active pressure on gravity walls supporting purely frictional soils

Active pressure on gravity walls supporting purelyfrictional soils

D. Loukidis and R. Salgado

Abstract: The active earth pressure used in the design of gravity walls is calculated based on the internal friction angle ofthe retained soil or backfill. However, the friction angle of a soil changes during the deformation process. For drained load-ing, the mobilized friction angle varies between the peak and critical-state friction angles, depending on the level of shearstrain in the retained soil. Consequently, there is not a single value of friction angle for the retained soil mass, and the activeearth pressure coefficient changes as the wall moves away from the backfill and plastic shear strains in the backfill increase.In this paper, the finite element method is used to study the evolution of the active earth pressure behind a gravity retainingwall, as well as the shear patterns developing in the backfill and foundation soil. The analyses relied on use of a two-surfaceplasticity constitutive model for sands, which is based on critical-state soil mechanics.

Key words: finite elements, plasticity, retaining walls, sands.

Rsum : La pression active des terres utilise dans la conception des murs gravitaires est calcule partir de langle defriction interne du sol ou du remblai retenu. Cependant, langle de friction dun sol change durant le processus de dforma-tion. Dans le cas dun chargement drain, langle de friction mobilis varie entre langle de friction au pic et celui ltatcritique, dpendant du niveau de dformation en cisaillement dans le sol retenu. En consquence, il ny a pas de valeurunique dangle de friction pour une masse de sol retenue, et le coefficient de pression active des terres varie mesure quele mur se spare du remblai et que les dformations plastiques en cisaillement augmentent dans le remblai. Dans cet article,la mthode par lments finis est utilise pour tudier lvolution de la pression active des terres derrire un mur de soutne-ment gravitaire, ainsi que les patrons de cisaillement qui se dveloppent dans le remblai et dans le sol de fondation. Les ana-lyses sont ralises laide dun modle constitutif de plasticit deux surfaces pour des sables, qui est bas sur lamcanique de ltat critique des sols.

Motscls : lments finis, plasticit, murs de soutnement, sables.

[Traduit par la Rdaction]

IntroductionThe active earth pressure acting on the back of a retaining

wall controls its design. The active earth pressure is ex-pressed as the product of the vertical effective stress s 0v inthe retained soil mass or backfill1 and the active earth pres-sure coefficient KA. The earliest and simplest methods for thecalculation of the active earth pressure for purely frictionalbackfills are those based on the Coulomb and Rankine theo-ries. For a backfill with horizontal surface, the Rankine solu-tion is mathematically exact for a vertical and smooth wallbackface. Coulombs solution assumes a planar slip surfaceand is equivalent to an upper bound solution. For a horizon-tal backfill and a vertical wall backface, Coulombs solutionyields

1 KA cos2f

cosdf1 sin f d sinf=cosdp g2

Caquot and Kerisel (1948) produced solutions in tabulatedform, assuming slip surfaces with logarithmic spiral shape.More recently, Paik and Salgado (2003) estimated the activeearth pressure behind rigid walls by improving the formula-tion of Handy (1985), which considers soil arching concepts.Limit analysis has also been used to study the active earth

pressure problem. Rigorous upper bound values for KA estab-lished by Chen (1975) and Soubra and Macuh (2002) usinglimit analysis are in very close agreement with the values of Ca-quot and Kerisel (1948). Sokolovski (1965) solved the problemof active and passive earth pressure using the method of charac-teristics. More recently, Lancellotta (2002) provided a rigorouslower-bound solution for active pressures in closed form:

2 KA cosd1 sinfcosd

sin 2f sin 2d

pedarcsin sind=sinf tanf

Received 21 March 2011. Accepted 26 September 2011. Published at www.nrcresearchpress.com/cgj on 20 December 2011.

D. Loukidis. Department of Civil and Environmental Engineering, University of Cyprus, Nicosia 1678, Cyprus.R. Salgado. School of Civil Engineering, Purdue University, W. Lafayette, IN 47907-1284, USA.

Corresponding author: D. Loukidis (e-mail: [email protected]).1The paper is not restricted to backfilled walls. To call attention to applicability of the discussion to walls supporting natural ground aswell as completely backfilled walls, the terms retained soil mass and backfill are used interchangeably throughout.

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Can. Geotech. J. 49: 7897 (2012) doi:10.1139/T11-087 Published by NRC Research Press

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The upper bound values for KA by Coulombs solution,Chen (1975), and Soubra and Macuh (2002) are very closeto the corresponding lower bound values using Lancellottasequation (eq. [2]); the differences do not exceed 7%. The KAvalues by Sokolovski (1965) lie between the narrow banddefined by these lower and upper bounds.Lower and upper bounds produced by limit analysis are

valid for perfectly plastic soils following an associated flowrule (dilatancy angle j equal to the friction angle f). In thecase of materials commonly used for backfills (sands andgravels), j is significantly lower than f. In fact, the complex-ity of soil behavior goes beyond the difference between jand f, as discussed in detail later, but this does not appearto have been studied in connection with the analysis of re-taining walls.Three stability checks are traditionally done in wall design,

namely bearing capacity failure, sliding, and toppling. In es-sence, these checks deal with assuring vertical, horizontal,and moment equilibrium of the wall. While these separatechecks are easy for engineers to understand and apply, thehorizontal and moment resistances that the foundation soil(including any embedment in front of the wall) can provideto the wall are in fact coupled with the vertical bearing ca-pacity. For example, toppling failure occurs in theory whenthe foundation load eccentricity e becomes greater than one-half the foundation width B. Unless the wall base is restingon rock or very stiff soil, the wall foundation will actuallyfail due to the excessively high contact pressure at the wallbase caused by large load eccentricity before toppling. In ad-dition, wall sliding on its base is more likely to have the formof a shallow one-sided bearing capacity mechanism with alarge horizontal displacement component (Loukidis et al.2008) rather than pure sliding along the basesoil interface.This paper aims to investigate the gravity wallsoil interac-tion and the development of these different failure scenariosby modeling the soil mechanical behavior in a realistic wayin a series of finite element (FE) analyses. This allows thedevelopment of displacement and stress fields within the soilthat are not constrained by the simplifying assumptions ofperfect plasticity and associativity. These results are useful ininforming design decisions, the most important of whichbeing how to calculate the active pressures on the backfaceof the wall. The FE analyses, which take into account nonas-sociativity, stress dependence of sand strength and dilatancy,stress-induced anisotropy, fabric-induced anisotropy, and pro-gressive failure, focus on the evolution of KA with wall dis-placement u. This permits establishing the soil friction anglevalue that is suitable for the estimation of the design KAvalue, which is the one that corresponds to the wall displace-ment required to bring the wall to an ultimate limit state(ULS).

Problem statement

Dependence of active earth pressure on wall movementIn methods of analysis currently used in design practice,

the main input for the calculation of KA for purely frictionalbackfills is the internal friction angle f of the soil. Thesemethods, which include the Rankine, Coulomb, and Lancel-lotta methods discussed earlier, assume that f is constant, i.e.,its value is the same at all points inside the backfill and

does not change as the wall moves. This would be validfor a very loose backfill, where all soil elements reach fail-ure directly at critical state (CS), with f equal to the CSfriction angle fc. However, most practical cases involvebackfills consisting of medium dense and dense sands andgravels, which are strain-softening materials when shearedunder drained conditions, meaning that the mobilized fric-tion angle of an element of any of these soils will firstreach a peak value fp and then decrease towards fc. Cer-tain regions inside the backfill mass will fail and start tosoften early in the loading process. The shear strain leveldeveloped in these regions may be large enough for thefriction angle to drop to its CS value fc before the wallreaches a ULS, while f is close to fp in other regions.This phenomenon is commonly referred to as progressivefailure. In addition, fp depends strongly on the level ofmean effective stress p, which varies from point to pointinside the backfill and evolves continuously during wallmovement. It should also be noted that, given that retainingwalls have a much larger length than width, the deformationof the backfill and foundation soil happens under plane-strain conditions (so the CS friction angle is the plane-strainCS friction angle (Loukidis and Salgado 2009)). Given thatthe friction angle varies from point to point in the backfill,the representative f value to be used in KA calculationmethods assuming perfect plasticity and associated flow isunknown; it cannot be determined precisely based on intu-ition or judgment.Let us idealize the gravity wall initial condition as one in

which there has been no horizontal movement; as a result,the coefficient of lateral earth pressure K is equal to its at-rest value (K0). If we allow the wall to move away from thebackfill, K first decreases to a minimum value KA, min (pointM in Fig. 1) and then increases to an ultimate (residual)value KA, cr (point C in Fig. 1). Between points M and C, thesupported soil is in an active state. Point M is associated withan active state for which the average mobilized f in the sup-ported soil is closer to fp than fc. Point C is associated withfull mobilization of CS (f fc) along all failure surfaces(shear bands) formed in the retained soil.To design a wall, we are interested in the value of KA at a

limit state (KA, LS), which is not necessarily equal to eitherKA, cr or KA, min. At present, there are two approaches to deter-mine KA (Salgado 2008), one based on calculations using anestimate of fp and the other using an estimate of fc. The for-mer approach, which is most common in practice, wouldunderpredict the active earth pressure on the wall at the limitstate, making it unconservative. On the other hand, using fcmay be overly conservative, since a well-designed wall wouldnot move as much as to cause more than 20% shear strain inthe shear bands developing in the backfill before the wallreaches its limit state (Salgado 2008). The following sectionexamines in more detail what happens between points M andC, and what would constitute an appropriately defined ULSfor a gravity wall.

