experimental investigation on principal stress rotation in kaolin clay

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Experimental Investigation on Principal Stress Rotationin Kaolin Clay

Han Lin, M.ASCE,1 and Dayakar Penumadu, M.ASCE2

Abstract: A combined axial–torsional testing system was developed to investigate the effect of rotation of principal stressethree-dimensional mechanical behavior of Kaolin clay. Uniform and reproducible cohesive specimens having a specimen shollow cylinder were obtained using a two-stage slurry consolidation technique. Precise stress paths~triaxial compression to pure torsionshear to triaxial extension!, corresponding to a fixed rotation of the major principal stress axis, were achieved by using the propintegral-derivative~PID! feedback control technique. Kaolin clay specimens were tested under a variety of stress paths associaconstant principal stress rotation anglesbd under undrained conditions. Typical test results, such as effective friction angle, undshear strength, stress–strain relationship, pore pressure evolution, and stress paths are presented as a function ofb. During shearing, thprocedure to use advanced servo-hydraulic control~using PID algorithm in this study! to maintain a fixedb value that involves updatinspecimen geometry in real-time is described. A new approach for data analysis and visualization is presented for providing away of incorporating the effect of major principal stress rotation angle considering the degradation of stiffness as a function of sin three dimensions.

DOI: 10.1061/~ASCE!1090-0241~2005!131:5~633!

CE Database subject headings: Kaolin; Clays; Stress; Rotation; Anisotropy.

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Introduction

It is well known that the magnitude and orientation of the pripal stresses acting on soil deposits constantly change for a vof field loading conditions. To better understand the fundambehavior of soil, the effect of change in magnitude and orientof principal stresses should be investigated. Conventional tritesting on solid cylindrical specimens is a commonly usedproach to study the effect of varying magnitude of the princstresses on the behavior of soil in the laboratory, using aelement that is subjected to an axisymmetric stress state.triaxial tests with independent control of the three princstresses on cubical soil specimens have been performedvestigate primarily the effect of the intermediate principal st~e.g., Wood 1975; Lade and Musante 1978; Kirkgard and L1993!. However, both in a conventional triaxial test and atriaxial test, the orientation of principal stresses cannot be rot

One approach to study the effect of principal stress rotaconsists of rotating the specimen orientation during a test toate an angle between the direction of the applied major prinstress and the direction of consolidation, and involves manperimental difficulties. An alternative way is to use combi

1 ANSYS, 12B Guangzhon International Trade Center, No. 1, LinRoad, Guanzhou, P.R. China, 510620, E-mail: [email protected]

2Professor, Dept. of Civil and Environmental Engineering, UnivTennessee, Knoxville, TN 37996-2010. E-mail: [email protected]

Note. Discussion open until October 1, 2005. Separate discusmust be submitted for individual papers. To extend the closing daone month, a written request must be filed with the ASCE ManaEditor. The manuscript for this paper was submitted for review andsible publication on January 21, 2003; approved on October 6, 2004paper is part of theJournal of Geotechnical and GeoenvironmentEngineering, Vol. 131, No. 5, May 1, 2005. ©ASCE, ISSN 1090-02
2005/5-633–642/$25.00.
JOURNAL OF GEOTECHNICAL AN

J. Geotech. Geoenviron. Eng

axial–torsional loading to apply normal and shear stress simneously so that the presence of shear stress will cause thepal stress to rotate from the vertical direction. It should be nthat the combined axial–torsional test could also be used tothe effect of the magnitude of principal stresses because thplication of shear stress causes a change in the values of theand minor principal stresses. In order to generate a relativelyform shear stress along the cross section, thin wall hollow cdrical specimens are commonly used instead of solid cylindspecimens. The loading scheme and stress state of a speduring a combined axial–torsional test are shown in Fig. 1.ing the consolidation stage, an isotropic confining pressureplied and the specimen is consolidated until it reachescompletion of the primary consolidation. In the shearing stvertical load and torque are applied simultaneously and the smen is tested under a three-dimensional~3D! stress state, ashown in Fig. 1~b!, in which sc is the isotropic confining presure,Dsn is the change of the vertical stress due to the verload, andDt is the change of the shear stress due to the toBecause of the presence of the shear stress, the major andprincipal stresses rotate, as shown in Fig. 1~c!. The angle betweethe direction of the major principal stress and the vertical dtion ~axis of rotational symmetry! is defined asb, and it can bobtained using the following equation:

