i v-1 •


1000

Fig. 7 E ffec t o f C o n fin in g S tre ss on S h ea r S treng th : (a) G lobal V o id R atio , (b) In te rg ra n u la r V o id R atio , and (c) In terfin e V o id R atio

72

m eth o d at the sam e c o n fin in g stress.

3.2 Stress-Strain Response - Some Trends

B ased on c ritica l sta te th eo ry the an tic ip a ted co n tra c tiv e (o r d ila tiv e ) b e h av io r o f a so il can be w ritten in te rm s o f th e trad itio n a l sta te p a ram ete r \\f (see p 9 1 -9 2 , T h ev a n ay a g a m 1989, T h ev an ay ag am et al. 1996b):

MAe!’Aei:

w here

2-W

y_l

6sin03-sin0

(4)

and A8q = in crem en ta l p lastic c o m p re ss io n an d sh e a r s tra in , resp ec tiv e ly ; vj/o= in itia l s ta te p a ra m e te r at the iso tro p ic no rm ally c o n so lid a te d sta te ; \|/ = sta te p a ram e te r at any stage d u rin g lo ad in g in triax ia l co m p ress io n ; R =2 acc o rd in g to the w o rk -a ssu m p tio n o f R o sco e and B u rlan d (1 9 6 8 ); and (j)= m o b ilize d ang le o f fric tion at c ritica l sta te .

In the case o f silty sand , in a m an n er s im ila r to the d e riv a tio n o f the in te rg ran u la r vo id ra tio (F ig .2) it is p o ss ib le to d e riv e an in te rg ran u la r state p a ram e te r \\Js (F ig. 14) g iv en by (T h ev an ay ag am et al. 1996b):

W¥s =

1 - -FC100

(5)

H ence , w ith in the lim ita tio n s o f the c ritica l state theo ry , it m ay a lso be p o ss ib le to ap p ro x im ate ly in fe r the a n tic ip a te d b e h av io r o f a silty soil (FC<FCth) in te rm s the b e h av io r o f the host sand u sin g E qs. 4 and 5 w ith ex ce p tio n s as in d ica ted later. E q s.4 -5 m ay a lso e x p la in w hy a silty sand at low FC b eh av es a lm o st s im ila r to the host sand w hen c o m p a red at the sam e sta te pa ram ete r(T h ev a n ay a g am e t al. 1996b). T h is is no t d iscussed fu rth er in th is p aper.

4 E X P E R IM E N T A L S T U D Y

4.1 Experiments

G a p -g rad ed so il m ix e s w ere p re p are d u sing a single h o st san d (O S -F 5 5 , F o u n d ry S and , U S S ilica C o m p an y , Illin o is) m ix e d w ith d iffe ren t am oun ts o f n o n -p las tic c ru sh ed silica fin es (S il co sil #40 , p a ss in g U. S. S e iv e # 2 0 0 ) at (a) 15% , (b) 25% , (c) 4 0 % , and (d) 60% fin es by dry w eigh t. T ests w ere a lso c o n d u c ted on c le an san d and 1 0 0 % silica fines.

T hese so ils are n am ed O S 15, O S 2 5 , O S 4 0 , O S 60 , OSO, and O S 100, re sp ec tiv e ly . S p e c im e n s w ere p rep ared by p lac in g so ils in fo u r layers in a triax ia l m o ld u sin g dry a ir d e p o sitio n m eth o d and sa tu ra ted u sing b ack p ressu re as p re sen te d b efo re (T h ev an ay ag am 1998a).

A ll sp ec im en s w ere iso tro p ic a lly c o n so lid a ted to lOOkPa (o r 400 kP a) and stra in c o n tro lled m o n o to n ic u n d ra in ed triax ia l c o m p re ss io n tes ts w ere done at a s tra in ra te o f 0 .6 p e rce n t p e r m inu te . T he final vo id ra tio o f each sp e c im en w as ca lcu la te d based on the w eigh t o f the dry so lid g ra in s in the spec im en , the net v o lu m e o f w a te r in tro d u c ed in to the sp ec im en d u ring sa tu ra tio n , and the m easu red v o lum e ch an g e da ta d u rin g c o n so lid a tio n .

C o n stra in ts w ere p laced e ith e r on (1) g lo b al vo id ra tio [e= 0 .6 7 ± 0 .0 1 ], o r (2) in te rg ran u la r vo id ra tio [es=0.85<emax,Hs; es= 0 .94±0 .01 n e a r enmx.us; and es=1.05±0.005>emax,, each rep re se n tin g cases i th ro u g h iii, re sp ec tiv e ly ], o r (3) in te rfin e vo id ra tio [ef=1.12±0.01; and 1.10±0.01 each re p re se n tin g case-iv -1 and iv-2 , re sp ec tiv e ly ]. F ig .5 sh o w s the spec im en loca tions . T he p u rp o se w as to s tu d y the in flu en ce o f five fac to rs at play: (a) in te rg ran u la r co n tac t fric tio n (case-i), (b) b e n efic ia l c u sh io n in g effec t by the fines (case -ii) , (c) a d v erse e ffec t o f fines c o n trib u tin g to trig g e rin g frag ility (case -iii) , (d) re in fo rcem en t by co arse r g ra in s (c ase -iv -2 ), and (e) in te rfine co n tac t fric tion (c a s e - iv -1).

F ig s .6-7 show the u n d ra in e d sh ea r s tren g th Sus da ta at large s tra in (20 to 25% ax ia l stra in ). F ig s .8 a- c show the s tre ss-s tra in and the e ffec tiv e s tress pa th da ta fo r six sp ec im en s fro m c lean sand to p u re silt (OSO-1, O S 15-3, O S 2 5 -1 0 , O S 4 0 -9 , O S 6 0 -6 ,OS 100-1, F ig .5 ) p rep ared at n early the same global void ratio (e= 0 .6 7 ± 0 .0 1 ) at the same confining stress o f lOOkPa. In itia lly the co llap se p o ten tia l increases and Sus d ecreases (from OSO-1 to O S 2 5 -1 0 ) w ith an increase in FC up to FCth ju s t b e y o n d 25% . F o r th is soil m ix , FCth c o rre sp o n d in g to e=0.67 is less than abou t 37% . B eyond tha t the co lla p se p o ten tia l d ecreases w ith fu rth er in cre ase in fines c o n ten t ( f ro m O S 4 0 -1 0 to OS 100-1).

4.2 Intergrain Contact Friction Effect

OSO-1 is den se (c lean) san d at es=0.674. OS 15-3 at 15% fines c o n ten t is at e=0.66, es=0.953, and ef=4.4. OS 15-3 is lo o se r than OSO-1 in te rm s o f e,s. T he m ag n itu d e o f ef is very h ig h and h en ce in te rfin e co n tac t fric tio n has on ly a seco n d ary e ffec t. D ue to reduced in te rg ran u la r c o n ta c t (h ig h e r eg) OS 15-3 is w eak er than OSO-1. W ith fu rth e r in crease in FC , at 25%, OS25-10 b eco m es m u ch lo o se r in te rm s o f eg

73

1000 p (kPa)

Fig. 8 Increase in Fines Content at the Same Global Void Ratio: (a) Stress-Strain and (b) Effective Stress Path

p (kPa) p (kPa)

Fig. 9 Increase in Fines Content at the Same Intergranular Void Ratio- Case-i:(a) Stress-Strain & (b) Effective Stress Path

Fig. 10 Increase in Fines Content at the Same Intergranular Void Ratio- Case-ii:(a) Stress-Strain & (b) Effective Stress Path

74

(=1.18>emax,Hs) w ith ef=2.6. T h e Cf is s till large to be o f h ig h sig n ifican ce . D u e to the s ig n ifican t increase in es (and re d u ce d in te rg ran u la r co n tac t) OS25-10 is m o re frag ile th an OS 15-3 and OSO-1.

W ith fu rth e r in crease in FC (>FCth), at 40% , O S 4 0 -9 is m u ch lo o se r in te rm s o f es (=1.80>emax,Hs). B u t ef (=1.7<emax,HF) IS reduced . In te rm s o f eg, O S 4 0 -9 is w e ak e r th an O S 2 5 -1 0 (es=1.18>emax.Hs, ef=2.6>emax,HF). B u t due to a s ig n if ic a n t in c re ase in in te rfin e co n ta c ts (reduced eO O S 4 0 -9 is s tro n g e r th an O S 2 5 -1 0 . T h is reversa l o ccu rs in th e v ic in ity o f FCth b e tw ee n 25 and 40% .

A s F C in c re ases fu rth e r to 60% , O S 6 0 -6 beco m es d e n se r th an O S 4 0 -9 in term s o f ef (= 1 .13 ) w hereas es (= 3 .2 ) is in c re ased sig n ifican tly . P rim arily the in te rf in e c o n ta c t c o n tro ls the b eh av io r. H ence , O S 60 -6 ten d s to be m o re d ila tiv e c o m p a red to the sp e c im en O S 4 0 -9 (a t ef=1.7 and es=1.8).

T h e ten d e n cy to d ila te in creases w ith fu rth er in crease in F C due to co n cu rre n t re d u c tio n in Cf. OS 100-1 (a t Cf=0.68) is h ig h ly d ila tiv e co m p ared to OS60-6 (at ef=1.13). T h e re aso n is tha t, in a dom ain w h ere th e in te rfin e fric tio n is p rim ary , OS 100-1 is s im p ly m u ch denser th an OS 60-6 in te rm s o f ef.

T h e in te rg ra in c o n ta c t e ffec t is a lso p re sen t in the sh e a r s tren g th Sus (F ig .6a). A t the same e and the same initial confining stress, Sus d ecreases w ith in crease in FC. T h en Sus in c reases w ith fu rther in crease in FC b ey o n d FC=FCth (F ig .6a). T he tran s itio n o c cu rs at FCth b e tw ee n 25 and 40% .

W h en c o m p a red in term s o f eg, at FC<FCth, Sus co rre la te s w ell w ith eg (F ig .6b ) w ith som e e x ce p tio n s in the v ic in ity o f eg»emax,Hs (case-ii). T his e x ce p tio n is cau sed by the cu sh io n in g e ffec t p ro v id ed by the fines p re sen t in the in te rg ran u la r vo ids. C lean san d at su ch very lo o se s ta tes is very u n sta b le (w ith o u t the su p p o rt by the fin er grains). B u t a s ilty san d at the sam e eg c o n tin u e s to be stable (re la tiv e to c le an sand) due to the c u sh io n in g effec t p ro v id ed by the fin es in case-ii.

A t FCth<FC<FCi, (case -iv -2 . F ig . lb ) , a lthough ef is lo g ic a lly the p rim a ry fac to r, Sus does no t un iquely c o rre la te w ith ef a lo n e (e.g . O S 4 0 and O S 6 0 in F ig .6 c). T h e re aso n fo r th is is the d iffe rin g degrees o f the se c o n d ary re in fo rc em e n t e ffec t [depend ing on the san d s co n ten t] in th is ran g e o f tran s itio n fines co n ten t. N e v e rth e le ss , as ef b e co m es low (denser f ines) Sus c o rre la te s w ith ef. T h is due to re la tive ly low e ffe c t o f re in fo rc em e n t c o m p a red to h igh in te rfin e fr ic tio n at low Cf due to sign ifican tly in c re ased in te rfin e c o n tac ts .

A t F C > F C i (> 6 0 % fo r th is so il m ix ), Sus tends to co rre la te w ith ef (O S 6 0 and O S 100; F ig .6c).

D en sity o f silty so ils can p ro v id e fa lse c o m fo rt w h ile they can be very frag ile . O ne sh o u ld lo o k at the in te rg ran u la r m atrix s tru c tu re to fo rec a s t w h a t to an tic ip a te . In the lim ited z o n es o f FC<FCth and FC>FCi, eg and ef, re sp ec tiv e ly , c an be u se d as the p rim ary ind ices to m ak e th is fo recast.

It is a lso re lev an t to reco g n ize the in flu e n ce o f in itia l co n fin in g stress on Sus as sh o w n in F ig .7. W h en c o m p ared at the sam e eg, Sus is h igh ly sen sitiv e to in itia l co n fin in g stress w h en loose in te rm s o f eg (case-iii) (T h ev a n ay a g am 1998a). A lth o u g h no t show n it is a lso p re ssu re sen sitiv e w hen lo o se in te rm s o f ef w h en in case-iv -1 and iv -2 (T h ev an ay ag am et al. 1998).

4.3 Beneficial and Adverse Effects of Fines: FC<FCm

A t low fines co n ten t, w h ile the in te rg ran u la r fric tio n p lays an im p o rta n t ro le , the ro le o f fin er g ra in s is no t en tire ly neg lig ib le . T h ey do p lay seco n d ary ro les c au s in g b e n efit o r co n trib u te to trig g e rin g frag ility . W h ich one is d o m in an t m atte rs a g rea t deal d e p en d in g on w h e th er the fines o ccu p y the in te rg ran u la r vo id space (p ro v id in g c u sh io n in g e ffec t) o r lie b e tw een som e o f the c o a rse r g ra in c o n tac ts (sep ara tio n ) and c rea te a m etas tab le sk e le to n (ty p ica lly eg>emax,Hs)- T h e fo rm er is the case w hen the fines o ccupy the in te rg ran u la r v o id s and the s ilty so il is no t loose in te rm s o f eg (ty p ica lly es<emax,HS, casc-i, ii). T h e la tte r o ccu rs w h en the so il is in C ase-iii. F ig s.9 -1 3 d ep ic t su ch b eh av io r.

Case-i: es<e,naxm: F ig s .lO a -b show the d a ta fo r OSO-5, O S 15-7, and O S 25-1 at n early the sam e eg (0 .8 5 5 ± 0 .0 0 5 <emax,Hs)- T h ey e x h ib it a lm o st s im ila r b eh av io r w ith a sligh t d iffe ren ce . T h e silty sand sp ec im en s b eh av e a little b e tte r due to the c u sh io n in g e ffec t p ro v id ed by the fines th a t re s is ts a little the ten d en cy to c o llap se . T h e e ffec t is m ore p ro m in en t in C ase-ii as o b se rv ed next.

Case-ii: es ^ e,nax,HS (Transition): F ig s .9 a -b show the d a ta fo r OSO-9, O S 15-3, O S 2 5 -3 at n early the sam e eg (= 0 .94± 0 .01 n ear emax.us)- OSO-9 is very lo o se c lean sand. It is m u ch m o re c o lla p s ib le than the silty sands O S 15-3 and O S 2 5 -3 th a t are eq u ally loose in te rm s o f eg. In fac t the la tte r sp ec im en s are sligh tly lo o se r on that a cco u n t (Cg=0.95) than the c lean h o st sand sp ec im en OSO-9 (eg=0.93). T he an sw er to th is p u zzle is the sam e as p re sen te d b e fo re fo r Sus in case-ii.

Case-iii: es>e,nax,HS: F ig s . l la - b sh o w the d a ta fo r tw o silty san d s O S 15-5 and O S 2 5 -6 at n early the sam e eg (= 1 .0 5 0 ± 0 .0 0 5 >emax,Hs)- A n in crease in FC tends to slig h tly reduce the co lla p se p o ten tia l. E v en

75

Fig. 11 Increase in Fines Content at the Same Intergranular Void Ratio- Case-iii:(a) Stress-Strain & (b) Effective Stress Path

Fig. 13 Increase in Fines Content at the Same Interfine Void Ratio- Case-iv-2:(a) Stress-Strain & (b) Effective Stress Path

Fig. 12 Increase in Fines Content at the Same Interfine Void Ratio- Case-iv-I:(a) Stress-Strain & (b) Effective Stress Path

Fig. 14 Intergranular and Interfine State Parameters - Schematic Diagram (after Thevanayagam et al. 1996b)

76

though OS25-6 was at a slightly higher Cs (1.056) it shows a slight tendency to dilate following initial contraction compared to OS 15-5 (es= 1.045) which shows contraction. The reasons for this behavior are the same as the reasons presented for Case-ii. OS15- 5 has more physical space (ef=4.92) for a coarser- grain particle to fall into than OS25-6 (ef=2.17) at a slightly higher FC.

Among all cases (i to iii) silty soils in Case-iii (and very loose clean sands in case-i) generally show fragility. Case-iii appears fragile regardless of confining stress. The reasons for this appears to be that, in Case-iii, (1) the intergranular void ratio is looser than in case-i or ii, and (2) a fair number of coarser grain contacts are separated by the finer grains (to reach es>emax,Hs)- With straining these contacts are easily dislodged into voids that are relatively large compared to the finer grain size.

4.4 Reinforcement by Coarser Grains: FC>FCth

Case-iv-1: FC>FCi: Figs.l2a-b show the data for OS60-6 and OS 100-6 at nearly the same ef (=1.12±0.01<emax,HF)- OS 100-6 falls in case-iv-1. OS60-6 falls in the vicinity of the theoretical boundary for case-iv-1 and iv-2. OS 100-6 is loose silt at ef= 1.12. It shows collapse behavior. OS60-6 is equally loose in terms of ef=1.13. In fact it is a little looser than OS 100-6. But it is at es=3.2 compared to OS 100-6 which has no coarser grains. Despite looser, even at 60% fines content, due to the slight reinforcement effect, OS60-6 is stronger than OS 100-6. This is reminiscent of the effect of fines on Case-ii although the mechanism is different. Had a specimen been tested at the same ef but at a higher fines content of 70 or 80% (>FCi) its behavior would have been more close to OS 100-6.

Case-iv-2: FCth<FC<FCi‘. Figs.l3a-b showsimilar data for OS60-5 and OS40-1 at nearly the same ef (=1.10±0.01<emax,HF). OS40-1 at 60% sands content is only a little looser (ef=1.10) than OS60-5 (ef=1.09) in terms of interfine void ratio. But it is much denser in terms of at eg (=1.4) compared to OS60-5 at es=3.14. Both eg are much higher than Cmax.HS- Due to relatively higher degree of reinforcement effect by the coarser grains (at decreased average spacing between the coarser grains), OS40-1 is much stronger than OS60-5. The soil in this range of FC can not be uniquely characterized using either eg or ef alone. The interfine, intergranular, and inter-coarser-finer grain contact friction affect the behavior of soils in Case- iv-2.

More detailed discussions on the role of coarser and finer grains on the mechanical response of granular mixes may be found elsewhere (Thevanayagam 1998b, Thevanayagam et al. 1998).

5 CONCLUDING REMARKS

Experimental data on stress-strain response and effective stress path for clean sands to pure silt is presented. The results indicate that the undrained behavior of gap graded silty soils may be characterized using eg or ef as indices.

At FC<FCth, when the silty sand is dense in terms of eg, its behavior is similar to the host sand at the same eg (case-i). The intergranular friction is the dominant mechanism affecting its mechanical response. Fines provide a secondary cushioning effect. The silty sand may be a little more resistant to collapse than the host sand. Similarly a silty sand is a little more resistant to collapse compared to another silty sand at lower fines content but at the same eg. At the same FC, the effect of fines become gradually more important as the eg increases. Silty sand that is loose in terms of eg (case-ii) is much stronger than loose clean (host) sand at the same eg. When a silty sand is very loose at eg>emax,Hs (case- iii), it is generally fragile. In general the effect of fines is beneficial in terms that it increases the resistance to collapse when compared at the same eg. But its effect is adverse in the sense it allows creation of loose (in terms of eg) and fragile soil matrix at eg>emax,HS- In general intergranular void ratio eg (and confining stress) can be used as index to evaluate steady state strength and collapse potential of silty sands in this region.

At FC>FCi, the behavior of a sandy silt is similar to the host pure-silt at the same ef. Interfine friction is the dominant mechanism of its mechanical response. Interfine void ratio ef (and confining stress) can be used as index to evaluate steady state strength and collapse potential behavior of sandy silts in this region.

At FCth<FC<FCi, the undrained behavior of the granular mix is governed by the interfine friction and a ‘reinforcement’ effect provided by the coarser grains embedded within the finer grain matrix. The strength is typically higher than a pure-silt at the same ef.

The data presented herein pertains to gap graded soils with large disparities in grain size and consolidated to the same confining stress. Its extrapolation to well graded granular mixes should be carried out judiciously. The relationships for FCth and FCi were derived for a simple two-size particle

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system and are rather approximate.While there are many other factors (NRC 1985)

that may affect the fragility of silty soils the above framework can have relevant contributions in understanding the past case histories of failures.

The framework presented herein can be used as a starting point for further research on the behavior of granular mixes and develop rational methods for laboratory and (in situ) field characterization of such soils. It may then be used rationalize various current procedures for fragility evaluation of such soils under earthquake conditions or develop improved methods.

Other issues such as the effect of sample preparation and field deposition methods on the microstructure and the resultant effects on the mechanical response also need to be studied further.

REFERENCES

Chameau, J.L. & K. Sutterer 1994. Influence of fines in liquefaction potential and steady state considerations. Proc. 13th Inti. Conf., New Delhi, India, 183-84

Chang, N.Y. 1990. Influence of fines content and plasticity on earthquake-induced soil liquefaction. Contract Rep., US Army WES, Vicksburg, MS Contract No. DACW3988-C-0078

JGS 1996. Soils and Foundations - Special issue on geotechnical aspects of the January 17 1995 Hyogoken-Nambu Earthquake, Japanese Soc. Geotechnical Eng.

Kenny, T.C. 1977. Residual strength of mineral mixtures. Proc. 9th Int. Conf. Soil Mech., Tokyo, 1, 155-160.

Koester, J.P. 1994. The influence of fines type and content on cyclic strength. Proc. ASCE Conv., Atlanta, Geotech. Spec. Pub. 44, 17-32.

Kuerbis, R., D. Nagussey, & Y.P. Vaid 1989. Effect of gradation and fines content on the undrained response of sand. Proc. of Conf. on Hyd. Fill Struc., ASCE Geotech. Spec. Publ. 21, 330-45.

Mitchell, J. K. 1993. Fundamentals of soil behavior, second ed. Wiley Interscience Publ.

NRC 1985. Liquefaction of soils during earthquakes. Committee on Earthquake Engineering, National Research Council, Washington, DC, Rept. No. CETS-EE-001,1985

Pitman, T.D., P. K. Robertson & D.C. Sego 1994. Influence of fines on the collapse of loose sands. Can. Geotech. J., 31,728-39

Robertson, P. K. & C. E. Wride 1997. Evaluation of cyclic liquefaction potential based on the CPT. Seismic Behavior of Ground and Geotech

Structures, ed. P.S. Pinto, Balkema Pubis., 269- 278.

Roscoe, K. H. 1970. The influence of strains in soil mechanics. Geotechnique, 20(2), 129-170.

Roscoe, K.H. & J.B. Burland 1968. On the generalized stress-strain behaviour of ‘wet’ clay. Engrg. Plasticity, Eds. J. Heyman and F. A. Leckie, Cambridge Univ. Press, 535-609.

Seed, H. B., I.M. Idriss & I. Arango 1983. Evaluation of liquefaction potential using field performance data. J. Geotech. Eng., ASCE, 109(3), 458-482

Seed, R. B. & L. F. Harder, Jr. 1990. SPT-based analysis of cyclic pore pressure generation and undrained residual strength. Proc. Seed Memorial Symp., Berkeley, 2, 351-76

Seed, H.B. 1987. Design problems in soil liquefaction. J. Geot.. Eng. Div. , ASCE, 113(8), 827-45.

Stark, T. D. & G. Mesri 1992. Undrained shear strength of liquefied sands for stability analysis.J. of Geotech. Eng., ASCE, 118(11), 1727-47.

Thevanayagam, S. 1989. Fundamental framework for strain space soil modeling. Ph.D. Dissertation, Purdue Univ., IN

Thevanayagam, S., K. Ravishankar, & S. Mohan 1996a. Steady state strength, relative density and fines content relationship for sands. TRB Transp. Res. Rec. 1547, 61-67.

Thevanayagam et al. 1996b. Intergranular void ratio - stress-strain behavior of silty sands, in Review, Geotechnique.

Thevanayagam, S. 1998a. Effect of fines and confining stress on steady state strength of silty sands. J. Geotech. & Geoenv. Engrg. Div., ASCE, 124(6), 479-491.

Thevanayagam, S. 1998b. Relative role of coarser and finer grains on the undrained behavior of granular mixes, in Review, J. Geotech. & Geoenv. Engrg. Div., ASCE

Thevanayagam, S. & S. Mohan 1998. Intergranular void ratio - steady state strength relations for silty sands. ASCE Geotech. Spec. Publ. 75, Eds. P. Dakoulas et. al., nird Conf. on Geotech. Earthq. Eng., 349-360.

Thevanayagam, S. et al. 1998. Undrained fragility of clean sands, silty sands and sandy silts, in review, J. Geotech. & Geoenv. Engrg. Div., ASCE

Vaid, Y.P. 1994. Liquefaction of silty soils. Proc. ASCE Conv., Geotech. Spec. Publ. 44, 1-16.

Zlatovic, S. & K. Ishihara 1997. Normalized behavior of very loose non-plastic soils: effects of fabric. Soils and Foundations, 37(4), 47-56.

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Triggering and post-liquefaction strength issues in fine-grained soils

Joseph RKoesterUS Army Engineer Waterways Experiment Station, Vicksburg, Miss., USA

A B S T R A C T : F in e s a re b e lie v ed to a ffec t b o th cyclic s tren g th an d p e n e tra tio n re s is tan c e o f so ils , an d the in te rre la tio n sh ip is n o t w e ll u n d e rs to o d . S ince o b se rv a tio n s d u rin g stro n g e arth q u ak es in C h in a an d p u b lic a tio n o f so -c a lled “ C h in ese C rite r ia ” in 1979, so m e c layey silts o r silty c lay s are c o n sid ere d su sce p tib le to s tren g th lo ss d u rin g sh a k in g , ev en lead in g to liq u e fac tio n . C lay ey and s ilty m ix tu re s co n ta in in g b e tw e e n 15 an d 25 p e rce n t fin es o f v a ry in g c o n sis ten c y are w o rth y o f a little ex tra co n se rv a tism ; th e ir re s id u a l s tre n g th m ay be on ly 5 o r less p e rce n t o f th e ir p e ak sh ea r s tren g th , and th ey do n o t b eh av e d ila tiv e ly . T he b en efic ia l c o n tr ib u tio n o f p la s tic ity to th e c y c lic s tre n g th o f fin e -g ra in e d so ils is very s ligh t. G rad a tio n ap p ea rs to be a m o re in flu en tia l fa c to r w ith trig g e rin g o f liq u e fac tio n ; c o n sis ten c y lim its m ay be b e tte r co rre la tab le to p o s t- liq u e fa c tio n streng th . R e d u c tio n in sh e a r s tre n g th fro m p e ak to re sid u a l w as fo u n d to be less w ith in creased fin es co n te n t and p las tic ity .

1 B A C K G R O U N D

R esearch e m p h a s is w as on cy c lic s tre n g th o f c lean san d s u n til re p o rts su rfaced (n o tab ly W ang , W . S., 1979, 1981) in th e g eo te ch n ic a l en g in e e rin g lite ra tu re o f liq u e fac tio n in "so m e w h a t co h esiv e" so ils as a re su lt o f s tro n g e a rth q u ak e s in th e P e o p le 's R ep u b lic o f C h in a (P R C ). C o n tem p o ra ry re sea rc h and re- e v a lu a tio n o f h is to ric a l d a ta h av e a lso sh o w n th a t l iq u e fac tio n o c cu rre n ce is n o t re s tr ic te d to c lean , u n ifo rm , lo o se d e p o s its o f sa tu ra ted sand . A w ide ran g e o f so il g ra d a tio n s an d c o n sis ten c ie s m ay be a sso c ia ted w ith sev e re sh ea r s tre n g th loss on u n d ra in e d cy c lic lo ad in g . T h e N a tio n a l R esearch C o u n c il (1 9 8 5 ) re c o m m e n d e d as a "N ew in itia tiv e" the s tudy o f "the lim its (e .g ., on g ra in size d is tr ib u tio n , p la s tic ity in d ex , l iq u id ity index , and pe rm e ab ility ) b e y o n d w h ic h th e d y n a m ic lo ss o f soil s tren g th an d liq u e fa c tio n in s tab ility n e ed n o t be co n sid ered ." T h e e ffe c ts o f g ra d a tio n and o th er en g in e erin g p ro p e rtie s o n so ils co n ta in in g fines have b een s tu d ied b y a se lec t fe w re sea rc h ers in recen t years , h o w e v e r a g re a t m an y p ro jec t o w n ers are b e co m in g in cre as in g ly co n ce rn ed w ith th ese so ils in se ism ica lly ac tiv e lo ca tio n s . S o il "fines" are d efin ed as th o se so il m a te ria ls p a ss in g a U S S ta n d a rd N o. 200 sieve (silts , o r c lays, o r m ix tu re s o f b o th ) in the

co n tex t o f th is p aper. T he te rm "fin e-g ra in ed " so il h e re in d en o tes m ix tu re s o f so il m a te ria ls th a t c o n ta in ap p rec iab le fines , y e t do n o t c la ss ify as a c lay (C L or C H ) in th e U n ified Soil C la ss if ic a tio n S ystem .

P ra c titio n e rs h ave o b se rv ed th a t an in cre ase in fines co n te n t g en era lly resu lts in an in crease in th e ra tio o f liq u e fac tio n re s is tan ce (or, cy c lic s tre ss ra tio req u ired fo r liq u e fac tio n , C S R ) to p e n e tra tio n re s is tan c e (ty p ica lly , (N,)^^ from S tan d ard P e n e tra tio n T ests or c o n v erted fro m o th er p e n e tra tio n tes ts ) in san d y soils. A d d itio n o f m o re than a b o u t 2 0 % to 30% fin es fills the vo id space b e tw een th e c o a rse r p a rtic le s and so m ay re su lt in fu ll sep a ra tio n o f th e co a rse r sandy p a rtic le s , h o w ev er, and fu rth e r in c re ases in fines co n ten t b e y o n d a b o u t 35% re su lt in no fu rth er ch an g es in the re la tio n sh ip b e tw ee n C S R an d (N J^ q.

Soil fines p re sen t in th e v o id s b e tw ee n san d g ra in s o b v io u sly in flu en ce the re sp o n se o f the s tru c tu re (fab ric , an iso tro p y ); the p re se n t s tudy e x am in es the e ffec ts o f th e p re sen c e o f fin es o f v a ry in g co n ten t and p ro p e rtie s o n b e h av io r o f so ils in u n d ra in e d cyclic lo ad ing . R e se a rc h by K a u fm an (1981), P uri (1984), W alk er an d S te w a rt (1 9 8 9 ), K o e ste r (1992) and o th ers h as e x te n d ed the s ta te o f k n o w le d g e on the m ec h an ism s o f e a rth q u ak e -in d u ce d soil liq u e fac tio n to in c lu d e san d s c o n ta in in g fin es and m ix tu re s o f silt and c lay , b o th p la s tic an d n o n p las tic . T he e ffec ts o f

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such soil particle characteristics as angularity, sphericity, and surface texture on liquefaction potential o f granular soils are not well understood; shape and texture considerations for silt and clay particles are not discernable except by their collective influence on soil behavior through consistency effects. Fines are believed to affect both cyclic strength and penetration resistance, and the interrelationship is not well understood.

2 FIELD OCCURRENCE

2.1 Japan

Japan has experienced strong earthquakes and related damage more often during the past century than has perhaps any other area in the world. Japanese geotechnical researchers have been afforded an unpleasant wealth of field occurrence data against which to evaluate the seismic response o f soil deposits, with concomitant experience in liquefaction investigation. Tsuchida (1970) proposed boundaries the boundaries shown in Figure 1 to distinguish liquefiable and non-liquefiable deposits studied following several previous Japanese earthquakes and from laboratory shake table test data. According to this figure, fine-grained soils (silts and finer) whose mean grain size (i.e., 50 percent o f the sample weight is finer) is at least 0.02 millimetres are potentially vulnerable to liquefaction under some unspecified level o f shaking. In fact, liquefaction potential is indicated in soils which are entirely composed o f silt- and-fmer particles (that is, particles smaller than 0.074 millimetres, which would pass through the openings in a US Standard No. 200 sieve). Ishihara, et al. (1980) contend that the Tsuchida (1970) chart is based on performance of soils o f alluvial, diluvial, or volcanic origin, and that the boundaries o f "most liquefiable soils" may be unconservative with regard to soils containing a higher fraction yet o f low plasticity clay-size particles such as are present in mine tailings. Tokimatsu and Yoshimi (1983) compiled field performance data from Japanese earthquakes and correlated observed ground behavior with gradation characteristics; soils containing up to 60 percent by weight silt-size particles and 12 percent clay-size particles (that is, particles smaller than 0.005 millimetres) exhibited moderate-to-extensive liquefaction (in terms of affected land area). Their compilation did not catalog soil index properties, for example, Atterberg limits, which have been shown to influence cyclic strength.

Figure 1. Gradations o f potentially liquefiable soils (after Tsuchida, 1970)

Koester and Tsuchida (1988) reviewed laboratory and field studies by Japanese researchers that assess the influence of variations in grain size distribution and soil index properties on liquefaction potential o f fine-grained soils. The geomorphology o f Japan has produced predominantly uniform sand deposits that typically contain less silt and clay than those found in the peneplain and coastal regions o f the PRC (Chang, 1987). Tohno and Shamato (1986) studied deposit stratigraphy and soil properties observed at liquefied and non-liquefied sites within the wide geographic region affected by the 1983 Nihonkai-Chubu (Japan Sea) earthquake and support this contention. Mine tailings and other man-made fine-grained deposits such as some compacted sand fills, however, often do contain appreciable fine grain size fractions and are important to the industry and economy o f Japan. The cyclic strength o f these soils has been extensively studied to develop seismic design criteria (Ishihara, et al. 1980, and Tatsuoka, Ochi, and Fujii, 1984).

2.2 People's Republic o f China

Chang (1987, 1990) reports from preliminary inquiries into the PRC data base on earthquake response associated with the two strong earthquakes that struck the city o f Tangshan on July 29, 1976 (Richter magnitude 7.8 main shock, 7.1 aftershock later that same day). The effects o f liquefaction were observed throughout the region (areas totaling over 20,000 km^) southeast o f Tangshan city. The recent alluvial fan of the Ruan river experienced the most pervasive liquefaction; damage and other surface manifestations o f liquefaction became progressively less intense toward older deltaic courses. Young alluvial deposits near Loutian and Luanan experienced the most severe liquefaction effects, at an epicentral distance between 60 km and 80 km.

Wang (W. S., 1979, 1981) catalogued the

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occurrence o f liquefaction in soils containing fines and soils exhibiting cohesion during both the 1975 Haicheng and 1976 Tangshan events. Some soils with clay content (particles finer than 0.005 microns) less than 15% by weight, liquid limit less than 35%, and occurring at natural water contents greater than 90 percent o f their liquid limit were found to have liquefied. There is, however, no available information (based on the observations in China) on the ground motion characteristics required to trigger this behavior, except that occurrences were reported for earthquakes ranging in Modified Mercalli Intensity from VII to IX. These observances evolved into the infamous “Chinese Criteria” published in a definitive EERI monograph by Seed and Idriss (1982).

It must be emphasized that the constraints proposed by Wang (1981) are boundaries, not average values. Koester (1992) examined the effects of misinterpretation and conservatism with regard to correlations that evolved from these findings. The author investigated PRC practice to measure consistency limits, and performed a limited series of experiments to compare results from PRC procedure (using a laboratory cone penetrometer) to results obtained on the same soils by means o f US standard procedures (using a Casagrande device). On one project, namely the seismic stability evaluation of Sardis Dam, Mississippi, US Army Engineers adopted the following changes to measured index properties o f foundation soils based, in part, on the slight, but consistent differences between PRC and US liquid limits:

1) decrease fines content by 5 percent

2) increase liquid limit by 1 percent3) increase water content by 2

percentThe very slight change (1 percent) in liquid limit alone reduced the length o f embankment requiring remediation by 1000 ft.

2.3 Fine-Grained Soil Liquefaction in the United States

The flow slide o f the upstream face o f the Lower San Fernando Dam consequent to the 1971 San Fernando earthquake has been attributed to liquefaction of "very silty" hydraulic fill sands (Marcuson, Hynes, and Franklin, 1990, Seed, et al. 1989, Vasquez- Herrera and Dobry, 1989, and Castro, Keller and Boynton, 1989). The low residual strength and associated deformability of these low-plasticity fme-

grained soils has raised worldwide awareness o f the risks o f these soils to dams, locks, power plants and other critical infrastructure facilities.

Liquefaction in soils containing silty or clayey fines is likely to have occurred as a result o f the 1886 Charleston, South Carolina earthquake and other events indicated by liquefaction recurrence features in the same area (Obermeier, et al. 1985) due to similarities between the peneplain deposits o f the PRC and the piedmont geomorphology in the southeastern region of the US.

Alternating layers o f silty, or clayey, or both glaciomarine sand deposits have been contended to have liquefied during several northeastern US earthquakes (e.g., Tuttle and Seeber, 1989). Clayey glacial soils abound throughout the region and are often sedimented with fine sands.

The New Madrid, Missouri seismic zone is associated with a series o f very strong earthquakes during the period December 1811 through January 1812. Wesnousky, Schweig, and Pezzopane (1989) detail a comprehensive evaluation of geologic evidence o f extensive liquefaction and massive sliding o f loessial bluff soils throughout the Mississippi embayment as a result o f these events. Clay layers are implicated to have exacerbated pore pressure retention in many studies; although the literature is inconclusive on gradational and index properties o f the liquefied materials in the New Madrid event, it is certain that fines are prevalent in sand deposits distributed in the Mississippi River floodplain.

2.4 Elsewhere

Ishihara, et al. (1990) reported that an earthquake of magnitude 5.5 shook the Dushanbe region of the Tadjikistan Republic in the USSR on January 23, 1989, and wetted, low-plasticity silts (80% silt, 15% clay, liquid limit = 30, plastic limit = 20, natural water content = 40%) were found to have slumped and flowed as far as 2 km. The back-calculated residual strengths of these soils ranged from 2 to 15 kPa (42 to 313 psf). Leighton and Willman (1950) found loessial silt deposits ranging in thickness from 3 ft to 100 ft over much o f the Mississippi River Valley. Puri (1984) contended that the liquefaction potential o f these soils merited evaluation based on the following factors: (1) similarities o f most loessial soils in the central US to fine-grained soils described by Wang (1979); and (2) the extreme seismic hazard posed by the New Madrid seismic zone.

As the data base on field occurrence continues to

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grow, it is becoming increasingly evident that finegrained, low- to medium-plasticity soils are no longer ruled out as being potentially liquefiable, and must be accounted for in seismic stability evaluations. Liquefaction potential analysis techniques have historically been based on experience, both field and laboratory, with clean sands; in some cases, analysis based on clean sand data may be overly conservative. Research funding is justified in consideration o f the high cost o f remediation for liquefaction potential, particularly at existing projects where remediation involves loss o f function.

3 LABORATORY INVESTIGATIONS OF CYCLIC STRENGTH

The author conducted a Civil Works Research and Development (CWRD) study at the US Army Engineer Waterways Experiment Station (WES) from. 1983 to 1992 to evaluate the earthquake-induced liquefaction hazard posed by fine-grained alluvial soils to Corps of Engineers dams. Four principal stages o f the CWRD study were to: (1) collect and report field occurrence data on fine-grained soil liquefaction; (2) conduct a reconnaissance cyclic triaxial test program to evaluate the liquefaction potential o f fine-grained soil mixtures on the bases of grain size and index properties; (3) conduct hollow

cylinder torsional simple shear cyclic tests on selected soil mixtures to establish correlations between cyclic simple shear and cyclic triaxial strengths; (4) assess pore pressure generation characteristics and residual strength o f soils varying in gradation and plasticity for use in post-earthquake stability analyses.

3.1 Cyclic triaxial tests

Nearly 500 stress-controlled cyclic triaxial strength tests were conducted on behalf o f the author by Professor N. Y. Chang and several o f his students and staff at the University of Colorado at Denver (UCD) Geotechnical Laboratory for the second phase o f the CWRD study (Koester, 1992). A total o f 129 soil mixtures were prepared to generate a data base o f the effects o f fines content and type on cyclic triaxial strength. Test soil mixtures were prepared from stockpiles o f commercial concrete and granular silica sands, low-plasticity Vicksburg, Mississippi loess (a uniform, eolian silt), and air-dried Buckshot plastic clay from the region around Vicksburg, Mississippi. The rigorous procedures followed to blend the various materials and maintain control o f gradation and consistency are detailed by Chang (1990).

Three parent sands were blended from sieved fractions of the concrete and granular silica sands depicted in Figure 2: uniform fine sand (F), uniform

U.S. stondard sieve number

20 40 60 100 200

Figure 2. Gradations o f supplied concrete sand and test parent sands

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T ab le 1. S o il T y p e M atrix^ fo r S p ec im en s W ith M ed iu m P a re n t S an d (V o id R a tio o f P a re n t S an d a t D , - 50% , C5o = 0 ,5 5 8 ')

P. I.of

Fines(%)

Fines Content of Specimen, %

12.5 20 30 45 60

M22 M32 M42 M52' M62 M72

10 M23 M33 M43 M53 M63 M73

15 M24 M34 M44 M54 M64 M74

20 M25 M35 M45 M55 M65 M75

25 M26 M36 M46 M56 M66 M76

30 M27 M37 M47 M57 M67 M77

40 M28 M3 8 M48 M58 M68 M78

' a. The format for abbreviated codes in these matrixes is LN,N2, where: L is M, F, or W for medium, fine, or well-graded parent sand, respectively; N, ranges from 2 through 7, respectively representing fines contents of 5%, 12.5%, 20%, 30%, 45%, and 60%; and N2 ranges from 2 through 8, respectively representing plasticity indexes o f 4%, 10%, 15%, 20%, 25%, 30%, and 40%.

b. The three parent sands. Ml 1, FI 1, and W 11 were tested, as well.c. Each tabulated soil type was tested using effective consolidation pressures of 15 and 30 psi (103.4 and 206.8 kPa).

A limited test series was conducted on Ml 1, M22, M23,M32, and M42 specimens prepared to = 30% (e =0.605), but is not discussed in this paper.

Underlined soil types were not tested (see text).

N u m b e r o f lo a d in g c y c le s

F ig u re 3. C y c lic tr ia x ia l s tre n g th c u rv e s fo r m ed iu m san d m ix tu re s

m ed iu m sand (M ), an d w e ll-g ra d e d m e d iu m sand (W ). S ilt an d c lay w ere m ix e d in p re se le c te d p ro p o rtio n s w ith e ac h o f th ese p a re n t sa n d s in acco rd an ce w ith a m a tr ix o f so ils ty p es , fo r exam ple th e m ed iu m sa n d -b ased m a trix in T ab le 1. A s tes tin g

p ro g resse d , it b ecam e e v id e n t th a t so m e o f th e h ig h - p la s tic ity m ix tu res w ere n o t liq u e fiab le ; in th e e x am p le o f th is tab le , th e u n d e rlin ed m ix tu re s w ere

n o t tes ted .

83

T h is s tudy em p h a size d th e e ffe c ts o f fin es co n sis ten cy on cy clic s tren g th - n o t th e consistenc)^ or the en tire g ra d a tio n a l frac tio n p a ss in g th e U S N o. 40 sieve as sp e c ified by A S T M D 4 3 18-84 (A S T M 1991). C o n sis te n cy an d g ra d a tio n a l fa c to rs w ere th u s iso la ted ; th e fin es th em se lv es , p a rtic u la rly th e c lay - size co n stitu e n ts , a re th e so u rce o f so il p las tic ity . C o n tro l o f co n sis ten c y p ro p e rtie s w as re ad ily a ch iev ed by ex c lu d in g the fine san d fra c tio n p ass in g the U S N o . 40 sieve an d re ta in e d o n th e U S N o . 200 sieve.

R e p lic a te sp e c im en s w ere p re p a re d by m o is t c o m p a c tio n (w a te r c o n te n t ra n g in g fro m 5% to 7 .5% ) o f five e q u a l-h e ig h t lifts to h av e id en tica l p o s tc o n so lid a tio n v o id ra tio s . T h ree ta rg e t v o id ra tio s w ere se lec te d (o n e fo r e ach p a re n t san d m atrix ), sp ec ifica lly , th o se c o rre sp o n d in g to 5 0 % re la tiv e d e n sity in sp e c im en s o f th e re sp ec tiv e c lean p a ren t sand.

F ig u re 3 p re se n ts a g ro u p o f cy c lic tr ia x ia l s tren g th cu rv es g e n e ra te d fo r sp e c im en s c o n stru c ted o f m ed iu m san d to w h ic h h as b e en fin es p ro p o rtio n e d to h ave a p la s tic ity in d ex o f 4% . In th ese cases, no c lay (V ic k sb u rg , M iss is s ip p i, “ B u c k s h o f ’, C H ) is p re sen t in th e m ix tu re s , an d p la s tic ity o f th e so il fin es is c o n tr ib u ted b y v a ry in g a m o u n ts o f V ic k sb u rg loess (silt). T h e e ffe c tiv e co n fin in g stre ss in each tes t in th is fig u re w as 15 p si (1 0 3 .4 kP a). T h e stro n g est m ate ria l re p re se n te d in F ig u re 3 is th e c lean m ed iu m p a ren t san d i t s e l f T h e a d d itio n o f up to 2 0 % (by w e ig h t) lo w -p la s tic ity s ilt fin es ap p ea rs to p ro g ress iv e ly re d u ce cy c lic s tren g th ; s tren g th s in crease w ith in c re ased fin es b e y o n d th is am oun t.

T h e lo w e s t cy clic s tre n g th w as a lw ay s fo u n d in g ra d a tio n s co n ta in in g a q u a n tity o f silt o r s ilt-c lay fin es in th is study . F ig u re s 4 an d 5 d e p ic t s im ila r cy c lic s tre n g th c u rv es d e v e lo p ed fo r m ix tu re s w ith fin e an d w e ll-g ra d ed p a re n t sands, re sp ec tiv e ly . T he ad d itio n o f 5% fin es w as fo u n d to in crease liq u e fac tio n re s is tan c e (reg a rd le ss o f p la s tic ity in d ex ) th ro u g h o u t th e c o m p le te te s t m a tr ix es fo r fin e and w e ll-g ra d ed sands. T h e m e a n g ra in size, D 50, o f th e m ed iu m p a ren t san d w as ab o u t 0 .48 m m ; u n ifo rm ly g ra d ed san d s o f th is g ra d a tio n m ay be su b jec t to o v e res tim a tio n o f cy c lic tr ia x ia l s tre ss ra tio s su ff ic ie n t to cau se liq u e fa c tio n in 30 cy c les by as m u ch as 3 5% as a c o n se q u en c e o f m em b ran e c o m p lian c e (M artin , F in n , an d S eed 1978). C o m p lia n ce m ay be re sp o n s ib le fo r th e c o n sp icu o u s ly h ig h cy c lic s tre n g th s o b se rv e d in sp e c im en s o f c le an m ed iu m sand . A s f in es are a d d ed to fill v o id s b e tw ee n co a rse r p e rip h e ra l san d p a rtic le s , the p o ten tia l fo r m em b ran e p e n e tra tio n and c o n se q u en t c o m p lian c e in u n d ra in e d tes ts is red u ced . M e m b ran e c o m p lian c e is n o t lik e ly to a ffe c t cy c lic s tren g th m ea su re m e n t in 2 .8 - in ch d iam e te r sp e c im en s o f th e fin e o r w e ll-g ra d ed p a re n t san d m ix tu res .

C y c lic tr ia x ia l s tre n g th s w ere n o t fo u n d to be p re d ic ta b ly re la te d to p la s tic ity in d ex o f th e fines f rac tio n a t fin es c o n te n ts less th a n 45 % . C y c lic tr ia x ia l s tre n g th in c re ased w ith in c re as in g p la s tic ity in sp ec im en s co n ta in in g 6 0 % fines. O v era ll, th e e ffec t o f p la s tic ity in d ex o f fin es o n cy c lic tr ia x ia l s tren g th w as m u ch less p ro n o u n c ed th a n th e e ffe c ts o f g rad atio n .

N u m b e r o f lo a d in g c y c le s

F ig u re 4 . C y c lic tr ia x ia l s tre n g th c u rv e s fo r fine san d m ix tu re s

84

N u m b e r o f lo a d in g c y c le sF ig u re 5 . C y c lic tr ia x ia l s tre n g th c u rv es fo r w e ll-g ra d ed sand sp ec im en s

Number of shear stress cycles to = 100S5

F ig u re 6 . C y c lic s tre n g th s o f H C T sp ec im en s iso tro p ic a lly c o n so lid a ted to 30 p s i (2 0 6 .8 k P a ) e ffe c tiv e c o n fin in g s tre ss

3.2 Cyclic torsional simple shear tests

T he au th o r p e rfo rm e d a lim ite d se ries o f u n d ra in e d sim p le sh ea r te s ts o n se lec te d m ix tu re s fro m the e a rlie r cy clic triax ia l te s t p ro g ram , u s in g a h o llo w cy lin d e r to rs io n a l/ax ia l te s t ce ll a t th e U n iv e rs ity o f C o lo rad o a t D en v er. T h e d es ig n , fa b ric a tio n , and in itia l te s t p ro g ram s co n d u c ted w ith th e H C T A -8 8 are d e ta ile d by C h en (1 9 8 8 ). T es t sp e c im en s w ere 25 .4 cm ( 1 0 .0 in .) ta ll, w ith in n er an d o u te r d iam e te rs o f20.3 an d 25 .4 cm (8 .0 an d 10.0 in .), re sp ec tiv e ly , and w ere su b jec ted to u n d ra in e d to rs io n a l s im p le shear

(cyclic and m o n o to n ie ) by an In stro n ™ M o d e l 1322 cyclic a x ia l/to rs io n a l loader.

H o llo w c y lin d e r sp ec im en s w ere c o n stru c ted by m o is t c o m p a c tio n o f ten 2 .5 4 cm (1 .0 in .) lifts to have a ta rg e t p o s t-c o n so lid a tio n v o id ra tio o f 0 .7 2 8 , w h ich is id en tica l to th a t o f the p a re n t fine san d at a re la tiv e den sity , D^, o f 50% . T est sp e c im en s w ere p re p a re d fro m the p a re n t sand (co e ff ic ie n t o f u n ifo rm ity , C^ = 2 .3 , m ean g ra in size, D 50 = 0 .18 m m , sp ec ific g rav ity o f so lid s, Gj = 2 .65 ) and th ree m ix tu re s o f th is sand w ith silt an d c lay acco rd in g to th e p ro p o rtio n s sh o w n in T ab le 2. T he c o m p ac ted sp e c im en s w ere

85

b a ck p re ssu re -sa tu ra ted an d c o n so lid a te d to the e ffec tiv e s tress c o n d itio n s d e s ired fo r u n d ra in e d shear tes ting .

C y c lie to rs io n a l sh ear s tre n g th s are p lo tte d in F ig u re 6 ; th o se m ea su re d in c le an fin e san d sp ec im en s w ere ad ju s ted to a c o m m o n re la tiv e d e n sity o f 5 0% in the m an n e r d e sc rib e d b y D eA lb a, Seed , and C h an (1976). C y c lic s tre n g th s o f c lean sand sp e c im en s co n so lid a ted to w ith in 1 0 % o f the ta rg e t p o st-c o n so lid a tio n re la tiv e d e n sity o f 50% g en era lly eo llap se on a re aso n a b le cu rv e . N o a d ju s tm e n ts w ere m ad e to any o f th e cy e lic s tren g th s o f the sand , silt, and c lay m ix tu re s to a cc o u n t fo r v a ria tio n s in p o st-c o n so lid a tio n v o id ra tio s aw ay from the targe t. R e la tiv e d e n s ity is n o t re liab ly m ea su ra b le in f in e-g ra in e d o r p la s tic so ils; vo id ra tio s w ere in te n tio n a lly m a in ta in ed as c lo se to co n stan t as p o ss ib le fo r th ese tes ts , so th e d e p en d e n ce o f cyclic s tren g th on v o id ra tio w as n o t e s tab lish e d . P o s tc o n so lid a tio n v o id ra tio s w ere n e a r th e ta rg e t v a lu e o f 0 .728 in m o st sp ec im en s ; F64 m ix tu re s , ho w ev er, c o n so lid a ted to a s lig h tly d e n se r c o n d itio n th an desired .

T h e F43 m ix tu re w as fo u n d to be h ig h ly su scep tib le to liq u e fac tio n a t th e v o id ra tio tes ted . R e su lts from a co m p a n io n cy c lic tr ia x ia l tes t p ro g ram on th ese and o th er m ix tu re s (C h an g , 1990 and K o este r, 1992) in d ic a te d th a t cy e lic s tren g th s o f sand , silt, and clay m ix tu re s p re p a re d in th is p ro g ram w ere lo w est at a g iven v o id ra tio w h e n th e fines co n te n ts w ere b e tw ee n 2 0 -2 6 % . S p ec im en s w ith th e sam e p ro p o rtio n o f san d to fin es w ith s to o d th e sam e in ten sity o f ey c lic to rs io n a l sh ea r lo ad in g slig h tly lo n g er w h e n th e p la s tic ity index o f th e fines frac tio n w as in c re ased to 2 5 % (i.e ., F 4 6 soil).

4 L A B O R A T O R Y IN V E S T IG A T IO N O F RESIDUAL S T R E N G T H

O ne h o llo w c y lin d rica l sp e c im en o f e ac h o f the m ix tu re s in T ab le 2 w as su b je c ted to slow , m o n o to n ic

s im p le sh ea r in to rs io n c o n tro l to ev a lu a te la rge d e fo rm a tio n u n d ra in e d re sp o n se ; F ig u re 7 is one ex am p le fro m th e re su lts , n a m e ly th e s tre ss-s tra in cu rve fo r a te s t on an F43 sp ec im en . T he v irg in c lean fine san d (F I 1) sp e c im e n b e h av e d d ila tiv e ly in u n d ra in e d m o n o to n ic sh e a r a t a v o id ra tio o f 0 .749 (co rre sp o n d in g to 4 4 .6 % re la tiv e d en sity ). T he cause fo r th e u n lo ad in g sp ik e s e v id e n t in its s tre ss-s tra in re sp o n se is u n k n o w n , b u t is n o t b e liev ed to h ave ad v erse ly a ffe e te d re su lts . M ix tu res o f sand , silt and c lay b e h av e d c o n tra c t!v e ly . E arg e s tra in s a p p aren tly in d u ced a m o re g lo b a l e o lla p se o f stru c tu re w ith in s ilty o r c lay ey sp ec im en s .

M e m b ran e to rq u e c o rre e tio n s w ere c a lcu la te d as a fu n c tio n o f to rs io n in m o n o to n ic , la rg e s tra in tes ts , a ssu m in g a c o n s ta n t m em b ran e th ic k n e ss and a shear m o d u lu s d e te rm in e d by e la s tic ity th eo ry and s tre tch in g te s ts o n th e m e m b ra n e s th em se lv es (F rost, 1989, and K o este r, 1992). M e m b ran e to rq u e w as su b trac ted fro m th e to ta l to rq u e m ea su re d a t each p o in t du rin g to rs io n a l sh ea r tes ts . C o rre c tio n s to shear stress d e te rm in e d in th is m a n n e r a m o u n te d to ap p ro x im ate ly 0 .345 k P a (0 .05 p s i) fo r ev ery one p e rcen t sh ea r stra in . M e m b ran e to rq u e -c o rrec te d shear s tre n g th a p p ea rs to c o n tin u e d e c re as in g w ith s tra in in the u n d ra in e d m o n o to n ic s im p le sh ea r tes ts on m ix tu re so ils. N o c o rre c tio n s w ere ap p lie d to cyclic te s t re su lts fo r m em b ran e effec ts .

O b se rv a tio n s b y Seed , e t al. 1973 o f d is tre ss cau sed to the U p p e r San F e rn an d o D am by th e 1971 e arth q u ak e su g g est th a t sh e a r s tra in s o f a b o u t 15% m ay be n ecessa ry to d ev e lo p re s id u a l s tre n g th s in silty san d s (M arcu so n , H y n e s an d F ra n k lin 1990). F o r the p u rp o se s o f c o m p a riso n w ith p u b lish e d re s id u a l s tre n g th v a lu es, re sid u a l s tre n g th s w ere e s tim a te d fo r m o n o to n ic H C T te s ts in th e p re se n t s tu d y a t a sh ea r s tra in o f 15% . P eak u n d ra in e d m o n o to n ic to rs io n a l sh ea r s tren g th s are eo m p a red to re s id u a l s tren g th s d e te rm in e d a t 15% sh ea r s tra in in T ab le 3. "C ritica l s tre n g th ra tio s" sh o w n co m p a re w e ll w ith v a lu e s c o m p iled by S ta rk an d M esri (1 9 9 2 ) fro m

86

F ig u re 7 . S h e a r s tre ss v e rsu s sh e a r s tra in m ea su re d in m o n o to n ie to rs io n a l tes ts o n v irg in sp e c im en s o f c le a n san d an d m ix tu re so ils

T ab le 3. S h ear s tren g th red u c tio n in v irg in sp ec im en s

T es t N o . (m ix tu re )

4>' S y(peak)', k P a S “ kPa

reduction"^

25 ( F l l ) 35" (d ila tiv e ) (N /A ) (N /A ) (N /A )

2 6 (F 4 3 ) 33" 129.9 7.6 0 .037 94%

27 (F 4 6 ) 28.8" 109.9 17.2 0.083 84%

28 (F 6 4 ) 26.6" 96 .7 26 .9 0 .130 7 2 %

a, tan(j)', where o^=a,' in these isotropically consolidated tests Jmembrane-corrected strength at 15% shear strain from Table 2 ^"critical strength ratio" for comparison to Stark and Mesri 1992 values " (S„(peak)-S^TSu(peak)x 100%

liq u e fac tio n case h is to rie s fo r so ils c o n ta in in g up to 4 0 % fines. T he re d u c tio n in sh ea r s tre n g th fro m peak to re sid u a l is s ig n if ic a n tly h ig h e r in th e sp ec im en s co n ta in in g 20 % fin es (F43 an d F 4 6 ) th an in the m ix tu re c o n ta in in g 4 5 % fin es (F 6 4 ). P eak u n d ra in ed sh ear s tren g th w as a lso re d u ce d by o v e r 99% by cyclic tes ts to liq u e fac tio n , on av erag e , as m easu red in p o st-cy c lic , u n d ra in ed , m o n o to n ie to rs io n a l tes ts on liq u e fied sp e c im en s o f b o th F43 an d F 46 m ateria l.

5 C O N C L U S IO N S

N e arly 500 u n d ra in e d c y c lic tr ia x ia l te s ts w ere co n d u c ted on re c o n s titu te d m ix tu re s o f sand , silt, and p las tic c lay to s tudy th e in flu e n ce th e g ra d a tio n and in d ex p ro p e rtie s o f th e fin es f rac tio n o n liq u e fac tio n re s is tan c e and p o re p re ssu re g en e ra tio n c h arac te ris tics . A c o m p a n io n se ries o f und ra in ed

h o llo w c y lin d e r cy clie to rs io n a l shear tes ts w as also p e rfo rm e d on m ix tu re s se lec ted from the cyclic triax ia l te s t p ro g ram to in v es tig a te th e ir b e h av io r w h en su b je c ted to cy clie s im p le sh ea r and very large m o n o to n ie sh ea r stra in s. T h e re su lts o f the lab o ra to ry p ro g ram are p re sen te d and in d iea te th a t the low est liq u e fac tio n re s is tan c e in m ix tu re s p rep ared to a u n iq u e g lo b a l vo id ra tio (eo rre sp o n d in g to 50% re la tiv e d e n sity o f the san d frac tio n be fo re ad d itio n o f fines) o c cu rs a t fines c o n te n ts b e tw ee n 2 0 % and 26% . P la s tic ity o f th e fines e x erts a less p ro n o u n ced effect.

M o n o to n ie , u n d ra in e d to rs io n a l shear tes ts w ere p e rfo rm e d b o th on h o llo w cy lin d rica l sp e c im en s to in v es tig a te re sid u al u n d ra in e d streng th . R esid u al s tren g th s o f sp e c im en s c o n ta in in g 2 0 % lo w -p las tic ity fines w ere fo u n d to be v e ry low ; d e fo rm a tio n p o ten tia l in su ch so ils w o u ld be e ssen tia lly u n lim ited .

87

ACKNOWLEDGMENT

T h e te s ts d e sc rib e d an d th e re su ltin g d a ta p re sen te d h e re in , u n le s s o th e rw ise n o ted , w ere o b ta in e d fro m re sea rc h c o n d u c te d u n d e r th e C iv il W o rk s In v e s tig a tiv e S tu d y p ro g ra m (W o rk U n it 32255 - L iq u e fac tio n P o te n tia l o f F in e -G ra in e d S o ils) o f the U n ited S ta te s A rm y C o rp s o f E n g in eers . P e rm iss io n w as g ran ted by th e C h ie f o f E n g in e e rs to p u b lish th is in fo rm a tio n .

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N a tio n a l R e se arc h C o u n c il 1985. Liquefaction of soils during earthquakes. C o m m itte e o n E arth q u ak e E n g r., C o m m iss io n o n E ngr. an d T e c h n ic a l S y stem s, N a tio n a l A cad em y P ress , W ash in g to n , D .C .

O b erm eier, S. F ., G o h n , G . S., W eem s, R . E .,G e lin as , R . L ., an d R u b in , M . 1985. "G eo lo g ic ev id e n ce fo r re cu rre n t m o d era te to la rg e e a rth q u ak e s n e a r C h arle sto n , S o u th C a ro lin a ," Science, V o l. 227 , 40 8 -4 1 1 .

P u ri, V . K . 1984. "L iq u e fa c tio n b e h a v io r an d d y n am ic p ro p e rties o f lo ess ia l (s ilty ) so ils ," P h . D . T h es is , U n iv e rs ity o f M isso u ri-R o lla .

S eed , H . B ., an d Id riss , I. M . 1982. Ground motions

8 8

and soil liquefaction during earthquakes, E ngr. M o n o g ra p h s o n E a rth q u ak e C rite ria , S tru c tu ra l D esig n , an d S tro n g -M o tio n R e co rd s , E arth q u ak e E ngr. R e se a rc h In s titu te , B e rk e ley , C a lifo rn ia .

Seed , H . B ., L ee , K .L ., Id riss , I.M ., an d M ak d isi, F. I. 1973. "A n a ly s is o f th e S lid es in th e S an F e rn an d o D am s D u rin g th e E a rth q u ak e o f F e b ru a ry 9, 1971," R e p o rt N o . E E R C -7 3 -2 , C o lle g e o f E n g r., U n iv e rs ity o f C a lifo rn ia , B e rk e ley , C A .

Seed , H. B ., S eed , R . B ., H ard er, L. F ., an d Jong , H. L. 1989. "R e -ev a lu a tio n o f th e L o w e r S an F e rn an d o D am - R e p o rt 2: E x a m in a tio n o f th e p o st-e a rth q u ak e slide o f F eb ru a ry 9, 1971," C o n trac t R e p o rt G L -89-2 , U S A rm y E n g in e e r W ate rw ay s E x p erim en t S ta tion , V ic k sb u rg , M iss iss ip p i.

S tark , T. D . an d M esri, G . 1992. "U n d ra in ed shear s tre n g th o f l iq u e fied san d s fo r s ta b ility an aly sis ," J., Geot. Engr. Division, A S C E , 118 (N o v em b er): 1727- 1747.

T a tsu o k a , F ., O ch i, K ., a n d F u jii, S. 1984. "E ffec t o f sam p le p re p a ra tio n m e th o d on cy c lic u n d ra in e d s tre n g th o f sa n d in tr ia x ia l an d to rs io n a l sh ea r tests ," Bulletin of Earthquake Resistant Structure Research Center, N o. 17, M arch , 2 9 -62 .

T o h n o , I., an d S h am ato , Y. 1986. "L iq u efa c tio n d am ag e to th e g ro u n d d u rin g the 1983 N ih o n k a i- C h u b u (Ja p an S ea) E a rth q u ak e in A o m o ri P re fec tu re , T o h o k u , Jap an ," Natural Disaster Science, 8(1), 85- 116.

V asq u ez-H erre ra , A ., an d D o b ry , R . 1989. "R e- e v a lu a tio n o f the L o w e r S an F e rn a n d o D a m - R ep o rt 3: T he b e h av io r o f u n d ra in e d c o n tra c tiv e san d an d its e ffec t o n se ism ic liq u e fac tio n f lo w fa ilu re s o f ea rth s tru c tu res," C o n trac t R e p o rt G L -8 9 -2 , U S A rm y E n g in e e r W aterw ay s E x p erim en t S ta tio n , V ick sb u rg , M iss issip p i.

W alker, A . J., and S tew art, H . E. 1989. "C yc lic u n d ra in e d b e h av io r o f n o n p las tic an d lo w p la s tic ity silts ," T ech n ica l R ep o rt N C E E R -8 9 -0 0 3 5 , N a tio n a l C e n te r fo r E arth q u ak e E ngr. R e se arc h , S ta te U n iv e rs ity o f N e w Y o rk at B u ffa lo , Ju ly .

W ang , W . S. 1979. "S om e fin d in g s in so il liq u e fac tio n ," R e se arc h In s titu te o f W ater C o n se rv an cy and H y d ro e lec tr ic P o w er, B e ijin g , P R C .

W ang, W . S. 1981. "F o u n d a tio n p ro b lem s in a se ism a tic d e s ig n o f h y d ra u lic s tru c tu res." In Proc. of the Joint US - PRC Microzonation Workshop, 11-16 S ep tem b er, H arb in , PR C .

W esn o u sk y , S. G ., S ch w eig , E. S., an d P e z zo p a n e , S.K. 1989. "E x ten t and ch a ra c te r o f so il liq u e fac tio n d u rin g the 1811-1812- N e w M a d rid e a rth q u ak es ," Earthquake Hazards and the Design of Constructed Facilities in the Eastern United States, A n n a ls o f the N e w Y o rk A cad em y o f S c ien ces , V ol. 558 , eds.Jacob , K. H . an d T u rk stra , C. J., 20 8 -2 1 6 .

T o k im a tsu , K . an d Y o sh im i, Y. 1983. "E m pirica l c o rre la tio n o f so il liq u e fa c tio n b a se d o n S P T N -v a lu e an d fin es co n te n t," Soils and Foundations, Jap an ese S o c ie ty o f S o il M ech . & F dn . E n g r., 23 (4 ), 56-74.

T su ch id a , H . 1970. "P red ic tio n an d co u n te rm easu re a g a in s t liq u e fa c tio n in sa n d d ep o sits ," A b s tra c t o f the S em in a r o f th e P o rt an d H a rb o u r R e se a rc h Institu te , M in is try o f T ran sp o rt, Y o k o su k a , Jap an , 3 .1 -3 .33 (In Jap an ese).

T u ttle , M . P ., an d S eeb er, L. 1989. "E arth q u ak e- in d u ced liq u e fa c tio n in th e n o rth e a s te rn U n ited S tates: h is to rica l e ffec ts an d g e o lo g ic a l c o n stra in ts ," Earthquake Hazards and the Design o f Constructed Facilities in the Eastern United States, A n n a ls o f the N e w Y o rk A c ad e m y o f S c ien ces , V o l. 558 , eds. Jaco b , K . H . an d T u rk stra , C. J., 196-207 .

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Developments in gravelly soil liquefaction and dynamic behavior

MarkD. EvansUnited States Military Academy, West Point, N.Y., USA

Kyle M. RollinsBrigham Young University, Provo, Utah, USA

A B S T R A C T : T h is p a p e r p re sen ts a c ritica l lo o k at g rav elly so il liq u e fac tio n and d y n am ic b e h a v io r fro m the lab o ra to ry p e rsp ec tiv e : (1) U n d ra in ed cyclic triax ia l tes tin g m ay re liab ly p red ic t cyclic b e h av io r i f m em b ran e co m p lian ce is e lim in a ted . M e m b ran e c o m p lian ce m itig a tio n p ro c ed u re s are b rie fly d escrib ed . (2) L oose , u n ifo rm ly -g rad ed g ravel m ay h ave s im ila r cyclic s tren g th as sand . D iffe ren ces in s tre ss—stra in b eh av io r, ax ia l s tra in , and p o re p re ssu re ra tio are illu s tra te d fo r so ils w ith d iffe ren t g ravel co n ten ts . S c a lp in g m ay be e ffec tiv e bu t a lso m ay lead to u n d e res tim a tin g liq u e fac tio n p o ten tia l. (3) S h ear m o d u li and d am p in g ra tio s are p re sen ted fo r g rav e lly so ils. S h e a r m o d u lu s , n o rm alized sh ea r m o d u lu s , and d a m p in g c u rv es are d e v e lo p ed to d efine th e ir v a ria tio n w ith sh ea r s tra in fro m a c o m p ila tio n o f stud ies. (4) F ina lly , p re lim in a ry re su lts from large-scale p re ssu re ch am b er tes ts on g rav el are d iscu ssed . D a ta w ill be a v a ilab le fro m S P T tests , sh ea r w ave ve lo c ity m easu rem en ts , and cone p e n e tra tio n tests p e rfo rm ed on gravel sp ec im en s in the p re ssu re ch am b er.


L iq u e fac tio n o f g rav e lly so ils is a g ro w in g issu e in the g e o tech n ica l co m m u n ity . G rav e lly so ils and ro ck fills in d am s, d am fo u n d a tio n s , p o rts , and w h a rf stru c tu res have all b een e v a lu a te d fo r liq u e fae tio n p o ten tia l. E v an s & H a rd er (1993) su m m arized severa l case h is to rie s w here g rav e lly so il has liq u efied in situ , in c lu d in g g rav elly so il in tw o em b a n k m en t dam s. E m b a n k m en t d am s c o n sistin g o f g rav elly so il o r fo u n d e d upon g rav e lly so il w here g ravel liq u e fac tio n has b een c o n sid e re d include:

• A sw an H ig h D am , E gyp t• E o lsom and M o rm o n Islan d D am , C A• R irie and M ack ay D am s, Idaho. O ro v ille and S even O aks D am s, C A• S h im en and B aihe D am s, C h in a• T erzag h i and S ey m o u r D am s, B ritish C o lu m b ia• D aisy L ake D am , B ritish C o lu m b ia• S c o tt’s E lat and S an ta F e lic ia D am s, C A• V e in F reem an D iv e rs io n S tru c tu re , C A. D evil C anyon S eco n d A fte rb ay , C A

G rain size d is tr ib u tio n s fo r th ese so ils ran g e from rock fill to sandy gravel o r g rav e lly sand.

G ra v e l-s iz ed p a rtic le s p re sen t un ique co m p lica tio n s to co n v en tio n a l sam p lin g and lab o ra to ry tes tin g tech n iq u es. G rav e l p artic les c rea te m em b ran e c o m p lian c e p ro b lem s in triax ia l tests , a rtific ia lly in creas in g the labo ra to ry

liq u e fac tio n re sis tan ce , re su ltin g in an u n c o n se rv a tiv e a sse ssm e n t o f in situ liq u e fac tio n p o ten tia l. G ravel p a rtic le s a lso c o m p lica te fie ld sam p lin g , n ecess ita tin g m o re co m p lex p ro ced u res , su ch as in situ freez ing . A nd , finally , g ravel p a rtic le s m ak e fie ld a sse ssm e n t by c o n v en tio n a l m eth o d s m ore d ifficu lt, i f no t im p o ssib le . N ew d e v e lo p m en ts in the B e ck e r P e n e tra tio n tes t, large p e n e tra tio n test, and f ie ld free z in g and sa m p lin g h av e all resu lted . T h u s, a sse ss in g the liq u e fac tio n p o ten tia l o f a g rav elly so il p re sen ts un iq u e c h a llen g e s to the desig n e n g in eer. T h is p a p e r w ill ad d ress how som e o f th ese c h a llen g es m ay be ov e rco m e.

2 C Y C L IC T R IA X IA L T E S T IN G

2.1 Introduction

It is a lw ays p re fe rab le to sam p le and test h igh q ua lity , u n d is tu rb ed sam p les fro m the so il lay er o f in te res t. S am p lin g g rav e lly so il can be ex trem e ly d ifficu lt, ho w ev er, due to lack o f c o h es io n and large p a rtic le sizes. T h ere fo re , sp e c im en s are o ften re co n s titu te d in the lab o ra to ry to accu ra te ly m odel in s itu co n d itio n s , e sp e c ia lly d ensity , s tru c tu re , and stress h is to ry (M u lilis e t al. 1977). T he sp ec im en s are in s ta lled in the triax ia l cell, su b jec ted to late ra l and ax ia l s tresses re p re se n ta tiv e o f the in situ

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e ffec tiv e stress , a llo w e d to c o n so lid a te , an d th en su b jec ted to a cy clic d e v ia to r stre ss , a ^ , u n d e r

u n d ra in e d c o n d itio n s u n til the sp e c im en liq u efies . S ev era l te s t sp e c im en s are su b je c ted to v a rio u s cyclic stress lev e ls to d e fin e a re la tio n sh ip b e tw ee n cyclic s tress ra tio , a j / 2 a 3 Q, and n u m b e r o f cycles

req u ired to cau se liq u e fac tio n , N / .

2 .2 Membrane Penetration and Compliance

M e m b ran e p e n e tra tio n and c o m p lian c e can cau se s ig n ifican t e rro rs in lab o ra to ry -m e asu red liq u e fac tio n p o ten tia l. B e fo re any e ffec tiv e c o n fin in g p re ssu re is ap p lie d to the triax ia l sp ec im en , th e c o n fin in g m em b ran e is s tre tc h ed fla t o v e r the su rface o f the sp e c im en , b rid g in g the p e rip h e ra l sa m p le v o ids. A s c o n fin in g p re ssu re is a p p lied an d the sp e c im en is a llo w e d to co n so lid a te , the m em b ran e w ill p e n e tra te in to th e p e rip h e ra l v o ids, c o n tin u in g to p en e tra te fu rth e r w ith each e ffec tiv e p re ssu re in crease u n til no m o re p e n e tra tio n is p o ss ib le . F ig u re 1 show s a p h o to g ra p h o f a 71- m m d iam e te r g rav e l sp ec im en (9 .5 -m m by 4 .7 5 -m m p a rtic le s) c o n fin e d w ith a s in g le m em b ran e . T he sev ere d eg ree o f m em b ran e p e n e tra tio n in to p e rip h e ra l v o id s is a p p are n t in th is F igu re .

reb o u n d s . N o v o lu m e c h an g e can o c cu r w ith in the m em b ran e , thus the o u tw a rd f lo w o f p o re w a te r fro m the in te rio r sam p le v o id s to the p e rip h e ra l v o id s m u st b e b a la n ce d by c o n so lid a tio n o f the g ra in s tru c tu re (E v an s e t al. 1992).

2 .4 Measured Volume Changes

H eig h t and to ta l v o lu m e ch an g es can b e m ea su re d in h y d ro sta tic c o m p re ss io n and re b o u n d tes ts p e rfo rm e d on g rav el sp e c im en s , as sh o w n in F ig u re 2. S p ec im en s are g e n era lly a ssu m e d to b eh av e iso tro p ica lly , th u s, the sk e le ta l v o lu m e tric stra in ,

8 vs, re p re se n ted by cu rv e (1) in F ig u re 2, m ay be

co m p u te d as th ree tim es the ax ia l s tra in , £a- V o lu m etric s tra in d u e to m em b ran e p e n e tra tio n m ay be d e te rm in e d by su b tra c tin g the sk e le ta l v o lu m etric s tra in , cu rv e ( 1), fro m the to ta l m ea su re d v o lu m etric s tra in , cu rv es (2) an d (3). It m ay be seen th a t the to ta l v o lu m etric s tra in m ea su re d in 1 0 0 % g ravel sp ec im en s (cu rv e 3) is ab o u t 10 tim es g rea te r than th a t m easu red in the san d -g rav e l co m p o s ite sp ec im en s (cu rve 2). A lso a p p are n t is th a t m em b ran e p e n e tra tio n v o lu m e ch an g e in the c o m p o s ite sp ec im en s is a sm all p e rce n ta g e o f the to ta l v o lu m etric stra in .

F ig u re 1. P h o to g ra p h o f triax ia l sp e c im en sh o w in g m em b ran e p en e tra tio n .

2.3 Density Changes Due To Membrane Compliance

D u rin g u n d ra in e d cyclic lo ad in g , th e e ffec tiv e c o n fin in g p re ssu re is red u ced as p o re p re ssu re d ev e lo p s , an d the m em b ran e reb o u n d s fro m the p en e tra tio n sites . W a te r d ra in s fro m in te rio r v o id s and m ig ra te s to th e p e rip h e ra l v o id s p re v io u s ly o c cu p ied by th e m em b ran e as th e m em b ran e

0 20 40 60 80 100 120

E ffec tive C onfin ing P re ssu re (kP a)

F ig u re 2. C o m p ress io n and reb o u n d cu rv es for san d -g rav e l c o m p o s ite s .

D en sity ch an g es in u n d ra in e d tes ts c au sed by m em b ran e c o m p lian c e m ay b e co m p u te d fro m m em b ran e p e n e tra tio n v o lu m e ch an g es m easu red d u rin g d ra in ed h y d ro sta tic reb o u n d . D a ta like tha t sh o w n in F ig u re 2 m ay be u se d to c o m p u te the to ta l v o lu m e tric re b o u n d th a t w o u ld re su lt fro m a sp ec ific ch an g e in e ffe c tiv e p re ssu re d u rin g u n d ra in e d load ing . V o lu m etric s tra in v a lu es m ay th en b e c o n v e rted to v o lu m e ch an g e and c o rre sp o n d in g in creases in re la tiv e density . O nce re s id u a l p o re p re ssu re ra tio s are d e te rm in e d at the en d o f a tes t, o n e can d e te rm in e th e in crease in re la tiv e d e n sity c au sed by m em b ran e c o m p lian c e as d e sc rib e d by E v an s & H a rd e r (1993). F o r ex am p le .

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if a 25% re la tiv e d e n sity g rav el sp e c im en d ev e lo p ed 80% resid u al p o re p re ssu re at fa ilu re , sp ec im en v o lum e w o u ld d ecrease by a b o u t 2 .5% as sh o w n in F igure 2, c au s in g the re la tiv e d e n sity to increase d u ring the tes t by a b o u t 2 0 p e rce n ta g e p o in ts to 45% . T h u s, a lth o u g h the in te n t w as to test a sp ec im en w ith a re la tiv e d e n sity o f a b o u t 25% , the re la tiv e d en sity g rad u a lly in cre ased to 45% due to m em b ran e c o m p lian ce . T he re su ltin g va lu e o f cyclic lo ad in g re s is tan ce is, th e re fo re , e rro n eo u sly high and u n c o n se rv a tiv e and d o es no t rep resen t actual in situ m ate ria l p ro p e rties .

2.5 Cyclic Loading Resistance

A rtific ia l in creases in sp ec im en d en sity serve to increase the cyclic lo ad in g re s is tan c e o f the soil. C o m p ariso n o f the cyclic lo ad in g re s is tan ce o f slu iced and u n slu iced 9 .5 -m m by 4 .7 5 -m m gravel at a re la tiv e d en sity o f 58% is sh o w n in F ig u re 3. It m ay be seen tha t the cyclic lo ad in g re s is tan c e o f the slu iced gravel is co n sid e ra b ly lo w e r than th a t fo r the u n slu iced gravel. In fact, the s lu iced sp ec im en s on ly d e v e lo p ed ab o u t 70% o f the cyclic load ing resis tan ce o f the u n slu ice d sp ec im en s. T hus, to accoun t for the e ffec ts o f m em b ran e c o m p lian ce in such sp ec im en s, on ly 70% o f the cyclic load ing resis tan ce d e te rm in e d by lab o ra to ry tes tin g shou ld be used as a basis fo r e v a lu a tin g p ro to type pe rfo rm an ce fo r these p a rticu la r so ils.

2 .6 Membrane Compliance Correction

T he resu lts o f a p p ro x im ate ly 100 ad d itio n a l tes ts on g ravels w ere used to d ev e lo p a c o rre c tio n fo r m em b ran e c o m p lian c e , sh o w n in F ig u re 4. T h is figure w as d e v e lo p ed fo r u n ifo rm ly g rad ed g ravels, iso tro p ica lly c o n so lid a ted to ab o u t 2 0 0 k P a in 71- m m and 3 0 5 -m m triax ia l tests , and fa ilin g in

ap p ro x im ate ly 10 to 30 stress cycles . T he c o rre c tio n sh o w n in F ig u re 4 fo r 7 1 -m m d iam e te r sp ee im en s rep resen ts an av erag e v a lu e d ev e lo p ed fro m d a ta p re sen ted by E v an s e t al (1992) and M a rtin e t al. (1978). T h e n o n c o m p lian t cyclic lo ad in g re s is tan ce m ay be d e te rm in e d by m u ltip ly in g the c o m p lian t, lab o ra to ry -d e te rm in e d cyclic lo ad in g re s is tan c e by the p ro p o se d c o rrec tio n facto r. It sh o u ld b e n o ted th a t u n ifo rm ly g raded g rav e lly so ils w ill e x p e rien c e s ig n ifican t m em b ran e co m p lian c e e ffec ts w h ile very w e ll-g ra d ed g ravelly so ils w ill e x p erien c e lesse r m em b ran e co m p lian ce effec ts . T h ere fo re , the re su lts o f liq u e fac tio n tests p e rfo rm e d on very w e ll-g ra d ed g rav e lly so ils tes ted in the triax ia l test w ill req u ire sm a lle r co rrec tio n s fo r m em b ran e c o m p lian ce th an th o se show n in the figure.

2.7 Correction During Testing

N ic h o lso n et al. (1993a , b) d e sc rib e d a co m p u te r- c o n tro lled po re f lu id v o lu m e in jec tio n and e x tra c tio n d ev ice to e lim in a te m em b ran e co m p lian c e e ffec ts d u rin g cyclic tes ting . E v an s & Z hou (u n p u b l.) d e v e lo p ed a s im ila r sy s tem w ith so m e im p ro v e m en ts to c o rre c t fo r m em b ran e e o m p lian c e in tes ts on g rav els; ty p ica l re su lts are show n in F ig u re 5. T h e tes ts sh o w n by the lo w er line w ere a c tiv e ly c o n tro lled by in je c tin g and ex tra c tin g p rec ise w a te r v o lu m e s to a cco u n t fo r m em b ran e c o m p lian ce v o lu m e c h an g e du rin g tes tin g T h is system w as a lso u sed to d e te rm in e the m em b ran e p e n e tra tio n and v o lu m e ch an g e da ta sh o w n in F ig u re 2. A d e sc rip tio n o f th is sy s tem and c o m p u te r co n tro l co d es w ill be p u b lish ed shortly . S u ch sys tem s p resen t a s im p le , v e rifiab le m eth o d fo r e lim in a tin g m em b ran e c o m p lian c e in triax ia l tes ts on g rav e lly soils.

Num ber o f Cycles Causing 5% DA Strain

F igure 3. C yclic lo ad in g re s is tan c e o f 9 .5 -m m by 4 .7 5 -m m gravel specimens. F ig u re 4. C o rre c tio n fo r m e m b ran e co m p lian ce .

93

Number of Cycles Causing 5% DA Strain

Figure 5. Results of computer-controlled correction for membrane compliance.

2.8 Freezing and Sampling Insitu

Many Japanese investigators have frozen and cored gravelly soil insitu as a means to collect high- quality, undisturbed samples. Hatanaka & Uchida (1995) report dynamic properties measured in triaxial tests for “undisturbed” (i.e.: frozen,sampled, thawed) versus reconstituted specimens. Reconstituted specimens yielded similar values as “undisturbed” specimens in some cases, but thawed “undisturbed” specimens more often indicated higher strength values and greater shear moduli than reconstituted specimens. This technique should continue to be explored and should prove to be a valuable means to calibrate developing field testing techniques.

3 EFFECT OF GRAVEL CONTENT

3.1 Inttoduction

Field evidence has shown that most liquefied gravelly soils are comprised of both sand and gravel (i.e.: sand-gravel composites - Evans & Harder 1993; Andrus et al. 1986; Harder & Seed 1986; Ishihara 1985; Youd et al. 1985; Wang 1984; Tamura & Lin 1983; and Coulter & Migliaccio 1966). However, most of the previous laboratory research focused on the effect of membrane compliance on the liquefaction of uniformly-graded gravel. Laboratory studies concerned specifically with the liquefaction behavior of sand-gravel composites are limited. Siddiqi (1984) found that two prototype soils with 2-in. (50-mm) diameter maximum particles and their finer matrix soil fractions passing the 1/2-in. (12-mm) sieve have

similar cyclic loading resistances if tested at the same relative density. Conversely, Wang (1984) and Haga (1984) found that the liquefaction resistance of sand-gravel composites increased with the inclusion of gravel particles. The conflicting findings indicate that our understanding on the liquefaction of sand-gravel composites is incomplete. Since large-scale triaxial testing equipment is not available in most laboratories, it would be desirable to test only the finer soil fraction using conventional size (2.8-in. (71-mm) diameter) triaxial equipment. In order to use this approach, it must be determined how cyclic behavior is affected by the inclusion of oversized gravel particles.

In order to quantify the effect of gravel content on the liquefaction resistance of sand-gravel composites, undrained cyclic triaxial tests were performed on sand-gravel composite specimens with gravel contents of 0%, 20%, 40%, and 60% as described by Evans & Zhou (1995). The gravel particles were subangular and granitic with a maximum particle size of 3/8-in. (10-mm). For the triaxial specimen diameter of 2.8-in. (71 mm) used in this study, the ratio of the specimen diameter to the maximum particle size is about 7.5.

3.2 Composite specimen density

Figure 6 shows the relationship between the maximum and minimum void ratio versus gravel content for the materials described above. The maximum and minimum void ratios decrease significantly with increasing gravel content from 0% to 60%. For gravel contents between 0% and 60%, it appears that gravel particles Ooat in the sand matrix; there is little contact between them. When the gravel content reaches a critical value (about 60%), gravel particles begin to form a continuous structural frame and the sand particles fill most of the gravel voids. With increasing gravel content above 60%, gravel-to-gravel contact increases and the sand does not completely fill the gravel voids. Thus, the density decreases with increasing gravel content beyond 60%.

3.3 Cyclic Response Of Composites

Undrained cyclic triaxial tests were performed on different sand-gravel composite specimen groups: 0%, 20%, 40%, and 60% gravel at 40% relative density; 40% gravel at 40% matrix relative density; and sand at 65% relative density. The first four groups were tested to establish a relationship between gravel content and cyclic behavior. The puipose of the last two groups will be described below.

94

G ravel C o n ten t, G C (% )

Figure 6 . M a x im u m and m in im u m vo id ra tio versus gravel co n ten t.

0.6

0.5u.2 0 .4

^ 0.3OJ

^ 0.2

U 0.1

reach in g 5% d o u b le am p litu d e stra in in ab o u t 10 stress cycles . It m ay be seen th a t the sp ec im en s w ith 0 % and 2 0 % gravel c o n te n t hav e s im ila r pore p re ssu re and ax ia l s tra in re sp o n se s and illu stra te c la ss ic liq u e fac tio n b e h av io r o f m o d era te ly loose sand . P o re p re ssu re d e v e lo p ed g rad u a lly b u t no ap p rec iab le stra in d ev e lo p ed un til a p o re p re ssu re ra tio , ry , o f a lm o st 1.0 w as reach ed . O nce in itia l

liq u e fac tio n o ccu rred , these sp ec im en s su d d en ly re ac h ed 5% d o u b le a m p litu d e stra in and then q u ick ly in creased to 1 0 % stra in in 1 to 2 add itio n al stress cycles . P o re p re ssu re ra tio v aries w ith in a re la tiv e ly n arro w range o f ab o u t 0 .7 to 1.0. T he sp ec im en s w ith 40% to 60% gravel co n ten t, h o w ev er, show very d iffe re n t p o re p re ssu re and ax ia l s tra in resp o n ses. T h ese sp e c im en s d ev e lo p ed po re p re ssu re and ax ia l s tra in m u ch m ore rap id ly in the early stages o f testing . In ab o u t 6 s tress cycles , a p eak po re p re ssu re ra tio o f ab o u t 0 .95 w as reach ed and a b o u t 2 .5% d o u b le am p litu d e stra in w as a ccu m u la ted . A fte r th e peak p o re p re ssu re d ev e lo p ed , ax ia l s tra in acc u m u la te d g rad u a lly ra th e r than ca tas tro p h ica lly . O n ly ab o u t 3% d o u b le am p litu d e stra in d e v e lo p ed in 1 to 2 a d d itio n a l stress cycles . T he in crease in ax ia l s tra in c au sed the sp ec im en s to d ila te and red u ced the p o re p re ssu re ra tio fro m a h igh va lue o f 0 .95 to a low v a lu e o f 0 .4 0 w ith in each stress cy cle , th e reb y m ain ta in in g sig n ifican t residual cyclic lo ad in g resis tan ce . T he po re p re ssu re and ax ia l s tra in re sp o n ses o f sp ec im en s w ith 40% and 60% gravel co n ten t illu stra te c la ss ic cyclic m o b ility b e h av io r o f dense sand.

N um ber o f C ycles C ausing 5% D A Strain

F igiiic 7. C yc lic lo ad in g re s is tan ce o f sand- gravel co m p o s ite sp ec im en s.

F igure 7 show s a p lo t o f cyclic stress ra tio versus n u m b er o f stress cycles req u ired to cau se 5% doub le am p litu d e stra in in san d -g rav e l c o m p o s ite s at 40% re la tive d en sity w ith g ravel co n te n ts o f 0 %, 2 0 %, 40% , and 60% . It m ay be seen in th is figu re that the liq u e fac tio n re s is tan ce o f the san d -g rav e l co m p o site sp ec im en s tes ted in th is s tudy in creases s ig n ifican tly w ith in cre as in g gravel c o n ten t. A t a c o m p o site re la tive d en sity o f 40 % , the cyclic stress ra tio cau sin g 5% d o u b le am p litu d e stra in in 10 cycles,

in c reased fro m 0 .15 to 0 .32 w ith

in creas in g g ravel co n te n t fro m 0 % to 60% .

T he axial stra in and p o re p re ssu re re sp o n ses for san d -g rav e l co m p o s ite sp ec im en s w ith various g ravel co n ten ts are sh o w n in F ig u res 8 and 9, re sp ec tiv e ly . R esu lts sh o w n are fo r spec im ens

5

0aUi -5

-1 0<

-15

5

0c*c5

-50013'x -1 0<

-15

— — rx n1

— — — 1 --

GC= 0 % and 2 0 %

12 15

G C = 4 0 % and 60%

0 3 6 9 12

N u m b er o f S tress C ycles

F igu re 8 . A x ia l stra in vs: n u m b er o f cycles.

15

95

12 151.00.2

ê 0.80<L>S 0.60 £ 0.40

Ph(U 0.20 O Oh 0.00

-------------j g ^ -

H H

GC-0% and 20%

0 3 6 9 12 15

Number o f Stress Cycles

Figure 9. Pore pressure vs. number of cycles.

Stress — strain hysteresis loops are shown in Figure 10 for sand-gravel composite specimens with 0%, 20%, 40%, and 60% gravel. Shown are curves for the fifth stress cycle for specimens reaching 5% double amplitude strain in about 1 0 stress eyeles. Once again, it may be seen that the 0% to 20% gravel composite specimens exhibit loose soil behavior, deforming at modest stress levels and maintaining a narrow hysteresis loop. However, 40% to 60% gravel composite specimens require higher stress levels and show significantly different behavior at the fifth stress cycle. Because composite specimens with 0 % to 60% gravel eontents have similar membrane compliance eharacteristics, the pronouneed effeet of gravel inclusions on cyclic loading resistance was not believed to be caused by membrane eomplianee. The significant strength increase may be attributed to the effeet of gravel inclusions on both the matrix density and the overall density of the composite materials as described in the following sections.

Figure 11 shows a plot of CSR^^ versus void ratio for the sand-gravel composite specimens tested in this study. It may be seen that increaseswith decreasing overall void ratio of the sand-gravel composite at 40% relative density. The lower the void ratio, the denser the packing of granular particles, increasing the strength of the composite. All the data presented in Figures 7 - 11 are for sand-gravel eomposite specimens at 40% composite relative density. When the gravel content is small (about 40% or less), gravel particles may be considered to float in a sand matrix. The volume

100 50

0

-50

Q -100

st/)C/3<DV_

o

>

GC=0% and 2 0 %

1f

Fifth Str(2SS Cycle

-2 -1

Axial Strain (%)Figure 10. Stress — strain hysteresis curves.

occupied by sand in the composite specimen is equal to the difference between total specimen volume and gravel particle volume. Thus, the average density of the matrix sand in sand-gravel composite specimens can be determined by dividing the mass of the matrix sand by the matrix volume. For composite specimens at 40% relative density, the relative density of the matrix sand is determined to be 40%, 34%, 29%, and less than zero percent, respectively, for gravel contents of 0 %, 2 0 %, 40%, and 60%. Thus, the test results shown in Figures 7 - 1 1 indicate that the cyclic loading resistance of sand-gravel composites increases with increasing gravel content even though the density of the matrix sand decreases. This implies that overall composite specimen characteristics rather than matrix characteristics alone may control the cyclic loading resistance of sand-gravel composites.

Void Ratio of Sand-Gravel Composite

Figure 11. CSR vs. void ratio.

96

= l/[G C /p + ( l - G C ) / p ] ,o r

p = p / [ l + G C ( l - p / G )]

( 1)

(2)

N u m b e r o f C ycles C ausing 5% D A Strain

F igure 12. C S R vs. n u m b er o f s tress cycles .

T he last test g roup w as p e rfo rm e d on sand sp ec im en s w ith no gravel. T h e re la tiv e d en sity o f the sand w as ad ju s ted to e x h ib it e sse n tia lly the sam e cyclic b e h av io r as the 4 0% re la tiv e density co m p o s ite w ith 4 0% gravel. T h e ra tio o f C S R

for 40% g ravel sp ec im en s ve rsu s sand spec im ens, bo th at 40% co m p o s ite re la tiv e density , w as d e te rm in ed to be abou t 1.65. T h u s, it w asd e te rm in ed tha t a sand w ith a re la tiv e d en sity o f 6 6 % (1.65 X 4 0 % ) w o u ld have a p p ro x im ate ly the sam e cyclic b e h av io r as the 4 0 % g rav el c o m p o s ite at 40% composite re la tiv e density . T he cyclic b eh av io r o f 65% re la tiv e d e n sity sand w as d e te rm in ed and is show in F ig u re 12 a lo n g w ith da ta from 40%) re la tiv e d en sity co m p o s ite sp ec im en s w ith 40%; gravel. It m ay be seen that the cyclic load ing re sis tan ce o f the dense sand (Dj- = 65% ) is

s im ila r to the lo o se r san d -g rav e l co m p o s ite (Dj-

cnmposiw = 40 % , D,. = 29% ) ev en tho u g h the

m atrix and co m p o s ite re la tiv e d en sitie s are m uch low er. T h ere fo re , it ap p ears that the cyclic load ing resis tan ce o f the san d -g rav e l co m p o s ite s tes ted in th is study m ay be e s tim a te d by tes tin g the m atrix sand a lone at a re p resen ta tiv e d en sity acco u n tin g for the effec t o f g ravel inc lusions.

3.4 Proposed Equivalent Fraction Density Model

From the test re su lts d esc rib ed , it w as fo u n d tha t the average m atrix d en sity d ecreases w ith in creas in g gravel co n ten t, w h ereas the o v e ra ll d en sity increases s ig n ifican tly . T h ere fo re , the net e ffec t o f gravel inc lusions on the cy clic lo ad in g re s is tan ce o f sand- g ravel c o m p o s ite d ep en d s on b o th the reduced m atrix d en sity and the g rea te r o v e ra ll c o m p o site density . A n eq u iv a len t frac tio n den sity w as su g g ested by E v an s & Z h o u (1995) to acco u n t fo r the e ffec t o f g ravel in c lu sio n s. T h e p ro p o sed e q u iv a len t frac tion d en sity is e x p ressed as fo llow s:

p = eq u iv a len t frac tio n d en sity , p = d en sity o f the

san d -g rav e l co m p o s ite , p = av erag e d en sity o f the

f in er frac tio n o r m atrix san d in the to ta l co m p o s ite , G C = g rav el c o n te n t e x p ressed as a dec im al, G =

•sg

sp ec ific g rav ity o f g rav el p a rtic le s , and p is in un its

o f M g/m ^ o r g /cm ^. T h e e q u iv a len t frac tio n d en sity ap p ears v a lid fo r the so ils tes ted in th is s tudy ra n g in g fro m 0% to 60% gravel. T h e p ro p o se d e q u iv a len t frac tio n d en sity w as tes ted fu rth er tes ted u sin g d a ta p re sen ted by S id d iq i (1 984) on L ake V alley and O ro v ille G rav e ls w ith goo d re su lts (E v an s & Z hou 1995).

4 S H E A R M O D U L U S A N D D A M P IN G

4.1 Introduction

D y n am ic so il re sp o n se is o f c o n sid e ra b le im p o rtan ce fo r lo ad in g s p ro d u ced by earth q u ak es , m ach in e fo u n d a tio n s , w ind , w av es , and im pacts . T w o o f the m o st im p o rta n t p a ram ete rs in any d y n am ic analysis in v o lv in g so ils are the shear m o d u lu s and the d am p in g ra tio . B oth the shear m o d u lu s , G , and d am p in g ra tio , D , are d e p en d en t on the cyclic shear stra in , y. T he sh ea r m o d u lu s is n o rm ally d e fin ed as the slo p e o f a secan t line w h ich co n n ec ts the ex trem e p o in ts on a h y ste res is loop at a g iven sh ea r stra in . A s the s tra in level in creases , the sh ea r m o d u lu s d ecreases. W h en cyclic triax ia l tests are p e rfo rm ed , a s im ila r h y ste res is loop w ill be fo rm ed by p lo ttin g d e v ia to r stress , Gd, versu s axial stra in , e. T he slope o f the secan t line c o n n ec tin g the e x tre m e p o in ts on th is h y ste res is loop is the e lastic m o d u lu s , E w here:

E - Gd / £

y = ( l + | i ) e

G = E / 2 ( I + | i )

(3)

(4)

(5)

\i is P o is s o n ’s ra tio and m ay be e s tim a te d as 0 .5 for sa tu ra ted , un d ra in ed sp ec im en s. T he d am p in g ratio , D , is a m easu re o f d iss ip a te d energy , AW , versus e la stic energy . We and m ay be c o m p u te d as:

D = AW / We (6 )

97

A W is p ro p o rtio n a l to the e n tire a rea e n c lo se d in sid e the h y ste res is lo o p , an d Wg is p ro p o rtio n a l to 47t tim es the tr ia n g u la r a rea b e lo w the loop .

A t very low sh ea r s tra in leve ls (less th an 10 "^%), w h ich are ty p ica l o f fo u n d a tio n v ib ra tio n s p ro b lem s, G and D re m a in e sse n tia lly co n stan t. H o w ev er, fo r e a rth q u ak e p ro b lem s, the s tra in lev e ls can be m u ch h ig h er and the v a ria tio n o f G and D w ith sh ear stra in m u st b e tak e n in to accoun t. F o r e x am p le , the co m p u te r p ro g ram S H A K E (S ch n ab e l e t al. 1972) em p lo y s the e q u iv a len t lin e a r p ro c ed u re in w h ich the sh ea r m o d u lu s an d d a m p in g ra tio in a so il layer are ite ra tiv e ly a d ju s te d so th a t th ey are c o m p a tib le w ith the sh ea r s tra in co m p u te d in the layer.

O v er the p as t 11 years, re su lts h av e b eco m e a v ailab le fro m sev era l in v es tig a tio n s w h ere cyclic sh ear tes ts w ere p e rfo rm e d on g rav e ls , and sh ear m o d u lu s and d am p in g va lues w ere co llec ted . T h ese da ta w ere d e sc rib e d and tab u la te d by R o llin s et al. (1998) and the re fe ren ces are c ited in T ab le 1.

