settlement analysis of geosynthetic

8/19/2019 Settlement Analysis of Geosynthetic

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Settlement Analysis of GeosyntheticReinforced Soil Retaining Walls at

Foundation Level

Halil Murat Algın Associate Professor, Department of Civil Engineering, Faculty of Engineering,

Harran University, Osmanbey Campus, 63000, Sanliurfa, Turkey

e-mail: [email protected]

ABSTRACTThis paper presents the practical closed-form solutions for the settlement analyses of flexiblyfaced Geosynthetic Reinforced Soil (GRS) walls at foundation level. The analytical solutionsare developed for elastic settlement and 1D ultimate primary consolidation settlementanalyses. The presented expressions can be readily implemented into the limit equilibriumdesign methods currently used for GRS walls. Unlike the conventional settlement calculationmethods used in the current practice, the presented expressions adequately take into account

the linear foundation pressure assumed in the limit equilibrium design procedures. The presented solutions allow efficient and accurate prediction of elastic and ultimate primaryconsolidation settlements of GRS walls. The presented formulae are based on the theory ofelasticity which is widely used in the practical settlement analysis of shallow foundations. Theflexible linear foundation pressure on the surface of a single layer system is assumed in this

paper. The applicability of the solutions on multi-layered grounds is also explained. Thecommon assumption of linear plane strain bearing pressure at the foundation level of GRSwall is adopted for the solutions and their applicability to the current limit equilibrium designmethods is demonstrated.

KEYWORDS: GRS walls; elastic settlement; consolidation settlement; angulardistortion; limit equilibrium method.

INTRODUCTIONCurrent design practice of GRS retaining walls with flexible facing is based on the limit

equilibrium method that involves satisfying external and internal stabilities in which the requireddesign criteria and minimum safety factors are fulfilled. The limit equilibrium method is detailedin many specifications and guidelines (e.g. AASHTO, 2002; BS8006, 1995; Elias et al., 2001;Holtz et al., 1998; NCMA, 2002; NCHRP, 2006). External stability refers to the stability of thereinforced soil mass as a whole in relation to the soil adjacent to it. The internal stability of GRSwalls requires that the wall is sufficiently stable against failure within the reinforced soil mass.


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There are also local stability criteria, such as for the connections of reinforcement and facing unit,considered in the design. In the external stability, the entire reinforced zone that contains backfillsoil, reinforcement, and the facing units is considered to act as a monolith whose main role is toresist the destabilizing active earth pressure exerted by the retained soil. The behaviour of GRS

walls during and after construction exhibits some complexity and it is still a subject area of manynew researches (e.g. Bilgin, 2009; Lee et al., 2008; McGown and Brown, 2008; Reddy et al.,2008; Skinner and Rowe, 2005; Viswanadham and König, 2009; Yang et al., 2009). The externalstability checks generally considered in the design are sliding, overturning, bearing capacity andeccentricity, deep-seated failure and settlement. The foundation soil of GRS wall must havesufficient bearing capacity to prevent failure and excessive settlement. GRS walls havingunacceptable differential settlement and angular distortion may result losing the load bearingfunction and structural stability. Significant settlement can result in vertical cracks and distress tothe structure at the top of the reinforced fill.

The limit equilibrium method assumes the linear bearing pressure at the foundation level,resulting from the lateral forces considered in the wall design such as active earth pressure

exerted by the retained soil. The eccentricity is limited by many specifications and guidelines toavoid the tension between the base of wall and foundation soil, and the full compression case istherefore considered in the design (e.g. AASHTO, 2002; BS8006, 1995; Elias et al., 2001; Holtzet al., 1998; NCMA, 2002; NCHRP, 2006). The linear contact pressure assumption at thefoundation level is also used in the bearing pressure checks in the external stability analysis (i.e.Meyerhof’s effective area method is used). The assumption of uniform or linear contact pressureat the foundation level is not strictly valid, but it is generally considered sufficiently accurate forordinary problems of design. In fact, most soils show evidence of some plastic behaviour, thereinforced soils generally have a finite stiffness and the distribution of bearing pressure withinsoil varies with time. The actual distribution of base pressure within soil is depending on the typeof soil and the stiffness of reinforced soil. Since the behaviour of GRS walls involves manyuncertainties regarding the action of ground and the loading, the foundation pressure distributions

rather than linear are usually not considered in the present-day limit equilibrium design methodsand the linear contact pressure assumption in plane strain case is widely used in manyspecifications and guidelines (e.g. AASHTO, 2002; BS8006, 1995; Elias et al., 2001; Holtz et al.,1998; NCMA, 2002; NCHRP, 2006).