Wall limit state (WLS)To establish KA, LS, we need first to establish a way to

identify the ultimate WLS. We must stress that, in establish-ing a limit state, we are unconcerned with what the value of

Loukidis and Salgado 79

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the factor of safety (FS) would be to account for design un-certainties and with serviceability limit states, which must behandled separately. At early stages of wall movement awayfrom the backfill, the total horizontal resistance Hr and mo-ment resistance Mr increase at high rates, since the strains inthe foundation soil are still small and the soil stiffness istherefore large. At the same time, the driving horizontal forceHd and moment Md either decrease, as the earth pressure co-efficient decreases from K0 to KA, min, or increase at smallrates after the earth pressure coefficient bottoms and starts toincrease from KA, min to KA, cr (Fig. 1). The variations of thesequantities with wall displacement can be written mathemati-cally as dHr > dHd and dMr > dMd. Beyond a certain pointin the process (e.g., a certain amount of wall crest displace-ment u), the resistance starts increasing at a lesser rate thanthe driving action. This happens first for one of the two resis-tances (Hr or Mr), so that this stage of the loading process ismathematically identified as the state at which either dHr 1, the wall is stable, meaning that equilibrium(Hd = Hr and Md = Mr) is reached before the stationary stateor limit state is reached (Fig. 1). Artificial external forceswould need to be applied to the wallsoil system to bring itto the limit state, which we define as identical to the station-ary state first reached by the wall (i.e., if, by the addition ofexternal force, the Hd Hr reaches its stationary state beforeMd Mr, then the limit state is defined by the horizontalforce, not moment). This is analogous to having a foundationelement (e.g., a footing or pile) supporting a vertical load Qdless than its limit bearing capacity. To bring the foundationelement to its bearing capacity ULS, we must apply an artifi-cial external force Qext to the foundation element until it col-lapses, which happens when the foundation resistance Qrattains its maximum value QL. At this stage, both the Qr ver-sus settlement curve and the Qext = Qr Qd versus settlementcurve reach stationary (maximum) points (since Qd is con-

Fig. 1. Evolution of coefficient of lateral earth pressure and total resisting horizontal force, Hr, and moment, Mr, and total destabilizing hor-izontal force, Hd, and moment, Md, with displacement of wall crest.

80 Can. Geotech. J. Vol. 49, 2012


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stant). In the case of a retaining wall, the load to be sup-ported is not constant because of the dependence of KA onwall displacement. Therefore, the WLS can only be identifiedby the stationary point of the Hr Hd (or Mr Md) versus ucurve and not of the Hr (or Mr) versus u curve. If FS < 1,Hd Hr (or Md Mr) is always greater than zero and thewall is unstable, meaning that artificial external forces wouldneed to be applied to the wall to establish equilibrium. Inother words, wall movement never manages to mobilizeenough resistance to balance driving forces. In this case, thestationary point corresponds to the minimum value of theseexternal forces or, equivalently, the maximum value of Hr Hd (or Mr Md). The WLS is therefore the state at whichthe rate of increase (mobilization) of wall base resistance (interms of either force or moment) becomes smaller than therate of increase of the destabilizing actions (mainly the earththrust).The goal of this paper is to study the evolution of KA with

wall displacement and establish an indication of the KA value(and the appropriate f value for its calculation) at WLS con-ditions. For this purpose, we perform FE analyses of the re-taining wall stability problem using a two-surface constitutivemodel for sands, which is based on CS soil mechanics. TheFE analyses are performed for a rigid gravity wall with arough vertical backface supporting soil with level surfaceand purely frictional nature. The analyses apply to the typicalcase of backfilled walls but also to walls retaining naturalground if sandy or gravelly in nature. Both the retained soiland foundation soils are sands. The analyses do not simulatethe several complex stages involved in the construction ofgravity walls (such as backfill laying and compaction), whichwould lead to different initial stress conditions, but such isnot the focus of the analyses, which aim instead at bringingout the details of the mechanics of wall loading not ad-dressed in the literature and the implications and insightsthat they offer.

FE methodology

FE meshThe analyses use unstructured meshes consisting of eight-

noded, plane-strain quadrilateral elements with 12 quadraturepoints. A typical FE mesh is shown in Fig. 2. It includes thewall, the backfill soil, and the foundation soil. The wall hasa rectangular cross section, with width B and height H. Thethickness of the backfill soil layer is equal to H. The retain-ing wall is embedded a distance D into the foundation soil.All analyses start from an ideal state of the retained soil,reached without the wall having moved or rotated (as if thebackfill soil had been placed in one lift instantaneously).The wall is modeled as a block of linear elastic materialwith very large Youngs modulus so that it can be consid-ered rigid.No interface elements are placed between the soil and the

wall; i.e., wall and soil share the same nodes along the corre-sponding contact planes. As a consequence, slippage betweenthe wall and backfill occurs due to the formation inside thesoil mass of a shear band parallel to the wall backface. Thisroughness condition is realistic given the rough materialscommonly used for gravity walls, such as masonry, concrete,and cribs containing stone.

It is well known that analyses involving materials thatsoften and follow a nonassociative flow rule suffer from theproblem of solution nonuniqueness. This means that, as themesh gets refined, the FE analysis results change, and con-vergence to a unique solution does not happen. To tacklethis problem, FE analyses should either employ a regulariza-tion approach (such as Cosserat or gradient plasticity) or usemeshes with element sizes consistent with the known shearband thickness. The thickness of the soil elements inside theshear bands simulating slippage between a rough structureand granular soil is an important factor for the accurate pre-diction of the shear resistance acting on the structure (Louki-dis and Salgado 2008). Hence, the thickness of the backfillsoil elements that are in contact with the wall backface is setequal to 520 times the mean particle diameter of the sand(D50). This is roughly the thickness of the shear bands thatform in sandy soils, as observed in a number of experimentalstudies (e.g., Uesugi et al. 1988; Vardoulakis and Sulem1995; Nemat-Nasser and Okada 2001). Due to restrictions inmemory allocation and analysis runtime, the element sizes inother locations where shear bands are expected to develop (i.e.,inside the sliding wedge and in the foundation soil) werelarger than 520D50. Element size inside the sliding wedgeforming behind the wall was of the order of 500D50. Asshown later in the paper, this choice of the element sizehas only a small impact on the analysis accuracy.

Constitutive modelThe constitutive model used in this study is the two-surface

plasticity model based on CS soil mechanics developedoriginally by Manzari and Dafalias (1997). The model wassubsequently modified by Li and Dafalias (2000), Papadimi-triou and Bouckovalas (2002), Dafalias et al. (2004), andLoukidis and Salgado (2009). The model parameters weredetermined by Loukidis and Salgado (2009) for two sands:air-pluviated or dry-deposited Toyoura sand (Iwasaki et al.1978; Fukushima and Tatsuoka 1984; Lam and Tatsuoka1988; Yoshimine et al. 1998) and water-pluviated or slurry-deposited clean Ottawa sand (Carraro et al. 2003; Carraro2004; Murthy 2006; Murthy et al. 2007). Toyoura sand isa fine sand (D50 0.2 mm) with angular to subangular par-ticles, while Ottawa sand is a medium-sized sand (D50 0.4 mm) with rounded to subrounded particles. The modelconsiders four distinct surfaces having the form of opencones in stress space: the bounding surface, dilatancy sur-face, CS surface, and yield (loading) surface. Bounding andcritical surfaces represent peak and CS shear strengths, re-spectively. The dilatancy surface divides the stress spaceinto two regions: inside the dilatancy surface, the soil plas-tic behavior is contractive; outside it, it is dilative. Theyield (loading) surface defines a very narrow conical do-main inside which the soil develops no plastic strain. Theyield surface hardens kinematically upon shearing, leadingto the development of plastic strains prior to failure.Through this feature, the model simulates accurately the be-havior of the soil at small and large strains. The constitutivemodel takes into account the inherent anisotropy of sandsthrough the use of a fabric tensor (Dafalias et al. 2004),and the assumption that the position of the CS line in thevoid ratio (e) mean effective stress (p) space depends onthe direction of loading relative to the axis of sand deposi-



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tion. It also accounts for the dependence of the soil friction an-gle on the intermediate principal stress ratio b (stress-inducedanisotropy). Details of the constitutive model formulation,the determination of its input parameters, and its use insimulating element response in laboratory tests can befound in Loukidis and Salgado (2009). The parameter val-ues for the two sands considered in this study are shownin Table A1 in the appendix along with a short summaryof their role in the model.