1

2tans2bd =

Dt

Dsn

s1d

Therefore, the orientation of the principal stresses can betrolled at any desirable value by applying an appropriate conation of vertical load and torque.

In 1965, Broms and Casbarian~Broms and Casbarian 196!tested isotropically consolidated clays to study the effect of imediate principal stress as well as the rotation of princ
stresses. Saada~1968! developed an automated testing apparatus
D GEOENVIRONMENTAL ENGINEERING © ASCE / MAY 2005 / 633

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controlled by a pneumatic analog computer to perform axtorsional tests and investigated the anisotropy of clays. Instate-of-the-art paper in 1988, Saada gave a detailed reviewadvantages and limitations of combined axial–torsional testinhollow cylindrical specimens~Saada 1988!. Throughout his workSaada reported a large range of effective friction angle, 24for varying inclinations of major principal stress for Kaolin clLade ~1975, 1976! introduced an apparatus to perform torsshear tests on cohesionless soils. Later, an investigation coing the elasto–plastic behavior ofK0-consolidated clay was rported by Hong and Lade~1989!. They concluded that the failusurface obtained from the tests could practically be modelean isotropic failure criterion proposed by Lade and Mus~1977!.

Despite the versatility of the combined axial–torsional tenumber of problems were identified with respect to testing prdure and the interpretation of test data. First of all, since thinhollow cylindrical specimens need to be used, natural soil smens are very difficult to employ. Most clay specimens useprevious research were prepared by coring and trimming;excessive handling and disturbance to the specimen weravoidable. The high potential of nonuniformity of stress and sin the specimen during loading is another major concern~Sayaoand Vaid 1991!, and the nonuniformity can be exacerbatedusing nonhomogenous and disturbed specimens. Therefortaining reproducible and homogeneous specimens with mindisturbance is critical for the success of combined axial–torstesting. The stress and strain state within the specimen dcombined axial–torsional loading is complex and needs to bterpreted carefully with reasonable real-time corrections togeometry of the specimen. Incorporating the radii correcmethod proposed by Tatsuoka et al.~1986!, Lin and Penumad~2002! presented a detailed approach for the interpretatiomeasured data in a combined axial–torsional test, in terminitial specimen geometry, axial load, axial deformation, torrotation, pore pressure, volume change, and cell pressure,on a minimum number of assumptions. The complexity ofinterpretation of stress and strain components requires a nereal time automated control of the application of vertical loadtorque during a combined axial–torsional test in order to obtconstant inclination of major principal stress throughoutshearing phase for accurate assessment of the effect of pristress rotation.

In this study, a series of combined axial–torsional tests

Fig. 1. Loading scheme and stress state in combined axial–torstest

performed to investigate the effect of principal stress rotation on

634 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINE


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the mechanical behavior of Kaolin clay. The improved methospecimen preparation, the logic of automated control, as wtypical test results are presented in detail.

One-Dimensional Slurry Consolidation

The hollow cylindrical specimens used in this study werepared by using the one-dimensional slurry consolidation mefirst reported by Sheeran and Krizek~1971!. Four slurry consolidators were custom fabricated, as shown in Fig. 2. The condator was made of Teflon, which has a Young’s modulu480 MPa, and the thickness of the wall of the consolidator19.1 mm, providing a very strong radial constraint on the spmens. Since, the Teflon walls deformed instantly when the mmum load of consolidation was applied at slurry stage ofspecimen, the specimen consolidation process could be cered underK0 conditions. The inner surface of the consolidawas machined and hand-polished with Teflon wools alongaxial direction of the cylinder to minimize the friction betwethe specimen and inner surface of the cylinder. Kaolin clay pder with a liquid limit of 53%, plastic limit of 31%, and specigravity of 2.63, was mixed with de-air and de-ionized waterwater content of 155% and poured into the consolidatorK0-consolidated under 207 kPa axial stress which was appliethe hydraulic piston from the top. Both top and bottom drainwas allowed to shorten the duration of primary consolidation