The behaviour of GRS walls has recently been investigated by National CooperativeHighway Research Program (NCHRP, 2006) using the full scale measurements and numericalcomputer analysis, the part of study was summarised by Wu et al. (2006); the almost linearcontact pressure in the foundation level is observed in this research. It was stated that themeasured contact pressure was the highest beneath the wall face and decreased almost linearlywith the distance from the wall face (NCHRP, 2006). The assumption of linear foundation pressure is also justified by Yang et al. (2009) by conducting full scale field measurements. Some

other researchers (McGown and Brown, 2008; Reddy et al., 2008; Skinner and Rowe, 2005;Viswanadham and König, 2009; Otani et al., 1998; Yamaoka et al., 1990) are also agreed with thedish-shaped settlement profile and the linear contact pressure at the foundation level of GRSwalls. Bilgin (2009) investigated the reinforcement length using the internal and external stabilityanalyses by assuming the linear contact pressure at the foundation level.

Holtz et al. (1998) and NCHRP (2006) state that the tolerable angular distortion at thefoundation level of GRS walls is 1/200 for modular block walls and 1/50 for wrapped face walls.The limitation of tilt at the foundation level is given in order of magnitude one-tenth of 1% of the


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height of wall or less (NCHRP, 2006). Additionally, soil improvement at the foundation level isrecommended if the calculated settlement exceeds the project requirements (Holtz et al., 1998).Although the necessity of the settlement evaluation is emphasised by many specifications andguidelines (e.g. Holtz et al., 1998; NCHRP, 2006), the details of settlement analysis are not

provided in these documents. For instance, Holtz et al. (1998) refers to the conventionalsettlement analysis of shallow foundations used in geotechnical and foundation engineering text books for performing the settlement analysis of GRS walls. Similarly, NCHRP (2006) refers tothe well known text books and documents published by Terzaghi and Peck (1967), Perloff (1975)and Poulos (2000) for the foundation settlement analysis of GRS walls. However, the settlementexpressions in these literatures are for the uniform foundation pressure cases. For that reason, thesettlement analysis referred in the current literatures cannot directly be used since the linearcontact pressure is assumed at the foundation level of GRS walls in the design procedures.FHWA (2006) also states that the current design methods do not allow the designer to estimatetotal and differential settlements at the foundation level of GRS walls.

Since the practical settlement analysis is not provided by the specifications and guidelines

(e.g. AASHTO, 2002; BS8006, 1995; Elias et al., 2001; Holtz et al., 1998; NCMA, 2002; NCHRP, 2006), the required settlement checks cannot be performed directly on the bases of limitequilibrium method. Additionally, this shortcoming causes some further studies not performingthe settlement analysis in their researches. For instance, Bilgin (2009) excluded the settlementanalysis checks in his useful study. This gap in knowledge has brought about the need to developthe presented formulae for the settlement analysis of GRS walls at the foundation level byconsidering the linear foundation pressure assumed in the design procedures (e.g. Holtz et al.,1998; NCHRP, 2006).

In this paper the recently published elastic settlement solutions by the author (Algin,2009a; Algin and Algin, 2009) are evaluated to the plane strain case for the elastic settlementanalysis of GRS walls. Similarly, the vertical stress expressions for the linear foundation

pressures (Algin, 2000; Algin, 2001) are evaluated to obtain the practical average stressexpressions which are required in 1D ultimate primary consolidation settlement analysis of GRSwalls. Accordingly, the solutions at the foundation level are thereby developed for GRS walls both for the elastic settlement and the ultimate primary consolidation settlement analyses.However, the presented solutions have limited applicability for organic soils since the secondarycompression is usually the predominating settlement component in organic soils. Therefore, theamount of organic material should be very small for the presented solutions to be applicable.

The presented solutions are based on the theory of elasticity which is widely used for the practical settlement analysis of shallow foundations. Although the linear elastic soil models donot properly reflect the nonlinear response of soil, it is considered sufficiently accurate forordinary problem of design. The common assumption of linear bearing pressure at the foundation

level of GRS walls is adopted for the solutions and their applicability to the current limitequilibrium design methods is demonstrated. The applicability of the solutions on multi-layeredgrounds is also explained. By using the presented solutions, the settlement analyses under GRSwalls can swiftly be conducted and the resulting values can be compared with the projectrequirements. Accordingly, the decision on soil improvements at foundation level can be made,such as replacement, compaction, and stabilization of the soil or changing the reinforcementlength. The presented solutions are also useful for the confrontation of results obtained from themodern techniques such as the finite element method.