FE algorithmsThe FE analyses were performed using the open-source

code SNAC (Abbo and Sloan 2000). The stressstrain rateequations of the constitutive model were integrated using asemi-implicit Euler algorithm with subincrementation and er-ror control, details of which can be found in Loukidis (2006),

and a relative stress error tolerance of 0.01%. The FE analy-ses were performed using the modified NewtonRaphsonglobal solution scheme, with the elastic stiffness matrix asthe global stiffness matrix.All analyses start with an initial stage in which the geo-

static stress field is established in the FE mesh. The geostaticstage includes two phases. In the first phase, gravity is ap-plied to the mesh as a body force loading, and a uniformpressure equal to g(H D) is applied on the free surface ofthe soil in front of the wall. These loadings are applied inone increment (i.e., instantaneously). In addition, a geostaticstress state is prescribed at every Gauss-quadrature point inthe mesh. The kinematic hardening stress (normalized back-stress) tensor of the constitutive model is initialized so thatthe stress state lies at the axis of the conical yield surface(the initial stress state is inside the elastic domain). Becausethe initial vertical stress values are set to be consistent withapplied gravity loading, equilibrium is reached instantlythrough the execution of a single global solution step. In thenext phase, the uniform pressure acting on the free surface ofthe soil in front of the wall is removed in a small number ofsolution increments. During creation of the geostatic stressfield, the wall is not allowed to move horizontally but is freeto move vertically. The geostatic stage is followed by themain analysis stage during which the wall is allowed tomove according to the scheme described next.

Wall loadingTo achieve the goals of this study, we must be able to im-

pose large wall displacements from the initial position inwhich the wall is in equilibrium with soil in an at-rest condi-tion. In the beginning of the analysis, the wall is fully sup-ported at two points, namely the crest (node C) and the toe(node T), shown in Fig. 2, where the corresponding horizon-tal reactions are RC,0 and RT,0, respectively (Fig. 3). These arethe forces required for full equilibrium, given the tractionsexerted on the wall by the surrounding soil at rest. Equiva-lently, the wall is prevented to move horizontally or rotate be-

Fig. 2. Typical mesh and boundary conditions used in the FE analyses. DOF, degree of freedom.

Fig. 3. Schematic showing the forces acting on the wall, includingthe reactions, on nodes C and T due to the applied displacement onthese nodes. EA, x, EA, y, horizontal and vertical components of theactive earth thrust, respectively; Fx, horizontal foundation reaction;Fy, vertical foundation reaction.



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cause of the external application of a horizontal force Fext,0 =RC,0 + RT,0 and a moment Mext,0 = RC,0/H. The analysis pro-ceeds by the application of outward horizontal displacementincrements DuC and DuT (i.e., displacements pointing awayfrom the backfill) at nodes C and T (Fig. 3), while monitor-ing the values of external force Fext = RC + RT, where RCand RT are external reactions, and external moment Mext =RC/H. Applying static equilibrium principles, the excess ofthe driving forces throughout the process of wall movementmust be balanced by artificial external forces, which exist ex-clusively for the purpose of performing the analysis. It can beshown that Fext = Hd Hr and Mext = Md Mr, given that theunbalanced forces at the end of each increment of theNewtonRaphson solution are minimal (less than 1% of theexternal forces). As the wall moves, Fext and Mext decreaseprogressively. The wall is allowed to move vertically, sinceno restraints are imposed on its nodes in the vertical direc-tion. The prescribed displacements uC and uT are not constantduring the analysis and are not equal to each other. Theirmagnitude varies in such a way that Fext and Mext (and conse-quently RC and RT) change in the same proportion. This isachieved by setting DuT = 0 (a pure rotation step) after anyanalysis increment, resulting in Mext/Mext,0 > Fext/Fext,0, andDuT = DuC (a pure translation step) after any analysis incre-ment, resulting in Mext/Mext,0 Fext/Fext,0. This scheme relieson the fact that the wall rotation has a stronger effect on therate of increase of Mext than of Fext, while wall translation hasa stronger effect on the rate of increase of Fext than of Mext.The increment DuC is always equal to a specified value ofthe order of 106H. Hence, the analyses consist of alternatingphases of pure wall rotation and pure wall translation. Appli-cation of the loading in this manner, combined with the veryfine incrementation used in the present analyses, results inMext/Mext,0 Fext/Fext,0 (both ratios thus denoted by the singlevariable Y) throughout the analysis. As a result, if the wall isstable or marginally stable, Mext and Fext become equal tozero simultaneously at which point the wall is completely un-supported by external reactions (which means that this be-comes a point of equilibrium at which the wall comes to arest). In addition, Mext/Mext,0 and Fext/Fext,0 reach their mini-mum value (Ymin) simultaneously, which happens whendMd = dMr and dHd = dHr. Therefore, referring to our pre-vious discussion of the WLS, Ymin is reached at the WLS.It should be noted that there is an infinite number of load-

ing path formulations that can bring the wall to a limit state,and the formulation presented here is just one of them. Thepresent wall loading formulation makes it possible to performdisplacement-controlled analyses, instead of load-controlledanalyses that drive the wall to its limit state by increasingthe soil unit weight or a surcharge pressure. Displacementcontrolled analyses allow the wall to move beyond the limitstate all the way to CS (a requirement of this study) for allpossible outcomes (stable, marginally stable, and unstablewalls). In contrast, load-controlled analyses cannot proceedpast the point of limit state. This is because any increase ofthe applied load past this point results in unbalanced forcesthat cannot be mitigated, since they increase with eachNewtonRaphson iteration. The formulation used here offersalso simplicity, allowing clear understanding of the mechan-ics involved and straightforward derivation of conclusions

for a practical problem that is considerably complex once ex-amined using rigorous mechanics.In most field cases, the active state will be mobilized grad-

ually, and the wall base will translate and rotate as the back-fill is constructed before reaching full height. Moreover, thebackfills placed behind gravity walls in practice are com-pacted, resulting in initial stress conditions in each layerlarger than the K0 conditions assumed in this paper due tolocked-in stresses (which are difficult to simulate, requiringthree-dimensional FE analysis). These factors would generatedifferent stress paths in the soil mass than those produced inour analyses. Problems involving materials that soften andfollow a nonassociative flow rule exhibit path dependence, i.e.,the results depend on the stress paths followed at the stressintegration points of the mesh. Hence, it is expected thatthe results of these analyses would be somewhat differentif the exact backfill construction process were simulated.However, discrepancies due to wall motion during backfillconstruction are believed to be small because most of thewall displacement will occur when the backfill height isnear the wall height, since the earth thrust increases at leastquadratically with the rate of backfill height, taking alsointo account that the soil friction angle would decrease dueto the increase in mean effective stress as the backfill rises.Discrepancies due to non K0 initial conditions would existmostly during the early stages of the predicted response, de-creasing as the active state were approached.

Results of FE simulations

Finite element analyses were performed for values of wallwidth B, ranging from 1.5 to 3 m and wall height rangingfrom 6 to 8 m. The sand unit weight g was set equal to18 kN/m3. The wall unit weight was also set equal to 18 kN/m3,which corresponds more closely to the unit weight of ma-sonry, gabion, or a crib wall rather than a concrete wall.The coefficient K0 was set equal to 0.5 in all analyses. Nosurcharge is placed on the backfill free surface. The rangeof the wall dimensions was chosen such that the wall FS isnot excessively high or excessively low. As will be shownlater, the FS of the wall configurations analyzed is in the0.52.0 range. Analyses are performed for Toyoura and Ot-tawa sands, with relative density DR ranging from 30% to90%. For the sake of simplicity, the foundation soil is as-sumed to be of the same type and density as the backfillsoil.