Fig. 2. Slurry consolidators

ERING © ASCE / MAY 2005

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reduce the frictional effect from top to bottom of the specimalong the Teflon–clay interface and achieve better uniformityconsolidator was flipped upside down once during the consotion so that the vertical stress was applied simultaneouslytop and bottom of the specimen. It took approximately 50 h fspecimen to be fully consolidated, as shown in a typical sement history plotted in Fig. 3. The specimen was then extrfrom the consolidator, with an intact hollow cylindrical shapeflat end surface so that the need for any trimming and coringavoided.

The typical height of the specimen,H0, was about 23 cmouter radius,R0, 5.08 cm and inner radius,r0, 3.56 cm~shown inFig. 4!. The geometry of the specimen satisfied the followequations, proposed by Saada and Townsend~1981!, to ensurethat a relatively uniform deformation zone could be developethe middle part of the specimen as the frictional end platensstrained the radial deformation of the specimen near thezones, namely

H0 ù 5.44ÎR02 − r0

2 s2d

Fig. 3. Settlement history of slurry consolidation in termsspecimen height

Fig. 4. Hollow cylindrical specimen



r0

R0ù 0.65 s3d

The uniformity of the saturated specimens was evaluated bysuring the water content at different locations within the spmens. The water content profile along the height of a specafter the slurry consolidation is shown in Fig. 5. Even withuse of Teflon consolidator, a water content range from 41 towas observed. One can see that the water content at the midthe specimen is higher than that at both ends, which is expbecause of the drainage conditions and friction of Teflon–interface along the height during the consolidation. At the enthe isotropic consolidation, which will be addressed with mdetails later, a more uniform water content profile was obtaas shown in Fig. 5.

Assembly and Saturation

After the slurry consolidation, the hollow cylinder specimwere assembled in a custom built torsional cell~shown in Fig. 6!with minimum disturbance. The assembly followed the genprocedures in ASTM StandardD4767-95 ~ASTM 1995! for aconsolidated undrained triaxial compression test for cohsoils. In order to reduce the necessary time for consolidationpore pressure equalization, filter paper was used around thesurface of the specimen to provide radial drainage paths. Deing on the type of tests, the filter paper was designed in a pathat required no correction to the applied load~Berre 1982!. Tosaturate the specimen–boundary interfaces, the systemflushed with CO2 initially, and then purged with de-aired, dionized water. The use of the hollow cylindrical specimensvolved complex experimental setup and assembling, andsaturation is important for undrained tests. The high backpreof 265 kPa was used to ensure a high degree of satu~Skempton’s pore pressure coefficient,B, fell in the range o0.98–0.99 in all the tests!. This was necessary to saturateinterface of specimens and inner and outer membranes~since theclay specimen is already fully saturated at the end of slurry

Fig. 5. Water content profiles along height of specimens after sconsolidation and after isotropic consolidation

solidation!.


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Isotropic Consolidation

After saturation, the specimens were isotropically consolidunder a higher effective confining pressure, 276 kPa, compathe 207 kPa of vertical stress applied during the slurry consotion. The higher confining pressure overcame any disturbanthe specimen during its assembly and increased the uniformthe specimen. As indicated by the water content profiles in Fthe variation of water content after isotropic consolidationless than 2%. The volume change of the specimen was meaduring consolidation, and a plot of volumetric strain versus sqroot of time is shown in Fig. 7. The applied rate of deformaduring shear was primarily based on the data obtained fromconsolidation curve related to the time for the end of primconsolidation.