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ELASTIC SETTLEMENTS UNDER GRS WALLS

The practical elastic settlement formulae for the flexibly faced GRS walls on sand deposits

are derived from the settlement expressions recently developed by the author (Algin, 2009a) forthe eccentrically loaded shallow footings resting upon an elastic mass. These solutions are basedon the integration of strain expressions with the Boussinesq stress equations (Algin, 2009a). Thelinearly distributed contact pressures adopted by Algin (2009a) are generally assumed in practicefor rectangular footing having one or two-way eccentricities (Barnes, 2000; Bowles, 1996; Das,1999a; Das, 1999b; Poulos and Davis, 1974). The elastic settlement solutions (Algin, 2009a;Algin and Algin, 2009) are based on the linear contact pressure having full compression and theassumption of flexible foundation on the surface of single layered soil system. In these solutions,

the modulus of elasticity (Es) and Poisson’s ratio ( s µ ) for a given soil must be known to calculate

the elastic settlement of a foundation. Obtaining reliable values of elastic parameters is crucial forthe accurate estimation of settlement. There is a great tendency in practice to use the field testresults to obtain the reasonable values of elastic parameters when the reliable laboratory test

results are not available. The empirical correlations developed for the standard penetration test(SPT) and cone-penetration test (CPT) are widely used in practice to obtain the modulus ofelasticity of soil (Bowles, 1996; Das, 1999a; Das, 1999b). A comprehensive list of thesecorrelations is provided by Bowles (1996). In many cases, as suggested by D’Appolonia et al.(1971) the modulus of elasticity of saturated clay (undrained) is correlated with undrained shearstrength (cu). Duncan and Buchignani (1976) correlated Es/cu with the overconsolidation ratio(OCR) and plasticity index (PI) of several clay soils. In practice, the approximate range of typicalvalues is commonly used for Poisson’s ratio (Bowles, 1996; Das, 1999a; Das, 1999b) or it may beestimated from the empirical correlations (Bowles, 1996; Das, 1999b). Alternatively, Poisson’sratio can be estimated from the relationship between the representative initial elastic modulus andshear modulus which is correlated with mean effective stress, OCR and PI as suggested by Foyeet al. (2008). If there is stratification in the considered soil depth, more than one set of elastic

parameters must be obtained and the weighted average of elastic parameters may be applied assuggested by Bowles (1996) or alternatively the approximation technique presented in this papermay be used in the elastic settlement computation. This approximation technique may be adopted by dividing the soil deposit into multi-layered system in the cases where the elastic modulus of asoil varies with depth.

An illustration of a typical GRS wall, along with the forces acting on the wall used forexternal stability analysis, is shown in Figure 1. The resulting linear pressure considered in thesettlement analysis is illustrated at the foundation level. If the reinforced soil foundation isassumed to be perfectly flexible, the wall structure undergoes the settlement with tilt which canhave the dish-shaped settlement profile. The linear contact pressure at the foundation level isassumed in many practical design guides for GRS walls (e.g. AASHTO, 2002; BS8006, 1995;

Elias et al., 2001; Holtz et al., 1998; NCMA, 2002; NCHRP, 2006) and dish-shaped settlement profile agrees with the results from numerical models conducted by many researchers (e.g.Alfaro et al., 1997; Guler et al., 2007; McGown and Brown, 2008; Otani et al., 1998; Reddy etal., 2008; Skinner and Rowe, 2005; Viswanadham and König, 2009; Yamaoka et al., 1990).


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Figure 1: A typical GRS wall with the linear pressure at the foundation level

The assumption of perfect flexibility at the foundation level is not strictly valid, but it isconsidered sufficiently accurate for the ordinary problems of design. In fact, the stiffness ofreinforced soil depends on the number of reinforcements, the variation in reinforcement length,the reinforcement types etc. (Alfaro et al., 1997). Since the decrease in vertical spacing between

the geosynthetic reinforcements may result an increase in the rigidity of the reinforced backfill(i.e. the reinforcement acts as a stiffener), the settlement may be slightly reduced by a decrease invertical spacing between the reinforcements (Alfaro et al., 1997). This rigidity effect may beintroduced to the presented expressions in this paper by a reduction factor as it is used in thesettlement analysis of rectangular footings (Barnes, 2000; Bowles, 1996; Das, 1999a; Das, 1999b;Poulos and Davis, 1974). For example, as suggested by Barnes (2000) the elastic settlementexpressions of rectangular footing may be used with Fraser and Wardle (1976)’s stiffnesscorrection factors and Burland (1970)’s depth correction factors. The depth factor indicates thatthe settlement is reduced when it is placed at some depth in the ground, depending on Poisson’sratio and the shape factor of footing. However, analytical studies have shown that simplyassuming the surface of elastic medium at the level of loading and ignoring the soil above it givesrelatively good results compared with the solutions including the depth factors. The stiffnesscorrection takes account of the foundation stiffness effect on elastic settlement. Therefore, the presented expressions can directly be used for the flexible foundation of GRS walls but they can be used for less flexible foundations by introducing the relevant stiffness corrections.

The foundation pressure shown in Figure 1 can be obtained by modifying the pressureconfiguration introduced by Algin (2009a, 2009) to the plane strain case. Accordingly, themaximum elastic settlement under the eccentricity point can be obtained as follows.


