Computers and Geotechnics 39 (2012) 85–97

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Computers and Geotechnics

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Analysis of pile stabilized slopes based on soil–pile interaction

Mohamed Ashour ⇑, Hamed ArdalanDept. of Civil and Environmental Engineering, University of Alabama in Huntsville, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 13 May 2011Received in revised form 26 August 2011Accepted 7 September 2011Available online 7 October 2011

Keywords:Slope stabilizationSoil–pile interactionPile groupLateral loadsSafety factor

0266-352X/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.compgeo.2011.09.001

⇑ Corresponding author. Tel.: +1 256 824 5029; faxE-mail address: ashour@eng.uah.edu (M. Ashour).

The paper presents a new procedure for the analysis of slope stabilization using piles. The developedmethod allows the assessment of soil pressure and its distribution along the pile segment above the slipsurface based on soil–pile interaction. The proposed method accounts for the influence of pile spacing onthe interaction between the pile and surrounding soils and pile capacity. The paper also studies the effectof soil type, and pile diameter, position and spacing on the safety factor of the stabilized slope. Specificcriteria are adopted to evaluate the pile capacity, ultimate soil–pile pressure, development of soil flow-around failure and group action among adjacent piles in a pile row above and below the slip surface.The ability of the proposed method to predict the behavior of piles subject to lateral soil movementsdue to slope instability is verified through a number of full scale load tests.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

The use of piles to stabilize active landslides, as a preventivemeasure in stable slopes, has become one of the important innova-tive slope reinforcement techniques in last decades. Piles havebeen used successfully in many situations in order to stabilizeslopes or to improve slope stability and numerous methods havebeen developed for the analysis of piled slopes [1–5].

The piles used in slope stabilization are usually subjected to lat-eral force by horizontal movements of the surrounding soil andhence they are considered as passive piles. The interaction behav-ior between pile and soil is a complicated phenomenon due to its3-dimensional nature and can be influenced by many factors, suchas the characteristics of deformation and the strength parametersof both pile and soil.

The interaction among piles is complex and depends on soil andpile properties, and the level of soil-induced driving force. Further-more, the earth pressures applied to the piles are highly dependentupon the relative movement of the soil and the piles. In practicalapplications, the study of a slope reinforced with piles is usuallycarried out by extending the methods commonly used for the sta-bility analysis of slopes to incorporate the reaction force exerted onthe unstable soil mass by the piles.

The characterization of the problem of slope instability and theuse of piles to improve the stability of such slopes requires bettercharacterization of the integrated effect of laterally loaded pilebehavior, pile-structure-interaction, and the nonlinear behaviorof pile materials (steel and/or concrete) on the resultant slope

ll rights reserved.

: +1 256 824 6724.

stability condition. The driving force of the soil mass that actsalong the pile segment above the slip surface is transmitted tothe lower (stable) soil layers, as shown in Fig. 1. Such a scenario re-quires representative modeling for the soil–pile interaction abovethe failure surface that reflects and describes actual distributionfor the soil driving force along that particular portion of the pile.In addition, the installation of closely spaced pile row would createan interaction effect (group action) among adjacent piles not onlybelow but also above the slip surface.

One approach has been to calculate the soil passive resistance(driving force) based on Broms’ method [6] as characterized inNAVFAC [7]. Another alternative is to use the ultimate soil reactionfrom the traditional p–y curve. Neither of these ultimate resis-tances was envisioned for sloping ground, and neither considersgroup interference effects in a fundamental way, certainly not forsloping ground conditions. In addition, flow-around failure of soilaround the pile is a significant phenomenon that should be consid-ered in the current practice. It should be noted that the flow-around failure governs the amount of force (PD) acting on the pileabove the failure surface.