T ab le 1. S u m m ary o f G rav e lly S o il R esearch ersP e rcen t

u s e s G rav elR eferen ce S y m b o l > 4 .75 m m

R o llin s e t al (1 998) SP 20SP 40G P 60

G oto , e t al. (19 9 4 ) G P 66S P 22

G oto , e t al. (1 992) G P 60G P 55

H atan ak a, e t al. (1988) G P 55G P 65

H atan ak a & U c h id a (1995) G P N AH ynes (1 988) G P 84K o k u sh o , e t al. (1994) G P 8 0 -90

SP 22K onno , e t al. (1 994) G P 55lid a , e t al. (1984) G W N A

Seed , e t al. (1986) G P 70G W 50G W 60

S h am o to et al (1 986) S W 15

Sh ibuya , et al. (1 990) S P 0G P 90

S ou to , et al. (1994) SP 44SW 44

Y asu d a & G W 83M a tsu m o to (1 994) SP 48

G W 52

Y a su d a & G W 75M a tsu m o to (1993) G P 65

F o r the m o st part, the so ils sh o w n in T ab le 1 are p o o rly -g rad e d c le an g rav e ls and g rav elly sands; h o w ev er, a few w e ll-g ra d ed g rav e ls are a lso p re sen t in the d a ta set. R e la tiv e d e n sitie s o f the g ravels tes ted ran g ed fro m 27 to 9 5% , m ax im u m gra in size v a ried fro m 10 to 150 m m , c o effic ie n ts o f u n ifo rm ity ran g ed fro m 1.33 to 75 , and the p e rcen tag e o f g ravel size p a rtic le s v a rie d fro m 20 to 90. T h e large ran g e in the b as ic m ech an ica l p ro p e rtie s sh o u ld fac ilita te an e v a lu a tio n o f the in flu en ce o f th ese p ro p e rtie s on G and D re la tio n sh ip s .

T es tin g w as ty p ica lly p e rfo rm e d u sing cyclic triax ia l tes t (C T X ) ce lls 3 00 m m in d iam e te r and 6 0 0 m m in heigh t; h o w ev er, tw o in v es tig a to rs a lso u sed large d iam e te r cyclic to rs io n a l s im p le shear tes ts (C T S S ), and so m e sm a lle r d iam e te r C T X tests w ere a lso pe rfo rm ed . M o st o f the d a ta p re sen te d is fo r re co n stitu te d lab o ra to ry sp ec im en s. H ow ev er, six o f the in v es tig a to rs u sed u n d is tu rb ed sp ec im en s that w ere o b ta in ed by freez in g the g ravel d e p o sit in- situ and co rin g a la rg e d iam e te r sam p le in the frozen g round . T he frozen sp ec im en s w ere la te r th aw ed p rio r to tes tin g in the lab o ra to ry . T h ese six in v es tig a to rs a lso tes ted re c o n s titu te d sp e c im en s so th a t c o m p a riso n s co u ld b e m ad e w ith the b e h av io r o f the u n d istu rb ed sp ec im en s.

4 .2 Shear Modulus

T he v a ria tio n o f sh ea r m o d u lu s w ith cyclic shear s tra in is cu s to m arily re p re se n ted by d iv id in g the sh ea r m od u lu s , G , at a g iv en stra in level by the m ax im u m shear m o d u lu s , , at very sm all

s tra in s (less than o r eq u al to 10"^%). T h is n o rm a liza tio n p ro cess m akes it p o ss ib le to co m p are the re la tio n sh ip s o b ta in ed by v a rio u s in v estig a to rs and it a lso fac ilita te s the use o f the re la tio n sh ip in p rac tice . If the sh ea r w ave v e lo c ity , U , is

m easu red in -situ , then G„^,^^can be c o m p u te d using

the equation ;

(7)

p eq u a ls the m ass density . T he v a lue o f can be

m u ltip lied by the G / cu rv e at any y value to

o b ta in the a p p ro p ria te G value .F ina lly , the n o rm aliza tio n p ro c ed u re a lso appears

to e lim in a te the e ffec ts o f sa m p lin g d is tu rb an c e on the re su lts o f sh ear m o d u lu s tes tin g . Several re sea rc h e rs rep o rt tha t G w as s ig n if ic a n tly h ig h er

98

for frozen undisturbed samples than for reconstituted samples having the same grain-size distribution and relative density. Nevertheless, the G / G ^ versus y relationships were almost the same for the undisturbed and reconstituted samples (Goto, et al. 1992; Hatanaka, et al. 1988; Kokusho, et al. 1994; Konno, et al. 1994).

Normalized shear modulus, G / G^^ , versus y curves are a basic input parameter in the computer program SHAKE and other computer programs which employ the equivalent linear method. Over 850 data points for G / G ^ versus y data points complied for gravel are shown in Figure 13. The range of data for gravels proposed by Seed & Idriss (1986) is also shown in Figure 13 for comparison purposes. It may be seen that a large percentage of the data points fall outside the range of data reported for gravels by Seed & Idriss although the mean curve from this paper falls within their range.

A best-fit hyperbolic curve for all the data points is shown in Figure 13. The equation for the curve is:

G/ G,„ax = 1 / [ 1 + 2 0 y ( l + (8)

y is cyclic shear strain in percent. This best-fit curve is shown along with one standard deviation bounds. To explain some of the scatter in the data, extensive analyses were performed on all the available data to determine the influence of maximum grain size, relative density, fines content, percentage of gravel, and confining pressure on the shape of the G / G ^ curve. Although these factors

are generally considered to have some influence on Gmax > none of the analyses performed in this study had more than a minor effect on the shape of the G/Gn,ax curve with the exception of confining pressure. The results from the negative analyses can be made available, but are not presented in this paper.

Since the G / relationships for gravels appears to vary little from those relationships for sand, additional tests were performed by Rollins et al. (1998) to determine the effect of gravel content on the shear modulus of gravelly sands and sandy gravels. CTX test were performed on sand specimens containing 0, 20, 40, and 60 percent gravel. All test specimens were compacted to 40% relative density, thus the only variable in the tests was gravel content. G / G ^ vs. y relationships are shown in Figure 14. It may be seen that there is actually a slight increase in normalized shear modulus with increasing gravel content, thus pushing the 60% gravel curve farther in to the sand range reported by Seed and Idriss (1970) than are the 0% to 40% gravel specimens. These data for G / G ^ (for 0% to 60% gravel) plot right on the boundary between sand and gravel as reported by Seed et al. (1986) except at high shear strain values.

4.3 Damping

The D versus y data points for gravels are shown in Figure 15. Not all investigators in Table 1 reported information on damping ratios. The range of data identified by Seed et al., (1986) for sands

Cyclic Shear Strain (%)

Figure 13. Normallized shear modulus vs. shear strain for gravels.

9 9

reason, the equation should not be used above 1 % strain or the results could be erroneous. Most investigators assume that the D versus y curve flattens considerably at higher strain levels.

As reported previously, extensive analyses were performed on the available data to determine the effect of other variables such as relative density, gravel percentage, fines content, sample preparation method, and test type. These analyses are not presented here since no appreciable effect on damping ratio was observed.

Shear Strain, y (%)

Figure 14. Normallized shear modulus versus shear strain for composite specimens.

and gravels is also shown in Figure 15 for comparison. Although most of the data points fall within the range identified by Seed et al., (1986), they tend to be located near the low end of the range, particularly at smaller strain levels (< 1 0 '^%). Stokoe et al., (1986) also found that the damping ratio for gravels was closer to the lower bound curve based on cyclic testing of sands.

A best-fit hyperbolic curve for all the data points is shown in Figure 15 The equation for the curve is:

5 PRESSURE CHAMBER TESTING

Evans & Koester (unpubl.) have performed an investigation on gravel specimens in a large-scale pressure chamber. Sand and gravel specimens at 1 and 3 atmosphere overburden pressure were probed with different size cone penetrometers, shear wave velocity was measured, and SPT tests were performed. These data are being reduced and compared. It is hoped that once these data are available, they will help in the interpretation of SPT N-value and cone penetrometer data gathered from gravel deposits insitu. It is also hoped that these data may be used for further development and understanding of larger penetration tests for use in gravelly soils.

D = 0 .8 + 18(1+0.15 (9) CONCLUSIONS

D is the damping ratio in percent and y is the cyclic shear strain in percent. This equation provides a reasonable fit to the data for shear strains less than 1 %; however, there are very few data points to constrain the curve beyond this strain level. For this

0.0001 0.001 0.01 0.1

Cyclic Shear Strain (%)

Figure 15. Damping ratio vs. shear strain.

Many researchers have made great progress toward evaluating liquefaction potential and determining shear moduli and damping ratios for gravelly soils, both through field and laboratory investigations. The greatest future gains are to be made in improved field methods for determining insitu properties, and perhaps in advanced modelling techniques that allow us to more accurately predict behavior.

REFERENCES

Andrus, R.D., Youd, T.L., and Carter, R.R. (1986). "Geotechnical evaluation of a liquefaction induced lateral spread. Thousand Springs Valley, Idaho." Proc. of the 22nd Annual Symp. on Engrg. Geology and Soils Engrg., Idaho Dept, of Transportation, Boise, Idaho.

Banerjee, N.G., Seed, H.B., Chan, C.K. (1979). "Cyclic Behavior of Dense Coarse-Grained Materials in Relation to the Seismic Stability of Dams," EERC Report No. UCB/EERC-79/13, Univ. of Calif., Berkeley.

100

Castro, G. (1975), "Liquefaction and Cyclic Mobility of Saturated Sands," J. of the Geotech. Engrg. Div. (JGED), ASCE, 101(6).

Coulter, H.W., and Migliaccio, R.R. (1966). "Effect of earthquake of March 27, 1964 at Valdez, Alaska." U.S. Geol. Survey Professional Paper 542-C, U.S. Dept, of the Interior, Washington, D.C.

Rollins, Kyle M., Evans, Mark D., Diehl, N., and Daily, W., (1998), “Shear Modulus and Damping Relationships for Gravels”, Journal of Geotechnical Engineering, ASCE, May, 1998.

Evans, M.D. and Zhou, S., (1995), “Liquefaction of Sand-Gravel Composites”, Journal of Geotechnical Engineering, ASCE, vol. 121, no. 3, March, 1995.

Evans, M.D. and Fragaszy, R., (1995) editors. Static and Dynamic Properties of Gravelly Soils, ASCE Geotechnical Special Publication, Geotechnical Engineering Div. of ASCE, NY

Evans, M.D. and Zhou, S., (1994), “Cyclic Behavior of Gravelly Soil,” ASCE Geotechnical Special Publication No. 44, Ground Eailures Under Seismic Conditions, Geotechnical Engineering Division of ASCE, NY, 1994.

Evans, M.D. and Harder, L.F., (1993), "Evaluating Liquefaction Potential of Gravelly Soil in Dams", Geotechnical Special Publication No. 35, Geotechnical Practice in Dam Rehabilitation, Geotechnical Engineering Division of ASCE, N .Y .,N Y , 1993.

Evans, Mark D., Seed, H.B. and Seed, R.B., (1992), "Membrane Compliance and Liquefaction of Sluiced Gravel Specimens", Journal of Geotechnical Engineering, ASCE, Vol. 118, No. 6 , June 1992.

Evans, Mark D., (1992), "Density Changes During Undrained Loading - Membrane Compliance", Journal of Geotechnical Engineering, ASCE, Vol. 118, No. 12, December 1992.

Fragaszy, R.J., Su, J., Siddiqi, F. H., and Ho, C. L. (1992). “Modeling Strength of Sandy Gravel”, Journal of Geotechnical Engineering, ASCE, Vol. 118, No. 6 .

Fragaszy, R.J., Su, W., and Siddiqi, F. H. (1990). “Effects of Oversized Particles on the Density of Clean Granular Soils”, Geotechnical Testing Journal, GTJODJ, vol. 13, No. 2, p l06 - 114.

Goto, S., S. Nishio, and Y. Yoshimi, (1994), “Dynamic properties of gravels sampled by ground freezing.” Ground Failures Under Seismic Conditions, Geotechnical Special Publication No. 44, ASCE: 141-157.

Goto, S., Y. Suzuki, and H. Oh-Oka. (1992), “Mechanical properties of undisturbed Tone River gravel obtained by in-situ freezing method.” Soils and Foundations, JSMFE, 32(3): 15-25.

Haga, K. (1984). "Shaking Table Tests For Liquefaction Of Gravel-Containing Sand." Bachelor Thesis, Dept, of Civil Engrg., Univ. of Tokyo, (in Japanese).

Harder, L. F. (1992), “Investigation of Mackay Dam Following the 1983 Borah Peak Earthquake,” Proc. of Specialty Conf.: Stability andPerformance of Slopes-II, ASCE, Berkeley, California, June 28 to July 1, 1992.

Hatanaka and Uchida (1995), Effects of Test Methods on the Cyclic Deformation Characteristics of High Quality Undisturbed Gravel Specimens”, Static and Dynamic Properties of Gravelly Soils, ASCE Geotechnical Special Publication, Geotechnical Engineering Division of ASCE, NY, 1995.

Hatanaka, M., Y. Suzuki, T. Kawasaki, and M. Endo, (1988), “Cyclic Undrained Shear Properties of High Quality Undisturbed Tokyo Gravel.” Soils and Foundations, JSMFE, 28(4): 57-68.

Hynes, M.E. (1988). "Pore Pressure Generation Characteristics Of Gravel Under Undrained Cyclic Loading." Ph.D. Dissertation, Univ. of California, Berkeley, Calif.

Hynes, M.E., Whal, R.E., Donaghe, R.T., and Tsuchida, T. (1988) "Seismic Stability Evaluation of Folsom Dam and Reservoir Project: Report 4, Mormon Island Auxiliary Dam-Phase I," US Army Engineer Waterways Experiment Station Technical Report GL-87-14, Vicksburg, Mississippi.

Ishihara, K. (1985). "Stability Of Natural Deposits During Earthquakes." Proc. of the 11th Int. Conf on Soil Mechanics and Eoundation Engrg., Vol. I, Rotterdam, Netherlands.

Iwasaki, T., F. Tatsuoka, and Y. Takagi, (1976), “Dynamic shear deformation properties of sand for wide strain range.” Report ^ Civ. Engrg. Inst., 1085, Ministry of Construction, Tokyo..

Kokusho, T, (1980), “Cyclic triaxial test of dynamic soil properties for wide strain range.” Soils and Foundations, JSMFE, 20(2): 45-60

Kokusho, T., and Y. Tanaka, (1994) “Dynamic properties of gravel layers investigated by in-situ freezing sampling.” Ground Failures Under Seismic Conditions, Geotechnical Special Publication No. 44, ASCE: 121-140.

Konno, T., M. Hatanaka, K. Ishihara, Y. Ibe, and S. lizuka, (1994) “Gravelly soil properties evaluation by large scale in-situ cyclic shear tests.” Ground Failures Under Seismic Conditions, Geotechnical Special Publication No. 44, ASCE: 177-200

Martin, G.R., Finn, W.O.L., and Seed, H.B. (1978) "Effects of System Compliance on Liquefaction Tests," J. of Geotech. Engrg., ASCE, 104(4).

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Mulilis, J.P., Seed, H.B., Chan, C.K., Mitchell, J.K., and Arulanandan, K. (1977) "Effects of Sample Preparation on Sand Liquefaction," J. of Geotech. Engrg., ASCE, 103(2).

Nicholson, P.G., Seed, R.B., and Anwar, H.A. (1993a). “Elimination of Membrane Compliance in Undrained Triaxial Testing. I. Measurement and Evaluation”, Canadian Geotechnical Journal, vol. 30, p 727 - 738.

Nicholson, P.G., Seed, R.B., and Anwar, H.A. (1993b). “Elimination of MembraneCompliance in Undrained Triaxial Testing. II. Mitigation by Injection Compensation”, Canadian Geotechnical Journal, vol. 30

Schnabel, P. B., J. Lysmer, and H. B. Seed, (1972), “SHAKE: A computer program for earthquake response analysis of horizontally layered sites.” Report N o. EERC 72-12, Earthquake Engineering Research Center, University of California, Berkeley.

Seed, H. B. (1979), “Soil Liquefaction and Cyclic Mobility Evaluation for Level Ground During Earthquakes,” Journal of the Geotechnical Engineering Division, ASCE, Vol. 105, No. GT2, February, 1979.

Seed, H. B. (1983), “Earthquake-Resistant Design of Earth Dams,” Proc. of a Symposium on Seismic Design of Embankments and Caverns, ASCE, Philadelphia, Pennsylvania, May 6-10, 1983.

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Seed, H. B., Lee, K. L., Idriss, I.. M.. and Makdisi, F. (1973), “Analysis of Slides in the San Fernando Dams during the Earthquake of February 9, 1971,” Report No. EERC 73-2, Earthquake Engineering Research Center, University of California, Berkeley, June.

Seed, H. B., R. T. Wong, I. M. Idriss, and K. Tokimatsu, (1986), “Moduli and damping factors for dynamic analyses of cohesionless soils.” .” J. Geotech. Engrg., ASCE, 112(1): 1016-1032.

Seed, H.B., and Idriss, I.M. (1982) Ground motions and Soil Liquefaction During Earthquakes, monograph series, EERI, Berkeley, Calif..

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Shibuya, S., X. J. Kong, and F. Tatsuoka, (1990), “Deformation characteristics of gravels subjected to monotonic and cyclic loadings.” Proc. 8 th Japan Earthquake Engineering Symp. 1: 771- 776.

Siddiqi, F.H. (1984). "Strength evaluation of cohesionless soils with oversized particles", Ph.D. Dissertation, Univ. of California, Davis.

Stokoe, K. H., J. Kim, D. W. Sykora, R. S. Ladd, and R. Dobry, (1986),“Field and laboratory investigation of three sands subjected to the 1979 Imperial Valley earthquake.” Proc. 8 th European Conf. on Earthquake Engrg., Lisbon, Portugal. 2(5.2): 57-64

Tamura, C. and Lin, G. (1983), "Damage to Dams During Earthquakes in China and Japan," Report of Japan-China Cooperative Research on Engineering Lessons from Recent Chinese Earthquakes Including the 1976 Tangshan Earthquake (Part I), Edited by Tamura, C., Katayama, T., and Tatsuoka, F., University of Tokyo, November, 1983.

Tokimatsu, K and Nakamura, K (1986), "A Liquefaction Test Without Membrane Penetration Effects, Soils and Foundations, Vol. 26, No. 4, 1986.

Wahl, R. E., Crawforth, Stanley G., Hynes, M. E., Comes, Gregory D., and Yule, Donald E. (1988), “Seismic Stability Evaluation of Folsom Dam and Reservoir Project, Report 8 , Mormon Island Auxiliary Dam, Phase II,” Technical Report GL- 87-14, Waterways Experiment Station, U.S. Army Corps of Engineers.

Wang, W. (1984). "Earthquake damage to earth and Levees in relation to soil liquefaction." Proc. of the bit. Conf. on Case Histories on Geotech. Engrg., Vol.l, p51I-52], Univ. of Missouri- Rolla, Rolla.

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3 Factors affecting liquefaction susceptibility


Fundamental factors affecting liquefaction susceptibility of sands

Y.RVaid & S.SivathayalanUniversity of British Columbia, Vancouver, B.C., Canada

ABSTRACT;

Fundamental factors that influence liquefaction susceptibility of saturated sands are considered, from the background of comprehensive experimental evidence from test results on reconstituted specimens. It is shown that at identical initial void ratio-effective stress state, undrained (constant volume) behaviour is profoundly affected by the fabric that ensues upon sample reconstitution. Water pluviation simulates in-situ behaviour closely. Very loose moist tamped states are unlikely to be accessible to in-situ sands. The susceptibility to liquefaction, both static and cyclic, depends not only on the initial state variables, but is also strongly affected by the effective stress path during undrained shear. On post cyclic static loading, the virgin strain softening sand is strain softening no more, but deforms with a continually increasing stiffness if the cyclic loading terminates with a residual zero effective stress. Very small expansive volumetric strains due to pore pressure gradients during short duration loading, or after its cessation could transform a sand into a strain softening type, which otherwise would be dilative if completely undrained.

1 INTRODUCTION

Most o f our understanding o f fundamental mechanical behaviour o f soils has been derived from controlled laboratory studies. Laboratory tests measure the element properties. This requires tests on several homogeneous (uniform) test specimens which can be replicated. These requirements have promoted the use of reeonstituted, in preference to undisturbed, soils specimens, for fundamental characterization of soil behaviour. Uniform and replicable clay specimens are conveniently obtained by trimming from a large block o f clay consolidated from an initial slurry state. Since such a procedure is not possible for sands, each test specimen must be individually prepared. This makes ensuring uniformity and replication of specimens considerably more difficult.

The term liquefaction and liquefaction failure encompass all phenomena involving excessive deformations o f saturated cohesionless soils (NRC 1985). In laboratory tests liquefaction under static loading implies a strain softening type of undrained (constant volume) response (Fig. 1), that follows a peak stress mobilized at small strains (generally < 1%). This results in unlimited or limited ‘unidirectional’ flow deformation. Under cyclic undrained loading, liquefaction manifests itself

either as a strain softening response during a loading cycle, much in the same manner as under static loading, or due to the development o f cyclic mobility (Fig. 2). Cyclic mobility becomes the cause for the accumulation of large cyclic strains when the sand experiences excursions through states o f transient zero effective stress, a '3 = 0. The first time occurrence o f this a '3 = 0 condition was c alled in itia l liq u e fac tio n (S e e d 1979). At the conclusion o f cyclic loading following liquefaction, the residual stress state in the sand is normally assumed to correspond to a '3 = 0 , but it need not be necessarily so, depending upon the strain amplitude specified that is deemed to be liquefaction.

This paper deals with fundamental factors that affect liquefaction susceptibility o f saturated sands, including any experimental aspects which may render the measured response differ from its true behaviour. Four categories o f factors are considered which are related to: (i) the ability of the testing device, loading method and data acquisition system to measure true element behaviour, (ii) the effect of initial state variables, which are comprised of void ratio, effective stress state, the sand fabric and any strain history prior to undrained loading, (iii) the influence of effective stress path during loading. This embodies not only increments in stress components, but also any rotation o f principal

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Figure 1. Strain softening and dilative strain hardening response in static undrained loading.

I—Steady State ■ j£(í ^

CNx :

b

—

Figure 2. Liquefaction due to cyclic loading, (a) strain softening to steady state, (b) strain softening to quasi steady state followed by cyclic mobility and (c) cyclic mobility.

stresses (iv) the effect o f any departure from the undrained (constant volume) deformationassumption, as might occur in a given boundary value problem, as a result o f flow (and hence volume changes), due to the spatial variation of pore pressures generated either during the loading duration, or their subsequent dissipation after the loading ceases.

Experimental results from comprehensive fundamental studies for over 25 years, at the University o f British Columbia (UBC),

supplemented by other studies reported in the literature, are presented to answer the various issues raised in the previous paragraph. In experimentation at UBC, conscientious attention to basic experimental requirements such as minimizing effect o f frictional end restraint in the testing apparatus, specimen uniformity, the type of loading system together with high speed, high resolution data acquisition system, have always been emphasized in order to generate data with utmost confidence. Stresses are measured with a resolution o f better than 0.25 kPa and strains lO" For reasons outlined above most o f these studies were performed on reconstituted specimens. But test results are also presented on water deposited undisturbed (in-situ frozen) sand and its counterpart reconstituted by water pluviation (WP) to an identical initial state. This is intended to seek similarities in the response o f undisturbed and reconstituted initial fabrics. Furthermore, initial states accessible to in-situ hydraulic fill sands are examined from two sites, where undisturbed samples were retrieved by in-situ ground freezing, and compared to the states that can be simulated by laboratory reconstitution methods. In keeping with the spirit o f the workshop, the treatment o f the subject is restricted to the mechanics and physics of the liquefaction phenomenon. Hopefully this basic understanding will inspire more rational methods for analysis and design. Because o f space limitations, only the behaviour o f relatively clean sands is covered in this paper.

2 INFLUENCE OF SAMPLE RECONSTITUTION METHOD

Fundamental studies o f sand behaviour require laboratory tests on homogeneous specimens under uniform states o f stress and strain. In addition, the specimen reconstitution method should closely simulate the mode o f deposition o f the soil being modelled, if the results are to have meaningful application to in-situ soils. Reconstitution by WP has been considered to mimic closely the fabric o f fluvial and hydraulic fill sands (Oda et al. 1978). Laboratory studies on WP sands, thus provide a convenient means for a systematic study o f the undrained behaviour o f in situ sands. A large body o f research at UBC and elsewhere has been carried out on WP sands. Air pluviation (AP) and moist tamping (MT) have also been used by many researchers for sand sample reconstitution.

Undrained direct simple shear (DSS) response o f Syncrude sand (D 50 = 0.2 mm) reconstituted by WP, AP and MT to identical initial states is compared in Figure 3 (Vaid et al. 1995). Profound differences may be noted in the behaviour depending on the method o f reconstitution, which

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Shear Strain Y , %

Figure 3. Effect o f specimen reconstitution method on undrained simple shear response (after Vaid et al. 1995).

controls the ensuing fabric. MT fabric results in a very strain softening response, the strength ultimately reaching the steady state (SS). AP specimen is also strain softening, but to a milder extent, demonstrating a quasi steady state (QSS) type of response. WP specimen, in contrast, does not even strain soften and behaves in a strain hardening (dilative) manner. Comparison between the behaviour of WP and MT Fraser River sand (D50 = 0.3mm) in triaxial compression (TC) and triaxial extension (TE), illustrated in Fig. 4 also confirms similar differences (Vaid et al. 1998). DSS response of air and water pluviated Fraser River sand (Fig. 5) further shows differences similar to those observed for Syncrude sand (Fig.3).

The sand fabric that ensues on MT was described by Casagrande (1975) as honeycomb, and appears to be potentially collapsible and hence prone to liquefaction. Evidence o f such collapse, resulting in large decrease in void ratio during mere saturation of the specimens prior to undrained testing, has been reported by several researchers (Sladen et al. 1985, Chang et al. 1981, Marcuson & Gilbert 1972). Modelling water deposited in-situ sands by their MT equivalent may therefore unjustifiably label them as being liquefiable, while in reality they may not be.

Uniformity of reconstituted specimens is generally tacitly assumed, and only a few researchers (Castro 1969, Emery et al. 1973, Mullilis et al. 1977, Vaid & Negussey 1988) have sought its direct confirmation. The profile of void ratio with depth of a typical loose MT untested

-10 0 10

Axial strain, s (%)

Figure 4. Influence of specimen reconstitution technique on undrained triaxial response.

Figure 5. Influence of specimen reconstitution method on undrained simple shear response.

triaxial specimen o f Fraser River sand is shown in Figure 6(b). After saturation and consolidation, the specimen was solidified using the gelatin technique (Emery et al. 1973), and cut up in a number of horizontal slices, after peeling the rubber membrane away. The void ratio o f each slice was then computed after drying the solids in each slice.

Serious nonuniformity o f void ratio in MT specimens may be noted over the specimen height. The local relative density differs by as much as ± 10% from the average value for the entire specimen, if considered uniform. Similar serious nonuniformities have been reported by Castro

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(1969), especially while reconstituting specimens with low density, which are most prone to liquefaction (Fig. 6c). The WP specimen, however, is much closer to being uniform with height (Fig. 6a) as demonstrated by (Vaid & Negussey 1988), where the maximum local deviation in relative density is only ± 2% to 3% from the overall average value, which meets the requirements of an element test closely, unlike MT specimens.

evidence in support that water deposited in-situ sands are unlikely to exist in states looser than achievable by loosest deposition by WP. Similar evidence was found for another sand by Vaid & Pillai (1992). States looser than these are often simulated by MT (see Fig. 7), but their relevance to in-situ sands seems questionable.

4 BEHAVIOUR OF UNDISTURBED SANDS

Bottom

10 20 30 20

Relative Density, %

30

Figure 6. Direct assessment o f uniformity of reconstituted speeimens, (a) water pluviated Ottawa sand, (b) moist tamped Fraser River sand and (c) moist tamped sand (after Castro 1969).

3 ACCESSIBLE IN-SITU STATES

In-situ void ratio and effective stress state o f two hydraulic fill tailings sands at the Canadian Liquefaction Experiment (CANLEX) research sites (Wride & Robertson, 1997), where undisturbed samples were retrieved by in-situ ground freezing are illustrated in Figure 7. Void ratios were directly computed from the ice content o f the test specimens trimmed from the frozen cores. The compressibility relationships for their loosest WP states (assuming estimated Ko = 0.5) are also illustrated for comparison. For both sands, virtually all in-situ states may be seen to lie either below or near the WP compressibility relationships. The few data points that fall above these lines can be regarded as a normal scatter expected in experimentation. Figure 7 could thus be viewed as

In-situ ground freezing has been regarded as a means of retrieving undisturbed samples of saturated sands. Such specimens were retrieved by in-situ ground freezing from three CANLEX sites and tested in the laboratory. Thawing o f the frozen triaxial specimens was carried out by the method described in detail in Vaid et al. (1996). It essentially consisted o f allowing thawing to proceed with access to free water at both ends o f the specimen, which allows for compensation of the volume deficiency caused by the pore ice melting into water. Thawing was done under a small effective stress o f about 20 kPa. Since this stress was smaller than the in-situ stress at which the saturated ground was frozen, a small axial rebound occurred during thaw (Fig. 8). This may be regarded as evidence in support of the good quality of the undisturbed specimens possible by the in-situ ground freezing technique. The maximum void ratio decrease o f these specimens after restoration o f the in-situ effective stresses rarely exceeded 0.005. These procedures, with the objective o f minimizing volume changes of specimens during thawing, were developed at UBC during a comprehensive program o f triaxial and simple shear-static and cyclic-undrained tests for seismic assessment o f the stability of sands in the foundation o f Duncan Dam in British Columbia (BC Hydro 1993).

The restoration o f in-situ effective stress after thawing should result in no net change in void ratio in an ideal undisturbed saturated specimen. Evidence showing that this can be achieved has been reported for initially hydrostatically consolidated sand (e.g. Singh et al. 1982). This, however, is normally not possible, as in-situ stress state is often non-hydrostatic. Therefore unloading of the in-situ shear stresses will occur (and hence skeleton deformations) once the sample is removed from the ground, much in the same manner as does occur while sampling clays (Ladd & Lambe 1963). Sustaining in-situ shear stresses in the retrieved sample would require pore ice in the frozen sample to carry large shear stresses, which it may not due to its propensity to creep under shear. Reinstatement o f the in-situ effective stresses after thawing will therefore' result in some densification

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Figure 7. In situ states of undisturbed sand in comparison to states attainable by laboratory reconstitution methods.

0.50

0.25

0.00

-0.25

-0.50

] During Thaw

Total until EoCÀ

(Dû

. IV/1A

(Ub "S

f f u M T ^LJ

L (Dû.s ^

Uu- (Ug ‘X.

Undisturbed Massey sand ___1____1____ 1____1____ 1____ 1__

T

0.88 0.96 1.0

Figure 8. Height changes during thaw and consolidation o f undisturbed in situ frozen Massey sand.

because of the inelasticity in soil deformations. Alternative suggestions made favouring thawing

Shear strain Y, %

Figure 9(a). Comparison o f undrained simple shear response o f undisturbed and water pluviated sands at essentially identical initial states.

No of cycles to liquefaction (y > 3.75 %)

Figure 9(b) Comparison o f cyclic simple shear resistance o f undisturbed and equivalent water pluviated sands.

under full applied in-situ stresses (Hofmann et al. 1995, Konrad & Pouliet 1997) would result in serious stress nonuniformities in the specimens, that continuously change spatially as the thawing front advances, triggering unwanted void ratio changes (Wu & Chang 1982, Sivathayalan & Vaid 1998a). Also, the assumption o f zero radial strain during thawing is questionable, because a flexible cylindrical boundary o f the specimen carmot be a specified stress and displacement boundary simultaneously. Furthermore, Ko in the ground is generally not known, and any assumed value other than the actual is bound to cause additional

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unwanted alterations o f the in-situ void ratio.After the conclusion of undrained tests on the

undisturbed specimens, some o f their corresponding reconstituted counterparts were reformed by loosest WP using the entire solids retrieved. The specimens were densified, if needed, so that the void ratio after consolidation to the in-situ stresses matched closely that o f the undisturbed specimens.

Figure 9(a) compares static undrained simple shear response o f typical undisturbed sand specimens and their WP counterparts from the Massey and Kidd sites at identical initial states. The undisturbed sands and their reconstituted counterparts may be seen to exhibit similar type of undrained response. Similar comparative data is shown in Figure 9(b) for the cyclic resistance of Massey sand under cyclic DSS (Vaid et al. 1998). This implies that WP closely replicates the fabric of water deposited in-situ sands, enabling substitution of expensive undisturbed samples with reconstituted equivalents for confident material characterization.

5 EFFECT OF LOADING & DATA RECORDING TECHNIQUE

A non-inertial load controlled loading system may seriously modify the true strain softening behaviour of the sand, depending on the degree o f apparatus - specimen interaction, and the frequency response of the data recording device. This has been experimentally demonstrated in Figure 10 (Chern 1985), which illustrates comparative undrained strain softening response o f essentially identical specimens of Ottawa sand (D 50 0.4 mm). Whilethe response under constant rate o f strain (no inertia effects) and the dead weight inertial loading system recorded by an oscillographic recorder are essentially identical, the non-inertial pneumatic stress controlled loading recorded by a low frequency responding strip chart recorder yields very different measured behaviour. The measured response by the non-inertial loading system may be further modified by the rate at which the air regulator can bleed back the pressure, when reduction is required in axial load following the peak stress state. Only an inertial system (like the dead weight loading used by Castro 1969) can capture the true strain softening response o f sand under stress controlled loading. The stress decrease during the strain softening after the peak then occurs automatically, on account o f the increasing inertia force o f the accelerating dead mass, triggered by the deforming specimen. If the true material response is o f the steady state type (deformation at constant stress and volume after

Figure 10. Influence o f loading and data recording systems on measured stress-strain response.

strain softening), the mass will accelerate until a terminal constant acceleration is reached. This acceleration yields an inertia force that equals the reduction in vertical force required after the peak to the steady state conditions. Contrary to the notion that steady state deformation in an inertial loading system occurs at constant velocity, advocated by the proponents of the steady state concepts, it in fact occurs at constant acceleration.

A direct measure of the true load experienced by the specimen in the inertial loading system can only be made by an internal load transducer, located at the bottom pedestal. This indeed was done by Castro (1969). However, if the true sand response is o f the QSS type, the load recorded before and until the minimum deviator stress dictated by the QSS value will again be reliable, but not after QSS, due to the impact action on account of the increasing resistance o f the material with further strain (Fig. 10). No such inertial problems arise when deformation is imposed under constant rate of strain (or velocity).

6 STATIC UNDRAINED RESPONSE

Unless specified otherwise, the behaviour o f WP sands only is discussed. The initial fabric therefore, is no longer a state variable.

Effect of initial state variables

These are now comprised of void ratio ec, confining stress G3c and shear stress, conveniently characterized by Kc = in a triaxial test. The

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Figure 11. Influence o f initial state variables on undrained triaxial compression response of loosest deposited Brenda Mine tailings sand

effect of these variables on triaxial compression behaviour of a loosest deposited tailings sand (D50

= 0.4mm) is illustrated in Figure 11. It demonstrates that all state variables collectively influence the resulting response. Relative density, a parameter which is defined at close to zero stress level, is not a variable independent of the applied stress level. This makes (i) certain void ratio states not even accessible to a range o f stress levels, (ii) even dense relative density states at higher a'sc can be prone to strain softening, and (iii) increase in confining pressure at constant Kc, or increase in Kc at constant confining stress promotes strain softening, despite substantial increase in density. Similar behaviour manifested by other sands has also been reported in the literature (e.g. Bishop 1966, Vaid& Thomas 1995).

Loading direction and stress system dependence

Loading direction during shear can be conveniently specified by a, the inclination of cj] to the specim.en axis (deposition direction), and G2 under multiaxial stresses by the parameter, b = (a 2 -a 3)/(a i-a 3). Thus for TC, b == 0, a = 0 and for TE, b==l, a=90°.

TC and TE response o f loosest deposited Fraser River sand over a range o f confining stresses is shown in Figure 12. TC response may be noted to be dilative, even for the loosest accessible state. In contrast, TE response is strain softening over a range of initial states. This direction dependence of behaviour has also been reported by other researchers (e.g. Bishop 1971, Elanzawa 1980, Miura & Toki 1982, Kuerbis & Vaid 1989, Riemer & Seed 1997). At a given initial state, a gradual transformation of the response of Fraser River sand occurs from dilative to strain softening, reflecting the sole influence o f a as it increases from zero to 90° at constant b = 0 (Fig. 13) (Uthayakumar and Vaid 1998). With increase in b at constant a = 90° the strain softening response

Axial strain, z (%)

Figure 12. Undrained anisotropy of sand reflected in triaxial compression and extension.

Figure 13. Dependence o f undrained response on the direction of major principal stress and the relative magnitude o f the intermediate principal stress.

aggravates as b increases. Other researchers (Symes et al. 1985, Shibuya & Hight 1987) also report similar results, as to the influence of a on undrained behaviour. The direction dependent undrained sands is an expression of its inherent anisotropy that ensues on WP in the gravitational field (Arthur & Menzies 1972, Flight 1998).Bjerrum (1972) recognized the consequences of this anisotropy for clays a long time ago. There is no reason to expect anything different in sand behaviour.

It was demonstrated by Vaid & Chern (1985) that as long as strain softening occurs, QSS and SS

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conditions can be treated within the same framework in the effective stress space. This condition is defined by a unique straight line in the modified Mohr diagram. This is illustrated for Fraser River sand in Figure 1 4 , which implies that the friction angle (1)q s s /s s mobilized at these states is a material property. It applies regardless o f the initial state or stress path during undrained shear represented by a and b. The data illustrated encompasses a range o f initial states and TC, TE, DSS, and HCT test results. DSS data were interpreted assuming that the horizontal plane is the plane o f maximum shear stress (Roscoe 1 9 7 0 ) .

Although the QSS/SS line is unique in stress space, it is not so in the void ratio-stress space. For a given initial state, a sand may respond even dilatively or in a QSS manner in one loading mode, yet it may be strain softening o f the SS type in others. Nevertheless, if strain softening does manifest in a specific loading mode, the relationship between void ratio and QSS/SS strength, S q s s/s , is not unique, but is strongly dependent on the level o f initial confining stress (Figs. 1 5 & 1 6 ) . At a given void ratio, S q s s /ss increases with increase in confining stress. However, its normalized value Sqss/ss/ ( < ^ ic in triaxial and Gvc' in DSS) remains sensibly constant at a given void ratio. This behaviour is contrary to the usual SS concepts where ec - Sss is regarded as unique (e.g. Castro et al. 1 9 8 2 ) , based only on TC data.

Influence o f prestrain history

A sand that has been subjected to loading events

Figure 14. Effective stress states at quasi steady/steady states and phase transformation (if dilative) in triaxial compression, extension, simple shear and torsional shear.

before the current, has an initial state with some strain history, caused by the dissipation o f excess pore pressures generated during those events. Such a prestrain history can be simulated in the laboratory by subjecting triaxial specimens to undrained loading, static or cyclic, until a prescribed level o f strain is developed, followed by reconsolidation to the original stress condition by allowing excess pore pressure to dissipate. A significant amount o f densification o f sand can occur during this pore pressure dissipation if the prestrain amplitude was large (Vaid et al. 1989).

The TC behaviour o f virgin Ottawa sand, C-109 (Dso = 0.4 mm) at Drc« 36% is strain softening. Its reloading response after small prestrain levels o f +0.17 (compressional) and -0.15% (extensional) illustrated in Figure 17(a), shows that the strain softening response still persists on reloading, regardless o f the sense o f prestrain (Vaid et al.1989). The prestrain is considered small if it is less

0.80 0.85 0.90

Void ratio, e

0.95

Figure 15. Dependence o f undrained strength at quasi steady/steady state on void ratio and confining stress in triaxial extension.

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Figure 16. Dependence o f undrained strength at quasi steady/steady state on void ratio and confining stress in simple shear.

undrained reloading.

0 400200( a ; + a ; ) / 2 (kP a)

Figure 17(b). Effect o f magnitude and sense of large prestrain on undrained reloading.

than the value until the peak stress state of the virgin sand, at which strain softening is triggered. On the other hand, if the prestrain is large, which corresponds to straining beyond the QSS of the virgin sand, the behaviour on reloading depends on both the magnitude and sense o f prestrain relative to the reloading direction. For reloading in the same direction as the prestrain, the virgin strain softening response may be eliminated (Fig. 17b). In contrast, for reloading in the direction opposite to that o f the sense o f prestrain, the sand may get transformed into an increasing strain softening type, causing reduction in S qss/ss as the magnitude of prestrain increases (Fig. 17b). The virgin sand at the increased relative density by the prestrain phase was dilative in each case (Vaid et al 1989). Apparently, the nature o f inherent anisotropy has been reversed due to the prestrain. Other researchers (e.g. Finn et al. 1971, Seed et al. 1977) have presented similar results as to the effects of prestrain history, where the emphasis was as to its effect on cyclic, response only.

7 CYCLIC UNDRAINED RESPONSE

Cyclic loading causes progressive increase in excess pore pressures and strains with cycles of loading. In triaxial loading, strain softening can be responsible for liquefaction, which may develop either in the compression or extension mode, depending on the initial stress state, and the amplitude o f the cyclic shear stress. For an initial hydrostatic stress state, strain softening is invariably triggered in extension on account o f the latter line o f peak states in extension than in compression, together with the characteristic inclination of the stress path to the right during loading phases o f the cyclic stress (Fig. 18). But, when the loading involves either small amplitude or no stress reversal into the extension side, strain softening could develop in compression (Fig. 19). If strain softening is the mechanism leading to liquefaction, the QSS/SS lines, both in the effective stress and void ratio-shear stress spaces during cyclic loading are essentially identical to those

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observed under static loading. This is illustrated for Fraser River sand in Figures 20a and 20b in triaxial loading. Similar results for other sands are reported elsewhere under both triaxial and simple shear loading (Vaid et al. 1990, Vaid & Sivathayalan 1996).

Strain softening during cyclic loading will trigger only if the following conditions are satisfied simultaneously: (i) sand is strain softening under

25

-25

Fraser River sand (W P)

Strain softening in Extension

0 15050 100

(a ;+ a 'j^ )/2 (kPa)

Figure 18. Strain softening in extension during cyclic loading.

(kPa)

Figure 19. Strain softening in compression during cyclic loading.

static loading; (ii) maximum shear stress (static + cyclic) exceeds the SS or QSS strength on compression or extension side; (iii) sufficient number o f loading cycles occur. It happens at the instant when the friction angle mobilized during cyclic loading equals that at trigger under static loading (Vaid et al. 1989). Similar criteria were outlined by Castro & Poulos (1977) and Vaid & Chem (1985), but for the development o f strain softening confined to the compression mode only.

Effect of Initial state variables

The dependence o f cyclic resistance on initial state variables has been recognized for long. Cyclic resistance is often expressed as cyclic stress ratio amplitude, CRR, that causes liquefaction in a specified number o f cycles. CRR at a given relative density (or void ratio), is influenced by both initial confining and shear stress levels. Its value at a reference confining stress o f 100 kPa and no static shear is frequently multiplied by correction factors and K«, in order to estimate CRR at arbitrary levels o f confining and shear stress levels. Ka is assessed from cyclic tests over a range o f initial confining stresses, but zero static shear. Figure 21 shows data compiled by Seed & Harder (1990). Also, superimposed on this figure are the measured K<j values by cyclic triaxial tests on hydrostatically consolidated specimens (Vaid & Thomas 1995). A definite dependence of Kct on relative density, in addition to that on a', may be noted. Similar data on a tailings and Ottawa sands in DSS (Vaid et al. 1985) further confirms this feature. Ka values for loose states appear to be grossly underestimated. In fact, for the loosest density that is most prone to liquefaction, Ka is close to 1, regardless o f the confining stress level. The large scatter in the compiled data on Ka-a' relationship may partly be attributed to ignoring Ka dependence on relative density.

The presence o f static shear may either increase or decrease the measured cyclic resistance o f sand depending upon its initial state. This is illustrated for Fraser River sand in Figure 22 (Vaid et al. 1998), and for a tailings sand in Figure 23 (Vaid & Chern 1985). The suggested K« factors, proposed by Seed & Harder (1990), which are superimposed on data in Figure 22, may be seen to be too conservative, especially for the more liquefaction prone loose sand. It is important to recognize that the initial void ratio, confining stress and shear stress collectively influence undrained response (Fig. 11). The correction factors K^ and K^, at a given relative density, cannot therefore be independent of each other and applied sequentially as is currently practiced. The combined correction

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Figure 20. Equivalence o f static and cyclic loading, (a) effective stress states, (b) Dependence of normalized shear strength on void ratio.

factors K(jxKa, when sequentially applied, as suggested by Seed and Harder (1990), may grossly underestimate the cyclic resistance, especially at loose relative density states. This is illustrated in Figure 24 for Fraser River sand at the reference state o f a -100 kPa, a = 0, labelled (100, 0) as well as at a higher confining stress and two levels of static shear over a range o f density states (Vaid et al. 1998). The superimposed shaded regions in Figure 24 show the predicted cyclic resistance using Seed & Harder (1990) corrections. It may be noted that the degree o f conservatism by the current empirical method is high, and is most pronounced for looser density states which are most susceptible to liquefaction.

8 POST LIQUEFACTION BEHAVIOUR

Post-cyclic/liquefaction stress strain response is the key information needed in assessing liquefaction

0 1000 2000 300(in triax) or (in D SS) (kPa)

Figure 21. Dependence o f on confining stress and relative density.

Figure 2 2 . Dependence o f K« on a and relative density.

induced displacements. This response is highly influenced by the maximum strain amplitude experienced during and the residual effective stress state at the end o f cyclic loading. If the residual effective stress is zero then the post cyclic response is stiffening throughout with increasing modulus as illustrated in Figure 25 (Vaid & Thomas 1995). For clarity the initial region o f deformation that occurs at close to zero stiffness is not shown, and the stress strain curves shown for TC are plotted only after the mobilization o f a finite small Od = 5 kPa. The increasing stiffness with strain is opposite to the familiar response o f soils where straining normally leads to degradation in stiffness. Such a response stems from the fact that the deformation starts at zero effective stress and sand dilates all the way

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Figure 23. Influence o f initial confining and shear stress levels on cyclic resistance o f dense sand.

30 40 50D , %

60 70

Figure 24. Measured and predicted cyclic resistance.

along the line o f maximum obliquity noted under static undrained loading.

It may be noted that increase in density makes the response stiffer, but the initial confining stress level appears to influence it more at the looser than the denser states. The stress path dependency of post-cyclic response may also be noted by comparison o f TC data with similar data in TE. The rate o f increase in modulus with strain is much smaller in TE at each density state.

The length o f initial region o f deformation (at essentially zero stiffness) increases with amplitude of the maximum strain during liquefaction (Vaid & Thomas 1995). This implies that larger cyclic strains induced on earthquake loading would increase post liquefaction displacements.

If the cyclic loading terminates with a non-zero residual effective stress, the post-cyclic response depends on the magnitude o f this stress (Fig. 26).

0 5 10Axial strain, (%)

Figure 25. Range o f post liquefaction response.

Axial strain, 8 (%)

Figure 26. Post cyclic/liquefaction response o f sand when cyclic loading terminates at non zero residual effective stress.

The loading that terminated with residual a '3 states of 8 , 25 and 45 kPa had liquefied according to the strain criterion specified, but with residual a' = 105 kPa, 175 kPa, developed maximum strain during cyclic loading less than 0.4%. All test samples were identical and were hydrostatically consolidated to 400 kPa. Thus the stress strain curve at a ' 3 = 400 corresponds to the virgin static undrained response. When the residual effective stress is not zero, the modulus during post cyclic

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loading may be noted to first decrease with increasing deformation, in the same manner as on virgin loading, until the sand starts to dilate after crossing the phase transformation state. The stiffness increases thereafter with strain until it becomes essentially constant at larger strains.

9 LOADING NOT TRULY UNDRAINED

Undrained (constant volume) loading at ambient effective stress state represents a specified direction of strain increment vector. This would be associated with a unique effective stress increment vector, whose direction depends on the constitutive behaviour of the sand at the current stress state. Any stress increment vector other than that corresponding to the undrained deformation will imply volumetric changes.

Volumetric changes can occur in soil elements during short loading duration or after its cessation, due to the flow generated by spatial distribution of induced pore pressure, in a given boundary value problem. The actual effective stress path the soil elements get subjected to is not the undrained stress path, commonly assumed in liquefaction problems.

The consequences o f a stress path that is not completely undrained are examined in Figure 27. (Eliadorani 1999). The triaxial test was performed using a strain path control, described in Vaid & Eliadorani (1998). It may be noted that sand which is dilative, if undrained gets transformed into the strain softening type The volumetric strain represent the true skeleton volumetric strains after allowing for membrane penetration volume

Figure 27. Transformation o f dilative response under constant volume into strain softening on experiencing small volumetric strains.

changes specific to the current relative density (Sivathayalan & Vaid 1998b). The extremely small volumetric strain (< 0.5%) that triggered strain softening cannot be regarded as a physical loosening of this sand. Small volume changes if they do occur due to flow in a given field problem (even with permeability typical o f sands) can thus misjudge a sand as dilative, if assumed undrained, which in reality may become strain softening. Such a judgement would clearly be on the unconservative side.

10 CONCLUSIONS

Comprehensive experimental results on saturated sands have been presented in order to assess the influence of fundamental factors on their susceptibility to liquefaction. As is common in most fundamental studies o f soil behaviour, the results were obtained using water pluviated reconstituted specimens. However, the relationship of their behaviour to that o f the undisturbed sand, retrieved by in-situ ground freezing was also explored. Based on the data presented, the following conclusion may be drawn:• The true strain softening static response using

stress controlled loading can be measured with confidence only by using an inertial system, together with high frequency response data acquisition system.

• At a given initial void ratio and stress state, the undrained response is profoundly affected by the sand fabric that ensues depending upon the method of specimen reconstitution. Modelling in-situ undisturbed sands by their equivalent reconstituted counterparts should therefore mimic the in-situ fabric for a meaningful characterization of in situ sands. The behaviour of undisturbed sands retrieved by in-situ ground freezing was found to be both qualitatively and quantitatively similar to their water pluviated counterparts. The fabric that ensue upon moist tamping seems potentially collapsible which may unjustifiably label the sand as liquefiable, which it may not be with water pluviated fabric. The accessible in-situ void ratios o f three supposedly loose in situ sands were found close to or lower than those o f their reconstituted counterparts by water pluviation. Much looser void ratios can be simulated by moist tamping, which would be inaccessible to water deposited in-situ sands.

• For a given initial fabric, the type o f undrained response in a given loading mode, strain softening or strain hardening, depends collectively on all initial state variables, void ratio, confining and shear stress levels.

• The sands are inherently anisotropic in their

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undrained response. At a given initial state they may be dilative in one loading mode, yet strain softening in others. The type o f response depends both on the inclination o f g \ to the deposition direction as well as on the relative magnitude o f intermediate principal stress. Provided the sand is strain softening the stress conditions at the instants o f minimum undrained strength are defined by a unique QSS/SS line in the effective stress space regardless o f the loading mode. However no such unique line exist in void ratio - stress space. For a given loading mode, it depends both on the initial void ratio and the level o f confining stress.Strain softening can also be the mechanism of deformation causing liquefaction during cyclic loading. When this occurs in a given loading mode, the QSS/SS lines in both effective stress and void ratio effective stress spaces are essentially identical to those observed under static loading. Strain softening in cyclic loading triggers only if three conditions are satisfied simultaneously- the sand is strain softening in static loading, the maximum shear stress amplitude in either triaxial compression or extension pulse exceeds the static S q s s /s s strength in that mode and sufficient number o f load cycles are involved.When liquefaction due to cyclic loading is due to the occurrence o f strain softening, the effects of confining pressure and static shear on cyclic resistance cannot be isolated by the sequential factors Key and K«. The composite factor K^xK« is underestimated by wide margin by the current empirical method, especially for the loose liquefaction prone states. The K<j factor by itself depends not only on the & level but is significantly influenced by the initial density state. Ka is close to 1 for initial loose states, regardless o f the level o f confining stress.

' Post cyclic static response is dilative all the way with increasing stiffness, if the cyclic loading terminated with a zero residual effective stress. If the residual stress did not become zero, then initially the modulus decreased with strain, but increased continuously after the phase transformation state was crossed.

► Small expansive volumetric strains, if they occur either during or after the loading event, could transform a sand that is dilative under truly undrained loading into a strain softening, liquefiable type. This amounts to erring on the unsafe side.

ACKNOWLEDGEMENTS

The basic research reported herein has been primarily supported by grants from the Natural

Sciences and Engineering Research Council of Canada. It has been accomplished by the meticulous experimental work and innovative ideas o f many graduate students. The indispensable and expert technical assistance o f the Civil Engineering Workshop precision machinists in fabricating advanced testing apparatus, and o f the electronics technicians for instrumentation design, data acquisition and test control systems is gratefully acknowledged. Kelly Lamb and Sharon Walz prepared the manuscript.

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Elastic deformation properties o f sands containing fines during liquefaction

J.Koseki&T.SatoInstitute of Industrial Science, University of Tokyo, Japan

N. MaeshiroNuclear Power Department, Electric Power Development Company Limited, Japan

I.UranoTokyo Office, Oyo Corporation, Japan

ABSTRACT: A series o f undrained cyclic triaxial tests were performed on artificial samples prepared by mixing Toyoura sand and bentonite at a ratio o f 95% and 5% in dry weight and on undisturbed Holocene sand samples with a fines content o f 6% retrieved by in-situ freezing. Their elastic deformation properties were measured by applying very small amplitude cyclic axial loads. The results could be explained by considering inherent and stress state-induced anisotropy in modeling o f elastic deformation characteristics and by correcting for the effects o f membrane penetration. Gradual degradation in the elastic Young’s modulus was observed during liquefaction when compared to that measured during isotropic consolidation. It was also shown that longer consolidation time or higher temperature during consolidation resulted in increase in the liquefaction resistance o f the artificial samples, while only limited effects o f these conditions on the elastic deformation properties were observed within the range o f the tested conditions.

1 INTRODUCTION

Elasto-plastic deformation characteristics o f sands during liquefaction process is one o f the essential aspects in analyzing the process based on elastoplastic approaches, whereas they have not been fully understood due to technical difficulties in very accurately evaluating elastic and plastic strain components experimentally. However, recent developments in laboratory testing methods have made it possible to measure elastic deformation properties at a strain level as small as 10' or less, as summarized by Tatsuoka et al. (1997).

Effects o f fines content on liquefaction characteristics o f sands have also been one o f the major issues (Ishihara & Koseki 1989), while there still seems to exist a discrepancy between the field performances and the laboratory test results. In relation to these aspects, based on laboratory tests (Goto 1994) and case studies (Yasuda et al. 1994), it has been reported that aging due to long-term consolidation may largely affect the liquefaction resistance o f sands containing fines. It has been also attempted to reproduce the aging effects in a shorter time by consolidating the specimen under a high temperature (Goto 1994). However, the combined effects o f aging and fines content on the liquefaction

characteristics o f sands have not been fully understood.

In the present study, as the first test series, large amplitude undrained/drained cyclic triaxial tests were performed on saturated Toyoura sand, while applying very small amplitude cyclic axial loads at a number o f stress states to measure elastic deformation properties directly. Results from this test series have been presented in detail by Koseki et al. (1998), while some o f them are briefly shown in this paper in order to validate the modeling o f elastic properties during undrained triaxial tests that was employed in the whole part o f the present study.

By using similar testing procedures, the second series o f undrained cyclic triaxial tests was performed on artificial samples, prepared by mixing Toyoura sand and bentonite at a ratio o f 95% and 5% in diy weight, in order to investigate the effects of consolidation period and temperature during isotropic consolidation on its liquefaction characteristics.

The third series o f undrained cyclic triaxial tests was performed on undisturbed samples with a fines content o f 6%, retrieved by in-situ fi-eezing sampling from a Holocene sandy soil layer, in order to study the liquefaction characteristics o f such naturally deposited sandy soils.

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AC-servo Motor

Transducers 0 Dial Gauge 0 Load Cell0 Proximity Transducers(2mm, Smm)0 Local Deformation Transducer(LDT) (D Low Capacity Differential

Pressure Transducer (LCDPT) d) High Capacity Differential

_______ Pressure Transducer (HCDPT)

Figure 1. Triaxial testing apparatus with axial loading device driven by an AC servo motor

2 APPARATUS A N D TESTING PROCEDURES

2.1 Tests on mixture o f Toy our a sand and bentonite

T w o ty p e s o f tr ia x ia l te s tin g a p p a ra tu ses w ere em ployed for the tests on mixture o f T oyoura sand and bentonite. One is to load axially using an AC servo motor as shown in Figure 1, and the other is to load axially using a conventional air cylinder. The former w as em ployed in som e tests to evaluate the ch an ge in the e la s tic d eform ation p ro p erties by applying cyclic axial loads at an axial strain amplitude o f 10'^ (hereafter denoted as small cyclic loading), where the vertical displacem ent o f the top cap w as m easured by u sin g a p rox im ity tran sd u cer (gap sensor) having a capacity o f 2 mm. Typical stress- strain relationships m easured during drained small cyclic loading are show n in Figure 2. D etails o f this

^ - 1.2-0.0010 -0.0005 0.0000 0.0005 0.0010

Increment of axial strain, A e (%)

Figure 2. Typical relationships between increments o f effective vertical stress and axial (vertical) strain during drained small cyclic loading (on mixture o f Toyoura sand and bentonite)

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70

60

’oC/3coo00

.S3T3dJ

(Uo,B(UH

50

40

30

20

10 15 20Elapsed time (hour)

25 30

Figure 3. Typical change in the cell water temperature during consolidation at high temperature

testing apparatus will be described elsewhere (Santucci de Magistris et al. 1998).

The tested sample (emax=0,975, ^^¡„=0.561) was prepared artificially by mixing Toyoura sand and bentonite (wl= 357 %, wp=25.1 %) at a ratio o f 95% and 5% in dry weight. A solid cylindrical specimen 150 mm in height and 75 mm in diameter at a relative density about 50 % was prepared by putting the sample at a water content o f 5 % in a metal mold, which was located on the pedestal o f the triaxial cell, and tamping it in ten layers by using a cylindrical metal mass. After saturating the specimen at a confining stress o f 29 kPa by the double vacuuming method using partial vacuum as both the pore water pressure and the cell pressure, it was isotropically consolidated up to effective confining stress o f (7 ’= a h ’=98 kPa, where (J and (Jh denote effective

vertical (or axial) and horizontal (or radial) stresses, respectively.

In som e tests, the cell water was heated up to 40 or 65 degrees centigrade at maximum during consolidation for about 24 hours, as typically shown in Figure 3, and was restored to the regular

temperature (about 20 degrees centigrade). In tlie otlier tests, tlie cell water was maintained under the regular temperature condition, but the consolidation period was varied to be either half an hour (30 minutes) or 20 days.

During consolidation, when the apparatus with the AC servo motor was employed, the small cyclic loading was conducted under both drained and undrained conditions after som e drained aging (about 30 minutes) at several stress states.

After consolidation, undrained cyclic axial loading with a large constant amplitude o f deviator stress by keeping the cell pressure constant (hereafter denoted

* Classified based on in-situ elastic wave velocities ** Classified based on observation during bore hole survey

Figure 4. Results o f in-situ surveys conducted at the site where in-situ frozen samples were retrieved

as large cyclic loading) was executed on all specimens either by the air cylinder with input sinusoidal waves at a frequency o f 0.1 Hz, or by the AC servo motor with an axial strain rate o f 0.05 to0.1 %/min while conducting the small cyclic axial loading under undrained condition with an axial strain rate o f 0.01 %/min at several stress states without any pause (without aging).

2.2 Tests on undisturbed sandy soil retrieved by in- situ freezing method

The triaxial testing apparatuses with the AC servo motor as shown in Figure 1 was employed for the tests on undisturbed sandy soil, by which the change in the elastic deformation property was evaluated by conducting the small cyclic loading.

The tested sample (i4ux=0.85 mm, £/5o=0.18 mm, fines content= 6 %) was retrieved by in-situ freezing method from a H olocene sandy soil layer at a depth o f 11.5 m in a low land area developed along the Tone River, located at about 44 km upstream from the river mouth. Figure 4 shows the results o f boring

123

survey, standard penetration tests (SPT-N values), and in-situ elastic wave velocity measurements using the suspension method in the bore hole. The SPT-N value measured at the same depth as the frozen sample was retrieved was 33.

A solid cylindrical specimen 100 mm in height and 50 mm in diameter was trimmed from the frozen sample and set on the pedestal o f the triaxial cell. It was thawed under a confining stress o f 29 kPa and saturated by the double vacuuming method. It was isotropically consolidated up to effective confining stress o f o;r’=Oh’=107 kPa, which is equal to the estimated in-situ effective overburden pressure, and was subjected to undrained large cyclic loading. Small cyclic loading was conducted at several stress states during isotropic consolidation and large cyclic loading.

3 MODELING OF ELASTIC DEFORMATION PROPERTIES

The elastic deformation properties measured during isotropic consolidation and undrained large cyclic loading were compared with the calculated values based on the following modeling.

It has been experimentally reported by Hoque & Tatsuoka (1998) that the elastic Young’s modulus o f granular materials is basically a function o f the effective normal stress in the direction o f the major principal strain increment. Therefore, the vertical and horizontal Young’s moduli, denoted as Ev and Eh, respectively, were formulated by Eqs. (1) and (2), as proposed by Tatsuoka & Kohata (1995):

= E ^ ( d J a „ ) " ' • f ( e ) / f ( e g ) •••(1)

E , = E ^ { d , l d , r ■ f ( e ) / f ( e g ) - ( 2 )

inherent anisotropy (a = Evo/ Eho), and is the value o f hv when R=d '' . On the other hand, the Poisson’s ratio on horizontal plane hh is assumed constant and equal to i o-

By using Eqs. (1) to (4), the elastic normal strain increments and de^ in the vertical and horizontal directions, caused by effective stress increments do v’ and d o h’, can be evaluated as:

d < - - i —i/cr ' + 2 (j '

d e l = ^ ^^-d a \ + ^ ~ ^ d G '

In some cases, effects o f membrane penetration (hereafter denoted as MP) were considered by formulating the apparent volumetric strain increment d Bmp due to MP by Eq. (7):

d £ ,4 b

a , - d■da'^ "'('7)

where d is the diameter o f the specimen in cm, and b is a parameter that was experimentally obtained by Goto (1986) to be 1.7X10'Vlo^l0for Toyoura sand.

Based on these assumptions, the theoretical relationship between the undrained and drained Young’s moduli, denoted as Ev,u and Ev, respectively, at the same stress state was obtained by Tatsuoka et al. (1997) as:

E. = \ + v , x1 + X

•••(8)

where x is the stress increment ratio under undrained condition given by.

where o o’ and eo are the reference stress and void ratio, and f(^)=(2.17 -efl{\+ e) is the void ratio function to account for effects o f void ratio changes. These properties result in stress state-induced anisotropy in the elastic deformation characteristics (Tatsuoka & Kohata 1995).

By assuming a symmetricity for the elastic compliance matrix, the Poisson’s ratio is assumed to be basically dependent on the current stress ratio R= <7 vV CJh’ as formulated by Eqs. (3) and (4).

= - ( 3 ) , (4)

where a is a parameter representing the degree o f

1-2(0/?'”)° Vo- v„ - (oR")-'” v„ + 2{bE, /

In Figure 5, the ratio Ev,u/Ev measured during isotropic consolidation for a specimen of Toyoura sand (^max=0.965, ^min=0.603, ¿/5o=0.23mm with no fines content) prepared by air pluviation is plotted versus o^' ( = a h’) (Koseki et al. 19 9 8 ) . It is seen that the test results can be reasonably simulated by Eqs. (8) and (9 ) when setting the anisotropy parameter a and the reference Poisson’s ratio Vq to be 1 . 1 and0.15, respectively, based on the test results on the same sand by Hoque & Tatsuoka ( 1 9 9 8 ) , and considering the effects o f MP.

124

1.4X)uc

, 1.3W. - r(u ::::c 1.2

o>-

1.0

Figure 5. moduli at

Toyoura sand during isotropic consolidation

Test 6 (Dr^,^ =63.7% )

a= 1.0 , MP uncorrectedo

0= 1 .1 , MP uncorrected

V = 0 .1 50

: Measured by proximity transducer

; M easured by L P T ________

80 ------1------ 1------ 1—-Test 7

—I------ 'q

60 28.0

b " 40 ¿J7.5

b " 20 27.0

10 100 Effective vertical stress, OJ (kPa)

Ratio o f undrained to drained Young’s isotropic stress state (for Toyoura sand)

- ® ~ ® :_ Stress points where s

cyclic axial loadings were applied during first cyclei small

20 40 60 80 100Effective mean principal stress, p' (kPa)

Figure 7. Effective stress path during undrained large and small cyclic loadings (on Toyoura sand)

0.1 1 10 Stress ratio, R= OJ/ GJ

Figure 6. Direction o f effective stress path during undrained small cyclic loading (on Toyoura sand)

In Figure 6, the ratio dp'!dq, which denotes the average d irection o f the e ffe c tiv e stress path measured during undrained small cyclic loading applied at several stress states in the course o f undrained large cyclic loading (i.e ., liquefaction process as shown in Figure 7), is plotted versus R (= t^v’/ O’h’) on the isotropically consolidated specimen o f Toyoura sand (Koseki et al. 1998). Theoretical value for each ratio, equal to l-2 x /3 /(l+ x ) with x predicted by using Eq. (9) is also shown in the figure.It should be noted that, as the current value o f O’ was not uniquely evaluated from R, the theoretical value was obtained for each stress state where the small cyclic loading was applied. It is seen that, under triaxial com pression condition ( i .e ., R >1), the measured ratio can be reasonably simulated by the theory when considering the effects o f inherent anisotropy (<2=1.1) and MP, w hile under triaxial extension condition (i.e., 7?<1), the measured ratio deviated from the theoretical value. Reasons for the latter difference are not clearly understood, but it may indicate that, in the case o f Toyoura sand, the

-3 -2 -1 0

Axial strain, (%)Figure 8. Stress-strain relationsips during undrained large and small cyclic loadings (on Toyoura sand)

extent o f damage to the soil structure due to shear deformation is larger under triaxial extension condition than under triaxial compression condition.

In this case o f Toyoura sand, from values o f Ev.u measured during the liquefaction process as shown in Figure 8, values o f Ev were estimated by using Eqs. (8) and (9) while considering the effects o f inherent anisotropy (a=l .l) and MP. They are plotted versus <7 in Figure 9, where the average relationship obtained during isotropic consolidation by measuring Ev directly is also shown. It is seen that the estimated Ev during liquefaction process without aging is rather a unique function o f 0'y\ suggesting the applicability o f Eq. (1), but becomes smaller than that measured during isotropic consolidation after some aging as cr ’ decreases. This trend o f behavior may be caused by the damage to the soil structure due to shear deformation that occurred during liquefaction process, but to a larger extent because no aging effect is involved in the estimated Ev.

125

Effective vertical stress, (kPa)

Figure 9. Estimated drained Y oung’s modulus versus effective vertical stress (for Toyoura sand)

<N

G"o

oU

0.4

0.3

0.2

0.1

0.0

A : 24 hours at

m ax. 65 ”C, D =48-54% -

A : 24 hours

at max. 40 “C,

D =49-54%

o : 20 days at

20 °C, D =50-52% h

• ; Consolidated for 0.5 hour at 20 °C,

D (after consolidation)=49-51 %

D ouble amplitude o f axial straino pg

0.1 100 > -s= \0% T3(U

'c3Q

1 10 Number of cycles causing

Figure 10. Relationships between cyclic stress ratio and number o f cycles to cause liquefaction (on mixture o f Toyoura sand and bentonite)

4 RESULTS OF U N D RA IN ED CYCLIC TRIAXIAL TESTS ON M IXTURE OF TOYOURA SA ND A ND BENTONITE

4.1 Liquefaction resistance

In Figure 10, relationships between the cyclic stress ratio, c’), and the number o f cycles, Nc, tocause a double amplitude axial strain, £ da, o f 10 % are compared among specimens consolidated at different conditions, where o and o denote single amplitude o f the cyclic axial stress and the effective confining pressure at the end o f isotropic consolidation, respectively. It should be noted that the range o f the relative density o f the specimens after consolidation is also indicated in the figure, which w as not very different among different consolidation conditions.

A s seen in the figu re, sp ec im en s co n so lid a ted under regular temperature for longer period (i.e , 20 days com pared to h a lf an hour) exh ib ited larger

Consolidation period and temperature:

24 hours, max. 65 “C (hysteresis damping: h=0.149)

-6 -4 -2 0Axial strain, (%)

Figure 11. Typical relationships between deviator stress and axial strain during large cyclic loading (on mixture o f Toyoura sand and bentonite)

: during unloading after 24 hours sustenance at 20“C

150

o

^ ^ 1 0 0

50

a : during unloading after heating \

for 24 hours at max 40°C, m =0.598 ^ t

Eyf(e)=Eja'/0„')” /fl:e,)\_

▼ : during loading before

24 hours sustenance at 20 C

6 /I ---------- ------------------------------------------------------------- —. / I o : during reloading after heating, m =0.598A --------■------------------------------------------------------------------

A : during loading before heating, m =0.697

50 100E ffective vertical stress, (=Cij^') (kPa)

Figure 12. Drained Y oung’s modulus at isotropic stress state (on mixture o f Toyoura sand and bentonite)

resistance against liquefaction. In the present study, the value o f (Ja /(2 cr .’) to cause £ da o f 10 % in ten cycles increased by about 30 % from 0.17 to 0.22 when the consolidation period was extended from half an hour to 20 days. Compared to results by Tatsuoka et al. (1988), this increment is similar to their results on Sengenyama sand containing 2.4 % o f fines in weight, but larger than those on other clean sands.

It is also seen in Figure 10 that specimens consolidated under higher temperature (i.e., max. 65 degrees centigrade compared to 40 degrees centigrade) for the same period o f 24 hours exhibited larger resistance against liquefaction. This tendency is consistent with the results o f previous study by Goto(1994) on a mixture o f Toyoura sand and marine clay

126

0.10

0.08bB

0.06oJ

• 0.04

0.00

Isotropically consolidated and

heated for 24 hours at max. 40 C

: during loading before heating

V; during reloading after heating

I ° • ^^ring unloading after heating |

Legend for Figures 14 a), b)Symbol a 0 MP

A 1.0 0.15 imcorrectedB 1.1 t iC 1.2 i tD t 0.2 tB’ 1.1 0.15 corrected*C 1.2 t tD ’ t 0.2 t

* MP correction based on data for Toyoura sand

'0 20 40 60 80 100Effective vertical stress, QJ

Figure 13. Hysteresis damping during small cyclic loading at isotropic stress state (for mixture o f Toyoura sand and bentonite)

at a ratio o f 80% and 20% in dry weight. These results suggest the possibility o f consolidation under high temperature to simulate the aging effects due to long-term consolidation on sands containing fines with respect to their liquefaction resistance.

Typical stress-strain relationships at a cycle when the value o f ¿aUA was about 7.5% are compared in Figure 11, on which no clear effect o f long-term consolidation or consolidation at high temperature was observed. The values o f hysteresis damping, /?, evaluated for each stress-strain curve are also indicated in the figure, in which no remarkable change was observed either.

4.2 Elastic Behavior

Values o f Ev measured during isotropic consolidation are plotted in Figure 12 versus (= (Jh’). Values o fEv measured during isotropic unloading after consolidation under regular temperature for 24 hours, which was specially conducted for comparison purpose, and those measured during isotropic unloading and reloading after consolidation under high temperature (max. 40 degrees centigrade) for 24 hours are also shown. It is seen that the values o f Ev at the same stress state increased by about 10 % after consolidation under high temperature. On the other hand, during consolidation under regular temperature for the same period, the values o f Ev also increased slightly although number o f available data points are limited.

Values o f the hysteresis damping, h, at an axial strain amplitude o f 10' evaluated during and after consolidation under high temperature are compared in Figure 13 . It is clearly demonstrated that the values o f h in c r e a s e d a fte r th e h igh tem p era tu re consolidation. As typically shown in Figure 2, the

-aOJ.S’c3Vi-oO

T3(D.£

c3O.20

■o(Uc3-do

T3(U.2'c5•dc3o.2

3T3OB~b£)a3o

3 1.5

d^ 1-4

1.3

0.1.2oV io

1.1bOc

1.0

50 100Effective vertical stress, O ' (=CT ') (kPa)

3 15 .2d . .

!2 1-4 "oc/5§ 1.3oo

'H.1.2o

1.1 'tifi3

1.0

Measured; ;during loading before heating

- p :during unloading after heatingo during reloading after heating

b).................................................... A ........^.................................................. B ......

................................................ c .....- g;::..-------------------C P -------O------

I D': fl=1.2, V(3=0.2, Isotropically consolidated and

MP corrected heated for 24 hours at raax.40“C

10 50 100Effective vertical stress, OJ (kPa)

Figure 14. Ratio o f undrained to drained Young’s moduli at isotropic stress state (for mixture of Toyoura sand and bentonite); a) with specimen consolidated for half an hour under regular temperature and b) with specimen consolidated and heated for 24 hours under high temperature

linearity in the stress-strain relationship during small cyclic loading became slightly higher after the high temperature consolidation, which resulted in slightly larger values o f Ev and smaller values o f h at this strain amplitude.

The ratio Ev,u/Ev m easured during isotrop ic co n so lid a tio n is sh ow n in F igu res 14a, b on specimens consolidated under regular temperature for half an hour and under high temperature (max. 40 degrees o f centigrade) for 24 hours, respectively, where theoretical felaftionships derived by Eqs. (8)

127

bOao>o'■E(U>-o<L)a

:ioo

wc/T3 10 3 •T3 OB

bGC3O :ioo

^ 10w 3SI i

Isotropicall^onsoli^^

a) A '

> v

A :Tria?dal com pression side

V :TriaxiaI extension side

o :During isotropic consolidation■ ■I ”T....: :r □

1 10 100 Effective vertical stress, CJ ' (kPa) Effective vertical stress, O '(kPa)

Effective vertical stress, OJ (kPa)

Figure 15. Undrained Y oung’s modulus versus effective vertical stress (for mixture o f Toyoura sand and bentonite); a) with specimen consolidated for half an hour under regular temperature and b) with specimen consolidated and heated for 24 hours under high temperature


Figure 16. Estimated drained Y oung’s modulus versus effective vertical stress (for mixture o f Toyoura sand and bentonite); a) with specimen consolidated for half an hour under regular temperature and b) with specimen consolidated and heated for 24 hours under high temperature

and (9) are also shown. It is seen from both figures that by assuming the parameter a, representing the degree o f inherent anisotropy, to be 1.2, the reference Poisson’s ratio v o to be 0.2, and the effects o f MP to be the same as for the case with Toyoura sand as formulated by Eq. (7), the measured ratio could be reasonably simulated by the model. It may be expected that the effects o f MP are almost the same as those on Toyoura sand, because the tested sample consists o f 95 % o f Toyoura sand and 5 % o f finer materials. On the other hand, when differences in the other conditions such as the specimen preparation method are considered, it may also be accepted to obtain different values o f a and o from those o f Toyoura sand (a =1.1, o=0.15) as mentioned in 3.

Further study is required to directly evaluate these values and compare them with those fitted in the present study.

Values o f Ev,u measured at several stress states during liquefaction process by undrained large cyclic loading are plotted versus cr ’ in Figures 15a, b. By using Eqs. (8) and (9) under the condition as given above (i.e., a =1.2, o=0.2 with MP correction),values o f Ev were estimated from these results and compared with those measured during isotropic consolidation in Figures 16a, b. When Figures 15a and 16a are compared, it is seen that the difference in the values o f Y oung’s modulus under the triaxial compression and extension conditions could be reduced by converting Ev,u to Ev considering the effects o f inherent and stress system-induced anisotropy and those o f MP. The same trend o f behavior can be seen from Figures 15b and 16b. From Figures 16a, b, it is also seen that the estimated Ev was smaller than that during isotropic consolidation, similarly to the case with Toyoura sand (see Figure 9). On the other hand, when these

128

+

0.4

0.2

0.0

- 0.2

-0.4

- 0.60

0.6

0.4

0.2

0.0

- 0.2

-0.4

isotropically consolidated

for 0.5 hour at 20 °C

Triaxial extension side^<>

a)

Measured data0=1, Vg=0.2, MP uncorrected

0=1.2, Vg=0.2, MP uncorrected

0=1.2, Vq=0.2, MP corrected

based on data for Toyoura sand

1Stress ratio, R = 0 '/O'

ZJ10

Isotropically consolidated and heated for 24 hours

at max. 40 “C

Triaxial extension side

Triaxial compression side

sFqcP.

b)

: Measured data’ :o=l,Vg=0.2,MP uncorrected'

’ :o=l .2,Vq=0.2,MP uncorrected

' ;o=l .2,Vg=0.2,MP corrected

•' based on data for Toyoura sand

0.1 10Stress ratio, R=Q '/O '

Figure 17. Direction o f effective stress path during undrained small cyclic loading (on mixture of Toyoura sand and bentonite); a) with specimen consolidated for half an hour under regular temperature and b) with specimen consolidated and heated for 24 hours under high temperature

0r4

1.0

0.8

2 0.6

0.4

0.2oU

0.0

. The value o f did not reach 5%, because the axial .

strain shifted extensively to the extension side.

O /2 a ; = 0 .4 1 a tN = 2 0 '

o;=i()7kPa

_ a■a=3%, /2 0 ;= O .3 6 a tN = 2 C ) ■

Ie : Doubh

, .......... I; amplitude o f axial strain

I1 10 100

Number of cycles,Figure 18. Relationships between cychc stress ratio and number o f cycles to cause liquefaction (on in-situ frozen sample)

1.0

0.80tN

•S 0 ®I/Î IIS 2 0.4CO

00 U C0.2

U cC

0.0

V R eclaim ed (F <5% )A H olocen e (F^<5%)

o H olocen e (5<=F^<I0% )

a H olocen e ( 10%<=F^)A P leistocene (F^<5%)

• Pleistcene (5<=F^<10% )

■ P leistcenel (10% <F J

F : F ines content

( Other data compiled by Matsuo and Murata, 1997 on in-situ frozen samples)

10 20 30Corrected SPT-N value, N,

40

( = 1 .7N /(O ^'+0.7), OJ in kgf7cm^)

Figure 19. Relationships between liquefaction resistance by cyclic triaxial tests on in-situ frozen samples and corrected SPT-N value (modified from Matsuo & Murata, 1997)

figures are compared, no significant effects of consolidation under high temperature could be seen on these trends.

The measured and calculated ratios dp'Idq during undrained small cyclic loading in the course o f the liquefaction process are plotted versus the current stress ratio R (= cr V a h’) in Figures 17a, b. It is seen that, under the condition as given above, the measured ratio can be reasonably simulated by the theory under triaxial compression condition (i.e., R>\), while under triaxial extension condition (i.e., R<\) the measured ratio deviated from the theoretical one. This trend o f behavior is also the same as that of Toyoura sand as shown in Figure 6.

5 RESULTS OF UNDRAINED CYCLIC TRIAXIAL TESTS ON UNDISTURBED SANDY SOIL RETRIEVED BY IN-SITU FREEZING METHOD

5.1 Liquefaction resistance

Relationships between I{2 CJ ’) and number ofcycles to cause £ da o f 3 or 5 % are shown in Figure 18. It should be noted that for one specimen, the value o f £ d a did not reach 5 %, because the axial strain during undrained large cyclic loading had shifted extensively to the extension side. For this specimen, only a limited portion deformed largely due possibly to an existence o f partially loose or weak layer.

From Figure 18, the value o f (Td /(2 (7c’) to cause £ da o f 5 % in 20 cycles was evaluated to be 0.41. It

was plotted in Figure 19 versus the SPT-N value

129

.2 200

O ¿ 1 0 0S §.*2 Xo 4>> ^ 50

<0U

20

10

fl(e)=(2.17-e)7(l+e)U Ì

♦af

—♦---0“ÈB 00

6 aa

Test No. ®29kPa Eyf(e) Ev^fte)TFll 0.77 o •TF12 0.75 a ■TF13 0.77 Ò. ATF14 0.80 o ♦

0 20 50 100Effective vertical stress, OJ (=0 ') (kPa)

Figure 20. Drained and undrained Y oung’s moduli at isotropic stress state (for in-situ frozen sample)

bfiC3O £ 100

t:U>-a(U.S*é3Ui*3C

D

PQc/T3 103

T 3O6

11 10 100


Figure 22. Undrained Y oung’s modulus versus effective vertical stress (for in-situ frozen sample)

-o c 1.4s ^ , |

•g w ':§« Ò 1-3P 3 C/5^ o O.5 ^ 0-10^ ft§ o o

1.1O - B ^

.2 -c0) T3 >

I 1.0

Figure 21. Ratio o f undrained to drained Y oung’s moduli at isotropic stress state (for in-situ frozen sample)

50 100 Effective vertical stress, G ' (=G ') (kPa)

t:o>-o1)

ViT 3T 3(U"cdBC/3w

cdPhS

w'100

3T3o£c/3

"bfiC3O

10

1 10 100 Effective vertical stress, OJ (kPa)

Figure 23. Estimated drained Y oung’s modulus versus effective vertical stress (for in-situ frozen sample)

measured at the same depth as the sample was retrieved, which was corrected for the effects o f effective overburden pressure as indicated in the figure. For reference, results o f previous studies on in-situ frozen samples compiled by M atsuo & Murata (1997) were also shown. It is seen that the result obtained from the present study w as consistent with those o f the previous studies.

5.2 Elastic behaviorIn Figure 20, values o f Ev,u and Ev measured during isotropic consolidation that are normalized by the void ratio function f(e) are plotted versus Oy (= i,’)- The value o f Ev,u at the final consolidation pressure (=107 kPa) that is equal to the estimated in-situ effective overburden pressure w as about 150 to 180 MPa, which is equivalent to the shear modulus G o f about 50 to 60 M Pa when the apparent Poisson’s ratio under undrained condition is assumed to be 0.5.

This value o f G is considerably smaller than Gf=l 10 MPa that was evaluated by in-situ elastic wave survey as shown in Figure 4. The tested sample was relatively dense and had 6 % o f fines content, suggesting that its permeability was relatively low. Therefore, the above discrepancy in the values o f G and Gf may be explained by the disturbance o f the in- situ frozen sample caused by volume change o f pore water during freezing and thawing processes, as pointed out by Goto and Yoshimi (1995). Future study is required on this possible disturbance.In Figure 21, the ratio Ev,u/Ev measured during isotropic consolidation is shown with theoretical relationships derived by Eqs. (8) and (9). It is seen that by assuming the parameter a and the reference Poisson’s ratio v o to be 1.2 and 0.2, respectively, and by neglecting the effects o f MP, the measured ratio could be reasonably simulated by the model. The specimen was trimmed under frozen condition by

130

° ^

- 0.60.1

Measured data:a=l, Vq=0.2, MP uncorrected : a=1.2, Vj=0.2, MP uncorrected

;a=1.2, Vg=0.2, MP corrected** based on data for Toyoura sand

1Stress ratio, R = 0 VQ '

Figure 24. Direction o f effective stress path during undrained small cyclic loading (on in-situ frozen sample)

using an electric drill attached with a hollow cylindrical tip having the same inner diameter as the specimen. It may be, therefore, expected that the side surface o f the specimen was significantly fiat even after thawing, so that the effects o f MP were minimal.

In Figure 22, values o f Ev,u measured at several stress states during liquefaction process are plotted, while in Figure 23, values o f Ev estimated from these results and by using Eqs. (8) and (9) under the condition as mentioned above (i.e., a = 1 .2 , v o= 0 .2

without MP correction) are compared with those measured during isotropic consolidation. As were the cases with Toyoura sand and with mixture o f Toyoura sand and bentonite as mentioned above, the estimated Ev became smaller than that measured during isotropic consolidation as <7v’ decreased.

In Figure 24, the ratio dp*ldq measured during undrained small cyclic loading in the course o f the liquefaction process is plotted versus R (= (Jv'l c^’) with the theoretical relationships calculated by using Eq. (9). It is seen that under both triaxial compression condition (i.e., /^>1) and triaxial extension condition (i.e., R<\), the measured ratio can be reasonably simulated by the theory under the condition as mentioned above. On the other hand, it should be noted that the estimated Ev during liquefaction process w as relatively smaller under the triaxial extension condition than under the triacial compression condition as seen from Figure 23. These behaviors under triaxial extension condition are different from those obtained for the cases with Toyoura sand and with mixture o f Toyoura sand and bentonite as mentioned above. Further study is required on a possible difference in the elastic

properties during liquefaction process between reconstituted samples and undisturbed ones.

6 CONCLUSIONS

The results from a series o f undrained cyclic triaxial tests on tw o kinds o f sands containing fines could be summarized as follows.

B y considering inherent and stress-induced anisotropy in modeling o f elastic deformation characteristics and correcting for the effects o f membrane penetration, elastic deformation properties measured by applying very small amplitude cyclic axial loads during isotropic consolidation and liquefaction process could be reasonably explained. Gradual degradation in the drained vertical Y oung’s modulus that was estimated from the value measured under undrained condition was observed during liquefaction process when compared to that measured during isotropic consolidation.

Based on test results on artificial samples prepared by mixing Toyoura sand and bentonite at a ratio o f 95% and 5% in dry weight, it was shown that longer consolidation time or higher temperature during consolidation resulted in increase in its liquefaction resistance. On the other hand, only limited effects o f these conditions on elastic deformation properties, such as slight increase in the vertical Young’s modulus and decrease in the hysteresis damping at an axial strain amplitude o f 10'^ w ere observed within the range o f the tested conditions.

Based on test results on undisturbed samples retrieved by in-situ freezing sampling from a Holocene sandy soil layer with a fines content o f 6 %, it was shown that the relationship between its liquefaction resistance and the corrected SPT-N value was consistent with those obtained by previous studies. On the other hand, the shear modulus evaluated from the undrained vertical Y oung’s modulus measured in the present test was considerably smaller than that evaluated by in-situ elastic wave velocity surveys, due possibly to the sample disturbance caused by volum e change o f pore water during freezing and thawing processes. Some behaviors o f elastic deformation properties under triaxial extension condition during liquefaction process were also found to be different from those obtained with reconstituted samples.

ACKNOW LEDGEMENTS

The present study was undertaken with the financial support o f Grant-ih-aid for Scientific Research

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(project number 08650569), the Ministry o f Education, Science, Sports and Culture, Japan. The in-situ frozen samples and the relevant in-situ survey data were provided by the courtesy of Public Works Research Institute, Ministry o f Construction, Japan. Transportation and trimming o f these samples were made possible by the assistance o f Tokyo Soil Research Co., Ltd. and Kiso-jiban Consultants, Co., Ltd. The authors wish to thank Prof F. Tatsuoka, University o f Tokyo, for his thoughtflil suggestions on the present study.

REFERENCES

Goto, S. (1986): “Strength and characteristics o f granular materials in triaxial tests,” Dr. o f Eng. Thesis, University o f Tokyo.

Goto, S. (1994). “Effect o f curing under high temperature conditions for liquefaction resistance o f sandy soils,” Proc. o f the 29th Japan National Conference on Soil Mechanics and Foundation Engineering, Vol. 2, pp. 839-840 (in Japanese).

Goto, S. and Yoshimi, Y. (1995): “Effect o f a freeze-thaw history on the liquefaction resistance o f in situ frozen samples o f soils containing fines and a method to evaluate their in situ liquefaction resistance,” Proc, o f Symposium on Sampling, The Japanese Society o f Soil Mechanics and Foundation Engineering, pp. 63-70 (in Japanese).

Hoque E. and Tatsuoka, F. (1998): “Anisotropy in elastic deformation o f granular materials,” Soils and Foundations, Vol. 38, No. 1, pp.163-179.

Ishihara, K. and Koseki, J. (1989): “Cyclic shear strength o f fines-containing sands,” Proc. o f Discussion Session on Influence of Local Conditions on Seismic Response, 12th Int. Conf on Soil Mechanics and Foundation Engineering,p p .101-106.

Koseki, J., Hamaya, S., Tatsuoka, F. and Maeshiro, N. (1998): “Elastoplastic deformationcharacteristics o f Toyoura sand during liquefaction,” Geotechnical Engineering and Soil Dynamics III, Geotechnical Special Publication No. 75, ASCE, Vol. 1, pp. 385-397.

Matsuo O. and Murata, K. (1997): “Difference o f liquefaction resistance by sampling methods on sandy soils,” Proc. o f the 32nd Japan National Conference on Geotechnical Engineering, Vol. 1, pp. 711-712 (in Japanese).

Santucci de Magistris, F., Koseki, J., Amaya, M., Hamaya, S., Sato, T. and Tatsuoka, F. (1998): “A triaxial testing system to evaluate stress-strain behaviour o f soils for wide range o f strain and strain rate,” submitted for possible publication in Geotechnical Testing Journal.

Tatsuoka, F., Kato, H., Kimura, M. and Pradhan,

T.B.S. (1988): “Liquefaction strength o f sands subjected to sustained pressure,” Soils and Foundations, Vol. 28, No. 1, pp.l 19-131.

Tatsuoka, F. and Kohata, Y. (1995): “Stiffness o f hard soils and soft rocks in engineering applications,” Pre-failure Deformation of Geomaterials, Balkema, Vol. 2, pp. 947-1043.

Tatsuoka, F., Jardine, R.J., Lo Presti, D., Di Benedetto, H. and Kodaka, T. (1997): “Characterising the pre-failure deformation properties o f geomaterials,” Theme lecture of ICSMFE (in print).

Yasuda, S., Wakamatsu, K. and Nagase, H. (1994). “Liquefaction o f artificially filled silty sands,” Ground Failures under Seismic Conditions, Geotechnical Special Publication No. 44, ASCE, pp. 91-104.

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Physics and Mechanics of Soil Liquefaction, Lade& Yamamuro (eds)© 1999 Balkema, Rotterdam, ISBN 90 5809 038 8

Constitutive issues in soil liquefaction

S .S tu reDepartment of Civil, Environmental and Architectural Engineering, University of Colorado, Boulder, Colo., USA

A B S T R A C T : T h re e issu es r e la te d to th e m e c h a n ic s of p o re w a te r p re s su re g e n e ra tio n a n d liq u e fa c t io n of so ils is p re se n te d . F i r s t , d ra in e d c o m p re ss io n e x p e r im e n ts w ere c o n d u c te d o n s a n d a t v e ry low e ffec tiv e c o n fin in g s tre s se s in th e r a n g e of 0 .05 - 2 .00 k P a b o th in a m ic ro g ra v ity e n v iro n m e n t a n d on E a r th fo r d e n s itie s ra n g in g f ro m 10% to 85% . I t w as o b se rv e d th a t th e p e a k f r ic t io n a n g le s w ere as h ig h as 7 5 .O'" a t 0 .05 k P a c o n fin in g p re ssu re a n d Dr = 65% , a n d 52.0° a t 2 .00 k P a c o n fin in g p re s su re w ith Dr a lso e q u a l to 65% , w h ile th e d i la ta n c y an g le s w ere in th e ra n g e o f 30°. I t w as o b se rv e d t h a t ev en v e ry loose sa n d s t e n d to d i la te r a th e r th a n c o n tr a c t in v o lu m e a t th e s e low e ffe c tiv e con- h n in g s tre sse s . S eco n d , d ra in e d D ire c tio n a l S h e a r C e ll e x p e r im e n ts in v o lv in g ro ta t io n s o f p r in c ip a l s tre s s d ire c tio n s w ith r e sp e c t to th e m a te r ia l ax es , a n d w h ile th e m a g n i tu d e o f th e s tre s s c h an g e d o r re m a in e d c o n s ta n t , r e s u l te d in s u b s ta n t ia l ly d iffe re n t v o lu m e c h a n g e p a t t e rn s , w h ich w ill re su lts in s im ila r p o re w a te r p re s su re b e h a v io r in an u n d ra in e d s i tu a t io n . T h ird , th e o re tic a l a n d n u m e ric a l a n a ly s is re s u l ts show th a t lo c a liz a tio n of d e fo rm a tio n s in u n d ra in e d soils a n d soil s ta b i l i ty a re h ig h ly d e p e n d e n t o n th e c o m p re ss ib ih ty o f th e p o re flu id re la tiv e to th e so il sk e le to n , a n d t h a t c r i t ic a l b ifu r c a tio n d ire c tio n s in p la n e s t r a in a re a lw ays a t 45°, w h ile th e y re m a in h ig h ly v a r ia b le fo r o th e r s tre ss s ta te s . T h e d iffe re n ce b e tw e e n th e fr ic t io n a n d d i la ta n c y an g le s h as s u b s ta n t ia l in f lu e n c e on b e h av io r .

1. IN T R O D U C T IO N

T h is p a p e r su m m a r iz e s tw o d iffe re n t se ts of u n c o n v e n tio n a l t r ia x ia l e x p e r im e n ts c o n d u c te d u n d e r d ra in e d c o n d it io n s , a n d th e o re tic a l a n d n u m e ric a l a n a ly se s a t th e c o n s t i tu t iv e level in v o lv ing sa n d s u b je c te d to u n d ra in e d lo ad in g . T h e p u rp o s e o f th e d isc u ss io n of th e tw o e x p e r im e n ta l p ro g ra m s is to show t h a t u n u s u a l b e h a v io r can be o b se rv e d , a n d w h ile th e s e w ere d ra in e d e x p e r im e n ts , i t w ill b e a p p a re n t to th e re a d e r t h a t th e c o n s tr a in t o f n o -v o lu m e c h an g e , as w o u ld be th e case in u n d ra in e d e x p e r im e n ts , w ou ld re su lt in p o re w a te r p re s su re d e v e lo p m e n ts , c a u se d in la rg e p a r t b y d ila ta n c y , w h ic h a re id e n tic a l in p a t t e r n to th e v o lu m e tr ic s tr a in s . B o th se ts of e x p e r im e n ts w ere c o n d u c te d on a su b ro u n d e d to su b a n - g u la r O t ta w a s ilic a sa n d (F -7 5 ) p re p a re d a t d iffe re n t in it ia l d e n s itie s d e sc rib e d below .

2. B E H A V IO R A T L O W E F F E C T IV E S T R E S S E S

N in e d isp la c e m e n t c o n tro lle d , d ra in e d a n d cy clic c o n v e n tio n a l t r ia x ia l e x p e r im e n ts on u n ifo rm F - 75 O t ta w a sa n d w e re c o n d u c te d in th e m ic ro g ra v ity e n v iro n m e n t o f th e S p a c e H a b m o d u le o f th e S p a c e S h u t t le (S T S -7 9 , S e p te m b e r , 1996; S T S - 89, J a n u a ry , 1998). T h e e x p e r im e n ta l te c h n iq u e a n d d isc u ss io n of d a ta a re g iv en by S tu re e t al. (1 9 9 8 ). T h e c o n fin in g p re ssu re s in th e e x p e r i m e n ts w ere in th e ra n g e s 0 .05 , 0 .52 a n d 1.30 k P a , w ith tw o te s ts c o n d u c te d in e ach c a teg o ry . T h e sp e c im e n s m e a su re d 75 m m in d ia m e te r a n d 150 m m long . T h e d isp la c e m e n t r a te w as 35 m m p e r h o u r . T h e a v e ra g e g ra in size o f th e su b a n g u la r to su b ro u n d e d q u a r tz s a n d (F -7 5 ) w as 0.2 m m , a n d th e sp e c im e n s ’ re la tiv e d e n s itie s w ere 86 .5% a n d 65.0 % , w h ich a re d e n o te d F I a n d F 2 re sp e c tiv e ly in F ig s . 1, 2 a n d 3. T h e m o is tu re con-

133

a ’3i = 0.05 kPa

Figure 1 . Stress - Strain Responses for 85% (FI) and 65% (F2) Relative Density Specimens(0.05 kPa).

134

0.00 0.05

a \ , = 0 .5 2 k P a

0.10 0.15A xial S tra in

0.20 0.25

Figure 2 . Stress - Strain Responses for 85% (FI) and 65% (F2) Relative Density Specimens(0.52 kPa).

135

G \ ; = 1.30 kPa

0.00 0.05 0.10 0.15 0.20 0.25A xial Strain

Figure 3. Stress - Strain Responses for 85% (FI) and 65% (F2) Relative Density Specimens(1.30 kPa).

136

te n t in th e e x p e r im e n ts w ere 0 .08% , w h ich a p p e a rs to h a v e r e s u l te d in in s ig n if ic a n t c a p il la ry fo rces. E le c t ro s ta t ic e ffec ts , w h ic h w ere s ign ific a n t to w ith in five m in u te s a f te r sp e c im e n p re p a r a t io n , w ere a lso fo u n d to b e in s ig n if ic a n t a t th e

t im e of te s t in g , w h ich w as a m o n th a f te r p r e p a ra tio n . T h e re s u l ts fo r th e (a ) 0 .05 k P a (co n fin in g s tre s s ) e x p e r im e n ts w ere f r ic t io n a n g le s a t p e ak s t r e n g th in th e r a n g e o f 7 5 .0 ‘ to 7 0 .F a n d d ila- ta n c y a n g le s o f 31.0® ; a n d f r ic t io n a n g le s a t co n s ta n t v o lu m e (c ri t ic a l s t a te ) e q u a l to 34.0®. For th e (b ) 0 .052 k P a e x p e r im e n ts th e f r ic t io n ang les a t p e a k s t r e n g th w ere in th e ra n g e o f 58 .5 to 54.0®, w ith d i la ta n c y an g le s e q u a l to 30.0®. T h e fr ic tio n a n g le s a t c r itic a l s t a te w ere 35.0®. F o r th e (c) 1.30 k P a e x p e r im e n ts f r ic tio n a n g le s a t p e a k s t r e n g th w ere o b se rv e d to b e in th e ra n g e of 56 .4 to 53.8®, w ith d i la ta n c y a n g le s a lso a t 30.0® a n d c ritic a l s t a te f r ic t io n a n g le s a t 34.0®. T y p ic a l s t r e s s - s tr a in a n d v o lu m e c h a n g e re sp o n se s fo r th e s e te s ts a re sh o w n in F ig s. 1 ,2 a n d 3. T e r r e s t r ia l e x p e r im e n ts c o n d u c te d on th e sa m e m a te r ia l a n d a t th e sam e d e n s ity ra n g e s r e s u l te d in p e a k f r ic t io n a n g le s in th e ra n g e of 42 .0 - 41.0®, d i la ta n c y a n g le o f 10.5®, a n d a f r ic t io n a n g le a t c r it ic a l s t a te o f 34.2®.

F iv e u n lo a d in g a n d re lo a d in g cycles w e re c o n d u c te d a t r e g u la r in te rv a ls in th e e x p e r im e n ts , w h ich w ere c a r r ie d o u t to a x ia l s t r a in s o f 25% . T h e u n lo a d in g - re lo a d in g cycles show v e ry s im ila r stiffn ess m o d u lu s (Y o u n g ’s) b e h a v io r a n d v e ry m in o r c o u p lin g to d e fo rm a tio n level a n d e ffe c tiv e co n fin in g p re s su re . In a ll e x p e r im e n ts th e in it ia l s tiffn ess is s im ila r to th e u n lo a d in g -re lo a d in g m o d u li, w hich w ere in th e ra n g e of 11.8 - 20 M P a (a t 0 .05 k P a ) to 17.0 - 23.7 M P a (a t 1.30 k P a ) , c o m p a re d to m o d u li o f 21.0 - 39 .0 in th e co n fin in g p re ssu re ra n g e of ra n g e o f 12.0 to 69 .0 k P a . A n a tu r a l la te x m e m b ra n e h a v in g th ic k n e ss in th e ra n g e of 0.30 m m iso la te d e ac h sp e c im e n . T h e in flu en ce of th e m e m b ra n e ’s stiffn ess w as in c o rp o ra te d in th e d a ta a n a ly s is . T h e v e ry h ig h d i la ta n c y a n gles o b se rv e d in a ll th e low c o n f in e m e n t level e x p e r im e n ts a re u n u s u a l ly h ig h , a n d e x p la in to a c e r ta in e x te n t th e h ig h f r ic t io n an g le s . A p e r i o d ic in s ta b i l i ty p h e n o m e n o n , w h ic h a p p e a rs to be a s so c ia te d w ith fo rm a t io n o f m u lt ip le ra d ia l- fan sh e a r b a n d s a p p e a rs in a ll th e e x p e r im e n ts . X -ra y c o m p u te d to m o g ra p h y re c o rd s show th a t sh e a r b a n d s d id n o t fo rm u n t i l a x ia l s t ra in s of

3 .5% a n d fa r a f te r p e a k s t r e n g th w as re a c h e d a n d a t th e a p p ro x im a te c r it ic a l s t a te level. T h e low e s t c o n f in e m e n t te s ts (0 .05 k P a ) a re c h a ra c te r iz e d b y s u b s ta n t ia l s t r a in - s o f te n in g in te rm s of s te e p ly d e sc e n d in g s t r e s s - s tr a in re sp o n se s . T h e c u rio u s in c re m e n ta l e x p a n s io n seen in th e th ir d v o lu m e tr ic s t r a in vs. a x ia l s t r a in u n lo a d in g -re lo a d in g c y cle in F ig . 3 is e x p la in e d by a n o b se rv e d in s ta b ili ty in th e m e m b ra n e , w h ich su d d e n ly fo ld ed a t th is p o in t , a n d w h ich re s u l te d in a v o lu m e -c h a n g e p u lse . F ig u re 4 show s a su m m a ry of o b se rv e d f r ic t io n a n d d i la ta n c y a n g le s . T h e F 3 d a ta p o in t re fe rs to a n a d d it io n a l lo w -a m p litu d e cyclic se t o f e x p e r im e n ts a lso c o n d u c te d a t a r e la tiv e d e n s ity o f 65% , a n d w h o se d a ta a re n o t p re se n te d h e re .