Fig. 6. Axial–torsional cell

Fig. 7. Volumetric strain versus square root of time during isotroconsolidation under 276 kPa effective confining pressure



Loading Equipment

The loading equipment used in this study was a MTS 858 TTop System with the Series 359 axial–torsional load unit thaa configuration for testing under axial load up to 2.5 kNtorque up to 25 N m with measurable displacement rang±50 mm in the axial direction and rotation of ±140°. The TestIIm digital controller featured a data acquisition rate of 6 kHzused the multitasking Windows NT operating system that allorunning tests and analyzing data simultaneously. This testingtem provided various digital control modes, such asproportional–integral–derivative~PID! control, channel limitechannel control and dual compensation control, to have prautomated real-time control of the axial and torsional load ocorresponding displacements. Therefore, the present testintem could generate many loading functions of the axial~torque! and the displacement~rotation!, such as steady rampsine waves, and even a complex loading history, corresponda recorded earthquake history. Three transducers were incrated within the loading system by the manufacturer: a ftransducer, which was capable of measuring the linear force~axialload! and rotational force~torque! simultaneously; a linear vaable differential transducer, which measured the linear actutravel ~axial displacement!; a angular displacement transduwhich measured the amount of rotation produced by the ractuator. The testing system offered the flexibility to add etransducers to measure or control other variables to fit the urequirement specified in this study. The above features of loaequipment and control system show a significant advantagecurrent system in comparison to the previously developed hocylinder testing equipments~e.g., Wijewickreme et al. 1994!.

During a combined axial–torsional test, the axial load, adisplacement, torque, rotation angle, cell pressure, and poresure~or volumetric change for a drained test!, were the six variables that need to be measured or controlled. The axial loatorque were measured by the force transducer incorporatedload system. To measure the cell and pore pressure, two expressure transducers were used. The volumetric change wasured by monitoring the amount of water coming out of the spmen by using a differential pressure transducer and a buretttem. In addition, by using an electro-pneumatic transdautomated control of cell pressure was achieved. The spections of all these transducers are listed in Table 1. Therefore,principal stresses were computer controlled with this systemany desired stress paths with different rotation of princstresses could be achieved in a precise and completely automanner. The complete test setup, with the axial–torsional tesload frame, electronics, control panel and data acquisition syis shown in Fig. 8.

Loading Path and Tuning of Loading System

In this study, five different loading paths, corresponding to a fiprincipal stress rotation angle,b=0, 30, 45, 60, and 90°, weapplied to investigate the effect of principal stress rotation.overriding issue was to keep the value ofb constant throughothe shear phase. As shown in Eq.~1!, the value ofb is controlledby Dsn, the change of the vertical stress by the axial loathrough the axial actuator, andDt, the change of shear stregenerated by the torque applied on the specimen through thsional actuator of the loading unit. Assuming a uniform distr
tion of average vertical and shear stress across the cross-sectional

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area of the specimen, the change of vertical stress and the cof shear stress can be calculated by the following equations

Dsn =P − Pm

A;

s4dA = fsR,rd

Dt =3sT − Tmd

2psR3 − r3ds5d

whereP=measured vertical load;Pm=vertical load carried by thmembranes;A=current cross-sectional area of the specimenTm

=torque carried by the membranes;R=outer radius; andr=inner radius. The values ofR and r have to be updated in retime during shearing, by using the following equations, propby Tatsuoka et al.~1986!:

R=Î 1

1 − «zR0 s6d

r =Î 1

1 − «zr0 s7d

whereR0 andr0= initial outer and inner radii; and«z=axial strain~positive for decrease of height!. A more detailed descriptioninterpreting the complete state of stress and strain during isoconsolidation and the subsequent phase of applying shearduring a combined axial–torsional test, including the correcfor specimen geometry and correction for the forces taken b

Table 1. Transducer Specifications

Transducers

Axial torsional force transducer

M

C

A

Linear variable differential transducer

C

A

Angular displacement transducer

C

A

Pressure transducer

M

C

A

Differential pressure transducer

M

C

A

Electro-pneumatic transducer

M

S

O

A

membrane, was given by Lin and Penumadu~2002!.