Collapse mechanism patternsMost of the analyses were performed with the loading

scheme described in the previous section, which subjects thewall to both rotation and horizontal translation in such a waythat the stabilizing external reactions RC and RT decrease pro-portionally to each other. For comparison purposes, analyseswere performed with both the wall rotating about its heelwithout translating horizontally (pure rotation case) andtranslating horizontally without rotating (pure translation).Figure 4 shows contours of the incremental maximum shearstrain gmax (= 1 3, where 1 and 3 are the major and mi-nor principal strains, respectively) from analyses with purerotation, pure translation, and combination of rotation and



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translation. The deformation patterns depicted in these plotscorrespond to states well beyond the WLS.The failure mechanism in the backfill consists of a wedge-

shaped sliding mass delimited by the wall backface and anoblique shear band originating from the heel of the wall.This shear band, which is nearly straight, with a slight curva-ture at its lower part, will be referred to in the remainder ofthe paper as the main shear band. A shear band running par-allel to the wall backface also forms in all analyses, repre-senting sliding between the backfill sliding mass (wedge)and the wall. In Figs. 4a and 4b, we see that families of sec-ondary shear bands develop inside the sliding wedge. One ofthe shear band families runs parallel to the main shear band.The shear bands of the other family form an angle with re-spect to the vertical of the same magnitude as the first familybut with opposite sign. This is consistent with observationfrom the experiments performed by Milligan (1974) and thenewly reinterpreted radiographs of those experiments byLeniewska and Mrz (2001), as well as from the FE analy-ses by Gudehus and Nbel (2004). The families of the secon-dary shear bands vanish when the wall movement is a puretranslation (Figs. 4c, 4d), although a few secondary shearbands that do not propagate fully, fading inside the slidingmass, still form. Gudehus and Nbel (2004) also show thatthe web of secondary shear bands inside the sliding wedgepresent in the problem of a rotating wall is absent in thecase of a purely translating wall.Below the wall base, a bearing capacity mechanism forms.

The shape of this mechanism resembles that of mechanisms

presented by Loukidis et al. (2008) for the case of surfacestrip footings on purely frictional elastic perfectly plasticmaterial loaded by eccentric and inclined loads. For analyseswith a wall movement that contains a translational component(Figs. 4b4d), the base mechanism is largely one-sided, con-sisting of a fan region and a passive wedge. The same type ofmechanism can be seen in the examples of Fig. 5. This isconsistent with failure patterns observed in footings subjectedto inclined loads irrespectively of the value of the load eccen-tricity (as long as the eccentric load lies on the side of thefooting base the horizontal component of the inclined loadpoints to). For a purely rotating wall (Fig. 4a), most of theshearing in the base failure mechanism is concentrated in ashear band that has the shape of a roughly circular arc, withits end points lying on the two edges of the wall base. Louki-dis et al. (2008) observed a similar pattern for footingsloaded by vertical eccentric loads.Figure 5 shows contours of the incremental gmax from

analyses of walls that translate and rotate (the main loadingscheme used in the present paper) with a retained mass ofloose and dense sands. It is evident that the inclination angleof the shear bands in the retained soil mass with respect tothe horizontal is larger in the case of dense than loose sand.Based on the contours shown in Fig. 5, the shear band incli-nation angle with respect to the horizontal is approximately65 for DR = 90% and 55 for DR = 45%. The inclinationfor 90% relative density is comparable to the values of theshear band inclination observed in the centrifuge experimentsof Wolf et al. (2005) in very dense sands simulating the Rankine

Fig. 4. Examples of contours of incremental gmax from analyses with a wall subjected to different modes of movement: (a) pure rotation;(b) rotation and translation; (c) pure translation (B = 3 m); (d) pure translation (B = 1.5 m).



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problem (smooth wall, horizontally unrestrained backfill base)for wall displacements similar to those in the present problem.Regarding the wall base failure mechanism, it is hard to

distinguish a separate passive failure mechanism in the soilin front of the wall above the wall base level. Any potentialpassive failure mechanism at the wall toe is fully encom-passed by the bearing capacity mechanism. Thus, the stressdistribution above the toe of the wall (Fig. 3) contributes tothe wall stability, not as a passive resistance independentof the resistance at the wall base but as part of the lateral ca-pacity of an embedded footing. This observation reinforcesthe notion that the resistance provided by the soil below thebase of the foundation and that in front of the wall arecoupled, meaning that the lateral resistance of the wall shouldbe analyzed as the problem of an embedded strip footing sub-jected to eccentric, inclined loading. This holds throughoutthe process of the loading of the wall, even when a limitbearing capacity mechanism has not yet formed.An analysis is also done for a backfill consisting of two re-

gions: a triangular region that is in contact with the wall back-face consisting of Toyoura sand with DR = 75% and theremaining soil consisting of loose Toyoura sand (DR = 45%),as shown in Fig. 6. Similar backfill cross section is frequentlyencountered in quay walls, where a granular material withlarge strength is placed in contact with the wall backface,with the goal of reducing the earth thrust that would be ex-erted on the wall if the backfill were made entirely of loose

fill sand. In Fig. 6, we see that the main shear band in thebackfill delimiting the sliding mass changes inclination at thepoint it crosses the boundary between the dense and loosesand layers. The inclination of the main shear band inside thedense sand and the loose sand is 66 and 57, respectively.

Earth pressure evolution with wall movementFigure 7 shows examples of the normal (horizontal) stress

distribution along the back of the wall. All analyses startfrom geostatic stress conditions (K = K0), and thus a triangu-lar stress distribution with depth. With increasing wall dis-placement, the horizontal stress decreases progressively untila minimum active pressure state (MPS) is reached. From thatpoint on, the average horizontal stress increases, but at amuch lower rate than the rate at which it decreased earlier.Before the MPS, the stress distribution is smooth; afterwards,local peaks and valleys develop. This is a consequence of bi-furcation and the shear banding that develops inside the slid-ing mass. The local minima in the stress distributions roughlycoincide with the intersection of secondary shear bands withthe wall backface.In all three analyses shown in Fig. 7, the stress distribution

before the minimum active state is reached is intenselycurved at the lower third of the wall height. In fact, beyonda certain depth, the horizontal stress decreases with depth, aconsequence of soil arching, as noted by other authors (e.g.,Handy 1985; Paik and Salgado 2003). The curvature of the

Fig. 5. Contours of incremental gmax from analyses with dense and loose (a, c) Ottawa sand and (b, d) Toyoura sand.



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stress distribution in the case of a nonrotating wall (Fig. 7c)is more pronounced and happens at a shallower depth than inthe analyses with rotating walls (Figs. 7a, 7b). As a conse-quence, the point of application of the horizontal earth thrustfor translating walls is higher than for rotating walls. This isconsistent with observations from experimental (Fang andIshibashi 1986) and numerical (Potts and Fourie 1986; Dayand Potts 1998) studies. After the minimum active state, thecurvature of the stress distribution decreases, and the averagedistribution resembles again a triangular distribution, exceptfor purely translating walls.The evolution of the lateral earth pressure coefficient K

with crest displacement uC is shown in Figs. 8 and 9. The Kcoefficient is calculated from the lateral earth thrust, which isin turn calculated by integrating numerically the horizontalstress across the entire height of the wall. The stresses aretaken at the centroid of the elements that are in contact withthe wall. The results shown in Fig. 8 are all for Toyoura sandwith 60% relative density but different values of H, B, and D.All analyses shown, except one, are for a wall subjected toboth translation and rotation. The K drops sharply towards aminimum value (KA, min) at uC approximately equal to 0.003Hand, subsequently, rises smoothly, approaching an asymptoticvalue (KA, cr) related to the development of CS in the mainshear band and inside the sliding wedge. According toFig. 8, KA, min and KA, cr are practically independent of thewall dimensions and the embedment, which seem to only af-fect the rate of increase towards CS. These differences in therate of increase are due to the resulting small differences inthe proportion of uT over uC between these analyses (i.e., dif-ferences in how much of the motion is translation versus ro-tation). The ratio uT/uC at the KA, min state (MPS) in the

analyses of Fig. 8 ranges from 0.17 to 0.28 and is roughlyproportional to the wall safety factor. Figure 8 also includesthe response from the analysis with a purely rotating wall,which is in sharp contrast with the other analyses. The KA, minfor the purely rotating wall is about 38% higher than for wallsthat both translate and rotate. More importantly, KA, min isreached at uC equal to 0.016H, a much larger displacementthan for the other curves in Fig. 8. Moreover, transition fromKA, min to KA, cr is more gradual, K appearing to be almost con-stant for a large range of uC values after the attainment of KA,min.Model tests by Fang and Ishibashi (1986) demonstrate thatMPS is easily attained for a purely translating wall, withonly 0.0004H of wall displacement (in our purely translat-ing wall analyses, the corresponding value is 0.001H). Incontrast, this state is not reached in a model test for a wallin pure rotation about its base, even with 0.008H of crestdisplacement. Large displacements for a purely rotating wall,of the order of 0.015H, were needed in the model tests byMilligan (1974) to reach the active state, which is comparableto the value of 0.016H resulting from the present analysis.Data reported by Fang and Ishibashi (1986) also supportthe fact that a purely translating wall and a wall that bothtranslates and rotates develop similar KA, min values, but theKA, min for a purely rotating wall is distinctively larger.These findings suggest that the absence of a translation

component in the wall movement has an important effect onthe KA, min. Observed differences between wall problems in-volving different movement modes are a consequence of thepath dependence and progressive failure inherent in problemsinvolving strain-softening materials. In contrast, analyses withperfectly plastic materials following the MohrCoulomb fail-ure criterion produce KA values that dont depend on the wall

Fig. 6. Contours of incremental gmax from analysis with composite backfill.