F ig u re 5 show s v o lu m e tr ic s t r a in vs. a x ia l s t r a in r e s u l ts fo r sp e c im e n s s u b je c te d to an e ffec tiv e c o n f in e m e n t s tre s s o f 2 .00 k P a , w h e re low d e n s ity sp e c im e n s (D^ = 10% a n d h ig h e r) show dilative r a th e r th a n c o n tra c t iv e b e h a v io r , ev en a t r e la t iv e ly h ig h a x ia l s t r a in leve ls. T h is o b se rv a tio n is in c o n tr a s t to c o n v e n tio n a l c o n c e p ts , w h e re su c h sp e c im e n s w o u ld b e p e rc e iv e d to c o n tr a c t in vo lu m e . C lea rly , if th e se e x p e r im e n ts h a d b e e n c o n d u c te d u n d e r u n d ra in e d c o n d itio n s , w e w o u ld e x p e c t th e e ffec tiv e s tre sse s to in c re a se as a r e su lt of a v o lu m e in c re a se in th e fa b ric -so il sk e le to n .

3. D IR E C T IO N A L S H E A R C E L L (D S C ) E X P E R IM E N T S

D ire c tio n a l S h e a r C ell e x p e r im e n ts o n 178 m m c u b ic a l sp e c im e n s of O t ta w a F -7 5 sa n d w ere c o n d u c te d u n d e r p la n e s t r a in c o n d it io n s , w h e re u n ifo rm a n d c o n tro lle d n o rm a l a n d sh e a r t r a c tio n s w ere a p p lie d in d e p e n d e n t ly to th e sp e c im e n s ’ s u r faces. T h e D S C a p p a r a tu s a n d e x p e r im e n ta l te c h n iq u e h a v e b e e n d e sc rib e d p re v io u s ly a n d w ill n o t be r e p e a te d h e re (S tu re e t a h , 1988; M c F a d d e n , 1988; A s ta n e h , 1988). T h e a p p a r a tu s is o p e r a te d in lo a d c o n tro l a n d ro ta t io n s o f th e p r in c ip a l s tre s s d ire c tio n s w ith r e sp e c t to th e m a te r ia l ax es c an b e a p p lie d in a c o n tin u o u s , d is c re te ju m p - lik e m a n n e r , o r c o m b in a tio n s o f th e se . T h e s tre ss-

s t r a in r e sp o n se b e h a v io r fo r d iffe re n t se ts o f e x p e r im e n ts , w h e re th e p r in c ip a l s tre s s d ire c tio n s c o n tin u o u s ly r o ta te a lo n g a c ir c u la r s tre s s p a th , w h ile th e m a g n i tu d e o f th e p r in c ip a l s tre sse s re m a in c o n s ta n t , a n d se ts o f d is c re te p r in c ip a l s tre ss-

137

8 0

OX)c<

60

u. LEGEND"ed

50* FI

c — X F2S + Ground

E3

o CV

• F 3 +E 40 $><cd

$ 00

0 ♦0

30 _____1_______ 1_____L.... JL--1... 1 - . - ^ , ] _____________ L ______1_____ ................................................ . . 1 , , ,0.01 0.10 1.00

Confining Stress, kPa10.00 100.00

35

30

W)25

W)c<g 20ca

15

10

-1 . 1 . ’ ‘ > 1

- X

- X -- -_ _

-+ -

-LEGEND

+-

- ♦ FI X F2 + 4- -

- + Ground -f +

- -

- __■ ■ ■ . . . . 1 1_____L ^ .»- . >. i_____ -

0.01 0.10 1.00Confining Stress, kPa

10.00 100.00

Figure 4. Observed Friction and Dilatancy Angles Versus Effective Confining Stress.

138

Axial Strain

F ig u re 5. V o lu m e tr ic S tr a in (E x p a n s io n ) V ersus A x ia l S tra in .

F ig u re 6. P la n V iew I l lu s tr a t io n o f th e D ire c tio n a l S h e a r C ell, In i t ia l C o n f ig u ra tio n (C u ta w a y )

a n d D is to r te d C o n fig u ra tio n .

139

Figure 7. Specimen and Apparatus Axes.

(a)

Figure 9. Stress - Strain Response Curves (a, b, c, d), Straight Stress Path.

140

d ire c tio n ju m p s c o m b in e d w ith c o n tin u o u s s tre ss ro ta t io n e x p e r im e n ts a re d e sc r ib e d in th e fo llow ing . T h e c irc u la r s tre s s p a th m a y b e o f im p o rta n c e w h e n c o n s id e r in g cyclic lo a d in g o f su rfa ce d e p o s its a n d soil e le m e n ts a d ja c e n t to o r be low sh a llo w a n d d e ep fo u n d a tio n s . F ig u re 6 show s a sc h e m a tic d ia g ra m o f th e D S C (S tu re e t a h , 1988), a n d F ig s. 7, 8, 9, 10 a n d 11 sh o w d ia g ra m s of sp e c im e n a n d a p p a r a tu s a x es , s t re s s p a th s a n d s t r e s s - s tr a in a n d v o lu m e c h a n g e re sp o n se s fo r t y p ica l e x p e r im e n ts . F ig u re 8 show s tw o s t re s s p a th s . B o th se ts o f e x p e r im e n ts s t a r te d w ith u n ia x ia l s t r a in (Ko) lo a d in g to a s tre s s leve l o f 100.0 k P a (14 .5 p s i) . In th e h g u re th is is d e n o te d by A -B . A t B c o m b in a tio n s o f n o rm a l a n d s h e a r s tre sse s w ere a p p lie d in su ch a w ay t h a t lo a d in g , u n lo a d in g a n d re lo a d in g p ro c e e d e d a lp h a b e t ic a l ly fro m B th ro u g h H . T h e n u m b e r 30 re fe rs to th e o r ie n ta t io n (30°) o f th e s tre s s p a th in th is d ia g ra m .

In th e c irc u la r s tre s s p a th th e lo a d in g c o n tin u e d a t B a lp h a b e t ic a l ly to F , w h ile th e p r in c ip a l s tre ss m a g n i tu d e s re m a in e d c o n s ta n t . F ig u re 9 show s s t r e s s - s tr a in re sp o n se s in v a rio u s fo rm a ts in c lu d in g v o lu m e tr ic s t r a in fo r th e f irs t s tre s s p a th e x p e r im e n t. F ig u re 10 show s s t r e s s - s tr a in re sp o n se s for th e c irc u la r s tre s s p a th . I t is o b se rv e d th a t s u b s ta n t ia l d e fo rm a tio n a n d v o lu m e c h a n g e o c c u r, a n d th e r e sp o n se h a s a cy c lic p a t t e r n . T h e di- la ta n c y re sp o n se in th is d ra in e d te s t is s ig n ifican t. T h e se re sp o n se c u rv es a re ty p ic a l o f w h a t has b een o b se rv e d in o th e r D S C a n d H ollow C y lin d e r C o m p re s s io n a n d E x te n s io n a p p a ra tu s e s , an d w h ile m a n y of th e s e t e s ts w ere d ra in e d , th e y a re ag a in in d ic a tin g t h a t g iv en a n u n d ra in e d s i tu a tio n excess p o re w a te r p re s su re s w o u ld b e g e n e ra te d , w hose p a t t e rn s a n d h is to ry w o u ld b e very s im ila r to th o se of th e v o lu m e tr ic s t r a in s . M ost la b o ra to ry e le m e n t ( c o n s t i tu t iv e ) e x p e r im e n ts a re c o n d u c te d w ith fixed lo a d in g a x es , w h o se o r ie n ta

t io n s re m a in c o n s ta n t vs. th e m a te r ia l axes . T h e D S C e x p e r im e n ts show t h a t s ig n if ic a n t d e fo rm a tio n s a n d v o lu m e tr ic c h an g e o c c u r w h e n th e p r in c ip a l s tre s s d ire c tio n s r o ta te , even w h en th e p r in c ip a l s tre s s m a g n i tu d e s re m a in c o n s ta n t . M o st s t r e s s - s tr a in a n d p o re -w a te r p re s su re th e o r ie s or m o d e ls w o u ld n o t b e a b le to p re d ic t th is p h e n o m e n o n .

4. S H E A R B A N D F O R M A T IO N U N D E RU N D R A IN E D C O N D IT IO N S

A t th e a n a ly t ic a l c o n s t i tu t iv e level d isc o n tin u o u s b ifu rc a tio n s o f th e in c re m e n ta l so lu tio n s a re u s u a lly c o n s id e re d as p re c u rso rs o f lo c a liz a tio n p h e n o m e n a , in c lu d in g fo rm a t io n of sh e a r b a n d s . M o st o f th e s tu d ie s c a r r ie d o u t h a v e b e e n fo r o n e -p h a se m a te r ia ls (R u n e sso n e t a h , 1995). H ow ever, th e sh e a r b a n d p h e n o m e n o n is a lso re le v a n t to s a tu r a te d so ils a n d u n d ra in e d c o n d it io n s . In a m ix tu r e th e o ry a p p ro a c h R u n e sso n e t a l. (1995) a n d L a rs so n e t. a l (1998) s tu d ie d th e b e h a v io r o f e la s to p la s t ic so ils, t h a t fo llow M o h r-C o u lo m b th e o ry a n d e x h ib i t d i la ta n c y . B e h a v io r for d iffe ren t b u lk m o d u li r a t io s b e tw e e n th e sk e le to n a n d flu id w ere s tu d ie d , a n d it w as sh o w n th a t c o n d itio n s for in s ta b i l i ty a n d sh e a r b a n d fo rm a tio n a re h ig h ly d e p e n d e n t on s tre s s s t a te (a x is y m m e tr ic t r ia x ia l vs. p la n e s t r a in vs. fu lly th re e -d im e n s io n a l) . T h e s h e a r b a n d d ire c tio n s a re h ig h ly d e p e n d e n t on th e c o m p re s s ib il ity o f th e f lu id , a n d fo r a v e ry s tiff l iq u id th e sh e a r b a n d o r ie n ta t io n s a re a t 45° in p la n e s t r a in b u t c a n ta k e on v e ry d iffe re n t m a g n i tu d e s fo r o th e r s tre s s a n d k in e m a tic c o m b in a tio n s . T h e d iffe re n ce b e tw e e n th e f r ic t io n a n d d i la ta n c y a n g les , a n d th e P o is s o n ’s r a t io o f th e e la s t ic p a r t o f th e so il sk e le to n a lso h a v e s ig n if ic a n t in flu e n ce on th e c r it ic a l h a rd e n in g m o d u lu s , so f te n in g b e h a v io r a n d p o re w a te r p re s su re g e n e ra tio n . D e ta ile d a n a ly se s o f th e s e issu es a re fo u n d in R u n e sso n e t a l. (19 9 5 ) a n d L a rs so n e t a l. (1998).

5. S U M M A R Y

T w o c a te g o r ie s o f u n c o n v e n tio n a l t r ia x ia l e x p e r

im e n ts h a v e b e e n d e sc rib e d . I t h a s b e e n show n th a t u n u su a lly h ig h f r ic t io n a n d d i la ta n c y ang les a re o b se rv e d a t low e ffec tiv e s t re s s leve ls, a n d th a t soils t h a t u n d e r n o rm a l s t re s s c o n d it io n s te n d to c o n tra c t in v o lu m e , d i la te a t low s tre s s levels. T h is m a y in d ic a te t h a t n e a r su rfa c e d e p o s its , even v ery lo o se so ils, m a y n o t l iq u e fy u n d e r s tro n g g ro u n d m o tio n , b u t r a th e r re m a in in ta c t as soil s t r a ta b e lo w s u b je c te d to h ig h e r e ffec tiv e s tre sse s w ill liquefy . C h a n n e lin g o r j e t t in g o f h ig h excess p o re p re ssu re s th ro u g h th e in ta c t su rfa c e so ils re su lt in s a n d b o ils . D ire c tio n a l S h e a r C e ll e x p e r i

m e n ts sh o w th a t u n u su a l d e fo rm a tio n a n d v o lu m e ch an g es c a n o c c u r , ev en in s i tu a t io n s w h e re th e

141

(0

Figure 9. (Continued) Stress - Strain Response Curves (e, f, g, h)

bI

-(a) (c)

(b) (d)

Figure 10. Stress - Strain Response Curves for Circular Stress Path (a, b, c, d)

142

principal stress magnitudes remain constant, but where their orientations change. This may result in pore pressure generation patterns and magnitudes, which cannot be readily predicted based on current theories and conventional experimental concepts. Elastoplastic constitutive theories provide further insight to how shear bands form in saturated soils, and whether stabilizing or destabilizing behavior will follow.

Sture, S., Costes, N.C., Batiste, S.N., Lankton, M.R., Alshibh, K.A., Jeremic, B., Swanson, R.A., Frank, M,, 1998, Mechanics of granular materials at low effective stresses, ASCE, J. Aerospace Engineering, 11, 3, 67-72.

6. ACKNOWLEDGEMENT

The author acknowledges collaboration with N.C. Costes, S.N. Batiste, M.R. Lankton, K.A. Alshi- bli, B. Jeremic, R.A. Swanson and M. Frank, and support from NASA Contract NAS8-38779 for the low stress experiments and analytical constitutive work. The DSC experiments were conducted in collaboration with H.-Y. Ko and supported by US Army Waterways Experiment Station, Contract DACW-39-85-C-0080.

REFERENCES

Astaneh, S.M.F., 1988, Experimental investigation of sand behavior under nonproportional loading, MS thesis. University of Colorado, Boulder. Desrues, J., Mokni, M., and Viggiani, G., 1997, Experimental strain localization in undrained biaxial tests on sand, Symp. on the Theory and Prediction of Localized Failure in Materials, McNU ’97, June 29-July 2, 1997, Northwestern University.Larsson, R., Larsson J., Runesson, K. k Sture, S., 1998, Localization in an undrained hypoelastic porous medium, Proc. Biot Symposium, Louvain- la-Neuve, University of Louvain, Belgium, Sept. 14-16, 1998McFadden, J.J., 1988, Experimental response of sand during principal stress rotation, MS thesis. University of Colorado, Boulder.Runesson, K., Peric, D., and Sture, S., 1995, Effect of pore-fluid compressibility on localization in elastic-plastic porous solids, Int. J. Solids Structures, 33, 1501-1518.Sture, S., Budiman, J.S., Ontuna, A.K., and Ko, H.-Y., 1988, Directional Shear Cell experiments on a dry cohesionless soil, ASTM, J. Geotechnical Testing, 10, 2, 71-79.

143


Influence o f confining stress on liquefaction resistance

M.E. Hynes & R.S.OlsenUS Army Engineer Waterways Experiment Station, Vicksburg, Miss., USA

ABSTRACT: The confining stress factor is used in liquefaction evaluations to extend empirical charts for liquefaction resistance to confining stresses higher than the empirical field-performance database, approximately 1 atm. Estimates o f from Harder (1988) and Hynes (1988) indicated relatively large reductions in liquefaction resistance ratios with increasing confining stress. Laboratory work by Vaid and colleagues (1985,1995) indicated higher values of K„. In this study, a database was developed to investigate the reasons for the broad scatter in K . From our study we conclude that: 1) is strongly influenced by method of deposition, stress history, aging effects, and density; 2) reconstructed, pluviated specimens in the laboratory may represent recently deposited dredged materials or recently liquefied materials; however, 3) high quality undisturbed samples are needed to determine field-relevant values o f The MCEER International Liquefaction Committee (Youd & Idriss 1997) adopted the recommendations from this study.

1 BACKGROUND

Laboratory measurements typically indicate that for a given soil, consistency (relative density for sands and gravels) and stress history, there is a non-linear relationship between liquefaction resistance and confining stress (Seed & Idriss 1981; Seed 1983; Vaid et al. 1985; Hynes 1988; Harder 1988; Seed & Harder 1990; Pillai & Byrne 1994; Youd & Idriss 1997). Consequently, if cyclic strengths, either from laboratory measurements performed at a confining stress o f 1 atm or estimated from correlations to in situ measurements sueh as Standard Penetration Tests (SPT), are linearly extrapolated to higher effective confining stress levels, the calculated liquefaction resistances may be too high. The effect o f confining stress on liquefaction resistance is further complicated by soil compressibility and stress history.

The state-of-the-practice approach to account for the non-linear relationship between liquefaction resistance and vertical effective stress is to use published charts derived from existing laboratory data on similar materials or to determine a site specific relationship with a comprehensive laboratory testing program. Whichever approach is used, liquefaction resistance is conventionally represented as the Cyclic Resistance Ratio (CRR, the ratio of cyclic shear strength (i^y) divided by the vertieal effective stress, (a^ )). For a given soil at a given consistency and stress history, the CRR generally decreases with increasing vertical effective stress. This decrease is

described by the factor which is defined as the ratio o f CRR for a given o to the CRR at a vertical effective stress o f 1 atm, CRR| (compared at the same relative density).

The use of laboratory tests to establish CRR, for a material has decreased over the last deeade in favor of in situ test correlations because o f the cost- effectiveness o f in situ measurements, the robustness o f the Seed SPT-liquefaction chart (Seed et al. 1985, Youd & Idriss 1998), and concerns over sample disturbance and other issues associated with laboratory test results. The CRR, can be determined from in situ measurements such as the SPT, Cone Penetration Test (CPT), or shear wave velocity (VJ, or from laboratory measurements. The state-of-the-art for estimating CRR, using the SPT is given by Seed et al. (1985); using the CPT is given by Stark et al. (1995), Olsen et al. (1996), or Robertson & Wride (in Youd & Idriss 1997); and using is given by Andrus & Stokoe (in Youd & Idriss 1997).

The database for these CRR, correlations consists o f information from water-laid deposits o f sands and silty sands, level to slightly sloping ground, under vertical effective stresses o f less than 3 atm.

Consequently, laboratory tests have been used to provide a relative scale to adjust the CRR, values from in situ tests to higher confining stress levels and nonlevel ground stress conditions. The purpose o f this study was to review the current state o f knowledge with respect to the influence o f overburden stress on liquefaction resistance. An emerging concept will be

145

Figure

Vertical effective stress (atm units, e.g. tsf)1 Laboratory data and relationships

presented, namely the Stress Focus theory (Olsen1994), which provides an alternative framework for interpreting confining stress effects on in situ measurements such as penetration resistance, and soil properties such as liquefaction resistance.

2 HISTORICAL DATA AND CHARTS

2.1 Ka Data and Charts

Cyclic laboratory tests provide a means o f determining liquefaction resistance o f a soil under various controlled conditions-density, confining stress, stress history, applied cyclic load or strain history, and drainage boundary conditions. The influence of confining stress can be evaluated by conducting cyclic laboratory tests for a soil, holding the other parameters constant, at several confining stress levels. In this section, historical cyclic laboratory test data for a variety o f soils are examined to observe trends in from the historical database.

Early tests on sands and silty sands indicated considerable scatter in the values o f K ,. These data, summarized in Figure 1 and taken in part from Harder (1988), include Upper and Lower San Fernando Dams (Seed et al. 1973, Seed et al. 1989) and Fort Peck Dam (Marcuson & Krinitzsky 1976). Superimposed on Figure 1 is an early K„ relationship suggested by Seed(1983). As more data became available, the chart was updated by Harder (1988), and again by Seed & Harder (1990).

Olsen (1984) generalized the data trends from the preliminary relationship by Seed (1983), together with project data at WES into the following expression: K(,=(o‘y) . This expression is plotted inFigure 1. Olsen (1984) reported that the stress exponent, f, ranged from 0.6 to 0.95 with 0.7 recommended for sands. This recommendation is similar to the updated Seed curves shown in Figure 1.

Gravel data from Oroville Dam (Banerjee et al. 1979) and WES project files (Ririe, Folsom and Success Dams) were added to the database; these data are from large-scale cyclic triaxial tests on moist- compacted specimens. Silt, silty sand and sandy silt data was added from a number o f dam studies, notably Upper and Lower San Fernando, Fort Peck, Enid and Arcadia Dams.

Byrne & Harder (1991) selected K„ values for clean sands from previous work to develop a recommendation for the clean sands and gravels present at Terzahgi Dam, Canada. Their data set included the work by Vaid et al. (1985) and Vaid & Thomas (1995) as well as clean sand data from Seed & Harder (1990). The resulting “clean sand” curve is shown in Figure 1.

2.2 Stress focus plots o f cyclic strength

Trends in geotechnical data with confining stress are sometimes easier to see when the data are plotted in log-log plots. These log-log plots are termed stress focus plots from Olsen (1994). If data fit as a straight

146

Liquefaction Cyclic Resistance (atm)

1.01 0.10 1.00

Liquefaction Cyclic Resistance Strength Ratio (CRR)

10.00 0.01 0.10 1.00

Figure 2 Generalized stress focus plots o f cyclic shear strengths and stress ratios

line on a log-log stress focus plot, then these data are well fitted by a simple exponential curve. Stress focus plots were used in this study as a framework for investigating confining stress effects on cyclic strength and CRR.

Stress focus theory (Olsen 1994) shows that curves for cyclic strength, penetration resistance, and other soil properties that are functions of confining stress and density tend to converge as confining stress increases. This point (or zone) o f convergence is termed the stress focus, and is a function o f soil type and mineralogy (Olsen 1994).

The slope of a line in a cyclic strength stress focus plot corresponds to the inverse of the exponent used by Olsen (1984) to describe K : Ko==(o\,/“‘ (Figure 1). This is shown in the stress focus plot of cyclic strength in Figure 2, which shows generalized stress focus cyclic strength lines for a very loose to dense sand. As density increases, the cyclic strength at a confining stress o f 1 atm, CRRi, increases and the slope, f, decreases. The corresponding curves (Ko^(o J ’’) are shown in Figure 1. As density increases, the exponent f decreases and decreases, resulting in a more severe reduction to CRR.

2.3 Observations from the Database

The data were reviewed by soil type (sand, gravel and silt mixtures) and by method of deposition (laboratory pluviation, moist compaction and

undisturbed samples of water-laid deposits). The data in Figure 1 are identified by method o f deposition. We observed that is more strongly affected by stress- history, aging effects and density than by soil type. This was most clearly illustrated by the data from Fort Peck Dam. Marcuson & Krinitzsky (1974) report laboratory tests on undisturbed and wet-pluviated reconstructed specimens, as well as in situ blowcounts. The resulting cyclic strengths are plotted in Figure 3.

Figure 4 was used to estimate equivalent Ni 6o values (based on relative density) for the fine clean sands tested by Vaid et al. (1985) and Vaid & Thomas(1995). In situ Ni 60 values for the gravel data from WES were estimated from Becker blowcounts. Corresponding values o f CRRj were estimated from the Seed et al. (1985) liquefaction chart. A comparison o f the CRR, determined from laboratory tests with values determined from N, 6o are shown in Figure 5 as a function o f relative density.

Figure 5 indicates that cyclic strengths from laboratory pluviated specimens underestimate CRR, values by a factor of about 2 to 3; undisturbed specimens underestimate CRR, by about 10 to 20 percent; moist-tamped specimens overestimate CRR, at low relative density and underestimate at high relative density.

The pluviated specimens had low cyclic strength and high values o f (f > 0.9). However, laboratory strengths from undisturbed specimens and CRR, values determined from blowcounts are approximately

147

0.1

o

otr(D>

10.0

OStress F o c l s

(Liquefaction Res stance)

Ft. P eck D am

- e ~ F o un d a tio n - re c o n s titu te d

— K - S he ll - re c o n s titu te d

A C o re - u nd is tu rbe d

X S h e l l ' u nd is tu rbe d

■ F o un d a tio n - u nd is tu rbe d

8 S he ll - S P T d e te rm in e d

T F o un d a tio n - S P T d e te rm in e d

0.10 1.00 10.00

Field Liquefaction Cyclic Resistance Ratio (CRR)(N=10 and field equivalent values using Cr)

Figure 3 Stress focus plot o f field and laboratory estimates of cyclic stress ratios for Fort Peck Dam

SPT(Ni)eo

Figure 4 Relationship between relative density and N, go

148

crr12dr.grf OLSEN 09/21/98

PluviatedSamples

CRRi (SPT)

CRR^ (Lab)/

/TT

é '-Undisturbed

Samples

“Moist-tampedSamples

/ ♦Pluviated / ^Speciments \ ^

\ oUndisturbed / ▼

Samples ^

Moist-Tamped Gravels \. / □

\ □

Ottawa

Fraser R iver

Fort P eck Dam

Fort Peck Dam

Low er S an Fernando Dam

Folsom Dam

Ririe Dam

Success Dam

80 1000 20 40 60

R elative Density (D^), %

Figure 5 Comparison o f CRRi from laboratory tests with CRRi from SPT blowcounts

2.5 times the strengths from the pluviated specimens. This indicates that the values from the pluviated specimens are unconservatively high.

3 CONCLUSIONS AND RECOMMENDATIONS

3.1 Conclusions

We conclude from this study that method of deposition, aging, stress history and density strongly influence K . These effects are emphasized at low confining stresses, such as 1 atm, and are de- emphasized as confining stresses increase, and ultimately converge at the stress focus. Within the stress range o f interest for dams, typically less than 10 atm, Ko is not strongly influenced by soil type. Specimens pluviated in the laboratory may represent recently deposited materials such as dredged and liquefied materials. However, for water-laid foundation deposits typical for dams, high quality undisturbed specimens are necessary to determine field-relevant values o f K .

3.2 Recommendations

For practical liquefaction evaluations, it is recommended that K„ be estimated as suggested by Olsen (1984): Ko=(a\,)^’’. For relatively loosedeposits the exponent f is about 0.8; f decreases to 0.7 for medium dense, and to 0.6 for dense or slightly overconsolidated deposits. For very dense or higher overconsolidation (stress history and aging effects), the exponent f may be less than 0.6. In their August 1998 meeting, the MCEER International Liquefaction Committee (Youd & Idriss 1997) adopted the

recommendations from this study.

4 ACKNOWLEDGMENT

This study was sponsored by the Civil Works Earthquake Engineering Research Program o f the US Army Corps of Engineers, and the Panama Canal Commission. Permission was granted by the Chief o f Engineers to publish this information.

5 REFERENCES

Andrus, R. D. & Stokoe, K. H. 1996 (in prog.). Guidelines for evaluation o f liquefaction resistance using shear wave velocity, 1996 Salt Lake City Workshop on evaluation o f liquefaction resistance, Youd & Idriss, editors, NCEER publication.

Banerjee, N. G., Seed, H. B., & Chan, C. K. 1979. Cyclic behavior of dense coarse-grained materials in relation to the seismic stability o f dams. Report No. UCB/EERC-79/13, University o f California, Berkeley,CA.

Bieganousky, W. A. & Marcuson, W. F. III. 1976. Liquefaction potential o f dams and foundations. Report 1: Laboratory standard penetration tests on Reid-Bedford model and Ottawa sands. Research Report S-76-2, USAE Waterways Experiment Station, Vicksburg, MS.

Bieganousky, W. A. & Marcuson, W. F. III. 1977. Liquefaction potential o f dams and foundations,

149

R e p o rt 2: L ab o ra to ry s tan d ard p e n e tra tio n tes ts on P la tte R iv er sand and standard concre te sand, R esearch R ep o rt S -76-2 , U S A E W aterw ay s E x p erim en t S tation , V ick sb u rg , M S .

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H a rd e r, L. F. 1988. U se o f p e n e tra tio n tes ts to d e te rm in e th e cy c lic lo ad in g re s is tan c e o f g rav elly so ils d u rin g e a rth q u ak e sh ak in g , P hD D isserta tio n , U n iv e rs ity o f C a lifo rn ia at B e rk e ley .

H ynes, M . E. 1988. P ore p re ssu re characte riza-tion o f g rav els u n d e r u n d ra in e d cy c lic lo ad in g , PhD D isserta tio n , U n iv e rs ity o f C a lifo rn ia at B erkeley .

G ib b s , H . J. & H o ltz , W . G. 1957. R e se arc h on d e te rm in in g th e d en sity o f sand by sp o o n p e n e tra -tio n tes tin g . P ro c e ed in g s , F o u rth in te rn a tio n a l con feren ce on soil m ech an ics and fo u n d a tio n e n g in e erin g , vol. I, pp 35-39 .

M arcu so n , W . F. I l l & K xin itzsky , E. L. 1976. D ynam ic an aly sis o f F ort P eck dam , T echn ical R ep o rt S -76-1 , U S A E W aterw ay s E x p erim en t S ta tion , V ic k sb u rg , M S .

O lsen , R. S. 1984. L iq u e fac tio n a n a ly s is u sin g the cone p e n e tro m e te r tes t (C P T ), P ro c e ed in g s , E igh th w orld co n feren ce on earth q u ak e eng ineering , July, San F ran c isco , C A .

O lsen , R. S. 1994. N o rm a liza tio n and p red ic tio n o f g e o te ch n ic a l p ro p e rtie s u sin g the cone p e n e tro m e te r test (C PT ), PhD D isserta tion , U n iv e rs ity o f C a lifo rn ia a t B erkeley .

O lsen , R. S ., K o este r, J. P., & H y n es, M . E. 1996. E v a lu a tio n o f liq u e fac tio n p o ten tia l u sin g the C PT , P ro ceed in g s , 2 8 th Jo in t m ee tin g o f the U S -Jap an c o o p era tiv e p ro g ram in n a tu ra l re so u rce s-p a n e l on w in d and se ism ic e ffec ts , U S N a tio n a l In stitu te o f S tan d ard s an d T ech n o lo g y , G a ith e rsb u rg , M D , M ay 1996.

O lsen , R. S. 1996. T h e in flu en ce o f c o n fin in g stress on liq u efac tio n resistance . P roceed ings, F irst U S -Japan w o rk sh o p on ad v an c ed re sea rch on earth q u ak e e n g in eerin g fo r d am s, U S A E W aterw ay s E x p erim en t S ta tion , V ic k sb u rg , M S , N o v e m b er 1996.

O lsen , R. S. 1998. C y c lic liq u e fac tio n based on the cone p e n e tro m e te r test. P ro c e ed in g s , N C E E R w orkshop on ev a lu a tio n o f liquefac tion o f soils, Y oud,

L. & Id riss , I. M ., ed ito rs . T ec h n ic a l R e p o rt N C E E R - 9 7 -0 0 2 2 , S ta te U n iv e rs ity o f N e w Y o rk a t B u ffa lo , B u ffa lo , N Y .

P illa i, V . S, & B y rn e , P. M . 1994. E ffec t o f o v e rb u rd e n p ressu re o n liq u e fac tio n re s is tan c e o f sands, C an ad ian G eo tech n ica l Jo u rn a l, vo l. 31.

R o b e rtso n , P. K. & W ride , C. E. 1997. C y c lic liq u e fac tio n and its e v a lu a tio n b a se d o n th e S P T and C P T , Y oud , L. & Id riss , I. M ., ed ito rs . W o rk sh o p on e v a lu a tio n o f liq u e fac tio n re s is tan c e o f so ils. P roceed ings, T echnica l R ep o rt N C E E R -9 7 -0 0 2 2 , Sa lt L ake C ity , U T.

Seed, H. B ., L ee, K . L ., Id riss , I. M ., & M a k d is i, F. I. 1973. A nalysis o f the slides in the S an F ern an d o dam s during the earthquake o f F eb ru ary 9, 1971, R ep o rt N o. E E R C -7 3 -2 , C o lleg e o f E n g in e e rin g , U n iv e rs ity o f C a lifo rn ia , B e rk eley , C A .

Seed, H. B ., Seed, R. B ., H ard er, L. F ., & Jo n g , H. L. 1989. R e-eva lua tion o f the L o w er San F ernando d am - R eport 2: e x am in a tio n o f the p o s t-e a rth q u a k e slid e o f F e b ru a ry 9, 1971, C o n trac t R e p o rt G L -8 9 -2 , U S A E W aterw ay s E x p erim en t S ta tion , V ic k sb u rg , M S .

S eed , H . B. & Id riss , I. M . 1981. E v a lu a tio n o f liq u e fac tio n p o ten tia l o f san d d e p o s its b a se d on observations o f p e rfo rm a n ce in p re v io u s e a rth q u ak e s , P ro ceed in g s, A S C E n a tio n a l fa ll c o n v en tio n . S ess io n N o. 24, St. L ou is , M O .

Seed, H. B. 1983. E a rth q u ak e -re s is tan t d e s ig n o f earth dam s. P ro c e ed in g s , S y m p o siu m on se ism ic d esig n o f e m b a n k m en ts and c av e rn s. M ay , A S C E pg 41-64 .

Seed, R. B. & H arder, L. F. 1990. S P T -b ased analysis o f cyclic p o re p re ssu re g en e ra tio n an d u n d ra in e d stren g th . P ro ceed in g s , H . B. S eed m em o ria l sy m p o siu m . M ay, B itech P u b lish e rs , vol. 2, pg 351- 376.

S tark , T. D ., & O lso n , S. M . 1995. L iq u e fac tio n re sis tan ce u sing SP T and fie ld case h is to rie s , Jo u rn a l o f G eo technica l E n g in eerin g , A S C E , N e w Y ork , N Y , vol. 121(12), pp 856-868 .

U S A E D istric t, T u lsa. 1982. A rc ad ia L ak e , D eep F ork R iver, Suppl 1 to D esig n M e m o ran d u m N o. 9, E m b an k m en t and sp illw ay , T u lsa , O K .

U S A E D istric t, V ick sb u rg . 1988. T h e S ard is e a rth q u ak e study, S uppl 1 to D e sig n M em o ran d u m N o . 5 (1985), V ick sb u rg , M S.

150

V aid , Y. P., C h e m , J.C . & T um i, H . 1985. C on fin in g pressure , g ra in an g u la rity , and liq u e fac tio n . Jo u rn a l o f G e o tec h n ic a l E n g in e e rin g , A S C E , O cto b er, vol. 111(10), p g 1 229-1235 .

V aid , Y. P. & T h o m as, J. 1995. L iq u efac tio n and post liquefac tion b eh av io r o f sand. Jou rnal o f G eo techn ica l E n g in e erin g , A S C E , F eb ru a ry , vol. 121(2), pg 163- 173.

Y oud, L. & Idriss, I. M ., ed ito rs . 1997. W o rk sh o p on E v a lu a tio n o f liq u e fac tio n re s is tan c e o f so ils. P ro c e ed in g s , S a lt L ak e C ity , T ec h n ic a l R ep o rt N C E E R -9 7 -0 0 2 2 , sp o n so red by F H W A , N S F and W E S , p u b lish ed by N C E E R , B u ffa lo , N Y .

151


Pore water pressure in limit analysis calculations

Radoslaw L. MichalowskiThe Johns Hopkins University, Baltimore, Md., USA

A B S T R A C T : A c o n v e n ie n t tec h n iq u e is show n fo r in c lu sio n o f the p o re w a te r e ffe c t in lim it an aly sis o f sa tu ra ted so il s tru c tu res. T h e in flu e n ce o f the b u o y an cy fo rce and the seep ag e fo rce is sh o w n to b e eq u iv a len t to the in c lu s io n o f tw o a d d itio n a l te rm s in the w o rk ra te b a lan ce e q u a tio n . C ritica l h e ig h ts fo r s lopes are c a lcu la te d as an a p p lic a tio n ex am p le .


A n a ly ses o f s ta b ility o f g e o te ch n ic a l s tru c tu res, such as earth slo p es, e m b a n k m e n ts , re ta in in g w alls , fo o tin g s , etc., ty p ic a lly in v o lv e tec h n iq u es b a se d on the e q u ilib riu m o f fo rces . T h ey are o ften re fe rre d to as lim it e q u ilib riu m tec h n iq u es , and , in genera l, they do no t req u ire th a t th e loca l (d iffe re n tia l) eq u a tio n s o f e q u ilib riu m be sa tis fied . W h ile ap p ro x im ate , these tec h n iq u es h av e b een su ccessfu l ing eo tech n ica l e n g in e e rin g . A n o th e r m eth o d is b a se d on the k in em a tic ap p ro ac h o f lim it an a ly sis , in w h ich the e q u a tio n o f w o rk b a la n ce is u sed fo r k in em atica lly a d m iss ib le c o lla p se m ech an ism s.

T he e ffec t o f p o re w a te r p re ssu re in a sa tu ra ted soil can be c o n s id e re d in lim it eq u ilib riu m stab ility an aly ses in tw o d iffe re n t w ay s (T ay lo r 1948). In the first one the to ta l w e ig h t o f the so il is taken in the a n aly sis and the boundary neutral forces are acco u n ted for, w h ile in th e seco n d one the su b m erg ed w e ig h t o f th e so il is tak en and the seepage forces are c o n sid e re d . T h e seep ag e fo rce is a body fo rce w h ich can be c a lc u la te d as

dh( 1)

w here is the u n it w e ig h t o f w a te r, and h is the hy d rau lic head . T h e tw o te c h n iq u e s y ie ld , o f cou rse, the sam e resu lts .

A n a lte rn a tiv e m e th o d to lim it e q u ilib riu m is the k in em atic ap p ro ach o f lim it an a ly s is . T h is p a p er p resen ts how the p o re w a te r in flu e n ce can be acco u n ted fo r in lim it an a ly sis . T h is d e v e lo p m en t is p rim arily th eo re tica l, b u t all th e te rm s d ev e lo p ed fo r

use in the e n erg y b a la n ce eq u a tio n h av e a c lea r p h y sica l m ean in g .

2 K IN E M A T IC A P P R O A C H O F L IM IT A N A L Y S IS

T he th eo re m s o f lim it an a ly s is w ere p re sen te d by D ru c k e r et a l (1952), b u t th e c o n ce p t w as kn o w n earlie r (G v o zd ev 1938, H ill 1948). It is a ssu m ed th at p las tic d e fo rm a tio n is g o v e rn ed by the n o rm ality (o r asso c ia tiv e) flow ru le

" d(5

A. > 0 if / = 0

A = 0 if / < 0 (2)

where A is a nonnegative scalar m u ltip lie r ,/fa ,is the yield criterion, and ¿¡f' and 0, are the plastic Strain rate and the stress tensor, respectively. The upper bound theorem is based on the construction of admissible collapse mechanisms (or velocity fields), and it states that the rate of work done by traction and body forces is less than or equal to the rate of energy dissipation in any kinematically admissible failure mechanism

j D { t . . ) d V > J r +V 5^

+ + Jy,v,JV (3)

T he le ft-h an d side o f in eq u a lity (3) rep resen ts the ra te o f w o rk d iss ip a tio n d u rin g an in c ip ien t fa ilu re o f

153

a structure, and the right-hand side includes the work rates of all the external forces. T, is the stress vector on boundaries and S . Vector T, is unknown (limit load) on 5* , and it is known on (for instance, surcharge pressure), v- is the velocity vector in the kinematically admissible mechanism, y, is the specific weight vector, and V is the volume of the mechanism. Hence, the inequality in (3) can be used to calculate the upper bound to the force on boundary 5^, if all the other terms in eq. (3) are known, or it can be used to calculate the upper bound to the maximum height of an embankment, etc.

Including the influence of the pore water in eq. (3) is not trivial, and the development in the next section presents how the work of the buoyancy and seepage forces can be related to the work of the pore water pressure.

3 WORK OF THE PORE WATER PRESSURE

3.1 Continual deformation

In order to find a convenient way to include both the buoyancy and seepage forces in the kinematic approach of limit analysis, consider first the product of the pore water pressure (w) and the rate of the volumetric strain (¿¿,) of the soil: -ué^^. Such a product represents the rate of work of u on the volumetric expansion of the skeleton (pore water pressure is assumed to be unaffected by the skeleton deformation as in a drained process). Because the dilatancy is considered a negative strain in soil mechanics convention, a minus sign is included to indicate that positive (compressive) pore pressure does positive work on skeleton expansion. This product is related to the work of the buoyancy force and the seepage force (Michalowski 1995), therefore, it is useful to investigate its integral over the volume of the entire failure mechanism.

Let the vector of the displacement velocity in a failure mechanism be v, (v, is a function of x,y,z or Xi, i = 1,2,3). Derivative of product wVj is

dx( mv.) du

dx dx.(4)

= (un.w dS - (— w.dV J ' ' Idx. '

(5)

where S is the surface bounding volume V of the mechanism, and n¿ is an outward unit vector normal to surface S. The divergence theorem was used in (5), (14) to transform the volume integral into the surface integral. The hydraulic head, h, can be written as

h = Z + Z _Tw

(6)

and, since 3v,t9j:, = - (summation convention holds), we can write the integral of - hC;, as

(u é dV = f ^ ( i i v , ) d V - f 4 ^ v . dVd " e. dx •/. ax.

where Z is the elevation head. In further considerations we omit the kinetic part (the third term in eq. (6)). Substitution of u from the expression in eq. (6) (with the omission of the kinetic part) into eq. (5), (14) yields

■ ju è .. dV = ju n \ . dSV s (7)

r JT/ r 1 /y — \ dV + y — V dV

The second term on the right-hand side of eq. (7) represents the integral of the rate of work of the seepage force (see eq. (1)) over the entire volume of the collapse mechanism, and the third term is the work rate of the buoyancy force. The first term on the right-hand side represents the work rate of the pore water pressure on boundary S.

In order to account for the influence of the pore water in the mechanism, one needs to include terms that relate to the work rate of the buoyancy forces and seepage forces. From eq. (7) it follows that

- y V. dV + y w dV ='-¡dx^ ' ' - ¡d x , ' (8)

ju é ..d V - j u n . \ .dS

Thus, in order to account for the influence of seepage and buoyancy in limit analysis one can include in eq. (3) the two terms that represent the rate of work and buoyancy forces explicitly, or the two terms on the right-hand side of eq. (8).

To illustrate the physical meaning of terms in eq. (8) consider the soil element in Figure 1 moving with velocity v-. The work done by the pore water pressure acting on that element is equal to the work of the buoyancy force (acting on element A) plus the work of the seepage force. The total work rate of

154

Figure 1 Water flow in a slope.

b u o y a n c y a n d seepage forces in the collapse mechanism is, in this case, equal to the integral of - ue ■„, since the work of pore pressure on the slope boundary (surface S) equals zero. In the case i l l u s t r a t e d i nFigure 2, however, to account for both the buoyancy and seepage, one needs to use both the work of pore pressure on the skeleton expansion, and the work of pore pressure on boundary S (here, boundary AB). Notice also that if region ABC moves as a rigid block, then the pore pressure does work within volume V only on dilatancy along discontinuity BC.

The first term on the right-hand side of eq. (8) represents the work rate of the pore water pressure, w, on the v o l u m e t r i c s t ra i n (dilatancy) o f thec l f 'T 'l l i c t c

positive work similar to Hydrostatic porethe work of water pressure inside a spongeon sponge expansion. The second term on the right- hand side of eq. (8) is related to the work of the pore water pressure on boundary S of the mechanism. If the problem involves a phreatic surface within the soil mass, this term is equal to zero. However, if pore water pressure is not zero on boundary S, this term must be taken into account.

3.2 Velocity discontinuities

I f v e l o c i t y discontinuities appear in the failure mechanism, then the work of the pore p ressure on dilatancy along these discontinuities must be included in the first term on the right-hand pig j-e 3 Discontinuity as a side of eq. (8). Such finite-thickness layer, discontinuities can beregarded as finite-thickness layers with a linear distribution of velocity "jump" across them. Figure 3. The work of pore pressure u per unit area of the discontinuity (the area being perpendicular to the plane of Fig. 3) can be expressed as

- ^ u t..d z = J u dz = M[v]sin(p(9)

where cp is the internal friction angle (dilatancy angle for nonassociative material), and [v] is the magnitude of the velocity jump vector. Alternatively, the total work of u along a velocity discontinuity can be written as

D = un.w dl ( 10)

where n, is the unit vector normal to the discontinuity (Fig. 3), and L is the discontinuity length.

4 APPLICATION EXAMPLE

4.1 Collapse mechanism

A mechanism of a slope failure is shown in Figure 4, in which region ABCDA rotates about point O with velocity cb. The distribution of the pore water pressure, w, along the log-spiral discontinuity ABCD is described by coefficient , as introduced by Bishop and Morgenstern (1969)

y z( 11)

where y is the unit weight of the soil and z is the depth below the surface. The critical height of the slope can be calculated from the work balance equation

03

155

Table 1. Stability factors yH/c = 0, = 0.25,and = 0.5)

(p = 0 (p=10° (p=20° (p=30° (p=40°

15°

30°

45°

60°

5.53

75°

90°

5.53

5.53

5.25

4.56

3.83

45.4923.1814.03

13.50 41.2210.71 20.058.70 12.07

53.9018.00

9.31 16.167.95 10.946 . 8 8 7.99

35.5415.849.32

7.26 10.396.38 7.695.68 6.02

16.049.266.26

5.80 7.485.18 5.764.68 4.66

9.946.274.50

4.58 5.504.32 4.353.77 3.58

6.694.403.26

31.43

185.4925.7011.06

28.9111.236.43

13.976.654.21

8.294.262.82

P - slope angle; 9 - internal friction angle

inclination angle p. Angles Qq, 0;,, and p ' (Fig. 4) were variable in an optimization routine. The results are given in Table 1. When the internal friction angle of the soil is zero, there is no dilation of the soil, the work of the pore pressure is zero, and hence, there is no influence of the pore pressure on the critical height (column 2 of Table 1). Three values of yH/c given for each p (a = 0) and cp > 0 relate to the critical height when = 0, r^= 0.25, and = 0.5, respectively.

5 FINAL REMARKS

It was shown that the rate of work of the buoyancy forces and the seepage forces in a collapse mechanism can be alternatively expressed as the sum of the work rate of the pore pressure on the volumetric expansion of the skeleton and the pore pressure work on the mechanism boundary. Hence, the effect of pore water can be effectively included in the kinematic approach of limit analysis by using the two latter terms, which is more convenient than calculating the work rate of buoyancy and seepage forces explicitly.

u

+ jy^v.dV - J

( 12)

Since the slope in Figure 4 is not loaded on its surface, the first two terms on the right-hand side of eq. (12) are zero. The following equation results for the critical height of the slope

yH Hc

2 ( 9 ^ -0 g )ta n (p

2 tan(p ( / , - y - / 3 J 5)

Ratio H/vq, and coefficients /; through are functions of (p and the slope geometry, and they can be found in Chen (1975), whereas coefficient expresses the contribution of the pore water pressure (Michalowski 1995).

4.2 Computational results

Since the kinematic approach of limit analysis leads to the upper bound on the critical height of slopes, a minimum of yH/c was sought from eq. (13), for given internal friction angle of the soil (p and slope

REFERENCES

Bishop, A.W. & Morgenstem, N.R. 1960. Stability coefficients for earth slopes. Geotechnique, 10, No. 4: 129-150.

Chen, W.F. 1975. Limit Analysis and Soil Plasticity. Amsterdam: Elsevier.

Drucker, D.C., Prager, W. & Greenberg, H.J. 1952. Extended limit design theorems for continuous media." Quart. Appl. Math., 9: 381-389.

Gvozdev, A.A. 1938. The determination of the value of the collapse load for statically indeterminate systems undergoing plastic deformation (1960 translation from Russian by R.M. Haythomthwaite). Int. J. Mech. Sci., 1: 322-335.

Hill, R. 1948. A variational principle of maximum plastic work in classical plasticity. Quart. J. Mech. Appl. Math., 1: 18-28.

Michalowski, R.L. 1995. Slope stability analysis: a kinematical approach. Geotechnique, 45, No. 2; 283-293.

Taylor, D.W. 1948. Fundamentals of Soil Mechanics. New York: J. Wiley.

156

4 Soil fabric and its effect on liquefaction


Comparison o f tests on undisturbed and reconstituted silt and silty sand

R.Dyvik&K.H0egNorwegian Geotechnical Institute, Oslo, Norway

ABSTRACT: The differences in undrained stress-strain-strength behaviour between undisturbed andreconstituted silt and silty sand specimens tested at the same void ratio, may be dramatic. Results from triaxial and DSS tests on a natural silt and a discussion of test results from a hydraulically placed silty sand are presented. All tests on undisturbed specimens showed dilative and ductile behaviour, while most of the accompanying reconstituted specimens compacted to in-situ density, showed contractive and brittle behaviour. Therefore, when reconstituting specimens of silt and silty sand in the laboratory, it is not sufficient to simply satisfy the criteria of correct density and grain size distribution - the in-situ fabric is also very important. Otherwise, analyses based on reconstituted specimens may be totally misleading. Measurements of initial shear modulus (from shear wave velocity measurements) may prove useful.

1 BACKGROUND AND OBJECTIVES

1.1 Liquefaction, Steady State Strength and Progressive FailureThe behaviour of saturated sands subjected to cyclic loading has been studied extensively, mainly in connection with earthquake loading, but also for offshore wave loading. Terms such as liquefaction potential, cyelic mobility and undrained steady state strength have become familiar (e.g. Seed, 1987; Ishihara, 1993; Terzaghi et al., 1996). However, when it comes to predicting in-situ behaviour based on the behaviour of laboratory specimens of such materials, one encounters significant uncertainties.

In recent years, and especially in connection with tailings dams, there have been renewed efforts in studies of silty materials when subjected to monotonic loading. The term static liquefaction (or static collapse) is now commonly being used to indicate the situation that may trigger instability by a flow failure, as described in the classic paper by Casagrande (1936).

The stress-strain curve for a loose saturated cohensionless soil deformed under undrained conditions will rise to a peak strength and fall off to residual (ultimate) at steady state conditions. The degree of strain weakening (strain softening) and brittleness depends on the initial state of the material and its properties. Once collapse is initiated, excess pore pressures are generated if drainage is impeded. The triggering of localised yield zones in strain

weakening materials causes stress redistribution that can lead to a progressive process, which, if not contained, can result in overall collapse and flow failure.

1.2 Laboratory Testing and Empirical Correlations

The fundamental understanding of liquefaction, whether caused by monotonic or cyclic loading, is mainly based on laboratory research on reconstituted specimens tested in triaxial and direct simple shear (DSS) devices, as undisturbed sampling of silts and sands is difficult, time consuming and costly. Furthermore, reconstituting specimens allows a systematic study of the undrained behaviour as function of material density (void ratio), fines content, grain size distribution and other factors (e.g. Thevanayagam, 1998; Vaid et al., 1990; High ter and Tobin, 1980).

However, predicting in-situ behaviour based on reconstituted specimens entails many uncertainties. Therefore, in practice, the liquefaction potential as well as the undrained steady state strength, have been related to the standard penetration resistance (SPT), the cone penetration resistance (CRT) and the shear wave velocity (e.g. Seed and de Alba, 1986; Finn, 1996). However, as some of these empirical correlations are partly based on the behaviour of reconstituted laboratory specimens (and partly on back-analyses of field situations), some of the inherent uncertainties remain.

159

cLA

SILT SAND GRAVEL

Y Fine Medium Coarse Fine Medium Coarse Fine Medium Coarseu s standard Sieves 200 100

_ _ | __________| _50 30 16

______l _ _ ______I_________ I_______8 41 1

3/8" 3/4"1 1 1.5"1 3"

1

ISO standard Sieves .075 .125 .25 .5 1 :1 1

2 41 1

8 16 191

31.5 63

Figure 1. Typical grain size distribution curves for the natural silt and silty sand tailings material; (a) 40 m from dam crest, (b) 200 m from dam crest.

Table 1. Parameters for the triaxial specimens of natural silt.

Test Sample INITIAL PARAMETERS AFTER CONSOLIDATION AND PRESHEAR

no. prep Water Dry Void Relative aac' O rc £ vo l Dry Void Relative

aration content density ratio density density ratio density

(%) (kN/m^) (%) (kPa) (kPa) (%) (k N W ) (%)

1 U 31.2 14.32 0.835 63.4 49.9 32.9 1.25 14.50 0.812 65.52 U 30.3 14.43 0.821 64.7 49.9 25.9 0.60 14.52 0.810 65.73 u 31.2 14.57 0.804 66.3 49.9 32.9 1.05 14.72 0.786 6 8 . 0

4 MT 31.9 14.18 0.854 61.8 49.7 25.8 6.56 15.18 0.732 72.95 MT 28.6 14.88 0.766 69.8 49.8 25.9 1.87 15.16 0.733 72.86 MT 28.7 14.87 0.768 69.7 50.0 33.0 2.33 15.22 0.726 73.47 MT 24.6 15.84 0.659 79.6 50.0 26.0 -0.14 15.82 0.662 79.48 S 28.9 14.83 0.772 69.2 49.8 32.8 2.48 14.21 0.728 73.2

MT = moist tamped S = consolidated slurry U = undisturbed

Table 2 parameters for the DSS specimens of natural silt.

Test Sample INITIAL PARAMETERS AFTER CONSOLIDATION AND PRESHEARno. prep Water Dry Void Relative a max CTac’ vol Dry V oid . Relative

aration content density ratio density density ratio density

(%) (k N W ) (%) (kPa) (kPa) (%) (k N W ) (%)

9 U 31.5 14.49 0.814 65.4 50.0 50.0 0.87 14.62 0.799 6 6 . 8

1 0 u 30.7 14.37 0.830 64.0 90.0 50.0 0.74 14.48 0.816 65.21 1 MT 31.7 14.22 0.848 62.2 50.0 50.0 3.86 14.79 0.777 6 8 . 8

1 2 U 28.5 15.54 0.692 76.6 90.0 50.0 1.50 15.78 0 . 6 6 6 78.913 MT 25.4 15.64 0.681 77.6 90.0 50.0 1.06 15.81 0.663 79.2

160

In early cyclic liquefaction studies of sands the effects of various methods of specimen preparation were investigated. These investigations showed, for instance, that the number of cycles to reach large cyclic strains, depended on whether the sand specimens were reconstituted by building in the material dry or wet, by sedimentation or air pluviation, by the use of vibration or various forms of tamping (e.g. Zlatovic and Ishihara, 1997; Kuerbis and Vaid, 1988).

For sands containing fines or for silts, many of the laboratory methods previously used for coarser and more uniform materials, cannot be used due to problems of segregation during specimen preparation. Therefore, the procedure of moist tamping in layers, using the method of so-called undercompaction to achieve a homogeneous specimen of prescribed uniform density over its height, has been applied extensively both in research and consulting practice.

The much younger tailings material, which may be described as silty fine sand, was taken from a depth of 2.5 m in the gently sloping beach of a tailings dam built by the upstream construction method in Zelazny Most, Poland (Wemo et al., 1993). The samples were taken at three different distances (40, 120 and 200 m) from the dam crest towards the interior pond. Therefore, the grain size distribution among the samples varied, with a somewhat larger silt content in the samples closer to the pond (40% vs 20% silt content). Typical grain size distribution curves are shown in Figure 1. The layering in the deposited tailings was apparent, alternating between fine-grained and coarser grained strata.

The samples of tailings were taken at the bottom of 2.5 m deep excavations by manually pushing a thin-walled 260 mm long sampling tube vertically into the tailings. When a tube was filled with tailings, it was very carefully removed by excavating around and cutting under the tube.

1.3 Objectives of this Investigation

The main objective of the studies reported herein, is to compare the undrained stress-strain-strength behaviour of undisturbed and reconstituted (mainly by moist tamping) specimens of silt and silty fine sand. Due to capillary effects, it was possible to take reasonably undisturbed field samples, without in-situ freezing.

Two different materials were tested; one from a 10,000-year old natural silt, the other from a copper mining tailings dam presently under construction. Early undrained triaxial tests with monotonic loading on reconstituted specimens of both these materials gave very low peak strength values at low strain and very brittle behaviour. The question was raised whether these laboratory results really reflected in- situ behaviour and should be used in the design analyses for a high speed railway embankment on a silty foundation and the tailings dam, respectively.

2 MATERIALS TESTED

The samples of the old natural silt were taken in a fluvial deposit in Borlange, Sweden (Zackrisson, 1997). The deposit is practically normally consolidated below the ground water level at a depth of 2.5m, and a typical grain size distribution curve for the silt is shown in Figure 1. There was some layering from the natural sedimentation process, however, it was not very pronounced.

Samples from the Swedish silt site were taken by the SGI piston sampler with an interior plastic lining and inner diameter of 50 mm. Most of the sampling attempts were successful with generally full recovery when avoiding all forms of vibration.

3 LABORATORY TESTING OF NATURAL SILT

3.1 Specimen PreparationThe undisturbed specimens of the natural silt used the full 50 mm diameter from the sampling tube. Both triaxial (Table 1) and direct simple shear (DSS; Table 2) tests were performed, having initial specimen heights of 108 and 16 mm, respectively.

The silt material used for all but one of the reconstituted test specimens was taken from a batch prepared by combining several tube samples from the same depth range as the undisturbed specimens. Maximum and minimum dry densities for this material were 18.3 and 10.4 kN /m \ respectively.

3 .2 C on so lida tion an d P resh ea rin g

All triaxial specimens were anisotropically consolidated to an axial (vertical) effective stress of a ac = 50 kPa. This corresponds to the effective vertical stress in the field at the depth of 3 m, where the undisturbed samples were taken for this study. The imposed lateral effective stress, a rc, was either 33 kPa or 26 kPa. The DSS specimens were also consolidated to a ac ,= 50 kPa, although some had been prestressed to a ac = 90 kPa.

All specimens were subjected to cyclic preshearing before the actual undrained monotonic shearing to failure. The preshearing was identical for all the tests: 400 cycles of a symmetric cyclic shear stress = ±1 kPa with a cyclic period of 10 seconds and open specimen drainage throughout. As the preshearing stress was very low, the corresponding volume changes were extremely small. Most of the decrease in void ratio for the tamped specimens with moisture

161

E ffec tive M ea n Stress, p (k P a )

Figure 2. Effective stress paths for triaxial tests on natural silt (see Table 1).

content of 3%, occurred when they were saturated and the capillary tension was eliminated.

3.3 Undrained Shearing

The axial strain rate in the undrained triaxial compression tests was 2% per hour. The shear strain rate in the undrained (constant volume) DSS tests was 5% per hour.

Summaries of test parameters are shown in Tables 1 and 2. Figure 2 shows the effective stress paths for the triaxial tests, where q and p’ are defined as V2 (Gi - 03) and V2 (a 1 + a 3), respectively. Figure 3 shows some typical shear stress and pore pressure versus axial strain results for the triaxial tests. Figure 4 shows the stress plots (Th versus a a) for the DSS tests. Figure 5 shows the horizontal shear stress and pore pressure versus shear strain for the DSS tests.

4 TESTING OF SILTY SAND TAILINGS

4.1 Specimen PreparationPrior to extrusion, X-ray photos were taken of all sample tubes. The most homogeneous samples with least layering to make the best comparisons with the companion reconstituted specimens were chosen.

Only undrained triaxial compression tests were run on the tailings material. The specimen diameter used was the full sample tube diameter (73 mm). The specimens were trimmed to an initial height of 146 mm. Preshearing was not applied in these tests.

After an undisturbed triaxial specimen had been tested to failure (or large strains), the water content and the initial dry density of the undisturbed specimen were determined. The accompanying reconstituted specimen (diameter of 54 mm and height 108 mm) was prepared to the same density using only the soil in the undisturbed specimen just tested. This procedure gave two companion specimens with the same void ratio and grain size distribution curve; one specimen in each pair was undisturbed and somewhat layered, the other was reconstituted and homogeneous.

4.2 Consolidation

The consolidation stresses used for the tailings material were Gac = 50, 250 and 500 kPa, with a lateral stress ratio of 0 . 5 for each.

The shear wave velocity and thereby the maximum shear modulus, Gmax, were determined in the triaxial tests using the piezoceramic bender element technique (Dyvik and Madshus, 1985). The measurements were taken just before the start of the undrained shearing phase of the tests.

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Figure 3. Comparison of typical triaxial stress-strain curves and pore pressure development for undisturbed (Testl) and reconstituted (Tests 6 and 8) specimens of natural silt (see Table 1).

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4.3 Undrained ShearingThe axial strain rate in the undrained triaxial compression tests was 2% per hour.

The results for 9 pairs of specimens (3 locations with 3 consolidation stress levels, for each set of undisturbed and reconstituted specimens) were compared and analyzed.

5 DISCUSSION OF RESULTS

The test results are consistent (duplicate tests gave almost identical results), and the overall trend is clear. The differences in undrained stress-strain- strength behaviour between undisturbed and reconstituted specimens are dramatic for both materials.

5.1 Natural SiltFor the natural silt, the undisturbed triaxial specimens (ec = 0.81, Dr = 66%) exhibited dilative and ductile behaviour with no strain weakening, while the reconstituted specimens at significantly lower void ratio (ec = 0.73, Dr = 73%) exhibited contractive and brittle behaviour (Figures 2 and 3).

In order to produce dilative and ductile behaviour in a reconstituted triaxial specimen, it had to be initially compacted to a void ratio of 0.66 (Dr = 80%), as shown by the results from Test 7.In order to study the results from one other method of specimen reconstitution, a prescribed amount of

silt material was mixed with water to a slurry. This was poured into the specimen preparation mold and vertically compressed over a period of time to the desired specimen height for a relative density of about 70%. Then the specimen was consolidated to the same consolidation stresses as the previous specimens (see Test 8 in Table 1). The void ratio after consolidation and preshearing was 0.73, the same as the specimens reconstituted by moist tamping.

The moist tamping and consolidated slurry methods produced specimens which both yielded similar contractive stress-strain behaviour, very different in character from that of the dilating undisturbed specimens which had lower density.

Very similar observations are made in the DSS test results (Figures 4 and 5). Tests 9 and 10 on undisturbed specimens (Cc = 0.81, Dr = 66%), exhibited dilative and ductile behaviour with no strain weakening, while the slightly denser associated reconstituted specimen (Test 11; ec = 0.78, Dr = 69%) exhibited contractive and brittle behaviour. The reconstituted specimen in Test 13 (Cc = 0.67, Dr = 79%) exhibited dilative and ductile behaviour more similar to the much looser undisturbed specimens in Tests 9 and 10. Test 12, the undisturbed companion specimen to Test 13 (exactly the same material and the same density), also exhibited dilative and ductile behaviour, but had less (no) slight positive pore pressure generated at the very start of the test, as in all the other DSS tests.

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Shear Strain, y (%)

-2.0 2.0 6.0 10.0 14.0

Shear Strain, y (%)

18.0 22.0 26.0

Figure 5. Comparison of DSS stress-strain curves and pore pressure development for natural silt (see Table 2).

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5.2 Silty Sand TailingsFor the tailings material with the highest

consolidation stresses (a ’ac = 250 and 500 kPa), all the undisturbed triaxial specimens dilated and reached undrained strength values much higher than the companion reconstituted specimens. In contrast to what was the case for the undisturbed specimens, there was relatively little difference in the stress- strain curves among the reconstituted specimens. All showed peak strengths at very low strains and strain weakening.

For the lowest consolidation stress (a ’ac = 50 kPa) both the undisturbed and the reconstituted specimens showed dilative behaviour, but generally to a lesser extent for the latter.

5.3 Measured Shear Wave Velocities

The shear wave velocities, and hence Gmax values, were measured for each specimen after consolidation just prior to shearing. For the specimen pairs of the tailings material, Gmax for the reconstituted specimen was about 25% lower than for the companion undisturbed one. Hence, it seems that knowledge of the shear wave velocity, or Gmax , combined with the void ratio may be able to provide information that the void ratio by itself cannot.

5.4 Possible Reasons for Differences in Behaviour

A difference between undisturbed and reconstituted specimens is the existence of layering in the former. The layering was very slight in the natural silt, but more apparent in the tailings, although the most homogeneous samples were selected and tested for the purpose of these special comparisons

The test series included a natural silt, age approximately 10,000 years, and a man-made material hydraulically placed some 5 years ago. For both materials one found dramatic differences between undisturbed and reconstituted specimens. Thus, aging, secondary compression and cementation effects cannot be the main reasons for the significant differences in stress-strain-strength behaviour observed herein.

The complete change in character of behaviour must be caused by the differences in fabric between the undisturbed and the reconstituted specimens. Even though the field sampling may not have been truly undisturbed, and even when the in-situ fabric was disturbed by reconsolidation to stresses much higher than in situ, the remaining fabric was still much more resistant to imposed shear than that in the reconstituted specimens, even at large shear strains. Although the total void ratio is the same, the structural configuration of the particle assembly and the sizes and shapes of the individual voids may be

different in the undisturbed and the reconsituted specimens.

6 SUMMARY AND CONCLUSIONS

Depending on their initial state, saturated silts and silty sands may exhibit very brittle stress-strain behaviour during undrained monotonic loading, which may lead to progressive collapse and flow failure.

The objective of the studies reported herein was to compare the undrained stress-strain-strength behaviour of undisturbed and reconstituted (mainly by moist tamping) specimens. Two types of fine granular materials were tested; one a natural silt from a 10,000-year old fluvial deposit, the other manmade mine tailings deposited hydraulically some 5 years ago.

The laboratory investigation, using undrained triaxial compression and DSS tests, showed that laboratory stress-strain-strength results obtained on reconstituted silt and silty sand specimens prepared by moist tamping to in-situ density, cannot be used to predict in-situ behaviour. Based on the studies reported herein, one may conclude that the results from reconstituted specimens are much too pessimistic, as undisturbed specimens generally exhibited dilative and ductile behaviour while reconstituted specimens at the same void ratio showed contractive and brittle behaviour.

When reconstituting such specimens for laboratory testing, it is not sufficient to satisfy the criteria of correct in-situ density and grain size distribution. The in-situ fabric must also be modelled. Further studies should be undertaken to determine the type of specimen preparation required to achieve specimens that may model field behaviour. In this respect the measurement of seismic shear wave velocity may prove very useful.

Constitutive models based on the results from reconstituted specimens should be critically reviewed. Likewise, the interpretation of in situ site investigation results calibrated against the behaviour of reconstituted specimens should be reanalysed.

ACKNOWLEDGMENT

The authors thank the Swedish National Rail Administration (Banverket) and KGHM Polska Miedz S.A. of Poland, forproviding the test materials. The authors thank Mr R. Larsson of the Swedish Geotechnical Institute for providing the samples of natural silt, and Dr. M. W emo and colleagues from the Maritime Institute in Gdansk, for their co-operation and for taking samples of the tailings material. Furthermore, the assistance of our

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colleagues in the NGI laboratory, and the financial support of the Research Council of Norway, are gratefully acknowledged.

REFERENCES

Casagrande, A. (1936)Characteristics of cohesionless soils affecting the stability of slopes and earthfills,Contributions to Soil Mechanics, 1925-1940, Boston Society of Civil Engineers, 1940, pp. 257-276.

Dyvik, R. and Madshus, C. (1985)Laboratory measurements of Gmax using bender elements.Proc. ASCE Annual Convention. Advances in Art of Testing Soils under Cyclic Conditions, Detroit, pp. 186-196.

Finn, W.D. Liam (1996)Seismic design and evaluation of tailings dams: state-of-the-art.Proc. of International Symposium on Seismic and Environmental Aspects of Dam Design, Vol. I, 7-34, Santiago, Chile.

Highter, W.H. and Tobin, R.F. (1980)Flow slides and the undrained brittleness index of some mine tailings.Engineering Geology, 16, pp. 71-82.

Ishihara, K. (1993)Liquefaction and flow failure during earthquakes. Geotechnique 43, No. 3, pp. 351-415.

Kuerbis, R. and Vaid, Y.P. (1988)Sand sample preparation - the slurry deposition method.Soils and Foundations, 28(4), pp. 107-118.

Seed, H.B. (1987)Design problems in soil liquefaction.J. Geotech. Engng., ASCE, 113(8), pp. 827-845.

Seed, H.B. and De Alba, P. (1986)Use of SPT and CPT tests for evaluating the liquefaction resistance of sands.ASCE Geotechnical Special Publication No. 6, pp. 281-302.

Terzaghi, K., Peck, R.B., and Mesri, G. (1996)Soil mechanics in engineering practice.Third Edition, Article 20.9, John Wiley & Sons, Inc.

Thevanayagam, S. (1998)Effect of fines and confining stress on undrained

shear strength of silty sands.J. Geotech, and Geoenvir. Engng., ASCE, 124(6), pp. 479-491.

Vaid, Y.P., Chung, E.K.F., and Kuerbis, R.H. (1990) Stress path and steady state.Can. Geotech. J. 27, pp. 1-7.

Werno, M., Dembski, B., Juszkiewicz-Bednarczyk, B., Mlynarek, Z., and Tschuscke, W. (1993)Tailing dam Zelazny Most environmental hazard.3rd Int. Conf. on Case Histories in Geotechnical Engineering, St. Louis, Missouri, Vol. 1, pp. 469- 472.

Zackrisson, P. (1997)Effects of passing trains on the stability of railroad embankment foundations.Proc. 14th Int. Confr. on Soil Mechanics and Foundation Engng., Hamburg, Vol. 2, pp. 1057- 1062.

Zlatovic, S. and Ishihara, K. (1997)Normalized behaviour of very loose non-plastic soils: effects of fabric.Soils and Foundations, Vol. 37, No. 4, pp. 47-56.

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Quantitative characterization o f microstructure evolution

J. a Frost, C.-C.Chen & J.-Y. ParkSchool of Civil and Environmental Engineering, The Georgia Institute of Technology, Atlanta, Ga., USA

D.-J.JangTensar Earth Technologies Incorporated, USA

A B S T R A C T : T h is p a p e r d e sc rib e s h o w recen tly d e v e lo p ed ex p erim en ta l p ro c ed u re s h ave been used to q u an tita tiv e ly study th e in itia l an d e v o lv in g m ic ro s tru c tu re o f sand sp ec im en s. P ro c e d u re s for c ap tu rin g im ages u sing a m ic ro sc o p e m o u n te d C C D cam era and b rig h tfie ld illu m in a tio n fro m the su rfaces o f co u p o n s cu t from sp ec im en s w h o se s tru c tu res w ere fix ed at d esired s tages o f lo ad in g by resin im p reg n a tio n are d escribed . A n a ly sis o f the im ag es u s in g a u to m ated a lg o rith m s to qu an tify m ea su re s such as local void ratio d is trib u tio n and p a rtic le o rien ta tio n s sh o w s h o w g lobal re sp o n se m ask s the co m p lex co n d itio n s e x is tin g w ith in the sp ec im en s. D iffe re n c es in m ic ro s tru c tu re re su ltin g from sp ec im en p re p a ra tio n are illu stra ted . The ev o lu tio n o f s tru c tu re a t v a rio u s s tag es o f shearing in rep lica te d ila tan t sp ec im en s sh o w s h o w global vo id ra tio m easu res lead to e rro n e o u s d e te rm in a tio n s o f s tead y sta te and p ro v id es d irec t m ic ro s tru c tu re based ev id en ce o f the need fo r ro u tin e use o f lu b rica ted end p la te n s and local d e fo rm a tio n m easu rem en ts .


T he v isua lly o b se rv ed and co n v en tio n a lly reco rded g lobal re sp o n se o f a triax ia l sp e c im en su b jec ted to load ing in the lab o ra to ry m ask s the co m plex in te rac tio n s w h ich in rea lity are o c cu rrin g w ith in the spec im en . It is on ly th ro u g h ex p e rim e n ta l study at sm a lle r sca les tha t the in te rn al b eh av io r can be co rrec tly in vestiga ted . F o rtu n a te ly , s tu d ies w h ich can y ield d irec t q u a n tita tiv e m easu res o f the soil resp o n se at sm a lle r sca les are n o w p o ss ib le as a resu lt o f recen t d e v e lo p m en ts w h ich use d ig ita l p ro cess in g and a n aly sis o f o p tica l im ag es to p ro v id e u n ique q u an tita tiv e in sig h t in to m ic ro -stru c tu ra l behav io r. T he ex p erim en ta l d e v e lo p m en ts d escrib ed in th is p ap er p ro v id e d irec t ev id en ce o f the im p o rtan ce o f q u an tify in g the e v o lu tio n o f struc tu re in sp ec im en s at a m icro sca le an d u sing th is as a basis fo r a m ore ra tio n al u n d e rs tan d in g o f the ro le o f m ic ro -s tru c tu re and its e v o lu tio n on the m ac ro resp o n se o f so il sp ec im en s. T h e re sea rc h bu ild s on the p io n ee rin g w o rk o f O d a (1 9 7 2 a ; 1972b; 1972c; 1976) w ho p ro p o se d p ro ced u res fo r s tudy ing the d istrib u tio n o f local v o id ra tio an d m ore recen t research w h ich has re su lted in the d e v e lo p m en t o f d ig ita l im age p ro c ess in g an d a n a ly sis based tech n iq u es to q u an tify the m ic ro -s tru c tu re o f sp ec im en s o f p a rticu la te m a te ria ls (B h a tia and S o lim an , 1990; Ib rah im an d K ag aw a, 1991; F rost and K uo, 1996; K uo and F ro st, 1996; Jan g and F rost, 1998).

T o p ro v id e a b a ck g ro u n d fo r ev a lu a tin g the q u an tita tiv e m easu rem en ts , the p ap er first p rov ides an o v e rv ie w o f the p ro c ed u re s w h ich can be used for p re serv in g the m ic ro s tru c tu re o f both natura l and re co n stitu te d sp ec im en s and p rep arin g h igh quality co u p o n su rfaces fo r accu ra te m easu rem en t. D iffe ren ces in vo id s tru c tu re re su ltin g from dilTerent sp ec im en p re p ara tio n tec h n iq u es are use to show that vo id ra tio d e sc rip tio n s need to ex tend beyond the trad itional a p p ro ach o f re fe rrin g to 'd h e \ oid ratio o f the sp e c im en ” and re flec t that it is a d is trib u ted p a ram ete r w ith an ex p ec ted va lue , a standard d e v ia tio n and h ig h er o rd e r m o m en ts .

T he p a p er a lso in c lu d es re su lts w h ich q u an tita tiv e ly show h o w the m ic ro s tru c lu re evo lves du rin g sh ea rin g and d e m o n s tra te s that m easu rem en ts pe rfo rm ed at th ese sm a lle r sca les can p ro v id e un ique in sig h t in to v a rio u s te s tin g a rtifac ts such as end- p la ten re s tra in t and the n eed for local d e fo rm a tio n m easu rem en ts . D irec t q u a n tita tiv e ev id en ce that n o n -u n ifo rm e v o lu tio n o f s tru c tu re in te rn ally w ith in a sp ec im en ex p la in s d iffe re n ce s ob se rv ed betw een c ritica l sta te and steady sta te co n d itio n s , d ep en d in g on w h e th er sp ec im en s are tes ted from in itia lly d ila tan t o r co n tra c tiv e sta tes , is p resen ted . The im p lica tio n s o f th ese e x p erim en ta l tech n iq u es and fin d in g s on im p ro v in g the u n d e rs tan d in g o f the resp o n se o f liq u e fiab le so ils u nder sta tic and dynam ic lo ad in g are d iscu ssed .

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2. EXPERIMENTAL METHODS AND MATERIALS

The quantitative microstructure measurements presented in this paper are possible as a result of significant advances over the past decade in the development of imaging systems for studying natural and man-made materials at a range of scales. The adaptation and development o f supplemental experimental procedures and protocols to facilitate the use of imaging based techniques in studying the behavior o f particulate soil systems is summarized below.

Specimen PreparationThe majority o f the results presented in this paper are for specimens prepared using an air pluviation or raining technique (Miura and Toki, 1982; Gilbert, 1984; Jang, 1997). The technique allows for preparation of specimens over a broad range of densities to a high level o f global repeatability through careful control o f the intensity and fall height o f the sand particles during reconstitution and is well suited for use with uniformly graded sands. The particular implementation of the air pluviation technique including details o f the specially designed automated apparatus used in the present study are described at length by Jang (1997). A critical component o f the apparatus is a limit switch which automatically triggers the fall height to the flow of the sand and ensures the operator independence of the process.

A few additional specimens were prepared using moist tamping under-compaction (Ladd, 1974, 1978) for comparison purposes. The particular apparatus used in this study had a load cell integrated into the tamping device so that the incremental and cumulative force applied to the specimen during preparation could be recorded.

All tests reported herein were performed on specimens of ASTM graded sand (formerly Ottawa C-109 sand). This uniformly graded fine to medium quartz sand has sub-rounded particles with a mean grain size of 0.35 mm and a coefficient o f uniformity of 1.65. The maximum and minimum void ratios of the sand were determined to be 0.82 (ASTM D4254- 91) and 0.50 (ASTM D4253-93), respectively.

Stress-Strain Response of Control Specimens To verify the repeatability of the specimen preparation methods, initial tests were performed on sets o f control specimens prepared to the same global conditions (void ratio and initial effective confining stress) and tested along the same stress path. The specimens were prepared at an initial global void ratio o f approximately 0.58 (D = 75%). The specimens were back-pressure saturated, (B values greater than 0.99) and isotropically consolidated under a 50 kPa effective confining

stress. The specimens were then subjected to axial compression under drained conditions. These tests were performed using strain controlled loading to enable capture o f the post-peak axial stress, or strain softening, portions o f the stress versus strain curve. A strain rate o f 0.015% per minute was used. The results o f these tests confirmed the repeatability o f the procedures used. More importantly, the stress- strain response obtained in these control tests was used to identify stress conditions at which quantitative micro-structure measurements would be made in subsequent tests.

Shearing of Specimens to Different Stress Levels Drained axial compression tests were performed on additional specimens sheared along the predefined stress path. The shearing o f these specimens was teiminated at various stress-strain states as indicated in Figure 1 before the specimen characteristics were preserved using resin impregnation. Images of deformed specimens prepared using air pluviation are also shown in Figure 1. It is noted that the global response of these specimens is best described as “barreling” rather than one in which a distinct shear band or localization o f deformation can be observed. Due to their irregular shapes, the volumes of these specimens were determined by measuring the buoyant weight of the specimens in water rather than direct physical measurements. The global void ratio of each o f the specimens were calculated accordingly.

Specimen PreservationThe triaxial cell used for shearing was modified to allow for impregnation o f the pore space with epoxy resin (Jang, 1997; Jang et al., 1998). Once a specimen had been sheared to a predetermined stress-strain level, the loading was stopped and the specimens were impregnated with the two-part epoxy resin, EPO-TEK 301, manufactured by Epoxy Technology Inc. using the system shown in Figure 2. The resin has a relatively low viscosity (about 100 cps at 25°C) at room temperature and cures within about 12 hours o f mixing. It has a linear shrinkage of about 1.5% which is quite low compared to most other resins which can have shrinkage values as high as 5%, particularly if they have viscosities as low as the EPO-TEK 301 resin used in the present study. Despite the low shrinkage value o f EPO-TEK 301, global dimensions were monitored throughout all resin impregnation and curing phases and final volumes were corrected to account for any minor shrinkage recorded (Jang, 1997). Use of this procedure is limited at present to the study of dense specimens since volume change measurements are considered to be unacceptably large for loose specimens (Figure 3).

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Specimen

Initial Void Ratio e,

j26

0.583

j25

0.588

j28

0.592

j31

0.604

j29

0.600

j30

0.603

Final Void Ratio e, 0.567 0.574 0.578 0.588 0.617 0.639

Deviator Axial Stress Aa,’, kPa 89 163 182 183 162 145

Axial Strain e„ % 0.14 0.89 2.1 2.5 7.0 14.0

Note: 1. Specimens were prepared by air pluviation.2. Specimens were isotropically consolidated by 50 kPa confining stress.3. Confining stress during shearing was 50 kPa.

Figure 1 Evolution o f Specimen Properties and Shape during Drained Axial Compression Tests

Coupon PreparationThe overall reliability o f image analysis based measurements is critically dependent on the quality of the coupon surfaces prepared. The images used in this study were captured from horizontal and vertical coupons cut from the resin impregnated cylindrical specimens using the cutting scheme previously proposed by Kuo and Frost (1996) as shown in Figure 4. The individual coupons were cut from the complete specimen using a diamond wafering saw with a rotating chuck. The coupon surfaces from which images were to be captured were then subjected to an extensive sequence o f grinding and polishing stages to produce surfaces which would yield unbiased high quality images requiring minimal processing (Jang, 1997; Jang et al., 1998).

Figure 2 Epoxy Impregnation System for Specimen Preservation

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Figure 3 Axial Strain during EPO-TEK 301 Epoxy Impregnation and Curing o f Triaxial Cell Specimens - ASTM Graded Sand Prepared by Moist Tamping (mt) and Air Pluviation (pi)

Figure 4 Typical Locations o f Coupons and Images Taken from a Specimen

surface preparation procedures and brightfield illumination technique used.

Image AnalysisOnce all the images for a given specimen were

ready for analysis, a batch program written using the image analysis system was used to analyze each image in sequence using the algorithm previously presented by Frost and Kuo (1996). In addition to automatically generating a polygon network and computing the 2-D void ratio of each polygon as proposed by Oda (1976), the program summarizes a range o f prescribed statistical parameters pertaining to the image and its contents. A typical binary image which contains 172 particles that was taken from a specimen with a global void ratio o f 0.588 is shown in Figure 5. The mean value o f the local void ratio distribution o f the image is 0.584 and the standard deviation is 0.271 reflecting a coefficient of variation of about 46%. It is noted that the similarity between the global specimen void ratio and the mean value o f the local void ratio distribution is typical throughout specimens o f uniformly graded sands which have not been sheared. This is significant in that it indicates that for uniform specimens, a reliable estimate of the global void ratio can be obtained from a relatively small sample image (Shi and Winslow, 1991; Kuo and Frost, 1996).

3. INITIAL MICROSTRUCTURE OF SPECIMENS

To provide a reference for subsequent measurements, the micro structure of ASTM graded sand specimens reconstituted to a range of initial global void ratios using both air pluviation and

Image Capture and Processing Once the coupon surfaces were prepared to the appropriate condition, the complete coupon was placed on the stage of an optical microscope and images of areas approximately 5 mm by 5 mm were captured with a CCD camera mounted directly on top o f the microscope using brightfield illumination (Jang, 1997; Jang et al., 1998). For each specimen, 13 images were captured from each o f the 6 horizontal surfaces prepared and 15 images were captured from each o f the 4 vertical surfaces prepared for analysis. Accordingly, a total o f 138 images were captured from each specimen for processing and analysis. At this stage, each image was viewed and any processing necessary was conducted using the functionality of the image analysis system. In general, little or no processing was required because o f the high quality o f the images which resulted from the extensive coupon

Figure 5 Binary Image o f Image j21a01 and the Local Void Ratio Distribution o f the Image

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moist-tamping were quantified and compared (Jang, 1997; Jang and Frost, 1998). The results show that the. difference in local void ratio distribution for specimens reconstituted to the same density with the two different preparation methods (Figure 6) is comparable to the difference observed for two specimens prepared to relative densities 15% apart using one method o f reconstitution (Figure 7). It is clear from these results that global specimen response is strongly influenced by what might initially be considered to be minor variations in the local void ratio distribution.

Equally importantly, the results presented in Figure 5 show that while the distribution may have a mean value o f 0.584 which agrees closely with the global void ratio o f the specimen determined using physical measurements, locally there are 2-D void spaces defined by the polygon network which have a void ratio o f less than 0.1 and others which have a void ratio o f greater than 2.0. Accordingly, even at this scale, it is considered inappropriate to refer to the void ratio o f the specimen.

The lack o f sensitivity o f using the global or mean value o f the local void ratio distribution alone as a representation o f the void space in a specimen as illustrated in the above example is further evidenced by the data plotted in Figure 8 which shows the relationship between the mean and

oM T* 0-621 hmT - 0 027

-^ apL = 0.636hpl - 0.064

Moist Tamping - Horizontal Surfaces Moist Tamping - Vertical Surfaces Air Pluviation - Horizontal Surfaces Air Pluviation - Vertical Surfaces

- Linear Regression Lines

0.50*min

0.55 0.60 0.65 0.70 0.75 0.80

Mean (p) of the Distribution of Void Ratio

Figure 8 Relationship between Mean and Standard Deviation o f Local Void Ratio Distribution

Standard deviation o f the local void ratio distributions for specimens prepared using both moist tamping under-compaction and air pluviation over a range o f initial void ratios. It can be seen that for a given method o f preparation, the standard deviation increases approximately linearly as the mean value increases. More importantly, it can be seen that at a given mean void ratio, the standard deviation o f specimens prepared using moist tamping under-compaction are consistently about0.03 higher than specimens prepared using air pluviation reflecting their higher degree of variability as a result o f the operator being more intimately involved in the preparation procedure than with the automated air pluviation process.

4. EVOLUTION OF MICROSTRUCTURE OF RECONSTITUTED SPECIMENS

Figure 6 Void Ratio Distributions on Horizontal Surfaces for Different Methods o f Preparation

Figure 7 Void Ratio Distributions on Horizontal Surfaces for Different Density

Having established through quantitative microstructure measurements that 2-D void ratio is a distributed parameter, it is o f interest to examine how this distribution evolves during shear. To study how evolution at a given location within a specimen occurred, images were captured on 6 horizontal coupon surfaces for each specimen (surfaces a,b,c,d,e and f shown in Figure 4). A total o f 78 images (13 per surface) were analyzed and the mean and standard deviation o f the local void ratio distribution for all the images on a given coupon surface were determined. Figure 9 shows the mean of the local void ratio distribution for each horizontal coupon surface plotted versus the strain level to which the specimen from which they were cut was sheared. In addition, the global void ratio based on physical measurements and the shear stress are plotted versus axial strain on the plot for reference

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Figure 9 Evolution o f the Mean o f Local Void Ratio Distributions on Horizontal Surfaces

purposes. As the specimens are sheared along the pre-defined stress path, there is minimal change in the mean value of the local void ratio distribution (Figure 9) below the peak axial deviator stress level (183 kPa at 2.5% axial strain) although the values are generally slightly less than or equal to the global specimen value, likely reflecting the initial volume decrease w^hich is observed at small strain levels even in shearing of dilatant specimens. As the specimen is sheared through peak stress level, a significant increase in the mean value of the local void ratio distribution is observed for coupons c and d (center of specimen) and thereafter the mean of the local void ratio distribution increases for all horizontal coupons throughout the specimen. From Figure 9, it can also be readily seen that the mean coupon value for coupons a, b, e and f is typically less than the corresponding global value at a given strain level whereas the mean coupon value for coupons c and d (near center) is greater than the global value. Thus it can be seen that the global measure, as routinely used in interpreting specimen behavior, does not discern the significantly different conditions which exist in the center of the specimen from those at the ends. This is clearly reflective of the influence of rough end platens and membrane restraint effects and clearly demonstrates the need

for use of lubricated end platens and local deformation measurement systems. The difference in mean coupon local void ratio between less dilated regions and fully dilated regions is about 0.07 (difference in relative density o f about 22%).

It is feasible to study the evolution o f the local void ratio distribution on horizontal coupon surfaces by examining the average values of the parameters as described above because the surfaces are nominally perpendicular to the direction of applied loading and thus any image on a given surface should be expected to yield comparable information. Use of a similar strategy for studying the mean of the local void ratio distribution on vertical coupon surfaces is not appropriate since some of the images will be reflective o f material response near the center o f the specimen and others indicative of the response influenced by end platen effects. Accordingly, a different approach was used in studying evolution on the vertical coupons in that the averages were computed for rows of images on vertical surfaces located at equal distances from the center of the specimen. These results are plotted in Figure 10 and shows the significant variation in mean local void ratio which evolves during shearing as a function of distance from the center (or ends) of the specimen. For example, it can be seen that at an axial strain o f 14%, the mean local void ratio at the ends of the specimen is about 0.61 while at the center of the specimen, it is about 0.68. It is thus evident why local deformation measurements are critically important in correctly interpreting the response of specimens.

0 50 0 52 0 54 0.56 0 68 0.60 0.62 0 64 0 66 0 68 0 70

iin (7o) e(=0 56

, ef=0 567

1. e(=0 574

ef=0 578

ef=0 588

e(=Q617

I. ef=0 639

Figure 10 Average Local Void Ratio Along Vertical Axis of the Specimen During Shearing Test

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Figure 11 ASTM Graded Sand Triaxial Isotropic Consolidation Lines and Critical State Lines

The state diagram showing the critical state line obtained for ASTM graded sand based on drained tests on contractive specimens as well as the corresponding line based on drained tests on dilatant specimens including those described above are shown in Figure 11. The void ratios used in plotting these results are the global values based on measurements o f the specimen geometry. Based on the stress-strain plot for the tests reported in Figure 9, it might be argued that at least a quasi critical or steady state condition has been reached at an axial strain of 14%. However neither the global void ratio o f specimen j30 o f about 0.64 or the void ratio of about 0.68 in the middle portion o f the specimen based on microstructure measurements summarized in Figure 10 support that conclusion. In fact, based on an extrapolation o f the critical state line determined from tests on loose specimens, the void ratio, at least locally within the specimen, would have to be about 0.74 for the behavior to correspond to the critical state. Accordingly, it is concluded that specimen j30 has not reached critical or steady state at an axial strain o f 14%, a fact that is consistent with the observed global barreling response of the specimen. Had shear bands formed, then a void ratio corresponding to critical state would be expected, at least locally. As noted earlier, an additional series of experiments were performed on specimens prepared to the same initial global conditions using moist-

tamping. As before, the specimens were sheared to different strain levels before the structure was fixed and coupons were prepared for image analysis. Of particular interest to the present discussion are the results for the specimen sheared to 14% axial strain where a distinct shear band was observed to form (Figure 12). The quantitative microscopic measurements show that while the global void ratio of this specimen at an axial strain of 14% was 0.61, the void ratio in the shear band zone was consistent with what would have been predicted based on the results o f tests on contractive specimens. Equally importantly, this result is o f significance in that it clearly demonstrates that the specimen preparation procedure has a controlling influence on the strain level at which axial compression tests on dilatant specimens reach critical state. Based on the results presented herein, it appears that specimens prepared using air pluviation need to be sheared to larger strain levels to reach the critical state condition than those prepared using moist tamping. This result is consistent with the fact that during moist tamping preparation, the specimen is already to some extent being sheared, at least locally by the tamping action and thus while the axial strain applied during the shear stage may be nominally reported as 14%, in reality, the specimen has already been sheared to a significantly higher level.

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6. CONCLUSIONS

Sam pte : p08ASTM G raded Sand (c>109)Prepared by M oist Tam ping

initial Void Ratio « 0.582Final Void Ratio « 0.612Confin ing S tress * 50 kPaD eviator Stress ** 135 kPaAxial Strain » 14%

Figure 12 Moist-Tamped Specimen Sheared to 14% Axial Strain Showing Shear Band

5. IMPLICATIONS OF FINDINGS ON LIQUEFACTION STUDIES

The experimental methods and findings presented in this paper have important implications for the routine study o f liquefaction. As illustrated with the results presented herein, significantly different interpretations are possible when the behavior of sand specimens under loading is studied at a microstructural level and not the traditional global scale. More importantly, these measurements are able to resolve long-standing discrepancies regarding the uniqueness o f steady/critical state and provide insight into the different responses obtained depending on whether specimens are loaded from initially contractive or dilatant states.

In addition to the specific issues described in this paper, the experimental techniques presented herein provide the necessary vehicle to study a range of issues which have limited current understanding of liquefaction and its consequences including:• how micro structures evolve within specimens

during cyclic shearing• what role fine particles play in the micro

response of a material with a matrix o f coarse particles

• what role coarse particles play in the micro response o f a material with a matrix o f fine particles

• how initial non-uniformity impacts global specimen response

• what relative roles particle shape and angularity play in overall specimen response

• what role particle surface roughness play in overall specimen response

• how microstructure evolution in reconstituted specimens varies from that in natural deposits

This paper has presented the results o f a study which has used image analysis based measurements to quantify how the micro-structure throughout dilatant triaxial specimens o f uniform fine quartz sand evolves during drained axial compression loading. The main conclusions are:• Automated image analysis based methods can be

readily used to study the evolution o f microstructure in sand specimens. When aggregated, measurements made at the particle level are consistent with the global specimen response but demonstrate significant variations in response mechanisms locally.

• The use o f a single value for parameters such as void ratio can be misleading and can mask important variations which may exist within a specimen. Evaluation o f parameters such as void ratio should carefully consider scale to ensure that the measured values are representative o f the scale sensitivity o f the parameter.

• The local void ratio distribution and its descriptors (mean, standard deviation) provide valuable insight into how a specimen is locally responding to the application o f a global boundary load.

• Shear induced increases in the mean of the local void ratio distribution initiate at the center of the specimen and migrate towards the ends o f the specimen as axial strain increases. At any given strain, the mean o f the local void ratio distribution is largest at the center o f the specimen, reflecting the influence o f end platen and membrane restraining effects.

• Local deformation systems which measure response over distances L/3 or L/4, where L is the length o f the specimen, should provide for reasonable estimates o f the true response o f the specimen in most cases. For tests conducted at high axial strain levels (15 to 20%), use of systems which measure response over shorter distances (L/6 or less) may be appropriate provided acceptable resolution can be maintained.

• Microstructure measurements reported herein suggest that critical state and steady state are the same condition and discrepancies reported widely in the literature merely reflect the fact that internal strain localization as a result o f testing artifacts such as specimen preparation method and end platen/membrane restraint are not reflected in global measures o f response. Comparison o f microstructure evolution for specimens prepared to similar initial global conditions indicates how specimen preparation can induce microstructure within a specimen which subsequently influences the global strain

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level at which shear banding or other localization phenomena are initiated.

7. ACKNOWLEDGMENTS

The research described in this paper has been supported by NSF Grant # CMS 9457549. This support is gratefully acknowledged.

8. REFERENCES

Bhatia, S. K. and Solimán, A. F., (1990), "Frequency Distribution o f Void Ratio of Granular Materials Determined by an Image Analyzer", Soils and Foundations, Vol. 30, No. 1, pp. 1-16.

Frost, J.D., and Kuo, C.-Y., (1996) "Automated Determination o f the Distribution o f Local Void Ratio from Digital Images", ASTM Geotechnical Testing Journal, Vol. 19, No. 2, pp. 107-117.

Desrues, J., Chambón,. R., Mokni, M., and Mazerole, F., (1996), “Void Ratio Evolution Inside Shear Bands in Triaxial Sand Specimens Studied by Computed Tomography”, Geotechnique, Vol. 46, No. 2, pp. 529-546.

Gilbert, P. A. (1984), “Investigation o f Density Variation in Triaxial Test Specimen o f Cohesionless Soil Subjected to Cyclic and Monotonic Loading”, Tech. Report GL-84-10. U.S. Army Eng.. Waterways Experiment Sta., Vicksburg, Miss., 100pp.

Ibrahim, A. A. and Kagawa, T., (1991),"Microscopic Measurement o f Sand Fabric from Cyclic Tests Causing Liquefaction", ASTM Geotechnical Testing Journal, GTJODJ, Vol. 14, No. 4, pp. 371-382.

Jang, D.J., (1997), “Quantification o f Sand Structure and Its Evolution During Shearing Using Image Analysis”, Ph.D. Dissertation, The Georgia Institute of Technology, Atlanta, 259 pp.

Jang, D.J., and Frost, J.D., (1998), “Sand Structure Differences Resulting from Specimen Preparation Procedures”, ASCE Specialty Conference on Geotechnical Earthquake Engineering and Soil Dynamics”, Seattle, Vol. 1, pp. 234-245.

Jang, D.J., Frost, J.D., and Park, J.Y., (1998), “Preparation o f Epoxy Impregnated Sand Coupons for Image Analysis”, in review for possible publication in ASTM Geotechnical Testing Journal.

Kuo, C.-Y. and Frost, J. D., (1996) "Uniformity Evaluation o f Cohesionless Specimens Using Image Analysis", ASCE Journal o f Geotechnical Engineering, Vol. 122, No. 5, pp. 390-396.

Ladd, R.S., (1974), “Specimen Preparation and Liquefaction of Sands”, ASCE, Journal of Geotechnical Engineering Division, Vol. 100, No. GTIO, pp. 1180-1184.

Ladd, R. S. (1978), "Preparing Test Specimens Using Undercompaction", ASTM Geotechnical Testing Journal, GTJODJ, Vol. l , No. l ,pp. 16-23.

Miura, S., and Toki, S., (1982), “A Sample Preparation Method and Its Effect on Static and Cyclic Deformation Strength Properties of Sand”, Soils and Foundations, JSSMFE, Vol. 22, No. 1, pp. 61-77

Oda, M., (1972a), "Initial Fabrics and Their Relations to Mechanical Properties o f Granular Material", Soils and Foundations, Vol. 12, No. 1, pp. 17-36.

Oda, M., (1972b), "The Mechanism of Fabric Changes During Compressional Deformation of Sand", Soils and Foundations, Vol. 12, No. 2, pp. 1- 18.

Oda, M., (1972c), "Deformation Mechanism of Sand in Triaxial Compression Tests", Soils and Foundations, Vol. 12, No. 4, pp. 45-63.

Oda, M., (1976), “Fabrics and Their Effects on the Deformation Behavior o f Sand”, Special Issue, Department of Foundation Engineering, Faculty of Engineering, Saitama University, Japan.

Shi, D., and Winslow, D.N., (1991), “Accuracy of a Volume Fraction Measurement Using Areal Image Analysis”, ASTM Journal o f Testing and Evaluation, Vol. 19, No. 3, pp. 210-213.

Scholey, G.K., Frost, J.D., Lo Presti, D.C.F., and Jamiolkowski, M., (1995), "Instrumentation for Measuring Local Strains during Triaxial Testing of Small Specimens", ASTM Geotechnical Testing Journal, GTJODJ, Vol. 18, No. 2, pp. 137-156.

Shockley, W. G. and Ahlvin, R. G., (1960), “Non- uniform Conditions in Triaxial Test Specimens”, Research Conference on Shear Strength of Cohesive Soils, ASCE, pp. 341-357.

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Undisturbed sampling o f loose sand using in-situ ground freezing

D.C.Sego, B. A. Hofmann, RK. Robertson & C.E.Wride (Fear)Geotechnical and Geoenvironmental Group, Department of Civil and Environmental Engineering,University of Alberta, Edmonton, Alb., Canada

A B S T R A C T : A sse ssm e n t o f the po ten tia l fo r sta tic or cyclic liq u e fac tio n o f lo o se san d re q u ire s in fo rm a tio n on the u n d ra in e d re sp o n se o f the d eposit. U n d istu rb ed sam ples o f loose san d d e p o sits a re n e ce ssa ry to p ro p e rly o b ta in th is u n d ra in e d re sp o n se , w h ich is a fu n c tio n o f the in -situ sta te o f the d e p o s it and th e ap p lied s tress pa th d u rin g lo ad in g . In -situ g ro u n d freez in g for sam p lin g w h ich p reserv es the in -s itu v o id ra tio and fabric is d e sc rib e d in th is paper. Its a p p lica tio n at six sites du rin g the C an ad ian L iq u e fac tio n E x p erim en t (C A N L E X ) are d e sc rib e d to illu stra te the challenges in the fie ld and to o u tlin e h o w the d iffe re n t site c o n d itio n s w ere m an ag ed . T he tech n iq u es to freeze the g round , to o b ta in and p re se rv e sa m p le s and to p rep are lab o ra to ry tes t sp ec im en are d esc rib ed a long w ith a re co m m e n d e d p ro c ed u re to th aw th e fro zen lab o ra to ry tes t sp e c im en w ith o u t d is tu rb in g the in -situ con d itio n . T h e frozen co re and in -s itu f ie ld tes ts at the sites illu s tra te the e x tre m e h e te rg en ie ty o f sands p laced h y d rau lica lly by m an o r n a tu re . T h is v a ria b ility is a ch a llen g e fo r the e x p e rim e n ta lis t to cap tu re the m ate ria l b e h av io r and then in co rp o ra te th is in to an e co n o m ica l design .


T he m ain fac to rs w h ich a ffec t liq u e fac tio n su sce p tib ility o f a so il d ep o sit in c lu d e gra in c h a ra c te ris tic s (g ra in size d istrib u tio n , partic le shape , p a rtic le h a rd n ess , fines co n ten t and p las tic ity and m in e ra lo g y ), in -situ sta te and stress h is to ry (vo id ra tio , e ffe c tiv e stress, fab ric ), age and cem en ta tio n . D ire c t a sse ssm e n t o f the net e ffec t o f these fac to rs on the u n d ra in e d resp o n se o f sand to ce rta in lo ad in g c o n d itio n m ay req u ire ap p ro p ria ted lab o ra to ry te s tin g o f u n d is tu rb ed sam ples. T estin g re co n sititu ted sam p les m ay no t ad eq u a te ly in co rp o ra te the e ffec ts o f fab ric , age and stress h isto ry .