The presented method allows the determination of the mobi-lized driving soil–pile pressure per unit length of the pile (pD)above the slip surface based on soil–pile interaction in an incre-mental fashion using the strain wedge (SW) model techniquedeveloped by Norris [8] and Ashour et al. [9]. The buildup of pD

along the pile segment above the slip surface should be coherentwith the variation of stress/strain level that is developed in theresisting soil layers below the slip surface. The mobilized non-uniformly distributed soil pressure (pD) is governed by the soil–pileinteraction (i.e. soil and pile properties) and developing flow-around failure above and below the slip surface. In addition, the

Sliding surface

Mobilized soil

pressure (pD)

Slope surface

Sliding soil mass

Pile extended into stable soil

Soil-pile resistance (p)

Fig. 1. Driving force induced by displaced soil mass above the sliding surface.

Sliding surface

Slope surface

Sliding soil mass

Soil-

pile

res

ista

nce

(Bea

m o

n E

last

ic F

ound

atio

n)

Mobilized soil

pressure (pD)

Stable soil

Fig. 2. Proposed model for soil–pile analysis in pile-stabilized slopes.

86 M. Ashour, H. Ardalan / Computers and Geotechnics 39 (2012) 85–97

presented technique allows the calculation of the post-pile instal-lation safety factor (i.e. stability improvement) for the wholestabilized slope, and the slope portions uphill and downhill thepile. The size of the mobilized passive wedge of sliding soil masscontrols the magnitudes and distribution of the soil–pile pressure(pD) and the total amount of the driving force (PD) transferred viaan individual pile in a pile row down to the stable soil layers.The presented technique also accounts for the interaction amongadjacent piles (group effect) above and below the slip surface.Fig. 2 shows the soil–pile model as employed in the proposed tech-nique. The ability of this method to predict the behavior of pilessubject to lateral soil movements due to slope instability is verifiedthrough a comparison with two case histories. Also, the efficiencyof using stabilizing pile in a slope is discussed by examining theinfluence of pile location in the slope, pile spacing, and pilediameter and stiffness.

2. Methods of analysis

Ito et al. [1] proposed a limit equilibrium method to deal withthe problem of the stability of slopes containing piles. The lateralforce acting on a row of piles due to soil movement is evaluated

using theoretical equations, derived previously by Ito and Matsui[10] based on the theory of plastic deformation and consideringplastic flow of the soil through the piles. The ultimate soil pressureon the pile segment which is induced by flowing soil depends onthe strength properties of the soil, overburden pressure, and spac-ing between the piles and is independent of pile stiffness as a rigidpile with infinite length. Also, the equations are only valid over alimited range of spacings, since, at large spacing or at very closespacings, the mechanism of flow through the piles postulated byIto and Matsui [10] is not the critical mode [2]. Large increase inthe value of the soil–pile pressure (pD) can be observed by reducingthe clear spacing between piles.

Hassiotis et al. [11] have extended the friction circle method bydefining new expressions for the stability number to incorporatethe pile resistance in slope stability analysis using a closed formsolution of the beam equation. The ultimate force intensity (soil–pile pressure) is calculated based on the equations proposed byIto and Matsui [10] assuming a rigid pile. The finite differencemethod is used to analyze the pile section below the critical sur-face as a beam on elastic foundations (BEF). However, the safetyfactor of the slope after inserting the piles is obtained based onthe new critical failure surface, which is not necessarily the one be-fore pile installation [11].

Poulos [2] and Lee et al. [12] presented a method of analysis inwhich a simplified form of boundary element method [13] was em-ployed to study the response of a row of passive piles incorporatedin limit equilibrium solutions of slope stability in which the pile ismodeled as a simple elastic beam, and the soil as an elastic contin-uum. The method evaluates the maximum shear force that eachpile can provide based on an assumed input free field soil move-ment and also computes the associated lateral response of the pile.The prescribed soil movements are employed by considering thecompatibility of the horizontal movement of the pile and soil ateach element. While pile and soil strength and stiffness propertiesare taken into account to obtain soil–pile pressure in this method,group effects, namely piles spacing, are not considered in the anal-ysis of soil–pile interaction. Poulos [2] recommends the installationof stabilizing piles be located in the center of the failure surface toavoid any slope failure behind or in front of the pile. A constant soilYoung’s modulus that varies linearly with depth has been usedalong with an ultimate lateral pressure, pD. For the practical use,Poulous [2] promoted the flow mode that creates the least damageeffect of soil movement on the pile where the soil movement is lar-ger than the pile deflection. Such a slope-pile displacement mech-anism coincides with the suggested soil–pile interaction modelpresented in this paper.