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Fig. 7. Examples of distribution of horizontal stress acting on thewall backface at different stages during analyses, with H = 7 m, B =1.5 m, and D = 0.5 m and different modes of wall movement:(a) Ottawa sand; (b, c) Toyoura sand.

Fig. 8. Variation of normalized lateral earth pressure coefficient withwall crest displacement from analyses with medium dense Toyourasand (DR = 60%).

Fig. 9. Variation of normalized lateral earth pressure coefficient withwall crest displacement from analyses of a wall that is allowed totranslate and rotate, with H = 7 m, B = 1.5 m, and D = 0.5 m:(a) Toyoura sand; (b) Ottawa sand.



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movement mode. As to the value of KA for a purely rotatingwall, Ichihara and Matsuzawa (1973) measured static KA of0.16 for Toyoura sand with DR = 85% for a smoother wallthan considered here. This value still compares well with thevalue of 0.172 for our analyses with purely rotating wall andDR = 60%.Finite element simulations for soils that strain soften and

follow nonassociated flow rules suffer from mesh depend-ence. To assess the accuracy of our simulations, an analysiswith element size equal to 100D50, instead of 500D50, in theregion the sliding wedge develops was performed, and resultsare also compared in Fig. 8. The differences between thecurves from the fine mesh analysis and the correspondingcoarse mesh analysis do not exceed 8%.Figure 9 shows the K/K0 evolution resulting from analyses

with the same wall configuration (H = 7 m, B = 1.5 m, D =0.5 m) for Toyoura and Ottawa sands with different values ofrelative density. The figure also shows the KA/K0 value re-sulting from FE analyses for an elastic perfectly plasticsoil following the MohrCoulomb failure criterion (MCanalyses) with f fc and j = 0 using the same code andloading scheme as the main series of analyses. The fc forplane-strain conditions (i.e., fc; PS) for Toyoura and Ottawasand predicted by the two-surface constitutive model de-scribed earlier is 36.6 and 34.6, respectively. These valuesare roughly 45 larger than the fc values for triaxial com-pression conditions (31.6 and 30.2, respectively). To placethe KA calculated from fc in this manner in context, addi-tional results are shown in Table 1. These results includethose of MC analyses for associated flow (j = f) and non-associated flow with j = 0 as well as the correspondinglimit analysis lower and upper bounds. The results for an as-sociated flow rule are inside the lower and upper bounds.The KA values for j = 0 are about 18% greater than thosefor associated flow and lie above the KA range delimited bythe limit analysis bounds. As discussed in the introduction,limit analysis holds for an associated flow rule, and numeri-cal analysis is currently the only way to arrive at solutionsvalid for problems with j

Table 1. KA/K0 from FE analyses with elastic perfectly plastic soil and corresponding limit analysis lower and upper bounds.

FEM (elastic perfectly plastic) Lower bound

(Lancellotta 2002)Upper bound(Chen 1975)*

Upper bound (Soubra andMacuh 2002)*f () j = f j = 0

36.6 0.403 0.480 0.404 0.393 0.39634.6 0.437 0.505 0.444 0.432 0.436

Note: FEM, finite element method.*Interpolated values based on plotted or tabulated data.

Fig. 10. Evolution of key problem variables with increasing wall crest displacement for (a) loose and (b) dense Toyoura sand and wall withH = 7 m, B = 1.5 m, and D = 0.5 m. Deax/H, relative height of active thrust application; FSH, FS based on horizontal equilibrium; FSM, FSbased on moment equilibrium; m (= tand), mobilized friction coefficient at wall backface.



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only at very large wall displacements (Figs. 10a and 11a).The WLS is reached when the slow base resistance develop-ment can no longer match the increase in destabilizing ac-tions due to the increase of KA towards KA, cr. The WLS canbe described mathematically as the state at which dHr = dHdor dMr = dMd; beyond the WLS, gains in resistance do notmatch gains in driving forces (i.e., dHr < dHd or dMr 0 and dMd > 0) with wall dis-placement past the KA, min state. As a consequence, the walldisplacement required to reach the WLS is smaller than thatrequired to reach base failure.Although WLS and base failure state occur at distinctively

different wall crest displacements, the Hb and Mb values atWLS are practically identical to the peak Hb and Mb values.This occurs because, after attainment of the WLS, Hb and Mbincrease at very small rates towards their peak values due tothe development of regions of intense plastic straining in thefoundation soil. Consequently, the peak Hb and Mb values,which can be determined in practice with relative ease based

Fig. 11. Evolution of key problem variables, with increasing wall crest displacement for (a) loose and (b) dense Ottawa sand and wall withH = 7 m, B = 1.5 m, and D = 0.5 m.



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on bearing capacity calculations, can be used as good ap-proximations of the values of Hb and Mb at the WLS.Table 2 summarizes the values of certain key variables of

interest in design at the state of minimum active pressure andat the WLS: the normalized coefficient KA/K0, the mobilizedfriction angle at the wallbackfill interface dmob, normalizedcrest displacement uC/H, and the relative height Deax/H ofthe point of application of the active earth thrust from theheel of the wall. Table 2 also contains the value of the FSmobilized at the WLS. The reported FS is taken as the small-est value of the FS against overturning FSM (based on mo-ment equilibrium about the wall toe) and sliding FSH(based on horizontal equilibrium). The FS values are calcu-lated using the following equations:

3a FSH X

stabilizing forcesXdestabilizing forces

HbEA; x

1 RC RTEA; x

3b FSM X

stabilizing momentsXoverturning moments

WB=2 MOb

EA; xDeax EA; yB 1RCH

EA; xDeax EA; yBwhere EA, x and EA, y are the horizontal and vertical compo-nents of the active earth thrust, W is the wall self-weight,Deax is the height from the base of the point of applicationof the earth thrust, and MOb is the moment of the base resis-tance taken about the toe of the wall (not to be confused withMb). The peak values of the mobilized FS values do not hap-pen at the WLS (Figs. 10 and 11). This is because the ex-trema of the FSH and FSM depend on the denominators ineqs. [3a] and [3b]. The minimum value Ymin would occur si-multaneously with the peak mobilized FS and the peak totalbase horizontal or moment resistance only if these denomina-tors were constant during the analysis.Figure 12 compares KA,min, KA, LS, and the inferred KA, cr val-

ues for analyses with rotating and translating walls. We see thatthe KA, LS values lie approximately halfway between the mini-mum and CS values of KA. The value of KA, LS is 25%80%greater than KA,min, with the differences increasing with increas-ing relative density. Figure 12a also plots results from analysesNos. 1317 (Table 2), which have different wall dimensions (H,B) and embedment D but the same sand relative density (DR =60%). Figure 12a indicates that the wall dimensions and embed-ment have a more pronounced effect on KA, LS than KA,min.

Wall displacement to reach characteristic statesThe ratio uC/uT, resulting from the loading scheme adopted

for the analyses of walls moving in both rotation and transla-tion, is in the 38 range for MPS. Beyond the MPS, uC/uTincreases a further 20%40% by the time the WLS isreached, remaining practically constant for the remainder ofthe analysis, with the exception of the simulation for DR =90% for which uC/uT can reach values in the 1012 range.In the analyses in which the wall is allowed to rotate and

translate, the crest displacement required for reaching theMPS is in the 0.003H0.006H range (Fig. 13), with the ex-Ta

ble2.

Summaryof

FEM

results

with

respectto

stateof

minim

umlateralearthpressure

coefficientandwalllim

itstate.

No.