O ne o f the p rim a ry o b jec tiv es o f the C an ad ian L iq u e fac tio n E x p erim en t (C A N L E X p ro jec t) w as to e v a lu a te the in -situ und ra in ed re sp o n se o f v a rio u s sand d e p o sits and, u ltim ate ly , to p ro v id e a fram e w o rk fo r lin k in g lab o ra to ry and fie ld d a ta that can b e u sed fo r d esig n ag ain st soil liq u e fac tio n (W rid e and R o b ertso n , 1997). W ith th is fram ew o rk , in fo rm a tio n o b ta in ed from u n d is tu rb ed sp ec im en s reg a rd in g the in -situ vo id ra tio and stre ss-s tra in re sp o n se co u ld be e x tra p o la ted b ey o n d the reg io n w h ere u n d istu rb ed sam p les h ad b een reco v e red . O b ta in ing

u n d is tu rb ed sam p les w as seen as an in te g ra l p a rt o f d ev elo p in g the fram ew o rk fo r lin k in g the in -situ response o f sand to da ta p ro v id ed by lab o ra to ry and in -situ testing . A s part o f th e C A N L E X p ro jec t, a s tudy w as u n d e rtak en to d e te rm in e the su b so il and ground co n d itio n u n d e r w h ich in -s itu g ro u n d free z in g u sing liq u id n itrogen is an a p p ro p ria te m eth o d fo r ob ta in in g h ig h qua lity u n d is tu rb ed sam p les o f lo o se sand.

T he fac to rs a ffec tin g g ro u n d free z in g and the feasib ility s tu d ies p e rfo rm e d as p a rt o f the C A N L E X p ro jec t are d esc rib ed . T h e d e ta ile d th eo re tica l p red ic tio n s o f the v o lu m e o f liq u id n itrogen and tim e re q u ire d to ca rry o u t in -situ g round freez in g are p re sen te d in H o fm a n n e t al (1998a). R esu lts fro m la rg e sca le free z in g ex p erim en ts co n d u c ted to e v a lu a te h o w w ell the availab le h eat flow e q u a tio n s p re d ic t the a c tu al freez in g p ro cess are su m m arized . T h e use o f in- situ g round freez in g to o b ta in sam p les at six s ites is o u tlin ed to illu stra te how the d iffe re n t fa c to rs th a t a ffec t its use w ere m an ag ed . T h e m e th o d s to d rill and sam p le the frozen san d s, to p re se rv e the sam ples p rio r to tes ting and to trim the fro ze n co re to o b ta in test spec im ens are d esc rib ed . A p ro c ed u re to p reserv e the in -situ s ta te d u rin g th aw o f the sam ple is a lso described .

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2 L IT E R A T U R E R E V IE W O F S A M P L ED IS T U R B A N C E

2.1 Conventional Sampling

O b ta in in g h ig h q u a lity u n d is tu rb ed sam ples o f loose , sa tu ra ted sand is o ften d ifficu lt u sing c o n v en tio n a l sa m p lin g tech n iq u es . B ro m s (1980) su m m ariz es the cau ses o f sam p le d istu rb an ce due to co n v en tio n a l tube sam p lin g , w h ile , M ight (1993) and M ight and G e o rg ian n o u (1 995) d iscu ss the e ffec ts o f sam p le d is tu rb an c e on c la y ey sands. T h ese s tu d ies , as w ell as th o se by Y o sh im i et al. (1994) and S eed et al. (1 9 8 2 ), h ave c lea rly show n th at c o n v en tio n a l h igh q u a lity tu b e sam p lin g tends to d en sify lo o se san d and lo o sen den se sand. M ight (1993) a lso sh o w ed th a t s tra in s in d u ced during tube sa m p lin g o f c lay ey san d s g en era lly ex ceed the y ie ld stra in .

I f a sam p le o f g ra n u la r so il is to be co n sid ered as tru ly u n d is tu rb ed , the sam p lin g and h an d lin g p ro c esses sh o u ld no t a lte r the in -situ void ra tio , fab ric , stru c tu re , s tress h is to ry o r d eg ree o f sa tu ra tio n (M ofm ann, 1997). C h an g es in the vo id ra tio o f g ra n u la r so ils can a ffec t th e ir stren g th and d e fo rm a tio n a l p ro p e rties . S lad en et al. (1985) also n o ted th a t u tiliz in g the co llap se su rface c o n cep t to ev a lu a te flow liq u e fac tio n in the f ie ld req u ires the in -situ v o id ra tio . M o reo v er, d is tu rb an ce o f the in- situ fab ric a n iso tro p y ten d s to in flu en ce the vo lum e ch an g e b e h a v io u r o f a so il d u rin g defo rm atio n . A lte ra tio n o f the in -situ d eg ree o f sa tu ra tio n can also a ffec t the d e v e lo p m en t o f po re p re ssu re an d /o r v o lu m e ch an g e . L ab o ra to ry tes tin g has illu stra ted the im p o rta n ce o f age on the re sp o n se o f fine g ra in ed so ils. A ge w ill lik e ly a lso have a s ig n ifican t in flu en ce on the u n d ra in e d re sp o n se o f sandy so ils. T h e re fo re , d is tu rb an ce a sso c ia ted w ith c o n v en tio n a l sa m p lin g o ften re su lts in m is lead in g lab o ra to ry tes t resu lts .

2 .2 In-Situ Ground Freezing

T he tec h n iq u e o f carry in g o u t in -situ g round freez in g has b e en d em o n s tra ted to b e a su p erio r m eth o d fo r o b ta in in g u n d is tu rb ed sam p les o f sand by b o th Ja p a n ese and N o rth A m erican researchers. S ev era l au th o rs , in c lu d in g Y o sh im i e t al. (1984, 1989, and 1994), T o k im a tsu and M osaka (1986), M atanaka et al. (1985 and 1995), S eg o e t al (1994) and S in g h e t al. (1982) have d e m o n s tra ted that g ro u n d free z in g o f san d y soils, u n d e r c o n d itio n s o f u n im p e d e d d ra in a g e can b e an e ffec tiv e w ay o f o b ta in in g u n d is tu rb ed sam p les o f sand.

N u m ero u s s tud ies h ave d e m o n s tra ted th a t w h en freez in g is ca rried o u t the in -s itu s tre n g th and d efo rm a tio n a l c h a ra c te ris tic s c an be p re se rv e d . Y o sh im i (1978), S in g h et al. (1 9 8 2 ) an d S eed e t al. (1982) have sh o w n th at, p ro v id ed d is tu rb an c e d id no t o ccu r du rin g the freez in g p ro c ess d u e to im p e d e d d ra in ag e , the u n d ra in e d sta tic o r c y c lic sh e a r s tre n g th o f a sand w as no t a ffec ted . Y o sh im i e t al. (19 9 4 ) a lso sh o w ed that u n id ire c tio n a l free z in g and th aw in g d id no t affec t the u n d ra in ed cy c lic s tre n g th o f san d in e ith e r a loose o r den se state . In ad d itio n , S a s ith a ra n et al. (1994), and K o n rad and S t-L au re n t (19 9 5 ) sh o w ed that the stiffness c h a ra c te ris tic s m ea su re d b y the sm all s tra in m o d u lu s w as no t a ffec ted b y o n e free z e -th aw cycle , p ro v id ed tha t the v o id ra tio d id n o t c h an g e d u rin g freez ing . Y o sh im i e t al. (1 977 an d 1978) sh o w ed that the m ean stre ss and sh e a r s tre ss are no t a lte red by the freez in g p ro cess , p ro v id ed th a t the ov e rb u rd en stress e x ceed s 15kPa.

T he above s tu d ies h av e sh o w n th at, p ro v id ed d ra inage is not im p ed ed and no c h an g e in v o id ra tio occu rs du rin g freez in g and th aw , the in -s itu so il s tru c tu re can be p re se rv e d and th e re fo re , fro zen u n d is tu rb ed sp ec im en s are v a lu a b le fo r a sse ss in g the liq u efac tio n p o ten tia l o f a sa n d d ep o sit. M ow ever, p rio r to u n d e rta k in g g ro u n d f ree z in g fo r u n d is tu rb ed sam p lin g , fe as ib ility s tu d ie s sh o u ld be c o n d u c ted to c o n firm th at a g iv en so il d e p o sit can be frozen w ith o u t risk o f d is tu rb an c e d u e to fro st heave or im p ed ed d ra in a g e co n d itio n s . T he re lev an t subso il c h a ra c te ris tic s an d site c o n d itio n s , w h ich sh o u ld be e v a lu a ted , as p a rt o f the fe as ib ility study w ill be d isc u sse d in the fo llo w in g sec tio n s.

3 F A C T O R S A F F E C T IN G U S E O F G R O U N D F R E E Z IN G

M ofm ann et al (1 9 9 8 a) e la b o ra te s in d e ta il on the facto rs tha t co n tro l the u se o f in -s itu g ro u n d freezing . T he fo llo w in g c o n d itio n s m u s t be u n d e rsto o d and ev a lu a te d in d e ta il to e n su re th a t the site can be fro zen w ith o u t d is tu rb in g th e in te r partic le a rran g em en t:• C o n d itio n s in the d e p o sit n e a r th e free z in g fro n t

p e rtin en t to the ab ility to freeze the so il w ith o u t a ttrac tin g w a te r to the free z in g fro n t (fro s t heave) o r th a t re su lt in im p e d e d d ra in a g e o f in- situ w a te r aw ay fro m th is fro n t w h ic h re su lts in d is tu rb an ce to the fab ric an d s tru c tu re d u e to the vo lum e ex p an s io n o f the in -s itu w a te r as it ch an g es phase .

• T h e freez in g sy s tem m u st b e se lec te d to m in im ize the d is tu rb an c e a sso c ia te d w ith its

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in s ta lla tio n w h ile en su rin g th a t the so il o f in te res t can b e sam pled .

T h e so il and site c h a ra c te ris tic s w ith in the zone to be fro zen th a t c o u ld c o n trib u te to d is tu rb an ce d u rin g free z in g o r im p ac t on the ab ility to u n d e rta k e the g ro u n d free z in g m u st be studied . T h ese include:• G ra in size d is tr ib u tio n and m in e ra lo g y o f fines

(D av ila e t a l., 1992).• S tra tig ra p h y and d ra in ag e c o n d itio n s (H o fm an n

e t al., 1998a).• O v erb u rd en stress in sa m p lin g zone and ra te o f

c o o lin g a sso c ia ted w ith freez in g sys tem (K o n rad and M o rg e n ste rn , 1980; and H o fm an n e t al., 1998a).

• G ro u n d w a te r tem p e ra tu re , sa lin ity and flow c o n d itio n s (H ash em i and S liep cev ich , 1973; S a n g e r and S ay les , 1979; and H o fm an n e t al., 1998a).

E v a lu a tio n o f the fro st su sce p tib ility o f the sand d e p o sit m u st be ca rr ied ou t p rio r to u sin g in- s itu g ro u n d free z in g at any site. L ab o ra to ry frost heav e tes ts on so il fro m the zo n e to be frozen sh o u ld be c a rr ied o u t and these tes ts m u st sim u la te the in -situ s tress co n d itio n s and freez in g g rad ien t a n tic ip a te d at the ra d ia l d is tan ce w h ere the sam ples w ill be o b ta in ed . W h en liq u id n itro g en is u sed to freeze the san d a Im rad iu s is ty p ica lly frozen and the sam p les are o b ta in e d at 0 .6 m rad iu s from the freeze p ipe. F o r th ese c o n d itio n s H o fm an n (1997) re co m m e n d s use o f tem p e ra tu re g rad ien t o f 0 .4 0 C /cm in the fro st heav e test.

4 T H E O R E T IC A L P R E D IC T IO N O F T H E G R O U N D F R E E Z IN G P R O C E S S

A fte r c o n firm in g th a t the c h ara c te ris tics o f a sand d e p o sit and the site c o n d itio n s are ap p ro p ria te fo r co n d u c tin g in -s itu g ro u n d freez in g , it is n ecessa ry to assess the h ea t ex tra c tio n req u irem en ts to es tim a te the tim e and co sts a sso c ia ted w ith th is m eth o d o f u n d is tu rb ed sam pling . D e ta ils o f the th eo re tica l so lu tio n to p red ic t the g ro u n d freez in g p ro cess are g iv en b y H o fm an n (1997) and H o fm an n e t al. (1 9 9 8 a).

5 C A N L E X SIT E S

T he C A N L E X p ro jec t in v o lv e d d e ta iled in v es tig a tio n o f six sites in W es te rn C anada, all o f w h ich c o n ta in ed re la tiv e ly lo o se sand deposits . T he P hase I and P h ase III sites (M ild red L ake S e ttlin g B asin an d J-p it, re sp ec tiv e ly ) co m prised

h y d rau lica lly p laced san d d e p o sits a sso c ia ted w ith the o ilsan d in d u stry at the S y n c ru d e C a n ad a L td . m in e in A lberta . T he P h ase II sites (M a ssey an d K idd) in c lu d ed natu ra l sand d e p o sits in the F ra se r R iv er D e lta o f B ritish C o lu m b ia (B C ).

T he Phase IV sites (L L D a m and H ig h m o n t D am ) are h y d ra u lica lly p lac ed san d d ep o sits a sso c ia ted w ith the h a rd ro c k m in in g in d u stry at the H ig h lan d V a lley C o p p er (H V C ) M in e in B C .

A t each site the targ e t z o n es w ere se lec te d by a p re lim in a ry su rv ey u s in g the co n e p e n e tra tio n tes t to ch arac te rize a loose , u n ifo rm , re la tiv e ly c lean sandy deposit. V ario u s m eth o d s o f g ro u n d sa m p lin g w ere p e rfo rm ed at each site. T h ese in c lu d e d g ro u n d freez in g and sam p lin g , fix ed p is to n tube sam p lin g , C h ris ten sen d o u b le -tu b e co re sam p lin g , la rge d iam e te r sam p lin g using the L ava l sa m p le r and son ic (ro ta ry -v ib ra to ry ) c o n tin u o u s co rin g . G ro u n d freez in g and sa m p lin g w as p e rfo rm e d at all six sites; the o th er m eth o d s w ere u sed at on ly so m e sites.

A d e ta iled c o m p a riso n o f the q u a lity o f sam p le o b ta in ed u sin g the v a rio u s sa m p lin g m e th o d is p re sen ted in W rid e et al, (1998). T h e tec h n iq u es u sed fo r the g ro u n d freez in g and sa m p lin g at e ach site are desc rib ed below .

6 T E S T SIT E S

T he loca tion , g eo lo g y and ta rg e t zo n es fo r each o f the six sites are d esc rib ed by R o b e rtso n e t al. (1998). T he typ ica l lay o u t o f the d e ta ile d site c h a ra c te riz a tio n at each o f the six C A N L E X sites is a lso d e sc rib e d by R o b ertso n e t al. (1998a). F ro z e n sam p les o f sand w ere o b ta in e d from the ta rg e t zo n e at the c en tre o f each o f the six sites (H o fm an n , 1997; H o fm a n n et al., 1998b; B ig g ar and Sego , 1996). In ad d itio n , a lo n g a ty p ica lly 5 m rad iu s c irc le a ro u n d the c en tra l g ro u n d freez in g lo ca tio n , the fo llo w in g c o n v en tio n a l sam p lin g w as p e rfo rm ed : fix ed p is to n tu b e sam p lin g at the P h ase I site (P lew es, 1993) and the P h ase II sites (P lew es, 1995); C h ris ten sen d o u b le -tu b e co re sam p lin g at the P h ase I site (P lew es 1993); L av a l large d iam e te r sam p lin g at th e P h ase II sites (K o n rad et al., 1994a& b) and the L L D a m site (K o n rad , 1996); and son ic (ro ta ry -v ib ra to ry ) c o n tin u o u s c o rin g at the P hase II sites (M o n ah an e t a l., 1995).

A su m m ary o f the g ro u n d free z in g and sam p lin g co n d u c ted at the six C A N L E X sites is g iv en in T ab le 1.

7 G R O U N D F R E E Z IN G A N D S A M P L IN G

T h e g ra in size d is trib u tio n and fin es m in e ra lo g y o f a so il d e p o sit w ill a ffec t the ab ility to p e rfo rm

181

Table 1. Summary of ground freezing and sampling conducted at the six CANLEX sites (Wride et al., 1998)S a m p lin g p ro ced u re an d com m en ts

I M ildred Lake Liquid nitrogen w as used to radially freeze a 2 m diam eter by 10 m lon g colum n o f the sand deposit; dry coring w ith a CRREL barrel w as used to sam ple the frozen so il (H ofinann et al., 1994a) (see Figure 1 for illustration o f ground freezing & sam pling configuration at the Phase I site; Hofmann et al., 1998b)

A total o f 20 m o f sandy so il core w as obtained (H ofinann, 1997)

n M assey«&Kidd

Liquid nitrogen w as used to radially freeze a 2 m diam eter by 5 m long colum n o f the sand deposit; dry coring w ith a CRREL barrel w as used to sam ple the frozen so il (H ofm ann et al., 1995)

A total o f 40 m o f sandy so il core w as obtained from the Phase II s ites (H ofm ann, 1997)

m J-pit Liquid nitrogen w as used to radially freeze a 2 m diam eter by 4 m long colum n o f the sand deposit; dry coring w ith a CRREL barrel w as used to sam ple the frozen so il (H ofm ann et al., 1996)

A total o f 6 .9 m o f 200 m m diam eter and 3.9 m o f 100 m m diam eter sandy so il core was obtained (H ofm ann, 1997)

IV LL Dam Liquid nitrogen w as used to radially freeze a 2 m diam eter by 4 m long colum n o f the sand deposit; dry coring w ith a CRREL barrel w as used to sam ple the frozen so il (B iggar & Sego, 1996)

A total o f 18 m o f 100 mm diam eter sandy so il core w as obtained (B iggar & Sego, 1996)

HM Dam Liquid nitrogen w as used to radially freeze a 2 m diam eter by 4 m long colum n in each sand deposit Dry coring w ith a CRREL barrel w as used to sam ple tlie frozen so ilA total o f 16 m o f sandy so il core (13 m o f 100 m m diam eter core and 3 m o f 200 mm diameter core) w as

obtained (B iggar & S ego, 1996)

T ab le 2. S u m m ary o f m in e ra lo g y o f fines fo r the sand d ep o sits at the six C A N L E X sites (W rid e e t a l., 1998)

S ite d a ta A v e r a g e M in e r a lo g y o f f in e s (p a ss in g N o . 2 0 0 s ie v e ) , in p e rcen tP h a se S ite F C (% )* Q u a r tz F e ld sp a r K a o lin ite M ica C h lo r ite & S m ectite Illite C a lc ite

I M ildred Lake 12 90 5 5 trace -- --

n M assey < 5 70 15 5 5 5 -- --

K idd < 5 70 15 5 5 5 - -

m J-pit 10 A ssu m ed to be the sam e as for Phase I

IV LL D am 8 36 9 (plagioclase feldspar) 2 (potassium feldspar)

3 2 7 5 (smectite) trace (chlorite)

15 3

H M D am 17.5 57 21 (plagioclase feldspar) 5 (potassium feldspar)

4 1 2 (smectite) trace (chlorite)

7 5

F ines content (FC); based on lim ited S P T data

T ab le 3. C o m p ariso n o f v o id ra tio s fo r sam p les o b ta in ed u sin g d iffe re n t sa m p lin g m e th o d s (W rid e e t a l., 1998)

Site data V oid ratio (e) and relative d en sity (Dr)Phase S ite G round freezing

& sam pling ^Fixed piston tube C hristensen L aval large

sam p ler^ tt d ou b le-tu b e d iam eter sam pler ^G eophysical

logging^1 M ildred Lake e = 0.768 (0 .040)

Dr = 65.5% (13.8% ) (52 sam ples)

e = 0 .694 (0.034) Dr = 91.0% (11.7% )

(14 sam ples)

sam ples disturbed due to handling N /A

e = 0.788 (0 .053) Dr = 58.6% (18.2% )

n M assey e = 0 .970 (0 .050) Dr = 32.5% (12.5% )

(42 sam ples)

e = 0 .984 Dr = 29%

(2 sam ples)N /A

e = 0.942 (0.077) Dr = 39.5% (19.2% )

( 14 samples)

e = 0.99 (0.07)Dr = 27.5% (17.5% )

Kidd e = 0.981 (0.076) Dr = 29.8% (19.0% )

(28 samples)

e = 0 .922 (0.046) Dr = 44.5% (11.5% )

(8 sam ples)N /A N /A

e = 0.78 (0.06)Dr = 80.0% (15.0% )

very poor

m J-pit e = 0.762 (0 .053) Dr = 42.7% (10.1% )

(47 sam ples)N /A N /A N /A

e = 0.721 (0.068) Dr = 50.5% (13.0% ) based on 1 good log

IV LL Dam e = 0 .849 (0 .041) Dr = 40.3% (8.0% )


N ot calculated (only 2 small p ieces

o f core obtained)

e = 0.929 (0.120) Dr = 24.6% (23.5% )

H M D am e = 0.825 (0 .075) Dr = 37.4% (14.8% )


N /A e = 0.862 (0.074) Dr = 30.1% (14.6% )

Numbers are given as overall average values in target zone (numbers in brackets are overall standard deviations in target zone); values of e„ , and e ^ used to calculate relative density (D,) are given by Robertson et al. (1998a).The numbers of samples indicated for ground freezing & sampling and the Laval large diameter sampler are the number of samples trimmed from the frozen core for testing; for the fixed piston tube sampler, the number of samples are the number of high quality (Type 1 & II) tube samples obtained from the target zone at each site.Based on S, = 100%; comment below void ratio indicates quality of geophysical logs based on measured compensation values (Robertson et al., 1998b)

182

su ccessfu l g ro u n d free z in g and sam p lin g , w ith m in im al d is tu rb an c e to the v o id ra tio and fabric (H o fm an n e t ah , 1998a). T ab le 2 su m m arizes the av erag e fines c o n te n t and m in e ra lo g y o f the fines fo r the san d d e p o sit at each C A N L E X tes t site. B ased on the m in e ra lo g y o f the fines, H o fm an n (1997) and H o fm a n n e t al. (19 9 8 b ) p e rfo rm e d frost h eave su sce p tib ility e v a lu a tio n s o f the various C A N L E X tes t sites , u sin g the c rite rio n d ev e lo p ed by D a v ila e t al. (1992). S om e sites had re la tiv e ly h igh fines c o n te n ts (e .g . up to as h igh as 22% in certa in zo n es at the P hase III s ite); ho w ev er, based on the m in e ra lo g ica l co m p o s itio n o f the fines, the c rite rio n su g g e ste d by D a v ila e t al. (1992) in d ica ted tha t the risk o f fro st heave d u rin g ground f reez in g in all o f the d e p o sits w o u ld be neg lig ib le (H o fm an n e t al., 1998b). E rost h eave tests that w ere p e rfo rm e d on b u lk sam p les in the lab o ra to ry c o n firm ed th ese fin d in g s (H o fm an n , 1997). In ad d itio n , the sand d ep o sits w ere fo u n d to be su ffic ien tly p e rm e ab le (co m p ared to the ex p ec ted ra te o f freez in g ) th a t p o re w a te r ex p u ls io n w ou ld be u n in h ib ited d u rin g g ro u n d freez in g (H o fm an n et al., 1998b).

H o fm an n e t al. (1 9 9 8 b ) p ro v id e a d e ta iled su m m ary o f the g ro u n d free z in g and sam p lin g that w as p e rfo rm e d at each o f the C A N L E X tes t sites. A s an e x am p le , E igu re 1 illu stra tes the co n fig u ra tio n o f g ro u n d free z in g and sa m p lin g that w as p e rfo rm e d at the P h ase I test site w h ich w as the d eep est and m o st c h a llen g in g site. A t the cen tre o f each tes t site, liq u id n itro g en w as used to rad ia lly freeze a co lu m n o f soil (ty p ica lly 2m in d iam e te r) th ro u g h the sp ec ified targe t zone. T he targe t sa m p lin g zo n es at the C A N L E X test sites w ere lo ca ted at d iffe re n t d ep th s in sand deposits w ith d iffe re n t d en sitie s ; th e re fo re , the freeze p ipes at the v a rio u s sites w ere in s ta lled u tiliz in g d ifferen t tech n iq u es. D e ta iled d e sc rip tio n s are p ro v id ed by H o fm an n e t al. (1 9 9 8 b ). R esis tan ce tem p era tu re d ev ices (R T D s) w ere u se d to m o n ito r tem p era tu res w ith in and a ro u n d the freez in g sy s tem and to co n firm that the fro zen co lu m n o f so il had reached the d es ired ra d iu s p rio r to sam p lin g . S am p lin g w as then c arried ou t in sev e ra l b o reh o les, w h ich had been p re -a d v a n ce d u sin g w et ro ta ry co rin g to ju s t above the ta rg e t-sam p lin g zo n e ( ty p ica lly at a 0 .6m rad ius fro m the freeze p ip e), lin ed w ith large d iam e te r (260 m m ) cas in g , filled w ith w a ter to rep lace the d rillin g flu id and sea led w ith b en to n ite p lugs (see E igu re 1). E o llo w in g the co m p le tio n o f g ro u n d freez in g and p rio r to sam p lin g , the w ater w as b lo w n ou t o f each cas in g . C o rin g o f the in- s itu frozen sand w as p e rfo rm e d u sing a C o ld R eg io n s R esearch E n g in e e rin g L ab o ra to ry

(C R R E L ) co re barre l w ith a tu n g sten ca rb id e tip p ed cu tting shoe and a d ry c o rin g tec h n iq u e (H o fm an n et al., 1998b). A co re c a tch e r at the b o tto m o f the C R R E L b arre l w as used to p re v en t lo ss o f the fro zen core as the barre l w as b ro u g h t to the g ro u n d su rface . B o th 100 m m d iam e te r and 2 0 0 m m d iam e te r C R R E L core b arre ls w ere u sed d u rin g the C A N L E X p ro jec t, as in d ica ted in T ab le 1.

A s o u tlin ed by H o fm an n et al. (1 9 9 8 b ), co re runs o f ap p ro x im ate ly 0 .6 m lo n g w ere reco v e red , ex tru d ed at the g ro u n d su rface u sin g a h y d ra u lic co re ex tru d er, m easu red fo r len g th , p lac ed in an in su la ted box filled w ith c ru sh ed ice p lac ed above d ry ice, tem p o rarily s to red in freezers on site b e tw een layers o f in su la tio n and dry ice, and su b seq u e n tly tran sp o rted to co ld room s (-2 0 ”C ) at the U n iv e rs ity o f A lberta . T he frozen co re w as th en c are fu lly ca ta lo g u ed and p reserv ed fo r lo n g -te rm sto rage . S am ples w ere trim m ed as re q u ire d fro m the fro zen core fo r lab o ra to ry testing .

S am p les w ere trim m ed to the re q u ire d len g th using a d iam o n d c u t-o ff saw . T h en a m ac h in is t lathe w ith specia l m o d ifica tio n w as u sed to trim sam p les to the req u ired sp ec im en d iam e te r. T he sa m p le s w ere then w rap p ed in c e llo p h an e and p ack ed in to a bed o f snow or c ru sh ed ice fo r sto rag e o r sh ip m en t. T he sam ples w ere s to red in deep freezers m a in ta in ed at - 20°C w ith at least 10cm o f c ru sh ed ice co v er, to reduce the risk o f ab la tion .

T he sam p les, w h ich w ere to be sh ip p ed to a labo ra to ry fo r testing , w ere p lac ed in to an in su la ted c o o le r co n ta in in g a bed o f lo o se c ru sh ed ice o v e rly in g a layer o f d ry ice. T he sam p les w ere th en c o v ere d w ith c ru sh ed ice and the c o o le r sea led to m in im iz e the m elting o f the c ru sh ed ice cover. T he c o o le rs w ere then a ir lifted to the ap p ro p ria te test lab o ra to ry .

8 V O ID R A T IO

V oid ra tio s w ere c a lcu la te d (u sin g vo lu m e ca lcu la tio n s) fo r each sam p le tr im m ed fo r lab o ra to ry testing from co re o b ta in ed by g ro u n d freez in g . T hese vo id ra tio s are su m m arized in T ab le 3. D e ta iled c o m p ariso n s on an o v e ra ll p ro file b ases are also show n in F ig u re 2 to F ig u re 4. In each o f these figures, the vo id ra tio sca le has b een p lo tte d from a p p ro x im ate ly emin to emax fo r the p a rticu la r site (as g iven by R o b ertso n et al., 1998); th e re fo re , va lu es o f re la tiv e d en sity (Dr) can be e s tim a te d d irec tly from each figure. T h e average v a lu es o f re la tiv e d en sity fo r each site are also su m m arized in T ab le 3. T h e th ick sem i-v ertica l line in each fig u re re p re se n ts vo id ra tio s c o rre sp o n d in g to the re lev an t re fe re n ce u ltim ate sta te line (U S L ) (R o b ertso n e t al 1998).

183

Table 4. Comparison of ground freezing and sampling costs for the CANLEX project (after Hofmann et al.,1998b)

P hase N o. o f S ites L en g th o f C o r e (m ) V o lu m e T o ta l C o s t * (C A D )

U n it C o st100 m m «1» 200 m m (|> T o ta l o f C ore

(cm^)

S ite

(C A D /s ite )

L en g th

(C A D /m )

V o lu m e

(C A D /cm ^ )

I I 20 0 20 157 ,080 9 4 ,2 0 0 9 4 ,2 0 0 4 ,7 1 0 0.60

n 2 40 0 40 3 1 4 ,1 5 9 100,100 5 0 ,0 5 0 2 ,503 0 .3 2

m 1 3.9 6 .9 10.8 2 4 7 ,4 0 0 4 8 ,0 0 0 4 8 ,0 0 0 4 ,444 0 .1 9

IV 2 31 3 34 337,721 8 1 ,8 2 2 40 ,911 2 ,4 0 7 0 .2 4

Includes cost o f liquid n itrogen, drilling fees, engineering supervision , labour, and equipm ent.(N ote: costs associated w ith sample: handling, sh ipp ing and storage are not included)(N ote: costs associated w ith travel, accom m odation , and m eals are not included)

T ab le 5. C o m p ariso n o f fix ed p isto n , C h ris ten sen d o u b le -tu b e and L av a l la rge d iam e te r sa m p lin g cost:e t a l., 1998)

S a m p lin g P h ase N o. o f S ites S am p les T o ta l C o st * U n it C ostM eth od N u m b er T o ta l T o ta l V o lu m e (C A D ) S a m p le L ength V o lu m e

L en g th (m ) (c m h E S T IM A T E D (C A D /sa m p le ) (C A D /m ) (C A D /cm ^)

Fixed-piston I I 22 11.66 4 8 ,8 0 2 18,000 818 1,544 0 .37

n 2 30 15.90 66 ,548 20,000 667 1,258 0.30

Christensen I 1 „ 15.86 66 ,3 8 0 500 0 _ 315 0 .08

double-tube

Laval large n 2 4 1.77 60 ,144 12,000 3 ,0 0 0 6 ,780 0.20diam eter IV 1 2 0 .50 16,990 10,000 5,000 20,000 0 .5 9

Includes cost o f drilling fees, engineering supervision , labour, and equipm ent.

(Note; costs associated with sam ple handling, sh ipp ing and storage are not included) (Note: costs associated with travel, accom m odation, and m eals are not included)

F ig u re 1. S ch e m a tic o f g ro u n d freez in g and sam p lin g at the P h ase I C A N L E X te^t s ite (a fte r H o fm a n n e t ah , 1998b)

184

A lso g iven in T ab le 3 is a su m m ary o f the vo id ra tio s (and re la tiv e d en sitie s) p red ic ted by g eo p h y sica l (g a m m a-g a m m a ) lo g g in g at each site. C o m p arin g th ese d a ta to the vo id ra tio d a ta for the sam ples, as g iv en in T ab le 3, is a s im p listic co m p ariso n , since it is re co m m e n d e d that the data be e x am in ed and co m p a red on a co m p le te p ro file basis. S u ch c o m p a riso n s are p ro v id ed by R o b ertso n et al. (1998). T h e in te rp re ta tio n s o f vo id ra tio fro m g e o p h y sica l lo g g in g a ssu m ed that the sand w as fu lly sa tu ra ted (i.e. Sr = 100% ). F u rth e r d e ta ils are g iv en b y R o b ertso n et al. (1998).

In g en era l, at the C A N L E X sites , w hen the sand d ep o sits w ere fu lly sa tu ra ted and there w ere no d iffic u lties in c o n d u c tin g g eo p h y sica l logg ing , the vo id ra tio s o f sam p les o b ta in e d u sin g g round freez in g and sa m p lin g ag reed qu ite w ell w ith the in te rp re ted v o id ra tio p ro file s fro m the g eophysica l logs. F ig u re 5 illu s tra te s th is co m p ariso n at the M assey site. C o m p ariso n s fo r all the sites and a d d itio n a l d e ta ils re g a rd in g the geo p h y sica l lo g g in g are p ro v id ed b y R o b e rtso n et al. (1998). A t all o f the sites , b o th the g e o p h y sica l logg ing re su lts and g ro u n d free z in g sam p les in d ica ted that the sand d e p o sits a p p ea r to be h ig h ly h e te ro g en e o u s w ith larg e v a ria tio n s in d en sity over sh o rt d is tan ces , b o th v e rtica lly and h o rizon ta lly .

9 C O S T S A S S O C IA T E D W IT H S A M P L IN G

T ab le 4 p re sen ts a co m p ariso n o f the costs a sso c ia ted w ith g ro u n d freez in g and sam p lin g for the v a rio u s p h a se s o f the C A N L E X p ro jec t (after H o fm an n e t al., 1998b). A s the p ro jec t p ro g ressed and m o re e x p e rien c e w ith in -situ g round freez ing and sam p lin g w as g a in ed , the un it costs o f g round freez in g and sa m p lin g (in te rm s o f to ta l soil v o lu m e) d e c re ased s ig n ifican tly . B y the en d o f the p ro jec t, the c o st o f re triev in g sam ples u sin g g round freez in g w as a b o u t $C D N 0 .2 5 /c m \

T ab le 5 p re sen ts a co m p ariso n o f the costs asso c ia ted w ith the o th e r m eth o d s o f sam p lin g at the v a rio u s p h ases o f the C A N L E X pro jec t. In genera l, the co st o f re tr iev in g sam p les u sin g these o th er m eth o d s w as in the o rd e r o f abou t $C D N 0 .40/cm ^ w h ich is s lig h tly h ig h e r than those using g round freez ing . It sh o u ld be n o ted tha t g round freez in g has a fix ed c o st o f ab o u t C D N $4 0 ,0 0 0 to 50 ,0 0 0 to freeze the site, h o w e v er a large v o lum e o f h igh q u a lity sam p les can b e reco v e red fo r th is cost.

10 T H A W IN G O F U N D IS T U R B E D S A M P L E S

T o avo id d istu rb an ce o f the in -s itu c o n d itio n s cap tu red by the freez in g p ro c ess it is im p e ra tiv e that frozen spec im ens be th aw ed in the lab o ra to ry in a co n tro lled m anner. D u rin g the th aw in g p ro cess , the sand m u st be a llow ed to reco v e r the e x ce ss 9% pore w ater vo lu m e that w as e x p e lled d u rin g free z in g and to resto re the in -situ stress co n d itio n (H o fm an n et al., 1996).

O ne m eth o d used to th aw sp e c im en s w as to thaw sam ples m u ltid ire c tio n a lly , u n d e r a sm all e ffec tiv e stress o f abou t 20 k P a and then c o n so lid a te the th aw ed sp ec im en s to the in -situ e ffe c tiv e stress c o n d itio n s to avo id sh ea r stress c o n ce n tra tio n s at the th aw in g fron t. A n o th e r m eth o d u sed w as to th aw the sam ple u n id irec tio n a lly u n d e r th e ir in situ s tress sta te .

T o ev alu ate w h ich o f these tw o th aw in g tech n iq u es resu lts in the least am o u n t o f d is tu rb an c e , the C A N L E X p ro jec t c o n d u c ted a s tudy on bo th u n id irec tio n a lly frozen re co n stitu te d sp e c im en s and u n d istu rb ed frozen sp ec im en s o b ta in e d by in -situ g round freez in g at the P h ase I tes t site. T o e x am in e the e ffec t o f stress level a lone , the vo id ra tio ch an g es ex p erien ced by re co n stitu te d sp ec im en s th aw ed u n id irec tio n a lly , e ith e r u n d e r the in -situ e ffe c tiv e stress o r u n d e r a sm all e ffec tiv e stress w ere also com pared . D eta ils reg ard in g the s tu d y are p re sen te d by H o fm an n (1997), h o w ev er, on ly the re su lts o b ta ined fro m the u n d is tu rb ed sp e c im en s are su m m arize below .

T o q u an tify d is tu rb an ce , the v o id ra tio c h an g e d that occu rred during c o n tro lled th aw in g o f the u n d istu rb ed sp ec im en s and re -a p p lic a tio n o f the in- situ s tresses, w ere m o n ito red . F ive sp e c im en s w ere thaw ed u n d e r stresses th a t w ere c lo se to the in -situ e ffec tiv e stress. T h aw in g w as u n d e rta k en u n id irec tio n ally , u n d e r 90% o f the e s tim a te d an iso trop ic in -situ e ffec tiv e s tresses. T h e sp ec im en s w ere su b jec t to on ly 90% o f the e s tim a te d in -situ e ffec tiv e stress to p rev en t ex p o sin g the sp e c im en s to h ig h er s tresses than th o se e x is tin g in the fie ld , in case the in -situ sta te o f the sam p le w as c lo se to the y ield surface and the e stim a ted in -situ s tre sses w ere not accu rate (H o fm an n , 1997). B a se d on the sam ple dep th and g ro u n d w a ter tab le lo ca tio n , the in -situ to ta l stresses po re w ater p re ssu re and e ffe c tiv e s tress w ere de te rm ined . T he e ffec tiv e stress w as then red u ced to 90% and by add ing the in -s itu po re w a te r p re ssu re co rre sp o n d in g to the sam p le d ep th , the to ta l ax ia l stress and cell p re ssu re w ere ca lcu la ted . D u rin g thaw ing , the b a ck p ressu re w as set equal to the in -situ pore p re ssu re b ased on the sam p le d ep th to a llo w for recovery o f the 9% pore w a te r v o lu m e e x p e lled during freez in g and to re s to re the in -situ deg ree o f

185

0 7 0.75 0.8 0.85 09 0.95

m sMipla — Syncnide Refe

F ig u re 2. V o id ra tio s o f (a) u n d is tu rb ed frozen sam p les and p iston tube sam p le rs o b ta in e d a t th e P h a se I (M ild red L ake) site, and (b) u n d istu rb ed frozen sam ples at the P h ase III (J-P it) site. (W rid e e t al 1998)

0.8 0.9

• V

F ig u re 3. V o id ra tio s o f (a) u n d is tu rb ed fro zen sam ples, L aval la rge d iam e te r sa m p le r sa m p le s an d p is to n tube sa m p le s fro m M assey site, and (b) u n d istu rb ed frozen sam p les and p is to n tu b e sa m p le s fro m the K id d site. (W rid e et al., 1998).

sa tu ra tio n . T h e re su lts fro m th ese tes ts w ere c o m p a red w ith the re su lts fro m e ig h t sp ec im en s th aw ed m u ltid ire c tio n a lly u n d e r a sm all e ffec tiv e s tress w ith ze ro p o re p re ssu re and then c o n so lid a te d to the in -situ e ffec tiv e stress once th aw in g w as co m p le te .

T h e to ta l c h an g e s in vo id ra tio th a t occu rred are p lo tte d a g a in s t d eg ree o f sa tu ra tio n in F ig u re 6. A s sh o w n , the tes t re su lts in d ica te tha t the sp e c im en s th aw ed u n d e r 90% o f the in -situ e ffec tiv e s tre ss u n d e rw en t an av erag e to tal d ecrease in the v o id ra tio o f a p p ro x im ate ly 0 .02 w h ile th o se th aw ed u n d e r a sm all e ffe c tiv e stress

and then c o n so lid a ted to the in -s itu stress leve l u n d e rw en t an av erag e to ta l d e c re ase in the vo id ra tio o f 0 .08 . T h ere fo re , fo r th e u n d is tu rb ed sam p les reco v e red b e tw ee n 27 and 37 m b e lo w the g ro u n d su rface o f the P h ase I tes t site , th aw in g u n d e r an e ffe c tiv e an iso tro p ic s tre ss th a t is s lig h tly less th an th a t e s tim a te d to e x is t in -situ , u n d e r the in -situ p o re p re ssu re c o n d itio n , re su lts in s ig n ific a n tly less d is tu rb an ce o f the v o id ra tio than tha t e x h ib ited by sp ec im en s th aw ed u n d e r a low e ffec tiv e s tress and th en c o n so lid a ted to the in -situ stress o n ce th aw in g w as co m p le te .

T h e ab o v e stu d y w as ca rr ied o u t on P h ase I

186

Void mrto, •0.35 0.65 0.73 0.83 0.93 1.05

F ig u re 4. V o id ra tio s o f (a) u n d is tu rb ed frozen sam ples fro m the L L D am site and (b) u n d is tu rb e d fro zen sam p les fro m the H ig h m o n t D am site. (W ride et al., 1998)

0 .7 0.8

Void ratio, e

0 .9 1.0

-----Geophysical logging • Frozen samples " Fraser River Reference USL

F igure 5. C o m p ariso n o f v o id ra tio in te rp re ta tio n o f g e o p h y sica l log g in g re su lts w ith v o id ra tio s o f u n d is tu rb ed g ro u n d freez in g sam ples from the M assey site. (W ride e t a l., 1998).

187

0.00

0.01

I 0.02i 0.0301 0.04 ua 0.05Mt 006JC0 0 07 c

1 o.Oi

« 0 09

O 0.10 o5 oil•oO 0.12

0.13

0.14 I

Specimens thawed under a small effective stress

Specimens thawed under the in-situ- effective stress :

•Linear Regression for a Small Effective Stress

- Linear Regression for In-Situ Effective Stress

Q._________

.1 -

Degree of Saturation (% )

Figure 6 . Comparison of Change in Void Ratio During Thawing and Consolidation of Undisturbed Phase I specimens subject to the In-situ effective stress or a small effective stress during thawing. (Hofmann, 1997).

(Mildred Lake) samples, which were not fully saturated in-situ and where the in-situ stresses were high (>500 kPa). Test results on samples from the other sites, where in-situ stresses were lower (lOOkPa) and samples were fully saturated in-situ, showed that both thaw/consolidation methods worked well and the average change in void ratio was generally limited to around - 0 .0 2 .

11 CONCLUSIONS

Prior to conducting in-situ ground freezing for undisturbed sampling, it is prudent to carry out feasibility studies that take into account both the subsoil and site conditions. The subsoil characteristics related to frost susceptibility include: the soil grain size distribution, thepercentage of fines and their mineralogy, the potential unfrozen water content and the rate of cooling compared to the permeability of the deposit. The site characteristics which also affect the feasibility of ground freezing include: thestratigraphy and drainage conditions, the overburden stress and the groundwater conditions. The combined effect of most of the above factors can be evaluated by conducting simple onedimensional laboratory freezing tests on bulk soil samples obtained from the site, and using the

corresponding in-situ overburden stresses, rates of cooling, pore water chemistries and approximate in- situ densities that would exist during ground freezing.

At the six CANLEX sites where ground freezing was performed. Comparison, in terms of void ratio.

with the results of geophysical (gamma-gamma) logging generally confirmed that the samples were of high quality. In addition, as the project progressed and more experience with in-situ ground freezing and sampling was gained, the technique was refined. As a result, the unit costs of ground freezing and sampling (in terms of total volume) decreased significantly. Thus, by following the techniques developed as part of the CANLEX project, high quality undisturbed samples of sandy soil can be obtained from a discrete target zone in a cost effective manner. (Wride et al. 1998).

Based on a limited number of thawing tests conducted on undisturbed samples of sand obtained by in-situ ground freezing, the thawing methodology which appears to result in the least amount of disturbance involves thawing specimens unidirectionally under 90% of the in-situ effective stress and pore water pressure conditions. Complete thawing in this manner results in preservation of the in-situ void ration, structure, stress history and degree of saturation that existed prior to in-situ ground freezing.

Ground freezing to obtain samples of sandy soils is generally quite expensive (typically CDN$40,000 to $50,000 per site.- For low risk projects this expenditure is generally not cost effective and design is generally based on less expensive semi-empirical techniques using in-situ test results. However, for high risk projects the cost of ground freezing, sampling, and testing maybe cost effective when the application of traditional in-situ testing based approaches result in conservative, costly remediation.

188

A recent example to illustrate this was the Duncan Dam project (Little et al, 1994). B.C. Hydro carried out an evaluation of the existing Duncan Dam in B.C., Canada. Results of the analyses using traditional in-situ testing based techniques suggested remediation works with a total cost of about CDN$25 million. A more detailed study was performed that included ground freezing, sampling and careful laboratory testing. The results of this more detailed study suggested only minor remediation at a cost savings of about CDN$24 million.

For moderate risk projects it maybe possible to improve the evaluation of liquefaction potential by performing laboratory tests on representativereconstituted samples. However, results from the CANLEX Project suggest that the use of reconstituted samples should be limited to relatively clean, uncemented, normally consolidated sands (fines content less than 5%) with an age of less than around 100 years. Further research is required to clarify the importance of fabric and the most suitable mode of deposition for reconstitutedsamples as a function of geologic depositional history and grain characteristics.

The CANLEX Project has also highlighted the extreme variability of most sand deposits. This variability requires performing a sufficient number of laboratory tests to quantify the undrained response over the full range of in-situ state (void ratio and stress level). Further research is required to identify what is the representative average response for a given deposit.

12 ACKNOWLEDGMENTS

This work was partly supported by CANLEX (Canadian Liquefaction Experiment), a project funded through a Collaborative Research and Development Grant from the Natural Science and Engineering Research Council of Canada (NSERC), Syncrude Canada Ltd., Suncor Inc., Highland Valley Copper, B.C. Hydro, Hydro Quebec and Kennett Corporation. The collaboration also includes the engineering consulting companies: EBA EngineeringConsultants Ltd., Klohn-Crippen Consultants Ltd., AGRA Earth and Environmental Ltd., Golder Associates Ltd., and Thurber Engineering Ltd., as well as faculty, staff and students from the Universities of Alberta, British Columbia, Laval and Carleton.

13 REFERENCES

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Broms, B.B., 1980. Soil Sampling in Europe: State-of-the-Art. Journal of Geotechnical Engineering Division, ASCE GTl, Vol. 106, Paper 15149, pp. 1108-1136.

Colbeck, S.C., 1981, Introduction to the Basic Thermodynmaics of Cold Capillary Systems,U.S. Army CRREL Special Report 81-6, Hanover New Hampshire, USA, 9 p.

Davila, R.S., Sego, D.C. and Robertson, P.K., 1992. Undisturbed sampling of sandy soil by freezing, Canadian Geotechnical Conference Proceedings, Toronto, pp. 13A-1 to 13A-10.

Hashemi, H.T. and Sliepcevich, C.M., 1973, Effect of seepage stream on artificial soil freezing, Proceedings, Ground Freezing Conference, Developments in Geotechnical Engineering, V28, 189-201.

Hatanaka, M., Sugimoto, M., and Yoshio, S., 1985. Liquefaction resistance of two alluvial volcanic soils sampled by in-situ freezing. Soils and Foundations, Vol., 25, No.3, pp. 49-63.

Hatanaka, M., Uchida, A., Oh-Oka, H., 1995. Correlation between the Liquefaction Strengths of Saturated Sands Obtained by In- situ Freezing Method and Rotary-Type Triple Tube Method, Soils and Foundations, Vol. 35, No.2, pp.67-75.

Hight, D. W., 1993. A review of sampling effects in clays and sands. Offshore Site Investigations and Foundation Behavior, Vol. 28, pp. 115-146.

Hight, D.W. and Georgiannou, V.N., 1995. Effects of Sampling on the Undrained behaviour of clayey sands. Geotechnique, Vol. 45, No. 2, pp. 237-247.

Hofmann, B.A., 1997. In-situ Ground Freezing to Obtain Undisturbed Samples of Loose Sand for Liquefaction Assessment. Ph.D. University of Alberta, Edmonton, Alberta, 485 p.

Hofmann, B.A., Sego, D.C., Robertson, P.K. and Fourie, A.B., 1996. Thawing Protocol of undisturbed samples of loose sand, obtained by Insitu Ground Freezing for laboratory triaxial testing. Canadian Geotechnical Conference, St. John's, Newfoundland, September 23-25, 1996, Vol. 1, p. 571-580.

Hofmann, B.A., Sego, D.C. and Robertson, P.K.

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1998a, Feasibility of In-Situ Ground Freezing to Obtain Undisturbed Samples of Loose Sand ASCE, JGGE (submitted), 34 pp.

Hofmann, B.A., Sego, D.C., and Robertson, P.K., 1998b. In-Situ Ground Freezing and Undisturbed Sampling of Sand Carried out for the CANLEX Project. ASCE, JGGE (submitted), 35 pp.

Hofmann, B.A., Sego, D.C., and Robertson, P.K., 1998c. Thawing Protocol for Undisturbed Samples of Loose Sand Obtained by In-Situ Ground Freezing. (In Press).

Konrad, J.-M. and Morgenstern, N.R., 1980, A Mechanistic Theory of Ice Lens Formation in Fine Grained Soils, Canadian Geotechnical Journal, V 17, 473-486. Plewes, H.D. 1993. Conventional sampling summary report, CANLEX Technical Report, Phase I Activity 4A Klohn-Crippen Consultants Ltd.

Konrad, J-M. 1996. Large diameter sampling of sands. , CANLEX Technical Report, Phase IV Activity 4C, Université Laval.

Konrad, J-M., Gilbert, F., Pouliot, N. and Saint- Laurent, S. 1995a, Large diameter sampling of sands. , CANLEX Technical Report, Phase II Activity 4C, Université Laval

Konrad, J-M., Pouliot, N. And Hofmann, B.A.. 1995b, Evaluation of the performance of Laval's Large diameter sampler in loose tio medium dense sands. 48 * Canadian Geotechnical Conference Proceedings, Vancouver, September, 1995,

Konrad. J.-M and St-Laurent, S., 1995, ControlledFreezing and Thawing as a way to Test Intact Sand: A Laboratory Investigation., 48'^Canadian Geotechnical Conference Proceedings, Vancouver, September, 1995, pp.213-222.

Little, T.E. Imrie, A.S. and Psutka, J.F. 1994. Geologic and seimic seetting pertient to dam safety review of Duncan Dam, Canadian Geotechnical Journal, 31 (6)919-926

Monahan, P.A, Luternauer, J.L. and Barrie, J.V. 1995. The geology of the CANLEX Phase II sites in Delta and Richmond , British Columbia, Proceedings of the 48 Canadian Geotechnical Conference, Vancouver, BC, 59-68

Plewes, H.D. 1993. Conventional samplingsummary report, CANLEX Technical Report, Phase I Activity 4A Klohn-CrippenConsultants Ltd.

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Sasitharan, S., Robertson, P.K. and Sego, D.C., 1994. Sample Disturbance from Shear Wave Velocity Measurements. Canadian Geotechnical Journal, 31: 119-124.

Seed, H.B., Singh, M., Chan, C.K., and Vilela, T. F., 1982. Considerations in Undisturbed Sampling of Sands. Journal of Geotechnical Engineering Division, ASCE GT2 Vol. 108, pp. 265-283.

Sego, D.C., Robertson, P.K. Sasitharan, S. Kilpatrick, B.L. and Pillai, V.S., 1994. Ground freezing and sampling of foundation soils at Duncan Dam. Canadian Geotechnical Journal,3 1(6):939-950.

Singh, S., Seed, H.B. and Chan, C.K., 1982, Undisturbed Sampling of Saturated Sands by Freezing. Journal of Geotechnical Engineering Division, ASCE GT2 Vol. 108, pp. 247-263.

Sladen, J.A., D’Hollander, R.D., and Krahn, J., 1985. The Liquefaction of Sands, a Collapse Surface Approach. Canadian Geotechnical Journal, Vol.22, No.4, pp.564-578.

Tokimatsu, K. and Hosaka, Y., 1986. Effects of Sample Disturbance on Dynamic Properties of Sand. Soils and Foundations, Vol. 26, No.l, pp. 53-64.

Wride, C.E. and Robertson, P.K., 1997. CANLEX Technical Publication: Introductory DataReview Report. University of Alberta, 90 pp.

Wride (Fear) C.E., Hofmann, B.A., Sego, D.C., Plewes, H.D., Konrad, J-M., Biggar, K.W., Robertson, P.K., and Monahan, P.A. 1998. Ground sampling at the Canlex test sites. Canadian Geotechnical Journal (submitted for review).

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Yoshimi, Y., Hatanaka, M., and Oh-Oka, H., 1977.A Simple Method of Undisturbed Sand Sampling by Freezing. Proceedings of Specialty Session 2 on Soil Sampling. 9 - International Conference on Soil Mechanics and Foundation Engineering, pp. 23-28.

Yoshimi, Y., Hatanak, M., and Oh-Oka, H., 1978. Undisturbed Sampling of Saturated Sands by Freezing. Soils and Foundations, Vol.18, pp. 59-73.

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5 Methods of characterizing liquefaction potential

Physics and Mechanics of Soii Liquefaction, Lade & Yamamuro (eds) © 1999 Baikema, Rotterdam, ISBN 90 5809 038 8

The critical state line and its application to soil liquefaction

K.BeenColder Associates Limited, Nottingham, UK

ABSTRACT: This paper reviews some o f the discussion regarding the critical or steady state line and its application in hquefaction evaluation. In particular, the approach has been criticised on the basis that a unique critical state line does not exist for sands. Once a distinction is made between transient or quasi-steady states and ultimate steady states, and appropriate consideration is given to test conditions and shear band formation, it appears that a unique critical state line can be defined for a sand. The critical state line can be used in hquefaction evaluation as a reference state, both for insitu test interpretation and constitutive modelling to determine the undrained shear strength. The undrained strength at the critical state is not necessarily the appropriate undrained shear strength.

1. INTRODUCTION

The steady state o f sand is defined by Poulos (1981) as ""The steady state o f deformation for any mass of particles is that state in which the mass is continuously deforming at constant volume, constant normal effective stress, constant shear stress and constant velocity''. The critical state is more simply defined by Roscoe et al. (1958) as the state at which a soil ""continues to deform at constant stress and constant void ratio". These ideas o f an ultimate state which sands will reach after large deformations associated with hquefaction, lead logically to a very simple approach to hquefaction evaluation. This so called steady state approach conceptually consists o f the foUov^dng steps (Figure 1):

1 . determine the critical or steady state line o f the material

2 . determine the insitu density and stress level in the sand, i.e. its state

3. by assuming undrained (constant volume) behaviour during hquefaction, the ultimate steady state o f the insitu material can be determined

4. compare the steady state shear stress with the applied field stresses to determine a factor o f safety.

The procedure is described in detail by Poulos et al. (1985) but in reahty is more complex because of differences between insitu soils, undisturbed samples

and reconstituted samples. The steady state line is determined in the laboratory fi-om reconstituted samples, and it has been shown in several studies that fines content has a significant impact on the steady state line. The steady state hquefaction evaluation procedure therefore requires testing o f ‘"undisturbed” samples to determine their steady states and a procedure to determine the steady state for insitu material fi-om the tests on reconstituted and undisturbed samples.

Recognising that undisturbed sampling o f loose sands was close to impossible and very expensive, insitu tests such as the CPT have been extensively studied to determine the insitu state o f sands. Been et al. (1986, 1987a) developed an interpretation approach based on determining the state parameter (Been & Jefferies, 1985) directly fi-om the CPT. The state parameter \|/ is simply a measure o f the state o f a sand in terms o f the difference between the void ratio o f the sand and the void ratio at the critical state (Figure 1). If the interpretation method were accepted as completely accurate, this approach would eliminate many o f the objections to the steady state hquefaction evaluation procedure, in particular those associated with samphng error, the impact o f fines content and variabihty o f natural soils compared to reconstituted laboratory samples. However, there are uncertainties in the CPT interpretation which have

195

Effective stress: kPa

Figure 1: Simplified liquefaction evaluation procedure

been extensively aired in the literature (Sladen, 1989, 1990; Been et al., 1989; Konrad, 1997).

The steady state hquefaction procedure identified above does not consider the triggering mechanism. The material behaviour o f consequence is the undrained shear strength afi;er hquefaction. In describing the approach Poulos et al. (1985) advocate using the steady state strength and support then- methodology with extensive analyses o f the San Fernando Dam (Castro et al., 1992). Seed (1987) raised the question o f whether the steady state strength based on the pre-earthquake void ratio was appropriate as the post-hquefaction residual strength, based on residual strengths back-analysed from case histories. "rhis question o f the undrained shearstrength o f hquefied sands has probably been the most discussed topic in geotechnical journals in the last 1 0 years, including the earher international workshop sponsored by the National Science Foundation titled “Shear Strength o f Liquefied Soil”.

In this paper some o f the aspects o f soil behaviour that have caused much o f the above discussion are considered. Recognising the similarity o f the critical and steady state definitions at the beginning o f this paper, the “critical” rather than “steady” terminology is used for the critical state line because o f the link to the broader framework o f so called “critical state soil mechanics”, which provides additional insight through constitutive models and behaviour o f other soil types, although “steady state” is the more common terminology in hquefaction evaluation and is sometimes used in this context as well.

2. UNIQUENESS OF CRITICAL STATE LINE

We can assume for this paper that the steady state and critical state are the same thing (following Been

et al., 1991), an ultimate state at which shearing takes place without volume changes or stress level changes. This definition does not include the so called pseudo- or quasi-steady states obseived in many tests (Alarcon et al., 1988; Zhang & Garga, 1997) as these are not ultimate states. They are transient states o f zero volume and stress level changes, which may nevertheless be important in terms o f selecting a minimum undrained shear strength for design after hquefaction.

The definitions o f critical and steady state, and apphcation o f the concepts to hquefaction evaluation, clearly require that the critical state line is unique and independent o f test conditions or stress path followed to reach the critical state. Published studies on the existence and uniqueness o f the critical state line include a range o f conclusions from:- there is a unique critical state hue, but care is

needed in testing techniques and interpretation to estabhsh the location o f the critical state line (Poulos et al., 1988; Been et al., 1991; Ishihara, 1993)

- there is a band o f states between a UF and LF line (Komad, 1993) that represent steady state conditions, depending on the initial density and stress level

- there is an S-line, from drained tests, and an F- Line from undrained tests, that differ as a result of the collapse potential o f the soil (Alarcon et al, 1988)

- extension and compression tests wih result in very different stress paths and steady states (Vaid et a l, 1990; Negussey & Islam, 1994; Vaid & Thomas, 1995)

- silty sands exhibit “reverse” soil behaviour and nonunique steady states are found from tests performed from different isotropic compression lines (Yamamuro & Lade, 1998)

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Figure 2: Critical state lines for Toyoura and Erksak Sands on a) semi-log and b) arithmetic scales (after Verdugo, 1992)

Figure 2 shows examples o f apparently unique critical state lines for Erksak and Toyoura sands (Verdugo,1992), tested under a variety o f conditions. In contrast Konrad (1993) shows a band o f steady states on Figure 3 and indicates that his data imply nonuniqueness o f the critical state line. However, Konrad’s ideas have grown from an initial attempt (Konrad, 1990a, b) to determine the minimum undrained shear strength o f the sand rather than the ultimate, critical state. Examination o f his more recent work indicates that the accepted critical state line is in fact identical to his UF line which is used as a reference condition for CPT interpretation (Konrad, 1997). Clarity in terminology and interpretation is needed. The state at wliich the minimum undrained strength in a triaxial test on a sand occurs is not always the critical or steady state. It is frequently the so-called phase transformation point (Ishihara et al., 1975) or the quasi-steady state which represents the minimum undrained shear strength. It is quite clear that these states, and the minimum or maximum undrained shear strength o f a sand, will depend very much on the initial state o f the sand and the loading conditions (direction relative to fabric, extension or

Figure 3: Range of critical states between UF and LF h for Hostun RF sand (after Konrad, 1993)

compression, drainage conditions, etc.) as pointed out by Vaid et al. (1990). This erroneous linking o f transient conditions o f “steady” shearing, during which shearing temporarily takes place under conditions o f constant effective stress and void ratio, with the critical state line has caused much confusion and difficulty with acceptance o f critical state concepts into hquefaction evaluation procedures.

Casagrande (1975) and Alarcon et al. (1988) identified separately “S” and ‘T ” hnes based Castro’s (1969) data, where the F line represents the ultimate state from consolidated undrained tests and the S line was determined from ultimate conditions in drained triaxial tests. The imphcation is again that the critical state line is not unique, in that different tests result in different ultimate states. This is incorrect and is an artefact o f test procedures and interpretation. The main reason the data are misinterpreted in this way is that drained and undrained triaxial tests on dense sands seldom reach the critical state. We can demonstrate that drained tests on samples tend to the critical state (determined from undrained tests) by plotting the rate o f volume change (or dilatancy) against distance the sample state is from critical state at any time during a test (usually at peak stress conditions and before locahsation effects occur in the sample.) Figure 4 shows a set o f such data for 29 sands (Been et al. 1992); the dilatancy data are from conventional drained triaxial tests, while the x-axis is the difference between the void ratio o f the sample and the critical state line at the same stress level. It is clear from these data on Figure 4 that the rate o f volume change is proportional to distance from the critical state line. Similar methods were used by Parry (1958) to support the existence o f a critical

197

Figure 4: Peak dilatancy rate from drained tiiaxial tests plotted against distance from critical state line determined from undrained tests on loose samples.

state line for London and Weald clays. If the critical state from drained tests were different from that determined from undrained tests, a mean line through the data on Figure 4 should not pass through the origin.

It is less easy to demonstrate that compression and extension tests on sands tend to the same unique critical state. The data on Figure 2 indicate that this is the case but both referenced pubhcations stress that care is needed to use only test results where there is httle doubt that the critical state has been reached in extension. In contrast, Vaid & Thomas (1995) show data. Figure 5, in which large differences in extension and compression behaviour o f identical sand samples occur. This strongly anisotropic behaviour o f sands is not surprising, given the large body o f evidence related to the anisotropic strength and behaviour o f clays. However, Vaid et al. (1990) use “steady state” and ‘ hase transformation” as the same thing and conclude that “¿7/ a given void ratio Cc, PT or SS strength was smaller in extension than in compression, the difference increasing as the sand became looser"" It is readhy apparent from then- tests, in particular extension tests, that the samples pass through the phase transformation state and are still dilating at the end o f the tests. It is not clear what the true, ultimate, steady state o f these samples might be. Vaid et al. do not distinguish phase transformation from steady state because they coincide in q-p' space, however, they are not coincident in e-p' space except when there is no phase transformation. They are perfectly correct in their observations that samples which are dilatant (reducing pore pressures) in compression are contractive (increasing pore pressures) in extension at

( a 'a + a',)!2. kPa

Figure 5: Difference between extension andcompression behaviour o f sands (after Kuerbis & Vaid, 1989)

strains o f up to about 5%, but it would be a mistake to use stress-strain behaviour early in the test when loading direction relative to sand fabric is a major factor as indicative o f ultimate conditions.

Silty sands have been reported by Yamamuro & Lade (1997) to show “reverse” behaviour, the term they adopted to describe the fact that when samples are prepared at the same initial conditions the samples consohdated to the higher confining stresses show greater resistance to hquefaction. Yamamuro & Lade (1998) in a more recent paper present further evidence o f reverse behaviour and nonuniqueness o f the steady state obtained from undrained tests on Nevada sand with 6 % fines. It is important within the framework o f this paper to note that Yamamuro & Lade use the initial void ratio after preparation (and before consoUdation) in presenting their data, and that the sands used were silty. The explanation given for reverse behaviour is related to the distribution o f silt grains between sand grains, which

198

results in a very high compressibihty and low confining stresses. In the context o f a critical state fi'amework, this means that at low stresses the isotropic compression curve is steeper than the critical state line and therefore the state parameter \\f (Been & Jefferies, 1985) decreases as confining stress increases, and therefore stabihty against hquefaction is increased. Viewed within this critical state fi'amework the behaviour is not ‘Reversed”, but nevertheless highlights an important aspect o f the behaviour o f silty sands.

Figure 6 a is taken directly from Yamamuro & Lade (1998), their Figure 9, to illustrate the evidence for non-uniqueness o f steady state lines. The steady state points are re-plotted in Figure 6 b on the same scale as Figure 2 with the critical state lines from Figure 2. It is apparent that ‘ uniqueness” may be interpreted differently by different researchers and will depend on the confidence people place in their laboratory data as well as the apphcation in which they are interested.

3. SHAPE OF THE CRITICAL STATE LINE

As noted above, confidence in laboratory measurement and data defining the critical state line will differ between different researchers. Attention has been focussed on the shape o f the critical state line in e-log p' space at both high (Konrad 1998; Been et al., 1991; Verdugo, 1992) and low stresses (Ishihara, 1993), and alternative representations on e - log (pVpa)“ with a ^ l space (K. M. Lee, personal comm). Curvature or shape o f the critical state line is not an issue o f great importance. There is no intrinsic reason why the critical state line should be linear in e-log p'space; it is simply a matter of mathematical convenience that it is usually assumed to take a semi-log form.

At high stresses, the shape o f the critical state line is important in addressing interpretation o f the CPT in which very high stresses are induced insitu. There has been discussion on whether curvature o f the critical state line at stresses in the order o f a few MPa is due to crushing o f the grains or whether it is simply an artefact o f the semi-log plot. Verdugo (1992) illustrates how an apparent change in gradient o f the critical state line vanishes when the data are plotted on arithmetic rather than semi-log axes (Fig 2b.) Extensive testing o f carbonate and other crushable sands has been carried out (eg. Hyodo et al. 1998) with the general conclusion that the concept o f a critical state line remains vahd, but the gradient o f the

0.01 100 10,000 0.1 10 1,000

Effective Confining Pressure (kP a)

Figure 6 : Data on nonunique critical state line, a) as plotted by Yamamuro & Lade (1998), and b) plotted on similar scale to Figure 2 with Erksak and Toyoura critical state lines.

line may be steeper and the curvature greater than for typical clean shica sands used for research purposes.

At low stresses, the location o f the critical state line is important because it may define the undrained shear strength o f very loose sands after hquefaction. In fact, zero stresses are frequently reported for hquefaction tests on loose sands (eg. Ishihara, 1993; Yamamuro & Lade, 1998), leading to definition by Ishihara o f an upper limit o f void ratio for sands and an emphasis on testing at low stresses. The author’s own experience is that measurement o f very low effective stresses is rather inaccurate, as the effective stress is obtained by the difference between two large pressures (the total pressure and the pore water pressure.) The problem is further exacerbated by plotting stress on a log scale and the fact that the critical state line at low stresses corresponds to high void ratios which are also very difficult to measure accurately (Sladen & Handford, 1987). While careful

199

Figure 7: Effect o f sample size on stress-strain behaviour (after Jefferies et al. 1990)

techniques are required to make measurements at low stresses, there is nothing otherwise exceptional about the behaviour o f sands at low stresses.

appears that the ultimate critical state stresses o f all samples may be the same. The volumetric strains at the end o f each o f the tests is also dependent on sample size; less volumetric strain occurs in the larger samples. Jefferies et al (1990) attribute the observed behaviour to bifurcation or shear band zonation and undertake a simple theoretical analysis to support this mechanism. Essentially, the behaviour observed is consistent with the attainment o f a critical state in a locahsed shear band (as occurs in the tests) and some elastic unloading o f the remainder o f the samples. Noting that field failures occur at a scale several orders o f magnitude greater than even the largest laboratory tests, shear band locahsation is clearly an important issue for liquefaction evaluation.

A detailed study o f evolution o f void ratio within shear bands in triaxial tests has been reported by Desrues et al. (1996). They showed the development o f locahsation at strains o f about 7 to 16%, depending on the density and height to diameter ratio o f the sample. Aspect ratio o f the samples also had a major effect on the observed patterns o f locahsation. Figure 8 reproduces their Figure 19, showing void ratio evolution o f the samples as a fimction o f strain. Looking at global void ratio, based on conventional measurements made during triaxial tests, the samples approach a range o f ultimate steady void ratios o f0.76 to 0.86. In contrast, when local void ratio within the shear bands is considered, ah samples tend to the same critical state void ratio o f 0.86.While there are many studies o f shear strain locahsation in sands, Figure 8 is interesting because it raises the question o f whether many o f the problems and differences o f opinion on the critical state hne

4. SHEAR B A N D LOCALISATION A N D SCALE EFFECTS

To date laboratory measurements o f the critical state hne and hquefaction behaviour have largely ignored tw o important factors; the effect o f scale (or sample size in the laboratory) and locahsation o f shear strains in triaxial tests.

Jefferies et al (1990) report drained triaxial test data on 4 different sized samples, with ah other factors unchanged. Sample sizes ranged from 35mm diameter x 70mm high to 300mm diameter by 675mm high. Figure 7 reproduces the test results. The most obvious effect o f sample size is on the post-peak stress-strain behaviour and dilatancy. Larger samples show a much more brittle response in that the stress drops more quickly after peak conditions, although it

Figure 8: Evolution o f global and local void ratio during triaxial tests (after Desrues et al. 1996)

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and its uniqueness are related to shear localisation. In particular, necking is a form o f strain localisation commonly observed in triaxial extension tests at 5 to 10% strain and may account in large measure for differences between the apparent end points o f extension and compression tests on similar samples discussed earher (Figure 5).

Locahsation and scale are related. Shear band thickness appears to be related to the grain size, with the range o f shear band thickness given as 10 to 30 times the mean grain size (R oscoe, 1970; Vardoulakis & Graf, 1985; Desrues et al, 1996). A given shear band thickness o f 3mm in which shear strains are concentrated will have a different impact on the behaviour o f a 100mm laboratory sample compared to a 10m high earth structure. This apphes not only to displacements, but also to pore pressure distribution. A thin shear band in a large sand mass may rapidly take up sufficient water to dissipate the negative (dilatant) pore pressures without significantly affecting pore pressures in the sand mass.

5. APPLICABILITY OF CRITICAL STATE LINE TO FIELD BEH AVIO UR

In development o f the critical void ratio concept (Casagrande, 1975) and the steady state hquefaction procedure (Poulos et al, 1985), there is a clear expectation that the shear strength at the critical void ratio or steady state measured in the laboratory is directly apphcable to the field. Hard evidence to justify this expectation is lacking, and the expectation has been questioned. For example, Lmdenberg & Koning (1981) state in relation to the critical void ratio that “../Y turned out to be unsuitable as a basis for criteria relating to flow slide sensitivity.^" Seed (1987) talks about rearrangement o f the soil into looser and denser zones during hquefaction, also suggesting a simple critical void ratio concept is not apphcable. Vaid & Thomas (1995) draw attention to the dangers o f assuming that a steady state line derived from compression tests on loosely compacted soils is apphcable to field behaviour, while Vaid et al. (1990) advocate laboratory tests that match both the field fabric and void ratio. Shear strain locahsation and scale effects discussed above impact how the concepts can be apphed in the field. Natural variabihty o f materials insitu, i.e. the fact that void ratio and fines content o f a natural sand deposit may vary significantly over quite short distances, also

raises questions regarding the apphcabihty o f sinqyle critical state concepts to field situations.

Two case histories have been widely discussed in the hterature, where the I beheve the question o f apphcabihty o f the critical state line is key to the discussion. The first is the Lower San Fernando Dam (eg. Seed et a l, 1988; Castro et a l , 1992; Marcuson et a l, 1990) and the second is the Nerlerk Berm (eg. Sladen et a l, 1985a, 1987; Been et al, 1987b; Rogers et a l, 1990; Lade, 1993). What is interesting about many o f these papers is that where the back analyses do match the expected critical or steady state shear strength, the authors frequently focus on the measurement o f the insitu void ratio as the key problem Discussion then focuses on corrections to sampled void ratios to obtain field void ratios (Castro et al., 1992), on interpretation o f the CPT (Sladen, 1989b), uniqueness o f the critical state line (Komad, 1991), or on hypothetical coUapse mechanisms (Sladen et a l , 1985b) to explain the failures.

A s discussed above, there appears to be sufficient evidence that a unique critical state or steady state line can be measured for any one sand, at least within the practical limits o f engineering interest and laboratory measurement o f void ratio (a void ratio range o f about ±0.02 or 5% relative density). A s detailed by Been & Jefferies (1985) this critical or steady state line can be used as a reference condition for sand behaviour, with the state o f a sand characterised by distance from this reference condition. Several alternative forms o f state parameter have been suggested (Been & Jefferies, 1986; Hird & Hassona, 1986; Konrad, 1988; Verdugo & Ishihara, 1991).

The key question is whether state, or position relative to the critical state line, is a useful indicator o f hquefaction potential. Assuming that sand which is dilative in triaxial conq>ression tests (i.e. a sand which hes below the critical state line) wiU not be susceptible to large strains on hquefaction is too simple a concept. It is necessary to consider variabihty insitu, the fabric o f the sand relative to loading, the flih stress strain response o f the sand and strain locahsation. This dictates an approach to hquefaction along the lines of:- select one or more representative samples o f the

sand (in terms o f grain size distribution)- determine the critical state line the sand(s)- determine appropriate parameters and/or

constitutive behaviour o f the sands- carry out insitu tests (e.g. CPT) to determine insitu

state and variabihty

201

- select a characteristic state based on the insitu tests- design structure based on insitu state, constitutive

behaviour o f sand at that state and imposed loading conditions

Within this context the interpretation o f the CPT or other insitu tests is very important, because the range o f variation o f sand insitu is continuous and because the critical state line can vary significantly with relatively modest changes in fines content or grain size distribution. Measurement or interpretation o f insitu void ratio (e.g. from the CPT, gamma logs or tube samples) is not recommended because sand behaviour within the same deposit is not directly related to void ratio. A shghtly silty sand at the same void ratio as a clean sand will not have the same behaviour. The CPT has the advantage that it measures a mechanical response o f the sand, which can be related to the state relative to the critical state line. A shghtly silty sand and a clean sand that have similar CPT resistance will not be at the same void ratio, but they do have a similar mechanical response to stress change. Liquefaction is also a response to stress changes which can be related to state (eg. Jefferies, 1993, 1998). It is therefore rational to relate hquefaction to insitu tests through state and a critical state framework. The variation o f this relationship will be much less than one based on density or void ratio alone.

The approach described above may at fiist appear difficult, but as with all engineering problems an empirical rule o f thumb frequently emerges. The author’s experience from practice is that a sand needs to be denser than the critical state line by a void ratio of at least 0.08 (i.e. a state parameter \|/ < -0.08) to ensure satisfactory engineering performance. Recognising that sands insitu are variable, this characteristic value o f state must be “exceeded” in about 90% o f CPT profiles. Apphcations with high loads or low tolerance to displacements may require higher specifications.

6 . CONCLUSIONS

Uniqueness o f the critical state fine has been much discussed within the context o f liquefaction evaluation and the undrained strength o f sand. The arguments have been reviewed in this paper and an attempt made to explain the differences in interpretation. Care is needed with terminology, accuracy o f test data and, most importantly, distinction between quasi- or pseudo-steady states

and the true steady state. Shear strain locahsation is also considered. Within practical limits, the critical state line is unique for any sand. However, the stress-strain behaviour between the initial conditions and the ultimate steady state is highly dependent on a large number o f factors, including initial fabric, void ratio, stress level, load path, strain rate, etc. The quasi-steady state, phase transformation and minimum undrained shear strength are examples o f such ‘J)ehaviours”.

Some workers have placed emphasis on the shape o f the critical state line, in particular whether it is linear in e-log p space and the curvature at low or high stresses. While the shape is important in the context o f certain problems, such as undrained strength at low stresses and penetration resistance, there is no intrinsic reason to assume any particular shape is more appropriate than another.

Apphcation o f the critical state line to hquefaction behaviour should not be in the direct form of the steady state hquefaction evaluation procedure. The critical state hne does, however, provide a usefiil reference condition for quantification o f state. A complete engineering approach also requires a method to characterise the insitu state o f a sand, and a methodology that considers hquefaction in the context o f an appropriate constitutive model.

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Comments on the determination of the undrained steady state strength

of sandy soils

G. CastroGEI Consultants Incorporated, Winchester, Mass., USA

ABSTRACT: Seismically induced failures of earth structures generally involve relatively loose sandy soils. The failures can be divided into: (a) those caused by a loss of stability and (b) those in which limited, but large, deformations accumulate during the earthquake to constitute cause of "failure" for structures or lifelines. In both cases, the key soil parameter is the soil shear strength at large strains. The value of this strength determines whether instability could be triggered by the earthquake, and if instability is not possible, it determines the amount o f soil displacement that will be accumulated. The strength that governs the two types o f seismically induced failures discussed above is the undrained steady state strength (refen'ed to as S^J. The laboratory test methods that are appropriate for determining steady state strength depend on the type of soil. The most important test characteristic is the ability to apply sufficiently large strains while maintaining specimen uniformity. The determination of in situ values o f must consider the heterogeneity of natural soil deposits and the changes invoid ratio than even the most careful sampling procedure will cause in "undisturbed" soil samples. Empirical information based on field index tests (blowcounts, cone) is useful as a first approximation. However, in some cases these index tests do not properly represent field conditions.

1 INTRODUCTION

Seismically induced failures o f earth structures generally involve relatively loose sandy soils. The failures can be divided into: a) those caused by a loss of stability and b) those in which limited but sufficiently large deformations accumulate during the earthquake to constitute cause of "failure" for structures or lifelines. In Case a) the deformations are very large and occur mostly following the earthquake. In Case (b) the earth structure has not actually failed in the sense o f a loss o f stability, and the deformations occur mostly during the earthquake.

A typical case o f a loss o f stability is the slide of the Lower San Fernando Dam caused by the 1971 San Fernando earthquake. Cross sections of the dam prior to and after the slide are shown in Figure 1. Detailed descriptions o f the slide are presented in Seed et al. (1975) and Castro et al. (1989). The slide was caused by the loss in strength o f the soil in the lower part of the hydraulic fill shell which is shown darkened in Figure 1. This zone o f the hydraulic fill consists of silty sands and sandy silts with standard penetration test (SPT) blowcounts mostly in the range of 15 to 20 blows/foot and cone tip resistance typically in the range o f 50 to 100 tsf.

A review o f the stability of the dam prior to the earthquake indicates that the shear stresses within the failure zone in the hydraulic fill average about 900 psf Computations of the dynamics o f the movement of the center o f gravity o f the sliding mass indicated that the average shear resistance in the same zone during the slide was about 500 psf (Davis et al. 1988). The peak seismic shear stresses in the same zone were estimated by Seed et al. (1975) to be about 2000 to 3000 p sf Based on this information, one can infer that the stress strain behavior of the soil in the lower part of the hydraulic fill was as shown in Figure 2 and that it represents undrained behavior. Thus, even though the dam was stable since its construction in 1915 until the 1971 earthquake, there was a potential for instability because the undrained strength available at large strains was lower than the statically applied shear stresses. However, actual instability occurred only when a) an earthquake occurred causing rapid enough loading so that the soil behaved undrained, and b) the earthquake was large enough to overcome the peak strength and to strain the soil sufficiently so that the mobilized shear resistance became lower than the statically applied shear stresses. At that point the slide movements were driven by the static and not the seismic shear stresses.

205

1100 Zz01

1160buiu.

1100 zz01

Note that during the slide the available strength in the hydraulic fill o f about 500 psf was a small fraction of the drained strength o f about 3500 psf, i.e. the soil was strongly contractive and large pore pressures were present in the soil.

A typical case o f large deformations without a loss of stability is the lateral spreading that occurred at a site adjacent to Heber Road in the Imperial Valley in Southern California during an earthquake in 1979 (Bennett et al. 1981). A cross section along the area of movements is shown in Figure 3. The movements are believed to have occurred mostly along a zone of loose silty sands at a depth o f about 10 to 12 feet. The standard penetration resistance was only about one blow/foot, and the cone tip resistance was about 1 0

ts f Because o f the flatness o f the terrain, the static shear stresses in this zone

San Fernando D am .

BORINGS 5 & 6 BORINGS

13 Sc 14

206

are very low, about 40 psf. The earthquake shear stresses at this level had peak values of about 450 psf, based on a peak ground surface acceleration recorded at a nearby site o f 0.8 g (Castro 1987). Based on the observed lateral movements and a Newmark type of analysis, it was estimated that the shear resistance of the soil during the movement was about 100 psf. A possible mechanism for the movements is illustrated by the stress strain behavior o f the soil along the failure zone shown in Figure 4. The soil mass is inherently stable, both prior to and during the earthquake; however, the high seismic stresses caused a successive accumulation of strains, initiated each time the sum of static plus seismic shear stresses exceeded the available resistance. Note also that the available strength of about 1 0 0 psf was much smaller than the drained strength o f about 500 psf, indicating that again the soil was strongly contractive. Thus large pore pressures were present in the soil during the movements, which is consistent with the observation of sand boils in the area.

Poulos (1971) defined the steady state strength as "the state in which the soil mass is continuously deforming at constant volume, constant normal effective stress, constant shear stress, and constant velocity." Even though in the two cases of seismically induced failures discussed above, the velocity of deformation was not constant, the effect o f rate deformation on the value o f undrained steady state strength has been shown to be negligible (Castro et al. 1982). Thus the strength that governs the two types of seismically induced failures discussed above is the undrained steady state strength (referred to as 8 ,3). Laboratory determinations of 8^3 indicate that 8^,3 is only a function of void ratio for a given soil and also that it is a sensitive function of void ratio. For sandy soils, changes in values of 8^,3 by a factor of 1 0 correspond to changes in void ratio, typically of 0.08 to 0.15.

3 LABORATORY DETERMINATION OF 8 TEADY 8 TATE 8 TRENGTH

2 8 TEADY 8 TATE 8 TRENGTH

In the two cases discussed above, the key soil parameter is the soil shear strength at large strains. The value of this strength determines whether instability could be triggered by the earthquake, and if instability is not possible, it determines the amount o f soil displacement that will be accumulated. In both cases the soil behavior can be assumed to have been undrained given the relatively short duration of the movements and the relatively low permeability of the soil. In both cases the undrained strength at large strains is a small fraction o f the drained strength; however, the available strength is not zero.

Laboratory test methods used to determine steady state strength in the laboratory are shown in Table 1. The most widely used method for sands is the triaxial compression test, generally undrained (Castro 1969). Results obtained by four laboratories on a sand from the Lower 8 an Fernando Dam are shown in Figures 5 and 6 . The results obtained by the four laboratories are generally in good agreement. The correlation between void ratio and 8^3 in Figure 5 is independent of stress path and method o f loading. Results as shown in Figures 5 and 6 require the preparation of uniform specimens and the use o f methods to prevent the development of nonuniformities during shear, i.e. lubricated end platens. Tests involving axial extension reported by Vaid et al. (1990) result in considerable scatter, indicating probably that substantial nonuniformities developed in axial extension and that the strains that can be applied in an axial extension test are not large enough to approach steady state.

Table 1. Laboratory tests for determination of 8 ,.

Heber Road.

Type: TriaxialCompression

Vane RotationShear

Condition: Drained or Undrained

Undrained Drained

8 and y

Silt •j C

Clay C

207

Figure 5. Steady state line obtained with various stress paths

Figure 6 . Steady state line obtained from four laboratories.

208

The results discussed above relate to the determination of Sus on laboratory-prepared specimens of an homogeneous batch of soil at known void ratios. The determination of in situ values of S„3 must consider the heterogeneity of natural soil deposits and the changes in void ratio that even the most careful sampling procedure will cause in "undisturbed" soil samples. A procedure proposed by Poulos et al. (1985) is presented schematically in Figure 7.

The results of the application of the Poulos et al. procedure to the hydraulic fill from the Lower San Fernando Dam are presented in Figure 8 . The results presented were obtained from tests performed by two laboratories, indicating no significant difference among the two laboratories. More importantly the results are in good agreement with the strengths estimated from the mechanics of the actual slide thus providing verification of the soundness of the method used to determine in situ values of

For soils other than sandy soils, the strains required to reach steady state are generally larger than those that can be achieved in the triaxial compression test. The vane test can be used to obtain values for clays (Poulos et al. 1985b), as noted in Table 1. For nonplastic silts the vane test can be used if it is performed fast enough so that the test is undrained. Castro & Troncoso (1989) present results of tests on silts from copper tailings performed at high rates of rotation to ensure that the silt along the failure zone remained undrained during the test. Drained rotation shear tests on thin samples have also been used to determine the steady state strengths of clays and silts (LaGatta 1970).

e ^ = VOID RATIO OF U N D IS TU R B ED SAM PLE AFTER CO NSO LID ATIO N IN LABORATORY

e ^ = V O ID RATIO OF SAM PLE IN -S IT U

(S u s ), = STEADY STATE STRENGTH OF SOIL AS DETERMINED IN LABORATORY AT VOID RATIO Gl

(S u s )^ = STEADY STATE STRENGTH AT VOID RATIO

STEADY-STATE STRENGTH. Sus (LOG SCALE)

Figure 7. Procedure for determining in situ steady state strength (after Poulos et al., 1985).

A successful test for the determination of must comply with two key characteristics, namely: a) sufficient strains must be possible in the test so that 8 ,3 can be reached, and b) the sample must maintain its initial uniformity of void ratio so that the void ratio in the zone of failure is known.

4 EMPIRICAL DATA FROM PAST FAILURES

Analysis of past failures can be performed to obtain estimates of in situ values of S,j3, as presented above for the Lower San Fernando Dam and for the Heber Road site, see for example. Seed (1987), Ishihara (1989), & Castro (1995). These authors compared the backfigured S„3 values with either blowcounts or cone tip resistance. Both SPT and cone tip resistance in sandy soils correspond to at least partially drained conditions in the soils being penetrated. In the cases of interest the soils are contractive, and thus the undrained strength is generally substantially lower than the drained strength. Thus the penetration resistance is strongly influenced by the degree of drainage during the penetration test, which is generally unknown and depends on minor stratification details, soil permeability, and velocity of penetration. Therefore, one cannot expect a unique correlation of S ,3

with SPT or cone penetration resistance applicable to all sandy soils. Nevertheless, a collection of well-documented cases is valuable. Preliminary evaluations can be performed by comparing the case being evaluated with actual failures.

The evaluation of the foundation of an existing earth dam is presented below and serves to illustrate the limitations of the use of index penetration tests. A typical soil profile is shown in Figure 9. The soils of concern for seismic stability are the silty sand layers in the stratum of stratified layers of clay and silty sands. The reason for the concern were the low blowcounts, often lower than 1 0 , and the potential for the sand layers to be continuous, raising the possibility of a failure along sand layers with low 8 ,3 values.

A program of sampling and testing of the sands following the procedures in Poulos et al. (1985) resulted in a recommended 8 ,3 value of 1200 psf This value was selected conservatively to be equal to the average minus one standard deviation of all tests results. There was a concern that this relatively high value of S„3 may be inconsistent with the low SPT and cone penetration resistances.

An expanded plot of the cone tip resistance is shown in Figure 10. The tip resistance has a "base value" of about 5 tsf (about 10 tsf in the example shown in Fig. 9). Sharp peaks are superimposed on the base value and are interpreted to correspond to sand layers based on the associated decreases in the values of friction ratio (Fig. 9). Electric resistivity plots confirmed this interpretation. Practically all the peaks of the cone resis-

209

1030

1025

1 0 2 0 |— _ ( 2 8 )

t

P 1015 :

r DRIVING SHEAR STRESS UPSTREAM SLOPE

(7)15

- 1 3■( 1 6 )

1 6

( 5 2 ) ■=>

(4) 12 •—1 .9 7

1 7

1005 ■

1000L J _

-------AVERAGE Sus- ’I'W O-THIRDS” Sus J ____ ^ ^ ^ ____ L

0 0.2 0.4 0 .6 0 .8 1.0Sus OF CRITICAL LAYER ON UPSTREAM SIDE OF DAM

AT TIME OF 1971 EARTHQUAKE

♦ EXPLORATION SHAFT SAMPLES■ BORING U111 AND U111A SAMPLES♦ BORING U103 SAMPLES

NOTES:NUMBER_NEXT TO EACH POINT INDICATES R OR CRR TEST NUMBER NUMBERS IN PARENTHESES ARE STANFORD UNIV. TESTSR12 EXCLUDED FROM AVERAGING

Figure 8 . In situ S s values for Lower San Fernando Dam

CONE TIP RESISTANCE, ts f

STIFFCLAY

STRATIFIED CLAY &

SILTY SAND

DENSESAND

LEGEND ^ SPT— CONE PENETRATION

Figure 9. Typical soil profile - earth dam foundation

CONE PENETRATION RESISTANCE, q ts f

Figure 10. Expanded cone log - earth dam foundation.

tance in the sand layers are essentially triangular. The resistance increases rapidly and approximately linearly as the cone enters the sand layer and then abruptly drops, again about linearly. The shape of the peak

suggests that the sand layers are not sufficiently thick for the cone resistance to be representative only of the properties of the sand. Rather the measured maximum cone resistance in the relatively thin sand layers is

210

strongly influenced by the properties of the clay above and below the sand layer. This observation is in agreement with a Federal Highway Administration report (1978) which states that the minimum layer thickness needed to develop the full value of in a layer is equal to 15 times the cone tip diameter. The cone used in the investigations presented in Figs. 9 and 10 has an area of 15 cm , i.e. a diameter of about 4.4 cm. Thus the minimum layer thickness to obtain a true penetration resistance in the sand is about 65 cm or 2.2 ft, which is about equal to the maximum sand layer thickness encountered in the stratified stratum.

The peaks can be analyzed by defining a width of the peak as shown in Figure 10 as the distance between the beginning and the end of the increased cone resistance. This distance is probably equal to or slightly larger than the thickness of the layer. Cone penetration data are presented in Figure 11 as a plot of the peak values of cone penetration versus the width of the peaks. The plot shows that larger peaks correspond to thicker layers, with a relatively narrow range for peak resistance for layers thinner than about one foot. This result indicates that the peak cone value for layers thinner than about one foot is primarily a function of the thickness of the layer and to a lesser degree on the denseness of the sand. At thicknesses over about one foot, the scatter increases, indicating a larger effect of the density of the sand on the peak cone resistance.

A comparison of the SPT and CPT (cone penetration test) data from borings is shown in Figure 9. The SPT and CPT correlate well in the stiff clay layer, indicating a gradual decrease of the strength of the clay with depth. However, the SPT does not reflect the presence of the sand layers disclosed by the CPT logs. The sand layers are too thin for the SPT to reflect the sand properties. Schmertmann (1979) has indicated that for cone friction ratios of 2 to 4, more than 50% of the SPT blowcount resistance is derived from the frictional resistance along the outside of the spoon. Thus, if the tip of the spoon is in a sand layer but a significant length of the spoon length is in clay, the blowcount is mostly due to the clay. Furthermore, similar to the cone penetration resistance, even the tip resistance of the SPT spoon would be influenced strongly by the strength of the clay above and below the sand layers.

The results of the analysis of the penetration test data indicate that the SPT does not reflect the presence of the sand layers. Thus the blowcounts should not be used for estimating sand properties, since they are not an index of the denseness of the sand.

The cone data can be interpreted to indicate a "true" tip penetration resistance of the sand layers of at least 60 tsf, indicating a lower to medium dense sand, which is consistent with the S s values obtained from laboratory tests of 1 2 0 0 psf.

The case discussed above illustrates the need for a careful examination of soil conditions and of the signifi-

Figure 11. Peak cone resistance as a function of width o f peak.

cance of the results of laboratory and field tests, whether one is examining a past failure or evaluating the behavior of an earth structure under a potential earthquake.

5 CONCLUSIONS

The Sus is a key parameter for assessing the behavior of soil masses under load in general and particularly under seismic loading.

The determination of S in the laboratory must comply with two conditions, namely: a) sufficient strains must be possible in the test so that S s can be reached, and b) the sample must maintain its initial uniformity of void ratio so that the void ratio in the zone of failure is known. Even though undrained triaxial tests in compression are most commonly used, other tests with larger strain capabilities, such as vane or rotation shear, may be required in some soils to reach

Empirical information on from past failures has been related to index penetration tests, such as SPT blowcounts, and cone, and can be used for initial assesments of Syg values. However, these empirical techniques cannot be used for soil deposits in which the critical soils occur in relatively thin layers, a rather common occurrence. In such cases, an example of which is described in this paper, the SPT and cone data do not properly reflect the presence and properties of the critical layers, and thus cannot be used for estimating Sus values.

REFERENCES

Bennett, M.J., Youd, T.L., Harp, E.L. & Wieczorek,G.F. (1981). Subsurface investigation of liquefaction, Imperial Valley earthquake, California, Octo

211

ber 15, 1979. U.S. Geological Survey Open File Report 81-502.

Castro, G. (1969). Liquefaction of sands, thesis presented to Harvard University, Cambridge, Massachusetts, in fulfillment of the requirements for the degree of Doctor of Philosophy.

Castro, G., Poulos, S.J., France, J.W. & Enos, J.L. (1982). Liquefaction induced by cyclic loading, report by Geotechnical Engineers, Inc. to the National Science Foundation, Washington, D.C. March, 1-80.

Castro, G. (1987). On the behavior of soils during earthquakes— liquefaction. Soil Dynamics and Liquefaction, A. S. Cakmak, Editor, Elsevier.

Castro, G. & Troncoso, J. (1989). Effects of 1985 Chilean earthquake on three tailings dams. Fifth Chilean Congress of Seismicity and Earthquake Engineering, August 1989.

Castro, G., Keller, T.O. & Boynton, S.S. (1989). Re- evaluation of the Lower San Fernando Dam, report 1, an investigation of the Feb. 9, 1971 slide, 2 Vols. GEI Consultants, Inc., U.S. Army Corps of Engineers Contract Report GL-89-2, September.

Castro, G. (1995). Empirical methods in liquefaction evaluation, Primer Ciclo de Conferencias Internationales, Leonardo Zeevaert, Mexico City, November.

Davis, A.P., Castro, G., & Poulos, S.J. (1988). Strengths backfigured from liquefaction case histories, the Second International Conference on Case Histories in Geotechnical Engineering, Rolla, Missouri.

Federal Highway Administration (1978). Office of Research and Development, "Guidelines for cone penetration test - performance and design," Report FHWA TS-78-209, July.

Ishihara, K., Yasuda, S., and Yoshida, Y. (1989). Liquefaction-induced flow failure of embankments and residual strength of silty sand. International Seminar on Dynamic Behavior of Clays, Sands and Gravels, Kitakyusku, Japan, Nov. 1989.

LaGatta, D.P. (1970). Residual strength of clays and clay-shales by rotation shear tests, thesis presented to Harvard University, Cambridge, Massachusetts, in fulfillment of the requirements for the degree of Doctor of Philosophy.

Poulos, S.J., Castro, G., & France, J.W. (1985). Liquefaction evaluation procedure. Journal of Geotechnical Engineering, ASCE, Vol. Ill, GT6 , 772-791.

Poulos, S.J., Robinsky, E.I. & Keller, T.O. (1985b). Liquefaction resistance of thickened tailings, Journal of Geotechnical Engineering, ASCE, Vol. Ill, GT12, December, 1380-1394.

Poulos, S.J. (1971). The stress-strain curves of soils. Geotechnical Engineers, Inc. Winchester, Massachusetts, 1-80.

Schmertmann, J.H. (1979). Statics of SPT, Journal of the Geotechnical Engineering Division, ASCE, Vol. 105, GT5, Proc. Paper 14573, May, 655-670.

Seed, H.B. (1987) "Design Problems in Soil Liquefaction," Journal of Geotechnical Engineering Division, ASCE, Vol. 113, GT8 , 827-845.

Seed, H.B., Lee, K.L., Idriss, I.M. & Makdisi, F.I. (1975). The slides in the San Fernando Dams during the earthquake of February 9, \91\, Journal of the Geotechnical Engineering Division, ASCE, Vol. 101, GT7, 651-688.

Vaid, Y.P., Chung, E.K. F. & Kuerbis, R.H. (1990). Stress path and steady state, Canadian Geotechnical Journal, Vol. 27, No. 1, February, 1-7.

2 1 2


A methodology to evaluate the susceptibility of soils for liquefaction flow failures

J.-M. KonradDepartment of Civil Engineering, Université Laval, Sainte-Foy, Que., Canada

ABSTRACT: An important factor in evaluating the stability of hydraulic fills against flow sliding is the undrained steady state strength mobilized in the field. This paper proposes an empirical relationship between three factors: the undrained strength back-calculated from fills which failed by flow sliding, equivalent clean sand normalized blow count values and soil specific parameters from steady state laboratory testing. It is shown that Suo. which is a reference value of steady-state strength at maximum void ratio, is an important soil parameter.

A methodology to evaluate the soil's susceptibility to develop liquefaction flow failures once strain softening is triggered in the field is presented based on case-histories. The proposed approach gives undrained strengths close to the post-liquefaction strengths obtained from simple shear tests for the foundation sand at Duncan Dam. These values are much higher than those inferred from the original Seed's relationship because the new method incorporates soil specific parameters obtained from laboratoi7 testing.

The proposed method offers also an explanation for the performance of many artificial sand islands in the Beaufort Sea, indicates the extreme sensitivity of Suo to soil type and the usefulness of Suo for assessing the potential strength loss of soils for use in safety assessments of existing hydraulic fills.

1 INRODUCTION

The problem of assessing the safety of loose deposits of freshly deposited sand masses subjected to shear stresses such as in embankments is complex and consists of two separate issues: ( 1 ) recognizing the triggering event(s) and (2 ) evaluating the average undrained strength mobilized in the field during flow failure.

The first issue, related to triggering of strength loss, is by far the most complex. Furthermore, it must be emphasized that shear failure must occur in undrained conditions. Only soils that tend to decrease in volume during shear, i.e. contractive soils, can suffer the loss of shearing resistance that results in large flow slides when the driving shear stress is considerably larger than the minimum undrained strength of the soil mass. Considering that undrained conditions prevail, possible triggering mechanisms are, for example, (i) rapid static loading loading (fills with steep slopes), (ii) earthquake loading, (iii) foundation movements leading to undrained creep in the sand fill, (iv) a combination of two or several of these individual mechanisms.

The second issue is discussed in details in this paper. In view of the above discussion, it is con

sidered that the stability of soils that are loose enough to present a substantial risk for flow failures can be directly evaluated using the average undrained strength that is mobilized in the field assuming that strength loss has been triggered by the relevant mechanism or a combination thereof. As stated by Seed (1987), it may be adequate and economically advantageous to simply ensure the stability of the embankment against major sliding after liquefaction has occun'ed, at least for cases where large defoiTnations can be tolerated. Seed (1987) proposed an approach for estimating the undrained shear strength during flow failure based on field case-histories. The average undrained strength, refen*ed to as the residual strength by Seed, is obtained from a relationship between some in situ soil characteristics, such as standard penetration resistance, and back-calculated strength from case-histories. This strength is re- feiTed to herein as the ultimate strength.

One of the objectives of this paper is to demonstrate that Seed's approach can be improved by including a soil specific parameter describing its behaviour during undrained shear of reconstituted soil specimens. Another objective is to show that this soil specific parameter may be used successfully to evaluate the susceptibility of a soil sub-

213

jected to undrained shear to develop liquefaction flow failures.

2 SUMMARY OF CASE STUDffiS ON RESIDUAL STRENGTHS

The original results of the analysis of twelve earth structures are presented in Figure 1 in terms of residual strength (ultimate strength) and equivalent clean sand blow count SPT (N1)5Q • The undrained strengths were back-calculated using limit equilibrium analyses for the final geometry of the slide mass. In order to account for a lower penetration resistance in silty sands, an equivalent clean sand value was used by correcting the SPT blow count value as a function of fines content. The penetration values were also normalized with respect to effective overburden pressure and energy efficiency of the system. As noted by Seed, there is a considerable scatter in the results, possibly reflecting variable soil properties and intrinsic- difficulties in the back-analysis of the failures. For instance, the residual strength back-calculated from a limit equilibrium analysis is in fact an average strength that may not fully consist of the lowest possible strength of the liquefied earth mass. Scatter in the results may also be caused by the stress path dependency of undrained strength in liquefied sand, as evidenced by recent laboratory tests by Vaid et al. (1990). Failure in paitially drained conditions as suggested by Stark and Mesri (1992) may explain high values of back-calculated residual strength.