Chow [14] presented a numerical approach where the piles aremodeled using beam elements as linear elastic materials and soilresponse at the individual piles is modeled using an average mod-ulus of subgrade reaction. In this method, the sliding soil move-ment profile are assumed or measured based on the fieldobservation and the problem is analyzed by considering the soil–pile interaction forces acting on the piles and the soil separatelyand then combining those two by the consideration of equilibriumand compatibility. Ultimate soil pressure acting on the piles in thismethod for cohesive and cohesionless soils are calculated based onthe equations proposed by Viggiani [15] and Broms [6], respec-tively. These equations are strictly for single piles, while studiessuch as those by Chen and Poulos [16] shows that the ultimate soilpressure are affected by the pile spacing and group arrangement.

The influence of one row of pile groups on the stability of theweathered slope was investigated by Jeong et al. [17] based onan analytical study and a numerical analysis. A model to computeload and deformations of piles subjected to lateral soil movementbased on the transfer function approach was presented. In thismethod, a coupled set of pressure–displacement curves induced

M. Ashour, H. Ardalan / Computers and Geotechnics 39 (2012) 85–97 87

in the substratum determined either from measured test data orfrom finite-element analysis is used as input to study the behaviorof the piles which can be modeled as a BEF. The study assumes theultimate soil pressure acting on each pile in a group to be equal tothat adopted for the single pile multiplied by the group interactionfactor evaluated by performing three-dimensional finite elementanalysis.

Ausilio et al. [18] have used the kinematic approach of limitanalysis for the stability of slopes that are reinforced with piles.The case of a slope without piles is first considered where the slid-ing surface is described by a log-spiral equation, and then a solu-tion is proposed to determine the safety factor of the slope,which is defined as a reduction coefficient for the strength param-eters of the soil. Then, the stability of a slope containing piles isanalyzed. To account for the presence of the piles, a lateral forceand a moment are assumed and applied at the depth of the poten-tial sliding surface. To evaluate the resisting force (FD), which mustbe provided by the piles in a row to achieve the desired value of thesafety factor of the slope, an iterative procedure is used to solve theequation obtained by equating the rate of external work due to soilweight and surcharge boundary loads to the rate of energy dissipa-tion along the potential sliding surface. Nian et al. [19] developedthe similar approach to analyze the stability of a slope with rein-forcing piles in nonhomogeneous and anisotropic soils.

Zeng and Liang [4] presented a limit equilibrium based slopestability analysis technique that would allow the determinationof the safety factor (SF) of a slope that is reinforced by drilledshafts. The technique extends the traditional method of slice ap-proach to account for stabilizing shafts by reducing the intersliceforces transmitted to the soil slice behind the shafts using a reduc-tion (load transfer) factor obtained from two-dimensional finiteelement analysis generated load transfer curves.

A similar approach presented by Yamin and Liang [20] uses thelimit equilibrium method of slices where an interrelationshipamong the drilled shaft location on the slope, the load transfer fac-tor, and the global SF of the slope/shaft system are derived basedon a numerical closed-form solution. Furthermore, to get the re-quired configurations of a single row of drilled shafts to achievethe necessary reduction in the driving forces, a newly generateddesign charts utilizing three-dimensional finite element are usedwith arching factor.