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The test withb=0° was simply a triaxial compression twith zero increment of shear stress and positive incremevertical stress. Similarly, the test withb=90° was an extensiotest. These two types of tests could be readily performed iaxial strain controlled mode, because the axial strain was afunction of the axial displacement, and the present loading syhad precise automated displacement control along the axialtion. Stress control mode was not employed in this resemainly to obtain data corresponding to the post-peak behavthe Kaolin clay. To ensure that the change of shear stress wafor b=0 and 90°, the torque applied to the specimen needszero. However, the authors found that if the rotation of the a

meters Specifications

ufacturer MTS

number 662.20D-01

ity 2.5 kN/25 N m

cy 0.3% of full-scale axial

0.15% of full-scale torsiona

ufacturer MTS

ity 10 cm

cy 0.25% of full scale

nufacturer MTS

ity 280°

cy ,0.3% of full scale,throughout 280°

ufacturer Data Instruments Inc.

number Model AB/HP

ity 1,400 kPas200 psidcy 0.25% of full scale

ufacturer Validyne Engineering C

number P55D-1-N-2-28-S-4-A-1

ity 5.5 kPas0.8 psidcy 0.25% of full scale

ufacturer Bellofram Corp.

number T1001

pressure 110–130 psi

t pressure 0–100 psi

cy 0.10% of output span

Fig. 8. Testing setup

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lar actuator, instead of the torque, was held to zero valueobserved maximum change of the shear stress was very smain the range of ±2.5 kPa, which was essentially negligible. Thfore, the reaction force due to the restriction of rotation was sThis implied that the development of rotation, due to the apption of vertical load, was negligible, otherwise, a more significreaction force should have been observed, given that the rowas constrained. This also justified the well-accepted concepunder triaxial compression or extension conditions, the direof principal stress and that of principal strain were along saxes, so-called coaxiality. In this study, holding the rotatiozero value was used forb=0 and 90°.

For b=45°, the change of vertical stress should be zero, thfore it was a pure torsional shear test with only the incremeshear stress. It was similar to a direct shear test except thfailure plane was not fixed or predetermined. To ensure thachange of vertical stress was zero for theb=45° test, the verticaload must be held constant, which could be easily achieved bMTS automated control system. Therefore the vertical defotion was not restrained. During the shear phase of such a tethe shear strain was increased, substantial vertical strain waserved, as shown in Fig. 9. It can be seen in Fig. 9 that after1% shear strain, negative vertical strain~extension! increases continuously, which suggests the strong coupling between theand normal displacement. Therefore, the direction of princstress was no longer the same as the direction of principal sand a noncoaxiality condition existed. It is interesting to notewhen axial displacement was held constant and the specimerotated in deformation or rotation control, substantial changvertical stress was observed~maximum value of 50 kPa!, whichprovided further evidence of noncoaxiality.

For the test withb=30° or b=60°, the ratio between thchange of shear stress and vertical stress@1

2tans2·30°d=0.866 or12tans2·60°d=−0.866#, must be constant during the shearHowever,Ds andDt were functions of many coupled variablsuch as axial displacement, rotation, and real-time radii ospecimen. A constant ratio betweenDs andDt could not be easily achieved by simply applying a function of load or displament. A rather complex control mode was required to maintaconstant value ofb during the test.