D esp ite the d iff ic u ltie s a sso c ia ted w ith the an aly sis o f f lo w fa ilu res , it is c lea r th a t the re la tio n sh ip p ro p o sed by S eed is still w ide ly u sed in p ractice , at le a s t as a reaso n ab le g u ide fo r e v a lu a ting th e stab ility o f earth s tru c tu res a fte r l iq u e fac tion has been trig g e red . W ro th (1984) coiTectly s ta ted tha t any su ccessfu l re la tio n sh ip (em p irica l)

should ideally be:(a) based on a physical appreciation of why the

properties can be expected to be related;(b) set against a background of theory, however

idealized this may be.A careful examination of Seed's empirical relationship in light of the above points may prove relevant for the practice.

3 FRAMEWORK FOR THE RELATIONSHIP BETWEEN UNDRAINED STRENGTH, SOIL TYPE AND SPT (N l)60

The Konrad/Watts approach (1995) couples steady state laboratory test results with Seed's backcalculated strength values. A basic assumption in the use of Seed's database is that all cohesionless materials have the same liquefaction potential and the same residual strength if their corrected penetration resistances are the same. In contrast, laboratory results yield a wide range of steady state strengths depending on gradation, fabric and compressibility. These laboratory results suggest that ultimate strength must be dependent on factors other than penetration resistance or density. Ultimate strengths derived using our method account for these other factors but are still limited by the confining stresses of the Seed case histories.

The proposed approach states that Suo which is a reference value of steady-state strength at maximum void ratio (Figure 2), is an important soil parameter. The position of the steady state line in the void ratio-undrained strength plane can be described by the magnitude of the steady-state strength at a reference void ratio or by the magnitude of void ratio at a reference steady-state strength. Rather than selecting an arbitrary value of either void ratio or steady-state strength, it is proposed to consider the maximum void ratio as the reference void ratio for a given soil since it is an index property which can be determined independently.For loose deposits, i.e. (N^)60 < 15, the field

strength, , can be approximated by:

SuL o g ^ = X (N i )60 (1)

Fig. 1 Residual strengths from field data After Seed (1987)

where is the average undrained shear strength mobilized during flow failure as back-calculated by Seed (1987), however questionable its value may be. Suo is the reference steady state strength obtained from CIU triaxial tests on reconstituted specimens of the most representative soil in the failed zone or in the expected failure zone. % is a

214

Log of steady-state strength

Fig. 2 Typical steady-state characteristics of a sand

parameter reflecting both steady-state characteristics of reconstituted specimens and the relationship between density and normalized blow count in the field.Specific correlations between relative density and SPT penetration resistance are not available for most flow-sliding case-histories and would not be available for the majority of projects where Su (field) is required for stability analyses. Hence, some other approach is needed to derive the value of c for each soil. It is proposed to relate % solely to the slope of the steady state line,X , by means of an empirical correlation obtained from the analysis of case-histories.

4 ANALYSIS OF CASE-HISTORIES

The relationship between % and X must be established from case-histories where sufficient field and laboratory data are available. Current Seed (1987) derivative approaches are based on about 2 0 case-histories involving flow slides or lateral spreads, for which three only include com-

Table 1. Summai7 of case-histories analysis

Fig. 3 Relationship between % and X After Konrad and Watts (1995)

píete laboratory testing programs with data on steady-state lines on reconstituted specimens and magnitude of maximum void ratio of dry soil. These three case-histories are (1) Fort Peck Dam (Marcuson and Krinitzsky, 1976) (2) the Lower San Fernando Dam (Seed et al., 1975; (Marcuson et al., 1990) , and (3) the Nerlerk Berm (Mitchell, 1984; Sladen et al. 1985a, b, 87; Been et al., 1987). Two flow-slide events are added to the above three cases: (4) a flow failure in uncompacted beach sands at the upstream face of Tar Island Dyke (Alberta) (Plewes et al. 1989) and (5) a road embankment failure at Asele (Sweden) following submergence during impounding a reservoir (Ekstrom and Olofsson, 1985; Konrad. 1990a).

Because of uncertainty in input parameters, a sensitivity analysis was used to estimate upper and lower bounds for % as a function of X . The results of the analysis are summarized in Table 1.

Figure 3 presents the relationship between an average value of % and X for the five case-histories analysed above. These few data points can be fit

Structure Material characteristics from laboratoi7 tests

Field data X

( 1 )emax S„„(kPa) X (N ,),o S„ (kPa)

(7)(2 ) (3) (4) (5) (6 )Nerlerk 0.94-0.98 .0002-0.0015 0.044 8 - 1 0 3.0 - 5.0 0.33-0.55

ar Island Dyke 0 .98 -1 .03 ).0024-0.024 0.057 8 - 1 0 8 .0 - 1 0 0.25-0.45Fort Peck 0.97-1.05 3.008 - 0.12 0.087 1 0 - 1 2 [2.5-22.5 0.17-0.34

.S.F. > 50% 0.9-1.0 O.Ol-.Ol 0 . 1 0 15-17 [5.0-25.0 0.13-0.23Asele 0.8-0.87 0.3-0.7 0.145 8 - 1 0 5-7.5 0.085-0.17

215

ted to a power relationship as:

X = 0.0138 (2)

5 EXAMPLE APPLICATIONS

5.1 Artificial islands in the Beaufort sea

Hydraulic sand fills placed underwater have been used to support waterline penetrating caissons for hydrocarbon exploration in the Canadian Beaufort Sea since 1972. About 20 artificial sand islands have been constructed. Most have performed successfully but a few have not. The extensive geotechnical data base of these artificial islands reported in the literature allows an illustration of the proposed method. The results of geotechnical investigations on four subsea berms, Uviluk, Ner- lerk, Kogyuk, and Alerk, were summarized by Sladen and Hewitt (1989). Flow slide failures were reported at two of these fills, namely Nerlerk and Alerk. The other fills did not fail.

STEP 1 Fill characterization

Sladen and Hewitt (Op.Cit.) have shown that placement technique has an important influence on the in-situ density of hydraulically placed sands. Material placed by the bottom-dumping technique is significantly denser than pipeline-placed material. Analysis of CPT data indicates that ECS(Nj)^ would be higher than 20 for hopper placed sands while pipeline-discharged materials generally display ECS (N^)^ values around 10 in the upper 10 m of the fills.

Fig. 4 Steady state characteristics for Beaufort Sea sandsAfter Konrad and Watts (1995)

STEP 2 Laboratory test results

Soil index properties for each site are summarized in Table 2 and in Fig. 4.

STEPS

The value of % are calculated from eqn (2) for each soil and summarized in Table 3.

STEP 4

Figure 5 shows the graphical determination of undrained shear strength for each sand. Su is respectively 240 kPa, 115 kPa, 8 kPa and 5 kPa for sands from Ukalerk, Kogyuk, Erksak and Nerlerk.

Table 2. Index properties of some Beaufort Sea sands

Sand D5 0 (% fines) Cmax Suo. kPa ReferenceUkalerk 0.35 (2%) 0.82 0.1 6.0 Klohn LeonoffLtd(1983)Erksak 0.355 (3-6%) 0.963 0.054 0.005 Been et al. (1987)Kogyuk 0.36 (5%) 0.866 0.095 2.3 Been and Jefferies (1985)Nerlerk 0.28 (12%) 0.96 0.044 0.0007 Konrad (1991)

Table 3. Values of undrained strength during flow failure for pipeline-placed sands

Sand X(eqn 6) Su (field) kPa Pipeline placed

Ukalerk 0.16 240Erksak 0.32 8Kogyuk 0.17 115Nerlerk 0.40 5

216

Fig. 5 Ultimate strength for Beaufort Sea sand islandsAfter Konrad and Watts (1995)

5.2 Discussion of Results

Extremely large differences in minimum undrained strength mobilized during potential undrained and unconfined failure are predicted despite fairly close grain size distributions of the Beaufort Sea sands. For instance, Ukalerk sand

S PT-N values40 60

■b 6

10

Boreholes • D H 88-9 O D H 88-8 V D H 88-7 □ D H 90-5D ■ D H 90-6D A D H 90-7D

' N curve for^ A loosest zones

V w V

1 —

(N , >60 minV v

Fig. 6 Duncan Dam field data After Pillai and Stewart (1994)

and Kogyuk sand have minimum undrained strength about one to two orders of magnitude higher than that for Erksak and Nerlerk sands. This may explain why liquefaction did not occur at Kogyuk in the zone placed with the pipeline- discharged method although CPT tip resistance profiles were about the same as those at Nerlerk where flow slides occurred as discussed above. Kogyuk was built with a sand that has, according to the proposed approach, a much larger undrained shear strength for equal ECS (Nj)^ values, and hence is less susceptible to flow sliding in the field.

The results discussed above indicate that subtle variations in soil characteristics are well encapsulated by Suo which is not the case for CPTsoundings or SPT borings. The proposed approach, which has the merit of combining adequate soil characterization with respect to a given mode of failure (here strain-softening during undrained shear) and field averaged data from case-histories, should provide an improved means of assessing the safety of hydraulically-placed fills.

5.3 Duncan Dam

Duncan Dam is one of three dams constructed in the 1960s as part of the Columbia River Treaty. The dam is located on the Duncan River in southeastern British Columbia 8 km upstream of Kootenay Lake. Duncan Dam is a zoned earthfill dam approximately 39 m high with a crest length of 792 m. The dam is founded on approximately 380 m of alluvial sands, silts and gravels. Seepage through the pervious foundation soils is controlled by an upstream blanket, slurry trench cutoff and pressure relief wells. Foundation investigations, started in 1988 and continued in 1990 and 1991, identified a fine sand horizon (Unit 3C) that was susceptible to liquefaction.

The liquefaction potential, liquefaction-induced deformation, and seismic flowsliding stability of Duncan Dam have been extensively investigated and documented by BC Hydro (see Canadian Geotechnical Journal, Vol.31, No.6 ). Two approaches were used to assign ultimate strengths to the liquefied zone for the flowslide stability assessment.The first approach was to assign ultimate strength on the basis of (N ) from the standard Seed chart

of residual strength versus (Nj)^ . That approach predicted a flowslide for the design earthquake. The low strength from the traditional Seed approach was questioned because the case histories on which the chart was based were for confining

217

stresses apparently much less than that in most of the foundation zones predicted to liquefy.The second approach was to estimate the ultimate strength on the basis of laboratory testing at the appropriate confining stresses on high quality samples of Unit 3C (Pillai & Salgado 1994). An undrained strength normalized to confining stress ratio of 0 . 2 1 was proposed to calculate the ultimate strength in the liquefied zone. The direct approach predicted that a flowslide would not occur for the design earthquake because the predicted ultimate strengths were higher for higher confining stresses.

Laboratoiy tests conducted on samples from Unit 3C, a fine grained, uniform sand = 0.2 mm) with about 5 % passing the No.200 sieve, a specific gravity of 2.76 (20% quartz, 45 % lithic fragments, 2 0 % feldspar, 1 2 % dolomite) with a minimum void ratio of 0 . 6 and a maximum void of 1. 13 to 1.15 suggested a value of of 0.53 kPa. (Konrad et al. 1997).

Figure 6 shows a plot of SPT-N and (Nl)60 values vs. effective vertical stress at Duncan Dam (Pillai & Stewart 1994). The N values increase with depth and present moderate scatter which is associated with variations in relative density in this natural sands deposit. In order to evaluate the strength which would be mobilized in the loosest zones, (Nl)60 values were calculated using the lower bound of the N values. The average energy con*ection was determined to be 43% (Plewes et al. 1994) while the overburden correction factor that accounts for the increased penetration resistance due to increase in effective confining stress were close to those predicted by Liao and Whitman (1986). Thus,

(M)60 = y V C ,f = (3)

The (N 1 )6 0 values of the loosest zones increase from about 7.0 to 11.0 with increasing effective overburden pressures from 1 0 0

to 600 kPa and remains constant at about 11.0 for stress larger than 600 kPa.The field residual strength for the loose zones at Duncan dam estimated using equation (4) ranges thus from about 20 to 150 kPa when the overburden stress increases from 100 to 600 kPa. For oV

> 600 kPa, (Nj)^ is approximately constant and the estimate of Su field remains constant at about 150 kPa.

log Su (field) = log (0.53) + 0.223(Ni)^o (4)

(0•UC33«E

300r1,250

I" 200

! 150

100

50

U .-1 ■ 1 " " f .. 1 I IO Seed, 1987 A CIU reconstituted samj:

------ SS direct method

° ® max = 1-13 L .w p r o c ■ ®max ■ 1*15j

)lesU f

— lirr)p e r&lits

lower

rO-7-A acP 77Z?zv?. 777/4X2.

0 100 200 300 400 500 600 700 800vertical effective stress a'vo (kPa)

Fig. 7 Ultimate strength for Duncan Dam After Konrad et al. (1997)

Figure 7 summarizes the different approaches used to determine the undrained strength that would be mobilized in the loosest zones if a flow slide would occur. The direct method for assessing Su consisted of obtaining the postcyclic stress- strain response under undrained conditions using simple shear tests. Details of the direct methods are given in Pillai and Salgado (1994). Clearly, The original Seed approach yields the lowest values for undrained strength and the direct lab method, on the orther hand, results in an upper value of Su- The Konrad/Watts (1995) approach

reflects variations in (Nj)^ values with depth and accounts for soil type. The predicted undrained strength values are close to the upper values obtained from postcyclic simple shear tests in a stress range between 100 and 600 kPa. For stresses higher than 600 kPa, backcalculated Cn correction void ratio, the undrained shear strength is likely to remain constant despite increasing stress level. Again, it must be recognized that as confining stress increases, shear-induced grain crushing becomes more important and may affect the steady state strength.

6 SUGGESTED LABORATORY PROCEDURE

The extensive laboratory studies conducted since the late sixties by many researchers suggest that the steady state line is indeed an important characteristic of a given soil subjected to undrained shear. However, because the vertical position of this line depends on many factors including the specimen preparation technique (Dennis, 1988) a standard steady state laboratory test procedure needs to be adopted to develop the systematic soil characterization required to evaluate the suscepti

218

bility to develop liquefaction flow failures. Actual field conditions reflect the influence of many factors such as the depositional environment, the stress history, the aging... While it would be desirable to replicate the field conditions, it may not be always feasible as for instance reproducing the aging phenomenon in the laboratory . Rather, we take the view that a standard test procedure for the above described approach need not to replicate field stress state and stress paths if we only seek the soil's response to a given testing procedure. Adopting a standard test procedure will enable the comparison of the response of different soils in a relative manner.

The strain-controlled CIU test on reconstituted soil specimens using the moist-tamping method described by Been and Jefferies (1985) and Konrad (1990a) is proposed as the standard test procedure because of the preponderance of such test data in the literature. The tests should be conducted well above the anticipated steady-state line so that a well-defined steady-state line is produced. Use of high initial confining stresses also yield the highest position of the steady-state line.

The position of the steady state line in the void ratio-undrained strength plane can be described by the magnitude of the steady-state strength at a reference void ratio or by the magnitude of void ratio at a reference steady-state strength. Rather than

selecting an arbitrary value of either void ratio or steady-state strength, the maximum void ratio obtained from the ASTM D4254 zero relative density procedure is proposed as the reference void ratio for a given soil since it is an index property which can be determined independently. ASTM D4254 is limited in strict application because it is not recommended for fines content in excess of 1 2 %. However, Kuerbis et al. (1988) have used it successfully to determine zero relative density for soils with fines content up to 30%. For sands with a significant percentage of fines, where ASTM D4254 does not apply, the method given by Kol- buszewski (1948) is proposed as the standard testing technique for determining maximum void ratio.

A survey of available data on different soils summarized in Figure 8 shows that Suo is indeed very sensitive to soil type and ranges over about 4 orders of magnitude for the soils reviewed herein. For the same soils, X varied between 0.04 and 0.15. Again, it is emphasized that anchoring the steady state line at p' = 1 kPa would show variations in void ratios rather than in stresses. The main advantage of using the proposed approach lies in the fact that the reference void ratio is not arbitrarily choosen but has a physical meaning, i.e. coiTe- sponds to the loosest packing of dry soil.

7 CONCLUSIONS

• Kogyuk ■ L B /M ic a A N e rle rk♦ Toyoura O Till sand

ffl H ostu n A C a s tro a n d Poulos □ R Peck (S e ll)s R Peck (fo u n d )

100T------ 1------- 1 ^

^ 1 (0 a

</i 0.1

Q QQ n----- 1-----f-.A— I------ ------ 1------ 1------h -

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0

% Fines

Fig. 8 Reference strength for different soils After Konrad and Watts (1995)

When saturated cohesionless fills are placed in a loose to medium dense state, flow failure can be triggered by events such as earthquake loading, foundation deformation, undrained static loading or a combination of these events. As stated by Seed (1987), it may be adequate and economically advantageous to simply ensure the stability of the earth structure against major sliding after strength loss has been triggered rather than to prevent triggering. The geotechnical engineer must therefore assess the undrained strength that would be mobilized in the field during flow failure. This paper suggests that this can be done by using an empirical relationship between the undrained strength back-calculated from field performance studies and equivalent clean sand normalized blow count values, which incorporates soil specific parameters (Suo and %)■

8 REFERENCES

Been, K., and Jefferies, M.G. (1985). "A state parameter for sands." Geotechnique. 35(2), 99-112. Been K., Conlin, B.H., Crooks, J.H.A., Fitzpatrick, S.W., Jefferies, M.G., Rogers, B.T. and Shinde, S. (1987). "Back-analysis of the Nerlerk berm lique-

219

faction slides: Discussion" Can. Geotech. J. 24,(2), 170-179.Dennis, N.D.(1988). "Influence of specimen preparation techniques and testing procedure on undrained steady state shear strength." Proc. Advanced Triaxial Testing of Soils and Rock (ASTM STP 977), Am. Soc. for Testing and Mater., Philadelphia, Pa., 642654 Ekstrom, A. and Oloffson, T. (1985). "Water and frost-stability risks for embankments of fine grained soils." Proc. of the Symposium on Failures in Earthworks., I.C.E. London, U.K. Publ. Thomas Telford. 155-166.Kolbuszewski,J.J. (1948). "An experimental study of the maximum and minimum porosities of sands." Proceedings, 4th International Conf. on Soil Mechanics and Foundation Engineering, Rotterdam, Holland, 158-165.Konrad, J.-M. (1990a) "The minimum undrained strength of two sands" ASCE J.Geotechnical Engrg. 116(6), 932-947Konrad J.-M. (1991) The Nerlerk berm case- history: some considerations for the design of hydraulic sand fills. Can. Geotech. J. 28, (5) 601-612. Konrad, J.-M.& Watts, B.D. 1995 Undrained shear strength for liquefaction flow failure analysis Canadian Geotechnical journal Vol. 32, N.5, pp 783-794Konrad, J.-M., Watts, B.D., Stewart, R.A. 1997 Assigning the ultimate strength of foundation sand at Duncan Dam. proc. 14th Int. Conf. on Soil Mech. and Found. Engng. 143-146. Hamburg, Ger. BalkemaKlohn Leonoff Ltd. (1983) Report to Dome Petroleum Limited.Kuerbis, R., Negussy, D. and Y.P. Vaid (1988) " Effect of gradation and fines content on the undrained response of sand. ASCE Specialty Conference on Hydraulic Fill Structures, Fort Collins, Co. 330-345Liao, S.C.,& Whitman, R.V. 1986 Overburden correction factors for SPT in sand. ASCE Journal of Geotechnical Engineering, 112: 373-377 Marcuson, W.F., III and Bieganousky, W.A. (1977). "Laboratory standard penetration tests on fine sands." J. Geotech. Engrg. , ASCE, 103(6), 565-588.Marcuson, W.F. Ill and Krinitzsky, E.L. (1976). "Dynamic analysis of Fort Peck Dam." Techniocal Report S76-1, U.S. Army Engineer Waterways Experiment Staion, Vicksburg, Miss.Mitchell, D.E.(1984) "Liquefaction slides in hydraulically placed sand." Proc. Int. Symp. Landslides, Toronto, 141- 146.Pillai, V.S. & Stewart, R.A. 1994 Evaluation of liquefaction potential of of foundation soils at Duncan Dam.. Canadian Geotechnical journal Vol. 3L N .6 , pp 951-966

Pillai, V.S. & Salgado, F.M. 1994 Postliquefaction stability and deformation analysis of Duncan Dam (Canadian Geotechnical journal Vol. 31,N .6, pp 967-978Plewes, H.D., O'Neil, G.D., McRoberts, E.C. and Chan, W.K. (1989). Liquefaction Considerations for Suncor Tailings Ponds. Procedings of Dam Safety Seminar, Edmonton, Alberta, September, 1989. Bi Tech Publ. ,39-50.Plewes, D.H., Pillai, V.S., Morgan, M.R & Kilpatrick, B.L. 1994 In situ sampling, density measurements, and testing of foundation soils at Duncan Dam . Canadian Geotechnical journal Vol. 3L N .6 , pp 927-938Seed, H.B., et al. (1975). "Dynamic analyses of the slide in the Lower San Fernando Dam during the earthquake of February 9, 1971." J. Geotech. Engrg., ASCE, 101(9), 889912 Seed, H.B. (1987) "Design problems in soil liquefaction." J. Geotech. Eng. Vol. 113, (8 ), 827- 845 Sladen, J.A., D'Hollander, R.D., Krahn, J. and Mitchell, D.E. (1985 a). "Back-analysis of the Nerlerk berm liquefaction slides. Can. Geotech. J., 22(4), 579-588.Sladen, J.A., D'Hollander, R.D., Krahn, J. and Mitchell, D.E. (1987). "Back-analysis of the Nerlerk berm liquefaction slides. Reply" Can. Geotech. J.,24, 179-185.Sladen, J.A. and K.J. Hewitt (1989) " Influence of placement method on the in-situ density of hydraulic sand fills. Can. Geot. J. 26.,453-466.Stark, T. D. and Mesri, G. (1992) Undrained shear strength of liquefied sands for stability analysis. J. Geotech. Engrg., ASCE 118, (11), 1727-1747 U. S. Army Corps of Engineers (1939). "Report on the slide of a portion of the upstream face at Fort Peck Dam." U.S. Government Printing Office, Washington, D.C.Vaid, Y.P., Chung, E.K.F. and Kuerbis, R.H. (1990). "Stress path and steady state." Can. Geotech. J .,27(l), 1-7.Wroth, C.P., 1984. The interpretation of in situ soil tests. Geotechnique 34, NO 4, 449-489.

2 2 0


A critical state view of liquefaction

M.GJefferiesColder Associates (UK) Limited, Nottingham, UK

ABSTRACT: Liquefaction, in all its forms, is simply another aspect o f the constitutive behaviour of soil and can only be understood in the context o f a theoretical model that sensibly reproduces soil behaviour. One such proper model - NorSand - is outlined and the fit to test data illustrated for static liquefaction. Several issues are then considered using NorSand including: behaviour at low effective stress; the pseudo steady state; silty soils; inference o f state from CRT (including stress level normalisation); and, an appropriate framework for understanding the residual strength case histories. The paper concludes by illustrating the importance o f localisation to liquefaction o f compact soils. Although localisation may seem to be o f only academic interest, it is crucial to practical engineering of many potentially liquefiable soils and needs urgent study.

1. INTRODUCTION

It is self-evident that liquefaction, in all its forms, is simply another aspect o f the constitutive behaviour o f soil. Despite depressingly widespread use o f emotive phrases like ‘collapse surface’ the reality is that, even during the most extreme liquefaction, stresses and strains remain related - we are not dealing with tensile failure of a metal. It then follows that a properunderstanding o f liquefaction will only follow in the context o f a theoretical model that sensibly reproduces soil behaviour - the time for “concepts” in explaining liquefaction is long past. Moreover, a proper model must explain (predict) the response o f soil to density change, drainage and stress path; it must not treat each aspect as a separate behaviour with separate parameters.

In this contribution, one such proper model - NorSand - is outlined and the fit to test data illustrated for static liquefaction (the fit for cyclic mobility can be found in Been et al, 1993). NorSand is especially useful for liquefaction because it includes a critical state locus and is intrinsically a large strain model so that issues of post liquefaction strength are readily addressed.

Having illustrated that NorSand sensibly captures liquefaction, the response o f the model to issues of this workshop is presented. Specific interest centres on:

• liquefaction behaviour at low effective stress;• the pseudo steady state;• liquefaction behaviour o f silty soils;• determining state parameter from the CRT;• an appropriate framework for residual strength

case histories.

Many o f the issues currently debated within the liquefaction literature are captured and explained by NorSand despite the model explicitly being based on a unique and rate-independent critical state. A limiting maximum looseness (the low stress issue) is readily dealt with and presents no computational difficulty. But, in contrast, there are theoretical aspects o f substantial practical importance yet requiring much further work, including localisation and intrinsic scale.

Because contributions are limited in length, it is assumed that readers are familiar with the basic concepts o f the liquefaction literature and the standard terminology used. Figures follow the text.

221

F igure 1. D efin ition o f \\r and the concept o f an infin ity o f N CL

2. NORSAND

NorSand (Jefferies, 1993; 1997) is anisotropically hardening - isotropically softening, single yield surface plastic model derived from two axioms o f critical state theory which are that:

• a CSL exists (the First Axiom);• soil state moves to the CSL with shear (the

Second Axiom).

NorSand is extended to cyclic loading by invoking:

• principal stress rotation anneals plastic hardening (the Third Axiom).

The first o f these axioms has been discussed by many workers. A principal source o f error over possible non-uniqueness of the CSL in e-p space as a function o f stress path arises through the definition that the critical state is the condition in which the soil deforms without volume change, otherwise expressed as zero dilatancy. While this is a necessary condition, it is not sufficient for criticality. At a critical state there must also be the condition that the rate o f change o f dilatancy is also zero. This error is found in virtually all o f

the contributions in the literature asserting nonuniqueness o f the CSL.

Standard critical state models (e.g. CamClay) assume that any yield surface intersects the CSL so directly coupling the yield surface size to void ratio. Real soils, however, display a far richer behaviour and in particular exhibit an infinity o f normal consolidation loci (NCL) which are not parallel to the CSL. NorSand uses the state parameter v|/ (where vy = e - eJ to capture this rich behaviour of a spectrum of yield surfaces in the general stress-void ratio domain, see Figure 1. Over-consolidation ratio (OCR) continues to exist in its usual sense o f defining the location o f a stress state within a yield locus, also shown on Figure 1.

NorSand involves just 3 more soil properties than the familiar CamClay model: an elastic shear modulus, G; a volumetric coupling coefficient, N; and a plastic hardening modulus, H. The power of NorSand derives from not requiring that the yield surface intersect the CSL in e-p space. Instead NorSand uses a hardening law that forces the yield surface to the CSL with shear strain, exactly in conformance with the Second Axiom.

The original form of NorSand was derived in the context o f monotonic loading; however, the extension to cyclic loading is not difficult.

2 2 2

Introducing the Third Axiom that principal stress rotation anneals hardening provides the mechanism for plastic volumetric strain (or excess pore water pressure) caused by cyclic loading. In effect, the Third Axiom over-rides the Second Axiom under the prescribed conditions and allows shear stress to move the soil away from the CSL. Some of the more unusual aspects o f NorSand were anticipated by Drucker & Seereeram (1987).

3. IMPLICATIONS OF UNIQUE CSL

NorSand starts from the axiom o f a unique CSL, noting that the CSL is a surface in 4-D e-a,, a 2, Q3 space - not a line. Interesting consequences derive from uniqueness o f the CSL. However, before looking at the consequences it is helpful to understand the nature o f uniqueness.

One view o f uniqueness is that the projection o f the CSL onto the e-p plane forms a single line regardless o f Lode angle, stress path to attain the critical state etc. The CSL can be represented in

e-p space using a variety of monotonie functions in addition to the usual = F - À log(/? . ) where r , X are material properties; this will be discussed later.

The other aspect o f the CSL is the relationship between the stresses at critical. Commonly critical state theory is introduced tlirough the familiar q, p variables o f triaxial space which then leaves the impression that the critical state friction ratio M is the same as triaxial compression under other stress conditions. This could not be further from the reality o f soil behaviour, as initially pointed out some 30 years ago (eg Bishop, 1966).

Before proceeding it is now necessary to introduce appropriate stress and strain invariants. Following Zienkiewicz & Naylor (1971) the deviatone stress is generalised as the invariant:

= [ > 2 v J

where s j = cr - and

.= ( cr, + cr. + cr. ) / 3

[1]

[2]

Fig 2. C om parison o f stress d ilatancy in plane strain and triaxial conditions

223

The invariant <j is the mean stress and the generalised distortional or deviatoric stress. The ratio o f these two stresses invariants, rj = a I retains its familiar meaning of

critical state theory and in particular we can continue to use 77 = M as one o f the conditions at the critical state.

As there are three principal stresses a third measure is needed in addition to Thethird parameter is taken as the Lode angle, 0. Conventional triaxial compression tests have 0 ^30 deg while triaxial extension tests correspond to 0= -30 deg. Plane strain conditions in soils have a variable Lode angle generally in the range 1 0 < 9 <20 deg.

The corresponding work conjugate strain increment invariants to ,cr^,(9 are:

and:

[3]

[4]

plastic strain increments:

D" = ¿a / ¿ ; [5]

where s = s - —5 s Defining the ratio o f thel) IJ l] V O

gives a strain rate variable corresponding to the stress ratio 77. Stress dilatancy is expressed as the relationship between 77 and DP. Use o f these invariants to generalise the original triaxial form of NorSand to 3-D stress space is given in Jefferies & Shuttle (1998).

Now let us return to Bishop’s point that it is erroneous to treat M as a constant. Figure 2 is a stress dilatancy plot in triaxial compression, extension, and plane strain from data on Brasted sand (Comforth, 1961). Clearly M is not remotely near a constant. Test data suggests that the critical friction angle is about the same in triaxial extension as compression and that it is no more than about 2 deg greater under plane strain. Such behaviour is poorly fitted by both the Lade & Duncan (1975) and Matsuoka & Nakai (1974) yield surfaces. A closer representation o f the data is given by a function near a Mohr-Coulomb idealisation with smoothed vertices (Jefferies & Shuttle, 1998) and which is adopted for Norsand. Figure 3 compares these function in the tt-plane.

Fig 3. E xpanded view o f segm ent o f n - plane w ith alternative criteria for M

224

state parameter at image stress, \|/jFig 4. C om parison o f m easured and predicted m axim um dilatancy

A most interesting result now follows. Because the CSL is taken as unique, the mean stress. Pi, associated with the critical condition, rj = M IS invariant with Lode angle. This mean stress is referred to as the image stress. The maximum dilatancy is related to the state parameter at this image condition, from which it then follows that the variation in maximum dilatancy with Lode angle is an intrinsic consequence o f the theory as and is given by:

D^(9) = XW,M{9) N , M , N(0) [6 ]

where x is the fabric dependent dilatancy parameter. On average x does not vary from one sand or silty sand to another and can be sensibly treated as a constant. Figure 4 shows the fit o f [6] to the Brasted sand data. There is a slight tendency to over predict dilation in plane strain, and an excellent fit to triaxial extension. Notice that NorSand predicts that the dilatancy in extension is half that in compression...

4. ALTERNATIVE CSL IDEALISATIONS

Ishihara (1993), in his Rankine Lecture, noted that the susceptibility to alternative liquefaction behaviours did not scale particularly well with if/ at high void ratios (or low mean stress). An alternative measure, called the state index 1 , was proposed. The basic difference between the two measures is that the 1 includes the formation or maximum void ratio, eg (where the 0 subscript indicates at zero mean effective stress), in its definition while ^does not. This gets back to the issue o f whether the familiar semi-log relationship between e-p is a reasonable idealisation for the CSL, since in such an idealisation as p 0 then e , =i> oo. And it is generally thought that infinite void ratio are absurd (although this is not necessarily true if we have an infinite number of particles). However, there is test data suggesting that the CSL is not semi-logarithmic as can be seen in the case of Erksak sand (eg Fig 17 o f Been et al, 1991) or Toyoura sand (eg Fig 32 o f Ishihara, 1993).

An earlier suggestion by Ishihara & Watanabe (1976) was that the densification potential, e-emm- might be a useful normalising parameter for sand

225

mean effective stress, p ' : kPa

Fig 5. D ensification potential norm alised isotropic com pression

Fig 6. A lternative e-p idealisation o f CSL

226

behaviour. Jefferies & Been (1998) found that this is indeed the case for the isotropic compression o f sand. Further, switching from void ratio to specific volume (v = 1+e) then allows integration in a closed form:

ln(---------------- ) ={\-b)C [ p ' P f ]

i\-b)[7]

where C, b, are material properties (density independent constants for any sand). Equation [7] not only includes a formation void ratio but also a minimum void ratio, and as such is an appealing idealisation for cohesionless soil as these two limiting cases ought to appear in a self- consistent theory. The formation void ratio changes with particle packing - Figure 5 illustrates the pattern o f isotropic compression given by [5] for different choices o f formation void ratio.

Extensive testing o f Erksak sand included many variables but produced a sensibly unique CSL within the experimental scatter. Figure 6 shows this data (after Fig 17 o f Been et al, 1991) together with a fit o f [7] and a conventional semilog model. It is not immediately obvious which is the better representation o f the test data... Neither model captures the consequence o f grain crushing at p>2000 kPa. Below this stress, because o f the scatter in the data, it is unclear which is the preferable idealisation for the data which extends to stresses as low as p=8 kPa. And although [7] introduces the apparently theoretically desirable aspects o f formation and minimum void ratios, the parameter count has increased from the two o f the semi-log idealisation to five. The benefit is questionable.

NorSand is tractable with any proper definition o f the ec~p relationship for the CSL. Proper functions must be single valued with arbitrary choice o f 6c or p as the independent variable; and we also expect ec to decrease with increasing p. Figure 7a and 7b show, respectively, the fit o f NorSand to a load-controlled liquefaction test on very loose Erksak sand using the curved CSL and the conventional semi-logarithmic idealisation. Although either idealisation o f the CSL fits NorSand to actual behaviour, it would not be unreasonable to suggest that the semi-logarithmic idealisation gives a better representation o f the extreme nature o f this liquefaction test.

Importantly, notice that the liquefaction

behaviour is captured by NorSand explicitly excluding any “collapse surface” or other “instability line” ; liquefaction is simply a consequence o f the plastic volumetric strain producing excess pore water pressure at a faster rate than the volumetric hardening and M remains the only friction parameter in the formulation.

Returning to grain crushing, Gerogiannopoulos & Brown (1978) and Brown & Michelis (1986) have shown how to include the fracture energy o f crushing within a critical sate framework. It would be useful to extend NorSand using these ideas for high mean stress modelling.

axial strain, %Fig 7ao Stress strain behaviour for curved CSL

axial strain, %Fig 7b. Stress strain behaviour for sem i-log CSL

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5. THE PSEUDO STEADY STATE

An aspect o f liquefaction that has attracted considerable controversy is the pseudo steady state, also called the phase change condition. Several workers use this as a reference condition including Ishihara (1993) and Konrad (1990a,b).

Figure 8 a and 8b show the stress strain behaviour and stress paths respectively from a compact (dense o f critical) sample o f NorSand in undrained triaxial compression. In each case, two samples are illustrated differing only in their elastic modulus. Both samples exhibit a pseudo steady state marginally before 1% axial strain, and the corresponding stress paths show the sharp vertex often called the phase change point.

Two points are made from Figure 8. First, these simulations had an explicit unique critical state (at p’ = 2 5 1 kPa). Confusing the pseudo condition with the real critical state causes an error o f about a factor o f four in estimating pc in this instance (by no means an extreme error). Second, the pseudo steady state is not a property or otherwise unique behaviour. In this instance, relatively minor changes in the elastic modulus caused marked change in the pseudo steady state.

Going one step further, it is well known that sample preparation (eg moist tamping versus wet pluviation) markedly changes sand behaviour all else equal. There are two ways this effect is seen with NorSand. First, the dimensionless plastic hardening modulus {H) can reasonably be expected to be a function o f particle arrangement. Second, NorSand invokes an average relationship between maximum dilatancy and the state parameter, i|/, equation [6] above. Although this is a useful simplification, we can retain all aspects o f the NorSand framework and introduce the additional sophistication that x depends on soil particle arrangement (which o f course requires that we can measure such arrangements...).

The effect o f particle arrangement on the behaviour o f loose NorSand in undrained triaxial compression is illustrated on Figure 9. The behaviour is entirely consistent with the experimental data reported in the literature and illustrates that part o f the difficulty in interpreting laboratory tests is the practical maximum strain limitations o f the triaxial or simple shear apparatus - theoretically, shear strain to the critical state for denser soils may exceed 60%.

F igure 8a. E ffect o f elasticity on stress path

Figure 8b. E ffect o f elasticity on stress strain behaviour

The potential for confusion is large when measurements use test equipment where strains greater than 15% are problematic.

6. LIQUEFACTION OF SILTY SOILS

Figure 10 shows a further static liquefaction test on a soil comprising a medium fine sand with some 30% by weight finer than the #200 sieve. The test was conventional strain controlled triaxial compression, and both the stress-strain behaviour and stress path followed are shown. Also shown is the behaviour computed using NorSand. As can be seen, NorSand closely captures the test data and the fact the sample had a 30% fines content neither prevented liquefaction nor caused any difficulty in modelling - the state parameter measure works

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Fig 9. E ffect o f soil fabric on undrained behaviour

just fine in such silty sands. Which then has implications for silt content “correction” factors in liquefaction analysis. However, before discussing this topic it is essential to first consider how state is determined in situ.

7. STATE DETERMINATION WITH CPT

Within a critical state framework, it is not sufficient to know the void ratio. The CSL must also be known. Thus although there is a presently a fashion in favour o f freezing to directly measure

Fig 10a. Stress and strain during liquefaction o f silty sand

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the void ratio o f in situ cohesionless soils, this merely hides a difficult issue: the CSL is markedly affected by seemingly small changes in the soil’s gradation. A better approach is to measure the state parameter in situ using either the CPT or the SBP (or both).

State determination with the pressuremeter has been pursued by Yu (1994, 1996). My preference is for the CPT largely because the SBP does not impose sufficient shear strain for the limiting conditions to be resolved.

Interpretation o f state from the CPT was developed by dimensionless analysis o f chamber test data (Been et al, 1986, 1987) giving:

\\) = ln(k/Q) / m [8]i|/ true

Fig 11. P erform ance o f general inversion

where k, m were thought to be constants for any sand. It was further suggested that both k, m were functions o f X (the work was based on the usual semi-log idealisation for the CSL).

Although [8] seemed to fit the test data rather well, it did not fit with the preferred explanation of the Nerlerk offshore island failure - a $100 million loss to Canadian taxpayers. Sladen(1989) evaluated [8] against the chamber test data and concluded that while [8] fit the trends, there was a different fit at different stress levels - a stress level bias despite the dimensionless form.. Collins et al (1992) used a state parameter based model to confirm a stress level bias, but did not offer a general method o f CPT interpretation.

Shuttle & Jefferies (1998) implemented NorSand within a large strain finite element model o f spherical cavity expansion for extensive numerical simulations o f the influence o f various parameters on the CPT resistance. Stress level bias was a consequence o f neglecting the dimensionless group G/p’. More generally, [8] was an excellent representation o f the CPT behaviour in sand but k, m were strong functions o f the soil’s properties:

k = f,(G/po) f(M ) f3(N) f,(H) f ( ) f,(v) [9a]

m - f,(G/po) fs(M) f,(N) f,o(H) f„(^) fi2(v) [9b]

The functions f, - f ,2 were determined by fitting analytic expressions to the numerical results in systematic parametric variations and are given in Shuttle & Jefferies (1998). The effect o f the various properties on the dimensionless CPT resistance Q is summarised on Table 1.

Table 1: Results o f sensitivity analysis

Parameter Variation Effect on Q0.01 to 0.04 small

M 1.0 to 1.50 ± 25%N 0.00 to 0.40 ± 15%H 50 to 350 ± 25%

G/po 100- 1000 ± 30%V 0.1 to 0.3 negligible

Equations [9] combine with [8] to offer an approximate framework for CPT interpretation once the soil properties and in situ stress conditions are known. Figure 11 shows the performance o f the proposed general framework for 10 sands with randomly chosen properties - the recovered \\f falls with ± 0.01 o f the true value for nine cases and only slightly outside this uncertainty band in the tenth, importantly, the approximate inverse form is sufficiently simple to be readily applied in CPT data processing software.

In applying the general framework, three of these properties (M,N, T) can be determined from triaxial compression tests on reconstituted samples. One, the Poisson’s ratio, has minimal effect and can be treated as constant (say assuming v = 0.2). But this then leaves two parameters, G and H, strongly related to soil fabric.. .And, the in situ horizontal geostatic stress needs to be measured.

The shear modulus is easily measured with modem seismic CPT equipment - it is simply a matter o f attitude. And a thorough attitude is

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essential because interpreting CPT data to infer in situ state is an inverse boundary value problem which amplifies minor approximations to substantially degrades the accuracy o f the estimate.

The plastic modulus is more difficult. It is a function o f the soil fabric and so cannot be measured on reconstituted samples. This is an avenue that needs to be explored with the SBP, and the SBP almost certainly needs to be used to determine the horizontal geostatic stress.

One can question whether the above view of CPT interpretation is specific to the mathematical idealisation used. Although the parameters used are specific to NorSand, related parameters will occur in any good constitutive model. M is simply an identity o f the critical state friction angle and that is widely accepted. / / is a plastic modulus and any work hardening model will have at least one such parameter (and many models have several). G and v will always occur because there is at least some elasticity, and in fact volumetric elasticity can be o f the same order of importance as volumetric plasticity with sands. The volumetric compressibility under shear is governed by X and it is difficult to deny its relevance since the extreme strain adjacent to the CPT takes the soil to the critical state.

It will be noticed that there is no silt content “correction” in a general framework o f penetration test interpretation based on applied mechanics.

8. AN APPROPRIATE FRAMEWORK FOR POST-LIQUEFACTION STRENGTH

Present accepted practice for estimating the postliquefaction residual strength is derived from the proposal by Seed (1987): Measured penetration resistance is adjusted to what might have been obtained at a vertical effective stress o f 1 tsf and the residual strength is taken as a simple function of this adjusted resistance with the function being obtained by back analysis o f previous failures. There are two objections to this formulation. First, correlation cannot establish causality - applied mechanics is needed. Second, Seed’s method for cyclic liquefaction takes the same normalised penetration resistance and correlates it to a cyclic stress ratio - both o f Seed’s proposals cannot be correct since in one instance it is asserted that the adjusted penetration resistance

has the dimension o f stress while in the other instance it is asserted to be dimensionless. Of course, neither might be correct since neither is based on applied mechanics...

A further regrettable aspect o f Seed’s work is the reliance on the SPT. It is disingenuous to suggest that adopting the SPT is essential to use the experience base: half the case histories have estimated, not measured, penetration resistances and the CPT resistances can be equally well estimated as the SPT. And some o f the other case histories have CPT data as well or instead o f the SPT. Because the SPT has such poor repeatability, its behaviour is uncertain, and the dimensions o f N, are inconsistently understood, any proper approach using mechanics should use the CPT as this tests has no such problems.

If we rely on critical state theory, and insist on undrained conditions in the small (ie no bifurcation, localisation etc), then for the usual semi-log idealisation o f the CSL the postliquefaction strength Sr is given by:

Sr / Po = M J2 exp (- ij/ZA.) [10]

assuming that plane strain strength is similar to that in triaxial compression and where X is expressed in terms o f natural logs and po is the initial mean stress. Substituting [8] in [10] gives:

S r / p o - M , / 2 (Q/k)" [11]

Equation [11] shows that critical state theory requires that field experience be viewed in terms of the dimensionless framework o f the ratio s /p ’o versus the dimensionless resistance Q. Further, if Q/k is used rather than Q, the effect o f stress level, critical friction angle, shear modulus etc is readily incorporated (although this key data is usually unknown for most case histories so that crude estimates have to be used at present). In a way, using Q/k could be viewed as the proper fines content “correction” . Figure 12 plots such field experience reported by Seed (1987), Poulos(1989) and Seed & Harder (1990). The size o f the uncertainty bands shown represents the differences in back-analysed strengths and inferred characteristic penetration resistance between the different authors. The k values used are those for Ticino sand recognising the stress level bias given in Sladen (1989) - undoubtedly better estimates are possible, but this approximate representation is sufficient for now.

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characteristic normalized dimensionless penetration resistance, Q/k

Fig 12. Comparison of critical state predictions with case histories

Equation [11] is also plotted on Figure 12 assuming typical parameters for sand with a few percent silt and K^=0.7.

There are clear trends in the case history data, even with the relatively crude way in which k has been estimated and using the same geostatic stress ratio for each case history etc. But why does [11] so poorly fit the data?

The poor fit o f [11] is not a consequence of measurement errors or errors in interpreting the penetration test data. This topic has been discussed at length in the literature in connection with Nerlerk, with Hicks & Boughrarou (1998) conveniently summarising the issues. The key issue at Nerlerk is that, while a liquefaction failure can be readily computed if the sand is assumed loose enough, such looseness cannot be reconciled with the CPT resistances actually measured. Conversely, if the CPT is used to infer state, then the sand seems anomalously weak. Nerlerk lies in the middle o f the case histories plotted on Figure 12, and the issues raised at Nerlerk are there in all the other case histories. What is going on? NorSand offers insight.

9. LOCALISATION

The mathematical derivation o f NorSand is based on Drucker’s (1959) stability postulate. Interestingly, this same postulate also leads us to expect instability in NorSand when (with total stresses):

( n ¿n < 0 [12]

During [12], undrained conditions can no longer be maintained locally. For semi-loose soils such as the silty sand shown on Figure 10, the postpeak strength drop corresponds to the occurrence of [12]. At such time, the steady state doctrine (Poulos, 1981) that the soil will proceed to critical conditions at the same void ratio as it existed in prior to loading is false.

The introduction o f instability criteria [12] to geomechanical constitutive models is a very new and active subject so definitive conclusions are as yet difficult. However, intriguingly, the minimum strength expected from NorSand while

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[12] applies is the low point o f the post-peak strength drop, which is what was previously discussed as the pseudo steady state. At this low point, work hardening restarts and the behaviour becomes stable. The minimum post-peak strength predicted using NorSand for typical clean sand parameters (M=1.2, N=0.2, H^200, G/p’=250, v=0.2, >^=0.02) is plotted on Figure 12 as triangles for 5 numerical simulations - there is no closed form solution for NorSand on any stress path, and numerics are essential. A further 2 simulations lie well o ff the upper strength on the graph. The computed behaviour has been fitted by bi-linear trend line.

There is a remarkable coincidence o f the minimum undrained strength predicted by NorSand and the case history data. Interestingly, NorSand does not show a gentle upward curve that might have been expected as a variation on [10] but instead shows only modestly increasing residual strengths with density until the normalised penetration resistance Q/k> 2.2. This normalised resistance approximately corresponds to the soil being denser than \\Jq < -0.08.

Dilatancy is commonly defined as the ratio of strain rates, as earlier in this paper. However, there is an alternative definition found in some of the literature (eg Lindenberg & Koning, 1981) in which a dilatant sand is taken to have a net volumetric increase at peak strength - in effect the integration o f the more usual definition over a particular stress path. For sands, net volumetric expansion occurs when i|/o<-0.06 for in axial compression. Which is intriguingly like the numerically found density at which instability no longer occurs under undrained conditions with NorSand.

The strain during which low post-liquefaction strengths persist depends on the availability of pore water to move into the intensely shearing zone - which depends on the size of the stressed zone and the imposed strain rates. And there is also evidence (Jefferies et al, 1990) that the plastic modulus is itself a function of the size of the stressed zone. Further, the natural variability of even uniform deposits means that there will be some zones still contracive and being sources o f pore water while others, perhaps only a few metres away, are trying to dilate. The recent work by Popescu et al (1997) indicates than something quite close to the loosest void ratio actually is the controlling value for a deposit during liquefaction.

10. CONCLUSION

NorSand closely predicts undrained behaviour of sand and silty sands. And, NorSand captures those aspects o f soil behaviour which are often cited as indicating non-unique CSLs while being itself theoretically based on a unique CSL. Much o f the confusion over non-uniqueness has arisen from the limitations o f the testing equipment and misunderstanding the nature o f the CSL.

Applying NorSand to post-liquefaction strengths shows errors in existing practice. On one hand Seed’s approach is incorrect on simple dimensional grounds as well as having no basis in mechanics. But on the other hand, the steady state school is based on dogma inconsistent with the underlying theory.

NorSand indicates that an instability limit (in the sense o f applied mechanics, not the erroneous collapse surface idea) controls post liquefaction strength and this sensibly matches the case history experience. Correspondingly the stress path, elastic modulus, and in situ plastic hardening become important.

The above conclusions are neither comfortable nor convenient. Perhaps limit equilibrium calculations based on some simple undrained strength should never be used for postliquefaction analysis and that fully coupled finite element solutions are essential And site investigation requires more than cmde SPTs..

Practically, NorSand offers reasonable guidance . But, we need to understand localisation, how it scales with size o f the stressed domain, and how it is affected by non-uniform conditions. These leading edge research issues in geomechanics are actually crucially important to confident engineering with semi-loose soils.

Of course, both theory and experience show that you stay out of undrained trouble provided VKo<-0.i......

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Bishop, A.W. (1966); Strength o f soils as engineering materials. 6* Rankine Lecture. Geotechnique 16, 89-130.

Collins I.F., Pender M.J. and Yan W. (1992); Cavity expansion in sands under drained loading consitions. International journal for Numerical and Analytical Methods in Geomechanics 16, 3-23.

Comforth, D.H. (1964); Some experiments on the effect o f strain condition on the strength o f sand. Geotechnique 14, 143-167.

Drucker, D.C. (1951); A more fundamental approach to stress-strain relations. Proc. US National Congress o f Applied Mech., ASME, p487-491.

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Gerogiannopoulos, N. & Brown, E.T. (1978); The critical state concept applied to rock. Int. J. Rock Mech. And Mining Science and Geomechanics Abstracts 15, p i -10.

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Ishihara, K. andWatanabe, T. (1976); Sand liquefaction through volume decrease potential. Soils and Foundations 16, 61-70.

Jefferies, M.G. (1993). NorSand: a simple critical state model for sand. Geotechnique 43, 91-103.

Jefferies, M.G. (1997). Plastic work and isotropic softening in unloading. Geotechnique 47, 1037-1042

Jefferies, M.G., Been, K., & Hachey, J.E. (1990); Influence o f scale on the constitutive behaviour o f sand. 43e Can. G. Conf, Quebec, 1,263-273.

Jefferies, M.G. & Shuttle, D.A. (1998); Critical state sand mechanics. For submission to ASCE EMJ.

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Konrad, J. M. (1990a);Minimum Undrained Strength o f Two Sands. ASCE, JGED 116,No. 6, 932-947.

Konrad, J. M. (1990b); Minimum Undrained Strength Versus Steady State Strength o f Sands. ASCE, JGED, Vol. 116, No. 6, pp. 948-963.

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Matsuoka, H. & Nakai,T. (1974); Stress-deformation and strength characteristics o f soil under three different principal stresses. Trans. JSCE 6,pl08-109.

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Popescu, R., Prévost, J.H. & Deodatis, G (1997); Effects o f spatial variability on soil liquefaction: some design recommendations. Geotechnique 47, 1019-1036.

Poulos, S. J. (1981), “The Steady State o f Deformation”, ASCE, JGED 107, 553-562.

Poulos, S. J., Castor, G., and France, J. W.(1985), “Liquefaction Evaluation Procedure” , ASCE, JGED 111,772-792.

Seed, H.B. (1987); Design problems in soil liquefaction. ASCE JGED 113, 827-845.

Seed, R.B. & Harder, L. (1990); SPT-based analysis o f cyclic pore pressure generation and undrained residual strength. Seed Memorial Symp 2, 351-376.

Shuttle, D. & Jefferies, M. (1998); Dimensionless and unbiased CPT interpretation in sand. IJNAMG 22,351-391.

Sladen J.A. (1989); Problems with interpretation of sand state from cone penetration test. Geotechnique 39, 323-332.

Yu, H.S. (1994); State parameter from self boring pressuremeter tests in sand. ASCE JGED 120,2118-2135.

Yu, H.S. (1996); interpretation ofpressuremeter unloading tests in sands. Geotechnique 46, 17-31.

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Zienkiewicz, O.C. & Naylor, D J. (1971); The adaption o f critical state soil mechanics theory for use in finite elements. Proc. Roscoe Memorial Conf 537-547. Foulis.

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Physics and Mechanics of Soil Liquefaction, Lade & Yamamuro (eds) © 1999 Balkema, Rotterdann, ISBN 90 5809 038 8

Influence of grain-size characteristics in determining the liquefaction potential o f a soil deposit by the energy method

J. Ludwig Figueroa, Adel S.Saada & Mark D. RokoffDepartment of Civil Engineering, Case Western Reserve University, Cleveland, Ohio, USA

Liqun LiangGRL and Associates Incorporated, Cleveland, Ohio, USA

ABSTRACT: The significant influence o f parameters such as relative density and effective confining pressure in determining the amount o f unit energy required for hquefaction was previously demonstrated. Similarly, it was found that the miit energy was nearly independent o f the shear strain amplitude and the loading rate. Grain-size distribution has been traditionally identified as one o f the most important factors affecting the liquefaction characteristics o f sands. Torsional shear liquefaction testing o f several soils with different grain- size characteristics made possible the development o f a simple statistical relationship including relative density, effective confining pressure and well known grain-size distribution parameters such as unifonnity coefficient and coefficient o f curvature, to determine the amount o f unit energy required for liquefaction. Inclusion o f the latter two parameters considers the influence o f particle size range as well as symmetry and shape o f the gradation curve on the unit energy level required for liquefaction. Such statistical regression equation provides a measure o f the resistance o f a soil to liquefaction, in terms o f energy per unit volume. This value can then be compared with the unit energy induced by a credible earthquake as determined by a suitable site response model to vertically propagating shear waves, to detennine the hquefaction potential o f a soil deposit.

1 INTRODUCTION

Following the original introduction o f the energy concept in the analysis o f the densification and liquefaction o f cohesionless soils by Nemat-Nasser and Shokooh (1979), a number o f experimental and theoretical investigations were conducted to establish relationships between the pore water pressure developed during motion and the dissipated energy; as well as to study the influence o f the amphtude of the shear strain, the confining pressure, the relative density, the soil type, the loading pattern and the fi*equency o f excitation on the level o f energy needed for liquefaction [Simcock et al (1983), Berrill and Davis (1985), Law et al (1990), Figueroa (1990) and Figueroa and Dahisaria (1991), Figueroa et al. (1994), Liang et al (1995), Kusky (1996), Kern(1996) Ostadan et al. (1996) and Figueroa et al.(1997) ].

Models for the degradation o f the maximum shear modulus and of the shear strength as a fimction o f the energy have been developed and used with a hyperbolic stress-strain relationship to provide a very effective numerical procedure that can be used to

calculate the seismic response and the energy dissipation o f a soil deposit [Liang et al (1995)].

This paper examines the influence o f particle size range as well as symmetry and shape o f the gradation curve on the unit energy level required for hquefaction. Data obtained from liquefaction testing under torsional shear o f four soils was analyzed to develop a relationship between the unit energy required for hquefaction and relative density, effective confining pressure and grain-size distribution parameters such as uniformity coefficient and coefficient o f curvature.

2 REVIEW OF PERTINENT ENERGY-BASED LIQUEFACTION RESEARCH AT CWRU

This work has encompassed extensive laboratory testing o f several granular soils, the development of degradation models based on the results o f these tests and existing theories, as well as the development o f a computer code to calculate soil response and energy dissipation based on the fimdamentals o f the energy concept. A partial summary o f this work follows.

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Grain Size Distribution

U .S . s tandard Sieve Num bers H ydrom eter

Particle Diameter (mm)

Figure 1. Grain-Size Distribution o f Studied Soils

2 .1 Torsional Shear Testing

The laboratory testing used a low frequency torsional shear device to conduct liquefaction tests on tliin- hollow cylinders. The tested soils included Reid Bedford Sand, obtained from the Reid Bedford Bend, located south o f Vicksburg, Mississippi, and Lower San Fernando Dam (LSFD) Silty Sand, obtained from the Lower San Fernando Dam, in the Los Angeles, California area. Liang (1995) also conducted liquefaction tests using LSI-30 Sand (Lapis Lustre Dried Sand). Tests were conducted on specimens at nominal relative densities o f 50, 60 and 70 percent for the Reid Bedford and LSI-30 Sands, and at relative densities ranging between 57 and 92 percent for the LSFD Silty Sand. Three initial effective confining pressures were used, namely 41.4 kPa, 82.7 kPa and 124.1 kPa; for each relative density. In addition, similar testing was conducted by Rokoif (1998) on Nevada Sand, a soil widely studied during the VELACS Project (Arulanandan and Scott,1993).

2.2 Sinusoidal Torsional Shear Tests

eccentric mechanical drive. The remaining tests on the Reid Bedford, as well as all tests on the LSFD Silty Sand were conducted with a controlled-stress type device applying a random torsional loading following a synthetic earthquake time series. Grain- size curves for each o f these soils are shown in Figure 1, whereas other index properties and grain- size characteristics are presented in Table 1.

Results o f 27 sinusoidal torsional tests on Reid Bedford Sand showed that the accumulated unit energy to liquefaction is constant for a certain combination o f parameters affecting the development o f hquefaction. The accumulated energy per unit volume (5W) absorbed by the specimen up to hquefaction can be calculated from the hysteresis loops (Figueroa et al., 1994):

= X L r . + r , - „ X / = 1 ^

where:

Y i ) ( 1)

T = shear stress; y = shear strain;n = number o f points recorded to hquefaction.

Some o f the Reid Bedford Sand and all o f the LSI-30 and Nevada Sands tests were conducted using a controlled-strain type device which apphes a sinusoidal torsional deformation, through an

Generalized relationships were obtained by Figueroa et al. (1994) by performing regression analyses between the energy per unit volume needed for hquefaction as the dependent variable and the

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Table 1. Index Properties and Classification o f Tested Sands

Pronertv R eid B edford Sand LSI-30 Sand LSFD SUtv N evada Sandu s e s G roup SP SP SM SP-SM

Specific G ravity 2.65 2.66 2.67 2.66M ax. V oid Ratio 0.85 0.83 1.22 0.82M in. V oid Ratio 0.58 0.52 0.71 0.53

D50 0.26 mm 0.39 mm 0.13 mm 0.15 mmUnif. Coeff. C„ 1.71 2.75 5.77 2.27

C oeff.of C urvat. Cc 0.92 0.99 1.48 0.95

relative density, confining pressure and amplitude of the applied shear strain as the independent variables, as follows;

Logio(bW )- 1.982 + 0.00477 0^ + 0.0116 +0.0376 r

r 2=0.942 (2)

Log|o(5W )= 2.002 + 0.00477 CTc' + 0.0116r 2=0.937 (3)

where;6W = Energy per unit volume (J/m^);Cc' = Initial effective confining pressure

acting on the sample (kPa);D, = Relative density o f the sample (%); r = Amplitude o f the applied shear strain

(%);R^= Coefficient o f determination;

Equation 2 includes all o f the parameters in the regression while equation 3 only includes two o f the three parameters (relative density and efifective confining pressure). By comparing equations 2 and 3, it can be seen that including the effect o f the amplitude o f shear strain (E) barely changes the coefficients corresponding to other parameters. It can be concluded that for the tests conducted in this program, the effect o f the shear strain amplitude (E) can be ignored m estabhshing the relationship between the energy per unit volume for liquefaction and the influence parameters.

2.3 Random Torsional Shear Tests.

Liang et al. (1995) also conducted torsional shear liquefaction tests applying a non-uniform (random) shear stress. The response time history o f the resisting shear stress and the corresponding power spectrum of these tests showed a frequency band

width similar to that o f the excitation (Liang et al.,1995).

As in the sinusoidal torsional tests, a relationship represented by Equation 4, was obtained by performing regression analyses between the energy per unit volume at the onset o f liquefaction and the relative density and the initial efifective confining pressure;

Logio(SW )= 2.062 + 0.0039 r 2=0.925

0.0124 D,(4)

Equations 3 and 4 were found to be equivalent following the statistical F-test, as described by Sen and Srivastava (1990). Thus, it can be concluded that the energy per unit volume needed to induce liquefaction is independent o f the type o f dynamic loading and can be used to evaluate the liquefaction potential o f a soil under earthquake excitation.

2.4 Rate-Dependent Torsional Shear Tests

Kusky (1996) examined the influence o f cychc torsional shear loading rate on the energy per unit volume required for liquefaction, by conducting 27 torsional shear hquefaction tests on Reid Bedford Sand at nominal Relative Density (Dr) o f 50, 60, and 70%, Initial Efifective Confining Pressure (Qc) o f 41.1, 82.7, and 124.1 kPa and Cychc Loading Rate (f) o f 0.2, 0.6, and 1.0 Hz. A regression equation relating the energy per unit volume required for hquefaction, relative density, initial efifective confining pressure, and cychc loading rate was developed, in which;

Log(ÔW )- 1.8281 + 0.0051 a'e + 0.0147 Dr- - 0.1448 f

R = 0.938 (5 )

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Analyses o f variance indicated that (f) could be removed from Equation 5 without significantly affecting the value o f the unit energy, to obtain:

Log(5W) = 1.8198 + 0.0051 a'c + 0.0147 Dr= 0.938 (6)

which demonstrates the small influence o f the loading frequency (Q in determining the level o f unit energy at the onset o f hquefaction. Kusky (1996) also concluded that the loading rate (within the tested limits) appears to have no significant influence on the size and shape o f hysteretic loops, pore water pressure build up, dissipated energy per unit volume per cycle, accumulated energy per unit volume, equivalent shear modulus, and equivalent damping ratio. Equation 6 was also foimd to be statistically equivalent to Equation 3.

2.5 Degradation Models

Figueroa et al (1997) expanded on prehminary findings by Liang (1995) regarding a degradation model, based on the energy concept, which can be used to determine the seismic response o f horizontal soil layers and the accompanying energy dissipation. The model uses the hyperbohc shear stress-strain relationship to reconstruct hysteresis loops for a granular soil.

The familiar shear stress-strain loops which result from cychc torsional loading o f a granular soil can best be described by a ‘backbone” curve. The hyperbohc model (Equation 7) proposed by Hardin and Dmevich (1972) is considered moreadvantageous because o f its simphcity, e.g., it contains only two parameters both having physical meaning, namely, the maximum shear modulus (Gm) and the shear strength ( t f ) , and the stress is expressed as an exphcit fimction o f the strain (y). Gm is the shear modulus at low shear strain and Xf is the asymptotic value o f the shear stress, developed at high shear strain.

1 + ^ YTf

(7)

It is well known that the shear modulus and the shear strength decay as pore water pressure builds up; thus, a means o f deterraining their degradation must be incorporated into the hyperbohc model. Liang (1995) proposed linear relationships between the maximum shear modulus (Gm) and the shear

strength (x f) as fimctions o f the energy per unit volume o f the form:

G„, = G „ ,« H -A<5w

1 -Ad\N

(8)

(9)

where:GmO = initial maximum or intercept

tangential shear modulusGmt, Gm = maximum shear modulus at time t

== initial or intercept shear strength= shear strength at time t

6w = dissipated energy per unit volume (kJ/m^) accumulated to time t

(5\ initial effective confining pressure (kPa)

A material parameter for property degradation model depending on the soil properties such as relative density, grain size distribution.

Data from 27 torsional shear hquefaction tests conducted by Figueroa et al. (1994) on Reid Bedford Sand was used by Figueroa et al. (1997) to examine the significance o f the degradation parameter ‘"A”. This parameter is determined by plotting both the maximum tangential shear modulus and the shear strength for each cycle against the dissipated energy per unit volume normalized with respect to the initial effective confining pressure. The ratio o f the dissipated unit energy with the effective confining pressure results in a dimensionless value identified as the normalized unit energy. The intercepts (with the vertical axis) o f the resulting linear regression curves Gmo and are used to plot the normalized shear modulus and the normalized shear strength versus the normalized unit energy. Linear regression on the normalized plots results in “A ” expressed by Equations 8 and 9. Once ‘‘A” is determined for each of the 27 tests, multivariable linear regression yields equations o f “A” as a function o f the relative density (Dr) and the shear strain ( T ) amphtude o f the form:

Shear Modulus data set:A °= 16 5 .6 - 1 .4 4 D r-9 .09T

R" 0.655 ( 10)

Shear Strength data set:

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170.63 - 1.52Dr- 15.65TR" 0.763 ( 11)

with both Dr and F in percentage.Statistical tests were conducted by Kern (1996)

on the relative significance o f Dr and F within each equation and whether or not the two equations are equivalent. She concluded that both the relative density and the apphed shear strain amplitude are significant at a level o f 0.05 with Dr being more influential in determimng A in both cases. F-test results also supported the hypothesis that Equations 10 and 11 are equivalent. Thus, any o f the two equations could be used in determining “A” to be incorporated in both the shear strength and the shear modulus degradation models expressed by Equations 8 and 9.

Shear stress-strain loops obtained during torsional shear liquefaction tests may be reconstructed by updating the shear modulus (Gm) and the shear strength (if) in the hyperbohc model, as liquefaction progresses using the degradation models expressed by Equations 8 and 9. These equations require the calculation o f the dissipated energy per unit volume (accumulated area o f the hysteresis loops) at every point where loadmg changes to unloading and where unloading changes to reloading. In addition, because of the tendency o f the stress-strain loops to shift upward with each cycle, occasionally spiraling toward infinite stress when modeling liquefaction, the scale factor ‘"c” suggested by Pyke (1979) is incorporated into the generalized hyperbohc model;

( 12)c ^r-T a

-X ac

c V g „. r - r ac

where;

± 1- (13)

with (+) for reloading and (-) for unloading, and y represent a point on the shear stress-strain curve where loading changes to unloading or unloading changes to reloading.

Hysteretic loops for all 27 tests conducted by Figueroa et al. (1994) were reconstructed using the modified hyperbohc relationship and the unit energy- based degradation equations. The unit energy for liquefaction obtained from the reconstucted loops was compared with the unit energy obtained from actual torsional shear tests. For the most part ah

points he very closely to the line o f equality indicating the high quahty o f the reconstruction process. Thus, the degradation models expressed by equations 8 and 9, could be used in the prediction of the response o f horizontal soil layers under vertically propagating shear waves; to assess their potential for hquefaction in an energy-based method.

3 EFFECT OF GRAIN-SIZE CHARACTERISTICS ON THE UNIT ENERGY TO LIQUEFACTION

Tlie influence o f grain-size on the amount of energy per unit volume at the onset o f hquefaction was initiaUy examined by conducting random-loading torsional shear tests on soils that hquefied during the Northridge Earthquake (Lower San Fernando Vahey Dam). The LSFD Silty Sand contains up to 28% of sht, as compared to a neghgible amount in the Reid Bedford Sand. Testing was conducted using the same time series o f non-uniform torsional stress as in the Reid Bedford Sand with combinations o f four nominal relative densities and three effective confining pressures for a total o f twelve tests (Figueroa et al., 1995).

The finer LSFD soil requires lower unit energy for hquefaction, within the ranges tested, than the coarser Reid Bedford Sand at the same effective confining pressure. The influence o f relative density on the energy per volume is practically ehminated with increased silt content, regardless o f the value o f the effective confining pressure, as can be seen in the foUowing equations;

L og|o(5W )- 2.484 + 0.00471 Gc' + 0.00052 D,r 2=0,995 (14)

Logio(5W )= 2.529 + 0.00474r 2=0.994 (15)

This may be the result o f modifying the kinematics o f the granular soil by the significant presence o f silt in the inter granular spaces.

Liang (1995) also used LSI-30 Sand (coarser than both Reid Bedford and LSFD Sands) to expand the study o f the effect o f soil type in determining the energy per unit volume required for hquefaction. Knowing that the effect o f loading pattern on the hquefaction resistance m terms o f energy could be ignored, ah constant-strain torsional shear hquefaction tests foUowed a sinusoidal pattern. Results o f nine tests conducted at nominal Relative Density (Dr) o f 50, 60, and 70% and Initial Effective

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Confining Pressure (a c) o f 41.1, 82.7, and 124.1 kPa allowed the development o f the following regression equation:

Logio(5W )= 2.0554 + 0.004824 Cc' + 0.01267r 2=0.888 (16)

Comparison o f Equations 3 and 16 indicate that the shghtly coarser LSI-30 Sand offers higher hquefaction resistance in terms o f the energy per unit volume than the Reid Bedford Sand, regardless o f the value o f the confining pressure. Similarly, relative density has a more significant influence on the unit energy in the LSI-30 Sand than in the Reid Bedford Sand.

The study o f the effect o f soil type in determining the energy per unit volume required for hquefaction was recently expanded by Rokoff (1998). He conducted nine torsional shear hquefaction tests on hoUow cylinders prepared with Nevada Sand at nominal Relative Densities (Dr) o f 50, 60, and 70% and Initial Effective Confining Pressure (Gc) o f 41.1, 82.7, and 124.1 kPa. A regression analysis between the energy per unit volume required for hquefaction as the dependent variable and the relative density and effective confining pressure as the independent variables yielded the expression:

Logio(6W ) = 1.33 + 0.006155 g ' + 0.0219 Dr

R = 0.882 (17)

where both the Effective Confining Pressure and Relative Density strongly affect the energy per unit volume needed for hquefaction, as determined by the corresponding coefficients.

Graia-size distribution has been traditionahy identified as one o f the most important factors affecting the hquefaction characteristics o f sands. In addition, the soil type, represented by the characteristics o f the grain-size curve, affected the energy per unit volume required for hquefaction, as determined by the individual comparisons shown above. It is then possible to develop a generalized statistical relationship including relative density, effective confining pressure and weU known grain- size distribution parameters such as imiformity coefficient and coefficient o f curvature, to detemhne the amount o f unit energy required for hquefaction. Inclusion o f the uniformity coefficient and the coefficient o f curvature considers the influence o f particle size range as well as symmetry and shape o f the gradation curve on the unit energy level required for hquefaction.

Liquefaction test data by torsional shear used to develop Equations 2 to 6 and 14 to 17 for ah four sohs: LSFD Silty Sand, Nevada, Reid Bedford and LSI-30 Sands, along with pertment parameters extracted from the grain-size curves shown in Figure 1, ahowed the development o f such relationship, in which:

Logio(5W ) = 3.6303 + 0.004964 Gc' + 0.01057 D

+ 0.2123 Cu- 2.1056 Ce

= 0.8171 (18)

where:Cu = Uniformity Coefficient Cc = Coefficient o f Curvature

This statistical regression equation provides a measure o f the resistance o f a soil to hquefaction, in terms o f energy per unit volume. As noted from Equation 18, the energy per unit volume increases with increased Cu and decreases with increased Cc.

Analysis o f variance is employed to determine the influence o f the uniformity coefficient, the coefficient of curvature, the relative density and the initial effective confining pressure on the resulting energy per unit volume required for hquefaction in Equation 18, as weh as the possibility o f interactive effects.

In the analysis o f variance factors are defined as the parameters whose effects on the dependent variable (or experimental unit. In this case the unit energy required for hquefaction ) are being examined (Mead, 1988). The fixed factors constituting the entire population o f interest are: relative density, initial effective confining pressure, uniformity coefficient and coefficient o f curvature. Tire experimental unit is the undrained, torsional shear hquefaction test, performed on a saturated, hoUow cylinder o f one o f the four types o f sands. Levels of each factor are defined as variations in the factor magnitude, as previously indicated for each soil type. A particular combination o f factors and levels forms a treatment combination, and the resulting unit energy required for hquefaction is termed a population (Nelson, 1990). With only one observation (test) for each treatment combination (population), the design forms a balanced, complete layout (Nelson, 1990).

Comparing the F values in Tables 2 and 3 for the main and interactive effects several observations are made. Variations due to relative density, initial effective confining pressure, uniformity coefficient and coefficient o f curvature are ah highly significant because their F values are much higher than F„.

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Table 2. Results o f the Analysis o f Variance (ANOVA)

Source Degrees of Freedom

Sum of Squares Mean Sum of

Sauares

F

(1) (2) (3) (4)=(3)/(2) (5)=(4)/Error

Or 3 175.44 58.48 52.12

rtr' 3 220.74 73.58 65.58

c„ 3 652.84 217.61 193.95

Cr 3 1217.90 405.97 361.82

Or CTr' 9 27.87 3.10 2.76

Or C„ 9 82.42 9.16 8.16

G / Ce 9 153.76 17.08 15.23

Gp’ C„ 9 103.71 11.52 10.27

Gp’ Cc 9 193.47 21.50 19.16

Cu Cc 9 572.18 63.58 56.67

Error 189 212.13 1.12

Total 255 3612.46 Unit Energy in kJ/m^

Table 3. F-Distribution Values

Degrees of Numerator

Freedom in:

Denominator

a Fa

3 189 0.010 3.89

Main Effect 3 189 0.025 3.19

3 189 0.050 2.66

9 189 0.010 2.51

Interactive Effect 9 189 0.025 2.19

9 189 0.050 1.93

Also, the relative sizes o f their F values indicate the relative importance (influence) o f the factors (Mead, 1988). Consequently, the coefficient o f curvature and the uniformity coefficient, representing the soil type and gradation have the strongest influence on the unit energy required for hquefaction, followed by initial effective confining pressure and relative density.

Tlie interactive effects are found to be significant when comparing the F values fisted in Tables 2 and 3. Flowever the interactive effects are probably weighed by both Cu and Cc, in view o f their high main effect values. It is noted also that the interactive effect between Dr and is low and close to the error range, as previously found by Liang (1995) and

Kusky (1996), indicating that their interactive effects do not significantly influence the unit energy to liquefaction.

4 ENERGY-BASED PROCEDURE TO DETERMINE THE LIQUEFACTION SUSCEPTIBILITY OF A SOIL DEPOSIT

Liang (1995) developed an energy-based numerical integration procedure to determine site response to dynamic loading using a one-dimensional shear beam element. By this approach, ground motions developed near the surface o f a soil deposit during an earthquake may be attributed primarily to the upward

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Figure 2. Determination o f the Liquefaction Potential o f a Soil Deposit using theEnergy Method (Liang, 1995)

propagation o f shear waves from an underlying rock layer (Idriss and Seed, 1968). The acceleration o f bedrock during an earthquake can be artificially generated or obtained from records. The numerical procedure is apphed to calculate the seismic response o f horizontal soil layers to give shear stress and shear strain histories for each layer. Then, hysteretic loops are formed and the dissipated unit energy can be calculated up to the end o f the earthquake which may be plotted against the deposit depth (Curve B in Figure 2).

The dissipated unit energy during the earthquake is compared with the resistance o f a soil to hquefaction, in terms o f energy per unit volume, as expressed by Equation 18. This amount can be plotted against depth (Curve A in Figure 2) for a particular soil, as the effective confining pressure increases with depth in the deposit.

Whether or not hquefaction occurs and if it does occur its location may be decided easily by comparing the amount o f the unit energy calculated in last two steps,. If the amount o f dissipated unit energy determined from site response is larger than the resistance; hquefaction is expected to develop.

demonstrated. These two parameters consider the influence o f particle size range as weU as symmetry and shape o f the gradation curve on the unit energy level required for hquefaction.

A statistical relationship hicluding relative density, effective confining, uniformity coefficient and coefficient o f curvature was developed to determine the amount o f unit energy required for hquefaction. Such a regression equation provides a measure o f the resistance o f a soil to hquefaction, in terms o f energy per unit volume, which can be compared with the unit energy determined from site response analysis to predict whether or not hquefaction is possible.

Both the coefficient o f curvature and the uniformity coefficient have more influence in the energy per unit volume for hquefaction than the effective confining pressure and the relative density. The unit energy increases with increased Cu and decreases with increased Cc.

For the most part, coarser soils require higher unit energy for hquefaction than finer soils, as expected. Similarly, the influence o f relative density on the unit energy decreases as the finer fraction o f the soil increases.

5 CONCLUSIONS ACKNOWLEDGMENT

The strong influence o f grain-size distribution parameters such as uniformity coefficient and coefficient o f curvature, to determine the amount o f unit energy required for hquefaction was

This research was supported by the National Science Foundation under Grants MSS-9215006, CMS- 9411018 and CMS-9416151

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REFERENCES

Arulanandan, K. and Scott R. F. "Verification o f Numerical Procedures for the Analysis o f Soil Liquefaction Problem," Eds:, V ol.l, A.A.BALKEMA /ROTTERDAM /BROOKFIELD.1993.

Benin, J.B. and Davis, R.O., "Energy Dissipation and Seismic Liquefaction o f Sands: RevisedModel," Soils and Foundations, Vol. 25, No. 2, pp. 106-118, 1985.

Figueroa, J.L., "A Method for Evaluating Soil Liquefaction by Energy Principles," Proceedings, Fourth U S. National Conference on Earthquake Engineering, Palm Springs, CA - May 1990.

Figueroa, J.L., Dahisaria, M.N., "An Energy Approach In Defining Soil Liquefaction," Proceedings, Second International Conference on Recent Advances in Geoteclmical Earthquake Engineering and Soil Dynamics - University o f Missouri-Rolla - March 1991.

Figueroa, J.L., Saada, A.S., Liang, L. and Dahisaria, M.N., "Evaluation O f Soil Liquefaction By Energy Principles," Jounial o f the Geotechnical Engineering Division, ASCE, Vol. 120, No. 9, Proc. Paper 1841, pp. 1554-1569, 1994.

Figueroa, J.L., Saada, A.S., and Liang, L. "Effect o f Grain Size on the Energy per Unit Volume at the Onset o f Liquefaction” Proceedings, Third international Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics - University o f Missouri-Rolla - April, 1995

Figueroa, J.L., Saada, A.S., Kern, D. and Liang, L. “Shear Strength and Shear Modulus Degradation Models Based on the Dissipated Energy” Accepted for Publication in the Proceedings o f the XFV International Conference in Soil Mechanics and Foundation Engineering, Hamburg, Germany, 1997.

Hardin, B.O. and Dmevich, V.P. 1972. “Shear Modulus and Damping o f Soils: Design Equation and Curves.” in Proceedings o f ASCE 98 (SM7). pp. 667-692.

Idriss, I.M. and Seed, H.B. “Seismic Response of Horizontal Sod Layers,” Journal o f Soil Mechanics and Foundations Division, ASCE, Vol. 94, SM4, 1003 - 1031. 1968.

Kern, D.W. “Vahdation o f Degradation Models Based on the Unit Energy for Evaluating the Liquefaction Potential o f Soils,” M.S. thesis. Dept o f Civil Eng., Case Western Reserve Univ., Cleveland, OH. 1996.

Kusky P. J., “Influence o f Loading Rate on the Unit Energy Required for Liquefaction,” M.S. thesis. Dept o f Civil Eng., Case Western Reserve Univ., Cleveland, OH. 1996.

Law, K.T., Cao, Y.L., and He, G. N., "An Energy Approach for Assessing Seismic Liquefaction Potential," Canadian Geotechnical Journal, Vol. 27, pp. 320-329, 1990.

Liang, L., J.L. Figueroa, and A.S. Saada, "Liquefaction Under Random Loading: A Unit Energy Approach," Journal o f the Geotechnical Engineering Division, ASCE, Vol. 121, No. 11, Proc. Paper 8034, pp. 776-781, 1995.

Liang, L. ‘T)evelopment o f an Energy Method for Evaluating the Liquefaction Potential o f a Soil Deposit.” Ph D. thesis. Dept, o f Civil Engineering, Case Western Reserve University, Cleveland, OH. 1995.

Mead, R., “The Design o f Experiments: Statistical Principles for Practical Apphcations,” Cambridge University Press, 1988.

Nelson, P. R. ‘TIandbook o f Statistical Methods for Engineers and Scientists,” FI. M. Wadsworth, editor, McGraw-Hill. 1990.

Nemat-Nasser, S., Shakooh, A., "A Unified Approach to Densification and Liquefaction o f Cohesionless Sand in Cychc Shearing," Canadian Geotechnical Journal, Vol. 16, pp. 659-678, 1979.

Ostadan, F., Deng, N. and Arango, I. ‘"Energy-Based Method for Liquefaction Potential Evaluation, Phase I Feasibility Study,” National Institute of Standards and Technology, Report NIST GCR 96- 701, August, 1996.

I^ke, R. 1979. “Nonlinear Soil Models for Irregular Cychc Loadings,” Journal o f the Geotechnical Engineering Division, ASCE, Vol. 105, No. GT6, pp. 715-726.

Rokoff, M.D. “Influence o f Grain-Size Characteristics in Determining the Liquefaction Potential o f a Soil Deposit by the Energy Method.” M.S. thesis. Dept o f Civil Eng., Case Western Reserve Univ., Cleveland, OH. 1998.

Sen, A. and Srivastava, M., "Regression Analysis: Theory, Methods and Apphcations," Springer- Verlage, New York Inc., 1990.

Simcock, J., Davis, R.O., Berrih, J.B. and Mahenger, G., "Cychc Triaxial Tests with Continuous Measurement o f Dissipated Energy," Geotechnical Testing Journal, GTJODJ, Vol. 6, No. 1, pp. 35-39, 1983

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6 Methods o f characterizing post-liquefaction deformation

Physics and Mechanics of Soil Liquefaction, Lade& Yamamuro (eds)© 1999 Balkema, Rotterdam, ISBN 90 5809 038 8

Experimental measurement o f the residual strength o f particulate materials

S.L. Kramer &C.H.WangUniversity of Washington, Seattle, Wash., USA

M.B. ByersHWA Geosciences Incorporated, Lynnwood, Wash., USA

ABSTRACT; Several different approaches to the estimation o f residual strength have been proposed. The earliest geotechnical approach was based on laboratory experiments. Later, geptechnical approaches based on insitu testing coupled with the backcalculation o f apparent shear strengths from actual flow failures have been developed. However, very high uncertainties are associated with the residual strengths estimated using each o f these approaches. The residual strength o f particulate materials is important in other fields outside o f mainstream geotechnical engineering. Evaluation o f debris flow behavior has led to fundamental research on the flow behavior o f particulates. The rheology o f concentrated suspensions o f particles in liquids is also important in industrial processes such as the hydraulic transport o f materials such as coal, powders, minerals, and animal feeds. Experimental and analytical research in those fields have produced results that could be o f use in evaluating residual strength o f liquefied soil. A review o f past experimental approaches to the measurement o f residual strength, including approaches developed outside the field o f geotechnical engineering, is presented. The strengths and weaknesses o f each experimental approach are discussed. The desirable characteristics o f an experimental apparatus that would combine the strengths, and minimize the weaknesses, o f existing devices are described. Finally, fabrication o f such an apparatus is described.

INTRODUCTION

The shear strength o f liquefied soil is one o f the most critical problems in contemporary geotechnical earthquake engineering practice. This strength, variously referred to using terms such as residual strength, steady state strength, and others, dominates the evaluation o f postearthquake stability o f dams, embankments, foundations, retaining walls, and other structures. Small variations in assumed residual strength can lead to large variations in estimated stability, and large variations in costs o f remediation and retrofitting.

A number o f different approaches have been proposed for evaluation o f residual strength. While laboratory testing-basdd procedures were initially favored, empirical procedures have recently become more popular in practice. Nevertheless, laboratory tests offer unique

capabilities for investigating the effects o f important parameters such as fines content, particle structure, initial stress conditions, and stress path on residual strength. With recent developments in undisturbed sampling using ground freezing techniques, laboratory tests may well see renewed use in site-specific residual strength evaluation.

STEADY STATE AND RESIDUAL STRENGTH

The concept that a granular soil will have some limiting shear strength at large strain levels originated with the critical state work of Casagrande in the 1930s. Since that time, great advances have been made in developing a fundamental understanding o f the shearing resistance o f soils at both low and high strain

249

levels. These advances occurred more quickly, however, with respect to cohesive soils than the types o f cohesionless soils typically involved in liquefaction failures. Indeed, a number o f important advances in the understanding o f the constitutive behavior o f liquefiable soils have been made only recently.

Castro (1969) established that cohesionless soils o f different densities could exhibit three general types o f behavior under undrained loading conditions, and termed these liquefaction, limited liquefaction, and dilation. As illustrated in Figure 1, these three types o f behavior are quite different over a broad range o f strain levels. At large strains, however, all converge to a state in which they shear at constant volume and constant effective confining pressure and with constant shearing resistance. This state, with the additional constraint o f constant velocity, has been defined as the steady state o f deformation (Castro and Poulos, 1977; Poulos, 1981). The actual value o f the steady state shearing resistance is strongly influenced by density, but loose and dense soils alike can reach the steady state o f deformation. The strains at which they do so, however, differ considerably. Very loose soils may reach the steady state at shear strains on the order o f 10 percent. Soils o f intermediate density that exhibit limited liquefaction behavior may reach a temporary minimum shearing resistance (at the quasi-steady state) after which they dilate to eventually reach the steady state. While the quasi-steady state may be reached at shear strains o f 1 0 percent or less, the steady state is generally not reached until shear strains o f 50 to 100 percent or more. Dense soils that reach the steady state through a process

Figure 1. Three types o f stress-strain behavior in undrained triaxial com pression (after Castro, 1969).

o f continuous dilation may not do so until they have been sheared to very large strains.

The shear strength o f a liquefied soil plays a critical role in the evaluation o f post-earthquake stability and strongly influences the cost o f potential remediation. As such, the availability o f accurate procedures for estimation o f this strength is extremely important. Poulos et al. (1985) proposed a procedure based on carefulundisturbed sampling, triaxial testing o fundisturbed and reconstituted specimens, and post-test density correction. The procedure is critically dependent on the retrieval o f undisturbed samples and on the accurate measurement o f insitu void ratio. However, undisturbed sampling and insitu void ratio measurement o f the loose, saturated soils most susceptible to liquefaction has always been difficult. Small errors in either can lead to significant errors in steady state strength. As a result, a number o f attempts have been made at backcalculation o f strength from case histories. Because all o f the conditions required for existence o f the steady state o f deformation rarely exist in the field (due to partial drainage, changing velocity, etc.), the strength backcalculated from case histories is commonly referred to as the residual strength. In a sense, the steady state strength may be thought o f as a special case o f the residual strength.

SHEARING RESISTANCE OF PARTICULATES AND PARTICULATE SUSPENSIONS

The available shearing resistance o f particulate materials has been investigated in detail in a number o f fields outside o f geotechnical earthquake engineering. The rheology o f such ‘‘granular fluids” has been studied in relation to phenomena such as debris flows, powder transport, and grain handling. Because these applications generally involve rapid flow s (high shear strain rates), fundamental principles o f fluid mechanics and thermodynamics have been applied to understand their behavior. Bagnold (1954) considered the behavior o f neutrally buoyant particles suspended in a viscous fluid. Using suspensions o f solid particles that would be considered quite dilute by geotechnical

250

engineering standards, Bagnold identified three flow regimes - a macroviscous regime at low strain rates where any rate effects are due to fluid viscosity, a grain-inertia regime at high strain rates where rate effects arise from momentum transfer during particle collisions, and a transitional regime where the effects o f both iluid viscosity and grain inertia may exist. Making a number o f simplifying assumptions, Bagnold was able to show the existence o f a component o f shear stress proportional to strain rate (arising from pore fluid viscosity) in the macroviscous regime and a component proportional to the square o f strain rate (arising from momentum transfer during particle collisions) in the inertial regime. Takahashi (1993) used Bagnold’s basic concepts, along with the existence o f a yield strength to derive the quadratic constitutive equations

T = ry + C \^ i y + { c 2P ,d - + p J - ) Y "

p = P s+ P Ï + < ^ " 4 Ps^~ ÿ

( 1)(2)

where t is the shear stress, p is the excess pore fluid pressure, ;Kis the shear strain at depth, z, Zy is the yield strength, // the viscosity o f the pore fluid, ps is the particle density, is the density o f the mixture, / ’is the mixing length, and py is the particle-to-particle contact stress. Takahashi assumed the yield stress, Zy, to be o f Mohr- Coulomb form generalized to include any yield strength contributed by the pore fluid. Takashashi’s model suggests the potential existence o f three components o f apparent shearing resistance: (1) a “static” component that results from the frictional resistance o f the soil skeleton and exists even as the strain rate vanishes, (2) a macroviscous component that results from the viscosity o f the pore fluid and is proportional to strain rate, and (3) and grain- inertia component that results from interparticle collisions and is proportional to strain rate squared. The existence o f the second and third components is implicitly neglected in typical geotechnical engineering calculations - both for prediction o f flow slide behavior and for backcalculation o f residual strengths from flow slide case histories.

The relative importance o f the three components o f apparent shear resistance to liquefaction flow slides can investigated using dimensional analysis. Following the derivation o f Iverson, but substituting standard geotechnical engineering nomenclature, dimensionless Savage, Bagnold, and friction flow numbers can be expressed as

^ Sav ~

N

(G ,.-l)g zta n (á

p â ' -y

f , ^ B a g /N f n c -

(3)

(4)

(5)

where e is void ratio. Experimental evidence suggests that grain-inertia stresses dominate frictional stresses in dry granular flows when NSav is greater than about 0.1 (Savage and llutter, 1989). Bagnold’s experiments indicated that grain-inertia stresses dominate viscous stresses when Npag exceeds a value o f approximately 100. Targe values o f suggest that frictional stresses exceed viscous stresses.

Consider a liquefaction-induced flow slide such as the infinite slope shown in Figure 2. Assuming that the flow slide results from liquefaction and subsequent shearing in a 1 -m- thick layer o f uniform sand (D 50 = 1 mm, e = 1 .0 , ^=^30 degrees) beneath a 1 -m-thick non-liquefied layer and results in a surface flow velocity o f 1 0

m/sec, the resulting dim ensionless flow numbers are:

Nsav - 0.00019 Nßag ^ 27 Nfyic = 1.42 . 10'

Figure 2. Hypothetical slope susceptible to flow sliding.

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Taken-together, these dim ensionless flow numbers indicate that grain-inertia effects and viscous effects are likely to be relatively small in typical liquefaction-induced flow slides. Examination o f the forms o f the dim ensionless flow numbers, however, suggest that this may not always be the case - particularly for thin, fast flow slides involving coarse-grained materials with viscous pore fluid (it should be noted that fines suspended within the porewater during flow can contribute to the apparent viscosity o f the pore tluid). Backcalculation o f residual strengths from such flow slides should consider the possible effects o f viscous and grain-inertia strength components.

EXPERIMENTAL MEASUREM ENT OF RESIDUAL STRENGTH

The analyses o f the preceding section suggest that the residual shear strength o f soils involved in liquefaction-induced flow slides is predominantly frictional in origin. The insignificance o f rate- dependent components resulting from viscous and grain-collision effects, indicates that residual strengths may be measured in quasi-static (low strain rate) tests. However, recent experimental results (e.g. Yamamuro and Lade, 1998) have shown significant rate effects at low to moderate strains in silty sands; their data suggests that such rate effects may influence residual strengths as well. Therefore, a review o f experimental methods for measurement o f residual strength must include methods that are well-suited to investigation o f rate effects.

The follow ing paragraphs present a brief review o f experimental methods that have been used to measure the shear strength o f particulate materials at high strain levels. Many o f the methods w ill be familiar to geotechnical engineers, but some have been developed and used in other technical fields. The purpose is to point out the advantages and limitations o f each method, so that the desirable characteristics o f methods for such measurements can be clearly identified.

Triaxial Test

The original, pioneering work on steady state

shear strength o f sand (Castro, 1969) was conducted using undrained triaxial testing, and the triaxial test has historically been the most commonly used experimental tool for measurement o f such strengths. In this well- known test, a cylindrical sample o f saturated soil is sealed within a rubber membrane and typically compressed axially under stress- or strain- controlled conditions. Axial stress, effective confining pressure, and axial strain are usually measured and used to infer shear stresses and shear strains. Triaxial apparatuses can be fitted with lubricated caps and bases to improve strain uniformity, but this approach has not commonly been used for steady state or residual strength measurement.

Castro (1969) performed an extensive series o f strain-controlled, consolidated-undrained triaxial tests to investigate the large-strain shearing resistanee o f loose sands. The results o f these tests formed the impetus for the eoneept o f the steady state o f deformation (Castro and Poulos, 1977; Poulos, 1981). Central to the steady state concept is the assumption that the steady state strength depends solely on void ratio,i.e. that it is not inOuenced by depositional and stress effects known to affect low-strain behavior.

Others (e.g. Vaid et al., 1990) have used triaxial tests to show that steady state conditions are different for compressive and extensional stress paths, particularly when the soil is deposited in a manner that produces an inherently anisotropic structure. Specifically, pluviated sands that exhibit dilative behavior in compression may exhibit contractive behavior (with lower residual strength) in extension.

Advantages and Limitations

The triaxial test is one o f the oldest and most commonly used tests in geotechnical engineering. It can be used to test both ‘"undisturbed” and reconstituted specimens, and procedures for the preparation and testing o f both are well established. Reconstituted specimens can be prepared in a variety o f different ways to produce specimens with different particle structures, friaxial tests can be performed under stress- or strain-controlled conditions. Drainage is easily controlled - both drained and undrained tests are

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commonly performed. However, the triaxial tests does have limitations for measurement o f residual strength. Primary among these is the limited range over which uniformity o f strains exist. Because triaxial specimens o f liquefiable soil tend to bulge at large (greater than about 5 to 10 percent axial) strain, inferred residual strengths become inaccurate due to uncertainty in the actual shape o f the specimen. This restriction is significant - it has a deleterious effect on the accuracy o f the measured strength that arises just as the conditions are o f greatest interest. In addition, this restriction may preclude the reliable achievement o f steady state conditions for soils that reach the steady state at higher strain levels. The maximum shear stresses induced in the triaxial test are on planes inclined to the generally horizontal planes o f soil deposition; the large lateral displacements observed in actual flow failures are strongly influenced by shearing on depositional planes. Furthermore, the triaxial test does not allow the continuous rotation o f principal stress axes that occurs during actual flow failures.

Direct Simple Shear Test

Cyclic simple shear testing has frequently been used to investigate the initiation o f liquefaction, but less frequently for investigation o f large-strain behavior. Three primary types o f simple shear apparatuses are available: the Cambridge-type (hinged, rigid platens), NGl-type (wire-reinforced membrane), and SGI-type (stacked metal rings).

Constant-volume direct simple shear tests have been performed using two different procedures. The first involves saturating the test specimen and applying loads so quickly that the finite permeability o f the soil prevents volume change. External pore pressure transducers are typically used with this procedure to allow monitoring o f effective stress changes. The second approach uses dry specimens and maintains constant volume conditions by mechanically constraining the height o f the loading cap (relative to the base). Changes in the normal stress acting on the specimen can be interpreted as being equivalent to the changes in effective stress that would have occurred if the specimen had been saturated (Dyvik et al., 1987).


The simple shear test is also well established in geotechnical engineering. It can be used to test both ''undisturbed” and reconstituted specimens, and procedures for the preparation and testing o f both are well established. Drainage is easily controlled - both drained and undrained tests are commonly performed. Reconstituted specimens can be prepared in a variety o f different ways to produce specimens with different particle structures. Direct simple shear tests can be performed under stress- or strain-controlled conditions. Unlike the triaxial test, the direct simple shear test allows rotation o f principal stress axes and applies shear stresses on depositional planes. However, the lack o f complementary shear stresses on the sides o f the specimen require that the moment produced by the horizontal shear stresses be balanced by non-uniformly distributed normal and shear stresses. This non-uniformity can be reduced by increasing the specimen width:height ratio, but ratios greater than 8:1 are required (Kovacs and Leo, 1981) to render its effects insignificant; simple shear devices with such width:height ratios are quite uncommon. The magnitude o f strain that can be imposed on simple shear specimens is also limited due to the potential for “pinching” in the corners o f the specimen that take on acute angles during shearing.

Ring Shear Test

The ring shear test is frequently used to measure the large-strain shearing resistance o f cohesive soils, and has also been considered for measurement o f the residual strength o f liquefied soil. In the ring shear test, a circular soil specimen is placed in the annular space between an upper and lower plate. Following application o f a normal stress, torsion is applied to the upper (or lower) plate to produce shearing on the horizontal plane between the two plates.


Like all rotational tests, the ring shear test has the advantage o f being able to reach virtually unlimited strain levels. Preparation o f

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reconstituted specimens is relatively straightforward. However, stress and strain conditions within the specimen are highly non- uniform. The ring shear apparatus is capable o f applying known shear stresses on a horizontal (depositional) shearing plane. However, volume change can only be constrained globally - local volume change on the failure plane can neither be controlled nor measured. For example, contraction (or dilation) on the failure plane could be masked by extension (or compression) in the unsheared portions o f the specimen above and below the failure plane.

Coaxial Concentric-Cylinder Test

Rotating concentric cylinders have frequently been used in fluid mechanics as viscometers - devices that measure fluid viscosity. Couette- flow shear cells, consisting o f concentric cylinders that rotate about a common axis, have been used to measure the shearing behavior o f concentrated suspensions o f particulates in fluids. An example o f such a device is shown in Figure 3. Bagnold (1954) used such a device (although with a flexible inner wall) with varying concentrations o f neutrally buoyant spherical particles to define the three flow regimes discussed previously.

Cheng and Richmond (1978) noted that viscometric experiments generally led to the observation o f (a) proportionality o f normal and

Figure 3. Schematic illustration o f concentric-cylinder device (after Savage and M cK eow n, 1983)

shear stresses, (b) dilation and contraction, depending on normal stresses and strain rates, (c) the formation o f shear bands, (d) step-like fluctuations in measured stresses as particles jammed, locked, and released, (e) different rate effects in loading and unloading, and (f) significant boundary effects when the particle size is large relative to the shear gap. Savage and M cKeown (1983) performed a series o f tests in this type o f device to investigate the effects o f varying particle size, wall roughness, and wall rigidity on flie behavior o f various concentrations o f neutrally buoyant spheres. Smooth walls were found to be susceptible to particle slip, particularly at higher particle concentrations. Rough walls were thought to have increased the magnitude o f particle-velocity fluctuations and, therefore, the grain-collision stresses. At high particle concentrations, rigid zones o f ‘‘locked” particles were observed, causing shearing to take place in a thin band. A lso, intermittent locking or jamming o f particles spanning the entire shear gap was thought to have occurred, particularly in tests with rigid walls.


The coaxial concentric-cylinder device is mechanically simple and has the ability to achieve virtually unlimited strains. However, it suffers from several important limitations. The shear stresses are not uniform in the radial direction, a fact that could lead to non-uniform straining. Also, shearing takes place on planes that are perpendicular to depositional planes. Because the annular shear gap is generally thin and deep, preparation o f representative geotechnical specimens is difficult. Finally, consolidation to a desired effective normal stress prior to shearing is problematic.

Annular Shear Cell Test

Annular shear cells have been used for over 60 years to investigate soil strength under static loading conditions (very low strain rates). Hvorslev (1936, 1939) developed such a cell (prior to development o f the modern split-ring ring shear device) for soil testing and others (e.g. Carr and Walker, 1967; Bridgewater, 1972) have

254

used them to investigate particulate flow tor the design o f materials handling equipment. An annular shear cell consists o f an annular trough into which a soil (or other particulate material) can be placed (Figure 4). The bottom surface o f the trough is intentionally roughened, but the sides are machined to a very smooth finish. An annular loading plate with a roughened bottom and dimensions that allow it to fit just within the annular trough is placed on top o f the specimen. The loading plate is then used to apply a specified normal stress to the surface o f the specimen. After application o f normal stress, torsion is applied to the lower (or upper) plate to shear the specimen. Measurement o f torque and rotation allow, with due consideration o f specimen geometry, determination o f shear stress and shear strain.

Savage and Sayed (1984) developed an annular stress cell with a 38.1 mm wide, 28.1 mm deep, and 254 mm mean diameter trough, and a loading assembly that allowed very high strain rates (approximately 1.6 revolutions per second). Normal loads were applied under stress-controlled conditions, thereby allowing dilation or contraction to occur. Dilation was observed during shearing; the amount increased with increasing strain rate. Rate dependence was generally observed to be consistent to that proposed by Bagnold (1954) for the grain inertia regime, except at high particle concentrations where the effects o f static friction became increasingly important. Interestingly, Savage and

Sayed also observed that the ratio o f shear to normal stress during flow, which increased with increasing strain rate, was higher for looser packings than denser packings. This behavior was noted to be consistent with that displayed by granular materials flowing down rough inclined chutes.


The annular shear cell is mechanically simple and allows development o f virtually unlimited strains. Normal stresses are easily applied, both under stress- and strain-controlled conditions, and easily measured. Specimen preparation is relatively straightforward, and shearing stresses can be applied to depositional planes. On the other hand, shear strains are not constant, increasing in the radial direction. A lso, shear stresses resisting rotation can develop between the specimen and the stationary inner and outer walls o f the annular channel.