3. Proposed method

3.1. Model characterization

The strain wedge (SW) model technique developed by Norris [8]and Ashour et al. [9] for laterally loaded piles based on soil-structureinteraction is modified to evaluate the mobilized non-uniformlydistributed soil–pile pressure (pD) along the pile segment abovethe anticipated failure surface (Fig. 1) assuming a flow mode for soilmass above the slip surface. The presented technique focuses on thecalculation of the mobilized soil–pile pressure (pD) based on theinteraction between the deflected pile and the sliding mass of soilabove the slip surface using the concepts of the SW model. The piledeflection is also controlled by the associated profile of the modulusof subgrade reaction (Es) below the sliding surface (Fig. 2). It shouldbe emphasized that the presented model targets the equilibrium be-tween the soil–pile pressure calculated above and below the slipsurface as induced by the progressive soil mass displacement andpile deflection. Such a sophisticated type of equilibrium requiresthe synchronization among the soil pressure and pile deflectionabove the failure surface and the accompanying soil–pile resistance(i.e. Es profile) below the slip surface. While pD is governed by thesoil–pile interaction and its ultimate value (i.e. soil and pile proper-ties and developing flow-around failure (Ashour and Norris [21]),

the pile capacity is limited to its plastic moment (structural/materialfailure). The capabilities of the SW model approach have been usedto capture the progress in the soil flow-around the pile and the dis-tribution of the induced driving force (PD = R pD) above the slip sur-face based on soil–pile interaction (i.e. soil and pile properties).

A full stress–strain relationship of soil within the sliding mass(sand, clay, C � / soil) is employed in order to evaluate a compat-ible sliding mass displacement and pile deflection for the associ-ated slope factor of safety. As seen in Figs. 1 and 2, the soil–pilemodel utilizes a lateral driving load (above the failure surface)and lateral resistance from the stable soil (below the failure sur-face). Shear force and bending moment along the pile are also cal-culated. Thereafter, the safety factor of the pile-stabilized slope canbe re-evaluated. The implemented soil–pile model assumes thatthe sliding soil mass imposes increasing lateral driving force onthe pile as long as the shear resistance along the sliding surfaceup-slope the pile cannot achieve the desired stability safety factor.

As seen in Fig. 3, a mobilized three-dimensional passive wedgeof soil will develop into the sliding soil zone above the slip surface(upper passive wedge) with a fixed depth (Hs) and a wedge face ofwidth (BC) that varies with depth (xi) (i.e. soil sublayer and pilesegment i).

ðBCÞi ¼ Dþ ðHs � xiÞ2ðtan bmÞiðtan umÞi xi 6 Hs ð1Þ

ðbmÞi ¼ 45þ ðumÞi2

ð2Þ

The horizontal size of the upper passive wedge is governed bythe mobilized fanning angle (/m), which is a function of the soilstress level (SL) (Fig. 3a). /m in clay is determined based on theeffective stress analysis (Ashour et al. [9], Fig. 4). It should be men-tioned that the effective stress (ES) analysis is employed with claysoil as well as with sand and C � / soil (Fig. 4) in order to define thethree-dimensional strain wedge geometry with mobilized fanningangle (Ashour et al. [9]). To account for the effective stress in clay,the variation of the excess pore water pressure is determined usingSkempton’s equation [22] where the water pressure parametervaries with the soil stress level [9]. The sliding mass of soil abovethe slip surface is assumed in the current analysis to experiencelateral displacement larger than pile deflection, (Fig. 5).

The mobilized fanning angle, /m, of the upper (driving) passivesoil wedge due to the interaction between the moving mass of soiland the embedded portion of the pile (Hs) increases with the pro-gress in soil displacement (i.e. SL in soil). e50 is the normal strain insoil at SL = 0.5 and /m is determined as a function of SL, which iscalculated from the constitutive stress–strain model presented byAshour et al. [9] (Fig. 6).