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)()1(

)(2)(1)( e se

s

sa

e E I I E

BqS µ

µ +

+= (1)

Where, B H n = ,ab

qqt = , t d += 21

, t d 212

+= ,ab

qqt = , )1)(1(12 21

t t t nc +++= ,

))1(52)(( 12 t t d c ++= , ))25(5)(( 23 t t d c ++= , )(96 12

24 d t d nc +−= , )1(35 t nc += ,2

122

6 )1(9 d t nc ++= ,22

227 )1(9 d t nc ++= ,

))ln()ln())/()/(()()1(361( 22732

162521

511

12

)(1 d ccd cccd Tancd Tanct I e ++++= −−

π (2)

)))ln(

))ln()ln()ln()1((()ln(

)ln()1())/()/(()()1(1441(

607

486

1202

961

487

606

962

1201

167

206

322

401

366

367

2207

166

402

321

367

366

252

151

14

2)(2

ccd d

ccd d ccd d t cct nt t ccd d

cct ncd Tancd Tanct I e

+

+++++

++++= −−

π

(3)

By using the similar notations, the elastic settlement expression under any point of thelinear foundation pressure (Figure 1) is evaluated and this expression is then integrated over thefoundation width and divided by the width of foundation to obtain the average settlement underthe pressure block. Similar technique is used by Janbu et al. (1956) to develop an average elasticsettlement equation for a uniform foundation pressure on saturated clay soils ( 5.0= s µ ) (Das,

1999a). The average settlement can be used if an approximate solution is required. The resultingexpression for the average elastic settlement under the linear foundation pressure is provided asfollows.

)()1)((

)( avs

s

sba

av E I E

qq BS

µ ++= (4)

Where, B H n = ,

))1ln()1())1(ln()1())11ln(2)(12(()(41( 22221 nnnnnnnCot n I s s savs +−−+−+++−−= − µ µ µ π (5)

The terms )(1 e I , )(2 e I and avs I (see Eqs. 2,3 and 5) are the influence factors for the elastic

settlement expressions. These factors are the functions of dimensionless parameters of n ( B H =

) and t (= ab qq ), and they can therefore be represented in a graphical form as shown in Figure 2.


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Figure 2: Influence factors for the elastic settlement expressions (see Eqs. 1, 4)

AVERAGE VERTICAL STRESS AND THE

CONSOLIDATION SETTLEMENT ANALYSIS

By using the experimentally determined recompression (Cr ) and compression (Cc) indexes,the ultimate primary consolidation settlement is commonly determined by using the expressionsrelated with the overconsolidation ratio (OCR) (Bowles, 1996; Das, 1999a; Das, 1999b). In theseexpressions the average pressure increase is required within the consolidated soil layer. Theaverage pressure expressions presented in this paper may be more useful for the considered soil

layer where the coefficient of volume compressibility ( vm ) is assumed be constant at least in

certain depths. This is a common case for many primary consolidation settlement analyses (suchas cone penetration test (CPT) and Dilatometer based analyses). For example, in practice, in the

CPT based compressibility assessment of soil, the 1D constrained modulus ( vm M /1= ) is

assumed to be constant within the certain depth of CPT-based soil profile data. M can bedetermined mainly in terms of the cone tip resistance, overburden stress and/or the soil type(Sanglerat, 1972; Kulhawy and Mayne, 1990; Mahesh and Vikash, 1995). This assumption may be more reasonable for stiff, overconsolidated soils in which the loading increment does not causethe preconsolidation pressure to be exceeded. In order to calculate the average pressure within thedepth (in which M is of constant value) a commercial computer software with advancedmodelling is normally required such as Flac 3D, Plaxis etc. The accuracy of the results dependson the accuracy of model, element type and size etc. The direct use of point-stress solutions at themiddle of soil layer however may provide inaccurate results and can be quite misleading when it

is compared with the computer-based results (Algin, 2009b). Whereas the average stress solutions presented for the linear foundation pressure of GRS walls simplify this computation and candirectly be used with an acceptable accuracy.

The average stress required in 1D consolidation settlement analysis of GRS walls has brought about the need to develop an analytical solution which can directly be used in thesettlement analysis. The average pressure increase in a soil layer is generally required for anaccurate estimation of the consolidation settlement resulting from a foundation pressure (Das,1999a; Das, 1999b). The current practice of estimating the average pressure increase in a soil