Loading

mode

H(m

)W

(m)

DR(%

)D(m

)Sand

Minim

umK

Astate

WLS

KA,m

in/K

0d m

ob()

feq

fc;TX()

u C/H

Deax/H

KA,L

S/K

0

d mob

()

feq

fc;TX()

u C/H

Deax/H

FSFailu

remode

1Rot+hor

71.5

600.5

Toyoura

0.249

35.9

15.1

0.004

0.337

0.383

30.8

5.9

0.021

0.260

1.04

Horizontal

2Rotation

71.5

600.5

Toyoura

0.344

30.8

8.6

0.016

0.267

0.344

30.8

8.5

0.016

0.266

1.38

Mom

ent

3Horizontal

71.5

600.5

Toyoura

0.269

38.0

13.0

0.001

0.358

0.396

30.8

5.1

0.007

0.334

1.65

Horizontal

4Rot+hor

71.5

300.5

Toyoura

0.408

31.4

4.2

0.006

0.319

0.461

30.9

1.2

0.163

0.311

0.47

Mom

ent

5Rot+hor

71.5

450.5

Toyoura

0.321

34.1

9.6

0.003

0.325

0.407

30.8

4.4

0.032

0.290

0.62

Mom

ent

6Rot+hor

71.5

750.5

Toyoura

0.192

37.7

20.2

0.004

0.342

0.326

30.9

9.9

0.020

0.254

1.43

Horizontal

7Rot+hor

71.5

900.5

Toyoura

0.136

38.5

26.3

0.004

0.336

0.247

31.0

16.0

0.019

0.257

2.01

Horizontal

8Rot+hor

71.5

300.5

Ottawa

0.456

29.7

3.1

0.010

0.328

0.483

29.6

1.6

0.160

0.319

0.40

Mom

ent

9Rot+hor

71.5

450.5

Ottawa

0.374

31.3

7.8

0.006

0.324

0.472

29.6

2.2

0.054

0.296

0.50

Mom

ent

10Rot+hor

71.5

600.5

Ottawa

0.304

31.8

12.7

0.006

0.327

0.391

29.6

7.1

0.025

0.292

0.82

Mom

ent

11Rot+hor

71.5

750.5

Ottawa

0.239

31.7

18.0

0.006

0.330

0.306

29.6

12.9

0.015

0.292

1.23

Horizontal

12Rot+hor

71.5

900.5

Ottawa

0.178

31.7

23.7

0.006

0.329

0.240

29.8

18.2

0.013

0.300

1.73

Horizontal

13Rot+hor

61.5

600.5

Toyoura

0.250

37.7

14.7

0.003

0.335

0.370

30.8

6.8

0.021

0.269

1.42

Horizontal

14Rot+hor

81.5

600.5

Toyoura

0.257

36.1

14.4

0.003

0.332

0.342

30.8

8.7

0.018

0.286

0.66

Mom

ent

15Rot+hor

72.0

600.5

Toyoura

0.248

37.9

14.9

0.003

0.340

0.405

30.8

4.5

0.023

0.260

1.49

Horizontal

16Rot+hor

72.5

600.5

Toyoura

0.248

36.6

15.1

0.003

0.337

0.399

30.8

4.9

0.020

0.269

1.98

Horizontal

17Rot+hor

71.5

600.2

Toyoura

0.247

38.0

15.0

0.003

0.344

0.349

30.8

8.2

0.021

0.277

0.83

Mom

ent

18Rot+hor

71.5

75+45

0.5

Toyoura

0.195

33.9

20.4

0.005

0.354

0.270

30.8

14.1

0.015

0.306

1.38

Horizontal

Note:

Rot+hor,rotatio

nandhorizontal;fc;TX,C

Sfrictio

nanglecorrespondingto

triaxial

compression

conditions;feq,equivalentsand

internal

frictio

nangle.



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ception of Ottawa sand, with DR = 30%. According to theCanadian Geotechnical Society (1992), the uC required fordeveloping the active earth pressure corresponding to peaksoil strength (i.e., uCp) is 0.001H for dense and 0.004H forloose sand. Our results are of the same order of magnitudebut dont exactly match the values proposed by the CanadianGeotechnical Society (1992). In addition, our analyses sug-gest that the relative density has no significant effect on uCpunless the tendency for strain softening is very weak to prac-tically absent (e.g., DR = 30%). One would expect that uCpshould decrease with increasing relative density as the failurestrain decreases with increasing relative density in laboratorytests, which in turn is due to the fact that the sands stiffnessincreases with relative density. However, in the present prob-lem, the stress and deformation conditions vary in both the

horizontal and vertical directions, in contrast with laboratorytests. In Fig. 9, we see that, as expected, the initial, roughlylinear, response prior to MPS is much stiffer for dense sandthan for loose sand. As K approaches KA, min, the responsebecomes nonlinear and is smoother for large DR values thanfor small ones. As a consequence, KA, min for dense sands isreached at roughly the same wall displacement as for looseand medium dense sands. This is a consequence of the pro-gressive failure developing prior to the attainment MPS. Theprogressive failure is evident by the fact that the mobilizedfriction angle on the wallsoil interface is very close to theCS value by the time MPS is reached, as demonstrated laterin the paper. Progressive failure is more intense in dense thanin loose sands, counterbalancing the effect of sand stiffnesson the wall displacement required to reach MPS.The crest displacement uC,LS required to reach WLS is in

the range of 0.013H0.026H, except for DR = 30%45%. Inaddition, for a given sand and relative density, the ratio uC,LS/uCp increases with increasing FS. The uC,LS lies in the rangeof displacements for which the wall foundation has not yetcollapsed (i.e., the peak base resistance has not yet beenreached) but is very compliant, yielding considerably foreven small changes in foundation load.In most of the analyses with a rotating and translating wall,

the crest displacement required to reach the peak Hb is in the0.01H0.09H range (corresponding to toe displacement of0.01B0.065B). The mobilization of the full horizontal basecapacity requires displacements that exceed those required toreach the WLS in the retained soil by 10%150%. The peak

Fig. 12. Minimum, limit state, and critical active earth pressurecoefficient from analyses with (a) Toyoura sand and (b) Ottawa sand.

Fig. 13. Wall crest displacement required to reach MPS (uCp) andWLS (uC, LS) from analyses with Toyoura and Ottawa sands. Analy-sis numbers follow the numbering shown in Table 2.



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moment base resistance requires even larger wall movementin all analyses performed in this study.

The variation of the earth pressure coefficient K with uCcan be described mathematically by the following equation:

4 K fc 1K0 KA; cr=K0 KA;min guCp cuCc 1uCp=K0 KA;min uCc=KA; cr KA;min uCpc1 KA; cr

The input parameters in eq. [4] are the characteristic valuesfor the earth pressure coefficient, K0, KA, cr, and KA, min, thecrest displacement uCp at which KA, min is attained, and a fit-ting parameter c. According to eq. [4], K is equal to K0 foruC = 0 and tends to KA, cr asymptotically for large values ofuC. The parameter c is introduced to control the rate at whichK increases towards KA, cr after the attainment of KA, min. Byfitting eq. [4] to the results of this study, shown in Figs. 8and 9, we obtain c in the 1.72.1 range, with an averagevalue of two. An estimate of the KA, LS to use for wall designcalculations could be obtained using eq. [4], with c = 2.0,uC = 0.025H for medium dense and dense sands, and 0.06Hfor loose sands.

Point of application of lateral earth thrustAn important parameter for retaining wall stability calcula-

tions is the location along the wall height at which the lateralearth thrust EA, x acts. Figure 14 shows the values of the ver-tical distance Deax of the point of application of EA, x from thewall base obtained from the analyses of a wall that both ro-tates and translates. We see that, for the MPS, Deax is roughlyequal to the widely used value of (1/3)H. Beyond that state,Deax starts decreasing, reaching a minimum value almostcoincidentally with the WLS. This decrease is negligible forloose sand, but it can be up to 25% for dense sand. Thevertical distance Deax subsequently increases but at a verysmall rate.The same trends of Deax with increasing wall displacement

were observed in the experiments of Fang and Ishibashi(1986). Specifically, for a purely rotating wall, Deax starts de-creasing from an initial value of 0.333H towards a minimumvalue of 0.22H and then rises slowly (but never exceeding0.28H, even at uC = 0.008H). Similar trends are found inIchihara and Matsuzawa (1973). Fang and Ishibashi (1986)also present data that supports the fact that Deax for purelyrotating walls is less than 0.3H, while it is around H/3 if themotion has a translational component.

Mobilized resistance along wallbackfill interfaceThe mobilized friction coefficient m (= tand) on the wall

face reaches a peak value at very early stages of the analyses,before the attainment of the MPS, suggesting the verticalshear band along the wall backface forms well before themain shear band delimiting the sliding wedge. This peakvalue is strongly dependent on the relative density of thesand (Figs. 10 and 11). After the peak, m decreases quicklytowards a residual value that is consistent with the develop-ment of CS (f fc;PS, j = 0) inside the thin backfill soilelements that are in contact with the wall. The residual valuesfor the angle d are 30.8 and 29.6 for Toyoura sand and Ot-tawa sand, respectively. These are consistent with the theoret-ical values calculated as dc = arctan(sinfc;PS) (Loukidis andSalgado 2008). Although the vertical shear band along the

wall backface forms well before the main shear band, the mo-bilized frictional angle dmob at MPS is clearly larger than dc(Fig. 15) for both rotating and translating walls and purelytranslating walls. The ratio dmob/dc ranges from 1.0 to 1.07for Ottawa sand, while for Toyoura sand, it ranges from 1.02to 1.25 (corresponding to dmob from 31.4 to 38.5). The uCpfor a purely rotating wall is so large that, by the time MPS isreached, dmob has become equal to dc.