The soil strain (es) in the upper passive wedge (i.e. sliding soilmass) is increasing gradually in an incremental fashion (a step bystep loading process). In each loading step, the distribution of pD

(Figs. 1 and 2) along the pile length embedded into the sliding soillayer(s) is determined as,

ðpDÞi ¼ ðDrhÞiBCiS1 þ 2siDS2 ð3Þ

where PD ¼Xi¼n at slip surface

i¼1

pD

pD is the soil–pile pressure per unit length of the pile (F/L) at thecurrent effective confining pressure �r3c (i.e. overburden pressureassuming isotropic conditions, K = 1) and soil strain es in the soilsublayer i at depth xi. D is the width of the pile cross section, andBC is the width of the soil passive wedge at depth xi. S1 and S2, onthe other hand, are shape factors that are 0.75 and 0.5, respectively,for a circular pile cross section, and 1.0 for a square pile [9]. s is thepile–soil shear resistance along the side of the pile (Fig. 3a). Drh is

φm

φm

φm

Pile

Real stressed zone

F1

F1

No shear stress because these are principal stresses

Aτ

Side shear (τ) thatinfluences the oval shape of the stressedzone

(a) Force equilibrium in a slice of the wedge at depth x.

(b) Forces at the face of a simplified soil upper passive wedge(Section elevation A-A).

Δσh

σV

O

βm

KσVO

Yo

Hs

x

Hi ii-1

Sublayer i+1

Sublayer 1

δ

Plane taken to simplify analysis (i.e. F1’s cancel)

C

B

A

Δσh

Slip surface

Slope surface

Sliding soil massMobilized soil passive

wedge (upper wedge)

Lower mobilized wedges

Soil sublayers

(c) Mobilized passive soil wedges.

Fig. 3. Characterization of the upper soil wedge as employed in the proposed technique.

88 M. Ashour, H. Ardalan / Computers and Geotechnics 39 (2012) 85–97

the deviatoric stress calculated at the current soil strain es in sublay-er i with confining effective stress ð�r3c ¼ overburden pressure �rvo).Therefore, the horizontal stress change at the face of the wedge atdepth x becomes,

Drh ¼ SLDrhf ð4Þ

where

Drhf ¼ �rvo tan2 45þu2

� �� 1

h iðsandÞ ð5aÞ

Drhf ¼ 2Su ðclayÞ ð5bÞ

Drhf ¼C

tan uþ �rvo

� �tan2 45þu

2

� �� 1

h iðC �usoilÞ ð5cÞ

The side shear stress, si, is determined as

si ¼ ð�rvoÞi tanðusÞi where tan us ¼ 2 tan um and tan us

6 tan u ðsandÞ ð6aÞ

si ¼ ðSLtÞiðsultÞi where sultis a function of Su ðclayÞ ð6bÞ

si ¼ ð�rvoÞi tanðusÞi þ 2Cs where tan /s ¼ 2 tan /m and Cs

¼ 2CmðC �u SoilÞ ð6cÞ

C and Cm are the cohesion intercepts for ultimate and mobilizedresistance, respectively. SLt is the stress level of the pile side shearstrain in clay (Ashour et al. [9]), and Su is the undrained shearstrength of clay soil. In Eq. (6), the mobilized side shear angle(/s) and adhesion (Cs) are taken to develop at twice the rate of

the mobilized friction angle (tan /m) and mobilized cohesion(Cm) in the mobilized wedge. Of course, /s and Cs are limited tothe fully developed friction angle (/) and cohesion (C) of the soil(Cs 6 C and tan /s 6 tan /).

The ultimate value of pD is governed by the soil full passivepressure (SL = 1) and the flow of soft/loose soil around the pile. Itshould be noted that pD could reach its ultimate value (i.e. soilstarts flowing around the pile) to cease the growth of the upperpassive soil wedge and its interaction with the pile segment.Flow-around failure in a soil sublayer i detected via parameter Aand its ultimate value Ault.