In addition to the automated control on the axial load,placement, torque, and rotation, the present testing system oflexibility to add extra controls on interpreted variables, wh

Fig. 9. Shear and vertical strains in test withb=45° indicatingnoncoaxiality



-

could be a function of the measured variables, such as the cof shear stress and vertical stress for theb=30 and 60° tests.commonly used approach for maintaining an interpreted varat its target value in real time is to use the PID controlle~adescription of PID controller and its application in geomatetesting were given by Mandeville and Penumadu 2003!. The performance of a PID controller is governed by three valuesproportional gainKP, integral gainKI, and the derivative gainKD.The procedure of searching the optimal values ofKP, KI, andKD

is called tuning. The values ofKP, KI, andKD strongly depend othe material being tested and the type of stress paths usebest way to perform the tuning in this study was to usespecimens to perform trial tests to determine the values. Howthe clay specimen was subjected to stiffness degradation orfailure during a trial test and having saturated and consolidclay for performing multiple tuning tests was time-consumingimpractical. Therefore, four dummy specimens made of ruand steel spring, with various modulii~3.70 GPa, 360, 230, a150 MPa!, were used in this research to perform the tuning. Sthe dummy specimens were reusable~all of them were practicalllinear elastic prior to damage!, they were used to determineappropriate values ofKP, KI, andKD for different loading pathsThe degradation of the stiffness of the clay specimen was slated by using different dummy specimens with different vaof modulus. A PID controller was developed to maintain a cstant value ofb for the test withb=30 or 60° based on a seriestuning tests on dummy specimens. Fig. 10 shows the variatithe measuredb during a tuning test with a targetb value of 60°

Fig. 10. Measured principal stress rotation angle in testb=60°

Fig. 11. Change of major principal stress,Ds1, normalized by initiaeffective confining pressuressc8d in terms of major principal strain


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which lasted more than 3 h during the shearing stage. Thevalue of the measured rotation angle was 60.03° and the stadeviation was 0.67°, indicating a very accurate control.

For all the monotonic tests performed under undrained cotions in this study, an appropriate loading rate needs to be usallow for equalization of excess pore pressure during the apption of deviator shear stress. It can be imagined that the loarate depended on axial displacement rate~or axial strain rate!,for all the principal rotation angles exceptb=45° Based on thconsolidation history shown in Fig. 7, an axial strain rate0.05% /min was determined appropriate for this study. Fob=45°, 0.05% /min of engineering shear strain was used.

Strain Localization

Significant strain localization interpreted as clear visualizatioshear banding, necking, and bulging, were observed postpeall the tests for varying principal stress rotation values. Oncenificant strain localization occurred, the specimen was distoseverely, and there was no reasonable approach to interprstress–strain state within the specimen with satisfactory accbased on the geometry of the distorted specimen. However,common practice in the literature to report the postpeak ststrain state~softening! in the stress–strain curves. It is the authopinion that softening in Kaolin clay may exist, but the tstress–strain state cannot be obtained with the current expertal facilities and interpretation techniques. The authors do not

Fig. 12. Friction angle, undrained shear strength, and pore preparameter

Fig. 13. Measured axial stress–



-

to use any postpeak data to draw any conclusions on the effb angle or develop any constitutive model that considers soing; hence, it is of little meaning to discuss the impact of stlocalization on the postpeak “softening” in Kaolin clay.

Test Results

Repeatability

In order to ensure a high degree of repeatability of the combaxial–torsional test data, significant care was taken duringdevelopment stage of testing related to clay specimen prepaand its uniformity, high degree of saturation using high back psure, andB value verification, and automated PID testing usthe servo-hydraulic loading system. Fig. 11 shows the typicasults from repeated tests forb=0, 30, and 45°, showing excellerepeatability.