Equivalent value of sand friction angle for calculation ofKA at limit stateIt is of practical interest to assess what the appropriate

(equivalent) value of the sand internal friction angle feq is foruse in the calculation of KA,min and KA, LS using an analyticalformula widely used in practice, such as Coulombs solution(eq. [1]), to obtain a value of KA, LS that is in agreement withthe present numerical simulations. Figure 16 shows the differ-ence between feq and the CS friction angle fc;TX correspondingto triaxial compression conditions. The feq values are back-calculated using eq. [1] from the KA values resulting fromthe FE analyses. We consider fc;TX instead fc;PS because itis easier to estimate it through either empirical relationshipsor a few triaxial compression tests. Even the frequently per-formed shear box tests would yield fc estimates that arecloser to fc;TX than fc;PS. According to Fig. 16a, the feqfor MPS is 326 larger than fc;TX, depending on the valueof the sand relative density. However, for calculating KA, LS,feq is only 118 larger than fc;TX (Fig. 16b). Figure 16bshows that existing walls are not necessarily poorly designed,even if the design is based on the prevailing practice of as-suming the soil to be perfectly plastic with a peak value of(triaxial compression) friction angle to calculate KA: practi-tioners would rarely use friction angles exceeding fc;TX bymore than 15 for a dense sand or more than 2 for a loosesand. So, whether by accident or proper intuition and judg-ment by engineers working on this problem years ago, stand-ard practice uses friction angles that are roughly consistentwith WLS rather than the state of mobilization of peakstrength in the backfill. Figure 17 shows the difference be-tween feq and the CS friction angle fc;PS corresponding toplane-strain conditions. The values plotted in Fig. 17 areabout 4.55 smaller than those in Fig. 16. In Fig. 17b, wesee that, for loose sand, feq for KA, LS is smaller than fc;PS.At first sight, this would seem to be a violation of the basicprinciple of soil mechanics that the minimum value of thesand friction angle is that for CS, but all analytical methodsfor calculating KA presented in the introduction produce re-sults that are valid for an associated flow rule (f = j) and,thus, underestimate the actual KA by roughly 20% (see Table 1).On the other hand, the FE simulations discussed in this paperuse a model that captures the sand dilatancy realistically. Hadwe had a formula that predicted KA for realistic j values, allresulting feq fc;PS values would have been positive.



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ConclusionsThis paper presents the results of a set of FE analyses of a

gravity wall subjected to the action of a mass of sand that thewall initially retains at a state of rest. After the wall is al-lowed to move due to the action of the retained soil mass,the pressures on the wall evolve towards active pressures.Based on the FE results and focusing on walls that are freeto rotate and translate, we arrive at the following conclusions:

1. The attainment of the minimum value of the active earthpressure coefficient (KA, min) requires wall crest displace-ments of the order of 0.001H0.010H.

2. The attainment of KA, min corresponds to a mobilized wallsoil interface friction angle d that is larger than the CSinterface friction angle dc by a factor ranging from 1.0(loose sand) to 1.3 (dense sand).

3. For dense and medium dense sand, the crest displacementrequired to bring the wall to its limit state is in the0.013H0.026H range. At the WLS, the mobilized inter-face friction angle has already reached the CS value of dc.

4. The limit state KA (KA, LS) lies between KA, min and thecorresponding CS value KA, cr. The KA, LS values are lar-ger than KA, min by a factor of 1.11.8, with the differ-ences increasing with increasing relative density.

5. The WLS does not necessarily coincide with the mobiliza-tion of the maximum base resistance, which may requiremuch larger wall displacements.

6. The height of application of the lateral earth thrust at limitstate conditions is less than one-third, ranging from 0.25to 0.32, suggesting that the current design practice isslightly conservative.

7. The equivalent friction angle to be used for the calculation ofKA values consistent with WLS design can be up to 18higher than the soil CS friction angle under triaxialcompression conditions.The results regarding the WLS depend on the base stiff-

ness and strength. Hence, our findings regarding the WLSare strictly applicable to foundation soils that are like the re-tained soil (i.e., purely frictional soils). It is expected that, forwalls founded on stiff clay or weak rock, the WLS may coin-cide with or even precede the MPS and the WLS, given thehigh stiffness and brittleness of such geomaterials. Althoughin all analyses the foundation soil had the same relative den-sity as the backfill, the results are expected to hold even forcases in which the relative densities are different. This is be-cause the displacement required to reach KA, min is practicallyindependent of the density of the backfill (Fig. 9). In addi-tion, we see in Fig. 9 that the shape of the curves is thesame for all densities. Hence, what matters regarding the dis-placement required to attain WLS is the density of the foun-dation soil. Therefore, the displacement needed to attainWLS for a loose backfill will not be much different fromthat for a dense backfill as long as the density of the founda-tion soil is the same.From a practical standpoint, this study suggests that the

minimum active earth pressure state is of limited relevanceto ULS design, since it happens for wall crest displacementsof the order of only 0.5% the wall height; it is possibly repre-sentative of a serviceability limit state (SLS). Given that theactive earth pressure coefficient is a function of the wall dis-

Fig. 14. Vertical distance of point of application of active earth thrustfrom wall base at (a) minimum earth pressure state and (b) WLS.

Fig. 15. Ratio of d mobilized along wallbackfill interface at mini-mum earth pressure state to d corresponding to CS conditions.



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placement, existing wall design methods can benefit in thefuture from a focus on estimating KA, using as reference thewell-defined CS. For example, KA could be calculated usingwell-established formulas (e.g., Coulombs equation) withrepresentative f values estimated based on DR and fc;TX andplots such as that of Fig. 16b. The interface friction angle dcan be conservatively set equal to the corresponding CSvalue dc to calculate KA for all characteristic states (MPS,WLS, and CS). Alternatively, the KA for ULS could be calcu-lated using equations such as eq. [4], with KA, cr, KA, min, uc,and uCp as input. The coefficient KA, min could be calculatedusing plots such as that of Fig. 16a, while KA, cr, which is aninvariant, could be directly calculated using fc;PS ( fc;TX +4). According to Fig. 13, uCp is practically 0.005. The dis-placement uc can be set equal to the desired crest displace-ment value compatible with an ULS established according todesign code provisions.

The present FE analyses demonstrate that the toppling,sliding, and vertical bearing capacity failure modes arecoupled. Wall stability can be assessed by considering twoequilibrium checks, one pertaining to horizontal equilibriumand one to moment equilibrium, where the KA estimated us-ing such equations or plots will be the basic input. The useof equilibrium checks with partial load and resistance orstrength factors accounting for the uncertainties of the prob-lem variables (as in load and resistance factors design (LRFD)or partial factors design (PFD)) instead of global FS checks(as in working stress design (WSD)) constitute the basis ofmodern codes. In these equilibrium checks, the horizontaland moment wall base resistances should be establishedbased on the appropriately factored bearing capacity failureenvelop of an embedded strip footing subjected to eccentricand inclined (i.e., combined) loading. Following this ap-proach, a vertical equilibrium check is redundant.

Fig. 17. Difference of equivalent value of friction angle to be usedin calculation of KA from CS friction angle in plane-strain condi-tions at (a) minimum earth pressure state and (b) WLS.

Fig. 16. Difference of equivalent value of friction angle to be usedin calculation of KA from CS friction angle in triaxial compressionconditions at (a) minimum earth pressure state and (b) WLS.



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ReferencesAbbo, A.J., and Sloan, S.W. 2000. SNAC. User manual. Version 2.0

[computer program]. Department of Civil, Surveying and Environ-mental Engineering, University of Newcastle, Callaghan, Australia.

Canadian Geotechnical Society. 1992. Foundation engineering manual.Canadian Geotechnical Society (CGS), Bitech, Vancouver, B.C.

Caquot, A., and Kerisel, J. 1948. Tables for the calculation of passivepressure, active pressure and bearing capacity of foundations.Gauthier Villars, Paris, France.

Carraro, J.A.H. 2004. Mechanical behavior of silty and clayey sands.Ph.D. thesis, Purdue University, West Lafayette, Ind.

Carraro, J.A.H., Bandini, P., and Salgado, R. 2003. Liquefactionresistance of clean and nonplastic silty sands based on conepenetration resistance. Journal of Geotechnical and Geoenviron-mental Engineering, 129(11): 965976. doi:10.1061/(ASCE)1090-0241(2003)129:11(965).

Chen, W.F. 1975. Limit analysis and soil plasticity. Elsevier SciencePublishers, B.V., Amsterdam, the Netherlands.