Rolling Sleeve Viscometer Test

An interesting, recently developed test is the rolling-sleeve viscometer (Johnson and Martosudarmo, 1997). The rolling-sleeve viscometer is based on a principle o f finite-strain theory - that an ellipse transforms itself into another ellipse if the internal deformation is homogeneous. In the rolling-sleeve viscometer, a mass o f soil is placed within a flexible sleeve such that it rests on a platform with a nearly elliptical shape. One end o f the platform is then raised (Figure 5) so that the sleeve rolls down the slope; the terminal (constant) velocity o f the sleeve is

R ubbersleeve

apparatus (after Savage and Sayed, 1984). Figure 5. Rolling-sleeve viscometer setup.

255

measured. The average shear stress within the mass can be obtained knowing the slope angle, soil density, and ellipse dimensions and the strain rate from the rolling velocity and ellipse dimensions. Johnson and Martosudarmo (1997) used the rolling-sleeve viscometer to investigate the rheological behavior o f sand mixed with slurries o f water and clay and found good general agreement with theoretical predictions.


The rolling-sleeve viscometer certainly allows large strains to develop in both loose and dense soils although the actual distribution o f the strains (and, therefore, the stresses) during How is difficult to determine. Preparation o f uniform, reconstituted specimens is not as straightforward as for some o f the previously described tests, but it appears that appropriate procedures could be developed to allow testing o f a variety o f sands and silt/sand mixtures. The testing equipment and instrumentation is extremely simple. There are, however, a number o f limitations associated with the rolling-sleeve viscometer test. First, the effects o f gravity and the boundary condition o f the underlying rigid platform does not allow the sleeve to form a perfect ellipse. There are also end effects to consider; Johnson and Martosudarmo used a cylindrical sleeve with the ends tied o ff with string. Because the sleeve is thin and flexible, the cross-sectional size and shape o f the sleeve can change as the material within contracts and/or dilates.

DESIRABLE CHARACTERISTICS OF EXPERIMENTAL APPARATUS FOR RESIDUAL STRENGTH M EASUREMENT

The preceding review o f experimental test capabilities allows identification o f a number o f desirable characteristics for a hypothetical experimental apparatus for measurement o f residual strength. The primary desirable characteristics are:

1. Ability to induce uniform stresses and strains in the test specimen - an ideal experimental apparatus should induce pure shear throughout

the entire test specimen so that stresses and strains measured on the boundary o f the specimen are representative o f the actual stresses and strains that exist within the specimen.

2. Ability to achieve large strains in loose and dense sands - the residual or steady state strength is only reached at large strains. For loose sands or silty sands that show no dilative behavior, the residual strength is reached at shear strains on the order o f 10 percent, but denser sands require shear strains o f 50 to 100 percent or more.

3. Ability to consolidate specimen but shear under constant volume conditions - important to be able to consolidate to stress levels found in the field; rapid flow failures in saturated materials occur under constant \olum e conditions.

4. Ability to test both undisturbed and reconstituted specimens - carefully sampled test specimens (e.g. from samples obtained by freezing) can give very useful results, even though most testing for residual strength measurement is conducted using reconstituted specimens.

5. Ease o f specimen preparation - a great deal o f useful information can be obtained from tests on reconstituted specimens, and it should be possible to prepare uniform reconstituted specimens with different grain structures.

6. Loading on depositional planes - because most natural liquefiable soils are deposited on nearly horizontal planes and because lateral deformations are strongly influenced by shearing on horizontal planes, it is desirable that an experimental device be able to apply shear stresses parallel to depositional planes.

A brief summary o f the extent to which each o f the previously described tests exhibit these desirable characteristics is presented in Table 1. It is apparent that none o f the tests possess all o f the desired characteristics. It is also apparent that only the rotational devices have the very large- strain capabilities required for measurement o f residual strength across a broad range o f soil densities. O f these, the ring shear and annular

256

Table 1. Desirable characteristics o f residual strength test devices.

Characteristic ►

Test

Uniform stresses and

strains

Large strains in loose and dense soils

Consolidation/constant-

volumeshearing

Undisturbedand

reconstitutedspecimens

Ease of reconstituted

specimen preparation

Loading on depositional

planes

Triaxial Withlubricatedends

S hear strains up to approx. 75% in loose soils with lubricated ends

Yes/Yes Both Good No

Direct simple shear

At high widthiheight ratios (>8)

No Yes/Yes Both Good Yes

Ring shear No Yes Yes/No Reconst, and undist. with small scale apparatus

Good Yes

Concentriccylinder

T,Y vary radially

Yes No/Yes Reconstitutedonly

Fair No

Annular shear cell

T,Y vary radially, and I exists on side walls

Yes Yes/Yes Reconst, and undist. with small scale apparatus

Good Yes

Rolling-sleeveviscometer

Approximate!y

Yes 999/799 Reconstitutedonly

Fair No

shear cell tests have a number o f desirable characteristics, but each has one critical flaw. In the case o f the ring shear test, the variation o f shear strain (and shear stress) across the height o f the test specimen is unacceptably large. In the case o f the annular shear cell, the shear stresses that exist on the stationary side walls o f the trough are unacceptably large.

DEVELOPMENT OF A RING SIMPLE SHEAR DEVICE

Development o f an experimental test apparatus

that possesses all o f the previously described desirable characteristics o f a device for measurement o f residual shear strength is possible, at least in concept. Such an apparatus can be visualized as a modified ring shear device or as a modified annular shear cell. In the former case, it could consist o f a ring shear device modified so that shearing occurred on an infinite number o f ‘'failure planes” spanning the full height o f the specimen. In the latter, it could consist o f an annular shear cell with side walls that moved as the specimen sheared, thereby eliminating the resisting shear stresses that develop when the side walls remain stationary.

Figure 6 . (a) Schematic illustration o f ring simple shear loading system and (b) stacked ring specim en retention system (outer diameter o f inner rings is 13 inches, inner diameter o f outer rings is 18 inches, specimen height is 2.5 inches).

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These interpretations would become equivalent in the case o f a ring simple shear (RSS) device that would apply normal and rotational shearing forces to an annular specimen constrained between stacks o f inner and outer frictionless rings. Ideally, there would be an infinite number o f frictionless rings, but a prototype device has been fabricated at the University o f Washington with 10 inner and outer rings (Figure 6). Preliminary testing o f the RSS device is currently underway.

CONCLUSIONS

A wide variety o f different laboratory tests have been used to measure the rheological properties o f particulate materials. These tests can impose different stress and strain paths on a soil specimen and load it at a wide range o f strain rates. Each o f the tests have specific advantages and limitations.

Improved understanding o f residual strength, and the factors that control it, is one o f the most critical research needs in geotechnical earthquake engineering. Laboratory tests can play an important role in the development o f this understanding.

The ring simple shear test retains the advantages o f the ring shear and simple shear tests while eliminating the critical limitations o f each. It offers the capability o f producing uniform stress and strain conditions from low to virtually unlimited strain levels. It can be performed at very low to very high strain rates and under stressor strain-controlled conditions. Based on the results o f preliminary tests, the ring simple shear device appears to offer considerable promise for advances in the understanding o f residual strength.

REFERENCES

Bagnold, R.A. (1954). “Experiments on a gravity- free dispersion o f large solid spheres in a Newtonian fluid under shear,” Proceedings, Royal Society o f London, Series A, Vol. 225, pp. 49-70.

Bridgwater, J. (1972). “Stress-velocity relationships for particulate solids,” ASME Paper 72-MH-21.

Carr. J.F. and Walker, D.M. (1967). “An annular shear cell for granular materials,” Powder Technology, Vol. 1, pp. 369-373.

Castro, G. (1969). “Liquefaction o f sands,” Harvard Soil Mechanics Series 87, Harvard University, Cambridge, Massaehusetts.

Castro, G. and Poulos, S.J. (1977). “Factors affecting liquefaction and cyclic mobility,” Journal o f the Geotechnical Engineering Division, ASCE, Vol. 106, No. GT6, pp. 501- 506.

Cheng, D.C.-H. and Riehmond, R.A. (1978). “Some observations on the rheologieal behaviour o f dense suspensions,” Acta Rheologica, Vol. 17, pp. 446-453.

Dyvik, R., Berre, T., Laçasse, S., and Raadim, B. (1987). “Comparison o f truly undrained and constant volume direct simple shear tests,” Geotechnique, Vol. 37, No. 1, pp. 3-10.

Hvorslev, M.J. (1936). “A ring shearing apparatus for the determination o f the reearing resistance and plastic flow o f so il,” Proceedings, International Conference on Soil Mechanics and Foundation Engineering, Cambridge, Massachusetts, Vol. 2, pp. 125-129.

Hvorslev, M.J. (1939). “Torsion shear tests and their place in the determination o f the shearing resistance o f soils,” Proceedings o f ASTM, Vol. 39, pp. 999-1022.

Iverson, R.M. (1997). “The physics o f debris flows,” Reviews in Geophysics,

Johnson, A.M. and Martosudarmo, S.Y. (1997). “Discrimination between inertial and macroviscous flows o f fine-grained debris with a rolling-sleeve viscometer,” Proceedings, Debris-Flow Hazards Mitigation: Mechanies, Prediction, andAssessment, American Society o f Civil Engineers, 817 pp.

Kovacs, W.D. and Leo, E. (1981). “Cyclic simple shear o f large-seale samples: Effects o fdiamter to height ratio,” Proceedings, International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, St. Louis, Missouri, Vol. 3, pp. 897-907.

Poulos, S.J. (1981). “The steady state o f deformation,” Journal o f the Geotechnical Engineering Division, ASCE, Vol. 107, No. GT5, pp. 553-562.

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Poulos, S.J., Castro, G., and France, J.W. (1985). “Liquefaction evaluation procedure,” Journal o f Geotechnical Engineering, ASCE, Vol. I l l , No. 6, pp. 772-792.

Savage, S.B. and Butter, K. (1989). The motion ofa finite mass o f granular material down a rough incline,” Journal o f Fluid Mechanics, Vol. 199, pp. 177-215.

Savage, S.B. and M cKeown, S. (1983). “Shear stresses developed during rapid shear o f concentrated suspensions o f large spherical particles between concentric cylinders,” Journal o f Fluid Mechanics, Vol. 127, pp. 453-472.

Savage, S.B. and Sayed, M. (1984). “Stresses developed by dry cohesionless granular materials sheared in an annular shear cell,” Journal o f Fluid Mechanics, Vol. 142, pp. 391-430.

Takahashi, T. (1993). “Dynamics o f inertial and viscous debris flow s,” Proceedings o f International Workshop on Debris Flows, Kagoshima, Japan, pp. 43-55.

Vaid, Y.P., Chung, E.K.F., and Kuerbis, R.J.(1990). “Stress path and steady slate,” Canadian Geotechnical Journal, Vol. 27, No. l ,p p . 1-7.

Yamamuro, J.A. and Lade, P.V. (1998). “Steady- state concepts and static liquefaction o f silty sands,” Journal o f Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 124, No. 9, pp. 868-877.

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Void redistribution in sand following earthquake loading

Ross W. BoulangerDepartment of Civil and Environmental Engineering, University of California, Davis, Calif, USA

ABSTRACT: The potential for void redistribution in the field and its effect of the in situ shear strength of liquefied soil are poorly understood and subject to continued debate. A mechanism for void redistribution in an infinite slope under post-earthquake loading conditions is described by consideration of the in situ loading paths that can occur under post-earthquake conditions and the results of triaxial tests designed to represent specific in situ post-earthquake loading paths. The mechanism is illustrated by application to an example problem. Void redistribution is shown to be a phenomenon that may be more pronounced at the field scale than at the laboratory scale.

1 E^iTRODUCTION

Evaluating potential instability in liquefying soils, or estimating the in situ residual shear strength (Sr) of a liquefied soil, remain a difficult task with considerable uncertainty. Recent experimental studies have contributed to an improved understanding of factors affecting Sr, and helped to reduce large differences between Sr values back-calculated from case histories and Sr values obtained from laboratory testing of field samples (with appropriate corrections for disturbance per the steady state approach). Laboratory testing by several investigators has shown that Sr, or the shear resistance over a large range of strains, is affected by stress path (extension vs. simple shear vs. compression), fabric, consolidation stress, fines content, and strain level. A basic question remains, however, whether or not laboratory testing fully captures the mechanisms of instability that act in situ.

In this regard, void redistribution due to earthquake loading has been identified as potentially having an important influence on the in situ residual shear strength, or steady state strength, of saturated sands (e.g., NRC 1985). The process of void redistribution within a globally undrained sand mass was termed Mechanism B by NRC (1985), and a potential situation where it might occur was illustrated by the schematic in Figure 1. Of related interest is Mechanism C (NRC 1985) where the outward flow of pore water due to excess pore pressures in a sand

mass, such as illustrated in Figure 2, could spread into overlying soils and/or cause a loosening of the upper portion of the sand. In this case, the sand is neither globally nor locally undrained.

The potential significance of in situ void redistribution, particularly with regard to mechanism B (Fig. 1), remains controversial (e.g.. Seed 1986, McRoberts & Sladen 1992, Castro 1995). Void redistribution was first observed to occur within laboratory sand specimens (Casagrande & Rendon 1978, Gilbert 1984). Casagrande (1980) subsequently suggested that void (or water content) redistribution was a phenomenon associated with cyclic laboratory tests and may not reflect in situ behavior. Since then, physical modeling studies have provided evidence that void redistribution may be more pronounced at the “field” scale. Extensive void redistribution resulting in the formation of water inter-layers between stratified soil layers was observed in shaking table models by Liu & Qiao (1984). Arulanandan et al. (1993) reported redistribution of densities within a globally-undrained sand layer, confined by clay layers, within a model embankment shaken in a centrifuge, but there are several limitations in the interpretation of these^Tesults as noted by Castro (1995). Centrifuge tests of gentle slopes by Kutter & Fiegel (1994) showed that the presence of a lower permeability soil layer affected the distribution of deformations with the slope; A concentration of deformations developed at the interface of a liquefying sand layer and an overlying

261

EFFECTIVE STRESSES

Figure 1. Mechanism B by NRC (1985) - Example of a potential situation for void redistribution within a globally undrained sand layer.

Figure 2. Mechanism C by NRC (1985) - Example of a potential situation for failure by spreading of excess pore pressures with global volume changes.

silt layer, whereas deformations were uniformly distributed in homogenous slopes of sand. Formation of a water inter-layer between an overlying silt layer and an underlying sand layer was inferred from pore pressure records in dynamic centrifuge model tests by Dobry et al. (1995). The introduction of thin silt layers into otherwise homogenous sand models on a shaking table, was shown by Kokusho (1998) to lead to the formation of water inter-layers or void redistribution that had a significant effect on the failure mode and timing of deformations (i.e. during versus after shaking).

Disagreement in the profession regarding the potential for earthquake-induced void redistribution in the field and its implications for design would seem to stem from two main issues. First, field observations only reflect the consequences of any void redistribution, and hence its occurrence or nonoccurrence in situ can only be inferred rather than conclusively demonstrated. For example, observations of ground deformations developing in the field after earthquake shaking has ended could be attributable to pore pressure or void redistribution, but the magnitude, extent, and location of such redistribution is impossible to directly determine and the contributions of other potential mechanisms generally cannot be ruled out. Secondly, physical mechanisms for void redistribution as derived from soil mechanics principles are not well developed, and the unanswered theoretical questions can lead to doubts as to the significance of such a mechanism.

Boulanger & Truman (1996) describe a mechanism for void redistribution using a specific example of post-earthquake loading of an infinite gentle slope, with a saturated sand layer confined above and below by less permeable layers, and with

the sand in a dilatant state (i.e., dense of critical) prior to earthquake loading. The mechanism is described by consideration of (1) the in situ loading paths that can occur under post-earthquake conditions and (2) the results of triaxial tests designed to represent specific in situ post-earthquake loading paths. In terms of the NRC (1985) classifications, the mechanism corresponds to type B as shown in Figure 1.

This workshop presentation is based on the paper by Boulanger & Truman (1996), and reviews the mechanism they described as a basis for suggesting that void redistribution is not just an artifact of laboratory testing, but rather is a phenomenon that may be more pronounced at the field scale. The implication is that the in situ Sr of liquefied soil depends on the in situ boundary and loading conditions (stratigraphy, permeabilities, earthquake characteristics, stress path) as well as on the pre-earthquake soil properties and state. It is hoped that this presentation will foster further discussion of the possible role of void redistribution in the field and its implications for practice.

2 POST-EARTHQUAKE CONDITIONS IN AN INFINITE GENTLE SLOPE

Consider an infinite slope consisting of a 3 m thick layer of sand at a relative density of Dr~55% with overlying and underlying layers of low permeability clay (Fig. 3). The ground surface slopes at 5 degrees, each soil layer is parallel to the ground surface, and the ground water table is parallel to the ground surface at a depth of 2 m. At its current Dr of 55%, the sand is dense of critical and thus is not susceptible to flow liquefaction. Properties of this sand layer will be taken

262

static Shear Stress (kPa)

0 4 8

03■o

O

3 -

4 -

5 -

6 -

“T "r

Effective Normal Pore Pressure Stress (kPa) (kPa)

0 50 0 50-1— I— I— — I— I— —

-L

\

-\

_L

Pore W ater Head (m)

0 2 4“T nr

Mobilized Friction Angle (degrees)

0 20 40’— r

I

T"

-L I

VolumetricStrain

- 0.02 0.00 0.02 “ T “T T

J _ I _L

Pre-earthquake conditions.

Maximum pore pressure condition after earthquake loading, assuming locally undrained behavior. Reference condition; hydrostatic pore pressures with top of layer mobilizing peak friction angle.

Figure 3. Example analysis of void redistribution within a confined sand layer in an infinite slope.

as those of Sacramento River sand as described by test results in this paper.

In the following analysis of earthquake and postearthquake behavior, it will be assumed that pore water flow does not occur, and thus the sand is locally undrained, during earthquake shaking. The void redistribution mechanism is not altered by this assumption while its illustration is greatly simplified.

Suppose that strong earthquake shaking brings the entire sand layer to the maximum possible pore pressure after shaking, which will be called the limiting residual pore pressure (ui,r). For sand that is initially dense of critical, the Ui,r corresponds to the soil maintaining the minimum effective stress required to resist the applied static shear stress (Ishihara & Nagase 1980, Boulanger et al. 1991). This is illustrated in Figure 4 showing the relationship between limiting residual excess pore pressure ratios (ru,r = Aui r/avcO and horizontal static shear stress ratios (a = Ts/cJv/) for undrained cyclic simple shear tests on Fuji river sand at Dr of 53-64% (Ishihara & Nagase 1980). Residual excess pore pressure ratios (i.e., when the cyclic stress passes through zero) reach a limiting value after a peak single amplitude shear strain of about 3%, and remain essentially unchanged during additional cyclic loading to shear strains in excess of 10% (note that the

Figure 4. Limiting residual pore pressure ratio versus initial static shear stress ratio in undrained cyclic simple shear tests (after Ishihara and Nagase 1980)

specimens were not susceptible to flow deformations under the imposed stresses). Ishihara & Nagase (1980) showed that the limiting ru,r in such simple shear tests can be estimated as:

r.. =1- (I)

263

where (|)'mob is the mobilized friction angle on horizontal planes, Ovc' is the vertical consolidation stress, and Xs is the static horizontal shear stress. The limiting residual pore pressure (ui,r) is then the sum of the initial hydrostatic pore pressure (Uo) and the limiting residual excess pore pressure (Aui,r= Tu,r CTvc')- Consequently, ui,r within the sand layer of our infinite gentle slope can be estimated from the Xs acting parallel to the ground surface and the total stress acting normal to the ground surface (cTn.o) as:

u, -tan(CJ (2)

where Xs/tan((|)'niob) equals the minimum <7n' required for stability of the slope. Values of Xs and Gn.o are obtained using the standard equations for an infinite slope. The variation of pre-earthquake Uo and postearthquake ui,r with depth in this example problem are shown in Figure 3, with Ui,r calculated for (j)'niob = 35°.

Consider the post-earthquake loading conditions that are imposed on the sand just beneath its contact with the overlying low permeability soil (point T in Figure 3): (1) the static shear stress parallel to the ground surface remains constant as long as the slope is stable; and (2) the sand (at point T) is subjected to water inflow driven by the upward hydraulic gradient across the sand layer. The response of sand to these loading conditions is illustrated by the following triaxial test results.

3 SAND BEHAVIOR IN PCV-CST TESTS

The response of sand to the post-earthquake loading conditions described in the previous section was investigated by performing post-cyclic, volumetricstrain-controlled, constant shear stress triaxial (PCV- CST) tests. These tests were performed on specimens previously subjected to an anisotropically consolidated, undrained cyclic triaxial (ACU-CT) test.

All triaxial tests were performed on specimens of a modified Sacramento River sand prepared by moist tamping to about 35 and 55% relative density (Dr). This sand has a maximum particle size of 0.295 mm, a 20th percentile particle size (D20) of 0.196 mm, zero fines (<No. 200 sieve), a coefficient of uniformity (Cu) of 1.3, a coefficient of curvature (Cc) of 0.98, a minimum dry density of 1.333 g/cm^, and a maximumdry density of 1.635 g/cm

0 50 100 150 200 250 300 350 400Mean Effective Stress, p ' (kPa)

Figure 5. Stress path for an ACU-CT test on a Dr = 57% specimen of Sacramento river sand.

3.1 Undrained Cyclic Triaxial (ACU-CT) Results

ACU-CT tests began with Gsc' = 200 kPa and Kc= Gic'/asc'= 1.2. A uniform cyclic stress ratio (q/2a3c') = 0.25 was applied at 0.1 Hz until the specimens reached a peak (single amplitude) axial strain of 8a = 3%. The q-p' stress path for a specimen at Dr =57% is shown in Figure 5. Initially, cyclic loading caused ru (= Au/asc') to progressively increase while 8a remained small. As approached unity, 8a increased rapidly until the test was stopped. As expected, ru approached unity only when the specimen was under isotropic stresses, and ru decreased as extension or compression loads were applied. The <t>'mob during the compression side of the cyclic loads reached a maximum values of about 36° for the Dr= 57% specimen, while a maximum value of about 34° was reached for a Dr =36% specimen. These values are comparable to the < 'moh obtained at similar p' in isotropically consolidated, undrained triaxial compression (ICU-TC) tests. In addition, these (l)'mob are 1° to 3° greater than the critical state friction angle

which is about 33°.

3.2 Post-Cyclic Constant Shear Stress (PCV-CST) Results

PCV-CST tests were performed on specimens previously subjected to an ACU-CT test. After the ACU-CT test had produced 8a = 3%, q was brought back to the pre-cyclic value of 40 kPa [= (Kc - 1 )cj3c']

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5 10 15Axial Strain (%)

Figure 6. Results of PCV-CST and ICD-TC tests on Dr ~ 55% specimens of Sacramento river sand.

while the sample was kept undrained. The deviatoric load was held constant for the remainder of the test; note that the test results will show q decreasing slightly because of the increase in cross-sectional area as £a increased. Very small increments of water were then injected into the sample at a controlled rate through a valve in the backpressure line. Between increments of injection, the valve was closed to ensure equalization of u throughout the specimen and system lines. Note that u, as', and £a are not controlled, and thus they describe the response of the specimen to the imposed PCV-CST loading conditions.

Shown in Figure 6 are the results of the PCV-CST test on the Dr= 57% specimen used in the ACU-CT test in Figure 5. In Figure 6, point A represents the conditions at the end of the ACU-CT cyclic loading. Initial injection of water moved the specimen from point A to B as u initially increased, thereby reducing p' [= (ai'-i-2a3')/3] and increasing ( |) 'm o b (i.e., increasing q/p') to a peak value ((|)'p) of 41°. At point B, u was also at a local maximum with a corresponding minimum p', and the volumetric strain (8v) was about 2.3%. Continued injection of water moved the specimen from point B to C as the u decreased slightly,

thereby increasing p' and reducing (])'m o b towards a value of about 36°. Note that as the specimen continued to dilate, there eventually was a slight increase in u and slight decrease in p' as £a reached about 18%, but this is attributed to the progressive decrease in q with increasing cross-sectional area of the specimen (i.e., deviator load, not stress, was being held constant).

Similar results were obtained for a PCV-CST test on a Dr = 36% specimen (Figure 6). Initial injection of water increased u and brought (|)'mob to its peak (¡)'p=35°. At (¡)'p, £v was about 1.3%. Continued injection decreased u as (j)'mob decreased to about 34°. As for the Dr= 57% result in Figure 6, u eventually increased again as £a reached about 21 % because of the increasing cross-sectional area.

3.3 Comparison With Drained Triaxial Compression (ICD-TC) Results

Isotropically consolidated, drained triaxial compression (ICD-TC) tests were performed on one specimen at Dr =36% and another specimen at Dr =50%. Both tests were initially consolidated to asc' = 200 kPa and then rebounded to asc' = 25 kPa

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prior to testing. Both specimens showed a dilatant response with (|)'p of 35° and 41°, respectively, which are about equal to the (j)'p obtained in corresponding PCV-CST tests. All PCV-CST and ICD-TC tests had (t)'mob~ 34°at 8a ~ 15-20% which suggests they were approaching ( | ) 'c v

Results of a ICD-TC test on a Dr = 50% specimen are also shown on Figure 6 for comparison with the PCV-CST result. As (|)'p was mobilized, 8v during the PCV-CST and ICD-TC tests are very similar. In effect, the PCV-CST and ICD-TC tests produced directly comparable behavior because the PCV-CST test is essentially a drained test with different loading constraints.

4 POST-EARTHQUAKE VOID REDISTRIBUTION IN AN INFINITE GENTLE SLOPE

Post-earthquake behavior of the sand layer in the infinite gentle slope example (Fig. 3) can now be evaluated by reference to the behavior observed in the PCV-CST tests. As stated before, Ui,r values within the sand layer were estimated by Equation 2 with 'mob = 35° (based on the ACU-CT tests) and assuming

locally undrained conditions during earthquake shaking. After shaking has ceased, the distribution of ui,r (and corresponding hydraulic gradient) will cause an upward seepage of pore water.

At the top of the sand layer (point T in Fig. 3), the inflow of water will initially cause u to rise to a post- cyclic maximum (Upc,max) as the sand dilates and mobilizes its (|)'p. Using Equation 2 with (|)'p = 41° (a reasonable value for Dr== 55%), u at the top of the sand layer can rise slightly to Upc,max = 51.8 kPa from ui,r=50.4 kPa as the sand dilates. Any continued inflow of water at point T would then cause u to drop as (|)'niob drops below (|)'p and towards (¡)'cv. During this process, the sand at point T would continue to dilate until it had reached a critical state condition with a corresponding Ucv=49.8 kPa (Equation 2 with ( | ) ' c v = 33°). When point T has reached critical state, it should be noted that its "steady state" strength, if it were loaded undrained at this time, would be equal to Ts acting parallel to the ground surface. Any further inflow of water to point T would cause instability of the infinite slope, as the sand would simultaneously experience a slight increase in u, a slight dilation under the reduced effective stress, and a drop in its steady state strength below that required to maintain stability of the slope. A schematic of the possible c-lnp' and Ts-cJn' path for sand at point T, as described above, is

Figure 7. Schematic of the possible Q-lnp' and Ts-Cn path for sand at the top of the confined sand layer.

shown in Figure 7. The potential for instability due to void redistribution depends on the post-earthquake consolidation/seepage pattern in the sand layer.

Post-earthquake consolidation/seepage produces very different conditions in the upper and lower portions of the sand layer. As pore water seeps upwards, the lower portion of the sand layer will consolidate; i.e., u decreases and the sand densifies slightly. Near the top of the sand layer, the inflow of pore water will cause dilation of the sand by an amount that depends on its capacity for dilation and the volume of incoming water. A useful reference condition is a hydrostatic distribution of u over depth (i.e., no hydraulic gradient perpendicular to the slope) that is anchored at point T by its Upc,max- Pore pressures at T cannot exceed Upc,max without instability of the slope. Therefore, if the slope is to remain stable, the final steady distribution of u cannot be above this reference condition. The reference condition for (|)'p = 41°, as marked on Figure 3, crosses the ui,r line at point S. Point S corresponds to a theoretical transition in behavior; the sand will consolidate below S, and will dilate above S. For this example, the thickness of the dilating zone is only 0.23 m.

The maximum volumetric increase that can be accommodated above S while maintaining stability

266

(denoted by Ydii) can be estimated as the integral of £v induced as u rises from the ui,r line to the reference condition. The maximum volumetric decrease that may be produced below S due to consolidation (denoted by Vcon) can be estimated as the integral of £v induced as u decreases from the uir line to the reference condition. If Vdii is less than Vcon, then there is a strong potential for instability of the slope. Estimating Vdii and Vcon based on the reference condition is reasonable because if dilation exceeds that required to develop ([)'p at T, then (1) (l)'mob will progressively decrease towards (|) 'c v at T, (2) u will decrease at T, (3) the thickness of the dilating zone will progressively decrease, (4) the potential Vcon will progressively increase, and (5) thus the potential for instability increases rapidly.

For the example in Figure 3, Vcon was calculated using Ae = X,/n(l+Aav7av') with X = 0.0053 to fit post- cyclic consolidation test data, and Vdii was calculated numerically by correlating £v to (|) 'm o b based on the PCV-CST results in Figure 6. The resulting estimates were Vdii = 0.0017 m /m" and Vcon= 0.0122 mVm . Since Vcon > Vdii, the slope in Figure 3 would be expected to become unstable with the upper portion of the sand layer dilating to a state where its steady state strength is less than the shear stress required for stability (e.g., path A to E in Fig. 7). Interestingly, if the sand layer were less than about 1.8 m thick (with its top still at a 3.0 m depth), then the preceding analysis would suggest that the slope could remain stable.

The example in Figure 3 was re-analyzed with the properties of the sand layer taken as those of Sacramento River sand at a Dr of 35%. For this case, the thickness of the dilating zone (between points T and S in Fig. 3) was only 0.07 m compared to the 0.23 m obtained with Dr= 55%. Furthermore, the sand layer would have to be less than about 0.6 m thick to remain stable, compared to the 1.8 m maximum stable thickness obtained with Dr= 55%.

These analysis results are sensitive to the input parameters, and thus additional research is needed on measuring and analyzing the stress-strain behavior of sand under these post-earthquake loading conditions. Regarding the PCV-CST tests, the equipment needs to be modified to improve its control of this loading path, and the effect of bifurcation on the test results needs to be considered. Numerical analyses of this transient problem are needed to address several issues, including the importance of pore water seepage during shaking, the behavior of the overlying low permeability soil at its contact with the confined sand layer, and two-dimensional effects. These testing and

analysis limitations do not, however, affect or alter the basic mechanism of void redistribution described in this paper.

The preceding simplified analysis of a confined sand layer in an infinite slope shows that the potential for instability by void redistribution (1) increases as the thickness of the sand layer increases, (2) increases as the Dr decreases (i.e., Vdii decreases and Vcon increases), (3) develops as a thin zone of soil directly beneath the overlying lower permeability layer progressively dilates to a steady state strength less than that required for stability, and (4) can be driven by in situ gradients of stress and pore pressure that are not recreated in laboratory tests. The primary conclusion drawn from these observations is that void redistribution is not just an artifact of laboratory testing, but rather is a phenomenon that may be more pronounced at the field scale.

5 CONCLUSIONS

A mechanism for void redistribution within a confined sand layer in an infinite, gentle slope under postearthquake loading conditions is described by consideration of (1) the in situ loading paths that can occur under post-earthquake conditions and (2) the results of PCV-CST triaxial tests designed to represent specific in situ post-earthquake loading paths. An example analysis of an infinite slope shows that void redistribution is likely to develop under certain field conditions, and can be driven by in situ gradients of stress and pore pressure that are not recreated in laboratory tests.

The primary conclusion is that void redistribution is not just an artifact of laboratory testing, but rather may be a phenomenon that is more pronounced at the field scale. The implication is that the in situ Sr of liquefied soil depends on the in situ boundary and loading conditions (stratigraphy, permeabilities, earthquake characteristics, stress path) as well as on the pre-earthquake soil properties and state. Considerable research is needed to better understand the contribution of void redistribution to instability in liquefied soils and to assess how it can be explicitly accounted for in design.

ACKNOWLEDGMENTS

This workshop presentation is based on the paper by Boulanger & Truman (1996), for which S. P. Truman performed the laboratory tests. Funds for the triaxial research equipment were provided by the National

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Science Foundation, under award number BCS- 9310669.

REFERENCES

Arulanandan, K., H. B. Seed, C. Yogachandran, K. Muraleetharan, & R. B. Seed 1993. Centrifuge study on volume changes and dynamic stability of earth dams. J. Geotechnical Engineering, ASCE 119(11):1717-1731.

Boulanger, R.W., R. B. Seed, & C. K. Chan 1991. Liquefaction behavior of saturated sands under uni-directional and bi-directional monotonic and cyclic simple shear loading. Report UCB/GT-90- 08, Univ. of California, Berkeley, 521 pp.

Boulanger, R. W. and S. P. Truman 1996. Void redistribution in sand under post-earthquake loading. Canadian Geotechnical]., 33:829-833.

Casagrande, A. 1980. Discussion. J. Geotechnical Engineering Div., ASCE 105(6):725-727.

Casagrande, A. 1984. Reflections on some unfinished tasks. First Nabor Carrillo Lecture of the Mexican Society for Soil Mechanics presented at the 6th National Meeting of the Society in November, 1972, and published in 1984.

Casagrande, A. & F. Rendon 1978. Gyratory shear apparatus design, testing procedures. Technical Report S-78-15, Corps of Engineers Waterways Experiment Station, Vicksburg, Mississippi.

Castro, G. 1995. Discussion. J. Geotechnical Engineering, ASCE 121(7):572-273.

Dobry, R., V. Taboada & L. Liu 1995. Centrifuge modeling of liquefaction effects during earthquakes. Proc. Inti. Conf. on Earthquake Geotechnical Engineering, Tokyo, Japan, 3:1291- 1324.

Fiegel, G. L. and B. L. Kutter 1994. Liquefaction- induced lateral spreading of mildly sloping ground. J. Geotechnical Engrg, ASCE 120(12):2236-2243.

Gilbert, P.A. 1984. Investigation of density variation in triaxial test specimens of cohesionless soil subjected to cyclic and monotonic loading. Report No. GL-84-10, Corps of Engineers Waterways Experiment Station, Vicksburg, MS.

Ishihara, K. & H. Nagase 1980. Closure to Ishihara & Yamazaki (1980), Soils and Eoundations, JSSMFE, 20(1).

Liu, Huishan & Taiping Qiao 1984. Liquefaction potential of saturated sand deposits underlying foundation of structure. Proc. Eighth World Conf. Earthquake Engineering, Vol. HI, San Francisco.

McRoberts, E. C. & J. A. Sladen 1992. Observations on static and cyclic sand-liquefaction

methodologies. Canadian Geot. J., 29(4):650-665. NRC, National Research Council 1985. Liquefaction

of soils during earthquakes. National Academy Press, Washington, D.C.

Seed, H.B. 1986. Design problems in soil liquefaction. J. Geotechnical Engrg., ASCE, 113(8):827-845.

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Physics and Mechanics of Soil Liquefaction, Lade& Yamamuro (eds) © 1999 Balkema, Rotterdam, ISBN 90 5809 038 8

Liquefaction constitutive model

Ahm^d-W .^lgSiindi- University of California, San Diego, Calif., USA

Ender Parra - INTEVEP, SA, Venezuela

Zhaohui Yang - Columbia University, New York, NY, USA

Ricardo Dobry & Mourad Rensselaer Polytechnic Institute, Troy, NY, USA

A B S T R A C T : A c o n s t i tu t iv e m o d e l is d e v e lo p e d to re p ro d u c e s a lie n t a sp e c ts a s s o c ia te d w ith se ism ic a lly - in d u c e d so il l iq u e fa c tio n . A t te n t io n is m a in ly fo cu sed on th e d e v ia to r ic (sh e a r) s t r e s s - s t r a in re sp o n se m e c h a n ism . Soil sh e a r b e h a v io r d u r in g liq u e fa c tio n is m o d e le d to d isp la y a s ig n if ic a n t r e g a in in s tiffn ess a n d s t r e n g th w ith th e in c re a se in d e fo rm a tio n d u r in g each cycle o f a p p lie d lo ad . T h is b e h a v io r a p p e a rs to p la y a m a jo r ro le in d ic ta t in g th e m a g n i tu d e o f sh e a r d e fo rm a tio n s as o b se rv e d in l a b o r a to r y te s ts a n d m a n ife s te d in a c c e le ra t io n re c o rd s fro m e a r th q u a k e s a n d c e n tr ifu g e e x p e r im e n ts .

K E Y W O R D S : L iq u e fa c tio n , c y c lic -m o b ility , sa n d , soil, c o n s t i tu t iv e m o d e lin g , e a r th q u a k e , p la s t ic i ty


D u rin g liq u e fa c tio n , re c e n t re c o rd s (H o lzer et al. [16]) o f se ism ic s ite re sp o n se h av e m a n ife s te d a p o ss ib le s t ro n g in flu en ce o f so il d i la t io n d u r in g cy clic lo a d in g . S u ch p h a se s o f d i la t io n m ay re s u l t in s ig n if ic a n t re g a in in sh e a r s tiffn ess a n d s t r e n g th a t la rg e cy clic sh e a r s t r a in e x cu rs io n s , le a d in g to : i) a s so c ia te d in s ta n c e s o f p o re -p re ss u re r e d u c t io n , ii) a p p e a ra n c e o f sp ik es in la te ra l ac c e le ra t io n re c o rd s (as a d ire c t co n se q u en c e o f th e in c re a s e d s h e a r r e s is ta n c e ) , a n d m o s t im p o r ta n tly , iii) a s t ro n g re s t r a in in g effec t on th e m a g n i tu d e o f cyclic a n d a c c u m u la te d p e rm a n e n t sh e a r s t ra in s . T h is r e s t r a in t on sh e a r s t r a in h a s b e e n re fe rre d to a s a fo rm o f c y c lic -m o b ility in a la rg e n u m b e r o f p io n e e r in g l iq u e fa c tio n s tu d ie s (e.g., Seed a n d Lee [26], C a s a g ra n d e [4], C a s tro [5], C a s tro a n d P o u lo s [6], S eed [27]). F o r th e im p o r ta n t s i t u a tio n s o f b ia se d s t r a in a c c u m u la tio n d u e to an in it ia l lo ck e d -in sh e a r s tre s s , th is p a t t e r n o f b e h a v io r m a y p la y a d o m in a n t ro le in d ic ta t in g th e e x te n t o f su c h d e fo rm a tio n s . C u rre n tly , th e a b o v e m e n tio n e d e ffec ts a re a lso th o ro u g h ly d o c u m e n te d by a la rg e b o d y o f e x p e r im e n ta l re sea rc h (e m

p lo y in g c le an sa n d s a n d c le a n n o n -p la s tic s i l ts ) , in c lu d in g c e n tr ifu g e e x p e r im e n ts {e.g., D o b ry et al. [9], T a b o a d a [28], D o b ry et al. [10]), s h a k e - ta b le

te s ts , a n d cyclic la b o r a to r y s a m p le te s ts (A ru l- m o li [1]). A th o ro u g h s u m m a ry is p ro v id e d (E l- g a m a l et al. [14]) o f th e re le v a n t: i) se ism ic re sp o n se case h is to r ie s , ii) re c o rd e d e x p e r im e n ta l (c en tr ifu g e , sh a k e ta b le a n d la b o ra to ry ) re sp o n se , a n d iii) c o n s t i tu t iv e m o d e ls d e v e lo p e d to a d d re s s th is p h e n o m e n o n .

In th e fo llo w in g p a g es , i l lu s t r a t io n s o f th e a b o v e -d e sc r ib e d sh e a r s t r e s s - s t r a in m e c h a n ism s a re p re se n te d . T h e re a f te r , th e c o n s t i tu t iv e m o d e l is d isc u sse d a lo n g w ith a n a p p r o p r ia te f in ite e le m e n t c o m p u ta tio n a l fra m e w o rk . F in a lly , th e s a lie n t m o d e l re sp o n se c h a ra c te r is t ic s a re d is p lay ed .

2. C Y C L IC L O A D IN G D U R IN G L IQ U E F A C T IO N

A th o ro u g h rev iew o f a v a ila b le l i t e r a tu r e h a s b e en p re se n te d re c e n tly by E lg a m a l et al. [14]. A n i l lu s t r a t io n o f th e m e c h a n ism s o b se rv ed in u n d ra in e d cyclic la b o r a to r y te s ts is sh o w n in F ig u re s 1 a n d 2 (A ru lm o li et al. [1]). S im ila r re sp o n se (F ig u re s 3 - 5 ) w as o b se rv e d (H o lzer et al. [16], Y o u d a n d H o lz e r [31], Z eg h a l a n d E lg a m a l [32]) a t th e U S Im p e r ia l C o u n ty W ild life R efu g e s ite (1987 S u p e r s t i t io n H ills e a r th q u a k e re c o rd s) . O n e-

269

Figure 1: S tress-strain curve and stress path for N evada Sand w ith/>, = 60% obtained from undrained cyclic sim ple shear (C SS) te st(A rulm oli et ah, 1992).

N evad a Sand (D r= 4 0 % )

A x ia l strain (% )

F i g u r e 2 : S t r e s s , s t r a in a n d E P P h i s t o r i e s d u r in g a n u n d r a in e d s t r e s s - c o n t r o l l e d c y c l i c t r ia x - i a l t e s t o f N e v a d a s a n d (Z >/ = 4 0 % ) w i t h a n i m p o s e d s t a t ic ( i n i t i a l ) d e v i a t o r i c s t r e s s ( a f t e rA r u l m o l i e t a l . 1 9 9 2 ) .

270

d im e n s io n a l s h e a r s t r e s s - s tr a in h is to r ie s (F ig u re 6) c a lc u la te d f ro m re c o rd e d c e n tr ifu g e e x p e r im e n t ac c e le ra t io n a n d L V D T re c o rd s (D o b ry et ai [9], D o- b ry et al. [10], T a b o a d a [28], E lg a m a l et al. [13]) a lso d isp la y a s im ila r re sp o n se m e c h a n ism . F ig u re s 2 a n d 6 d e p ic t th e m e c h a n ism o f a c c u m u la tio n o f c y c le -b y -cy c le d e fo rm a tio n s . A c c u ra c y in re p ro d u c in g th is m e c h a n ism is a m o n g th e m o s t im p o r t a n t g o a ls o f th e d e v e lo p e d c o n s t i tu t iv e m o d el.

3. T H E O R E T IC A L B A S IS

T h e m o d e l f ra m e w o rk fo llow s th e p ro c e d u re s d e v e lo p e d b y P ré v o s t [24], b a se d on th e m u lt i p le y ie ld su rfa c e p la s t ic i ty c o n c e p t (Iw an [19], a n d M ro z [22]). I t w as m o d ifie d ( P a r r a [23]) fro m its o r ig in a l fo rm (P ré v o s t [24]) to m o d e l th e sh e a r s t r e s s - s t r a in f e a tu re s d isc u sse d ab o v e (F ig s. 1 - 6 ). S p e c ia l a t t e n t io n w as g iv en to th e d e v ia to r ic - v o lu m e tr ic s t r a in c o u p lin g u n d e r cyclic lo ad in g ; in p a r t i c u la r d u r in g lo a d in g - u n lo a d in g - re lo a d in g a b o v e th e p h a se t r a n s fo rm a tio n line .

F o llo w in g th e u su a l cyclic so il p la s t ic i ty co n c e p ts {e.g., P ré v o s t [24]), a s t r a in in c re m e n t è is a s su m e d to b e th e su m o f e la s tic a n d p la s tic s t r a in in c re m e n ts , d e n o te d a n d re sp ec tiv e ly . T h e m a te r ia l e la s t ic i ty is l in e a r a n d iso tro p ic , a n d n o n l in e a r i ty a n d a n is o tro p y re su lt fro m p la s tic ity . In o rd e r to d e sc rib e th e m a te r ia l ’s p la s t ic i ty one n e ed s [24]: a) th e y ie ld c o n d it io n sp e c ify in g th e s ta te s o f s tre s s fo r w h ic h p la s tic flow o ccu rs; b) th e flow ru le r e la t in g th e p la s tic s t r a in in c re m e n t te n so r to th e s tre s s a n d s t re s s in c re m e n t te n so rs ; a n d c) th e h a rd e n in g ru le sp e c ify in g y ie ld c o n d it io n m o d if ic a tio n in th e c o u rse o f p la s tic flow. In th e fo llo w in g se c tio n s , s tre s s a n d s t r a in a re a ssu m e d p o s it iv e in te n s io n a n d n e g a tiv e in c o m p re ss io n . A ll n o rm a l s tre s se s a re e ffec tive , so t h a t d ra in e d , p a r t ia l ly d ra in e d a n d u n d ra in e d s i tu a t io n s m ay be a n a ly z e d u s in g th e sa m e fram e w o rk . C u rre n tly a v a ila b le c o n s t i tu t iv e m o d e ls t h a t re p ro d u c e im p o r ta n t a sp e c ts o f a b o v e sh e a r m e c h a n ism in c lu d e th o se by la i [17, 18] a n d T a te is h i et al. [29].

3.1 Constitutive Equations

T h e c o n s t i tu t iv e e q u a t io n is w r i t te n in in c re m e n ta l fo rm as fo llow s (P ré v o s t [24]):

cr = E : ( è — (1)

& = r a te o f e ffec tive C a u c h y s t re s s te n s o r € = r a te o f d e fo rm a tio n te n s o r

= p la s tic r a te o f d e fo rm a tio n te n s o r E = iso tro p ic e la s t ic c o effic ien t te n s o r

T h e p la s tic r a te o f d e fo rm a tio n te n s o r is d e fined by [15, 24]:

è '’ = P (L) (2)

w h e re P is a sy m m e tr ic se c o n d -o rd e r te n s o r t h a t defines th e d ire c tio n o f p la s tic d e fo rm a tio n in s tre s s sp ace , L is th e p la s t ic lo a d in g fu n c tio n , a n d th e sy m b o l ( ) d e n o te s th e M a c C a u le y ’s b ra c k e ts ,viz.,

(L) = [ ^ i f i > 0Otherwise

(4 )

T h e fu n c tio n L is d e fin ed by [15]:

L = — Q : &

w h ere Q is a sy m m e tr ic s e c o n d -o rd e r te n s o r t h a t defines d ire c tio n o f o u te r n o rm a l to th e y ie ld s u r face , a n d H' is th e p la s tic m o d u lu s . I t is co n v en ie n t to d e c o m p o se P a n d Q in to th e i r d e v ia to r ic a n d v o lu m e tr ic c o m p o n e n ts [24] su c h th a t :

P = E ' + P " 6 Q = Q' + Q"d

(5)(6)

w h ere 6 is th e s e c o n d -o rd e r id e n t i ty te n s o r .C o m b in in g E q s. 1 a n d 2, E q . 4 c a n b e r e w r i t te n

as

L =H ' e h .

Q : E : d- (7)

w here

w h ere

i/o = Q : E : P = P ( 3 P " ) ( 3 Q " ) -h 2 G P ' : Q '

(8)

3.2 Yield Function

T h e y ie ld fu n c tio n (F ig . 7) t h a t re p re s e n ts th e s ta te s o f s tre s s fo r w h ich p la s t ic flow o c cu rs , is s e le c te d o f th e fo llow ing fo rm [21, 24]:

3/ = 2 ( ® ~ P«“ ) ■ - PaOi) ~ m^pl = 0 (9)

w h ere

s = cr ~ p 6 = d e v ia to r ic s tre s s te n s o r a — e ffec tive C a u c h y s tre s s te n s o r

(n e g a tiv e in c o m p re ss io n )P a = p - a

271

Superstition Hills 1987 Eartliqualce, W ildlife Site

Figure 3; W ildlife-Refuge NS and EiW shear stress-strain histories during the Superstition Hills 1987 Earthquake C Zeghal and Elgamal 1994 ).

Superstition H ills Earthqualce, W ildlife Site

Eigure 4: Shear stress-strain history during selected loading cycles o f the Superstition Hills earthquake C Zeghal and Elgamal 1994 ).

272

Wildlife-Refuge Site Superstition Hills 1987 Earthquake

Figure 5: Wildlife-Refuge NS shear stress-strain and effective-stress histories during the Superstition Hills 1987 Earthquake (evaluated from acceleration histories and computed), (after Elgamal et al. 1995).

p = \ tr {(t ) = effective mean normal stress a = material constant [a = cj tan (j) ^vhere

c == cohesion and (j) = friction angle) a = kinematic deviatoric tensor defining

the coordinates of the yield surface center in deviatoric stress subspace

M — material parameter related to the friction angle 0

The adopted yield function, plotted in stress space forms a conical surface with its apex at “a” along the hydrostatic axis as shown in Figs. 5, 7 and 8. For cohesionless soils, a may be viewed as a low shear strength associated with the condition(p = 0).

The initial position of a yield surface given by a, reflects the degree of material or stress induced anisotropy, and it is considered as the material’s memory of its fabric or past loading history. If a = 0, the axis of the cone coincides with the space diagonal, and the model will result in an initially isotropic behavior. Neglecting the influence

of the Lode angle in the definition of M allows any deviatoric plane {p = constant) to intersect a circular cross-section of the yield surface. The center of this plane does not generally coincide with the space diagonal, but is shifted by the amount in principal stress space (Fig. 7) .

The outer normal to the yield surface, Q, may be normalized in any convenient fashion, and in the following:

Q : Q = Q ' : Q ' + i ( 3 Q " f = 1 (10)

3.3 Flow Rule

In order to characterize the volume change effects correctly, it is necessary to employ a nonassociated flow rule [2, 8, 24]. Typically, nonassociativity is restricted to the dilatational component of the plastic flow in accordance with ex-

273

Rensselaer Model 2

I O

O- I O

I O

O-IO

li?'^ I O

U OM

I O

o- I O

IO

o- I O -

Su

1 .2 5 m

12 2 6 sec -

2 . 5 m

Time scale2 4 6 8 lO-----------1---------------------^ ............ i--- 12 sec

S u ___

Time scale 2 4 6 8 1 0 12 sec

P i / l / ' l / ( / ' ^ V 1 1 1 1

Time scale2 4 6 8

\ y ---------------------------------------— ----------------

1 0 1 2 secSu___

______________________2 4 6 8 1012 sec -

0 2 4 6 8S h e a r s t r a in ( % )

F i g u r e 6 : R P I M o d e l 2 s h e a r s t r e s s - s t r a i n h i s t o r i e s w i t h s u p e r p o s e d s t a t ic s t r e s s d u e t o i n c l i n a t i o n ( T a b o a d a 1 9 9 5 , D o b r y e t a l . 1 9 9 5 , E lg a m a l e t a l . 1 9 9 6 b ) .

perimental observations of granular material response [2, 24].

A distinction between these main volumetric response mechanisms is made, so that the flow rule is defined separately for stress states above, on, or below the phase transformation line (Fig. 8) using a phenomenological approach. Thus, the flow rule is given by:

P ' = Q ' (associated) (11)

3P" = Vpt, P, CL, O (non-associated)(12)

where r] = ( | s : ¡Pa is an effective stress ratio, T]pt is a material parameter defining this ratio along the phase transformation (PT) line (Fig. 8), and is the cumulative plastic shear deformation (^p = : ePdt, where t is time). Contraction ordilation is defined according to the p value relative to r/pt. When r] < rjpt the stress point lies below the PT line and the soil behaves following a rule for contraction, and when rj > rjpt the stress point lies above the PT line and the soil behaves according to a rule for dilation. For the particular case when -q = the soil behavior will be controlled by the loading process. The function x will be defined according to the scenarios discussed below.

Figure 7: Conical y ield surface in principal stress space and deviato n e or 7T plane (P revost 1985, Lacy 1986, Parra 1996).

F igure 8: Yield function and phase transform ation line (Parra 1996).

274

3 .3 .1 Contraction zone

P ” is g iv en by;

3P" = x(??, ilpt, P, a) = Cp A (13)

T h e fu n c tio n Cn d e fin es th e r a te o f c o n tra c t io n a c c o rd in g to P ré v o s t [24]:

_ {p h Ÿ - 1

[riinf + 1(14)

T h e fu n c tio n i/'c is n ew ly in tro d u c e d ( P a r r a [23]) to sca le th e a m o u n t o f c o n tr a c t io n a c c o rd in g to th e

level o f c o n fin in g p re ssu re .

3 .3 .2 At and above phase transformation (PT) surface (Parra [23])

A s m ig h t b e in fe r re d f ro m F ig s . 1 - 5 , a b o v e th e P T line , te n d e n c y fo r d i la t io n a p p e a r s o n ly d u r in g loading to w a rd s th e fa ilu re su rfa c e , U p o n lo a d re v e rsa l o r unloading c o n tr a c t io n ta k e s over. In fa c t, F ig . 1 show s:

1. D ila t io n o c c u rs d u r in g sh e a r lo a d in g o r in c rease o f sh e a r s tre s s . D u r in g th is p h a se , th e r a te o f d i la t io n is seen to in c re a se w ith th e in c re ase o f s h e a r s tre ss .

2. C o n tra c t io n , u p o n lo a d re v e rsa l o r unloading, d e v e lo p s a lm o s t in s ta n ta n e o u s ly , a n d th e s tre s s p a th in th e p - q p lo t m oves to w a rd th e p o in t w h e re d i la t io n s ta r te d . In o th e r w o rd s , c o n tra c t io n a p p e a rs to d e p e n d on th e a m o u n t o f d i la t io n e x p e r ie n c e d by th e so il s t r u c tu r e .

3. In th e lo a d in g cy cles close to th e c o n d it io n p = 0 (F ig . 1), i t m a y b e o b se rv ed th a t a la rg e c h a n g e in sh e a r s t r a in o c c u rs w ith m in im a l c h a n g e in sh e a r s tre s s in th e v ic in i ty o f p h a se t r a n s fo rm a tio n , fro m c o n tra c tiv e to d i la t iv e re sp o n se . C o n se q u e n tly , i t w as d e c id e d to d ire c tly m o d e l th e a c c u m u la te d s t r a in a s a n a d d it io n a l re sp o n se p h a se b e tw e en c o n tr a c t io n a n d d ila t io n . I f th e P T lin e is re a c h e d d u r in g c o n tra c t io n a n d lo a d in g c o n tin u e s , a d d it io n a l s tre s s in c re m e n ts a re t r e a te d w ith th e c o n d it io n P ” — 0 u n til a u se r sp e c ified s h e a r s t r a in is a c c u m u la te d . T h e re a f te r , th e d i la t iv e p h a se s t a r t s a s d e s c r ib e d ab o v e .

4. In s i tu a t io n s w h e re a so c a lled “d r iv in g s t r e s s ” is p re se n t (e.g., t r ia x ia l te s t w ith in i

t ia l s t re s s b ia s a s sh o w n in F ig . 2), a f in ite in c re m e n t o f a c c u m u la te d p e rm a n e n t s t r a in is in c u r re d fo r e ach cycle o f lo a d (a t p 0). T h e m o d e l in c lu d e s a sp e c ia l sch em e to a c c o u n t fo r t h a t ( P a r r a [23]).

3 .4 Hardening Rule (Parra [23])

A ll su rfa c e s , b u t th e o u te rm o s t ( [19, 22, 24]), m a y b e t r a n s la te d in s tre s s sp a c e w i th o u t c h a n g in g in fo rm (in a n y d e v ia to r ic p la n e ) a n d w ith no in te rs e c tio n . T h e re fo re , th e d ire c tio n o f t r a n s la t io n ¡1 o f th e a c tiv e y ie ld su rfa c e fm w as d e fin ed by a new r e la t io n s h ip (P a r r a [23]) su ch t h a t n o o v e rla p o r in te r s e c t io n is a llow ed b e tw e e n th e y ie ld s u r faces. T h e o u te rm o s t su rfa c e re m a in s s ta t io n a r y a t a ll t im e s .

3.5 Model Performance

F ig u re s 5 a n d 9 show th e p e r fo rm a n c e a n d v e rs a t i l i ty o f th e d e v e lo p e d m o d e l. F ig u re 9 m a y b e c o m p a re d to F ig u re 2, a n d d e p ic ts th e im p o r ta n t e le m e n t o f t r a c k in g th e cy c le -b y -cy c le a c c u m u la t io n o f s h e a r d e fo rm a tio n s .

4. F IN IT E E L E M E N T E O R M U L A T IO N

Soil is m o d e le d as a tw o p h a se m a te r ia l u s in g th e B io t [3] fo rm u la tio n o f p o ro u s m e d ia . T h is fo rm u la t io n is in c o rp o ra te d in a g e n e ra l p u rp o se 2-D f in ite e le m e n t p ro g ra m (R a g h e b [25], P a r r a [23]) u s in g th e u - p a p p ro a c h (in w h ic h d is p la c e m e n t o f th e so il sk e le to n , u , a n d p o re p re ssu re s , p , a re th e u n k n o w n s) as su g g e s te d by Z ien k iew icz et al. [33]. T h e c o m p u ta tio n a l sch em e fo llow s th e m e th o d o logy o f C h a n [7], w h ich is b a se d o n th e fo llo w in g a s su m p tio n s : sm a ll d e fo rm a tio n s a n d ro ta t io n s , d e n s ity o f th e so lid a n d flu id is c o n s ta n t in b o th t im e a n d sp ace , p o ro s ity is lo c a lly h o m o g e n e o u s a n d c o n s ta n t w ith tim e , so il g ra in s a re in c o m p re s s ib le , a n d a c c e le ra t io n s a re e q u a l fo r th e so lid a n d flu id p h a se s . T h e re fo re , th e g e n e ra l c o u p le d fo rm u la tio n a f te r th e s p a t ia l d is c re t iz a tio n a n d G a le rk in a p p ro x im a t io n is e x p re sse d a s follow s:

M ü -(- J B^cr'dQ ~ Q p — = 0 (15)

G ü + Q ^ ü + H p + S p - F = 0 (16)

w h ere M is th e m ass m a tr ix , B is th e s t r a in - d isp la c e m e n t m a tr ix , <r' is th e e ffec tiv e s tre s s vec-

275

200

£ 1 5 0

f 100U

^ 50 a.

0

Axial Strain (%)

F igure 9: Sin:iulatioia of a cyclic triaxial uiidrained te st witH stressbias (ClUC^^c/ic), Farra (1990).

to r , Q is th e d isc re te g ra d ie n t o p e r a to r c o u p lin g th e so lid a n d flu id p h a se s , ü is th e d isp la c e m e n t v e c to r , p is th e p o re p re s su re v e c to r , G is th e d y n a m ic se e p ag e fo rce m a tr ix , H is th e p e rm e a b i l i ty m a tr ix , S is th e c o m p re s s ib il ity m a tr ix , a n d a n d P a re th e p re sc r ib e d b o u n d a ry c o n d it io n s fo r so lid a n d flu id p h a se re sp ec tiv e ly . A s u p e rp o s e d d o t d e n o te s t im e d e r iv a tiv e . V isc o u s d a m p in g m a y be a d d e d fo r th e so lid p h a se in th e fo rm o f R a y le ig h d a m p in g (C = a M 4- /fK, w h e re K is th e in i t ia l s tiffn ess m a tr ix ) . F o r e a r th q u a k e lo a d in g p ro b le m s, G is u su a lly n e g le c te d so t h a t sy m m e t r y o f th e g lo b a l m a t r ix is a t t a in e d .

E q . 15 a n d 16 a re in te g ra te d in t im e u sin g a s im p le s in g le s te p p r e d ic to r m u lt i - c o r re c to r sch em e o f th e N e w m a rk ty p e ( K a to n a a n d Z ien k iew icz [20]), w ith a n a u to m a tic t im e s te p p in g s p li t a lg o r i th m , in c o rp o ra te d to im p ro v e th e r a te o f co n v erg en ce . T h e p r e d ic to r is c a lc u la te d u s in g th e in i t ia l s tiffn ess m a t r ix m e th o d (Z ien k iew icz [34]), a s th e h ig h d e g ree o f n o n -a s s o c ia t iv i ty (in th e b e h a v io r o f th e so lid p h a se ) p ro d u c e s a n o n - s y m m e tr ic ta n g e n t s tiffn ess m a t r ix t h a t re q u ire s a n o n -sy m m e tr ic m a t r ix so lv e r. E x p e r ie n c e b a se d on a n a ly se s o f n o n -a s so c ia t iv e p la s t ic i ty sh o w s t h a t

th e in it ia l s tiffn ess m e th o d p e r fo rm s re a so n a b ly w ell (C h a n [7], V an L a n g e n a n d V e rm ee r [30]). T h e seco n d te rm in E q . 15 is d e fin e d by th e so il c o n s t i tu t iv e m o d e l as d e sc rib e d a b o v e ( P a r r a [23]).

T h e f in ite -e le m e n t a n d c o n s t i tu t iv e -m o d e l p a ck a g e w as c a l ib ra te d a n d e m p lo y e d to c o n d u c t a la rg e n u m b e r o f c o m p u ta tio n s ( P a r r a [23]) b a se d

o n re c o rd e d c e n tr ifu g e e x p e r im e n ta l re sp o n se . T h e c o m p u ta tio n in c lu d e d o n e -d im e n s io n a l s ite re sp o n se w ith a n d w i th o u t la te ra l sp re a d in g , a n d re sp o n se o f e m b a n k m e n ts o n liq u e fiab le so ils. R e m e d ia tio n e ffo rts by s a n d d e n s if ic a tio n u n d e r th e e m b a n k m e n t to e s w ere a lso a n a ly z e d ( P a r r a [23]).

F ig u re 10 d e p ic ts a c o m p a r is o n b e tw ee n re c o rd e d a n d c o m p u te d g ro u n d m o tio n fo r th e P o r t I s la n d s ite . In th is case h is to ry , th e n e c e ssa ry m o d e l p a r a m e te r s w ere o b ta in e d th ro u g h a s im p le sy s te m id e n tif ic a tio n te c h n iq u e b a se d on th e re c o rd e d d o w n h o le a c c e le ra t io n s (E lg a m a l [12]).

5. S U M M A R Y A N D C O N C L U S IO N S

A n ew c o n s t i tu t iv e m o d e l is d e v e lo p e d to m o d e l cy clic sh e a r b e h a v io r d u r in g l iq u e fa c tio n . T h e u n -

276

Port Island, ICobe (Japan); Hyogoken—Nanbu Eartliqualce, Jan. IV, 1995

Figure ): Port IsVC model

land shear stress histories estimated from acceleration histories and corresponding prediction (at 8.0 m, 24.0 m, and 57.5 m depths), after Elgamal et al. (1996a).

d e r ly in g m e c h a n ism s a re b a se d o n o b se rv ed soil re sp o n se d u r in g e a r th q u a k e s , c e n tr ifu g e e x p e r im e n ts a n d cyclic la b o r a to r y te s ts . In th is p a p e r , th e a n a ly t ic a l a n d c o m p u ta t io n a l fra m e w o rk b e h in d th is m o d e l w as p re se n te d . In a d d it io n th e s a l ie n t m o d e l re sp o n se c h a ra c te r is t ic s w ere i l lu s t r a te d .

6. A C K N O W L E D G M E N T S

R E F E R E N C E S

[1] A ru lm o li, K ., M u ra le e th a ra n , K . K ., H o ssa in , M . M . a n d T ru th , L. S. (1 9 9 2 ). “V E L A C S : V E L A C S : V e rific a tio n o f L iq u e fa c tio n A n a ly sis by C e n tr ifu g e S tu d ie s , L a b o ra to ry T e s tin g P ro g ra m , Soil D a ta R e p o r t” , The Earth Technology Corporation, Project No. 90-0562, Irv in e , C a lifo rn ia .

T h e re se a rc h r e p o r te d h e re in w as s u p p o r te d by th e P ac ific E a r th q u a k e E n g in e e r in g R e se a rc h C e n te r (P E E R ) , th e U n ite d S ta te s G e o lo g ic a l S u rv e y (g ra n t N o. 1 4 3 4 -H Q -9 7 -G R -0 3 0 7 0 ), IN T E V E P , SA , V en ezu e la , a n d th e N a t io n a l S c ien ce F o u n d a tio n (g ra n t N o. M S S -9 0 5 7 3 8 8 ). T h is s u p p o r t is g ra te fu lly a ck n o w le d g ed . T h e e m p lo y e d P o r t Is la n d d o w n h o le a c c e le ra t io n d a t a w ere p ro v id e d by th e C o m m itte e o f E a r th q u a k e O b s e rv a tio n a n d R e se a rc h in th e K a n sa i A re a (C E O R K A ) , J a p a n , w ith th e h e lp o f D r. Y . Iw a sa k i.

[2] B a k e r , R . a n d D e sa i, C . S. (1982). “C o n se q u e n c e s o f D e v ia to r ic N o rm a li ty in P la s t ic i ty w ith I so tro p ic S t r a in H a rd e n in g ,” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 6, p p . 383 - 390.

[3] B io t, M . A . (1962). “T h e M e c h an ics o f D efo rm a t io n a n d A c o u s tic P ro p a g a tio n in P o ro u s M e d ia ” , J . Appl Phys., Vol. 33, N o. 4, 1 4 8 2 - 1498.

[4] C a s a g ra n d e , A. (1 9 7 5 ). ’’L iq u e fa c tio n a n d C y c lic D e fo rm a tio n o f S a n d s - A c r it ic a l R e-

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v ie w ,” P ro c e e d in g s , 5 th P a n -A m e r ic a n C o n fe re n c e o n So il M e c h an ics a n d F o u n d a t io n E n g in e e r in g , B u e n o s A ire s, A rg e n tin a ; a lso p u b lish e d a s H a rv a rd Soil M e c h an ics S eries No. 88, J a n u a ry 1976, C a m b rid g e , M ass.

[5] C a s tro , G . (1975). L iq u e fa c tio n a n d C yclic M o b il ity o f S a tu r a te d S a n d s . J o u rn a l o f th e G e o te c h n ic a l E n g in e e r in g D iv is io n , A S C E ,

101, G T 6 , 551-569 .

[6] C a s tro , G a n d P o u lo s , S. J . (1 9 7 7 ). ’’F a c to rs A ffe c tin g L iq u e fa c tio n a n d C y c lic M o b ility ,” J o u rn a l o f th e G e o te c h n ic a l E n g in e e r in g D iv is io n , A S C E , Vol. 103, N o. G T 6 , J u n e , p p . 501-516.

[7] C h a n , A . H. C . (1988). “A U n ified F in i te E le m e n t S o lu tio n to S ta t ic a n d D y n a m ic P r o b lem s in G e o m e c h a n ic s” , Ph.D. dissertation, U n iv e rs ity C o lleg e o f S w an sea , U . K .

[8] D e sa i, C . S. a n d S ir iw a rd a n e H . J . (1984). Constitutive Laws for Engineering Materials - With Emphasis on Geologic Materials, P re n t ic e -H a l l In c ., N ew Je rsey .

[9] D o b ry , R ., T a b o a d a , V . a n d L iu , L. (1995). ’’C e n tr ifu g e M o d e lin g o f L iq u e fa c tio n E ffec ts D u r in g E a r th q u a k e s ,” P ro c . 1 st In ti . C onf. O n E a r th q u a k e G e o te c h n ic a l E n g in e e r in g (IS- T o k y o ), K e y n o te L e c tu re , I s h ih a ra , K . E d ., 3, B a lk e m a , N ov. 14-16, T o k y o , J a p a n , 1291- 1324.

0 0 ] D o b ry , R . a n d A b d o u n , T . (19 9 8 ). “P o s t- T r ig g e r in g R e sp o n se o f L iq u e fied S a n d in

th e F ree F ie ld a n d N e a r F o u n d a t io n s ” , P ro c . G e o t. E q . E n g rg . a n d Soil D y n a m ic s H I, V I , D a k o u la s , P ., Y eg ian , M . a n d H o ltz ., R .D . , E d s ., G e o t. S p e c ia l P u b l ic a t io n N o. 75, A S C E , S e a tt le , W a s h in g to n , A u g 3-6, k e y n o te le c tu re , 270-300 .

[11] E lg a m a l, A . -W ., Z eg h a l, M ., a n d P a r r a ,E . (1 9 9 5 ). ’’Id e n tif ic a tio n a n d M o d e lin g o f E a r th q u a k e G ro u n d R e sp o n se ,” P ro c . 1st In ti . C o n f. O n E a r th q u a k e G e o te c h n ic a l E n g in e e r in g (IS -T o k y o ), S p e c ia l, K e y n o te a n d T h e m e L e c tu re s V o lu m e, N ov. 14-16, T okyo, J a p a n .

[12] E lg a m a l, A . -W ., Z eg h a l, M ., a n d P a r r a , E . (1 9 9 6 a ). ’’L iq u e fa c tio n o f R e c la im e d Is la n d

in K o b e , J a p a n ,” J . G e o tec h . E n g in e e r in g , A S C E , 122, 1, J a n ., 39-49.

[13] E lg a m a l, A . -W ., Z eg h a l, M ., T a b o a d a , V . M . a n d D o b ry , R . (1 9 9 6 b ). ’’A n a ly s is o f S ite L iq u e fa c tio n a n d L a te r a l S p re a d in g u s in g C e n tr ifu g e M o d e l T e s ts ,” So ils a n d F o u n d a tio n s , 36, 2, Ju n e , 111-121.

[14] E lg a m a l, A . -W ., D o b ry , R ., P a r r a , E . a n d Y an g , Z. (1998) Soil Dilation and Shear Deformations During Liquefaction, P ro c . 4 th In ti . C o n f. o n C a se H is to r ie s in G e o te c h n ic a l E n g in e e r in g , S. P ra k a s h , E d ., S t. L ou is , M O , M a rc h 8-15, 1998.

[15] H ill, R . (1950) The Mathematical Theory of Plasticity, O x fo rd U n iv e r is ty P re ss , L o n d o n .

[16] H o lzer, T . L ., Y o u d T . L. a n d H a n k s T . C . (1989). ’’D y n a m ic s O f L iq u e fa c tio n D u r in g th e 1987 S u p e r s t i t io n H ills , C a lifo rn ia , E a r th q u a k e ,” S c ience , Vol. 244, 56-59.

[17] la i , S. (1991). ” A S t r a in S p a c e M u ltip le M ech a n is m M o d e l fo r C y c lic B e h a v io r o f S a n d a n d i ts A p p l ic a t io n ,” E a r th q u a k e E n g in e e r in g R e se a rc h N o te N o. 43, P o r t a n d H a rb o r R e se a rc h I n s t i tu te , M in is try o f T ra n s p o r t , J a p a n .

[18] la i , S ., M o r i ta , T ., K a m e o k a , T ., M a tsu n a g a , Y . a n d A b ik o , K . (1995). ’’R e sp o n se o f a D e n se S a n d D e p o s it D u r in g 1993 K u sh iro -O k i E a r th q u a k e ,” S o ils a n d F o u n d a tio n s , 35, 1, M a rch , 115-131.

[19] Iw an , W . D . (1967) “O n a c la ss o f M o d e ls fo r th e Y ie ld in g B e h a v io r o f C o n tin u o u s a n d C o m p o s ite S y s te m s ,” Journal of Applied Mechanics, ASME, Vol. 34, p p . 612 - 617.

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[21] Lacy, S. (1986) “N u m e r ic a l P ro c e d u re s fo r N o n lin e a r T ra n s ie n t A n a ly s is o f T w o -p h a s e Soil S y s te m ,” Ph.D. dissertation, P r in c e to n U n iv e rs ity , N J , U .S .A .

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[23] Parra, E. (1996). “Numerical Modeling of Liquefaction and Lateral .Ground Deformation including Cyclic Mobility and Dilative Behavior in Soil Systems” , Ph.D. dissertation, Dept, of Civil Engineering, Rensselaer Polytechnic Institute, in progress.

[24] Prévost, J. H., (1985) “A Simple Plasticity Theory for Erictional Cohesionless Soils,” Soil Dynamics and Earthquake Engineering, Vol. 4, No. 1, pp. 9 - 17.

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[28] Taboada, V. M. (1995) Centrifuge Modeling of Earthquake-Induced Lateral Spreading in Sand using a Laminar Box Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, NY.

[29] Tateishi, A., Taguchi, Y, Oka, E. and Yashima, A. (1995). ”A Cyclic Elasto-Plastic Model For Sand and Its Application Under various Stress Conditions,” Proc. 1st Inti. Conf. On Earthquake Geotech Engng, 1, 399- 404, Balkema, Rotterdam.

[30] Van Langen, H. and Vermeer, P. A. (1990). “Automatic Step Size Correction for Non- associated Plasticity Problems” , Int. J. Num. Meth. Engrg., Vol. 29, 579-598.

[31] Youd, T. L., and Holzer, T. L. (1994). “Piezometer Performance at the Wildlife Liquefaction Site.” J. Geotech. Engrg., ASCE, 120(6), 975-995.

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[33] Zienkiewicz, 0 . C., Chan, A. H. C., Pastor, M., Paul, D. K., and Shiomi, T. (1990). “Static and Dynamic Behaviour of Soils: A Rational Approach to Quantitative Solutions: I. Fully Saturated Problems,” Proc. R. Soc. Lond., A 429, 285-309.

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7 Centrifuge studies of liquefaction


Several important issues related to liquefaction study using centrifuge modeling

X.ZengDepartment of Civil Engineering, University of Kentucky, Lexington, Ky, USA

ABSTRACT: Centrifuge modeling provides a powerful experimental tool for liquefaction study. In recent years, considerable progress has been made in earthquake centrifuge modeling. This paper presents the results of some recent studies on three important issues related to liquefaction study using centrifuge modeling: boundary effects of model containers, the use of viscous fluids in model tests, and the accuracy of using centrifugal acceleration to simulate gravity.

1 INTRODUCTION

Considerable progress has been made in earthquake centrifuge modeling in recent years. Several geotechnical centrifuge centers in the US, UK, and Japan have developed the capability of earthquake centrifuge modeling and a significant amount of research, many of which are related to liquefaction study, has been conducted using data from model tests. The principles of earthquake centrifuge modeling were first studied by Schofield (1981) and Scott (1983). Some of the latest developments in earthquake centrifuge modeling were summarized by Steedman (1991), Ko (1994), and Kutter (1994). Data from centrifuge tests can be used to study the mechanism of complex problems in geotechnical engineering such as liquefaction of soils and to verify numerical procedures or new design concepts when existing standard design procedures are inadequate.

Earthquake centrifuge modeling is also a complex experimental technique. Like other experimental methods, centrifuge modeling has inherent inaccuracies arising from a number of factors such as the variation of centrifuge accelerations in both the radial and tangential directions, boundary conditions imposed by model containers, and system limitations of equipment, transducers and data acquisition system. The quality of experimental data and its interpretation depend critically on how well these problems are solved or addressed. In recent years, some of these problems

are studied by researchers such as Kutter et al(1990), Lee (1990), and Zeng and Schofield (1996).

There is hardly any doubt now that centrifuge modeling provide a powerful experimental tool for liquefaction study. As an earthquake in the field is unpredictable, it is very difficult, time consuming and expensive to record liquefaction data in the field. So far there are only a few cases where well-documented time history of acceleration and pore pressure during earthquakes were available. In contrast, an earthquake test can be conducted under controllable environment on a centrifuge with a wide range of instrument installed at desired locations. There have been numerous projects conducted on centrifuges in recent years that are related to liquefaction studies. For instance, one can test the behavior of a liquefiable soil under undrained condition by placing a layer of such soil underneath a layer of clay as shown in Figure 1. To prevent leakage of water from side walls, the top impermeable layer can be extended at the side walls. Another example is to study the sequence of liquefaction in a uniform saturated sand layer and then the consolidation of a liquefied sand layer after an earthquake as reported by Scott (1986). In the early 1990’s, the VELACS (Verification of Liquefaction Analysis by Centrifuge Studies) project used extensively data from liquefaction tests on centrifuges to verify numerical procedures (Arulanandan and Scott, 1993).

The challenge now for liquefaction study using centrifuge modeling is not whether it can be

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simulated in a centrifuge test but how to simulate it properly and how to interpret the test data. This paper present results of some recent studies on three important issues related to liquefaction study using centrifuge modeling.

2 BOUNDARY EFFECTS OF MODEL CONTIANERS

In the filed, a geotechnical problem typically involves soil in a large area while in a centrifuge test, a soil model is contained in a relatively small box. Thus, artificial boundary conditions are imposed on the earth structure in a model. For an earthquake test, the boundary effects of a model container can be significant if they are not addressed properly.For a uniform soil profile based on rigid rock in the field subject to base shaking in the horizontal direction, the stresses acting on a section of a layer of infinite lateral extent are shown in Figure 2 a). Superimposed on the initial geo-static force of selfweight W is the inertial force k^W on the soil mass. There are shear stresses on both horizontal and vertical planes. The distribution of normal stress and shear stress on the base must be uniform. The normal stress and shear stress on every vertical plane should be identical. This type of stress distribution should be realistically replicated in a model test. However if a model container has smooth end walls complementary shear forces cannot be sustained on the vertical planes near the end walls. The zero shear stress in the vertical planes must result in distortion of the overall stress field. Figure 2 b). The rocking of the soil relative to the base plane requires cyclic moments. In shaking table experiments these are called "overturning moment". In the field these moments are caused by shear forces on vertical planes, but in the absence of shear forces on

model container

smoothly ended model containers there must be a redistribution in normal stresses on both horizontal and vertical planes. Thus the resultant stress field in such a model is considerably different from that in the imagined prototype.

A second effect caused by a rigid end wall is strain dissimilarity. When a soil layer of infinite lateral extent based on rigid rock is subjected to base shaking, the response of the soil layer everywhere is treated as if it were a shear beam. If the properties of soil vary only with depth the deformation everywhere at a given depth will be the same. Figure 3 a). However in a model test the deformation of soil near the end wall is restricted by the deflection of the end wall, and for a model container with rigid end walls the deformation of soil is quite different from that in the imagined prototype, FigureS b). For a relatively long model container it is sometimes assumed that the deformation of the soil in the center of the model is close to that in the imagined prototype, but it is then difficult to make a sensible estimation about the extent which is influenced by a rigid end wall.

base shaking acceleration

a) distribution of stresses in an soil layer of infinite lateral extent

Figure 1. A centrifuge model for undrained test

b) distribution of stresses in model with smooth rigid end walls

Figure 2. Distortion of stress field due to smooth end walls.

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Thirdly in the imagined prototype the vibration of soil in horizontal direction is generated mainly by vertically propagated S waves, Figure 4 a). However in a model with rigid end walls the interaction between the walls and soil causes lateral compression and dilation in the soil and hence generates P waves, Figure 4 b). Rigid end walls also reflect earthquake waves, so that the vibration of soil in such a model container is the combined effect of the earthquake P and S waves.

displacem ent at the top of layer

soil layer

displa"oen^nt at th e ^ '^ ^ ^ ^base of layer base shaking acceleration

a) deformation of soil shear beam s in the prototype

b) deformation of soil in the actual model Figure 3. Difference in deformation due to rigid end walls.

soil layer

S w aves

base shaking a) S Wave in the prototype

XSNX---------rigid base

rigid wallsoil layer

P waves P waves-A»-

4S waves

____ 4____ 4rigid base

base shaking b) S and P waves in the model

Figure 4. Earthquake waves in model and prototype.

To a certain extent, an earthquake centrifuge test conducted in a rigid smooth model container is similar to a cyclic triaxial test. The stress condition in the soil is close to a cyclic variation of principal stress rather than an application of cyclic shear stress. Consequently, the resulting stress condition is different from that in the field.

In the past decade considerable efforts have been made to create either a flexible or an absorbing boundary. The concept of a flexible boundary was first introduced by Whitman et al. (1981) in a stacked circular ring apparatus which was made of separate aluminium rings stacked together. The friction between the rings was reduced so that the rings could move relative to each other, thus creating a flexible boundary. This first step forward in dynamic centrifuge modelling still had several unsatisfactory aspects: there was no direct control of the lateral stiffness of the apparatus, a smooth inner surface which could not sustain shear stresses and the circular shape and the relatively low height to length ratio of the model container created a three dimensional problem.

To solve the problem of incident waves being reflected by rigid end walls the concept of an absorbing boundary was introduced. The practice of using an industrial fill material called duxseal at the end walls has been proved to be effective in reducing the energy reflected from the end walls, Coe et al. (1985). However, the use of duxseal causes other concerns as the properties of duxseal such as friction and stiffness are difficult to determine in standard laboratory tests especially when working at a high stress level in a centrifuge test. It is not known what shear forces are between the duxseal and the soil body. It is also difficult to find a consistent numerical model for such a boundary so as to carry out theoretical and numerical analysis on the data of model tests. Moreover as duxseal is a relatively soft material such a boundary will deform laterally under the increased lateral pressure during the spin-up of a centrifuge and hence can not satisfy condition for zero horizontal strain. A recent detailed study by Campbell et al. (1991) concluded that such a boundary cannot satisfy all desired boundary conditions.

Many failures of soil structures during earthquakes are caused by liquefaction of saturated soil. To study liquefaction events on a centrifuge a modified version of stacked rings, a laminar box, was proposed and tested by Hushmand et al. (1988) and later by Law e t a l .{ \9 9 \ ) . A laminar box

285

consists of rectangular frames stacked together with bearings between the frames to reduce the friction so as to mirror the stiffness of a liquefied soil column. The possible slip of one frame relative to another is supposed to allow for the large displacement associated with liquefaction of saturated soil. However, the end walls of the container cannot sustain the complimentary shear stresses. It is also difficult to make the box itself water tight for saturated soil test. An inner bag made of plastic or latex is normally used to contain water. Similar to the rubber membrane used in a triaxial test, it is likely to introduce some undesired boundary conditions.

To reduce the boundary effects of model containers, a new type of model container called equivalent-shear-beam container was developed by Zeng and Schofield (1996) and has been adopted at several centrifuge facilities. The model container (Figure 5) is made of aluminium rings separated by soft rubber layers. For test on dry soils, the shear stiffness of the box can be made to match the shear stiffness of the soil contained by varying the thickness and/or stiffness of the rubber so that the box will have similar lateral deformation as the soil contained. A shear sheet (typically an aluminium sheet glued with sand and bolted onto the box) can be attached to the end walls and the base to sustain the complementary shear stress. The resulting stress condition in the model container is similar to that of a cyclic simple shear test, which would match that in the field. Data from a number of centrifuge tests showed that the shear sheets can provide the complementary shear at the end walls (Madbhushi et al, 1994) and achieve a uniform acceleration field cross the model (Zeng and Schofield, 1996). Therefore, this type of model container provides a more desired stress condition in the model than other types of containers. For tests on saturated soils with liquefaction potential, this type of model container has advantages too because the container can be

made water tight. Very soft rubber can be used so that it can simulate the stiffness of a liquefied soil. This modified version of model container is called flexible-shear-beam container and has been successfully used at UC Davis (Kutter, 1994).

3 USE OF VISCOUS FLUIDS IN MODEL TESTS

One of the major problems associated with earthquake centrifuge modeling is the conflict in time scale for dynamic events and for consolidation events. The most commonly used scaling laws for dynamic centrifuge modeling are listed in Table 1. As shown in the table, if the same soil and pore fluid as in the prototype are used in the model, the resulting time scale for dynamic events is N (N is the ratio of centrifugal acceleration over gravitational acceleration) while for consolidation event, the time scale is N . In tests on a saturated soil under earthquake loading, both events play important roles in determining how much excess pore pressure will be generated during an earthquake and how fast it will dissipate after an earthquake. If data from a model test is used for the verification of numerical codes or design procedures, this conflict in time scale has no effect on data interpretation as long as the permeability of soil is changed accordingly in the analyses. On the other hand, if a model test is intended to closely simulate a prototype situation, this conflict in time scale factors needs to be resolved so that experimental data from a model test is directly related to the response of the prototype structure not only qualitatively but also quantitatively.

One possible solution to this problem is to use soils of finer particles in model tests. However, changing particle size of soils can lead to other changes in the mechanical properties of soil such as strength and stress-strain relationship and hence, is seldom used. The most commonly used method to achieve identical time scale factors is to slow down the dissipation of excess pore pressure by using fluid of higher viscosity in the model. The most frequently used fluids are glycerin-water mixtures, silicone soil, or methyl cellulose-water mixture. According to the Kozeny-Carman equation, permeability of a soil is given by

e y

k = -

Figure 5. An equivalent-shear-beam container koS'p(l-f-e)

( 1)

286

in which)Li = viscosity of permeant e == void ratio of soil Y = unit weight of permeant S = specific surface area of soil particles, and k„ = factor depending on pore shape and ratio

of the length of actual flow path to soil bed thickness.

Table 1. Scaling relationship for centrifuge test.parameter

AccelerationDimension

AreaVolumeStressStrainForceMass

Mass density Unit eight

Time(dynamic) Time(diffusion)

Frequency Hydraulic gradient

Stiffness/width Moment/width

prototypea1

AVasFmPytTf

iElM

Centrifuge model (Ng)Na1/N

A/N'V/N'

as

F/N'm/N'

PNyt/N

T/N'Nf

NiEI/N'M/N'

If the same soil as in the prototype is used, e, S and ko will remain the same. Therefore permeability is expected to be inversely proportional to the viscosity of the permeant. If the permeant has a viscosity N times that of water and the same unit weight, its permeability is expected to be 1/N that of water. The mass density of silicone oil or glycerin- water mixture matches well to that of water and thus has been widely used in earthquake centrifuge tests.

caused by using viscous fluid is reasonably matched by the Kozeny-Carman equation.

However, the use of viscous fluid has the potential to bring in some problems. It was observed during permeability tests on 80 cSt silicone oil that for dense specimen (with relative density above 80%), silicone oil can hardly flow through the soil unless the hydraulic gradient (upwards) was raised to almost 1, at which time the soil specimen became unstabilized due to piping. This is why no data point is available in Figure 6 for dense sand with silicone oil as a permeant. It is likely due to the clogging effect of the viscous fluid. Similar effects were observed in permeability tests using glycerin-water mixture as the pore fluid. As shown in Figure 8, there is a strong effect of clogging when the hydraulic gradient is smaller than 0.1. At a hydraulic gradient greater than 0.1, the coefficient of permeability measured are quite stable with specimens at a wide range of void ratios. When the hydraulic gradient drops below 0.1, the coefficient of permeability decreased rapidly with the hydraulic gradient. When the hydraulic gradient dropped below 0.02, flow stopped almost completely. Thus, the clogging effect is significant because there is no such effect observed in tests on water.

V oid ratio , e

Figure 6. Coefficient of permeability of LB 52/100 sand with water and silicone oil as pore fluid.

J. 1 Effiict o f viscous fluids on permeability of sand

According to the Kozeny-Carman equation, permeability of a soil with a fluid that has N times the viscosity of water but similar unit weight is just 1/Nth of that with water as pore fluid. To verify this theory, a number of constant-head permeability tests were conducted on two sands at a wide range of void ratio using silicone oil or glycerin-water mixture as pore fluid. Some test results are shown in Figures 6&7. It indicates that the permeability reduction

Figure 7. Variation of coefficient ot permeability with void ratio, Ottawa sand.

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0.018

0.016 i

I Q014 !

^ 0-0 2 I

'4 QOl I Pa 0.008 I0

1 0.006 io£ë O.OM ! o

0.002 ,0 :

4a3a

- -i -- -- I- ! ,

♦ e=0.6898 . e =0.6674

AC=0.6367 x e =0.6136

- e =0.6052 * e =0.5839

+ e=0.5616

0.5 0.6

o e = 0.67, disti led water ■ e = 0.63 distilled water + e = 0.67, glycerin/water mixtureA e = 0.63, glycerin/water mixture

■

1

0.0 0.1 0.2 0.3 0.4a^draiJicg:adiert,i

Figure 8. Relationship between coeffieient of permeability and hydraulic gradient for 60% glycerin and 40% water mixture (Ottawa sand).

On the other hand, it needs to be pointed out that the hydraulic gradient in a centrifuge test, as shown in Table 1, is increased by N times, where N is the ratio o f centrifugal acceleration over gravitational acceleration. Therefore, the chance for clogging to occur is significantly reduced. Nevertheless, the effect o f the clogging needs further study because it did not occur in tests using water as pore fluid.

3-. 2 Effect o f viscous fluid on shear strength of sand

A viscous fluid may also affect the mechanical properties o f soil, mainly strength, stress-strain relationship, and damping ratio as the viscous fluid may lubricate the contact between solid particles or interact with minerals o f solid particles. Therefore, it is necessary to conduct laboratory tests to investigate the potential significance of such effects. A recent study carried out at Cambridge (Bielby, 1989) showed there is no obvious effect on shear strength of Leighton-Buzzard sand when silicone oil was used. At University of Kentucky, 24 stress- controlled drained triaxial tests were conducted on saturated Ottawa sand specimens at void ratio of 0.63 and 0.67, respectively, and saturated by distilled water or a 60% glycerin-40% water mixture. The confining pressure applied were 50, 100, and 150 kPa, respectively. Each test was repeated once, and the average value of the friction angle measured is used. The average friction angles measured o f the Ottawa sand at these conditions are

Cell pressure, (kPa)Figure 9. Relationship between friction angle and cell pressure (Ottawa sand).

shown in Figure 9. First, there is a clear trend that the friction angle reduces with confining pressure. This agrees with conventional strength theory for sand, such as the one proposed by Bolton (1986). Secondly, there is a slight difference in the friction angle measured for sand saturated with distilled water or glycerin-water mixture at the two relative densities. The maximum difference observed was just over 2 degrees and there was no apparent significant trend for one fluid to have a greater friction angle than the other. Considering the accuracy of the experiment and the possible difference between “identical” samples, the apparent effects o f the different fluids on the mechanical properties are insignificant. For most soil mechanics problems, such difference (even if it is true) can be ignored. Therefore, based on the data from these tests it is reasonable to conclude that the use of 60% glycerin-40% water mixture as pore fluid has no significant influence on the strength o f the sand.

3.3 Effect o f viscous fluid on stress-strain relationship of sand

Another potential effect o f using viscous fluid is whether it affects the stress-strain relationship o f the sand. In the triaxial tests reported here, the deviator stress and axial strain of the sample was recorded at a specified time interval. The results o f deviator stress versus axial strain for two groups o f tests are shown in Figure 10. Since each test was repeated, the data from the test which had the highest B value (an indication of sample saturation) is used here. As shown in the figure, the stress-strain curves o f the Ottawa sand saturated by distilled water or 60% glycerin-40% water mixture were very close. The pattern of stress-strain curve and the strain developed before reaching failure were similar.

288

b) cen trifuge m odel

Figure 10. Stress-strain relationship at cell pressure of 100 kPa: (a) e = 0.67, (b) e - 0.63.

Therefore, the secant modulus of Ottawa sand appears to be independent o f the type of pore fluid for drained triaxial tests.

4 A C C U R A C Y O F U S IN G C E N T R IF U G A L A C C E L E R A T IO N T O S IM U L A T E G R A V IT Y

The principle o f centrifuge modeling is typically explained as; in a centrifuge test, the dimensions of an earth structure is reduced by 1/N while the centrifugal acceleration is increased by N times, resulting in the same stress magnitude in the model as at the corresponding points in the prototype, as illustrated in Figure 11. The size o f a model and its relative dimension compared to the size of a centrifuge would not be a factor in the accuracy of a centrifuge test. In reality, the stress condition in a centrifuge model is much more complex than that described above and the size o f a model and a centrifuge is a crucial factor. Since the initial stress in soil play a very important role in liquefaction of soil under cyclic loading, a study on the accuracy o f using centrifugal acceleration to simulate gravity is

a) p roto type

Figure 11. Principle of centrifuge modeling.

of great relevance to liquefaction study on centrifuge.

One of the major sources of inaccuracies for a centrifuge test is the variation o f centrifugal acceleration in both the radial and tangential directions. For a soil layer in the prototype and its corresponding centrifuge model shown in Figure 12, there are obvious differences in the stress field. For a typical geotechnical problem, the gravitational acceleration everywhere in the field can be considered going vertically down and has a constant magnitude while in a centrifuge model, the magnitude o f centrifugal acceleration increases with radius and the direction varies from point to point. Apart from that, artificial boundaries (usually rigid) are imposed by model containers, which would further affect the stress distribution in the model. Even though these two factors exist in all centrifuge tests, most theoretical and numerical analyses of centrifuge tests did not take them into account. The effect o f the variation of centrifugal acceleration on stress at the center o f a model was analyzed by Schofield (1980) using a one-dimensional approach. The stress in the upper part o f a centrifuge model would be typically lower than that in the corresponding prototype while at the bottom of a model, the stress would be higher than its counterpart in the field. It was shown that if the depth o f a model is one-tenth o f the radius o f a centrifuge, the magnitude of stress error is under ± 2%. However, in reality the problem is two- dimensional and the model container is a source of further inaccuracy. Thus a more comprehensive analysis which can take into account these two factors is required. The following is a summary of the results o f a numerical simulation o f this problem using a finite element program (Zeng and Lim, 1998).

289

4.1 Methodology

Ideally, the best way to investigate the influence of the non-uniform centrifugal aeceleration on the accuracy o f a centrifuge test is to direetly compare the stresses measured in the field to the stresses measure in the corresponding centrifuge model. However, in reality, a number o f problems make such a comparison impossible. First, soils in the field are most likely to be anisotropic and inhomogenous. Such a field condition is very difficulty, if not impossible, to be replieated in a small scale model. Second, there will be some discrepancies between the properties o f soil in the model and that in the field, which would contribute to some o f the differences in stresses. Last but not the least, there will be experimental inaccuracies from instruments and operation o f devices used both in the field and centrifuge tests. Therefore, it is impossible to identify how mueh o f the difference in the stress field is due to eaeh of the contributing factors.

An alternative approach is to apply an analytical approach to this problem assuming that all the soil properties are the same between the

a) Gravitational acceleration and the resulting stresses in a prototype

modelcentrifugal acceleration contairjer

b) Centrifugal acceleration in a modelFigure 12. A soil layer in prototype and its corresponding centrifuge model.

prototype and the model. Thus it can exclude the influence of other factors so as to investigate the inaecuraey eaused exelusively by the variation of centrifugal acceleration in both radial and tangential directions. To simplify the analysis, soils in both the prototype and the model is assumed to be isotropic and homogeneous. For the stress field in the prototype, assuming the soil layer is o f infinite lateral extent, vertical and horizontal effective stresses can be determined by a hand ealculation. On the other hand, stress field in the model is a complex two-dimensional problem which is solved by using a finite element code SIGMA/W developed by Geo- Slope International (1995).

The accuracy of a finite element simulation is affected by the number of elements and the type of elements used. In this study 8 noded quadrilateral elements with integration order of 9 were used. A simple problem of a soil layer o f 10 m deep with an infinite lateral extent was simulated using a varying number of elements. It was found the when 50 (10x5) elements were used, the difference in stresses between hand analytical solution and the numerical simulation was less than 2%. Therefore, in the following study, a 50 element finite element mesh was adopted.

4.2 Simulation of stresses in a soil layer induced by self-weight

In the first attempt to investigate the influence of variation of centrifugal acceleration on accuracy of centrifuge modeling, the stresses induced by selfweight of soil in a horizontal soil layer o f infinite lateral extent is calculated and compared to the stresses in the corresponding centrifuge model. The soil layer in the prototype is 10 meter thick and has a saturated and buoyant unit weight of 19.81 kN/m^ and 10 kN/m^ respectively. The water table is at the surface of the layer. The corresponding centrifuge model is shown in Figure 13. The test is assumed to be conducted at a centrifugal acceleration o f 50g at the center o f the model and hence the thickness of the soil layer in the model is 20 cm. The study will concentrate on the influence o f the radius o f the centrifuge R and the width of the model container B. The boundaries o f the model container are assumed to be rigid and smooth. For the simplicity of simulation, it is assumed that during the test, the centrifuge swings up slowly so that only drained behavior of the soil will be considered. Also soil in the model is assumed to be normally consolidated.

290

4.4 Simulation o f Centrifugal Forces

The effect o f centrifugal acceleration is simulated by applying body forces on to each element. The body forces have both the vertical and horizontal components. As shown in Figure 14, supposing the center o f element i has a distance Ry to the center of rotation and is away from the center line o f a model, the centrifugal acceleration at this point would be

Figure 13. Centrifuge model o f a 10 m soil layer

4.3 Constitutive Models Used in Simulation

Two types o f constitutive models were used in the finite element simulation: linear elastic and Cam- Clay (Schofield and Wroth, 1968) models. Two parameters (Young’s modulus E and Poisson’s ratio v) are required in a linear elastic model and their values used in this study are E = 30 MPa and v = 0.333 (which would result in a Kg = 0.5). For the Cam-Clay model, soil parameters used are: X = 0.193, K = 0.047, M = 1.2, G’ = 2.4 MPa, and v = 0.333. When the linear elastic model is used, stress calculation is achieved in one load increment. On the other hand, for a non-linear model such as Cam- Clay, small load increment needs to be used in order to achieve accurate results. Also the first initial stress state has to be given or calculated by other procedure. In this study, stress calculation when using Cam-Clay was finished in 50 load steps. For the stress calculation in the field, the first step use a linear elastic model and a unit weight of 10/50 == 0.2 kN/m \ Then the next 49 steps use Cam-Clay model and each step has the same unit weight increase of 0.2 kN/m^ with the stress from the previous step as the initial stress state. For stress calculation in the centrifuge model, the initial stress due to Ig gravity is calculated by the linear elastic model. Using this as the initial stress state, the stress at 2g is calculated using Cam-Clay model with the body forces increased by Ig. This procedure is repeated until the final body force is increased to that corresponding to 50g.

(2)

where co = angular velocity o f the centrifuge. The resulting body forces per volume for this element are

fxi = p w ' R x ,

fyi = P r a ' R y i

(3)

(4)

where p = density o f soil. Obviously, variation in body forces can be quite significant between elements near the center and elements at the four corners.

4.5 Sample results of numerical simulation

Results o f two cases are used here to illustrate the effect: one on simulation of stresses due to selfweight o f soil 10 meter thick and the other the

Rotation Center

Figure 14. Body forces induced by centrifugal acceleration.

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settlement o f a rigid foundation based on a layer of soil 10 meter thick.

In the first example, the stresses due to selfweight o f a 10 m thick soil layer is calculated using a linear elastic model. For the stress distribution in the field, both horizontal and vertical stress increase linearly with the horizontal stress as the bottom of the layer equal to 50 kPa. For a centrifuge model with a width of 0.6m testing on a radius of Im centrifuge, the vertical stress in the model is similar to that in the field. However, as shown in Figure 15, the horizontal stress in the model is significantly different from that o f the corresponding prototype. On the other hand, if the same model is tested on a centrifuge model with a 4m radius, the resulting stress distribution is shown in Figure 16, which is much closer to that in the corresponding prototype. In general the effect o f model size relative to the radius o f the centrifuge on horizontal stress is much more significant than that on the vertical stress and needs to be taken into account.

In the second example, the settlement of a rigid foundation under a load o f 100 kPa is calculated using Cam-Clay model. The results for the prototype structure is shown in Figure 17, which has a total settlement o f 1.288 m. The results calculated for a number of centrifuge models are

20

302535

50 100 200 250 300 350 400 450

H orizon ta l D is tance (m ) (x 0 001)

Figure 15. Horizontal stress distribution in a centrifuge model (B = 0.6m, R = 1 m).

--------- 2 5 --------

I lorizontal Distance (m) (x 0.001 )

Figure 16. Horizontal stress distribution in a centrifuge model (B = 0.6m, R = 4m).

Horizontal Distance (m)

Figure 17. Settlement of a rigid foundation in the field.

Table 2. Settlement of a rigid foundationCase Settlement (m) Error (%)

Prototype 1.288 0R = Im, B = 0.6m 1.448 12.4R = Im, B = 0.8m 1.497 16.2R = 2m, B = 0.6m 1.326 2.9R = 4m, B = 0.6m 1.256 2.5

65 Çj6

listed in Table 2. Clearly, the relative size of the model has a profound influence on the accuracy of the test.

5 CONCLUSIONS

Centrifuge modeling has been proved to be a powerful research tool for liquefaction study. A number of issues related to liquefaction study on centrifuge need to be carefully addressed in order to achieve good simulation o f field situation in centrifuge tests.

Model containers for earthquake tests on centrifuge should have the capability to sustain complementary shear stresses induced by earthquake and match the stiffness o f the soil contained in order to achieve a stress and strain condition in the model similar to that in the field. An equivalent-shear-beam or flexible-shear-beam type o f model container offers a promising solution to reduce artificial boundary effects o f model containers.

It is desirable to avoid using viscous fluid in centrifuge tests as it may have unwanted effects on permeability, strength, stiffness, damping characteristics o f soil. If the use o f viscous fluid is absolutely necessary, a series o f soil tests ought to be conducted to ensure that there is no unexpected effect on the mechanical properties o f the soil.