Friction Angle, Undrained Shear Strength, and PorePressure Parameter

Before the shearing stage, all the specimens were initiallysolidated underK0 condition with vertical stress of 207 kPa, athen subjected to a higher isotropic confining pressures276 kPaduntil they reached primary consolidation. Therefore, all the smens were normally consolidated, and the cohesion was assto be zero. However, it cannot be assumed that the anisomicrostructure developed duringK0 consolidation was completedestroyed by the isotropic consolidation process, which widiscussed further based on the experimental observationsspecimens were considered failed once they reached thepoint in the stress–strain curves. The variation of the meaeffective friction anglef8 with the value ofb is shown in Fig. 12It ranges from 29.9 to 39.7°. The results suggest that the effefriction angle increases asb goes from 0 to 45°. A substantdecrease of effective friction angle betweenb=45 and 60° iobserved, then there is a slight increase of effective friction afrom b=60 and 90°. The friction angle had approximately avariation across theb range between 0 and 90°, and showenonmonotonic trend. Saada and Bianchini~1975! reported a similar nonmonotonic relation between the frictional angle andb forEdgar Plastic Kaolinite~EPK! clay with more than 20° variatioHong and Lade~1989! presented an experimental relationtweenf8 and intermediate stress ratiob sb=sin2bd with variationf8 of 10° for EPK. Lade and Wang~2001! reported similar trendfor Santa Monica Beach sand and concluded that the nonm

and shear stress–strain relationships
strain

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tonic trend was indicative of shear banding. The nonmonotrend presented in this paper for Kaolin clay could be relevashear banding, but further study is needed to gain better ustanding of the behavior of the material. Fig. 12 also illustrthe undrained shear strength normalized by the effective iconfining pressureSu/s

8c, which ranges from 0.24 forb=60° to

0.35 for b=30°. The Skempton’s pore pressure parameterAf isalso plotted in Fig. 12 with respect tob. Af is larger forb=90°sAf =1.70d than forb=0° sAf =1.13d, which is consistent with thgeneral trend observed in compression and extension tests.ever, Af is not a monotonic function ofb as shown in Fig. 12From Fig. 12, one can see that the rotation of principal stressignificant effect on the effective friction angle, undrained sstrength as well as pore pressure response.

Stress–Strain relationship

Fig. 13 shows the measured axial stress–strain and torsstress–strain relationships for allb angles. In order to compathe results in 3D stress space, a general shear stress, defithe following equation, is plotted against the major princstrain in Fig. 14 for allb values, normalized by the effectiinitial confining pressure:

Fig. 14. General shear stress and major principal strain

Fig. 15. Excess pore pressure evolution



-

y

q =Îss1 − s2d2 + ss2 − s3d2 + ss3 − s1d2

2s8d

where s1=major; s2= intermediate; ands3=minor principastress. It should be noted that forb=0 and 90°,q becomes thdeviator stress, which is widely used in presenting resultstriaxial compression and extension tests. It can be seen thprincipal stress rotation has a strong effect on the stress-behavior. A consistent trend of decreasing shear strengthincreasingb was observed forb from 0 to 60°. The shear strengfor b=90° was slightly higher than that forb=60°. This experimental observation can be interpreted as the combined inflof torsional shearing and extension, which will contributemore significant drop in shear strength than the influencmerely extension loading. It should be noted that in order tophasize that the postpeak stress–strain measurement is not rdue to strain localizations, the authors use dashed lines to dguish the postpeak portion of the curves shown in Figs. 13–

Before shearing, the specimens were under isotropic codation. However, due to theK0 consolidation during the specimpreparation, the specimens possessed transverse anisotroone would expect that the stiffness of the specimens alonvertical direction were higher than that along the horizontal dtion. When b=0°, the major principal stress was acting althe vertical direction; whenb=90°, the major principal strewas acting along the horizontal direction. It can be imagthat there is a reduction of stiffness as the value ofb increasefrom 0 to 90°.

Excess Pore Pressure Evolution

The excess pore pressure, normalized by the initial effectivefining pressure, is plotted against the major principal strain in15. As shown in Fig. 15, during shear, the evolution of expore pressure decreases asb increases. It should be noted thatb=60 and 90°, due to the reduction in vertical stress, initsmall negative excess pore pressure developed and a subsincrease was observed due to the shearing effect becausecontractive response of normally consolidated soil speciThere were some sharp increases in pore pressure towards tof the curves forb=60° ~slight! and b=90° ~more significant!.These sudden increases in pore pressure toward the endcurves could be a result of the strain localization, in which sbanding may have developed and the drainage paths withspecimen may be dramatically altered and caused the abn

Fig. 16. Effective stress path inq-p8 space

response of pore pressure.