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layer under GRS walls usually employs the numerical process (i.e. the sub-layer method using themid-depth stresses based on the well-known point-stress expressions) or direct use of mid-depthstress in a soil layer. In practice, the point-stress expressions are generally used to obtain the mid-depth stress in a soil layer. The point-stress that is the vertical stress at a point in a depth of a soil

stratum is usually determined by the integration of Boussinesq equation over the loaded surfacearea (Bowles, 1996; Das, 1999a; Das, 1999b; Poulos and Davis, 1974). Many point-stresssolutions adopted in practice are available for shallow foundations (Bowles, 1996; Das, 1999a;Das, 1999b; Poulos and Davis, 1974). The limitations and the percentage error encountered in thedirect use of mid-depth stresses are presented by Algin (2009b) with the confrontation of theresults from the exact analytical solutions for shallow foundations. The sublayer method howeverinvolves replacing the smoothly varying stress distribution within a soil by a staircase-likedistribution which assumes a constant stress (usually mid-depth stress) over each sublayer. Sincethe direct use of mid-depth stresses in a soil layer occasionally provides invalid results, thesublayer method is used in practice instead of direct mid-depth stress approach to obtain therealistic stresses. Usually in the sub-layer method, the mid-depth stresses are used in each sub-layer as an average stress. Although the sub-layer method reduces the error, the reliability of sub-

layer method significantly depends on the thickness of sublayer considered (Bowles, 1996; Algin,2009b). Since the coefficient of volume compressibility ( vm ) is usually assumed as constant over

a specific soil layer especially in the settlement analysis based on the CPT test results, the directaverage stress expressions can avoid the necessity of considering the compressible soil layer as aseries of sublayers unlike the sublayer method used in the consolidation settlement analysis. More practical and reliable settlement analysis can therefore be undertaken by using the direct average

stress expressions for the specific soil layer in which vm is assumed constant.

Although there are some charts (Griffiths, 1984; Brown, 2004) and the analytical solutionsof average stress (Algin, 2009b) for a uniform foundation pressure are exist, the analyticalsolutions of average stress for the linear foundation pressure shown in Figure 1 are not

mentioned in the current literature. The required expression for the average stress under the linearfoundation pressure shown in Figure 1 can be obtained from the point-stress equations previouslydeveloped by Algin (2001). Since the foundation pressure shown in Figure 1 can be obtained bymodifying the linear rectangular pressure configuration to the plane strain case, the point-stressexpressions for the eccentricity point (Figure 1) can be obtained as follows.

)()( e z ae z I q=σ (6)

Where, B z f = ,ab qqt = ,

221 1 f f += ,

21 )1( t t += , t t += 22 , t t 213 += ,

24 1 t t t ++= ,

15 9 ft t = ,225

26 t ft t += ,

235

27 t ft t += ,

)))()((2)()6(1( 731

621

42735

26251)( t t Sint t Sint t t t t t t t t I e z

−−+++= π (7)

The term )(e z I (see Eq. 7) is the influence factor for the point-stress expression which can

be represented in a graphical form shown in Figure 3(a).


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Figure 3: Influence factors for the point-stress solution given in Eq. (6) and for theaverage stress solutions given in Eq. (9)

If a single layer soil system is considered, the average stress under the linear foundation pressure shown in Figure 1 can now be obtained by the following integration of point-stressexpression (Eq. 6) over the depth of interest ( H ).

= H

z av dz H

0

1

σ σ (8)

H indicates the depth between the loading plane and the plane in depth H . The aboveintegration has been solved and the resulting average stress expression is presented as follows.

)()( eavaeav I q=σ (9)

Where, B H n = ,ab qqt = ,

21 )1( t t += , t t += 22 , t t 213 += ,

24 1 t t t ++= ,

22221 )2()1(9 t t ne +++= ,

22222 )21()1(9 t t ne +++= , )1(6 43 t nt e += ,

324 515124 t t t e +++= ,

325 412155 t t t e +++= ,

))21(ln())2(ln())()(())(18/(1( 2514231

121

31)( t eet eeet Sinet Sinet n I eav +++++= −−

π (10)

Therefore, the average stress under the loaded area shown in Figure 1 can be obtained as a

function of average influence factor ( av I ) over the depth of interest ( H ). The influence factor for

the average stress expression given by Eq.(10) depends on the dimensionless parameters of n (

B H = ) and t (= ab qq ), and can be represented in a graphical form as shown in Figure 3(b).

For a single layered soil system, the required consolidation settlement equation can then beexpressed as follows.

)()( eavveC H mS σ = (11)


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THE USE OF SOLUTIONS FOR MULTI-LAYERED

GROUNDS

As suggested by some of the methods used in the elastic settlement analysis of shallowfoundations (such as the strain influence factor diagram method developed by Schmertmann andHartman (1978)), the approximate variation of the cone penetration resistance or standard penetration numbers in the soil profile can be assumed to be constant within a specific depth ofthe classified soil. By using this common assumption, the approximate variation of the modulusof elasticity with depth can be evaluated. Several investigators have correlated the values of themodulus of elasticity (Es), with the field standard penetration number (NF) and the cone penetration resistance (qc) (Bowles, 1996; Das, 1999a; Das, 1999b). For example, Schmertmannand Hartman (1978) suggested that the equivalent modulus of elasticity for a layer of thickness (

i z ∆ ) can be obtained by multiplying the average cone tip resistance of the ith layer ( ciq ) by 3.5

for strip loadings on sand and silty sand (Es=3.5qc). Although this correlation is generally

considered valid for practical purpose (Bowles, 1996; Das, 1999a; Das, 1999b), some researchers(Sargand et al. 2003) suggest that the ratio of Es/qc for overconsolidated sands can be in the rangeof 3-6 times larger than those for normally consolidated sands. Bowles (1996) suggests thecorrelation of Es=(2-4)qc for sand and silty sand, and Es=(3-8)qc for clay layers. Some researchers(Lee and Salgado, 2002; Lee et al., 2008) have recently correlated the ratio of E s/qc with relativedensity of each sublayer, settlement and footing width. This correlation can also be used with thesettlement expressions presented in this paper.