Finally, in order to achieve a reasonable accuracy, the size o f a centrifuge model should be restricted within a certain range in comparison to the size o f the centrifuge. Within such a limit, the stress

2 9 2

condition in a model can simulate the stress field in the corresponding prototype pretty closely.

REFERENCES

Arulanandan, K. and R.F. Scott, (ed.) 1994.Verification o f Numerical Procedures for the Analysis o f Soil Liquefaction Problems, A.A. Balkema, Rotterdam.

Bielby, F. 1989. Triaxial tests on oil saturated sand. Project Report, Department of Engineering, Cambridge University, England.

Bolton, M.D. 1986. The strength and dilatancy of sands. Geotechnique 36(1): 65-78.

Campbell, D.J., Cheney, J.A. and Kutter, B.L.(1991). Boundary effects in dynamic centrifuge model tests. Proceedings o f Centrifuge 91, pp.441-448, Boulder, USA.

Coe, C.J., Prévost, J.H. and Scanlan, R.Ei. (1985). Dynamic stress wave reflection/attenuation: earthquake simulation in centrifuge soil models, Proc. J. Earthquake Eng. Soil Dyn., 13, pp.l09- 128.

Hushmand, B., Scott, R.F. and Crouse, C.B. (1988). Centrifuge liquefaction tests in a laminar box, Geotechnique 38, pp.253-262.

Ko, H. Y. 1994. Modeling Seismic Problems in Centrifuges. Centrifuge 94, Leung, Lee and Tan (eds.), Balkema, Rotterdam, 3-12.

Kutter, B. L. 1994. Recent Advances in Centrifuge Modeling o f Seismic Shaking. Proceedings of the Third International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, Vol. 3, University o f Missouri, Rolla.

Kutter, B. L., Sathialingan, N., and L.R. Herrmann. 1990. Effects o f Arching on Response Time of Miniature Pore Pressure Transducers in Clay. Geotechnical Testing Journal, 13(3): 164-178.

Law, H., H-Y. Ko, Sture, S. and Pak, R. (1991). Development and performance of a laminar container for earthquake liquefaction studies. Proceedings of Centrifuge 91, pp.369-376, Boulder, USA.

Lee, F.-H. 1990. Frequency Response of Diaphragm Pore Pressure Transducers in Dynamic Centriiuge Model Tests. Geotechnical Testing Journal, 13(3): 201-207.

Madabhushi, S.P.G., Schofield, A.N., and Zeng, X. (1994). Complementary shear stresses in dynamic centrifuge modeling. Dynamic

Geotechnical Testing II ASTM STP 1213, pp.346-359.

Sehofield, A.N. 1980. Cambridge geotechnical centrifuge operation. Geotechnique, 30(3), 227- 268.

Schofield, A. N. 1981. Dynamic and Earthquake Geotechnical Centrifuge Modeling. Proceedings of the International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, Vol.3, University o f Missouri, Rolla, 1081-1100.

Scott, R. F. 1983. Centrifuge Model Test at Caltech. Journal of Soil Dynamics and Earthquake Engineering, 2(4): 188-198.

Scott, R.F. 1986. Solidification and consolidation of a liquefied sand eolumn. Soils and Foundations, 26(4): 23-31.

Steedman, R. S. 1991. Centrifuge Modeling for Dynamic Geotechnical Studies. Proceedings of Second International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, University of Missouri, Rolla, 2401-2417.

Whitman, R.V., Lambe, P.C. and Kutter, B.L. (1981). Initial results from a staeked ring apparatus for simulation of a soil profile, Proc. Int. Conf. Rec. Adv. Geotech. Earthquake Eng. Soil Dyn., 1, pp.361-366, Univ. Missouri-Rolla, Rolla, USA.

Zeng, X. and A.N. Sehofield. 1996. Design and Performance of An Equivalent-Shear-Beam Container for Earthquake Centrifuge Modeling,. Geotechnique, 46(1): 83-102.

Zeng, X. and S.L. Lim. 1998. Accuracy o f using centrifugal aeceleration to simulate gravity, project report. Department of Civil Engineering, University of Kentucky.

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Investigations on the behavior of liquefying soils

R. H. Ledbetter & G. D. ButlerUSAE Waterways Experiment Station, Vicksburg, Miss., USA

R.S.SteedmanSteedman and Associates Limited, Caversham, UK

A B S T R A C T ; Im p ro v ed physical ev idence is needed o f the p ro cesses and m echanism s involved in th e o ccu rren ce o f liquefac tion as soil s tre n g th d e te rio ra te s to a residual s ta te to allow th e d ev e lo p m en t o f new , m ore refined analyses fo r dam safety and m o re cost-effec tive and safe seism ic rem ediation . R eliable physical ev idence can only com e from field o r equ iva len t-fie ld d a ta o f b ehav io r u n d e r well k n o w n and defined cond itions. It has been co n clu d ed th a t th e only p rac tica l ro u te by w hich th is can be ach ieved is th ro u g h th e use o f th e cen trifuge . This paper describes the cen trifuge experim ents being undertaken to cap ture data o f equivalent p ro to ty p e behavior under dynam ic load ing and p re lim inary resu lts . T he resea rch is p a rt o f th e o n g o in g U .S . A rm y E n g in eer E a rth q u ak e E n g ineering R e se arc h P ro g ra m (E Q E N ) at th e U .S . A rm y E n g in eer W aterw ay s E x p erim en t S ta tio n (W E S ) and is using th e dynam ic b ase shak ing capab ility o f th e un ique W E S re sea rch cen trifuge . O u r ob jec tives are: (1)

im prove the sim plified liquefaction m etho d o lo g y co rrec tion facto rs, K a and K a , because this m ethod will alw ays be used w ith in -situ m easu rem en ts fo r initial field investiga tions and fo r verifica tion o f dam and fo u n d a tio n im provem en ts, (2 ) define b e tte r th e b eh av io r o f liquefying soil and e ffec ts on dam behav io r, (3) expand o u r earth q u ak e case h isto ry d a ta base w ith b e tte r know n conditions and responses, and (4) p rov ide p rog ressive results fo r im m edia te u se in U .S . A rm y C o rp s o f E n g in e rs p ro jec ts . T h e ap p ro ach o f th is resea rch to investiga te the behav ior o f liquefying soils is to use labora to ry testing , analytical p ro ced u res and cen trifuge dynam ic m odel testing.

1 IN T R O D U C T IO N 2 E N O rN E E R IN G P R O B L E M

T his p a p er will p re sen t th e b r ie f b ack g ro u n d and the problem , objective, descrip tion o f w o rk and prelim inary resu lts fo r the E Q E N in v estig a tio n o f th e b eh av io r o f liquefying soil m ateria ls . T he s ta te -o f-p rac tic e assum ptions concerning th e occu rrence and behavior o f liquefied soil, residual s tren g th behav io r, and dam stability and d e fo rm a tio n s a re no t valid as show n by field behav io r, num erica l analyses and physical m odel tes t resu lts . O u r o b jec tiv es are to im prove the simplified liquefaction m eth o d o lo g y co rrec tion facto rs, define b e tte r th e b eh av io r o f liquefying soil and effects on dam b ehav io r, expand o u r case h is to ry d a ta base w ith b e tte r k n o w n c o n d itio n s and resp o n ses, and p rovide p rog ressive resu lts fo r im m ediate use in C orps pro jec ts . T he ap p ro ac h o f th is re sea rch to investiga te the b ehav io r o f liquefying soils is to use lab o ra to ry testing , analy tical p ro c e d u re s and cen trifu g e dynam ic testing .

2.1 Current state-of-practice

T he p resen t s ta te -o f-p rac tic e fo r de te rm in ing the p erfo rm an ce o f soils th a t u n d e rg o earth q u ak e -in d u ced shear-s tra in and c o n seq u en tly p o re w a te r p re ssu re buildup in sa tu rated soils is to determ ine if a soil will or will n o t liquefy. T he p e rfo rm an ce and safety o f s tru c tu re s are based on rigid s lid ing-b lock /slices lim it- equilibrium m eth o d s to de te rm in e slip-p lane stability and d e fo rm ation using residual stren g th s in the case o f liquefaction .

In -situ m eth o d s such as S tan d ard P en e tra tio n T est (SP T ), C o n e P en e tra tio n T est and shear w ave velocity m easu rem en ts are u sed to define the trig g erin g o f liquefaction . T he p o ten tia l fo r liquefaction relies on em pirical correlation betw een the penetration resistance and th e pe rfo rm an ce o f soil d ep o sits in past earth q u ak es (Seed, 1979). T he d a tab ase on triggering liquefaction is based on d a ta from level g ro u n d w here

295

su rface ev idence occu rred . Soil c o n d itio n s w ere shallow a t o v e rb u rd e n p ressu res less th an a b o u t 95.8 k P a (a b o u t 4 .6 m o f dep th ). T h e d a ta base is no rm alized to an e a rth q u ak e o f m ag n itu d e 7.5. C o rre c tio n s fo r o th e r e a rth q u ak e m ag n itu d es have to be m ade (S eed & H a rd e r, 1990, N C E E R , 1996).

T o ex ten d th e d a ta b ase to d ep th s re p re se n ta tiv e o f fo u n d a tio n soils u n d e r dam s req u ire s th e u se o f co rre c tio n fa c to rs (S eed & H a rd e r, 1990) fo r th e effec ts o f o v e rb u rd e n p ressu re and initial s ta tic shear- stress. C o rre c tio n fo r h igh o v e rb u rd en , K o , is based on lab o ra to ry te s t resu lts o f th e ra tio o f cyclic-shear- stress, C S S , to cau se liquefac tion at an o v e rb u rd en e ffec tiv e -stress s ta te , a'o, to th a t at a a'o = 95 .8 kPa. C o rrec tio n fo r initial sta tic sh ea r-s tre ss , K a , is based on the ra tio o f C S S to cau se liquefac tion w ith initial sta tic sh e a r-s tre ss app lied to th a t at no initial sta tic shear-s tress .

A fa c to r o f safety , F S L , against th e o c cu rre n ce o f liquefaction , defined as 100 p e rcen t p o re w a te r p ressu re , can be ca lcu la ted as;

FSL^ fK N |) 6 o ] K m K a K a / x e q

W here (N i)6o is from S P T re la tions, K m is e a rth q u ak e m agn itude o r du ra tio n co rrec tio n fac to r

and T eq is a p e rcen tage o f peak earthquake induced

shear stress.

T he F S L can be re la ted to p e rce n t excess p o re w a te r pressure .

T he c o rre c tio n fa c to r K a has a la rge in fluence for dam fo u n d a tio n s. It can re d u ce the C SS to cause liquefaction to a b o u t 45 p e rcen t o f its in-situ value at p re ssu res a b o u t 670 kP a th a t w o u ld ex ist beneath an em b an k m en t dam a b o u t 30 .5m high. A lternative ly , if Ave w ere deriving SPT criteria fo r rem edial trea tm ent o f this dam to lim it th e po ten tial level o f e a rth q u ak e g e n e ra te d p o re w a te r p ressu res, th e K a fa c to r w ould cause an in crease o f m ore than d o u b le in th e requ ired p enetra tion values to be m easured in the field. Clearly, the c o rre c tio n fa c to r can have a m ajo r im pact on the po ten tia l fo r trig g e rin g liquefac tion o r the excess residual p o re w a te r p re ssu res and on the co st o f rem ed ia tion .

T he c o rre c tio n fa c to r K a can also co n trib u te significantly to th e re d u c tio n o f th e in-situ streng th . H o w ev e r, fo r re la tive densities a b o v e 4 5 -5 0 p ercen t, K a can have a p o sitiv e effect on the in-situ streng th . T he K a re la tio n sh ip s a re n o t w ell defined.

In app lication o f the sta te -o f-p rac tice , w e inherently

m ake th e fo llow ing assum ptions; (1) the soil is a lw ays undra ined , (2 ) liquefaction o ccu rs in stan taneously and th e soil shear stren g th ju m p s to residual s ta te , (3) residual s tren g th is co n stan t w ith m o n o to n ie loading, (4) liquefaction is in d ep en d en t o f soil zo n e th ickness, perm eability , o r b o u n d a ry cond itions, (5 ) liquefaction is in d ep en d en t o f w hen th e ea rth q u ak e peak energy arrives, (6) b eh av io r o f th e liquefied soil and its re su ltan t effec ts on a dam are in d ep en d en t o f the soil zone th ickness, perm eability , and bo u n d ary conditions, (7) dam stability and d e fo rm a tio n are co n tro lled by slip -p lanes in d ep en d en t o f th e liquefied soil zone th ick n ess and behav io r, and (8) non-Iiquefied soil at a site is u naffec ted by the earth q u ak e . Field behav ior, num erical analyses, and physical m odel tes ts show that th ese a ssum ptions are invalid.

2 .2 Research problem

C u rren t stud ies fo r m o re th o ro u g h evaluation o f liquefaction and fo r rem ed ia tio n design and analysis have show n se rious lim itations in the sta te -o f-p rac tice . T he sta te -o f-p rac tic e can fo rce us to m ake costly excessive rem ed ia tio n s w hen possib ly no action is requ ired , bu t it can also lead us to m ake unsafe conclusions in o th e r cases.

S ignificant p ro g ress is be ing m ade in the d evelopm en t o f num erica l m eth o d s fo r analysis o f liquefaction and th e c o n seq u en ces . H o w ev er, the eng ineering p ro fessio n will m o st likely alw ays use em pirical co rre la tio n (S e e d ’s o r o th ers ) o f in-situ m easurem ents versus potential liquefaction , po re w ater p re ssu re g en era tio n and e a rth q u ak e response . Every tim e a site is ev alu ated fo r a seism ic design or po ten tially liquefiable soil is im proved and a dam rem ed ia ted , in-situ m easu rem en ts will be m ade. A v a lue /range o f in -situ m easu rem en t to ach ieve will be specified fo r a co n stru c tio n /re m e d ia tio n c o n trac to r. S om e in-situ m easu re will be u sed to ju d g e soil cond itions/im provem ent and seism ic safety o f a dam or site. T h ere fo re , im p ro v em en t in o u r c u rren t s ta te -o f- p rac tice and the em pirical c o rre la tio n s b e tw een in-situ m easu res and p e rfo rm an ce o f soil d ep o sits has to be m ade.

C urren t stud ies o f the se ism ically -induced deform ation behav io r o f dam s indicate th a t as soils are p ro g ressin g to w a rd liquefaction (p o re w a te r p re ssu re is increasing and shear strain is o c cu rrin g ) significant de fo rm a tio n s o f th e s tm e tu re can occu r. Failu re (d am ag in g levels o f d e fo rm a tio n ) can develop significantly b e fo re the co m p le te initial liquefaction stage (100 p e rcen t p o re w a te r p re ssu re ra tio ) is

296

reached . D epend ing on specific c o n d itio n s involving the location, dep th and ex ten t o f liquefying soil and the driving fo rces, a s tru c tu re m ay fail at only 50 percen t s treng th reduction . In th is case, rem ed ia tion to assure safe perform ance is required to p reven t serious dam age significantly b efo re an initial liquefaction condition and a residual s tre n g th s tag e are arrived at in the soil.

T he p ro b lem s in th e c u rren t s ta te -o f-p rac tic e stem m ainly from the fact th a t w e do no t k n o w fo r the sites that have liquefied and constitu te the em pirical basis for analysis; (1) the exact and com plete soil conditions and profiles, (2) the real b eh av io r th a t o ccu rred in the soils du ring and a fte r th e ea rth q u ak e s o r th e various influences on the b ehav io r, (3) th a t th e assum ed non- liquefied soils (u sed in c o m p ariso n to liquefied soils) did not develop p o re p re ssu res o r stra in s and change sta te during the e a rth q u ak es, and (4) w h e th e r artificial and possib ly in co rre c t c o n d itio n s in lab o ra to ry tes ting m ay have led to c o n c lu sio n s n o t to ta lly applicable to the field behav ior.

Im proved defin ition and physical ev idence is needed o f the p ro c esses and m echanism s involved as a soil p ro g resses to liq u efac tio n and residual streng th . This is needed to a llow refined analyses fo r dam safety and m ore co st-e ffec tiv e and safe rem ed ia tion design and analysis. B ecau se w e can m ake v arious a ssum ptions coup led w ith m eth o d o lo g ie s and num erical analyses that can give so lu tions o r answ ers to m ost anything, the reality -check o f so lu tio n s m ust com e from field or equivalent-field da ta o f behav ior under well know n and defined cond itions.

T he e a rth q u ak e re sp o n se d a tab ase needs to be expanded w ith m ore co m p le te data to provide; (1) the n ecessary ad v an ce in the s ta te -o f-p rac tice , (2) a basis for m od ifica tion and im provem en t o f curren t m etliodology and assum ptions, and (3) definition o f the physical p ro c esses and m echanism s involved in the liquefaction p ro cess and resu ltan t effec ts on dam behav ior. T h is w ou ld also p ro v id e the fundam en ta ls and basis fo r d ev e lo p m en t o f new m eth o d o lo g y and analyses. N ew m eth o d o lo g ie s have to be based on co rrec t m echan ism s and p rocesses.

C urren t specific needs fo r m ore th o ro u g h earth q u ak e eng ineering analyses can be identified from exam ination o f the last tw o d ecad es o f experience in seism ic evaluation o f em bankm en t dam s and the serious lim ita tions th a t a rise w hen rem ed ia tion design is a ttem pted . S tud ies invo lv ing liquefaction , stability, and se ism ic-induced d e fo rm a tio n b ehav io r o f dam s raise se rious q u e stio n s th a t im pact the safe perform ance and needs fo r rem ediation (e.g., L edbetter and Finn, 1993, L ed b e tte r, et. al., 1994, Finn and Ledbetter, 1991, Finn, et. a f , 1991 and 1994, Vaid and

C hern , 1985, V aid and T hom as, 1994, B ryne and Flarder, 1991). F o r exam ple, V aid and T hom as (1994) d em o n s tra ted th a t K a fo r specific sand ty p es m ay be substantially less (m o re than a fa c to r o f 2) than suggested by Seed and Flarder, Pillai and B yrne (1994) show ed fo r the fo u n d a tio n m ate ria ls o f D u n can D am , a K a o f 0 .6 co m p ared w ith 0 .4 from the Seed and H a rd e r relation . T h is m ade a d ifference be tw een recom m end ing rem ed ia tion and no rem ediation . T here is a large sp read o f K a re la tio n s and d a ta by v arious re sea rch ers th a t can in fluence w h e th e r to rem ed ia te a dam at co s ts in the ten s o f m illion ’s o f do llars o r not rem edia te .

F o r the past th irty years, research has prim arily co n ce n tra ted on the trig g e rin g o f liquefac tion o f soils bo th in the lab o ra to ry and in field sites. A significant d a tab ase has resu lted o f very im p o rtan t and necessary in fo rm ation co n cern in g th e s tre ss -s ta te trig g e rin g o f liquefaction , cyclic load s tre ss-ra tio and th e dynam ic p roperties o f soils. N ew m ark , 1965, stressed tha t w hat c o u n ted w as w h e th er th e d e fo rm a tio n s th a t a dam suffered du ring an e arth q u ak e w ere to le rab le o r not. Peck, 1992, s ta ted tha t o f all m easu res o f safety, the m ost d irec tly applicable resu lts are th e an tic ipated defo rm ations.

D ue to the lack o f k n o w led g e and experience involving th e b ehav io r o f liquefiable soils u n d e r field cond itions, w e are fo rced to m ake, fo r the critical safety o f dam s, sim plifying a ssu m p tio n s concern ing behavior. W e are fo rced to d isreg ard possib le significant con tro lling influences such as perm eability , bo u n d ary layers and p o re w a te r p re ssu re d issipation and m igration .

Som e specific needs are: (1) well defined and com ple te shear s tress-s tra in re sp o n se cu rves for e a rth q u ak e load ing includ ing the residual streng th po rtio n , (2) stra ins w ith in a p rob lem soil m ass, (3) effec ts o f soil zone th ickness, perm eability , and bo u n d ary cond itions, (4 ) in fluence o f ad jacen t soil m aterials and o f their perm eabilities, (5) dissipation and m ovem ent o f excess residual p o re p ressu re bo th during and after an earthquake, (6) redistribution o f stresses as a soil is losing streng th , (7 ) in te rac tio n o f rem edia tion m ateria ls and adjacen t soil, (8) dynam ic re sp o n se o f rem ed ia tion m ateria ls and o f rem ed ia ted zones, (9) im proved K a and K a facto rs for the field evaluation o f rem ed ia tion ach ievem ent and fo r im proved first e stim ates o f liquefaction po ten tial, (10) effec ts o f stro n g a fte rsh o ck s and (11 ) dam internal behav ior and failure m echanism s in re sp o n se to e a rth q u ak e loading and stren g th deg rada tion .

297

3 DESCRIPTION OF RESEARCH

This research is being conducted by investigations employing laboratory testing, analytical procedures, and centrifuge testing. Physical modeling o f field problems generally involves the construction and experimentation with scale models o f a prototype or field structure. The response o f the model to a physical perturbation such as cyclic loading, earthquake, ocean waves, explosion or even freezing or groundwater changes can be measured and interpreted in terms of the field problem under consideration. Realistic model behavior data can provide valuable information for designers about failure mechanisms and long term performance.

Scaling relationships can be derived from physical principles which interpret centrifuge model experimental investigation data in prototype terms (Schofield 1980 and 1981, Schofield and Steedman 1988). These are summarized in Table 1.

PARAMETER FIELD CENTRIFUGE MODEL (Ng)

Stress a a

Strain e e

Length,displacement

L L/N

Area A A/N^

Force F F/N^

Volume V V/N^

Mass M M/N^

Energy E E/N^

Frequency f N f

Velocity V V

Acceleration a a/N

Time (for inertial events)

t t/N

Time (for diffusion events)

t t/N"

The wide range o f physical phenomena that may be created in a centrifiige and the quality and detail o f the data that may be captured from a model in-flight clearly provides substantial opportunities for engineering research studies. The Corps o f Engineers has been

involved with centrifuge modeling since the 1970s, and the recent development o f the WES Centrifuge Research Center in Vicksburg demonstrates the Army’s full commitment towards the use of physical modeling as an integral part o f engineering analysis.

Soil behaves non-linearly and is stress-state dependent. Centrifuge testing is the best, most practical, most economical, and the only method for properly investigating and verifying earthquake induced prototype behavior in soil.

3.1 The WES Centrifuge

The design specification o f the centrifuge followed a review of available academic facilities which had shown that none were able to routinely conduct experimental models o f the large field structures and problems with which the Corps is principally concerned (Ledbetter, 1991). The facility was therefore designed with a unique operating envelope. It was required that model containers should be easily placed on and off the centrifuge and these requirements led to the design of a beam centrifuge with a swinging platform based on the French designed Acutronic 661, 665, and 680 series of geotechnical centrifuges. Other centrifuges in this Acutronic family include one at Rensselaer Polytechnic Institute, Troy, New York, at the Centre for Cold Oceans Resources Engineering, St. Johns, Newfoundland, and several in Japan and Europe. Figure 1 shows the WES Centrifuge in its containment structure; key parameters are listed in Table 2 and Figure 2 shows the performance envelope relating payload capability to centrifugal acceleration. Prototypes o f the order o f 300 m in breadth and 300 m deep can be simulated in models subjected to up to 350 gravities (around 3500 m/s^).

Figure 1. WES centrifuge.

298

Table 2, Key Characteristics o f the Army CentrifugeArmy Centrifuge

Radius to platform

Payload at 143 g

Payload at 350 g

Capacity

6.5 m

8000 kg

2000 kg

1144 g-tonne

WES CentrifugePerformanceEnvelope

100 200 300Acceleration, g's

Figure 2. WES centrifuge performance envelope.

manipulation o f the model materials and fluids, (6) miniature instrumentation, cameras and in flight site interrogation, and (7) high speed data acquisition and control systems.

The new capabilities that will flow from the centrifuge will depend on the ingenuity o f its users and the design o f its appurtenances. In this respect the design o f the centrifuge itself is merely one component of the development o f new capabilities in physical modeling.

The uniquely large stored-angular-momentum (SAM) shaker (Madhabushi, et. al, 1996) (Figure 3 & 4) designed to be capable o f exciting dynamic motions up to 200+ g will be used with the equivalent shear beam box (Figure 5) in this research.

A wide range o f modeling capabilities was required and actuators and appurtenances have been designed to fulfill these requirements. Models can be constructed in a range of containers that depend on the geometry o f the problem under investigation (plane strain, axi- symmetric, three dimensional, etc.) and the type of phenomenon to be recreated.

Recent world-wide interest in centrifuge modeling has concentrated on geotechnical applications; however, the WES centrifuge facility has a much broader mission. The WES centrifuge will address research needs in physical modeling across the full range of engineering applications. Investigations are possible under climatic conditions ranging from desert to polar to ocean regions. Key capabilities include: (1) force and displacement controlled load systems, (2) earthquake simulation, dynamic vibration loading and water wave generation, (3) blast loading, (4) model package environmental control, (5) in flight

Figure 3. View of SAM actuator without support walls.

Figure 4. Assembled system on WES centrifuge.

299

Figure 5. Stacked ring equivalent shear beam container.

3.2 Earthquake research

Centrifuge testing is being used to produce prototype response under laboratory conditions and with measured base shaking input motions and propagation. The experiments are to: (1) obtain high-quality detail and data for earthquake behavior case histories, (2) investigate the Ka and Ka correction factors under dynamic loading by shaking o f the continuum rather than by laboratory element tests, (3) measure and investigate pore pressure behavior and response under various conditions during and after earthquakes, (4) measure and investigate strain, deformation, and softening behavior during and after earthquakes, (5) measure and investigate the controlling effects of permeability on pore pressure behavior during and after earthquakes, and (6) measure and investigate the effects o f boundary conditions on the behavior of liquefying soil. Each centrifuge test will yield results relevant to several o f the objectives in defining the behavior o f liquefying soils and effects on dam response.

Laboratory testing will be used to: (1) develop and define the complete shear stress-strain curve for earthquake-induced liquefying soil behavior including the residual portion and the development o f simplified methods for obtaining the curve, (2) determine the properties o f soils used in the centrifuge dynamic tests for both pre and post test conditions, (3) determine the complete shear stress-strain curve for the soils used in the centrifuge dynamic tests and (4) conduct cyclic tests for the laboratory-based determination o f Ka and Ka for comparison to the centrifuge dynamic test results.

Analytical procedures employing both numerical dynamic-analysis and conventional static-analysis methods will be used for: (1) analysis o f the centrifuge results as an equivalent prototype and as a bridge between the results and existing field case history data, (2) identification o f anticipated important parameters and sensitivities for consideration in the centrifuge dynamic tests, (3) careful design of centrifuge dynamic tests to maximize the results and to obtain results from each test that are applicable to several of the objectives, (4) analyses of pre, during and post dynamic test conditions, (5) extrapolation and comparison of centriftige test results to limit the number and extent of needed tests and (6) important assistance in the necessary understanding and definition of the physics of the mechanisms and processes being investigated.

Results from the work of other researchers studying residual strength, causes of liquefaction and flow of liquefied soil will be incorporated and collaboration will be made. However, this study is unique in that it addresses the fundamental effective-stress behavior and mechanisms o f soil as it is in the process of liquefying and not just the end point o f a liquefied state. The entire process o f liquefaction and the controlling conditions are key to eventual accurate predictions of anticipated deformations; how much and where.

3.3 Centrifuge test plans

The first tests and studies are concerned with evaluating Ka in centrifuge tests o f the behavior of level ground for comparison with laboratory values. Two soils, Ottawa and Nevada sand, and a mixture with silts are planned for the tests. Both o f these soils are well known with extensive laboratory investigations. Another soil or mixture with silt will be used for low permeability and will be placed at a nonliquefiable density to bound/confiiie liquefiable test soil layers. It may also be used to investigate a deep foundation layer beneath the liquefiable soil and a transition from the rigid base through which the input motion propagates to the test layers.

At least three test layer depths and possibly five will be used for each soil at different relative densities and at prototype overburdens o f 95.8 to 575 kPa.

Pore pressure and acceleration transducers placed redundantly are used to measure behavior. Ka can be calculated for each layer in ratio to the top layer at 95.8 kPa. Several dynamic excitations will be used during each test period to determine the effects o f dynamic excitation history and previous liquefaction on soil and Ka behavior.

300

Cross-Section Through Model 2d;Prototype Depth 15 m

ACC 7314 was mounted horizontally on the bottom ring of the ESB.

A C C 12814 A C C 12815 300

--------Q-

70

P P T 8 P P T 46

Plan O n S ec t ion A -A S h o w in g L oc ation s O f T r ansd u cers

F igure 6. T ypical m odel c ro ss-sec tio n fo r 95 .8 k P a effective o v erbu rden .

D ista n ces In mni

Follow ing th e initial K a te s t p ro g ram , a sim ilar cen trifuge tes t p ro g ram will be d ev elo p ed fo r K a behavior. T he tes ts will be conducted w ith em bankm ent dam loading to induce initial sta tic shear stresses in the fo u n d a tio n layers.

T est p ro g ram s will a lso be c o n d u c ted in sim ilar fashion to get equivalent p ro to ty p e da ta addressing the influences o f perm eability , b o u n d a ry co n d itio n s and layer th ickness and liquefiable soil zo n e th ickness on the b ehav io r o f liquefying soil. T his will yield significant e ffec ts on dam re sp o n se b o th ex ternal and internal; strains, so ften ing , re sp o n se during and po st earth q u ak e , g lobal b eh av io r and fa ilu re m odes.

4 R E S E A R C H E X P E R IM E N T S R E S U L T S

This sec tion p resen ts typical and p re lim inary resu lts from K a cen trifu g e experim en ts. F ig u re 6 show s a typical in stru m en ted m odel o f N e v ad a sand w ith a loose layer b en ea th a d e n se r layer th a t im poses a 95 .8 kPa o v e rb u rd e n p re ssu re a t 50 g cen trifugal acceleration . T he sand layers w ere rained in p lace at a re la tive density o f 49 % in th e b o tto m and 74% in the top. T he in stru m en ta tio n o f p o re -p re ssu re and a cce le ro m ete r tran sd u ce rs is show n.

F igu re 7 show s tim e h isto ry ra w d a ta from pore- p ressu re tran sd u ce rs and accele ro m ete rs .

301

Mid depth, loose layer

Figure 7. Time history raw data from pore pressure tranducers and accelerometers.

302

Input acceleration on base o f m odel box

FourierAmplitude

Freq. (Hz)

Figure 8. Fourier analysis and wavelet map of a base input motion.

14

12

10

<§ 6'SX

.2 0 . 2 5

❖ 0 . 3 -

□ O C l

0 . 4 T S F

i 2 . 5

c

4

❖ ❖

♦ ♦

❖

0.5 0.7 0.9 1.1 1.3 1.5

Amplification (as function o f base input)

Figure 9. Typical acceleration profile.

Figure 8 shows the Fourier transform combined with harmonic wavelets analysis mapping (Butler, 1998). Conventional methods of signal analysis using Fourier

N u m b er O f E quiva lent Uniform C yc les To L iquefaction

Figure 10. Liquefaction data at 0.36 tsf overburden.

transforms provide frequency information that is averaged over the entire length o f the acceleration time history. This method o f analysis fails to address the changing spectral content o f a non-stationary signal that is produced by non-linear dynamic events and consequently, adversely effects attempts to validate

303

M8.□ (

8 -1 .6 T S F ) C R 2 .5

n

m m'L-J ■■ ■

D

# ;

H

N u m b e r O f E q u i v a l e n t U n i f o r m C y c l e s To L i q u e f a c t i o n

A▲ A

n' 'A

^ AA ^

5 10 15 2 0 25 30

N u m b e r O f E q u i v a l e n t U n i f o r m C y c l e s To L i q u e f a c t i o n

Figure 11. Liquefaction data at 1-1.5 tsf overburden. Figure 12. Liquefaction data 2-2.26 tsf overburden.

00

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0

❖ 0 .3-.4 TSF ^ .8 -1 .6 TSF A 2 -2 .6 TSF O O C R 2.5, 0 .3-.4 TSF □ OCR 2 .5 ,0 .8 -1 .6 TSF

<4

f►

rn

f ü ^ M

1_1

□

♦ ^ 1 1

❖ ^ AA ^ ■

0 5 10 15 20 25 30 35 40

Number O f Equivalent Uniform C ycles To Liquefaction

Figure 13. Summary o f liquefaction data from centrifuge experiments.

45 50

304

nu m erica l m o d elin g techn iques. T he ha rm o n ic w av ele t tech n iq u e fo r a n aly zin g the c h an g in g freq u en cy re sp o n se o f a ph y sica l system w ill p ro v id e s ign ifican t new insigh ts in to the ch arac te ris tics o f soil b eh av io r and o p en new w indow s o f u n d e rs tan d in g in to its co m p lex d y n am ic resp o n se .

F igu re 9 show s a typ ica l acce le ra tio n am p lifica tio n p rofile as a fu n c tio n o f base inpu t m o tion . F ig u res 10 th ro u g h 13 p re sen t sh ea r-s tre ss-ra tio and n u m b er o f eq u iv a len t u n ifo rm cy cles to liq u e fac tio n fo r a n u m b er o f cen trifu g e e x p erim en ts . F igu re 10 is fo r vertica l o v e rb u rd en co n fin in g p ressu res o f 0 .3 6 tsf; F ig u re 11 is for 0 .8 -1 .6 tsf, and F ig u re 12 is fo r 2 -2 .6 t s f F igure 13 p resen ts a sum m ary o f the liquefac tion data . A lso included on th ese figu res is d a ta rep resen tin g the response o f the soil w ith an over-co n so lid a tio n ratio o f

2.5 th a t w as induced by runn ing th e cen trifu g e to h igher accele ration and b ack to th e tes t acceleration o f 50 g. T he im plied resu lt is th a t o v e r-co n so lid a tio n do es cause a d ifferen t re sponse .

5 C O N C L U S IO N S

T he re sea rch d escribed in th is p a p e r will p rov ide definition and clarification o f the K a and K a correction fac to rs fo r u se in th e ev a lu a tio n o f dam rem ed ia tion and in the initial de term ination o f liquefaction potential. T he resu lts o f th is p ro g ram will enhance significantly o u r u n d erstan d in g o f dam re sp o n se and o u r capability to de te rm ine and define liquefaction occu rren ce , its potential to cause dam age, and the need for m itigation. E co n o m ic benefits will resu lt in im proved analysis, design, and rem ed ia tio n requ irem en ts. T he th rea t o f liquefac tion will be lessened th ro u g h b e tte r u n d e rs tan d in g o f th e p ro c ess and con d itio n s fo r e a rth q u ak e induced stren g th loss and liquefaction . S ignificant enhancem ent o f the da ta base o f earthquake re sp o n se will be m ade w hich will p rov ide; (1) m odification and im provem ent o f cu rren t m ethodology and assum ptions, and (2) defin ition o f p ro cesses and m echanism s fo r d e v elo p m en t o f new analysis m ethodo logy .

2 B u tle r, G .D ., (1 9 9 8 ). A D ynam ic A nalysis O f T he S to red A ngu la r M o m e n tu m A c tu a to r U sed W ith T he E q u iv a len t S hear B eam C o n ta in e r, Ph .D . thesis, U niversity o f C am bridge , E ng land .

3 Finn, W . D . L iam and L ed b e tte r , R . H ., (1991). E v alu atio n o f L iq u e fac tio n E ffec ts and R em ed ia tio n S tra teg ies by D e fo rm a tio n A nalysis, Proceedings, International Conference on Geotechnical Engineering for Coastal Development, GEOCOAST 91, Y o k o h am a, Japan.

4 Finn, W . D . Liam , L ed b e tte r, R . H ., Flem ing, R. L., Jr., T em pleton , A. E ., F o rre st, T. W ., and Stacy, S. T.,(1991). D am on L iquefiab le F o u n d a tio n : Safety A ssessm ent and R em ediation , 17th Congress on Large Dams, International Commission on Large Dams, V ienna, A ustria .

5 Finn, W . D. L iam , L ed b e tte r, R . H ., and M arcu so n , W. F., I l l , (1 9 9 4 ). Seism ic D e fo rm a tio n s in E m bankm ents and Slopes, Proceedings, Symposium on Developments in Geotechnical Engineering (From Harvard to New Delhi, 1936 - 1994), B an g k o k , Thailand.

6 Ledbetter, R. H., (1991). Large Centrifuge: A C ritical A rm y C apability F o r T he F u tu re , M isce llaneous P a p e r G L -9 1 -1 2 , U .S . A rm y E n g in eer W aterw ay s E x p erim en t S ta tion , V icksburg , M S .

7 L ed b e tte r, R. H. and Finn, W . D . L iam , (1 9 9 3 ). D evelopm ent and E valuation o f R em ediation S trategies by D efo rm a tio n A nalysis, Proceedings of the specialty conference Geotechnical Practice in Dam Rehabilitation, R aleigh , N o r th C aro lina , G eo techn ica l Special P u b lica tio n N o. 35.

8 L ed b e tte r, R . H ., F inn, W . D . L iam , H ynes, M . E ., N ickell, J. S., A llen, M . G ., and S tevens, M . G., (1994). Seism ic Safety Im p ro v em en t o f M o rm o n Island A uxiliary D am , 18th Congress on Large Dams, International Commission on Large Dams, D urban , S outh A frica.

6 R E F E R E N C E S

1 B yrne, P. M . A nd H a rd e r, L. F ., (1991). T erzagh i D am , R ev iew o f D eficiency In v estig a tio n , R e p o rt N o . 3, p rep ared fo r B C H y d ro , V a n co u v er, B ritish C olum bia.

305

9 Madhabushi, S. P. G., (1996). Preliminary Centrifuge Tests Using The Stored Angular Momentum (SAM) Earthquake Actuator, Cambridge University Engineering Department report, Cambridge University, England.

10 National Center for Earthquake Engineering Research (NCEER), (1996). Workshop on Evaluation of Liquefaction Resistance, Salt Lake City, Utah.

11 Newmark, N. M., (1965). Effects o f Earthquakes on Dams and Embankments, 5th Rarikine Lecture, Geotechnique, Vol. 15, No. 2.

12 Olsen, R. S., (1996). The Influence of Confining Stress on Liquefaction Resistance, Draft WES Report.

13 Peck, R. B., (1992). Written comments on the review o f remediation for Mormon Island Auxiliary Dam.

14 Pillai, V. S. and Byrne, P. M., (1994). Effect of Overburden Pressure on Liquefaction Resistance of Sand, Canadian GeotechnicalJournal, Vol. 31.

15 Schofield, A. N., (1981). Dynamic and Earthquake Geotechnical Centrifuge Modelling, Proceedings, International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, University Missouri Rolla, MO, Vol. 3.

16 Schofield, A. N. and Steedman, R. S., (1988). Recent Development of Dynamic Model Testing in Geotechnical Engineering, Proceedings, World Conference in Earthquake Engineering, Tokyo-Kyoto, Vol. VIII.

17 Seed, H. B., (1979). Considerations in the Earthquake-Resistant Design o f Earth and Rockfill Dams, 19th Rankine Lecture, Geotechnique, Vol. 29, No. 3.

18 Seed, R. B. and Harder, L. F., (1990). SPT-Based Analysis o f Cyclic Pore Pressure Generation and Undrained Residual Strength, Proceedings of the H. Bolton Seed Memorial Symposium, University of California, Berkeley, Vol. 2.

19 Vaid, Y. P. and Chern, J. C., (1985). Cyclic and Monotonic Undrained Response of Saturated Sands, Advances in the Art of Testing Soils under Cyclic Conditions, ASCE Convention, Detroit.

20 Vaid, Y. P. and Thomas, J., (1994). Post Liquefaction Behavior of Sand, Proceedings of the 13th International Conference on Soil Mechanics and Foundation Engineering, New Delhi, India.

21 Zing, X. and Schofield, A. N., (1996). Design and Performance o f an Equivalent-Shear-Beam Container for Earthquake Centrifuge Modelling, Geotechnique, Vol. 46, No. 1.

306


Modeling liquefaction in centrifuges

Hon-Yim Ko & Mandar M. DewoolkarUniversity of Colorado, Boulder, Colo., USA

A B S T R A C T : In th e p a s t tw enty years or so, num erous investiga tions on th e cen trifuge have b een carried ou t to rep ro d u ce seism ically induced liquefac tion ph en o m en a an d to s tu d y th e ir effects on th e s ta b ility o f such e a r th s tru c tu re s as hom ogeneous or s tra tif ied level g round , slopes, em b ankm en ts , w a ter fron t s tru c tu re s , sheet pile walls, b u ried s tru c tu re s , etc. In th is p a p e r, a review of som e of these investiga tions is p resen ted . A good cen trifuge ex p erim en t is ex p ec ted to p ro d u ce rep ea tab le , q u a n tita tiv e d a ta . In seism ic cen trifuge experim en ts, close a tte n tio n is req u ired on such issues as g en era tio n of e a rth q u ak e m otions, s im u la tio n of b o u n d a ry conditions, an d scale effects such as p a rtic le size an d th e conflict in th e tim e scaling for th e coupled d y n am ic po re p ressu re gen era tio n an d diffusive po re p ressu re d iss ip a tio n phenom ena. T hese an d som e o th e r issues are also discussed in th is p ap er, in th e co n tex t of th e ir effects on th e s tu d y of liquefaction .


Since th e e a rth q u ak es in N iig a ta a n d A laska in 1964, th e liquefaction phen o m en o n has been ex tensively s tu d ied by geo techn ical eng ineers w ith th e a id of field observations d u rin g an d a fte r earth q u ak es, ex p erim en ta l investiga tions, an d th eo re tic a l stud ies.

Since th e lo ca tio n of an e a rth q u ak e event is u n p re d ic tab le , in s tru m e n te d sites w hich are expensive an d requ ire h igh m ain ten an ce are seldom p re p a re d w aiting for an ea rth q u ak e to occur. T herefore, geo techn ical engineers have genera lly relied on lab o ra to ry and th eo re tica l m eth o d s to s tu d y liquefaction .

A ru la n an d a n (1993) classified liquefaction s tu d ies in two basic philosophies. T h e first ph ilosophy considers th e ev aluation of liquefaction as an a r t re q u iring considerab le ju d g m e n t an d experience as well as tes tin g an d analysis. T h e second ph ilosophy focuses on th e developm ent of m eth o d s w hich could m inim ize th e c o n tr ib u tio n o f experience an d ju d g m e n t an d re duce th e p rob lem to one o f ca lcu la tions su p p o rte d by the evidence from ex p erim en ta l m easu rem en ts. B o th approaches requ ire lab o ra to ry tes tin g . In th e first ap proach, sm all soil sam ples were te s te d in cyclic tr ia x ial, cyclic sim ple shear, or m ore recen tly in to rsio n al shear a p p a ra tu s . T hese m eth o d s do n o t reveal m echanism s of failure, no r th e ir consequences in realis tic b o u n d ary value p roblem s.

In th e early I9 7 0 ’s, th e use of shak ing tab les becam e p o p u la r for s tu d y in g th e consequences of earth q u ak es on sm all m odels of e a r th s tru c tu re s . A lthough th e resu lts from these tes ts c o n d u c ted u n d e r e a r th ’s g ra v ita

tio n a l accele ra tion p rov ided som e q u a lita tiv e insights, th ey suffered from no t be ing ab le to s im u la te realis tic p ro to ty p e stress levels. O n th e o th e r h an d , a fte r th e developm ent o f th e first m o d ern h y d rau lic shaker a t C alifo rn ia In s t i tu te of Technology in th e la te 1970’s, th e seism ic cen trifuge m odeling techn ique, hav ing th e ab ility to rep ro d u ce rea lis tic full-scale stresses, has been firm ly estab lish ed as a d ep en d ab le research too l to s tu d y e a rth q u ak e re la te d p rob lem s.

1.1 C entrifuge m odeling

In a cen trifuge ro ta tin g a t an a n g u la r speed u, h igh accele ra tion levels are c rea te d in a scaled m odel loca ted a t a ra d iu s R, p ro d u c in g an accele ra tion N tim es e a r th ’s g rav ity g, w here N = R cj^ /g . T h e p rincip le b e h in d cen trifuge m odeling is to c rea te a stress field in a geom etrically sim ilar m odel, id en tica l to th a t in a real or h y p o th e tica l p ro to ty p e . Since s tra in s are d im ensionless, th is will en su re th a t th e s tre ss-s tra in rela tio n sh ip s a t hom ologous p o in ts in th e two system s will be th e sam e if p ro to ty p e m a te ria ls are used in the m odel.

T h e ideal way to verify th e scaling re la tio n s involved is to com pare m odel te s t re su lts w ith th e a c tu a l p ro to ty p e behav ior. In th e absence of a p ro to ty p e , th e behav io rs of tw o or m ore m odels of th e sam e p ro to ty p e scaled co rrespond ing to g-levels (m odeling of m odels), a re com pared to each o th e r using th e scaling re la tions . If th e re su lts a re found in te rn a lly consis ten t, th e ir m odel behav io rs can be e x tra p o la te d to p ro to ty p e response.

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T h e cen trifuge m odeling tech n iq u e can n o t only be used to m odel real or h y p o th e tica l p ro to ty p e s , b u t also to investiga te new phenom ena, to pe rfo rm p a ra m e tric stud ies, an d to v a lida te an a ly tica l an d num erica l m ethods.

N um erous investiga tions on th e cen trifuge have been carried o u t to rep ro d u ce seism ically induced liquefaction phen o m en a an d to s tu d y th e ir effects on th e s ta b ility of various e a r th s tru c tu re s . Som e of these s tud ies are briefly add ressed here.

Seism ic cen trifuge m odeling is a com plex ex p erim en ta l techn ique. S im ilar to o th e r e x p erim en ta l techn iques, cen trifuge m odeling , especially s im u la tio n of liquefac tion phenom ena, has in h eren t inaccuracies a ris ing from a nu m b er of fac to rs such as th e v a ria tio n of g-level in ra d ia l an d tan g e n tia l d irec tions, p e rfo rm ance of shake tab les , b o u n d a ry con d itio n s im posed by con ta iners, an d sys tem lim ita tio n s o f equ ipm en t, tran sd u ce rs , a n d d a ta acq u isitio n system . In a d d ition , th e success o f a liquefac tion te s t in p ro d u c in g re p ea ta b le an d re liab le q u a n tita tiv e d a ta dep en d s on how well th e scale effects such as p a rtic le size an d th e conflict in tim e scaling are h an d led . T hese an d som e o th er asp ec ts o f th e m odeling tech n iq u es are also d iscussed here in th e co n tex t of th e ir effects on th e s tu d y of liquefaction .

2 C E N T R IF U G E L IQ U E F A C T IO N S T U D IE S

R esearchers have a tte m p te d to s tu d y liquefaction p h enom ena by co n d u c tin g cen trifuge ex p erim en ts to in v estiga te effects of com plete or n ear liquefaction in various e a r th s tru c tu re s . E x am p les of such stu d ies are as follows (ex p erim en ts were c o n d u c ted in rig id conta in e rs unless o therw ise s ta te d ) :

H om ogeneous level g ro u n d : (i) silicone o il-sa tu ra te d san d in a rig id co n ta in er w ith duxsea l end b o u n d arie s by V enter (1987); (ii) w a te r-sa tu ra te d san d in a lam in a r co n ta in er by Law, e t al. (1991); (iii) 3 ex perim en ts on M odel No. 1 for V EL A C S p ro jec t (A ru lan a n d a n an d S co tt, 1993) on w a te r-sa tu ra te d san d in lam in ar con ta iners; an d (iv) silicone-oil s a tu ra te d san d in a lam in a r co n ta in er by C ubrivosk i, e t al. (1995).

S tra tified g ro u n d : (i) a to ta l o f 6 experim en tson w a te r-sa tu ra te d san d u n d e rly in g a silt layer for V E L A C S, 3 in lam in a r con ta iners (M odel No. 4a) an d3 in rig id co n ta in ers (M odel No. 4b); an d (ii) w ater- sa tu ra te d silt an d san d layers by F iegel a n d K u tte r (1994).

S loping g ro u n d : (i) 3 ex p erim en ts on w a te r-sa tu ra te d san d in lam in a r con ta iners for V E L A C S (M odel No. 2); (ii) silicone o il-sa tu ra te d san d slope by P ilg rim an d Zeng (1994); an d (iii) w a te r-sa tu ra te d san d slope in a lam in ar c o n ta in er by N agase, e t al. (1994)

E m b an k m en ts an d dam s : (i) w a te r-sa tu ra te d sande m b an k m en t w ith silt cap in V E L A C S (M odel No. 6);(ii) w a te r-sa tu ra te d zoned em b an k m en t in V EL A C S (M odel No. 7); (iii) m odeling o f m odels of b o th w ater- an d m eto lo se -sa tu ra ted hom ogeneous san d em b an k m en ts by A stan eh (1993); (iv) w a te r-sa tu ra te d e a r th d am w ith a lte rn a tin g layers of clay an d san d by M u- ra le e th a ra n an d A ru la n a n d a n (1991); (v) m odeling of m odels of silicone o il-sa tu ra te d em b an k m en t on sand layer by K oseki, e t al. (1994); an d (v) silicone oil- s a tu ra te d em b ankm en t on san d layer in rig id co n ta in ers w ith flexible u re th a n e end b o u n d a rie s by A be, e t al. (1995) an d w ith silicone ru b b e r end b o u n d arie s Zheng, e t al. (1995).

R e ta in in g s tru c tu re s : (i) dike re ta in in g s t ru c tu re on silicone o il-sa tu ra te d san d layer by V enter (1987); (ii) Sheet pile an d an chored w alls re ta in in g silicone oil- s a tu ra te d san d by S teed m an an d Zeng (1990); (iii) g rav ity re ta in in g wall w ith w a te r-sa tu ra te d san d backfill in V ELA C S (m odel No. 11); (iv) T iltin g re ta in ing wall w ith w ater an d g lycerol so lu tio n -sa tu ra te d san d backfill by W h itm a n an d T in g (1993); (v) p ro to ty p e m odeling of a dike re ta in in g s tru c tu re , w ater- s a tu ra te d , by M u ra lee th a ra n , e t al. (1994); (vi) w ate rfro n t g rav ity quay w alls re ta in in g w a te r-sa tu ra te d backfill in rig id c o n ta in er w ith duxseal end b o u n d arie s by Zeng (1998); an d (vii) m odeling of m odels of can tilever re ta in in g walls w ith b o th w ater- an d m etolose- s a tu ra te d san d in a rig id co n ta in er w ith duxseal end b o u n d a ry by D ew oolkar, e t al. (1998a).

Footings an d offshore s tru c tu re s : (i) sto rage ta n k on glycerol so lu tio n -sa tu ra te d in a lam in a r con ta iner by W h itm an an d L am be (1988); (ii) foo ting on w ater- s a tu ra te d san d in a lam in a r c o n ta in er by Law and K o (1995); (iii) 3 ex p erim en ts on M odel No. 12 in V EL A C S on a foo ting in a s tra tif ied s ilt-san d w ater- sa tu ra te d soil; (iv) tow er s tru c tu re s on w ater- an d silicone o il-sa tu ra te d san d by M ad ab h u sh i (1994); (v) shallow fo u n d a tio n s on w ater- an d g lycerol so lu tion- s a tu ra te d san d by L iu an d D obry (1994); an d (vi) g rav ity based s tru c tu re founded on w a te r-sa tu ra te d sand-clay -sand layers by D ew oolkar, e t al. (1998c)

D eep fo u n d a tio n s ; (i) p ile g roup in silicone oil-s a tu ra te d san d by Sato , e t al. (1995); (ii) p ile g roups in m ethy l ce llu lo se-sa tu ra ted san d layers in a flexible sh ear b eam c o n ta in er by W ilson, e t al. (1997); an d(iii) a pile in w a te r-sa tu ra te d san d layers in a lam in a r box by A b d o u n , e t al. (1997).

B uried s tru c tu re s ; (i) b u ried s tru c tu re in silicone oil s a tu ra te d san d by K oseki, e t al. (1995); an d (ii) flexible (T ohda, 1995) an d rig id p ipes (T ohda, e t a l., 1997) b u ried in w a ter an d m e to lo se -sa tu ra te d sand .

C o u n term easu res ag a in s t liquefac tion : (i) ev alu atio n of deep cem ent m ix ing m e th o d ag a in s t liquefac tion of

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loose sandy g ro u n d in a lam in a r box, w a te r-sa tu ra te d by Suzuki, et al. (1991); (ii) “la te ra l im provem en t” of em bankm en t an d b u ried s tru c tu re m odels, silicone o il-sa tu ra ted san d by K oga, e t al. (1995); (iii) m ethy l cellu lose-sa tu ra ted co m p acted sa n d in a rig id conta in e r by H iro-O ka, e t al. (1995); (iv) sto rage tan k s on silicone o il-sa tu ra te d san d im proved using “sheet p ile” an d “R C -ring” m eth o d in a lam in a r con ta iner by Sakem i, et al. (1995); (v) e m b an k m en t fo u n d atio n liquefaction co u n te rm easu res by densification , cem ent deep-soil-m ixing, gravel berm s, an d sheet pile enclosure using w a te r-sa tu ra te d san d by A dalier, et al. (1998); an d (vi) w a te r-sa tu ra te d san d layer w ith gravel d ra in system in a lam in a r c o n ta in er (Yang and Ko, 1998).

From th e abovem en tioned list, it can be no ticed th a t soils were sa tu ra te d w ith so lu tions o th e r th a n w ater. Also, d ifferent con ta iners were used. D uxseal and o th er m ate ria ls were used a t co n ta in er b oundaries. These issues are d iscussed la te r in th is p ap er.

In th e above experim en ts , som e of th e im p o rta n t key fea tu res of liquefaction p h en o m en a were genera ted , such as th e gen era tio n an d d issip a tio n of excess pore p ressure , th e loss of stiffness of soil as ind ica ted by th e a tte n u a tio n of th e base accele ration , large se ttlem en ts an d la te ra l defo rm ations, an d san d boils.

T h is list of ex p erim en ts is by no m eans com plete; however, it p resen ts a genera l tre n d in th e seism ic centrifuge m odeling p ractice . For exam ple, cen trifuge exp erim en ts are very ra re ly ta rg e te d tow ards m odeling ac tu a l p ro to ty p es. T h ey som etim es m odel a sim plified, tw o-dim ensional version of a specific p ro to ty p e . E x p erim en ters alw ays p refer to use soils w ith know n p roperties . In m ost instances, san d is used. T y p ically, ex p erim en ts are co n d u cted for research pu rposes on m odels of sim p listic configura tions an d th ey are used to verify som e design, an aly tica l, or num erica l techniques. P a ra m e tric s tu d ies are o ften perform ed . T h e variab les include such facto rs as in ten sity a n d frequency of in p u t e a rth q u ak e m otions, re la tive density of sands, and p a ram e te rs specific to th e m odel under considera tion (for exam ple, d e p th of th e san d layer and its in c lin a tio n in a sloping g ro u n d m odel, height of th e wall in a re ta in in g wall m odel, an d so o n ) . Som etim es, centrifuge re su lts are com pared w ith Ig shak ing tab le tes ts of re la tive ly large m odels. M odeling of m odels is no t co n d u cted as o ften as it shou ld be.

T he m ost p o p u la r use of cen trifuge m odeling is p robab ly to provide a d a ta base for th e va lida tion of num erical p rocedures. T h e V E LA C S p ro jec t was a m ilestone in liquefaction re la ted cen trifuge research. Several centrifuge ex p erim en ts were re p ea te d a t different centrifuge ex p erim en ts were p red ic ted by different researchers using d ifferent uncoupled , p artia lly coupled, an d fully coupled fin ite e lem ent p rog ram s using a wide range of co n stitu tiv e m odels for soils. T he p a ram ete r iden tification for th e co n stitu tiv e m odels

was done by using d a ta from index, perm eab ility , and m onoton ic an d cyclic tr ia x ia l te s ts on th e soils. T he p ro je c t’s ou tcom e was review ed by A ru la n an d a n , et al. (1994), A ru la n an d a n an d Sco tt (1993), Ko (1994), a n d K u tte r (1995). R eg ard in g th e num erica l s im ulations, Sco tt (1993) s ta te d “th e re is som e in d ica tio n th a t fully coupled codes do b e tte r th a n p a rtia lly coup led codes, w hich in tu rn , p erfo rm b e tte r th a n uncoup led p ro g ram s” . In th e ex p erim en ta l side, it was observed th a t centrifuge te s ts were fairly re p ea ta b le only w hen iden tica l m eth o d s of m odel p re p a ra tio n were followed an d th e cen trifuge facilities were capab le of p ro ducing sim u la ted e arth q u ak e m otions w ith th e en tire range of frequency com ponen ts specified. Also, m uch g rea te r re p ea ta b ility could be a tta in e d by a single m odeler using th e sam e facilities to p erfo rm a num ber of cen trifuge te s ts (Scott, 1993). T h e V ELA C S p ro jec t clearly d e m o n s tra ted th a t th e re are several hardw are , sam ple p re p a ra tio n , and m odeling re la ted issues th a t need to be add ressed very carefully in o rder to rep licate liquefaction phenom ena, or as a m a tte r of fact any geo technical engineering s itu a tio n , in a centrifuge.

3 M O D E L IN G M E C H A N IC S O F L IQ U E FA C T IO N IN A C E N T R IF U G E

Sim ilar to any o th er lab o ra to ry m eth o d , centrifuge tes tin g is ex p ec ted to genera te re liab le an d rep ea tab le q u a n tita tiv e d a ta . C orrect s im u la tio n of th e m echanics involved in th e fam ily of com plex liquefaction p h enom ena dep en d s on d irec t an d in d irec t factors. T he d irec t facto rs include d iscrepancies due to g ra in size effects, th e use of su b s titu te po re fluid to overcom e the conflict in th e scaling of tim e, sim u la tio n of b o u n d ary conditions, an d sam ple p re p a ra tio n an d sa tu ra tio n techn iques. By m aking p ro p e r choices, a m o d eler m igh t becom e successful in re p ro d u c in g liquefactio n in a cen trifuge m odel; however, th e m odeler also needs p ro p e r h ard w are to g a th e r in fo rm a tio n from th is m odel in te rm s of m easurem ents. T hus, th e in d irec t facto rs include system lim ita tio n s on in p u t m otions, th e choice o f tran sd u ce rs , an d d a ta -ac q u is itio n system . Som e of these issues will be d iscussed in th e following.

3.1 C entrifuge m achines, shake tab le s an d in p u t m otions

T h e fin ite size of geo technical cen trifuges lim its th e size an d capacity of th e shake tab le an d therefore, the size of th e con ta iner an d th e soil m odel d im ensions. T h e larger th e centrifuge, sm aller are th e e rro rs due to th e v aria tio n of the g-level a long th e d e p th an d the w id th of th e m odel. Also, if th e d irec tio n of shak ing of th e tab le is p ara lle l to th e axis of ro ta tio n of th e shake tab le an d th e long axis of th e m odel, th e v a ria tio n in th e g-level a long th e w id th of th e m odel w ould be reduced.

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For exam ple, W ilson an d K u tte r (1993) a t U C D avis an d A dalier an d E lgam al (1993) a t R P I rep lica ted M odel No. 7 te s t (zoned em bankm en t) of th e V E LA C S p ro jec t. T h e p rim a ry ex p erim en ter was CU B oulder (A staneh , e t ah , 1993). A 11.7 cm ta ll em b an k m en t was te s te d a t 70g a t B oulder. D ue to th e lim ita tio n of th e shake tab le an d th e co n ta in er size, a 9.3 cm ta ll m odel was te s te d a t 88g a t R P I, an d a 8.8 cm ta ll m odel was te s te d a t 92.8g a t U C D avis. T h e rad ii of th e centrifuges a t B oulder, D avis, an d R P I a t th e shake tab le p la tfo rm were a p p ro x im ate ly 5.4, 2.7, an d 1 .1 m , respectively. T hus, th e e rro rs in th e g-level from th e to p to th e b o tto m of th e m odels were a b o u t 1.5, 3, an d 10%, respectively. Also, since w a ter was used as th e po re fluid, th e th ree m odels d id n o t even rep resen t th e sam e p ro to ty p e . In a d d itio n , in th e D av is’s tes t, th e d irec tio n o f th e shak ing was along th e len g th of th e m odel an d in th e p lane of ro ta tio n of th e centrifuge. T h a t w ould have in tro d u ced a ta n g e n tia l g-level com p o n en t of a b o u t 28g a t th e toes o f th e em bankm en t m odel. T herefore, in th e D av is’s te s ts , a curved false bcLse was used a t th e b o tto m of th e m odel to sim u la te th e h o rizon ta l base of th e p ro to ty p e . I t is n o t c lear if such a tre a tm e n t is indeed beneflcial. Also, such a tre a tm e n t c an n o t be effectively used in a lam in ar con ta iner.

T h e difficulties in achieving good rep lica tio n were fu rth e r ex acerb a ted by differences in th e sam ple p re p a ra tio n techn iques an d in th e in p u t base m otions am ong these tes ts . Som e of these p rob lem s can be overcom e w ith large centrifuges. T h e larger shake ta b les a t U C D avis an d R P I are a s tep in th a t d irec tion .

W h itm a n ' (1988), K o (1994), an d K u tte r (1995) com pared th e d ifferent techn iques of e a rth q u ak e sim u la tio n in th e centrifuges. I t is now genera lly agreed th a t th e e lectro -hydrau lic system u tiliz ing servo- con tro lled m ethodology is p ro b ab ly th e b e s t available m eth o d of seism ic sim ula tion . I t is capab le of delivering a w ide range of earthquake-like m otions ra n g ing from sinuso idal to scaled rea l e a rth q u ak e events in te rm s of m ag n itu d e as well as th e w ide range of frequencies involved. T h is techn ique has been show n to b e effective in p ro d u c in g fairly re p ea ta b le e a rth q u ak e like m otions. I t can also p roduce base m otions a t th e sam e g-level w ith different m ag n itu d es an d frequencies an d scaled base m otions a t d ifferent g-levels to cond u c t p a ra m e tric a n d m odeling of m odels ty p e stud ies, respectively.

To d a te , only one-d im ensional shak ing in th e p ro to ty p e h o rizo n ta l d irec tio n has b een a tte m p te d in th e e lec tro -h y d rau lic shake tab les. T h e analysis o f m odel m easu rem en ts is a lread y a difficult ta sk even in cases w hen th e in p u t m o tions are sinuso idal, especially in so il-s tru c tu re -in te ra c tio n tes ts . F u tu re tw o an d th ree d im ensiona l shake tab le s will tak e th e cen trifuge m odeling tech n iq u e closer to th e rea l life s itu a tio n ; how ever, analysis o f te s ts w ill becom e even m ore challenging.

In m ost one-d im ensional e lec tro -h y d rau lic shake t a bles, an u n p lan n e d v ertica l co m ponen t is u su a lly obta in e d a long w ith th e in ten d ed h o rizo n ta l base accele ra tio n . T h is v ertica l com ponen t o f accele ra tion can be m easu red an d accoun ted in th e analysis. In m ost s itu a tio n s , th e effects o f v e rtica l accele ra tio n could b e insigniflcant. For exam ple, in an ex p erim en t cond u c te d a t CU B oulder, a 13.4 cm th in k layer of w ater- sa tu ra te d N evada No. 100 sa n d in a rig id con ta iner was shaken a t 50g. T h e h o rizo n ta l an d v ertica l accele ra tio n s m easu red on th e shake ta b le an d th e ir Fourier tran sfo rm s are show n in F ig u re 1 a t m odel scale. A pu re ly ho rizo n ta l sinuso idal m o tio n of 50 Hz (1 Hz p ro to ty p e ) p re d o m in an t frequency w as desired . T h e ho rizo n ta l m o tion delivered by th e shake tab le was rough ly sinusoidal w ith 50 Hz frequency as show n in F ig u re 1(c). T h e vertica l accele ra tion was a b o u t 70% of th e horizon ta l accele ra tion in te rm s of th e m agn itu d e ; however, as seen from p lo t (d), it h ad high frequency con ten t (a b o u t 15 tim es th a t of th e horizon ta l m otion) an d insign iflcan t energy con ten t. T h e excess po re p ressu re m easu red a t th e cen ter of the b o tto m of th e san d layer, is show n in p lo t (e). T he te s t was s im u la ted using th e fin ite e lem ent p ro g ram DIANA-SWANDYNE I I . T w o analyses w ere conducted . In th e first, only th e h o rizo n ta l base in p u t m o tio n was considered . T h e excess p o re p ressu re c o m p u ted a t th e lo ca tio n of th e m easu rem en t is show n in p lo t (f) w hich com pares fairly well w ith th e m easu rem en t. In th e second analysis, b o th h o rizo n ta l a n d v e rtica l base m otio n s were included . T h e co m p u ted excess p o re p ressure is show n in p lo t (g). T h e h igh frequency of th e v ertica l base m otion is reflected in th e num erica l calc u la tio n s w hich was ab sen t in th e m easu rem en t. T h e c o m p u ted excess p o re p re ssu re in p lo t (g) was d ig ita lly filte red to rem ove frequencies h igher th a n 100 Hz an d th e filte red trace is show n in p lo t (h) w hich is a lm ost iden tica l to p lo t (f) o f th e analysis in w hich vertica l base m otion was excluded . T h u s, h igh frequency vertica l acceleration d id n o t have any significant effect on th e m ain tre n d of th e excess p o re pressures. S ettlem en t an d h o rizo n ta l accele ra tions in th e soil were also unaffected by th e v e rtica l base m o tio n b o th in th e te s t an d its sim u la tion . In th e level g ro und , re ta in in g wall, an d em b ankm en t ex p erim en ts c o n d u c ted a t CU B oulder, none of th e e x p e rim e n ta l re su lts show ed any significant effects w hich cou ld have b een a t t r ib u te d to th e v ertica l acceleration , excep t th e v ertica l acceleratio n m easurem ents. T h is could have b een because th e typ ica l in s tru m e n ta tio n such as p o re p ressu re tra n s ducers, LV D Ts, s tra in gages, loadcells, stress gages are n o t sensitive enough for frequencies in th e ne ighb o rh o o d of 800 Hz or so. T hese ob serv atio n s in d ica te th a t h igh frequency v e rtica l acce le ra tio n genera lly p ro duced in th e centrifuge can b e n eg lected from th e a n a lysis o f th e ex p erim en ts for m ost m odels. For m odels such as u n d e rg ro u n d s tru c tu re s , th e effects o f vertica l base accele ra tion m ay prove to b e sign ifican t.

310

(a) horizontal base motion (b) vertical base motion

I ‘ - m u -

0 0.2 0.4 0.6 0 .8 1 0 0.2 0 .4 0 .6 0 .8 1time (sec) time (sec)

(c) FFT of horizontal base motion (d) FFT of vertical base motion

.® 1000J l ìL.

10 10 frequency (Hz)

10’ 10 frequency (Hz)

(e) measured excess pore pr. (f) Num : horiz. base input only

k °-25

Figure 1: Effect o f vertica l accele ra tio n on excess po re pressures

3.2 In s tru m e n ta tio n an d d a ta acq u isitio n

T ypical q u a n titie s th a t are m easu red in liquefaction centrifuge experim en ts in th e soil include po re p re ssures, accelerations, se ttlem en ts , a n d occasionally, la te ra l soil de form ations. I f it is a so il-s tru c tu re- in te rac tio n ex perim en t such as a re ta in in g wall te s t, q u an titie s such as b en d in g s tra in s , la te ra l e a r th p ressures, wall accelerations an d deflections are m easured . In som e experim en ts , loads are m easured . D epend ing on the ty p e of m odel, up to a b o u t 40 to 60 tra n sd u c ers are typ ica lly deployed. M ost o f these tran sd u ce rs have to be as sm all as possib le since th ey are to be em bedded in th e soil.

M in ia tu re accelerom eters a re used very ro u tin e ly to m easure accelerations a n d have b een found very reliable. T hey are generally successful in cap tu rin g th e a tte n u a tio n or loss of base accele ra tio n from th e b o tto m to th e to p of th e soil due to liquefaction . For good perform ance, th ey have to be lightw eight an d th e ir cross-sensitiv ity has to be m in im um possible.

D isplacem ent m easu rem en ts a re done using AC or DC LVDTs, p rox im ity p robes, o r m ore recently, laser LVDTs. T h e a u th o rs have typ ica lly used AC an d DC

LV D Ts in th e ir experim en ts . D C LV D Ts are norm ally used to m easure gross d isp lacem en ts an d th ey are u n su itab le for m easu ring d y n am ic d isp lacem ents . O nce th e soil liquefies an d looses its s tre n g th , th e heavy core w ith an ex tension of a D C LV D T re s tin g on a ta rg e t sinks in soil, th u s m easu rin g h igher th a n a c tu a l se ttlem en t. In such s itu a tio n s , lightw eight m in ia tu re AC LV D Ts are m ore su itab le . Also, th ey are capab le of m easu ring dynam ic oscilla tions.

A n o th e r m ost im p o rta n t m easu rem en t is excess pore p ressures in soils. Excess po re p ressu res d u r ing an e arth q u ak e m igh t have very h igh frequency com ponents w hich need to b e c a p tu re d by th e pore p ressu re tran sd u ce rs . Also, th e response tim e has to b e m in im al. T h e significant fac to rs th a t affect th e perfo rm ance of these tran sd u ce rs are com pliance of th e d iap h rag m , th e p e rm eab ility o f th e po ro u s cap in th e tran sd u ce r, v iscosity of th e po re fluid, presence of a ir bu b b les inside th e tran sd u ce r, an d a rch ing an d stress co n cen tra tio n s a ro u n d th e tran sd u ce r. T h e effects of these facto rs on th e perfo rm ance of th e pore p ressure tran sd u ce rs are a n aly tica lly an d to a c e rta in ex ten t, ex p erim en ta lly evaluated by Lee (1990), K u tter, e t al. (1990), K önig, e t al. (1994), an d Sekiguchi, e t al. (1995). K önig, e t al. (1994) have recom m ended a p ro ced u re to im prove th e perfo rm ance of D ruck pore p ressu re tra n sd u c e r (P D C R 81, th e ty p e w hich is used com m only in cen trifuge app lica tions) in th e con tex t of s ta tic te s ts on clays based on th e experience gained a t five lab o ra to rie s . F rom th e descrip tion , it a p p ea rs th a t th e ir reco m m en d atio n w ill im prove th e qu a lity of dynam ic pore p ressu re m easu rem en ts also.

I t is b e tte r to cond ition an d d ig itize th e signals from in s tru m e n ts before going th ro u g h slip rings since d ig ita l d a ta is less suscep tib le to noise. A good d a ta acqu isitio n sys tem should have an analog filter, am plifier, an d ab ility to offset signal for each channel. T h e com b in a tio n of am plifier an d offsetting cap ab ilitie s shou ld give a m ax im um reso lu tion , w hile th e analog filte r will p reven t an aliasing p rob lem (Law, 1995). T h e d a ta acq u isitio n should be capab le o f collecting d a ta from a b o u t 50 to 60 channels a t a very high ra te (m in im um of 1 kHz a n d p referab ly up to 10 kH z). T h e frequency response th a t could be c a p tu re d is only h a lf th e sam p ling frequency. Also, th e buffer shou ld be ab le to accom m odate several m egabytes of in fo rm a tio n so th e d a ta a t th is h igh ra te can b e collected for long tim e, especially in cases w hen viscous po re fluids a re used w hich could take up to few m inu tes for excess po re p ressures to d issipate .

3.3 C on ta iners an d b o u n d a ry tre a tm e n ts

T h e fin ite sizes o f geotechnical centrifuges lim it th e size of a con ta iner carry in g th e soil m odel. C o n ta in er size is fu rth e r re s tr ic te d by th e cap acity o f th e e a r th quake sim u la tio n system . T h is ra ises a concern of in te ra c tio n of th e soil m ass w ith th e co n ta in er walls.

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R ecently, K o (1994) an d K u tte r (1995) d iscussed different ty p es of con ta iners for seism ic cen trifuge m o d eling.

In o rd er to m odel a p rob lem of one d im ensional shear wave p ro p ag a tio n th ro u g h an in fin ite soil layer in liquefaction centrifuge experim en ts correctly , W h itm an an d L am be (1986) p roposed a set o f c r ite r ia for designing a m odel co n ta in er for seism ic sim ula tions. A ccording to these c rite ria , th e con ta iner shou ld m ain ta in a co n stan t h o rizon ta l cross-section d u rin g shak ing, have zero m ass an d zero stiffness for ho rizo n ta l shearing , an d develop com plem en ta ry sh ea r stresses equal to those occu rring on h o rizon ta l p lanes. To s a tisfy these c rite ria , th ey used a c ircu lar, stacked ring con ta iner, whose la te ra l fiex ib ility allowed th e soil colum n to move as a v ertica l sh ear beam . A sim ilar idea was im p lem en ted by several researchers in developing re c tan g u la r lam in ar con ta iners (H ushm and e t al., 1988; Law e t al., 1991; V an L aak e t al., 1994). A long these lines. E qu ivalen t S hear B eam (Schofield an d Zeng, 1992), F lex ib le Shear B eam (K u tte r , 1995), an d H inged P la te (Fiegel, e t al., 1994) con ta iners were developed. T h e abovem en tioned investiga to rs have evaluated th e ir con ta iners to check if th e guidelines o u tlin ed by W h itm a n an d L am be (1986) have indeed been achieved.

F ixed end rig id con ta iners are s till w idely used b ecause, a lth o u g h th e end b o u n d a ry cond itions are u n re a listic , th ey are easily accoun ted in th e analysis, especially in th e num erica l s im ula tions. R igid con ta iners do n o t p e rm it la te ra l defo rm ations to occur a t th e end b o u n d arie s , co n stra in th e soil unrealis tically , an d allow stress wave reflections in to th e soil m odel. T h e ir use m ay b e ad eq u a te if th e p u rp o se of th e te s t is to valid a te a fin ite e lem ent p ro ced u re or m erely to observe basic failu re m echanism s.

To illu s tra te th e effects of d ifferent b o u n d a ry cond itio n s, two h y p o th e tica l cen trifuge te s ts of a level g ro u n d configu ra tion were s im u la ted using th e fin ite e lem ent p ro g ram DIANA-SWANDYNE I I (F igu re 2). I t is assum ed th a t th e two tes ts are c o n d u c ted a t 40g on N evada No. 100 san d a t 60% re la tive den sity an d s a tu ra te d w ith a su b s ti tu te pore flu id of viscosity 40 cs. T h e first te s t is assum ed to be c o n d u cted in a rig id c o n ta in er a n d th e second in a lam in ar co n ta in er (by ty in g th e nodes rep resen ted by th e hollow circles a t the sam e elevation) of sam e dim ensions. For th e dynam ic analysis, th e soil layer was su b jec ted to a co n stan t am p litu d e sine wave. F igu re 2 show s th e com plex p a tte rn of excess p o re p ressu res in th e rig id con ta iner. T he p o re p ressu res a t th e cen ter show insignificant oscilla tio n s. However, po re p ressu res a t th e left a n d th e rig h t b o u n d a rie s show th e sam e average excess pore p ressu res w ith large osc illa tions w hich are exac tly 180° ou t-o f-phase . T h e osc illa tions occur due to th e res tra in e d b o u n d a ry cond itions re su ltin g in s tress wave reflections. T h e ph ase difference o f 180° occurs due to th e fact th a t th e soil n ear th e co n ta in er b o u n d arie s is

u n d e r a lte rn a te tens ion an d com pression .O n th e o th e r han d , th e lam in a r co n ta in er sim u la tio n

gives th e sam e po re p ressu res th ro u g h o u t th e w id th of th e m esh, a t a p a r tic u la r e levation w hich is in d ica ted by m erg ing of th e th ree traces of p o re pressures. T h is analysis essen tia lly s im u la tes a one-d im ensional shear b e am m odel for soil (T he sam e re su lts could be obta in e d w ith th e use of 1 x 6 e lem ents in s tea d of 11 x 6). T h e p o re p ressu res g en era ted in th e lam in ar con ta iner have insign ifican t oscilla tions. T h e po re p ressu res gene ra te d in th e lam in ar co n ta in er s im u la tio n are differen t from those a t th e cen ter from th e rig id con ta iner. I t was observed th a t if th e m esh show n in F igu re 2 is ex ten d ed to be th ree tim es w ider, an d analyzed as a rig id con ta iner, in th e c en tra l o n e -th ird p o rtio n of th e m esh, th e soil behaves as a one-d im ensional shear b eam giving th e responses sim ila r to th o se from th e s im u la tio n of th e lam in a r con ta iner. T h u s, th is an a ly sis d e m o n s tra te s th e need to pay specia l a tte n tio n to b o u n d a ry effects in rig id con ta iners.

C e rta in cen trifuge m odels such as em b an k m en t m odels do n o t to u ch c o n ta in er ends an d hence a rig id co n ta in er can be used. In th e spec ia l case of re ta in ing wall con figura tion , w hen only one end of th e soil m odel touches th e co n ta in er b o u n d ary , it is u nc lear if a lam in a r co n ta in er is necessary. So far, as far as th e a u th o rs know , all th e re ta in in g wall te s ts have been c o n d u cted in rig id con ta iners. Zeng (1998) a n d De- w oolkar, e t al. (1998b) used d uxsea l b o u n d a ry a t th e co n ta in er end in th e ir te s ts w hich involved liquefactio n effects. A b so rb en t m a te ria ls a re o ften used by cen trifuge m odelers a t th e c o n ta in er en d bou n d arie s . T hese m a te ria ls have been show n to be effective in energy ab so rp tio n an d wave reflection p rev en tio n for fo u n d a tio n v ib ra tio n ty p e p rob lem s w hich are non- seism ic. D ew oolkar, e t al. (1998b) co n d u c ted two seism ic cen trifuge te s ts on a fixed-base, can tilever re ta in ing w all m odel w ith w a te r-sa tu ra te d san d backfill in a rig id con ta iner. T h e only difference betw een th e two te s ts was th a t only one te s t h ad a duxsea l b o u n d a ry a t th e con ta iner end. In b o th th e te s ts , th e ra tio of th e backfill leng th to th e he igh t of th e wall was 2.4. T h e in p u t m otions were very s im ilar. T hese te s ts were num erica lly s im u la ted w ith different fa r-end b o u n d a ry conditions. B o th e x p erim en ta l an d num erica l resu lts in d ica ted th a t a special b o u n d a ry tre a tm e n t such as duxseal is no t abso lu te ly necessary if th e ra tio of th e backfill len g th to th e heigh t of th e wall is g re a te r th a n a b o u t 2.4 as long as th e b eh av io r o f th e w all an d th e soil in its vicin ity is concerned. T h e excess pore p re ssures, accelerations, an d se ttle m e n ts in th e soil near th e w all an d th e la te ra l p ressu res, b en d in g s tra in s , accelera tions, and deflections on th e w all w ere u n a lte red . T h e accele ration an d p o re p re ssu re responses close to th e c o n ta in er w all w ould b e affected by th e presence of ab so rb in g boundary .

In th e a u th o rs ’ opin ion , som e so rt of lam in a r conta in e r shou ld ideally be used w henever soil is in con-

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free draining boundary

fixed boundary ------------ ^ base input

36.6 cm —

C : center

rigid container

R : right

at th e left bound arya t th e c en te ra t th e right b o und ary

laminar container

F igure 2; N um erical ev alu atio n of rig id versus lam in ar con ta iner b o u n d arie s

tac t w ith co n ta in er end walls. If it is no t possib le , a diixseal ty p e ab so rb in g m a te ria l m ay be used. Also, if th e co n ta in er is large an d th e p a r t o f th e m odel of special in te res t is sufficiently far from th e end b o u n d aries of th e con ta iner, a specia l co n ta in er m ay no t be necessary as d iscussed earlie r in th is section.

So far, th e tre a tm e n t to th e co n ta in er end b o u n d aries w hich are p e rp en d icu la r to th e d irec tio n of sh ak ing, has been considered . Usually, less a tte n tio n is pa id tow ards th e co n ta in er walls th a t a re p ara lle l to the d irec tion of shaking. P resence of fric tion betw een th e soil and th e co n ta in er walls m ay cause d ev ia tio n from th e p lane s tra in cond itions (w hich are norm ally assum ed in m ost cen trifuge te s ts an d th e ir analysis). O il-soaked latex m em branes on all th e con ta iner walls in con tact w ith soil seem to help in reducing friction .

3.4 Sam ple p re p a ra tio n

T h e san d specim ens are u su a lly p re p are d by ra in in g d ry san d from a funnel or a h o p p e r th ro u g h som e sieves. T h e re la tive den sity is con tro lled by changing th e heigh t or th e o pen ing size. T h is m eth o d is believed to genera te hom ogeneous, un ifo rm specim ens w ith re p ea ta b le density .

T h e sa tu ra tio n techn iques used a t d ifferent lab o ra to ries vary from ju s t le ttin g th e w ater pass th ro u g h tu b es from th e b o tto m to th e to p of th e specim en, to sa tu ra tio n un d e r vacuum th ro u g h san d specim ens flushed w ith ca rb o n dioxide. Som etim es, s a tu ra tio n is confirm ed by m easu ring P-w ave velocities th ro u g h th e san d specim en (W ilson, e t ah , 1997). W ith v iscous su b s ti tu te pore fluids, th e sa tu ra tio n process becom es m ore tedious. N evertheless, u tm o s t care has to be taken to achieve m ax im u m possib le degree of sa tu ra tio n in o rder to m odel liquefac tion ph en o m en a correctly.

3.5 Scale effects

Issues such as p a rtic le size effects, s tra in ra te effects, an d conflict in dynam ic an d diffusion tim e scales m ay b ias cen trifuge te s t d a ta . T hese facto rs m ay no t be very c ritica l if th e m odel is n o t m ean t to sim u la te a specific p ro to ty p e . If th e p u rp o se is to observe b a sic fa ilu re m echanism s, to verify num erica l m ethods, or to com pare re la tive m erits o f sim ila r s tru c tu re s as in p a ram e tric stud ies, th e different effects can be accounted for in th e analysis. To som e e x ten t, such u n c erta in tie s could be resolved or th e ir significance could be exam ined by conducting m odeling of m odels.

G ra in size effect

A ccording to scaling laws th e scaling fac to r for p a rtic le size should also be th e sam e as for th e linear d im en sions (1 /N ), w hich will requ ire d ra s tic re d u c tio n in p a rtic le sizes. However, if th e p a rtic le size is changed, th e co n stitu tiv e behav io r o f th e soil skeleton will also change. T h e use of p ro to ty p e soil as a m odel m ate ria l is usua lly p referred , b u t it in tro d u c es a conflict w hich m ay cause d is to rtio n of te s t resu lts . I f foreign objec ts such as piles, footings, p e n e tro m e ters , w hich are scaled dow n N tim es in size, a re in se rted in m odel soil w hich is sam e as p ro to ty p e soil, th ey m ay a p p ea r to have th e sam e size as th e larg est g ra in in th e soil. T he in te rac tio n betw een th e o b jec t an d th e soil m ay begin to dev ia te from th e con d itio n s im p lic itly assum ed in th e d e riv a tio n of th e scaling re la tio n s w hich are based on co n tin u u m concepts. T hese effects can be checked by co n d u ctin g ex p erim en ts a t d ifferent m odel scales w hich is also know n as m odeling o f m odels.

In th e specific case o f liquefac tion cen trifuge ex p erim ents, T an an d Scott (1985) in v estig a ted th e scaling- re la tio n s for liquefaction phenom enon . T h ey stu d ied

313

th e m o tion of a soil p a rtic le in a u n ifo rm Ng field and in a cen trifuga l force field. T h e size of th e p a rtic le was assum ed to be th e sam e in th e m odel an d th e p ro to type. T h ey concluded th a t for soil w ith p a rtic le size less th a n 0.1 m m , s im ila rity is re ta in e d in th e b eh av ior of th e m odel an d th e p ro to ty p e if th e m odel pore fluid has a v iscosity th a t is N tim es th a t of w ater, th e p ro to ty p e fluid. I f th e p a rtic le size is g re a te r th a n 0.1 m m , even w ith th e su b s ti tu te p o re flu id , s im ila rity is achieved only b riefly w hen th e R eynolds n u m b er of th e p a rtic le is less th a n u n ity in b o th th e m odel and th e p ro to ty p e . F u r th e r s tud ies need to be co n d u cted to gain a b e tte r u n d e rs tan d in g of th is asp ect.

S tra in ra te effect

A ccording to b o th th e d y nam ic an d conso lida tion tim e scaling laws, th e d u ra tio n of an event is sm aller in a centrifuge m odel th a n th a t of th e co rresp o n d in g d u ra tio n of th e p ro to ty p e event. Since th e stresses an d s tra in s are id en tica l in m odel an d p ro to ty p e , th e m odel ra te of change of s tress an d ra te of change of s tra in are N tim es g re a te r for a dynam ic p ro b lem an d tim es g rea te r for a conso lida tion p ro b lem th a n those of the p ro to ty p e . R a te effects in th e co n tex t dynam ic centrifuge m odeling of clay is d iscussed by K u tte r (1995). As s tra in ra te increases, th e soil s tre n g th increases. For a ty p ica l cen trifuge m odel, a t a g-level of N = 50 , th e d y nam ic s tre n g th o f th e m odel m ay be a b o u t 5 to 15% g re a te r th a n th e s tre n g th of th e p ro to ty p e (K u tter, 1995). S a th ia lin g am an d K u tte r (1994) suggested th a t in th e case of ra te d ep en d en t behav io r, th e void ra tio of th e physical m odel m ay b e increased in such a way th a t e ith e r th e tim e d ep en d en t conso lida tion (seco ndary com pression an d creep) can be s im u la ted or, in dynam ic p rob lem s, th e shear s tre n g th of th e m odel soil m ay be reduced . T h e significance of s tra in ra te effects in liquefac tion m odeling of san d s is generally assum ed to b e u n im p o rta n t; however, it needs to be proven.

C onflict be tw een dynam ic an d conso lida tion tim e

can s till be used as a p o re flu id in th e cen trifuge m odel of a h y p o th e tica l p ro to ty p e of th e sam e soil, w hich will now have an increased p e rm e ab ility by a fac to r of N th a t can be in co rp o ra te d in th e analysis.

If th e p e rm eab ility of th e soil is reduced by a facto r N, th e n a t Ng, th e p e rm e ab ility of th e soil in th e cen trifuge will be th e sam e as th e sam e soil in a Ig env ironm en t of th e p ro to ty p e . T h en , a com m on scale for dynam ic an d diffusion tim es (now b o th as 1/N ) can be ob ta ined . T h is can be achieved by e ith e r reduc ing th e size of th e soil p a rtic le s an d using w ater as th e pore fluid, or m a in ta in in g th e sam e soil skeletal s tru c tu re an d em ploy ing a su b s ti tu te p o re fluid w hich is N tim es m ore viscous th a n w ater. To ensu re sim ilar stresses an d s tra in s in m odel an d p ro to ty p e , th e change in g ra in size m u st n o t cause significant differences in th e m echan ical p ro p e rtie s of th e soil. Also, to achieve a fac to r of N red u c tio n in p e rm e ab ility (which is p ro p o rtio n a l to accord ing to H azen ’s eq u a tio n ), D iq o f th e m odel soil shou ld be y/N tim es sm aller th a n th a t of th e p ro to ty p e soil (K u tte r 1995). T hus, reducing th e g ra in size is u n a ttra c tiv e to a m odeler. T he second a lte rn a tiv e is frequen tly ad o p te d by (Exp erim en te rs .

T h e presence of a su b s ti tu te p o re fluid m ay affect th e co n stitu tiv e b ehav io r of th e soil and , therefore, its effects shou ld be th o ro u g h ly evaluated . Ideally, such a rep lacem en t p o re flu id shou ld behave like w ater, i.e. a N ew ton ian flu id w ith n early th e sam e m ass density , com pressib ility , an d surface ten s io n as w ater. I t m ust also be chem ically p o la r to en ab le its use w ith silts an d clays (A llard a n d Schenkeveld, 1994). F u r th e rm ore, th e p resence of a d ifferent p o re fluid should not a lte r th e d am p in g c h ara c te ris tics (M ad ab h u sh i, 1994). Lastly , th e scaling req u irem en ts for p e rm e ab ility m ust be satisfied in th e cen trifuge env iro n m en t. T h e su b s titu te pore fluid shou ld also possess o p e ra tio n a l qua lities such as easy p re p a ra tio n , a cc u ra te re p ro d u c tio n , easy sa tu ra tio n , m in im al ag ing effects, an d en v iro n m en ta l safety.

4 S U B S T IT U T E P O R E FL U ID S

P e rh a p s th e m ost serious issue in scale effects is th a t w hich concerns th e conflict in d y n am ic an d diffusion tim e. T h is effect a rises if th e sam e soil a n d th e sam e po re flu id (u sua lly w ater) are used in th e p ro to ty p e an d its cen trifuge m odel. T h e dy n am ic tim e is scaled as 1 /N w here as diffusion or con so lid a tio n tim e is scaled as 1 /N ^. In th e case of s a tu ra te d san d m odels su b je c ted to e a rth q u ak es, th e dy n am ic an d diffusion events occu r sim ultaneously . D u rin g th e sh o rt p e rio d of ea rth q u ak e sim u la tio n , significant am o u n t (g rea ter th a n its p ro to ty p e equ ivalen t) of d iss ip a tio n of excess po re p ressu res can occur du rin g th e ir g en era tio n b e cause of th e increased p e rm eab ility of th e soil due to increased gravity . I t has been a rg u ed th a t w hen m o d eling a p a r tic u la r p ro to ty p e is no t th e ob jec tive , w ater

Silicone oil, g lycerin -w ate r m ix tu res , th e D elft G eotechnics m odel p o re fluid, an d m ethy lce llu lose solu tio n s are genera lly used as s u b s ti tu te p o re fluids.

Silicone oil was first em ployed a t C am b rid g e U niversity over fifteen years ago an d has been a d o p te d by m any o th e r researchers; for exam ple, S teed m an an d Zeng (1990), M a d ab h u sh i (1994), K oseki, e t al. (1994, 1995), K oga, e t al. (1995), an d C ubrivosk i, et al. (1995). G lycerin -w ate r m ix tu re s have b een used by W h itm a n an d L am be (1988), W h itm a n an d T in g (1993), an d L iu a n d D obry (1994). Zeng, e t al. (1998) perfo rm ed co n stan t head p e rm e ab ility te s ts on w ater- s a tu ra te d an d silicone oil (of 80 cs v isc o sity )-sa tu ra te d L eigh ton -B uzzard 52 /100 san d a t d ifferent void ra tio s ran g in g betw een 0.68 to 0.88. T h ey also perfo rm ed

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Ig p erm eab ility te s ts on w a te r-sa tu ra te d a n d glycerin- w ater m ix tu res (3.2 cs an d 8.9 c s)-sa tu ra te d O ttaw a san d No. 40 a t different void ra tio s ran g in g betw een 0.55 to 0.7. In all cases, th e ra tio o f th e p erm eab ilities w ith w ater to w ith th e s u b s ti tu te p o re fluid was ap p ro x im ate ly th e sam e as th e ra tio of viscosities of th e su b s ti tu te po re flu id to w ater. T h ey also p e rform ed d ra in ed tr ia x ia l te s ts on w ater- a n d glycerin- w ater m ix tu re s -sa tu ra te d tr ia x ia l tes ts . No significant effects on th e fric tion angle an d s tre ss -s tra in behav ior of O ttaw a san d due to th e su b s ti tu tio n o f th e pore fluid was observed. S im ilar conclusion was rep o rted by M ad ab h u sh i (1994) reg ard in g silicone oil based on th e resu lts o b ta in e d by E y to n (1982). B ased on a s tu d y investiga ting th e effects of silicone oil on d a m p ing ch arac te ris tics by te s tin g tow er m odels, M ad ab hushi (1994) concluded th a t d am p in g is ra th e r less sensitive to th e viscosity of pore fluid, th u s ju stify in g th e use of h igh v iscosity po re fluids in cen trifuge tests. Silicone oil an d g lycerin -w ate r m ix tu re s have certa in d isadvan tages. T h e m ass densities of silicone oil and g lycerin -w ater m ix tu res are a b o u t 4% lower an d 10 to 15% h igher th a n th a t of w ater, respective ly (Zeng, et ah, 1998). T hus, th e effective stresses a t geom etrically sim ilar locations in m odel an d p ro to ty p e w ould be different. Also, a t sm all h ydrau lic g rad ien ts , clogging of dense sand was observed w ith b o th silicone oil and g lycerin -w ater m ix tu res (Zeng, et al., 1998). F u rth e r, because silicone oil is considered a haza rd o u s w aste, c lean-up and d isposal are difficult. In sp ite of these lim ita tions , these two pore fluids a p p e a r to be useful.

T he D elft G eotechnics m odel po re flu id (A llard and Sduaikeveld , 1994) was extensively ev alu ated th ro u g h physical, perm eab ility , an d m ono ton ie an d cyclic tr i ax ia l tes ts , an d show ed p rom ising resu lts . However, its com position , p re su m ab ly a m ix tu re of som e chem icals in w ater, has no t been revealed by its o rig inators. Also, as far as th e a u th o rs know, d a ta from centrifuge licpiefaction te s ts w ith th is po re flu id has no t been published .

M ethylcellulose was used by A stan eh (1993), Hiro- Oka, e t al. (1995), W ilson, e t al. (1997), D ewoolkar, e t al. (1998a), an d T ohda, e t al. (1997) in th e ir centrifuge experim en ts. E x cep t W ilson, e t al. (1997) who used 10 cs m ethylcellu lose in 30g tes ts , ail o th er researchers increased th e viscosity p ro p o rtio n a l to th e g-level (N). A t th e U niversity of C olorado a t B oulder, m ethylcellu lose (m etolose) has been used ex ten sively as a su b s ti tu te pore flu id for th e p a s t several years. To exam ine th e su itab ility of th is su b s titu te pore fluid, an e x p erim en ta l p ro g ram was conducted using w ater- an d m eto lo se -sa tu ra ted p e rm eab ility and triax ia l tests . Seism ic cen trifuge te s ts on w ater- and m eto lo se -sa tu ra ted san d m odels of level g round , em ban k m en t, an d re ta in in g wall were conducted . M odeling of m odels was c o n d u cted for th e la t te r two configu ra tions. R esu lts of these investiga tions are p resen ted here in som e deta il.

4.1 M ethylcellu lose (m etolose)

A fine w hite m etolose pow der o f ty p e 90SH-100 g rade m an u fac tu red by S h in -E tsu C hem ical Co., L td . of Tokyo was used in th is study . M etolose so lu tions of desired v iscosities can be p re p a re d by d issolv ing certa in am o u n ts of m etolose pow der by w eight in w arm , d is tilled , deaired w ater. Since th e am o u n t of m etolose pow der to be m ixed w ith w a ter is very sm all (usually less th a n 2%), th e d en sity o f m etolose so lu tio n is v ir tu ally th e sam e as th a t of w ater. Low viscosity m etolose so lu tions (15 to 100 cs) behave as a N ew ton ian fluid u p to a shear ra te of a b o u t 20 /sec w hich is h igher th a n th e ex p ec ted shear ra te g en era ted in centrifuge experim en ts . T h e viscosity of m etolose so lu tions is fa irly s tab le w ith tim e. T h e viscosity reduces w ith increasing te m p e ra tu re ; however, th is ad v an tag e could be overcom e if a co n stan t te m p e ra tu re is m ain ta in ed in a cen trifuge cham ber.

T h e surface tension of m etolose of g rade 90SH is a b o u t 75% of th a t of w a te r (M etolose B rochure, 1997). Surface ten s io n is believed to affect th e cap illa rity rise in p a r tia lly s a tu ra te d soils. Since all th e te s ts desc ribed here were co n d u cted on s a tu ra te d san d m o d els, th e difference in surface ten s io n was believed to be u n im p o rta n t. F u rth e r in vestiga tion on surface tension in p a rtia lly s a tu ra te d soil still need to be conducted .

As co m pared to s a tu ra tio n w ith w ater, it is re la tively d ifficult to s a tu ra te san d m odels w ith a h igh v iscosity m etolose. S a tu ra tio n w ith m etolose is re la tive ly less tim e consum ing if a ne t of tu b es or high .^-forces of centrifuges in-flight are used. A ne t of tu b es w ith a b o u t 15 openings was used a t th e b o tto m of centrifuge soil m odels to accelerate th e sa tu ra tio n process. A soil volum e of ab o u t 60 x 25 x 30 cm was s a tu ra te d w ith a 40 cs m etolose w ith re la tive ease in a b o u t 24 hr. In th e second m eth o d ad o p te d by T o h d a et al. (1997), th e m ax im um possible head of w ater to s a tu ra te the specific soil m odel a t a ce rta in re la tiv e d en sity w ith o u t causing quick san d cond itions was first d e te rm in e d a t Ig. A c o n ta in er full of m etolose so lu tio n (viscosity N cs) was p laced on to p of th e te s t package in such a way th a t th e head of m etolose a t Ig w ould no t be g rea te r th a n th is p red e te rm in ed h ead of w ater. T h u s, if the m odel w ith th e m etolose reservo ir is sp u n a t Ng, the s a tu ra tio n process can be as fast as th a t w ith w ater a t Ig.

C entrifuge c o n stan t h ead p e rm e ab ility te s ts p e rfo rm ed on w ater- an d m eto lo se -sa tu ra ted F-75 sand show ed th a t th e scaling req u irem en ts of th e centrifuge env ironm en t for p e rm eab ility were sa tisfied by m etolose (Chipley, 1996). Also, based on th e resu lts from tr ia x ia l com pression tes ts , it was found th a t th e co n stitu tiv e behav io r (s tre ss-s tra in behav io r, pore p ressu re genera tion , a n d fric tion angle) o f F-75 sand is no t a lte red w ith m etolose (D ew oolkar, e t al., 1998d).

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4.2 A level g ro u n d experim en t

F igu re 3 show s th e m odel con figu ra tion a n d m easu rem en ts a t m odel scale of a te s t th a t was co n d u c ted to d e m o n s tra te th e necessity of a su b s ti tu te p o re fluid in liquefaction ex p erim en ts (D ew oolkar, e t al., 1998d). T h e te s t co n ta in ed tw o san d m odels o f level g round of th e sam e sh ap e an d size se p a ra ted by a rig id p a r t i tio n in a rig id c o n ta in er as show n in F ig u re 3(a). O ne side o f th e soil sam ple was s a tu ra te d w ith d istilled , deaired w ater an d th e o th e r side was s a tu ra te d w ith 60 cs m etolose an d th e te s t was co n d u c ted a t 60g. T he effects o f th e p o re fluid on th e m odel b eh av io r could be s tu d ied th ro u g h these two iden tica l m odels su b je c ted to iden tica l e a rth q u ak e m otions.

W ith w a te r as th e po re fluid, th e a ccu m u la tio n of excess p o re p ressu res was reduced due to h igh p e rm eability. However, w ith m etolose, due to slower d issipa tion , h igh excess po re p ressu res were g enera ted . T h e a p p a re n t ra te of po re p ressu re g e n era tio n in th e m eto lo se -sa tu ra ted soil was considerab ly faster th a n th a t in th e w a te r-sa tu ra te d soil. T h e ra te of pore p ressure d iss ip a tio n w ith m etolose was considerab ly slower th a n th a t w ith w ater. T h e m easu red excess pore p ressu res in th e m e to lo se -sa tu ra te d soil reached th e ca lcu la ted values of in itia l v e rtica l effective stresses (cr^i), w hereas in th e w a te r-sa tu ra te d soil, th ey d id not. Also, th e accele ra tions in th e w a te r-sa tu ra te d soil t ra n s m itte d th e base in p u t m o tio n from th e b o tto m to th e to p of th e soil layer, w hereas in th e m etolose- sa tu ra te d soil, th e m o tio n w as n o t t ra n s m itte d effectively a fte r th e first few cycles due to th e loss of so il’s s tre n g th . B ased on these observations, it was clear th a t n e ith e r th e accele ra tions nor th e excess pore p ressures in d ic a te d occurrences of liquefac tion in th e w a te r-sa tu ra te d soil m odel. O n th e o th e r h an d , th e m eto lo se -sa tu ra ted soil liquefied com pletely.

T hus, it was show n th a t th e conflict be tw een th e d y nam ic an d conso lida tion tim e ex ists an d hence, th e resu lts from seism ic cen trifuge te s ts on w a te r-sa tu ra te d soil m odels could u n d e res tim a te th e consequences of an ea rth q u ak e . A su itab le su b s ti tu te p o re flu id is useful in o b ta in in g rea lis tic resu lts . T h e physical, p e rm eability , an d tr ia x ia l te s ts d e m o n s tra ted th a t m etolose is a su itab le su b s ti tu te pore fluid w hich m ain ta in s th e so il’s c o n stitu tiv e behav ior. T herefore, in theory, m etolose s a tu ra te d soil shou ld rep resen t a c tu a l p ro to ty p e behav ior; how ever, it can n o t be assu red unless th e ir re su lts a re com pared w ith a rea l p ro to ty p e or m odeling o f m odels is conducted .