Dafalias, Y.F., Papadimitriou, A.G., and Li, X.S. 2004. Sandplasticity model accounting for inherent fabric anisotropy. Journalof Engineering Mechanics, 130(11): 13191333. doi:10.1061/(ASCE)0733-9399(2004)130:11(1319).

Day, R.A., and Potts, D.M. 1998. The effect of interface properties onretaining wall behaviour. International Journal for Numerical andAnalytical Methods in Geomechanics, 22(12): 10211033. doi:10.1002/(SICI)1096-9853(199812)22:123.0.CO;2-M.

Fang, Y.-S., and Ishibashi, I. 1986. Static earth pressures with variouswall movements. Journal of Geotechnical Engineering, 112(3):317333. doi:10.1061/(ASCE)0733-9410(1986)112:3(317).

Fukushima, S., and Tatsuoka, F. 1984. Strength and deformationcharacteristics of saturated sand at extremely low pressure. Soilsand Foundations, 24(4): 3048. doi:10.3208/sandf1972.24.4_30.

Gudehus, G., and Nbel, K. 2004. Evolution of shear bands in sand.Gotechnique, 54(3): 187201. doi:10.1680/geot.2004.54.3.187.

Handy, R.L. 1985. The arch in soil arching. Journal of GeotechnicalEngineering, 111(3): 302318. doi:10.1061/(ASCE)0733-9410(1985)111:3(302).

Ichihara, M., and Matsuzawa, H. 1973. Earth pressure duringearthquake. Soils and Foundations, 13(4): 7586. doi:10.3208/sandf1972.13.4_75.

Iwasaki, T., Tatsuoka, F., and Takagi, Y. 1978. Shear moduli of sandsunder cyclic torsional shear loading. Soils and Foundations, 18(1):3956. doi:10.3208/sandf1972.18.39.

Lam, W.-K., and Tatsuoka, F. 1988. Effects of initial anisotropic fabricand s2 on strength and deformation characteristics of sand. Soilsand Foundations, 28(1): 89106. doi:10.3208/sandf1972.28.89.

Lancellotta, R. 2002. Analytical solution of passive earth pressure.Gotechnique, 52(8): 617619. doi:10.1680/geot.2002.52.8.617.

Leniewska, D., and Mrz, Z. 2001. Study of evolution of shear bandsystems in sand retained by flexible wall. International Journal forNumerical and Analytical Methods in Geomechanics, 25: 909932. doi:10.1002/nag.160.

Li, X.S., and Dafalias, Y.F. 2000. Dilatancy of cohesionless soils.Gotechnique, 50(4): 449460. doi:10.1680/geot.2000.50.4.449.

Loukidis, D. 2006. Advanced constitutive modeling of sands andapplications to foundation engineering. Ph.D. thesis, PurdueUniversity, West Lafayette, Ind.

Loukidis, D., and Salgado, R. 2008. Analysis of the shaft resistanceof non-displacement piles in sand. Gotechnique, 58(4): 283296.doi:10.1680/geot.2008.58.4.283.

Loukidis, D., and Salgado, R. 2009. Modeling sand response usingtwo-surface plasticity. Computers and Geotechnics, 36(12): 166186. doi:10.1016/j.compgeo.2008.02.009.

Loukidis, D., Chakraborty, T., and Salgado, R. 2008. Bearingcapacity of strip footings on purely frictional soil under eccentricand inclined loads. Canadian Geotechnical Journal, 45(6): 768787. doi:10.1139/T08-015.

Manzari, M.T., and Dafalias, Y.F. 1997. A critical state two-surfaceplasticity model for sands. Gotechnique, 47(2): 255272. doi:10.1680/geot.1997.47.2.255.

Milligan, G.W.E. 1974. The behaviour of rigid and flexible retainingwalls in sand. Ph.D. thesis, University of Cambridge, Cambridge, UK.

Murthy, T.G. 2006. Undrained static response of sands with fines. Ph.D. thesis, Purdue University, West Lafayette, Ind.

Murthy, T.G., Loukidis, D., Carraro, J.A.H., Prezzi, M., andSalgado, R. 2007. Undrained monotonic response of clean andsilty sands. Gotechnique, 57(3): 273288. doi:10.1680/geot.2007.57.3.273.

Nemat-Nasser, S., and Okada, N. 2001. Radiographic and micro-scopic observation of shear bands in granular materials. Gotech-nique, 51(9): 753765. doi:10.1680/geot.2001.51.9.753.

Paik, K.H., and Salgado, R. 2003. Estimation of active earth pressureagainst rigid retaining walls considering arching effects. Gotech-nique, 53(7): 643653. doi:10.1680/geot.2003.53.7.643.

Papadimitriou, A.G., and Bouckovalas, G.D. 2002. Plasticity modelfor sand under small and large cyclic strains: a multiaxialformulation. Soil Dynamics and Earthquake Engineering, 22(3):191204. doi:10.1016/S0267-7261(02)00009-X.

Potts, D.M., and Fourie, A.B. 1986. A numerical study of the effectsof wall deformation on earth pressures. International Journal forNumerical and Analytical Methods in Geomechanics, 10(4): 383405. doi:10.1002/nag.1610100404.

Salgado, R. 2008. The engineering of foundations. McGraw-Hill,New York.

Sokolovski, V.V. 1965. Statics of granular media. Pergamon, Oxford,UK.

Soubra, A.-H., and Macuh, B. 2002. Active and passive earthpressure coefficients by a kinematical approach. Proceedings ofthe Institution of Civil Engineers Geotechnical Engineering,155(2): 119131. doi:10.1680/geng.2002.155.2.119.

Uesugi, M., Kishida, H., and Tsubakihara, Y. 1988. Behavior of sandparticles in sandsteel friction. Soils and Foundations, 28(1): 107118. doi:10.3208/sandf1972.28.107.

Vardoulakis, I. 1980. Shear band inclination and shear modulus ofsand in biaxial tests. International Journal for Numerical andAnalytical Methods in Geomechanics, 4(2): 103119. doi:10.1002/nag.1610040202.

Vardoulakis, I., and Sulem, J. 1995. Bifurcation analysis in geome-chanics. Blackie Academic and Professional, Glasgow, Scotland.

Wolf, H., Knig, D., and Triandafyllidis, Th. 2005. Centrifuge modeltests on sand specimen under extensional load. InternationalJournal for Numerical and Analytical Methods in Geomechanics,29(1): 2547. doi:10.1002/nag.403.

Yoshimine, M., Ishihara, K., and Vargas, W. 1998. Effects ofprincipal stress direction and intermediate stress on undrainedshear behavior of sand. Soils and Foundations, 38(3): 179188.



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Appendix A

Table A1. Values of constitutive model parameters for Toyoura and clean Ottawa sands.

ParameterParametersymbol

Parameter value

CommentToyoura sandCleanOttawa sand

Small-strain (elastic)parameters

n 0.15 0.15* Poissons ratioCg 900 611 Parameter controlling the magnitude of the maximum shear

modulus Gmaxng 0.400 0.437 Exponent controlling the rate of increase of Gmax with effec-

tive confining stressg1 0.0010 0.000 65 Parameters controlling the decrease of para-elastic shear

modulus G with shear straina1 0.40 0.47CS Gc 0.934 0.780 Intercept of CS line in ep space

l 0.019 0.081 Parameter controlling inclination of CS line in ep spacex 0.70 0.196 Parameter controlling curvature of CS line in ep spaceMcc 1.27 1.21 Critical stress ratio in triaxial (TX) compression conditions

Bounding surface kb 1.5 1.9 Parameter controlling the increase of friction angle withsand density

Dilatancy Do 0.90 1.31 Inclination of the stressdilatancy curvekd 2.8 2.2 Parameter controlling the stress ratio at phase transformation

Plastic modulus h1 1.62 2.20 Parameters controlling the magnitude of plastic modulush2 0.254 0.240elim 1.00 0.81 Upper limit for void ratio for which the plastic modulus be-

comes zerom 2.0 1.2 Parameter controlling stress ratio in undrained instability

stateStress-inducedanisotropy

c1 0.72 0.71 Ratio of the critical stress ratio in TX extension to that inTX compression

c2 0.78 0.78* Parameter controlling the value of the magnitude of inter-mediate principal stress relative to the two other principalstresses under plain-strain conditions

ns 0.35 0.35* Parameter controlling the magnitude of the friction angle inplane-strain conditions relative to the friction angle in TXcompression

Inherent anisotropy a 0.29 0.31 Parameter controlling the intercept of CS line in ep spaceunder conditions other than TX compression

kh 0.11 0.39 Parameter controlling the variation of plastic stiffness, withthe direction of loading relative to the axis of sand de-position

m 0.05 0.05 Radius of conical yield (loading) surface

*Assumed.



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