Many researchers developed expressions for the constant constrained modulus ( M ) in thecertain depth of CPT-based soil profile data (e.g. Sanglerat, 1972; Kulhawy and Mayne, 1990;Mahesh and Vikash, 1995). Accordingly, by using the suitable expressions for the constrained

modulus the coefficient of volume compressibility ( vm ) for the specific soil layers can be

determined in terms of the cone tip resistance, overburden stress and/or the soil type. If there isstratification in the considered soil depth, more than one set of soil parameters must be obtainedand the superposition technique shown in Figure 4 can be used in the settlement analyses inwhich the soil deposit is divided into multi-layered system.

Figure 4: Application of the presented expressions for multi-layered grounds.

The approach shown in Figure 4 takes into account the deformation experienced by everylayer within the soil profile data. In this superposition technique, the elastic settlements (Eqs. 1and 4) and the consolidation settlements (see Eqs. 9 and 11) are calculated for each considered


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soil layer. At first, the soil parameters within the depth between the loading plane and the bottomof considered soil layer are taken as the layer’s soil parameters, and then, the discarded upperlayer having same soil parameters as the considered soil layer are subtracted as illustrated inFigure 4. The calculations are repeated for all subsequent soil layers. Then, the results are added

to obtain the values of total settlements. A simple spreadsheet program may be used for thesecalculations. This superposition technique was originally presented by Butler (1975) for theelastic settlement analysis of shallow foundations. This approximation is adopted in this paper forthe linear foundation pressure of GRS walls to obtain not just for the elastic settlement but alsothe consolidation settlement.

Unlike the strain influence factor diagram method developed for uniform loading bySchmertmann and Hartman (1978), the proposed elastic settlement analysis presented in this paper for the linear foundation pressure takes into account the variation of Poisson’s ratio byevery layer within the soil profile data. Analytical studies show that the variation of Poisson’sratio has a significant influence on the settlement results. This may be the reason why the straininfluence factor diagram method often over predicts the actual elastic settlements (Anderson et

al., 2007; Das et al., 2009). The proposed elastic settlement analysis in this paper also avoids anycertain strain influence factor diagram assumed by Schmertmann and Hartman (1978), since theexact elastic solutions are presented.

NUMERICAL EXAMPLE

Example: Figure 5 illustrates a GRS abutment with an integrated sill and a tall upper wall. NCHRP (2006) provided the detailed design solution of this example based on the limitequilibrium method. However, the calculation details of settlement analysis are not provided by NCHRP (2006). It only refers to the well known text books for the foundation settlement analysisof GRS walls, even though the referred settlement analyses cannot directly be used due to thelinear pressure assumption made at the foundation level of GRS walls in the design procedures.Only the result of maximum foundation settlement is provided by NCHRP (2006) for thisexample without explaining how it is obtained. The data given for this example are provided inFigure 5 (NCHRP, 2006). By assuming a flexible behaviour at the foundation level it is requiredin this paper to determine the settlement under the point of eccentricity (i.e. point e shown inFigure 5). Depending on the foundation settlement, it is also required to determine the maximumangular distortion under the GRS wall illustrated in Figure 5.


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Figure 5: A GRS abutment with an integrated sill and a tall upper wall considered inExample 1 (NCHRP, 2006).

Solution: As shown in Figure 5, since the soil deposit is only a single layered medium sandfoundation, the presented settlement equations (i.e. Eqs.(1, 4)) can directly be used. The requiredinfluence factors in Eqs.(2, 3 and 5) can be obtained from Figure 2 (see the dashed lines inFigures 2a and 2b) as follows,

86.076 === B H n and 14.0218.347633.48 === ab qqt . Thus, the influence

factors from Figure 2(a) are 231.0)(1 =e I and 315.0)(2 =e I . Hence, the maximum elastic

settlement can be estimated from Eq. (1) as,

m01.0))315.0()3.0()231.0((41400

)3.01)(218.347)(7()(

)1()(2)(1)( =+

+=+

+= e se

s

sae E I I

E

BqS µ

µ

Therefore, the maximum foundation settlement is obtained as 0.01 m (10mm). This result isidentical with the maximum settlement value provided by NCHRP (2006) .

Additionally, the influence factor for the average elastic settlement is 093.0=avs I (see

Eq.(5) and the dashed lines in Figures 2(b). Thus, the average settlement can be estimated fromEq.(4) as,


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6.