4.3 M odeling o f m odels o f an em bankm en t

Several seism ic cen trifuge ex perim en ts on w ater an d m eto lo se -sa tu ra ted , hom ogeneous san d em b an k m en ts were p erfo rm ed by A sta n e h (1993). Selected re su lts from six of his te s ts are p re sen ted here. All these te s ts were in te n d e d to s im u la te th e sam e h y p o th e ti

-----------------------------------------—P-m1

--------------------------------------- 1----- —P-w1

A-m1 A-w1

m eto lose- . P-w2 w a te r- ^ a -w2satu ra ted sa tu ra tedF-75 sand 7 ÿ l'^ A -m 3 F-75 sand ^ A-w3(RD = 70% ) (R D = 70% )

All dimensions are in centimeters. P; pore pressure transducer m : metolose-saturated soil w ; water-saturated soil

A : accelerometer H : horizontal V : vertical

tim e (sec)

F igure 3: A level g ro u n d ex p erim en t

tim e (sec)

cal p ro to ty p e em bankm en t of N evada No. 100 san d a t 40% re la tive density w ith d im ensions show n in F ig ure 4. T h e m odel d im ensions, in s tru m e n ta tio n locations, an d in p u t m otions (in te rm s of in ten sity and d u ra tio n ) were scaled p ro p e rly so as to s im u la te th e sam e h y p o th e tica l p ro to ty p e s itu a tio n . T h e tim e h isto ries of p o re p ressu re tra n sd u c e r P P 2 an d d isp lacem en t tran sd u ce r LV l from these te s ts are also show n in F ig u re 4.

A set of th ree te s ts w as co n d u c ted on w ater- sa tu ra te d , em bankm en t m odels a t 50, 75, a n d lOOg (tes ts H5, H16, an d H13, respec tive ly ). As expec ted , d ifferent excess pore p ressu re an d se ttle m e n t tim e h isto ries were observed. In te s t H13, th e d iss ip a tio n of excess po re p ressu re was fa ster th a n th a t in te s t H16 w hich itse lf was faster th a n H5. T h is is because of th e d ifference in th e values of p e rm eab ilitie s . T h eo re ti-

316

cally, soil pe rm eab ilitie s in te s ts H16 a n d H13 were1.5 an d 2 tim es h igher th a n th e value of p erm eab ility in tes t H5, respectively. B ecause o f fa ster d issip a tio n in these tes ts , th e m ag n itu d es of excess p o re p ressu re gen era ted were also different. T h u s, m odeling of m odels could no t be achieved w ith w a ter as th e pore fluid.

In te s t H7 w here m etolose was used as th e po re fluid, the p ro to ty p e in p u t base m o tio n was s im ila r to those in tes ts H5, H16, an d H13. T h e difference due to the change in th e po re flu id can be s tu d ied by com paring th e re su lts from te s t H7 to those from te s t H5. T he in itia l ve rtica l effective stress a t th e lo ca tio n of P P 2 was ca lcu la ted as 22 kP a . T h e m ag n itu d e of th e excess pore p ressu re in te s t H5 w ith w ater was only a b o u t 12 k P a as opposed to 23 k P a in te s t H7 w ith p roperly scaled perm eability . T h is in d ica tes th a t th e m etolose- s a tu ra te d em b an k m en t liquefied w hereas th e w ater- sa tu ra te d em b an k m en t d id n o t liquefy u n d e r sim ilar e a rth q u ak e m otion . Also, th e ra te of d issip a tio n of excess pore p ressu re w ith m etolose was m uch slower th a n th a t w ith w ater an d hence th e a p p a re n t ra te of g en era tio n of excess po re p ressu re w ith m etolose was g rea te r th a n th a t w ith w ater. T h e se ttlem en t a t th e crest of th e em b an k m en t was d ra s tic a lly g re a te r in tes t H7 th a n in te s t H5 due to g re a te r p o re p ressu res and th e occurrence of liquefaction .

T h e last set of te s ts c o n d u cted by A stan eh (1993) included two te s ts (H15 an d H14) w ith m etolose as the pore fluid. T h e in p u t m o tions in these two tes ts were sim ilar. T h e m ag n itu d e an d h isto ry of th e excess pore p ressures from th e two te s ts were very sim ilar as were th e se ttlem en ts . Hence, A s tan eh concluded th a t m odeling of m odels was achieved w ith m etolose solutions as th e po re fluid w ith v iscosities correspond ing to g-levels.

A stan eh (1993) fu r th e r s ta te d th a t th e h igher the g ra v ita tio n a l accele ra tion (N) th e m ore im p o rta n t is th e use of a su b s ti tu te fluid, since by using w ater as the pore fluid, th e h igher th e g-level is, th e m ore d issim ilar th e behav io r of th e m odel a n d p ro to ty p e w ould be. Seism ic m odeling of m odels can n o t be achieved w ith w ater. T hus, a su b s ti tu te po re flu id is necessary.

•— horizontal accelerometer o pore pressure transducer I vertical Accelerometer — vertical displacement transducer

test pore fluid g-level

H5 water (Ics) 50g

H16 water (Ics) 75g

H13 water (Ics) lOOg

H7 metolose (50 cs) 50g

H15 metolose (75 cs) 75gH14 metolose (100 cs) lOOg

pore pressure transducer ; P P 2 vert, displ. transducer ; LV1

ES 10

t im e (sec) tim e (sec)

o u t o f ra n a ef te s tH 7

t im e (sec) t im e (sec)

4.4 M odeling of m odels of a re ta in in g wall

A to ta l of four tes ts were p erfo rm ed by D ew oolkar, et al. (1998a) on two re ta in in g wall m odels as a p a r t of a m odeling of m odels study. T h e w alls were scaled according to th e scaling re la tio n for flexural stiffness. T he backfill con ta ined N evada No. 100 san d a t 60% relative density. T ests M M D6 a n d M M D 7 were p e rform ed a t 40g on th e 0.9525 cm th ick an d 22.86 cm ta ll wall m odel w ith m etolose- a n d w a te r-sa tu ra te d backfills, respectively. T ests M M D 12 an d M M DIO were perform ed a t 60g on th e 0.635 cm th ick an d 15.24 cm ta ll wall m odel w ith m etolose- an d w a te r-sa tu ra ted backfills, respectively. T hus, theo re tically , only tes ts M M D6 an d M M D12 were m odels o f each o ther. Com -

F ig u re 4; M odeling o f m odels of an em b an k m en t a t p ro to ty p e scale

317

pariso n betw een te s ts M M D 7 an d M M D 6 an d betw een te s ts M M DIO an d M M D 12 w ould show th e effects of th e p o re flu ids on th e m odel behav io r. T h e co m p arison betw een te s ts M M D 7 an d M M DIO w ould in d ica te th e e rro rs th a t a re in tro d u c ed in m odeling o f m odels ty p e of s tu d ies if w a ter is used as th e p o re fluid.

A ty p ica l m odel con figu ra tion is d ep ic ted in F ig ure 5. T h e w alls were also in s tru m e n te d w ith s tra in gages a n d flush m o u n ted e a r th p re ssu re tran sd u ce rs along th e he igh t of th e wall. T h e loca tions of th e tran sd u ce rs w ere such th a t th ey rep resen ted ap prox im ate ly th e sam e p ro to ty p e locations. T h e re su lts are p resen ted a t p ro to ty p e scale.

As expec ted , s ta tic m odeling o f m odels w as achieved in all four te s ts since p e rm eab ility o f th e soil is n o t a significant fac to r in s ta tic s itu a tio n s .

T h e h o rizo n ta l in p u t m o tions g en era ted by th e shake tab le in th ese four tes ts , excess p o re p ressu res in th e soil, a n d dy n am ic la te ra l th ru s t on th e w all are also show n in F ig u re 5. T h e ra te o f d iss ip a tio n of excess po re p ressu res wets co nsiderab ly slower in th e m eto lo se -sa tu ra ted te s ts th a n in th e w a te r-sa tu ra te d tes ts . T h e ra te s of g en era tio n of excess p o re p re ssures in m e to lo se -sa tu ra te d te s ts w ere fa irly co m p ara ble w ith each o th er. T h e m ost im p o rta n t an d su rp rising observations re la te to te s ts M M D 7 a n d M M DIO w hich h ad w a te r £ls th e p o re flu id an d w hich were co n d u cted a t tw o d ifferent g-levels. S ignificant differences betw een th e excess p o re p ressu res were originally expected . S u rp rising ly th e p o re p re ssu re traces were a lm ost iden tica l. N ot only th e m ag n itu d es of th e excess p o re p ressu res g en era ted in th e tw o te s ts were very s im ilar, b u t th e ra te s o f d iss ip a tio n o f excess pore p ressu res from th e tw o te s ts w ere also sim ilar. In fact, by coincidence th e ir com parison was b e tte r th a n th e m eto lo se -sa tu ra te d tes ts . In te s t M M DIO, d u rin g th e dynam ic event, p e rm e ab ility w as on ly 1.5 tim es g rea te r th a n th a t in te s t M M D 7 w hereas it was 60 tim es g rea te r th a n th a t in te s ts M M D 6 an d M M D12. T hus, a ra tio of 1.5 in th e p e rm e ab ility values was n o t very significant and , hence, th e re su lts from te s ts M M D 7 an d M M DIO were n o t very d ifferent from each o th er. O n th e o th e r h an d , b ecause o f a g re a te r difference in th e p erm eab ilities , excess p o re p ressu res g en era ted in te s t M M D 6 a n d M M D 12 were differen t th a n th o se in te s ts M M D 7 a n d M M DIO. T h e differences w ere m ore p ro n o u n ced in th e d iss ip a tio n phases. I t sh o u ld b e n o ted th a t s im ila r differences in p e rm e ab ility in w a te r-sa tu ra te d e m b an k m en ts (As- tan e h , 1993; F ig u re 4) show ed sign iflcan tly d ifferent resu lts . T h ese differences betw een th e re ta in in g wall an d em b an k m en t configura tions cou ld b e a t t r ib u te d to th e d ra in ag e b o u n d a ry conditions. In th e re ta in in g w all case, th e d ra in ag e could tak e p lace only a t th e to p b o u n d a ry o f th e backfill w hereas in th e case of an e m b an k m en t th e excess p o re p ressu res could d issip a te fa s te r since d ra in ag e was possib le a t th e crest a n d a long th e slop ing faces.

In te s ts M M D6 an d M M D 12, th e soil liquefied th ro u g h o u t th e d e p th o f th e soil layer as in d ica ted by th e m ag n itu d es of excess p o re p ressu res reach ing th e in itia l ve rtica l effective stresses. In te s ts M M D 7 an d M M DIO, th e in p u t m o tio n s were s tro n g enough to cause liquefaction in th e to p h a lf of th e soil layer. In th e b o tto m half, th e excess p o re p ressu res cam e close to th e in itia l effective v e rtica l stresses. T h e m ag n itu d e an d h isto ry of th e in p u t m o tio n affected th e oscillatio n s in th e th ru s t on th e wall. Since th e soil liquefied com plete ly in te s ts M M D 6 an d M M D 12, th e sam e th ru s t was g en era ted a t th e en d of th e e a rth q u ak e . In te s ts M M D 7 a n d M M DIO, th e soil layer d id n o t liquefy com plete ly an d there fo re, th e th ru s ts a t th e end of th e e a rth q u ak e were sm aller th a n those from te s ts M M D 6 an d M M D12.

T h u s, good com parison w as o b ta in e d betw een te s ts M M D 7 an d M M DIO th ere b y c rea tin g a false im pression th a t seism ic m odeling o f m odels w as successful w ith w ater as th e p o re fluid. T h ere were su b s ta n tia l differences betw een th e th ru s ts from th e te s ts w ith m etolose a n d w ater as p o re fluids in th e ir tem p o ra l aspects. T h e a ccu m u la ted d y n am ic th ru s t a t th e end of shak ing d iss ip a ted to a lo n g -te rm res id u a l value in a b o u t 2 to 3 m in of p ro to ty p e tim e w ith w ater as the p o re fluid. However, w ith m etolose, th is tim e could be 1 to 2 hr. A s tru c tu re w hich was b a re ly able to surv ive h igh in s tan ta n eo u s loads due to an e a r th quake could fail u n d e r th is long p e rio d of su s ta in ed loads. O n th e o th e r h a n d , tru e m odeling o f m odels was achieved w ith m etolose, as w as also su p p o rte d by th e b en d in g tra in s , deflections, an d accele ra tions m easu rem en ts from th e w all an d th e accele ra tio n an d se ttlem en t m easu rem en ts from th e soil (no t show n here).

A num erica l s tu d y was also c o n d u c ted to em p h asize th is a sp ect of th e false ach ievem ent of m odeling of m odels w ith w a te r in liquefac tion cen trifuge ex p erim en ts (Dew oolkar, e t al., 1998a). B ased on th e ex p erim en ta l an d num erica l observations, it w as found th a t a false ap p ea ran ce of successful m odeling o f m odels can be o b ta in e d w ith w a ter as th e p o re flu id due to insign ifican t differences in m easu red q u a n titie s . Such differences can be easily a t t r ib u te d to n o rm al ex p erim en ta l varia tions ra th e r th a n to a rea l phenom enon . T h is false ap p ea ran ce o f seism ic m odeling of m o d els w ith w ater, however, d ep en d s on th e ty p e of th e m odel, d ra inage b o u n d a ry co nd itions, an d th e in te n sity a n d n a tu re of th e e a rth q u ak e m otions. A “t ru e ” seism ic m odeling o f m odels can be achieved if a su itab le su b s ti tu te po re flu id is used.

U ndoub ted ly , th e use o f s u b s ti tu te p o re flu ids is a key fac to r in o b ta in in g rea lis tic re su lts from seism ic cen trifuge experim en ts p a r tic u la r ly w hen p ro to ty p e b eh av io r is to b e s im u la ted . In sp ite of th e fac t th a t m ost cen trifuge m odelers genera lly agree th a t a rep lacem en t p o re flu id is necessary, m an y ex p erim en te rs s till choose to use w a ter m ain ly due to th e absence

318

D im ensions are in centim eters (in m odel scale).

test

M M D 6

M M D 12

M M D7

M M DIO

wall thickness

0 .9525 cm

0.635 cm

0 .9525 cm

0.635 cm

wall height

22 .86 cm

15.24 cm

22 .86 cm

15.24 cm

g-level

40g

60g

40g

60g

pore fluid

m etolose (40cs)

m etolose (60cs)

water ( le s )

water ( le s )

horizontal base motions

(P P 4 ) G .= 2 2 kP a

(P P 6 ) G .= 6 6 kP a

tes t M M D IO

time (min) time (min)

F igure 5; M odeling of m odels of a re ta in in g wall a t p ro to ty p e scale

of a su itab le su b s ti tu te p o re flu id an d th e am o u n t of tim e involved in sam ple p re p a ra tio n . In m any cases, a reason is given th a t th e p rim a ry a im of th e ex p erim ent is to v a lid a te a n u m erica l p ro g ram an d n o t to m odel any real or h y p o th e tica l p ro to ty p e behav io r. In th e a u th o rs ’ opin ion, if possib le , seism ic cen trifuge exp e rim en ts shou ld b e c o n d u c ted w ith a su b s ti tu te po re fluid. If w a ter is used , som e te s ts shou ld be p erfo rm ed w ith a su itab le su b s ti tu te p o re flu id to d e m o n s tra te th e differences in th e m odel behav io r. D ep en d in g on th e ty p e of m odel, th e s a tu ra tio n p rocess m ay becom e difficult if m ore viscous so lu tions a re to b e used; however, it w ould s till be m ore a p p ro p ria te to co n d u ct an ex p erim en t a t lOOg using a su b s ti tu te p o re flu id o f 50 cs v iscosity ra th e r th a n using w ater. T h e ex p erim en ta l re su lts w ould m ore closely m odel p ro to ty p e s itu a tio n s , an d num erica l p rog ram s could s till be used to analyze th e m odel w ith th e su b s ti tu te p o re flu id used.

5 SU M M A RY

C entrifuge m odeling has b een e stab lish ed as a d e p en d able research too l to s tu d y liquefac tion effects in various e a r th s tru c tu re s . T hese investiga tions have h e lped geo technical engineers u n d e rs ta n d liquefac tion re la te d phenom ena, assess liquefaction p o ten tia l, an d develop useful eng ineering so lu tions to m itig a te liquefaction hazard . T h e in itia l days o f o b serv atio n al ex p erim en ts are long gone p as t. C en trifuge m odelers are expec ted to be self c ritica l of th e ir re su lts a n d gen era te re p ea t- able an d re liab le q u a n tita tiv e d a ta from th e ir tes ts . V arious m odeling issues affect th e success o f a liquefactio n cen trifuge te s t d irec tly or ind irectly . Som e of th e facto rs such as in p u t m otions, b o u n d a ry tre a tm e n ts , an d su b s ti tu te pore fluids were d iscussed here in som e d eta il.

C en trifuge m odeling, com plim en ted w ith conventio n a l lab o ra to ry tr ia x ia l te s ts a n d a n a ly tic a l a n d nu m erical techn iques, can offer a g rea t deal of u n d e rs ta n d in g of liquefaction phen o m en a an d th e ir effects in various b o u n d a ry value p rob lem s in th e m ost econom ical, re la tive ly fast, an d fairly a cc u ra te way. We will see th is techn ique flourish fu r th e r in th e years to come.

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Sekiguchi, H., K. K ita & T . S h im om ura (1995), D ynam ic response of s tra in -g au g ed po re p ressure tran sd u ce rs , IS -T O K Y O ’95, Vol. 2, Ish ih a ra (ed), B alkem a, R o tte rd a m , pp . 717-722.

S teedm an , R. S. & X. Zeng (1990), T h e seism ic response of w aterfro n t re ta in in g walls. D esign an d P erfo rm ance of E a r th R e ta in in g S tru c tu res , A S C E Special P u b lica tio n No. 25, pp. 872-886.

Su7Aiki, K ., R. B abasak i & Y. Suzuki (1991), C entrifuge te s ts on liq u e fac tio n -p ro o f fo u n d a tio n . C entrifuge 91, Ko & M cLean (eds), B alkem a, R o tte rd a m , pp. 409-415.

T ohda, J ., T . H am ada , H. Law & H. Y. Ko (1995), M easurem ent of s tra in d is tr ib u tio n s along a b u ried p ipeline u n d e r seism ic load ing in centrifuge m odels, IS -T O K Y O ’95, Vol. 2, Ish ih a ra (ed), B alkem a, R o tte rd a m , pp . 785-790.

T ohda, J ., Y. Inoue & S. A m ano (1997), C en trifuge m odel te s ts on seism ic response of large d iam e te r po lyethy lene p ipe d u rin g liquefaction . P ro ceed ings of 52nd A nnual M eeting of JS C E , 3/V ol.B , in Jap an ese , pp. 218-219.

V an Laak, P. A., V. M. T ab o ad a , R. D obry & A. W . E lgam al (1994), E a rth q u ak e cen trifuge m o d eling using a lam in ar box. D ynam ic G eotechnica l T esting II, A STM S T P 1213, pp . 370-384.

V enter, K. V. (1987), M odelling th e response of sand to cyclic loads, P h .D . thesis . D e p a rtm en t of E n gineering , C am bridge U niversity , UK.

W h itm an , R. V. & P. C. L am be (1986), Effect of b o u n d a ry cond itions u p o n cen trifuge ex p erim en ts using g ro u n d m otio n sim u la tion . Geotechnical Testing Journal 9, pp . 61-71.

W h itm an , R. V. (1988), E x p erim en ts w ith e a r th quake m otion s im u la tion . C en trifuges in Soil M echanics, C raig , Jam es k Schofield (eds), B alkem a, R o tte rd a m , pp . 203-216.

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W h itm an , R. V. & N. H. T in g (1993), E x p e rim en ta l re su lts for t il t in g w all w ith s a tu ra te d backfill. Verification o f N um erica l P ro ced u res for th e A nalysis of Soil L iquefaction P rob lem s, Vol. 2, A ru- lan a n d an & S co tt (eds), B alkem a, R o tte rd a m , pp . 1515-1528.

W ilson, D. & B. L. K u t te r (1993), E x p e rim en ta l re su lts of M odel No 7, V erification o f N um erical P ro ced u res for th e A nalysis of Soil L iquefaction P rob lem s, Vol. 1, A ru la n an d a n & Sco tt (eds), B alkem a, R o tte rd a m , pp. 809-816.

W ilson, D. W ., R. W . B oulanger, B. L. K u tte r & A. A bghari (1997), A spects of d y n am ic cen trifuge te s tin g o f so il-p ile -su p e rs tru c tu re in te rac tio n . O bservation an d M odeling in N um erica l A nalysis an d M odel T ests in D ynam ic S o il-S tru c tu re In te ra c tio n P rob lem s, A S C E G eotechnica l Special P u b lic a tio n No. 64, N ogam i (ed), pp . 47-63.

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8 Field studies o f liquefaction


Physics and mechanics of liquefaction from field records and experience

T. Leslie YoudBrigham Young University, Provo, Utah, USA

ABSTRACT: Accelerations and pore pressures recorded as liquefaction and ground deformation developed at the Wildlife site during the 1987 Superstition Hills earthquake define the following relationships: (1) Cyclic shear deformation is the primary mechanism leading to generation o f excess pore water pressures. (2) Once pore pressure ratios exceeded about 2 0 percent, ground oscillation became the dominant mode o f ground deformation. (3) The amplitude o f ground oscillation increased after strong ground shaking ceased due to excitation by low- amplitude, long-period seismic waves. (4) Increased oscillation amplitudes increased cyclic shear deformations and continued the generation of pore water pressure after strong shaking had ceased. (5) Shear-strain induced dilatency at the northern end of the oscillation excursions transiently decreased pore pressures, strengthened soils, arrested movements, and generated negative pore-pressure and acceleration spikes in instrumental records.

1 INTRODUCTION

Field records and observations provide insight into the mechanisms that occur during liquefaction and ground deformation under natural conditions. A unique set o f records were obtained irom the Wildlife site in southern California during the 1987 Superstition Hills, California, earthquake (Holzer et al., 1989; Youd and Holzer, 1994). These are the only records to date that monitor acceleration and pore pressure responses at a field site through the liquefaction and ground deformation processes. Mechanisms and processes effective during these processes are well defined by these records.

2 WILDLIFE SITE AND RECORDS

The Wildlife site is located in the Imperial Valley, about 160 km east o f San Diego, California (Figure 1). Because of high seismicity in the region, the fact that liquefaction occurred during the 1981 Westmoreland earthquake, and the limited use o f the area, the Wildlife site was selected for instrumentation by the US Geological Survey (USGS) in 1982 (Youd and Holzer, 1994). Two accelerometers were installed at the site, one at ground surface and the other at a depth

of 7.5 m, immediately below the liquefiable layer. Six piezometers were also installed at the site, five in the liquefiable layer (one o f which malfunctioned) and one in a deeper silt layer. Those instruments recorded ground motions and pore pressure responses during two earthquakes in November 1987, the Elmore Ranch event (M = 5.9) the evening o f the 23' and the Superstition Hills event (M = 6 .6 ) on the morning of the 24‘‘". No pore pressures or liquefaction effects were generated by the Elmore Ranch event. The larger Superstition Hills event, however, generated excess pore pressures leading to a liquefied condition. Surface evidences of liquefaction included sand boils, ground fissures, and lateral displacements as large as 230 mm northeastward obliquely toward the incised Alamo River.

The layout of instruments at the site and the general soil stratigraphy are shown on Figure 2. Records of acceleration and pore pressure responses are reproduced in Figure 3. Calculated pore pressures, in terms of pore pressure ratios, r , are plotted as a function of time in Figure 4. The pore pressure record from Piezometer 5 indicates an ultimate r o f 1.2, whereas the ultimate for the other three piezometers in the liquefiable layer were 1 . 0 or slightly smaller. Static r greater than 1.0 are not possible; thus an incorrect calibration factor must have been applied by

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Figure 1. Location of Wildlife site and earthquake epicenters, Imperial Valley, California (Holzer et al., 1989)

O CRT 6T CONE PENETRATION TEST

CONE PENETRATION RESISTANCE kg/cm' FRICTION RATIO % PIEZOMETER STRONG MOTION SEISMOMETER OSCILLOGRAPHIC RECORDER p5WATER TABLE

Figure 2. Plan o f Wildlife site showing stratigraphy and instrument locations (Youd and Holzer, 1994; used with permission o f ASCE)

USGS in deriving the pore pressures plotted for Piezometer 5. A corrected record for that piezometer, scaled to an ultimate o f 1.0, is plotted on Figure 5. Figure 5 also shows an expanded record of north-south accelerations recorded at ground surface. Figure 6

shows a time history o f ground displacement at ground surface calculated through double integration o f the acceleration record reproduced in Figure 5 (A). These records provide data and information from which liquefaction and ground deformation mechanisms can be clearly defined.

3 LIQUEFACTION AND GROUND DEFORMATION MECHANISMS

The first major surge o f pore water pressure was induced by the 0 . 2 1 g peak acceleration pulse that propagated through the site at the 13 second time mark. That surge o f pore pressure was recorded by all four functioning piezometers in the liquefying layer (Figure 4). The 0.21 g acceleration pulse produced an average shear strain amplitude o f about 0 . 2 percent between the two accelerometers. That shear strain is several times larger than typical threshold strains measured in the laboratory, but that strain also caused a major rise o f pore pressure, not just an onset.

Pore pressures continued to rise monotonically over the next 1 0 seconds o f record as five additional large pulses o f acceleration in the 0.15 g to 0 . 2 0 g range propagated through the site. Average shear strain amplitudes from those pulses were as large as 1 . 0 %. The increased average shear strain was due to softening o f the liquefying layer as pore pressures rose. Actual shear strains within the liquefying layer were likely much larger than the average strains, due to greater softening within that layer compared to the overlying nonliquefiable layer.

At the 23 second time mark, strong ground shaking essentially ceased and the earthquake was over in terms o f strong acceleration pulses, although a few acceleration spikes developed later in the record from the north-south accelerometer at ground surface. The cause and importance o f these spikes are addressed in a subsequent section.

Pore pressure ratios at the end o f strong ground shaking (23 second mark) ranged from about 60 percent at the top o f the liquefying layer (Piezometers 2 and 5) to about 40 percent at the bottom o f the layer (Piezometer 3). The pore pressure ratios at all levels continued to rise over the next 40 seconds, however, until pore pressure ratios near 1 0 0 percent were attained in the upper part o f the layer (Figure 4).

326

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Figure 3. Acceleration and pore-water pressures recorded at Wildlife site during 1987 Superstition Hills earthquake (Holzer et a l, 1989)

327

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Figure 4. Pore pressure ratio time histories from Wildlife site (Youd and Holzer, 1994; used with permission o f ASCE)

The continued rise o f pore pressures surprised several experts who had postulated that pore pressures should immediately begin to decay once strong ground shaking had subsided. Because o f the unexpected pore pressure behavior, a few o f these experts challenged the accuracy o f the records, contending that the piezometers had malfunctioned (Hushmand et al., 1992). The reasons and mechanisms for the continued pore pressure rise, however, is clear from the instrumental records.

The key to understanding the continued pore pressure rise is the displacement record reproduced in Figure 6 . The record shows that cyclic ground displacements at the ground surface did not cease, or even begin to decay, at the end o f the strong ground shaking, but continued to gain amplitude over the next 20 seconds. The increased displacement generated corresponding increases in cyclic shear strains within the liquefying layer which increased shear deformations and enhanced the pore pressure generation process. These actions led to the continued rise o f pore pressures.

A fundamental mechanism that led to the continued rise o f cyclic displacements was set in motion at about the 15 second time mark, which was shortly after the arrival o f the 0.21 g peak acceleration. At that juncture, the consistency o f the liquefying layer changed from a rather rigid medium to a softened, more plastic medium that was no longer capable o f transmitting coherent motions from the downhole accelerometer to the surface instrument. That change of state is illustrated on Figure 7 where the north-south acceleration traces from the downhole and surface accelerometers are superimposed. For this figure, the

Figure 5. North-south surface acceleration (a) and pore pressure ratio history from Piezometer 5 (b), Wildlife site (Zeghal and Elgmal, 1994; Youd and Holzer, 1994; used with permission o f ASCE)

TIM E (sec)

Figure 6 . Relative north-south ground displacement from Wildlife site (Thilkartne and Vucetic, 1989; Youd and Holzer, 1994; used with permission of ASCE)

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Figure 7. Superposition o f downhole and surface acceleration records from Wildlife site showing lack o f coherence between records after the 15 second mark (Holzer et al., 1989)

surface acceleration trace was advanced by 0 . 6 seconds to facilitate comparison o f the two traces. At about 1 2 . 6 seconds, the downhole-to-surface travel time increased by about another 0 . 6 seconds, indicating that the average shear-wave velocity between the instruments had decreased to half it original value (Holzer et al., 1989). During the first 15 seconds of record, distinct acceleration pulses can be traced form one record to the other. Beyond 15 seconds, the upper accelerometer recorded long period waves that were generally unrelated to higher-frequency acceleration pulses sensed by the lower instrument. This change of state led to a change o f character o f motions at ground surface, from low-amplitude motions with high- frequency components prior to the 15 second mark to larger amplitude harmonic oscillations beyond that time (Figure 6 ). Pore pressure ratios throughout the liquefying layer at the 15 second mark were 2 0 percent or less, but were rising rapidly (Figure 4). The change of consistency from a rigid to a softened medium developed at a lower pore pressure ratio than might generally be expected from laboratory test results. More testing and analysis are needed to verify the change of state at this low pore pressure ratio and to fully understand and correctly model the behavior of natural soil systems.

As the liquefying layer softened and the change of state occurred, ground oscillation became the dominant mode of surface motion. Long-period seismic waves, roughly in resonance with the one-second period o f the oscillating surface layer, became the major exciter o f ground response. Several large acceleration pulses with periods of about one second propagated through the site between the 15 second time mark and the end of strong ground shaking at the 23 second time mark. These pulses caused the amplitude o f ground

oscillations to grow from about 2 cm to 7 cm and the period of oscillation to increase from about 1 . 0 second to about 1.8 seconds. Pore pressure ratios within the liquefying layer rose from about 2 0 percent at the 15 second juncture to about 65 percent at the top and 45 percent at the bottom o f the layer at the 23 second mark.

After cessation o f strong ground motion, at 23 seconds, low-amplitude, long-period seismic waves became the principal exciter of ground oscillation. As noted, the amplitude o f oscillations continued to grow, reaching a maximum of about 1 0 cm at the 37 second time mark. Pore pressures also rose during this interval to about 90 percent at the top of the liquefying layer and to about 70 percent at the bottom. The increased pore pressures caused further softening of the layer and a lengthening of the period of ground oscillation to about 3.0 seconds at the 37 second time mark.

Beyond 37 seconds, the amplitude of ground oscillation decayed logarithmically with a second episode o f amplitude increase and decay between 70 and 100 seconds (Figure 6 ). Between 37 and 50 seconds, the period o f oscillation lengthened from 3 . 0

seconds to 3.8 seconds. Beyond 50 seconds, the period remained relatively constant. Pore pressures continued to rise during the 37 second to 50 second time interval, even though the amplitude of oscillation was decaying. Pore pressure ratios at 50 seconds were near 100 percent at the top o f the layer and about 80 percent al the bottom. Over the final 50 seconds o f record, pore pressure ratios remained near 1 0 0 percent at the top of the layer while ratios at the bottom of the layer increased to about 90 percent.

The maximum amplitude o f ground oscillation, about 10 cm, occurred 37 seconds into the record or 14 seconds after the cessation of strong ground accelerations (Figure 4). At the end o f 100 seconds, the amplitude had decayed to about 2 cm and the arriving seismic waves were so weak that the inertial switch turned off the recording equipment and the instrumentation returned to a standby condition, awaiting strong motions from a subsequent earthquake.

The extended occurrence of ground oscillation and the continued generation o f pore pressures, after the cessation o f strong ground motion, explains and adds credence to the many reports, primarily from Japan, of observed liquefaction effects occurring as much as several minutes after the cessation of strong earthquake shaking. At the Wildlife site, large ground oscillations continued for well over a minute after strong ground motions had ceased. Longer oscillation sequences would be expected for larger earthquakes with longer

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Total pore pressure (kPa)

Figure 8 . Total pore pressure at the Wildlife site at various times after earthquake shaking began (Holzer et al., 1989)

sequences o f low-amplitude, long-period waves. Where ground oscillations occur during the lateral spreading process, lateral ground displacements would also to continue for some time after the cessation of strong ground motion.

The mechanism that mobilized the long sequence of ground oscillation and continued rise o f pore pressure was resonance o f the oscillating layer with long-period, low-amplitude seismic waves that arrived at the site after strong ground motion had ceased. These low- amplitude waves are generally ignored in geotechnical engineering practice. Analytical or physical models that do not incorporate the influence o f these seismic waves, however, omit a fundamental mechanism in the liquefaction-ground deformation process and may not adequately reproduce the Wildlife behavior or ground deformations at other sites.

After ground oscillations had largely subsided at the Wildlife site, pore pressures in the liquefied layer finally began to dissipate. Figure 8 shows pore pressure ratios versus depth at several time marks during and after the earthquake. For example, at 97 seconds, which was near the end o f the record, pore water pressures were near 56 kPa or 100 percent r at the top of the layer (3 m depth) and near 110 kPa or about 90 percent r , at the bottom of the layer (7 m depth). The instrumentation was reactivated by an aftershock 19 minutes after the main shock. Pore pressure ratios at that time were still near 1 0 0 percent at the top and midpoint o f the liquefied layer, but had dissipated to about 96 kPa or a pore pressure ratio o f 78 percent at the bottom o f the layer (Figure 8 ). This initial pore pressure dissipation indicates that

reconsolidation was beginning at the bottom layer and propagating upward, a process that is consistent with theory and laboratory tests (Florin and Ivanov, 1961).

The Wildlife records clearly demonstrate that cyclic shear deformation is the primary generator o f excess pore pressure. Shear deformation induced by the arrival o f the peak acceleration pulse initiated the initial surge o f pore pressures. Additional shear deformation during the strong motion phase continued the generation o f pore pressure. The rise of pore pressures persisted into the ground oscillation phase as shear deformations continued to increase. Only when the amplitude o f oscillation decayed to a level at which dissipation occurred more rapidly than generation, did pore pressures finally begin to dissipate.

During the ground oscillation phase, the acceleration records contain periodic negative and intermittent positive acceleration spikes (Figure 5). Negative pore pressure spikes also occur in the record from Piezometer 5 that correlate both in time and sense of direction with the negative acceleration spikes (Figure 5). Numbers in parentheses on Figure 5 identify the spikes and show that correlation (Zeghal and Elgamal, 1994). Both the positive and the negative acceleration spikes occur at oscillation maxima, where ground displacement was arrested and reversed direction. These spikes also occur at ends of hysterisis loops on shear stress versus shear strain plots (Figure 9). Zeghal and Elgamal calculated shear stresses at various points in time by multiplying one- half the mass o f the soil in the liquefied and overlying unliquefied layer by the difference in instantaneous acceleration between the upper and lower accelerometers. They calculated shear strains by dividing relative displacements between the two accelerometers at the same point in time by the distance between the two instruments.

The spikes in the acceleration record reproduced in Figure 5 indicate that ground displacement toward the Alamo River was abruptly arrested by a dilatency- induced decreases o f pore water pressure and concomitant transient increases o f soil strength. Upon reversal o f the direction o f movement, the dilatent block released, the pore pressures again rose, and the mobilized ground began its traverse away from the river (Youd, 1977). At the end o f the swing away from the river, ground displacement was apparently arrested by an impact of the mobilized soil layer with the inland nonmobilized soil. The impact generated positive acceleration spikes without corresponding fluctuations of pore pressure, and hence no corresponding pore pressure spike.

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Figure 9. Plots o f average shear stress versus average shear strain at selected time increments from Wildlife site (Zeghal and Elgmal, 1994; Youd and Holzer, 1994; with permission o f ASCE)

331

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5 0 0 0 1 0 0 0 0 150 0 0 0 50 100 150 2 0 0 2 5 0 3 0 0

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clayey silt to sandy silt

Figure 10. Soil variability at Wildlife site shown by tip and friction sleeve resistances from 14 cone penetrationsoundings

332

4 SOIL VARIABILITY AT WILDLIFE SITE

Granular soils in the liquefiable layer at the Wildlife site are highly variable as indicated by large variations in cone penetration resistance. Across the site, 14 CPT logs yielded penetration resistances ranging from about 750 kPa to 10,500 kPa in the liquefiable layer (Figure 10). This variability undoubtedly led to inhomogeneous generation of pore pressures during the 1987 earthquake. Liquefaction likely developed in isolated pockets and then spread vertically and laterally. The consistency and parallelism o f the recorded pore pressure traces, however, indicate that pore pressures must have equilibrated rather quickly (within seconds) throughout the layer. Most attempts to model the Wildlife site have characterized the liquefiable layer as a single homogeneous medium. Analyses based on these models have generally predicted a more rapid rise o f pore pressure than was actually measured. These overpredictions may be due in part to the assumption o f a uniform layer and uniformly generated pore pressures when in fact the generation of pore pressures was likely quite nonuniform.

5 THICKNESS OF THE LIQUEFIED LAYER

however, dilation-induced suction will draw excess water into and loosen the shear zone (Youd, 1984). In many instances, shear zones form beneath impermeable layers as water collects due to both upward migration and suction. That combination appears to have occurred at the Wildlife site. Measurement o f the displacement of a slope- inclinometer casing placed prior to the 1987 earthquakes revealed the following two relationships (Holzer et al., 1989). (1) The top of the inclinometer casing deflected approximately 180 mm in a N15°E direction obliquely toward the Alamo River. (2) Subsurface horizontal shear strain, estimated from the curvature o f the casing, was greatest, approximately 4 percent, in the upper part o f the silty sand layer, which is immediately beneath the capping silty clay layer. This concentration of strain indicates that either water accumulated during the earthquake and softened the shear zone or that the softened zone was a relict of liquefaction during previous earthquakes.

Models for predicting ground displacement should include a thickness factor in their formulation. Many mechanistic models incorporate estimates of residual strength that are independent o f the thickness of the liquefiable layer. Such models may not yield true predictions of field behavior because of inadequate consideration of the thickness factor.

A final observation from the Wildlife and other field sites is that the thickness o f the liquefied layer is a primary factor influencing the amount of ground displacement. Empirical analyses by Hamada et al. (1987) and by Bartlett and Youd (1995) both identify thickness o f the liquefied layer as a primary variable controlling lateral spread displacement. Thickness could affect ground displacement by two different mechanisms. (1) For uniformly stiff layers, cumulative surface displacement is the product o f the induced permanent shear strain and the thickness o f the layer. (2) For uniformly dense layers, the amount of excess water generated in the liquefaction process is also function of the thickness of the layer. Migration of this excess water during the liquefaction-ground deformation process causes water to accumulate either beneath impermeable strata, within shear zones, or both. Where excess water accumulates within a shear zone, the amount of shear deformation is a function of the amount of softening, which in turn is a function of the amount of accumulated excess water.

Excess water normally migrates upward and accumulates beneath a low permeability layer or vents to the surface through sand boils. Where shear deformation leads to dilation o f granular soils.

CONCLUSIONS

Monitored behavior at the Wildlife site and other field observations led to the following conclusions concerning mechanisms and physical processes effective in development o f liquefaction and ground deformation:

1. Cyclic shear strain rather than acceleration or shear stress pulses is the primary mechanism causing generation o f excess pore water pressures leading to liquefaction. This relationship is demonstrated in the Wildlife records by the strong correlation between induced shear strain and pore pressure rise.

2. A change of character of surface ground motions recorded at the Wildlife site occurred at the 15 second time mark and shortly after the arrival of the 0 . 2 1 g peak acceleration pulse. At that juncture, the motions recorded at ground surface changed from low- amplitude waves with high-frequency components to harmonic oscillations with a period o f about one second. When this change occurred, pore pressure ratios were 2 0 percent or less, but rapidly increasing.

3. The primary mode of liquefaction-induced ground displacement at the Wildlife site was ground

333

oscillation. Ground oscillation dominated motions recorded at ground surface from the 15-second change of character onward. The amplitude o f oscillation increased markedly from about 2 cm at the 15 second time mark to about 7 cm at the 23 second time mark, the end o f strong ground shaking. The amplitude o f oscillation did not begin to decay at that point, but continued to rise, reaching a maximum o f 1 0 cm at the 37 second time mark. The increase o f amplitude was driven by long-period, low-amplitude seismic waves that continued to arrive at the site after strong motions ceased.

3. Pore pressures also continued to rise after the cessation o f strong ground shaking. The mechanism driving that rise was increased levels o f cyclic shear deformations in the liquefying layer as a consequence of the increased amplitude o f ground oscillation.

4. Ground oscillation toward the Alamo River was arrested by strain-driven dilatency within the liquefied layer. As each large oscillation reached its northward maximum, dialtency within the soil generated a sudden reduction of pore pressure, concomitant rise o f soil strength and sudden deceleration o f the mobilized soil layer. These actions produced paired negative acceleration and pore pressure spikes in the instrumental records.

5. Penetration resistances are highly variable in the liquefiable soils at the Wildlife site. This variability undoubtedly led to uneven generation o f pore pressure and liquefaction during the 1987 earthquake. Liquefaction likely developed in isolated pockets and then spread vertically and laterally causing pore water pressures to develop more slowly than predicted by analytical models incorporating homogeneous layers.

6 . Empirical studies have identified thickness o f the liquefied layer as a primary variable controlling lateral spread displacement. Thickness may influence displacement either o f the following mechanisms: ( 1 ) For uniformly stiff layers, cumulative surface displacement is the product o f the induced permanent shear strain and the thickness o f the layer. (2) For uniformly dense layers, the amount o f excess water generated in the liquefaction process is also function o f the thickness o f the layer. Excess water may accumulate in shear zones, further softening the soil and increasing shear deformation. Both mechanisms may occur simultaneously where shear zones form beneath impermeable layers. The latter combination apparently occurred at the Wildlife site where the greatest permanent shear strains occurred immediately beneath an impermeable layer.

REFERENCES

Bartlett, S.F. & T.L. Youd 1995. Empirical prediction o f liquefaction-induced lateral spread. Journal of Geotechnical Engineering, ASCE, 121(4):316-329.

Florin, V.A. & P.L. Ivanov 1961. Liquefaction of saturated sandy soils. Proceedings, 5*' International Conference on Soil Mechanics and Foundation Engineering, 1:107-111.

Hamada, M., I. Towhata, S. Yasuda, & R. Isoyama 1987. Study o f permanent ground displacement induced by seismic liquefaction. Computers and Geotechnics, Elsevier Applied Science Publishers, 4(4): 197-220.

Holzer, T.L., T.L. Youd, & T.C. Hanks 1989. Dynamics o f liquefaction during the Superstition Hills Earthquake (M = 6.5) o f November 24, 1987. Science, 244:56-59.

Hushmand, B., R.F. Scott & C.B. Crouse 1992b. In- place calibration o f USGS transducers at Wildlife liquefaction site, California, USA. Proceedings, World Conference on Earthquake Engineering: 1263-1268.

Thilakaratne V., and Vucetic, M., 1989, "Liquefaction at the Wildlife site - effect on soil stiffness on seismic response." Proceedings. 4th International Conference on Soil Dynamics and Earthquake Engineering, Mexico City, p. 37-52.

Youd, T.L. 1977. Packing changes and liquefaction susceptibility: Journal o f the GeotechnicalEngineering Division, ASCE, 103(GT8)918-922.

Youd, T.L. 1984. Recurrence o f liquefaction at the same site. Proceedings World Conference on Earthquake Engineering, 3:231-238.

Youd, T.L. & T.L. Holzer 1994. Piezometer performance at the Wildlife liquefaction site. Journal o f Geotechnical Engineering, ASCE, 120(6)975-995.

Zeghal, M. & A.W. Elgamal 1994. Analysis o f site liquefaction using earthquake records. Journal of Geotechnical Engineering, ASCE, 120(6)996-1017.

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In situ liquefaction resistance o f sands

Shamsher Prakash & TGuoUniversity of Missouri-Rolla, Mo., USA

ABSTRACT: There are two approaches in present engineering practice for evaluating liquefaction potential o f sands (1) by "Simplified Procedure" (Seed and Idriss 1971), and (2) analysis based upon SPT tests, "Liquefaction Assessment Chart" by Seed et al., (1985). In the later, the effect o f soil properties which have significant influences on the liquefaction potential o f sands and cannot be studied in the lab e.g. previous strain history, aging, soil fabric. Overconsolidation ratio (OCR) and Cementation is included. By comparing the liquefaction resistance o f sand by the above 2-methods, the effect of above variables has been studied on 24 sites with 92 soil profiles o f sandy deposits where earthquakes have occurred. It has not been possible to isolate the effect o f each of the five variables because o f lack o f adequate field data.

INTRODUCTION

There are several methods for evaluating liquefaction potential o f a site, (Guo 1998). The most important method is the one given by Seed et al (1971), ie. Simplified Procedure which is extensively used.

Soil properties which influence the liquefaction potential o f sands are:

1) Grain size2) Grain size distribution3) Relative density4) Initial effective confining pressure5) Initial Kc conditions6 ) Dynamic stress level7) Number o f pulses o f dynamic stress level8 ) Location o f drainage9) Previous strain History10) Aging11) Soil fabric12) Overconsolidation ratios (OCR) and13) CementationAmong these factors No. 1 to No. 8 can be

simulated in laboratory environment. The last five factors, cannot be studied directly by laboratory tests.

For studying the influence o f these factors, an approach based on correlation o f standard penetration resistance and stress causing liquefaction from field tests, based on Liquefaction Assessment Chart may be applied.

Thus there are two approaches in present engineering practice for evaluating liquefaction potential o f sands in the United States:

The “Simplified Procedure” has been modified continuously after it was proposed in 1971. During this time it appears that the standard penetration test is also used to estimate the liquefaction resistance even though its test methods is not ‘standard’. After the normalized SPT, (N|)6q, was introduced, the limitation o f its applicability only to level ground conditions was corrected by the development o f empirical corrections for confining stress, and anisotropic stress conditions, K„ (Seed 1981, 1983). On the other hand, though the laboratory method was developed almost three decades ago, it is still in use by many practicing engineers because o f its ‘simplified’ procedures and fewer field tests.

Sometimes the differences between the results o f these two approaches could be quite large, due to the fact that the specimen tested in the laboratory do not reflect the influences o f the last five factors. Therefore, the influence o f those factors are evaluated by comparing the difference between results o f two methods.

In this study, 24 sites with 92 soil profiles o f sandy deposit where earthquakes have occurred have been selected with provided SPT values and relevant soil properties in the literature.

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Mean grain size D50, mm

Figure 1 Cyclic Stress Ratio (CSR) causing liquefaction o f sands in 1 0 cycles (after Seed and Idriss, 1971)

•

V

- Triaxial compressi( o ^ /2 o , at liquefat

an test data for :tion

0-------------

Field vc estimati

ilue at t I o 'q causing 1 jd from results of sir

iquefaction nple shear tests

Relative densil No. of stress c

1ty 5 0 % ycles = 3 0

1 .0 0 . 3 0 .1 0 . 0 3 0 . 0

Mean grain size D ^ , mm

Figure 2 Cyclic Stress Ratio (CSR) causing liquefaction of sands in 30 cycles (After Seed and Idriss, 1971)

Methodology of analysis includes:1) Estimation at each point on the above

profile where SPT value is given, the following quantities:a) Corrected SPT [ (Ni)(,o or (N i)7q ];b) Relative density. Dr;c) Stress causing liquefaction (Ti b)

according to the simplified analysis (Seed and Idriss, 1971);

d) Stress causing liquefaction in the field (Xf) according to the field charts o f Seed et ah, (1984, 1985);

2) Carry out a statistical analysis o f Xf / x,ab with (N i)6o and/or depths o f the soil;

3) Analyze the differences between the two approaches and the reason causing these difference.

SHEAR STRESS CAUSING LIQUEFACTION BASED ON LABORATORY DATA (x )

In the ''simplifiedprocedure'' (Seed and Idriss 1971), the shear stress causing liquefaction o f a deposit is evaluated by examining the correlation between grain size, relative density and the liquefaction resistance o f sand. Results o f triaxial or simple shear tests are adopted to determine the shear stress at which liquefaction occurs after a number o f cycles o f shaking. A correction factor, c , is adopted to adjust the lab test result to field conditions. Figures 1 and 2 show the correlations between cyclic stress ratio causing liquefaction and mean grain size, D 50, in 1 0

and 30 cycles, respectively at the relative densities o f 50%. The stresses required to cause liquefaction for sands at other relative densities can be estimated based on the assumption that the shear stress to cause initial liquefaction is approximately proportional to the relative density, up to about 80%.

An important concept o f this method is that the effect o f earthquakes o f different magnitudes could be related in terms o f different equivalent number o f significant cycles o f motion with depend on the duration of ground shaking and thus on the magnitude o f the earthquake. Representative numbers o f stress cycles can be obtained in Table 1 below.

Table 1. Representative number o f cycles for various magnitude o f earthquakes (After Seed et al, 1975)

M Number o f representative cycles at 0.65 x ax

8.5 267.5 15

6.75 1 0

6 .0 5-65.25 2-3

The stress ratio causing liquefaction in the field for a given soil at a relative density Dr can be estimated from the equation:

L.(— )

D r5Ö (1)

and the shear stress causing liquefaction is:

'^ liq ~ ^ 0 (2)

336

where

( dc ^ a)l50 '

Cr

D. =

stress ratio causing liquefaction under field conditions; stress ratio causing liquefaction in triaxial tests, o¿ is the cyclic deviator stress and o \ is the initial ambient pressure under which the sample was consolidated;effective overburden pressure; correction factors listed in Table 2;relative density; percent; shear stress causing liquefaction from lab tests.

Table 2. Values o f correction factor c

Relative density Dr (%) Correction factor c

0-50

60

80

0.57

0.60

0.68

Relative densities for the deposit can be estimated based on in-situ tests such as SPT or CPT. Many such correlations exist, all o f which were obtained empirically. Two correlations between SPT N-values and relative density given below have been used in this study:

Skempton (1986)

D =

andYoshida(1988):

\ 32+0.288(3)

i> =25ar'v,);r (4)

where:N '70 = normalized SPT blow count corrected

to 70 percent energy transmission and overburden o f 100 kPa;

(N])6o ^ Normalized SPT blow count corrected for 60 percent energy and overburden pressure o f 100 kPa.

o ’o effective overburden pressure (kPa).Once relative density has been determined, then,

Eqs. 1 and 2 are used to compute the shear stress

causing liquefaction (iiiq).For a given magnitude o f earthquake, the

equivalent number o f significant stress cycles are given in Table 1.

SHEAR STRESS CAUSING LIQUEFACTION BY STANDARD PENETRATION VALUES (Xf)

Considerable field data where liquefaction occured during earthquakes has been accumulated and interpreted after the 1964 Niigata earthquake. Most developed correlations are based on the Standard Penetration Values which is the blow count in the SPT test, corrected for the depth o f overburden and for certain details in the performance o f the test. The Liquefaction Assessment Chart Figure 3 (Seed et al. 1985) is often used in practice. The curves drawn in the chart represent the boundary lines between liquefiable and nonliquefiable level sandy sites with various percentages o f fines for an earthquake of magnitude 7.5 on the Richter scale. The resistance to liquefaction for the site is measured by the normalized standard penetration resistance, (Nj)6o, which is the SPT blow count corrected to a vertical effective overburden pressure o f 100 kPa and an energy level o f 60 percent of the free-fall energy o f the hammer. The curves drawn in Figure 3 are dividing zones corresponding to liquefaction and non-liquefaction of sands with fines content o f 5, 15 and 35 percent.

The stress causing liquefaction is computed by timing the cyclic stress ratio (CSR) obtained in Figure 3 with effective overburden pressure. The procedure to determine the shear stress causing liquefaction of sand based on normalized SPT blow count can be summarized as follows:

1) Normalize SPT blow count to (Ni)6o,2) Find the fines content o f the soil and select

the appropriate curve in Figure 3. In this investigation, only clean sands have been analysed.

3) Find the cyclic stress ratio (CSR) from the curves in Figure 3 according to (N])6o values. Figure 3 is for magnitude 7.5 earthquakes. For earthquakes with magnitude other than 7.5, the ordinates o f a curve in Figure 3 are multiplied by the factors in Table 3;

4) Determine the cyclic stress level causing liquefaction (if) by timing the effective overburden pressure at the point considered with the CSR obtained in Figure 3.

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PO

00

U

Percent fines = 35

Fines content >5%Modified Chinese code proposal (day content = 5%)

Marginal NoLiquefaction Liquefaction Liquefaction

Pan-American data

Japanese data

Chinese data

20

Standard Penetration Test Blow Count (Ni)6o

Figure 3 Relationships between cyclic stress ratio causing liquefaction and (N\)eo values for sands for magnitude 7.5 earthquakes. (After Seed et al, 1985)

Table 3 Correction factors for the earthquake other than 7.5 (Seed et al 1985)

M Factor to correct the abscissa o f curve in Figure 3

8.5 0.897.5 1.0

6.75 1.136.0 1.32

5.25 1.5

DESCRIPTION OF SITE AND RESULTS

Figure 4 is profile o f predominently sandy soils. This site has fine and coarse sand and a thin gravel layer up to about 23 m. Below this sand is a 3m thick layer of sand-silt mixture.

Shear stress causing liquefaction was analyzed by the two methods described previously.

Figure 5 contains plot o f shear stress causing liquefaction by the two methods. It will be seen that Tf is consistently larger than below about 4 m depth. In some profiles, Xf was found to be even in

( m )O

Depth Soil Type

10

15 -

20-

5 0

809 0

10 0

109

22 0

ZZA

SPT N-valueO IQ 20 30 4 0 50

FillFine SandCoarse Sand

Fine Sand

Coarse SandGravelly‘Sand

Gravel

Fine Sand

Coarse Sand

Medium SandFine SandFine Sand Mixed with Silt

Fine Sand

i j Z

I i I

Figure 4 SPT Site 24, profile 1 - (After lai et al 1994).

I IKushiro Japan,

smaller than x,ab at shallow depths. The reasons for the above variations are being investigated.

It was found that (N^bo is a better index o f the variation o f Xf and Xj b.

In Figures 6, 7 and 8 are plots o f x/x^q for sites 12 (9-profiles), 18 (5 profiles) 24 (2-profiles). It will be seen that (Ni)bo is an important factor to control this ratio. In the sites analysed, the values o f (N i)6q at which x/Xbq is unity varied from 10 to 16. For (Ni)bo greater than the above values, x/x^q is greater than 1. However for (N i)6q smaller than these values, x/x^q is smaller than 1.

338

Figure

0 50 100 150

S h ear stresses causing liquefaction (kP a)

5 If and Xi b causing liquefaction

200

Figure 6

Ratio o fT | /

T/x,ab VS normalized SPT blow counts for site 12

Figure 7 Tf/T jab VS normalized SPT blow counts for site 18

profile 1 profile 2 , Regr '

^10

: 15

w20TD(D

E 2 5oz:

30

35 I - 0

Figure \R a t io o f

tf/Xiab VS normalized SPT blow counts tor site 24

CONCLUSIONS

Based on this analysis, the following conclusions are drawn:

1) The two computed shear stresses causing liquefaction i) by "Simplified Procedure" and ii) the Liquefaction Assessment Chart, both developed by Seed et ah, are different.

2) The ratio of x/tiab, is not constant. This ratio changes with depth and Standard Penetration values. This is due to the fact that several important factors which influence the liquefaction resistance o f sands cannot be accounted for in the lab approach.

339

3) There is limited field data which was analyzed. More studies are needed to draw more definite quantitative conclusions.

ACKNOWLEDGEMENT

The paper was typed by Charlena Ousley with painstaking effort. Comments were offered by Alex Wu. All help is acknowledged.

REFERENCES

Seed, H.B., K. Tokimatsu, L.F. Harder, and R.M. Chung (1985), "Influence o f SPT procedures in Soil liquefaction resistance evaluations," Journal o f the Geotechnical Engineering Division, ASCE, Vol. I l l , No. 12, pp 1425-1445.

Skemption, A.W. (1986), "Standard penetration test procedures...," Geotechnique, Vol. 36, No. 3, pp 425- 447.

Yoshida, I. et al (1988), "Empirical fórmalas o f SPT blow counts for gravelly soils," 1st ISOPT Vol. 1, pp 381-387.

Guo, T. (1998), "Liquefaction o f sands and silts," Ph.D. thesis. University o f Missouri-Rolla, under progress.

lai, S., Y. Matsunaga, T. Morita and H. Sukurai(1994), "Performance o f Quay Walls during the 1993 Kushiro - Oki Earthquake," Proc. Thirteenth Intern. Conf on SM&FE, New Delhi, Vol. - pp 69-76.

Seed, H.B. (1981), "Earthquake-resistant design of earth dams," State-of-the-Art paper. Proceedings, International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, University o f Missouri-Rolla, 17 pp.

Seed, H.B., (1983), "Recent developments in the evaluation o f soil liquefaction," Presented at Inaugral Meeting, Indian Society for Earthquake Engineering, Roorkee, India, Bulletin o f Indian Society o f Earthquake Technology, Vol. 20, No. 3 & 4, pp 53-77.

Seed, H.B., and I.M. Idriss (1971), "Simplified procedure for evaluating soil liquefaction potential," Journal o f Soil Mechanics, Foundation Division, ASCE, Vol. 97, No. SM 9, pp. 1249-1273.

Seed, H.B., I.M. Idriss, F. Makdisi, and N. Baneijee (1975), "Representation o f irregular stress time histories by equivalent uniform stress series in liquefaction analyses," Report No. EERC 75-29, Earthquake Engineering Research Center, University o f California, Berkeley, California.

Seed, H.B., K. Tokimatsu, L.F. Harder, and R.M. Chung (1984), "The influence o f SPT procedures in Soil liquefaction resistance evaluations," Report No. UBC/EERC/-84/15, Earthquake Engineering Research Center, University o f California, Berkeley, California.

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Physics an d M echanics o f S o il L iquefaction, Lade & Yamamuro (eds) © 1999 Balkem a, Rotterdam , ISB N 90 5809 038 8

Initial development o f an impulse piezovibrocone for liquefaction evaluation

J. A. Schneider, P W. Mayne & T. L. HendrenGeorgia Institute of Technology, Atlanta, Ga., USA

C M . WiseBlack and Veatch, Kansas City, Mo., USA

ABSTRACT: Current practice for assessing soil liquefaction susceptibility of sands and silts during earthquakes and their post-cyclic undrained shear strength relies strongly on empirical methodologies. Procedures for soil liquefaction evaluation include both in-situ and laboratory test methods that require correction factors which are not always fully-understood nor well-defined. Consequently, much uncertainty still remains after a routine analysis is conducted, particularly for natural soil deposits, reclaimed lands, and geologies for which the empirical databases were not developed. Under funding from both the USGS and NSF, the initial development and trial calibrations of an impulse-type piezovibrocone test have begun as a joint study by Georgia Tech and Virginia Tech. The piezovibrocone will serve as a specialized in-situ testing tool for the direct evaluation of soil liquefaction potential and post-cyclic residual undrained shear strength on site- specific projects. The data produced from preliminary field tests at historic liquefaction sites in Charleston, SC will be evaluated qualitatively and ongoing research will be reviewed to assess the potential for future quantitative analyses.

1 INTRODUCTION

Liquefaction evaluation of sandy and silty soils can include laboratory as well as in-situ methods. Laboratory methods involve series of static and cyclic triaxial or cyclic simple shear testing (e.g. Yamamuro & Lade, 1998), while in-situ tests may consist of the standard penetration test (SPT; e.g. Seed et ah, 1983), cone penetration test (CPT; e.g. Stark and Olson, 1995), flat plate dilatometer test (DMT; e.g. Reyna and Chameau, 1991), or shear wave velocities (Vs; e.g. Andrus and Stokoe, 1997). Of additional concern in seismic regions is the assessment of undrained residual strength. The determination of this parameter has also been evaluated on the basis of empiricisms (e.g. Seed & Harder, 1990). In order to provide a direct and more rational approach to site-specific liquefaction susceptibility and post-cyclic residual strength analyses, a piezovibrocone penetrometer has been under development in a collaborative effort between Georgia Tech and Virginia Tech.

Conceptually, the vibrocone consists of a cone penetrometer coupled with a vibrating shaker mechanism (Fig. la) that induces liquefaction locally in the vicinity of the probe during penetration. Vertical penetration tests are conducted both statically and under dynamic excitation in side-by

side soundings. Comparisons of cone tip resistance (q c ) , penetration pore water pressures (U m ), and sleeve friction (fs), from adjacent paired soundings are made to ascertain the liquefaction potential of subsurface soils. The geometry and conduct of the vibrocone penetration test (VCPT) permit a rational interpretation by analytical theories (bearing capacity, stress path, or cavity expansion) or via numerical simulation techniques (finite difference, finite elements, discrete elements, or strain path method) that can incorporate important soil behavioral aspects such as effective stress, dynamic loading, cyclic pore pressure generation, soil fabric, and initial stress state. It is hoped that the piezovibrocone will offer an improved and systematic framework for evaluating liquefaction susceptibility and residual undrained strength of loose and soft ground in seismically active regions.

A multi-element piezocone coupled with a vertical impulse pneumatic source has been used to form the initial vibrocone unit. The device is currently being evaluated in laboratory calibration chamber tests of saturated Light Castle quartzitic sand at Virginia Tech. The sand is placed at relative densities of 25 and 65 percent, corresponding to very liquefiable and borderline behavior, respectively (Mitchell et al., 1998). The effects of confining stress level, vibration frequency, and vibration mode (transient

341

vs. steady) are under investigation. In all tests, continuous measurements o f qc, fs, and pore water pressure at two locations (ui located mid-face and U2

located at the shoulder) are taken for evaluation. Additional trial field testing to evaluate the robustness and initial performance o f the "Mark-I" vibrocone have been performed by Georgia Tech in Spring Villa, AL, Atlanta, GA, and Charleston, SC. The analyses presented in this paper will concentrate on the Charleston sites, since those soils have historically been shown to have a high potential for liquefaction (Martin, 1990).

Friction S leeve 1 50 cm'

V ib ra to ry U n it----- U 'J- I

C one T ip - 1 0 cm'

a. Prototype piezovibrocone

-G eo p h o n e

Cone T ip - 1 0 cm^

b. 10 cm seismic piezocone

4 .3 7 cm F ric tio n S le ev e - 2 2 5 cm^

seismic events and related to the Standard Penetration Test (SPT), shear wave velocity (Vs) tests, the Cone Penetration Test (CPT), and the flat plate Dilatometer Test (DMT). Figure 2 shows the liquefaction curves for the four common in-situ tests that have been related to liquefaction susceptibility o f sandy soils.

Each curve relates a resistance parameter o f the individual test [i.e., (Ni)6o, Vsi, qd, Kd] to the soils resistance to cyclic loading (cyclic resistance ratio or cyclic stress ratio). The cyclic resistance ratio, CRR, is the average cyclic shear stress (xavg) normalized to the effective overburden stress. It is a function of earthquake duration (magnitude), maximum surface acceleration (amax), depth to soil element being analyzed, and total (ctvo) and effective (a'vo) vertical stress (Seed & Idriss, 1971). The normalized cyclic shear stress was initially evaluated in terms o f laboratory testing, but was later adapted for field case histories by Seed & Idriss (1971). To distinguish field studies from laboratory studies. Stark & Olson (1995) present their CPT data compared to the seismic shear stress ratio (SSR), which is equal to the cyclic stress ratio (CSR). To maintain consistency, the CPT data has been compared to the CSR. The CRS is generally presented as:

CSR = - ^ i 0 .6 5| ^ '"o-„ ^ (1)

C o n e T ip - 1 5 cm^ — /

c. 15 cm multi-element piezocone

Figure 1. Penetrometers used

2 CURRENT PRACTICE

2.1 Liquefaction Potential from Field Data

Due to the difficulty and expense associated with obtaining undisturbed field samples o f sandy and silty soils, in-situ tests have become popular for evaluating how a soil deposit will respond under earthquake loading. Data from post-earthquake field investigations have been used to generate simplified curves related to surface phenomena associated with subsurface liquefaction. Sites specifically showing evidence o f sand boils, intrusive dikes, lateral spreading, excessive settlement, and structural damage have been extensively used. Databases of sites which have experienced obvious liquefaction, as well as those where no apparent liquefaction occurred, have been evaluated for a number of

where rd is a depth correction factor presented in Seed & Idriss (1971), and the other parameters are as described above. To account for the duration of shaking, field performance curves have been normalized to a magnitude 7.5 earthquake using magnitude-scaling factors (MSF) as shown in Equation (2):

CRR,, = CSRMSF (2)

Additional uncertainty is added to liquefaction curves by this normalization. Magnitude-scaling factors were introduced by Seed et al. (1983), but current work by Youd and Noble (1997) has shown discrepancies in these factors.

Normalization schemes have been incorporated into the resistance parameters for each in-situ test. The SPT N-value has been corrected for rod energy and effective overburden stress to get the (Ni)6o parameter (Skempton, 1986). Additional corrections are also recommended for borehole diameter, rod length, and sampling method (Skempton, 1986). The stress normalized shear wave velocity, Vsi, is obtained by:

V si = V s (Pa/a'vo)" (3)

342

b.

c. d.

Figure 2. Observed boundaries for "Liquefy - No Liquefy" curves for various in-situ tests: a. SPT (NCEER, 1996) b. Vs (Andrus & Stokoe, 1997)c. CPT (Stark & Olson, 1995) d. DMT (Reyna & Chameau, 1991)

where Pa is a reference stress o f 100 kPa and n is a stress ratio exponent. There is still some debate on the approximate value of the exponent, but 0.25 is typically used (Andrus & Stokoe, 1997). Normalization schemes for the CPT are also based on functions of the ratio o f an approximately 1- atmosphere reference pressure to the effective overburden pressure. Some common normalization

schemes are presented in Olsen (1994), Wroth (1984), Kayen et al. (1992), and are reviewed by Wise (1998). Data used to generate the Stark & Olson (1995) CPT-based liquefaction curves used the Kayen et al. (1992) normalization. The DMT data are already normalized in terms o f the index K d , which is a dimensionless parameter (Marchetti, 1980).

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Due to a combination of many factors, the amount of uncertainty inherent in liquefaction curves is large. Most o f the data have been accumulated from reports of many different researchers, primarily in Japan, China, and western United States. The data used to generate these curves are derived predominantly from post-earthquake field investigations. During the field investigation, the soil has been altered from the state it was in prior to the earthquake. Loose zones that have liquefied are potentially denser due to settlement, and dense zones around layers that liquefied are potentially looser due to flow of pore water from the liquefied zones (Youd, 1984). Frost et al. (1993) and Chameau et al.(1998) examined data in fill soils o f the San Francisco area before and after the 1989 Loma Prieta earthquake. Their studies showed significant increases in Vs, qc, and Kd in the post earthquake soils when compared to pre-earthquake studies.

The effects of re-liquefaction need to be considered during susceptibility analyses. After an earthquake, soils may have formed a more compressible structure that will generate pore pressures more rapidly during cyclic loading, even if they are at a higher relative density (Finn et al., 1970; Youd, 1977). Occurrence of liquefaction at the same site has been discussed by Yasuda and Tohno (1984) for eleven Japanese sites over seven different earthquakes, and for California earthquakes by Youd (1984). Analyses of the effects o f reliquefaction on liquefaction databases can be studied using the Andrus and Stokoe (1997) shear wave velocity database. Shear wave velocities obtained from recent studies have been applied to four different southern Californian earthquakes (1979, 1981, 1987, and 1987), and two different San Francisco area earthquakes (1906, 1989) to verify liquefaction curves (Andrus & Stokoe, 1997). It is not unexpected that a poor agreement between the data and curves is achieved. Void ratio changes from liquefaction and seepage into non-liquefied areas, and an increase in pre-straining from cyclic loading will likely change shear wave velocities of soil deposits between earthquakes. Similar changes will likely affect SPT N-value, CPT tip resistance, and DMT horizontal stress index.

2 .2 P o st-cy c lic re s id u a l u n d ra in e d sh e a r s tre n g th

Post-cyclic residual undrained strength o f sands (Sus) is typically estimated by using a combination of in-situ tests and laboratory tests or in-situ tests alone. A method of combining laboratory evaluation of steady state strength and in-situ evaluation of void ratio was described by Poulos et al. (1985). Fear and Robertson (1995) utilized a combination of the state parameter for sands concept (Been & Jefferies, 1985), Critical State Soil Mechanics (CSSM; Wood,

1990), and estimation of in-situ soil state from shear wave velocity measurements (Cunning et ah, 1995), to develop undrained shear strength relationships for various sands. Correlations relying on in-situ tests alone have compared Sus and SPT (Ni)6o value (e.g. Seed & Harder, 1990), normalized Sus and SPT (N i)6o value (Stark & Mesri, 1992), and normalized Sus and CPT qd value (Olson, 1997).

Currently, combined use o f laboratory and field tests seems to be the most accurate way o f evaluating Sus- Two major problems that can arise from these methods are the accuracy with which in-situ void ratio can be estimated and the additional costs associated with laboratory testing. If undisturbed sampling is attempted without freezing, loose sands will tend to densiiy, while dense sands will tend to loosen (Seed, 1971). While freezing may provide a sample where in-situ void ratio can more accurately be estimated, as well as a relatively undisturbed sample for testing, the additional cost and difficulties in sampling will limit its use to large, critical projects. In-situ void ratio determined by Vs measurements may not have suitable accuracy, and may not provide the detail needed to identify weak layers needed for these analyses. Typically, shear wave velocities are taken at one-meter intervals, which would result in an average void ratio for the analyzed layer. An additional limitation o f the method presented by Fear and Robertson (1995) is that it is not unique for each soil type, and parameters in addition to steady state parameters are needed for analyses. For larger projects, the issue of cost may not be o f much concern, but for smaller projects direct Sus correlations may be desirable.

The use of in-situ tests to directly determine Sus is based on relatively few case studies (less than 30), different sands under different stress conditions, post-failure test results to estimate pre-failure state, drained to partially undrained test results, and predominantly western U.S., South American, and Japanese case studies. The scatter associated with the curves to directly relate Sus to penetration resistance (Seed & Harder, 1990; Stark & Mesri, 1992; Olson, 1997), combined with the relatively few case histories used to generate the curves, leaves a great deal of judgement necessary during analyses.

Complications are added to analyses by trying to normalize Sus to the effective vertical stress. Uncertainty in the normalization scheme coupled with uncertainty in the initial relationship compounds when a unique relationship is attempted. The work presented by Olson (1997) combines CPT- based cases with SPT-based cases converted to equivalent CPT qd values. These penetration resistance values are then compared to the undrained strength ratio (Sus/cr'vo)- In addition to the uncertainty mentioned previously, error is induced by the SPT to CPT conversion. The large amount of

344

scatter in these curves is likely due to dealing with different sands under different in-situ stress conditions (Fear & Robertson, 1995). A review o f data presented in Thevanayagam et al. (1996) as well as Fear & Robertson (1995) shows a great deal of scatter, but the scatter is predominantly induced by analysis o f different sands. Similarly to the uniqueness o f the steady state line (e.g. Been et al.,1991), each sand will have a unique relationship to Sus that may not be able to be determined by in-situ tests alone (Fear & Robertson, 1995). In some cases, post failure investigations were used to estimate prefailure response. The analysis o f the failure of the lower San Fernando dam by Seed and Harder (1990) is a good example o f this, where they present typical post-earthquake (Ni)6o values at various depths for the downstream side of the dam (which did not fail). The SPT and CPT are commonly believed to be indicators o f drained parameters. To additionally be able to determine Sus, an undrained parameter, seems fundamentally unsound. Since the case studies are from relatively few geologic areas, additional uncertainty can arise when trying to extrapolate the results to unstudied areas.

3 VIBRATORY CONE PENETROMETERS

3.1 P re v io u s V ib ro co n es

There have been a number o f prior attempts to develop a specific tool for liquefaction evaluation (Table 1). Liquefaction potential of a deposit was determined by comparing tip resistance o f a static sounding, qcs, to tip resistance of an adjacent dynamic sounding, qcv Figures 3a and 3b respectively show profiles o f static and vibratory tip resistance from Japanese sites where liquefaction typically did not occur, and where liquefaction has occurred repeatedly. A drop in tip resistance is shown for both soundings, but it is much more significant in the zone from 2 meters to 5 meters of the historically liquefiable site. The original vibrocone (Fig. 4a; Sasaki & Koga, 1982) applied a horizontal centrifugal force of 32 kgf and operated at a frequency of 200 Hz. Downhole vibratory excitation came from an electric bar-type concrete vibrator coupled to the cone penetrometer. However, the horizontal movement induced by the vibrator likely caused gapping between the cone and the soil, thus questioning reliability o f to the tip, sleeve, and pore pressure readings.

The Italian vibrocone is similar to the Japanese vibrocone with a downhole centrifugal force attached to a cone slightly larger than U.S. standards (Picolli, 1993; Mitchell, 1988). The Canadian vibrocone consists of an oscillating pair of eccentrically-loaded counter weights attached above-hole to the actuator

assembly in the University o f British Columbia (UBC) cone rig (Moore, 1987). Trial vibratory soundings did show a reduction in tip resistance, however, the applied force and frequency o f the system varied due to energy fluctuations from the hydraulic pump, which powered the rig and vibrator. There was also potential for additional energy loss with depth as more rods were added. A single element cone with pore pressure measurement behind the tip (U2) was used, and no excess pore pressures were recorded. This is likely due to fast dissipation o f tip pore pressures in sands before reaching the U2 element.

Table 1. Vibrocone developmental contributions

Nation Details Results ReferenceJapan • downhole

vibration• 32 kgf horizontal centrifugal force• 200 Hz

Potentiallyliquefiablezones showed a reduction in qc redings

Sasaki & Koga, 1982; Sasaki et al., 1984

Japan • downhole vibration• 80 kgf horizontal centrifugal force• 200 Hz

Chamber tests and paired field soundings

Teparaksa,1987

Canada • uphole vibration• Vertical force with unknown magnitude• 75 Hz average

Reduction in qc, but no identification of cyclic pore water pressures at U2 position

Moore,1987

Italy • downhole vibration• Horizontal centrifugal force with unknown magnitude• 200 Hz

Qualitativeinterpretation

Mitchell,1988;Picolli,1993

3 .2 D o w n h o le V ertica l-P u lse P ie zo v ib ro co n e

The initial design o f the current GT-VT piezovibrocone was aimed to address significant criteria that were limiting the development o f the vibrocone to be used in common practice. Four main issues were addressed in the design including direction o f oscillation, frequency o f operation.

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Depth(m)

a. Vibrocone results at a seismic site with no apparent settlement during cyclic loading

hydraulic hoses downhole, associated high costs o f the system, and need to cool the uphole reservoir against overheating. An electromechanical source, while easy to control, imparts forces that are frequency-dependent and the vibrator cannot be made small enough to produce sufficient forces (20 to 50 kg) at low frequencies to fit within a downhole module. Thus, a pneumatic unit was chosen for economy, adequate forces, and practical size considerations. The preliminary device applies impulse-type loading, however, improvements and modifications are being made at this time.

C e n tr ifu g a lM o tio n V ib ra to r 4 .1 c m fg i

C o m p o n e n t

C e n tr ifu g a l F o rc e = 3 2 k g f F re q u e n c y = 2 0 0 H z

Length = 79.0 cm Diameter = 4.1 cm

Depth(m)

a. Original Vibrocone (Sasaki & Koga, 1982)

Vertical Motion impact Mass

i i l l

Solenoid Air Air Valve Cylinder

MassVibration

Cone Tip Resistance (kg/cm")

b. Vibrocone results at a site historically experiencing extensive cyclic-induced settlements

Figure 3. Results from original vibrocone (Modified after Sasaki et al., 1984)

application of dynamic force, and economic considerations.

Many types o f dynamic force generators were considered in the initial U.S. prototype vibrocone device. A downhole system placed just above the penetrometer was desired since an uphole unit would lose energy efficiencies with depth (similar to the SPT problem). A closed-loop servo-controlled hydraulic system, similar to MTS or Instron, would be an excellent source for uniform sine-wave cycles of loading. However, this approach was discarded due to the difficult logistics o f placing large

b. Impact pneumatic piezo vibrocone (Wise, 1998)

Figure 4. Original centrifugal vibrating piezocone and GT-VT vertically vibrating unit

After a review o f various design alternatives (Wise, 1998), a downhole pneumatic impulse generator was developed using compressed gas to generate vertical impacts at frequencies o f 1 to 30 Hz. The fabricated prototype consists o f a housing, solenoid valve, air cylinder, and impact mass directly coupled to a single element piezocone for field studies (Fig. 4b), and a multi-element piezocone for calibration chamber tests. The single-element, ui, field piezovibrocone with its necessary components is shown in Figure 5. The piezovibrocone penetrometer is intended to provided a continuous log o f penetration pore water pressure and associated soil strength measured under partially undrained and locally-liquefied states. Significant drop in tip resistance (Fig. 3b) will likely be related to post- cyclic residual undrained shear strength. Multiple modes of pore pressure generation were reviewed to analyze readings at the ui and U2 positions.

346

2-Stage Regulator and Size C Nitrogen Tank

• AControl Panel

PneumaticImpulse

Generator

DigitalOscilloscope

LJÊ

Oavey (u,) : Piczocone

Figure 5. Components o f piezo vibrocone (Wise, 1998)

3.3 Analysis o f Quasi-Static-Cyclic Pore Pressures

Since liquefaction is a phenomenon resulting from the generation o f excess positive pore pressures, greater emphasis on the analysis pore pressure measurements has been involved with this study than previously reported vibrocone studies. It is expected that the measured pore pressures, Aumeas, will be equal to (Figure 6):

AUn. ■ AUshear AUoct (4)

where Aushear is a combination o f the shear-induced pore pressure from the zone along the face of the cone and the cyclic pore pressures induced by the vibratory module, and Auoct is the octahedral pore pressure induced by normal stress changes in the soil. Each o f these components will have different effects, depending upon where the pore pressure element is located.

During quasi-static penetration in sands, additional measured pore water pressures at the ui position will reflect the octahedral component induced by the triaxial total stress path under the cone tip. An evaluation o f embedded rigid loading in an elastic medium will give an estimated total stress path with a slope o f 3/4 for a soil element in the area o f a midface filter (Schiffman & Aggarwala, 1961). The mode o f failure at the U2 pore pressure filter location most resembles direct simple shear (DSS) loading (Baligh, 1984). At this location there would be no octahedral pore pressure component, and no shear induced pore pressure component in sands, thus resulting in readings close to hydrostatic. Impulse vibration is anticipated to add shear induced pore pressures to the ui and U2 readings.

At the U2 position, a ninety-degree rotation o f a DSS soil element will result from the configuration of the cone, and the configuration o f the vertical vibratory excitation. The normal stress is equal to a function of effective overburden and the coefficient

o f lateral earth pressure at rest, K©. Since the cone penetrometer is coupled to the impulse vibrator, a true cyclic motion is not induced into the ground. Cyclic pore pressures usually increase on a positive stroke, and then decrease on a negative stroke of cyclic loading (Seed & Lee, 1966). The Mark-I piezovibrocone is a pneumatic impulse generator with only positive force excitation and relaxation to the in-situ stress state, so increasingly positive excess pore pressures are expected in potentially liquefiable soils.

A magnitude 7.5 earthquake is expected to have about 15 equivalent stress cycles (Seed et al., 1983) and have a frequency o f about 0.3 to 5 Hz. During a quasi-static cone penetration test, the penetrometer moves at 2 cm/sec. Input frequencies that are slightly greater or at the high end o f typical earthquake frequencies will likely be necessitated by the continuous nature o f the piezocone test and the excess pore pressures measured at the U2 position from piezovibrocone tests in clean sands will solely be a result o f cyclic shear loading. While it is anticipated that the U2 pore pressures will dissipate rapidly, they are necessary for correcting qc to qt (e.g. Lunne et al., 1986; 1997).

Figure 6. Stress path approach for obtaining pore pressure components

Due to the difficulty in separating octahedral and shear components o f pore pressure readings at the ui position, pore pressure difference between dynamic and static soundings will be evaluated. Difficulties may arise in analyses since it is currently unknown whether localized liquefaction is fully occurring, partially occurring, or not occurring at all. To determine the actual failure mechanisms occurring

347

in-situ, a program o f laboratory tests, calibration chamber tests, and trial field tests is underway.

potentially liquefiable layer from about 1.4 meters to 3 meters (Fig. 8b).

4 FIELD RESULTS

In 1886, the largest magnitude earthquake recorded in the Eastern United States occurred near Charleston, South Carolina (Martin & Clough,1994). A number o f investigators have evaluated paleoliquefaction evidence (e.g. Obermeier, 1996), standard penetration test data (Martin, 1990), cone penetration test data (Martin, 1990), and laboratory test data (Cullen, 1985) to evaluate the occurrence and extent o f liquefaction during the 1886 Charleston earthquake. This study will evaluate trial field tests of the piezovibrocone performed at historic earthquake sites, and assess its potential as a tool for predicting liquefaction susceptibility o f sandy soils. In addition to piezovibrocone tests, seismic piezocone tests (SCPTu) have been performed at the selected test sites.

Preliminary testing o f the Mark-I piezovibrocone was performed in February, 1998 at previously studied (Clough & Martin, 1990; Martin, 1990; Martin & Clough, 1994) historic liquefaction sites in Charleston, SC. Hollywood Ditch (HW) and Thompson Industrial Services (TIS) were the two test sites selected. Thompson Industrial Services was not a site studied by Clough and Martin, but was in between the studied sites o f Ten Mile Hill and Eleven Mile Post. Prior Figures la & b show schematics o f the piezovibrocone and the seismic piezocone used for field tests in Charleston, SC. Tables 2 and 3 display tests performed at Hollywood and TIS respectively. The soundings at each site will be compared to evaluate the response of the piezovibrocone as a cone penetrometer in general, and as a site-specific liquefaction index tool.

At Hollywood, tip resistance (qc) results for a commercially-pushed 10 cm Cone Tec cone and results o f the static 10 cm Davey cone attached directly in front o f the vibrating unit are displayed in Figure 7a. It should be noted that the two static piezovibrocone soundings were separated by 3- meters. The agreement between the two soundings is good considering the natural variation in the subsurface soils. Figure 8a displays a comparison between static and dynamic tip resistance using the piezovibrocone. Previous vibrocone data analysis (Sasaki & Koga, 1984; Moore, 1987) was based on significant losses in tip resistance in potentially liquefiable layers (Fig. 3b). Even though there was no significant variation in tip resistance between static and dynamic soundings using the Mark-I piezovibrocone at Hollywood Ditch, an increase in ui pore pressures during dynamic excitation shows a

Table 2. Initial tests performed at Hollywood Ditch

TestNo.

Description

HW-1 Dynamic piezovibrocone(with mid-face pore pressure element, ui)Frequency: 5 Hz Pressure: 650 kPa

HW-2 Static piezovibrocone(with mid-face pore pressure element, ui)

HW-3 Dynamic piezovibrocone(with mid-face pore pressure element, ui)Frequency: 2.5 Hz Pressure: 650 kPa

HW-4 10 cm Seismic Piezocone(with shoulder pore pressure element, U2)

A generalized soil profile was developed (Fig. 8c) based on prior knowledge o f the site (Martin, 1990) and empirical CPT classification schemes (Robertson et al., 1986; Campanella & Robertson, 1988; Robertson, 1990; Lunne, Robertson, & Powell, 1997) utilizing tip resistance, friction ratio, and pore pressures measured behind the tip, U2 . Dynamic soundings were performed 1.5 meters from the static sounding. There is a general increase in pore pressure throughout the entire depth of the dynamic sounding, with a substantial increase in the clean sand layer at the beginning o f the water table (1.4 meters). This layer is considered to have partially liquefied under the impulse loading.

Future analysis will involve use o f the timer input (5 Hz) and results o f geophone or accelerometer output to provide an estimated number o f equivalent cycles at a specific peak particle velocity (maximum local acceleration) to perform a cyclic stress or cyclic strain based approach to liquefaction analysis. If local liquefaction had occurred, a drop in tip resistance related to the post-cyclic undrained shear strength would have been expected, however, tip resistance was similar in the static and dynamic soundings, and is a topic for further study.

A similar analysis o f the soundings at Thompson Industrial Services was performed. Figure 9 shows qc, ui, U2 , fs, and Vs results from the penetrometers used in this study. A comparison o f qc obtained by a commercially-pushed 10 cm Cone Tec cone with the results o f the static 10 cm Davey cone attached directly in front o f the vibrating unit shows good agreement between the two soundings, considering the natural variation o f the subsurface soils. The static piezovibrocone was about 3 meters away from

348

qe (M Pa) (kPa)0 5 10 15 20 -100 100 300

0

fs (kPa)0 50 100 150

COoCDsz+-•Q.OQ

•H W - 2; Static Vibrocone

Vs (m /sec)0 250 500

10„♦ HW - 4; Seismic CPT|

□ SASW (Indridason, 1992)

Figure 7. Static piezovibrocone and seismic piezocone soundings at Hollywood Ditch, SC a. tip resistance, qc; b. pore pressure, u^; c. sleeve friction, fs; d. shear wave velocity, Vg

qc (M P a )5 10 15 20

(k P a )

100 200 300;

ECOOCQJCw-»Q.O

Q

Figure 8. Comparison o f static and dynamic piezovibrocone soundings at Hollywood Ditch, SC a. tip resistance, qc; b. mid-face pore pressure, ui; c. soil profile

349

qc (M Pa)0 5 10 15 20

Um (k P a )-100 100 300

fs (kP a)0 50 100 150

Vs (m /sec)0 250 500

0 f-

Figure 9. Static piezovibrocone md seismic piezocone soundings at the TIS site, SC a. tip resistance, qc; b. pore pressure, Um; c. sleeve friction, fs; d. shear wave velocity. Vs

Figure 10. Comparison o f static and dynamic piezovibrocone soundings at the TIS site, SC a. tip resistance, qc; b. mid-face pore pressure, U]; c. soil profile

350

the commercial sounding, and dynamic soundings were about 1.2 meters from the staticpiezovibrocone. There was no significant variation in tip resistance between static and dynamic soundings using the Mark-I piezovibrocone at the TIS site (Fig. 10a), but an increase in ui pore pressures during dynamic excitation shows a potentially liquefiable layer from about 4 meters to 5 meters (Fig. 10b).

Table 3. Initial tests performed at the TIS site

TestNo.

TIS-01

TIS-02

TIS-03

TIS-04

Description

10 cm" Seismic Piezocone(with shoulder pore pressure element, U2)

Dynamic piezovibrocone (with mid-face pore pressure element, ui) Frequency: 5 Hz Pressure: 460 kPaStatic piezovibrocone(with mid-face pore pressure element, Ui)

Dynamic piezovibrocone(with mid-face pore pressure element, ui)Frequency: 5 Hz Pressure: 650 kPa

The profile for the TIS site (Fig. 10c) shows considerably more fines than Hollywood Ditch with no clean sands present. The water table was at approximately the same depth (1.4 meters), and the large rise in pore pressures came in a silt to sandy silt layer at depths o f about 4 to 5 meters. This layer showed increases in static U2 , as well as static ui and dynamic ui pore pressures. Positive static U2 pore pressures are indicative o f initial undrained to partially undrained penetration. Therefore, the analysis o f the dynamic ui pore pressures must consider potential shear-induced pore pressures along the Jface in addition to cyclically induced and octahedral pore pressures. The dynamic sounding at TIS (Fig. 10b) produced much higher pore pressures than the dynamic sounding at Hollywood (Fig. 8b), but still no reduction in qc was noticed (Fig. 10a). These increased excess dynamic pore pressures are possibly from shear induced pore pressures on the face of the cone from partially undrained behavior of the silt, and not a pure function o f the cyclic loading. It is not typically expected that a similar soil layer with a higher fines content will be more susceptible to liquefaction, but the site specific nature o f the piezovibrocone has the potential to identify layers that will be strongly affected by cyclic loading.

5 FUTURE WORK

Data provided by a vertically-vibrating penetrometer could ideally be evaluated using theoretical effective stress models developed for representing the behavior o f sands and silts. In particular, the concepts o f static liquefaction, instability, steady state, and compressibility, as well as the aspects o f contractive vs. dilative behavior could be incorporated. As such, the research program will include a full suite o f laboratory characterization tests on the Light Castle sand that is being used currently in the CPT chamber test series. Lab testing will consist o f static and cyclic triaxial tests using CK Chan apparatuses and companion sets o f direct simple shear tests. Resonant column testing will provide the fundamental small-strain stiffness measurements at varying relative densities. Complementary series o f undrained and drained triaxial testing will provide the necessary ingredients to permit the characterization o f the steady-state lines (e.g.. Been et al., 1991; Yamamuro and Lade, 1998).

For the next generation o f vibrocone unit, the transient impulse forces are ideally replaced with a form o f uniform sinusoidal loading. By the use o f a programmable air regulating (PAR) valve, the nitrogen gas pressure can be smoothed to produce sine waves. Alternative devices for producing cyclic or repetitive loading are also under consideration, including electronic solenoids and mechanical cams. Other important facets currently under investigation include the thermal effects on transducer measurements (Lunne, et. al. 1986), porous filter material (Campanella & Robertson, 1988), backpressurization of the hydrostatic water in saturated chamber tests, and technical details related to the accuracy o f measurements by the cone sensors. Of specific mention herein are the difficulties in choice o f filter face elements (e.g., ceramic, plastic, carborundum, sintered brass, stainless steel) due to effects o f smearing, heating, abrasion, compressibility, and wear. O f additional mention is the baseline drift o f transducers caused by frictional heating as the penetrometer is pushed in sands. These technical aspects will be shared in later reports issued by GT & VT.

6 CONCLUSIONS

The preliminary design and field testing o f an impulse piezovibrocone has been initiated to try to eliminate much o f the empiricisms and correction factors associated with common methods to determine liquefaction susceptibility and postliquefaction residual undrained shear strength of

351

sandy and silty soils. Research is continuing with calibration chamber tests, associated laboratory tests, and additional field tests in liquefiable and nonliquefiable deposits.

The initial design o f the GT-VT piezovibrocone has isolated vertical motion into a downhole impulse-vibrating unit. Preliminary field tests have shown an increase in mid-face pore pressures in potentially liquefiable layers, but no change in tip resistance. Analysis o f previous vibrocones relied solely on a change in tip resistance, but showed little effects in U2 pore pressure. Ongoing improvements to the piezovibrocone design are increasing the similarity between its vibratory mechanisms and typical earthquake shaking.

Preliminary results are promising, and future work will help to reinforce the understanding of controlling mechanisms that are the key to piezovibrocone analyses.

ACKNOWLEDGEMENTS

The authors appreciate the support o f Dr. John Unger of the U. S. Geological Survey and Dr. Cliff Astill of the National Science Foundation to conduct this research. The input o f Dr. J.K. Mitchell, Dr. Tom Brandon, and John Bonita o f Virginia Tech has been key to the progress o f this joint project. Recep Yilmaz and Rick Klopp o f Fugro Geosciences are thanked for the use of the multi-element piezocone and assistance during field tests, as well as to Brad Pemberton o f Gregg In-Situ for help with initial field tests in Charleston, S.C.

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354


List o f participants

Mr. Andrei Abelev Department o f Civil Engineering The Johns Hopkins University 3400 N. Charles Street Baltimore, MD 21218-2686

Phone: (410) 516-5057 FAX: (410)516-7473 Email: [email protected]

Dr. Clifford J. Astili, Program Director Division o f Civil and Mechanical Systems National Science Foundation 4201 Wilson Blvd.Arlington, VA 22230

Phone: (703) 306-1362 FAX: (703)306-0291 Email: castill@ nsf gov

Dr. Kenneth Been Colder Associates Landmere Lane, Edwalton Nottingham NG12 4DG England

Phone: +44(115)9456544 FAX: +44(115)9456540 Email: [email protected]

Professor Ross W. BoulangerDepartment o f Civil and Environmental EngineeringUniversity o f CaliforniaDavis, California 95616


Dr. Gonzalo Castro GEI Consultants, Inc.1021 Main Street Winchester, MA 01890


Mr. Lucas deMelo Department o f Civil Engineering The Johns Hopkins University 3400 N. Charles Street Baltimore, MD 21218-2686


Dr. Thiep DoanhEcole Nationale des Travaux Publics de l’Etat Département Génie Civil et Bâtiment (DGCB)Rue Maurice Audin URACNRS 1652 69518 Vaulx-en-Velin Cedex France

Phone: +33 4 72 04 70 72 FAX: +33 4 72 04 71 56 Email: [email protected]

Professor Ricardo DobryDepartment o f Civil and Environmental Engineering Rensselaer Polytechnic Institute Troy, NY 12180-3590


Dr. Rune DyvikNorwegian Geotechnical InstituteP.O. Box 3930Ullevâl HagebyN-0806 OsloNorway

Phone: +47 22 02 30 00 FAX: +47 22 23 04 48 Email: [email protected]

355

Professor Ahmed-W. Elgamal Department o f AMES Structural Engineering Program University o f California, San Diego 9500 Gilman Drive La Jolla, California 92093-0411

Phone; (619) 822-1075 FAX: (619) 822-2260 Email: [email protected]

Professor Mark D. Evans Civil and Mechanical Engineering Department U.S. Military Academy West Point, New York 10996

Phone: (914) 938-5502 FAX; (914)938-5522 Email: [email protected]

Professor J. Ludwig Figueroa Department o f Civil Engineering Case Western Reserve University 10900 Euclid Avenue Cleveland, OH 44106-7201

Phone: (216) 368-6247 FAX; (216) 368-5229 Email: [email protected]

Professor J. David FrostSchool o f Civil and Environmental Engineering790 Atlantic StreetGeorgia Institute o f TechnologyAtlanta, GA 30332

Phone: (404) 894-2280 FAX: (404) 894-2281 Email: [email protected]

Professor M. HamadaDepartment o f Civil EngineeringThe School o f Science and EngineeringWaseda University3-4-1, Okubo, Shinjuku-ku169-0072TokyoJapan

Phone: +81-3-5286-3406 FAX: +81-3-3208-0349 Email: [email protected]

Dr. Mary Ellen Hynes US Army Corps o f Engineers Waterways Experiment Station 3909 Halls Ferry Road Vicksburg, MS 39180-6199


Professor Lars Bo Ibsen Department o f Civil Engineering Sohngaardsholmsvej 57 Aalborg University DK-9000 Aalborg Denmark

Phone: +45 96 35 84 58 FAX: +45 98 14 25 55 Email: [email protected]

Michael Jefferies Golder Associates (UK) Ltd Landmere Lane, Edwalton Nottingham NG12 4DG England

Phone: +44(115)9456544 FAX: +44(115)9456540 Email: [email protected]

Professor Hon-Yim Ko Department of Civil, Environmental, and

Architectural Engineering Campus Box 428-ECOT 441 University o f Colorado Boulder, CO 80309-0428


Dr. Joseph P. Koester US Army Corps o f Engineers Waterways Experiment Station 3909 Halls Ferry Road Vicksburg, MS 39180


Professor J.M. Konrad Department o f Civil Engineering Université Laval Sainte-Foy, QC GIK 7P4 Canada


Professor Junuchi Koseki Institute o f Industrial Science University o f Tokyo Roppongi 7-22-1, Minato-ku Tokyo 106-8558 Japan

Phone:+81-3-3402-6231 FAX: +81-3-3479-0261 Email: [email protected]

356

Professor Steven L. Kramer Department of Civil Engineering 201 More Hall, Box 352700 University o f Washington Seattle, WA 98195


Professor Poul V. Lade Department o f Civil Engineering The Johns Hopkins University 3400 N. Charles Street Baltimore, MD 21218-2686


Dr. Richard H. Ledbetter US Army Corps o f Engineers Waterways Experiment Station 3909 Halls Ferry Road Vicksburg, MS 39180-6199


Mr. Carl LiggioDepartment o f Civil Engineering The Johns Hopkins University 3400 N. Charles Street Baltimore, MD 21218-2686


Professor Paul W. MayneSchool o f Civil and Environmental EngineeringGeorgia Institute o f TechnologyAtlanta, GA 30332-0332


Professor Radoslaw L. Michalowski Department o f Civil Engineering The Johns Hopkins University 3400 N. Charles Street Baltimore, MD 21218-2686


Professor Gary M. Norris Department o f Civil Engineering Mail Stop 258 University of Nevada Reno, NV 89557


Professor Shamsher Prakash Department o f Civil Engineering 1870 Miner Circle University o f Missouri-Rolla Rolla, Missouri 65409-0030

Phone: (573) 341-4489 FAX: (573) 341-4729 Email: prakash@no veil .civil. umr.edu

Mr. Christopher Sausier Department of Civil Engineering The Johns Hopkins University 3400 N. Charles Street Baltimore, MD 21218-2686


Professor David C. SegoDepartment o f Civil and Environmental Engineering University of Alberta Edmonton, Alberta T6G 2G7 Canada


Professor Stein Sture Department o f Civil, Environmental, and

Architectural Engineering Campus Box 428-ECOT 441 University o f Colorado Boulder, CO 80309-0428


Professor S. Thevanayagam Department o f Civil, Structural &

Environmental Engineering 212 Ketter Hall State University o f New York Buffalo, NY 14260

Phone:(716)645-2114 x2430 FAX: (716) 645-3733 Email: [email protected]

357

Professor Y.P. Vaid Department o f Civil Engineering University o f British Columbia 2324 Main Mall Vancouver, BC V6T 1Z4 Canada

Phone: (604) 822-2204 FAX; (604)822-6901 Email:

Mr. Zhaohui Yang Department o f AMES Structural Engineering Program University o f California, San Diego 9500 Gilman Drive La Jolla, California 92093-0411

Phone: (619) 822-1075 FAX: (619) 822-2260 Email:

Professor Jerry A. YamamuroDepartment o f Civil and Environmental EngineeringClarkson UniversityWilliam J. Rowley LaboratoriesPotsdam, NY 13699-5710

Phone: (315)268-2341 FAX: (315)268-7985 Email: [email protected]

Professor T. Leslie YoudDepartment of Civil and Environmental Engineering 368 Clyde Building Brigham Young University Provo, UT 84602-4081


Professor Xiangwu Zeng Department o f Civil Engineering LIniversity o f Kentucky Lexington, Kentucky 40506

Phone:(606)257-3157FAX:Email: [email protected]

358

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P hysics a n d M echanics o f S o il L iquefaction, Lade & Yam am uro (eds) © 1999 Balkem a, Rotterdam , IS B N 90 5809 038 8

Author index

Been, K. 195 Ibraim, E. 17 Robertson, PK. 179Boulanger, R.W. 261 Ibsen, L.B. 29 Rokoff,M .D. 237Butler, G.D. 295 Rollins, K.M. 91Byers, M. B. 249 Jang, D.-J. 169

Jefferies, M.G. 221 Saada, A.S. 237Castro, G. 205 Sato,T 121Chen, C .-C 169 Ko, H.-Y. 307 Schneider, J.A. 341Covert, K .M .55 Koester, J. P 79 Sego, D .C 179

Konrad, J.-M .213 Sivathayalan, S. 105Dewoolkar, M .M . 307 Koseki, J. 121 Steedman, R.S. 295Doanh, T. 17 Dobry, R. 269

Kramer, S.L. 249 Sture, S. 133

Dubujet, Ph. 17 Lade, PV 3, 55 Thevanayagam, S. 67D yvik,R . 159 Ledbetter, R.H. 295

Elgamal, A.-W. 269Liang, L. 237 Urano, I. 121

Evans, M. D. 91 Maeshiro, N. 121 Matiotti, R. 17

Vaid, YP. 105

Figueroa, J. L. 237 Mayne, PW. 341 Wang, C.H. 249Frost, J. D. 169 Michalowski, R.L. 153 Wise, C.M. 341

Wride (Fear), C.E. 179Guo, T. 335 Norris, G.M. 41

Yamamuro, J.A. 55Hendren, XL. 341 Olsen, R.S. 145 Yang, Z. 269Herle,I. 17 Youd,T.L. 325Hoeg, K. 159 Park, J.-Y. 169Hofmann, B.A. 179 Parra, E. 269 Zeghal, M. 269Hynes, M.E. 145 Prakash, S. 335 Zeng, X. 283

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