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Stress Paths and Failure Envelope

The octahedral~first stress invariant,I1=constant! and triaxiaplane ~s1,s2=s3 plane! are typically used for displaying strepaths and failure envelops. The triaxial plane is suitable for itration of axisymmetrical stress state, such ass2=s3. For theoctahedral plane, each data point needs to have identicalstress. Generally, in a combined axial torsional test,s2 is notequal tos3, while at failure the effective mean stress varies csiderably. Therefore, the octahedral and triaxial planes werused to present the stress paths corresponding to varyingb valuesin this research. However, general shear stressq can be plotteagainst the mean effective stressp8 representing the effectivstress paths for allb angles, as shown in Fig. 16. This figushows an approximate trend of decreasing shear stress acreasing contractive response~higher −Dp8 during undraineshearing! with increasingb angle. In a combined axial–torsiontest, the three varying stress components were vertical stresz,radial stresssr, and shear stresstuz. To better describe the strestate of a specimen under combined axial–torsional loadincoordinate system with abscissa representing the differenctween the vertical stress and radial stresssz−sr, and ordinate oshear stresstuz, was used as shown in Fig. 17. Note that both aare normalized by the initial effective confining pressure.stress paths for all fiveb values are plotted. The stress paths sthat theb value was controlled very precisely during the expment. If the peak points in the stress–strain curves in Fig. 14considered to be failure points, an unsymmetrical failure envewas obtained. Although the isotropic consolidation pressurefore shearing was 1.33 times the vertical effective stress dK0 consolidation for specimen preparation, both the stressand the failure envelope show strong anisotropy of the Kaclay specimens. Therefore, the anisotropic microstructure doped duringK0 consolidation was not completely destroyedthe isotropic consolidation, and the anisotropy was still thethe memory of the specimen.

Conclusions

A thorough experimental procedure related to specimen pretion, isotropic consolidation, and shearing, was developed toform high quality combined axial–torsional tests on cohesiveIt is demonstrated that to obtain reliable test data in a comb

Fig. 17. Stress path and failure envelope

axial–torsional test, careful consideration to the uniformity of



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specimen geometry, void ratio, disturbance during assembly,ration, consolidation, and feedback control during shear areportant. During shearing, it is critical to use an advanced cputer controller to ensure that a constant major principal srotation angle is maintained throughout the test with specgeometry being updated in real-time for accurate control of tloading conditions. A series of combined axial–torsional twere performed on hollow cylinder specimens made of Kaclay under undrained conditions and the test data were presin a novel way such that deeper insight into the effect of princstress rotation can be gained. The test data clearly showed thstiffness of the Kaolin clay decreases asb increases and the evlution of excess pore pressure is lower asb increases. The anistropic character of Kaolin clay is evident based on the experital data. The observed 3D mechanical behavior of Kaolinsuch asb-dependent stiffness and excess pore pressure evoanisotropy, as well as noncoaxiality, should be taken into accfor appropriate formulation of a generalized constitutive mod

Acknowledgments

Financial support from National Science Foundation~NSF!through Grant No. CMS 9872618 is gratefully acknowledThe writers would like to acknowledge the contributionsanonymous reviewers and Dr. Amit Prashant for helpingsuitable revisions.

Notation

The following symbols are used in this paper:

d«I 5 major principal strain increment;ds1 5 major principal stress increment;ds2 5 intermediate principal stress increment;ds3 5 minor principal stress increment;

E 5 Young’s modulus;KD 5 derivative gain;KI 5 integral gain;KP 5 proportional gain;

b 5 principal stress rotation angle;Ds 5 change of vertical stress;Dt 5 change of shear stress;

n 5 Poisson’s ratio;sr 5 radial stress;sz 5 vertical stress; andtuz 5 shear stress.

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experimental investigation on principal stress rotation in kaolin clay

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