Algin, H.M., (2009a) “Elastic Settlement under Eccentrically Loaded RectangularSurface Footings on Sand Deposits,” Journal of Geotechnical and GeoenvironmentalEngineering, ASCE, 135:10, 1499-1508.

7.

Algin, H.M., (2009b) “Analytical solutions of average pressure increments for primaryconsolidation settlement computations,” Proc. 2nd Int. Conf. on New Developments inSoil Mechanics and Geotechnical Engineering, Near East University, Nicosia, NorthCyprus, 206-213.

8.

Algin, H.M., Algin, Z., (2009) “Elastic settlements under linear surface pressures onrectangular areas,” Int. Jrnl. for Numerical and Analytical Methods in Geomechanics,33:8, 1087 – 1108.

9.

Anderson, J.B., Townsend, F.C., Rahelison, L., (2007) “Load testing and settlement prediction of shallow foundation,” Journal of Geotechnical and GeoenvironmentalEngineering, ASCE, 133:12, 1494-1502.

10.

Barnes, G.E., (2000) “Soil mechanics principles and practice,” 2nd Edn., Palgrave

Macmillan, New York.11. Bilgin, Ö., (2009) “Failure mechanisms governing reinforcement length of geogrid

reinforced soil retaining walls,” Engineering Structures, 31:9, 1967-1975.

12.

Bowles, J.E., (1996) “Foundation analysis and design,” 5th Edn, The McGraw-HillCompanies, New York.

13.

Brown, R., (2004) “Practical Foundation Engineering Handbook,” McGraw-Hill, 2ndEd., New York.

14. BS8006, (1995) “Code of practice for strengthened/reinforced soils and other fills,”British Standards Institution, BSI, London.

15.

Burland, J.B., (1970) “Discussion on session A,” Proc. Conf. on In-Situ Investigations inSoil and Rocks, British Geotechnical Society, London, 61-62.

16.

Butler, F.G., (1975) “Heavily overconsolidated clays. Settlement of Structures,” BritishGeotechnical Society Symposium, Pentech, London, 531–578.

17.

D’Appolonia, D.T., Poulos, H.G., Ladd, C.C., (1971) “Initial settlement of structures onclay,” J. Soil Mech. Found. Dev., ASCE, 97:10, 1354-1377.

18.

Das, B.M., (1999a) “Principles of foundation engineering,” 4th Edn., PWS Publishing, New York.

19.

Das, B.M., (1999b) “Shallow foundations: bearing capacity and settlement,” 1st Edn.,CRC Press LLC, Florida.

20.

Das, B.M., Atalar, C., Shin, E.C., (2009) “Developments in elastic settlement estimation procedures for shallow foundations on granular soil,” Proc. 2nd Int. Conf. on NewDevelopments in Soil Mechanics and Geotechnical Engineering, Near East University, Nicosia, North Cyprus, 9-41.

21. Duncan, J.M., Buchignani, A.L., (1976) “An engineering manual for settlement studies,”Department of Civil Engineering, University of California, Berkeley.


15/16

Vol. 15 [2010], Bund. G 711

22.

Elias, V., Christopher, B.R., Berg, R.R., (2001) “Mechanically stabilized earth walls andreinforced soil slopes, design and construction guidelines,” Publication No. FHWA-NHI-00-043, Federal Highway Administration (FHWA), Washington (DC).

23.

FHWA, (2006) “Promoting geosynthetics use on federal lands highway projects,” CentralFederal Lands Highway Division, Publication No. FHWA-CFL/TD-06-009, 12300 WestDakota Avenue Lakewood, CO 80228.

24.

Foye, K.C., Basu, P., Prezzi, M., (2008) “Immediate settlement of shallow foundations bearing on clay,” Int. J. Geomech., ASCE, 8:5, 300-310.

25. Fraser, R.A., Wardle, I.J., (1976) “Numerical analysis of rectangular rafts on layeredfoundations,” Geotechnique, 26:4, 613-630.

26.

Griffiths, D.V., (1984) “A chart for estimating the average vertical stress increase in anelastic foundation below a uniformly loaded rectangular area,” Canadian GeotechnicalJournal, 21:4, 710-713.

27.

Guler, E., Hamderi, M. Demirkan, M.M., (2007) “Numerical analysis of reinforced soil-retaining wall structures with cohesive and granular backfills,” GeosyntheticsInternational, 14:6, 330-345.

28. Holtz, R.D., Cristopher, B.R., Berg, R.R., (1998) “Geosynthetic Design & ConstructionGuidelines,” Publication No: FHWA HI-95-038, National Highway Institute FederalHighway Administration (FHWA), McLean, Virginia.

29.

Janbu, N., Bjerrum, L., Kjaernsli, B., (1956) “Veiledning ved losning av fundamenteringsoppgaver,” Publication No.16, Norwegian Geotechnical Institute, pp. 30-32.

30.

Kulhawy, F.H., Mayne, P.H., (1990) “Manual on estimating soil properties forfoundation design,” Electric Power Research Institute, EPRI, Palo Alto, CA.

31.

Lee, J., Eun, J. Prezzi, M., Salgado, R., (2008) “Strain influence diagrams fromsettlement estimation of both isolated and multiple footings in sand,” Journal ofGeotechnical and Geoenvironmental Engineering, ASCE, 134:4, 417-427.

32.

Lee, J.H., Salgado, R., (2002) “Estimation of footing settlement in sand,” Int. J.Geomech., ASCE, 2:1, 1-28.

33. Mahesh, D., Vikash, J., (1995) “State of art of CPT in India,” International Symposiumon Cone Penetration Testing, Vol.1, pp.87-95, Linköping, Sweden.

34.

McGown, A., Brown, S.F., (2008) “Applications of reinforced soil for transportinfrastructure,” Proc. of the 1st Int. Conference on Transportation, Geotechnics, Nottingham, UK., Advances in Transportation Geotechnics – E. Ellis, H.S. Yu, G.McDowell, A. Dawson, N. Thom (Eds), CRC Press, Taylor & Francis Group, London, pp

27-36.35. NCHRP, (2006) “Design and construction guidelines for geosynthetic-reinforced soil

bridge abutments with a flexible facing,” National Cooperative Highway ResearchProgram, Report 556, Washington D.C.

36.

NCMA, (2002) “Design manual for segmental retaining walls,” National ConcreteMasonry Association. 2nd ed., Collin, editor. Herndon, VA.

37.

Otani, J., Hirai, T., Ochiai, H., Shinowaki, S., (1998) “Evaluation of foundation supportfor geosynthetic reinforced soil wall on sloping ground,” Sixth International Conference


16/16

Vol. 15 [2010], Bund. G 712

on Geosynthetics, Atlanta, USA, 25–29 March 1998. Industrial Fabrics AssociationInternational, pp. 601–603.

38. Perloff, W.H., (1975) “Pressure distribution and settlement,” Chapter 4, FoundationEngineering Handbook (Winterkorn and Fang, editors) Van Nostrand Reinhold, New

York, pp. 148–196.

39.

Poulos, H.G., (2000) “Foundation settlement analysis–practice versus research,” TheEighth Spencer J. Buchanan Lecture, Texas A&M University.

40.

Poulos, H.G., Davis, E.H., (1974) “Elastic solutions for soil and rock mechanics,” 1stEdn., John Wiley & Sons, New York.

41. Reddy, G.V.N., Madhav, M.R., Reddy, E.S., (2008) “Pseudo-static seismic analysis ofreinforced soil wall—Effect of oblique displacement,” Geotextiles and Geomembranes,26:5, 393-403.

42.

Sanglerat, G., (1972) “The penetrometer and soil exploration,” Elsevier, Amsterdam, pp.464.

43. Sargand, S.M., Masada, T., Abdalla, B., (2003) “Evaluation of cone penetration test-

based settlement prediction methods for shallow foundations on cohesionless soil athighway bridge construction sites,” Journal of Geotechnical and GeoenvironmentalEngineering, ASCE, 129:10, 900-908.

44.

Schmertmann, J.H., Hartman, J.P., (1978) “Improved strain influence factor diagrams,”Journal of the Geotechnical Engineering Division, ASCE, Vol. 104, No. GT8, 1131-1135.

45.

Skinner, G.D., Rowe, R.K., (2005) “Design and behaviour of a geosynthetic reinforcedretaining wall and bridge abutment on a yielding foundation,” Geotextiles andGeomembranes, 23:3, 234-260.

46. Terzaghi, K., Peck, R.B., (1967) “Soil mechanics in engineering practice,” 2nd edition,John Wiley and Sons, New York.

47.

Viswanadham, B.V.S., König, D., (2009) “Centrifuge modelling of geotextile-reinforced

slopes subjected to differential settlements,” Geotextiles and Geomembranes, 27:2, 77-88.48. Wu, J.T.H., Lee, K.Z.Z., Pham, T., (2006) “Allowable bearing pressures of bridge sills on

GRS abutments with flexible facing,” Journal of Geotechnical and GeoenvironmentalEngineering, ASCE, 132:7, 830-841.

49. Yamaoka, I., Nishigata, T., Yasuda, K., Mondori, K., (1990) “Load tests and long termobservation of geotextile reinforced retaining wall,” Fourth International Conference onGeotextiles, Geomembranes and Related Products, Vol 1, The Hague, Netherlands. pp.123-124.

50.

Yang, G., Zhang, B., Lv, P., Zhou, Q., (2009) “Behaviour of geogrid reinforced soilretaining wall with concrete-rigid facing,” Geotextiles and Geomembranes, 27:5, 350-356.

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