Ai ¼ðpDÞi=DðDrhÞi

¼ BCiS1

Dþ 2siS2

ðDrhÞið7Þ

The progress in soil mass displacement (i.e. pD and soil–pile-interaction) continues until the targeted slope safety factor isachieved or the pile fails to interact with sliding soil mass. There-fore, no additional soil driving force is transferred to the stable soillayer(s) below the failure surface.

The SW model is applied to assess the modulus of subgradereaction profile (Es) along the pile length below the slip surface(i.e. p) as shown in Fig. 2). Ashour et al. [9] presents detailed infor-mation on the assessment of the Es profile below the slip surface asemployed in the current analysis for the BEF.

3.2. Failure criteria and ultimate soil–pile pressure above the slipsurface

The presented technique accounts for different failure mecha-nisms that include pile and soil failure and limiting values for

Normal Stress (σ)1)( voσ

1)2/45(tan

1)2/45(tan2

2

−+−+=

ΔΔ=

ϕϕ

σσ m

hf

hSL

She

ar S

tres

s (τ

)

ϕm

ϕ

2)( voσ 3)( voσ 4)( voσ

(a) Sand

Normal Stress (σ)

She

ar S

tres

s (τ

)

ϕ m

ϕ

SL Su

=_

hσΔ

uΔ

Lab total stress (or field total stress minus static

pore water pressure)Undrained excesspore water pressure Effective stress

voσuvo Δ−σ uhvo Δ−Δ+ σσhvo σσ Δ+

voσ

voσ

uhvo Δ−Δ+ σσ

uvo Δ−σ

(b) Clay

Normal Stress (σ)miC )(

She

ar S

tres

s (τ

)

ϕm

ϕ

hvo σσ Δ+ hfvo σσ Δ+voσ

(c) C-ϕ soil

Fig. 4. Mobilized effective friction angle with the variation of soil stress asemployed in current study.

Displacement

Dep

th b

elow

gro

und

leve

l

Failure surface

Soil movementDeflected pile

Fig. 5. Soil–pile displacement as employed in the presented model.

Fig. 6. Soil stress–strain relationship as developed by Ashour et al. [9].

M. Ashour, H. Ardalan / Computers and Geotechnics 39 (2012) 85–97 89

the soil–pile pressure (pD) that the sliding mass could deliver to thepile (per pile unit length) through the progressive soil–pile interac-tion. A structural (pile material) failure takes place when thebending moment in the pile reaches its ultimate value Mp (plasticmoment) to form a plastic hinge. However, this might not bepossible to achieve with short piles because of inadequate pile

embedment into the stable soil (i.e. less flexural deformation). MP

is determined from the moment–curvature relationship of the pilecross section.

The second failure mechanism reflects the development of aflow-around failure when parameter A reaches its ultimate value(Ault). The assessment of Ault in sand was initially developed byReese [23] and modified by Norris [8].

ðAultÞi ¼ðKaÞi½ðKpÞ4i � 1� þ ðKoÞiðKpÞ2i tan ui

ðKpÞi � 1ð8Þ

where Ka and Kp are the Rankine active and passive coefficients oflateral earth pressure, and Ko is the coefficient of earth pressureat-rest. (Ault)i of clay is presented by Norris [8]as

ðAultÞi ¼ðpultÞi

D

ðDrhf Þi¼ ðpultÞi

D2ðSuÞi¼ 5S1 þ S2 ð9Þ

Such a behavior may occur while pD in sublayer i is still lessthan its ultimate value (pD)ult (Ashour and Norris [21]), especiallyin soft clay where Ault can be reached at SL < 1. This ends theprogress of pD and the interaction between the pile section and

90 M. Ashour, H. Ardalan / Computers and Geotechnics 39 (2012) 85–97

slipping sublayer of soil. As a result, no additional soil pressure istransferred via the pile segment embedded into that soil sublayer(i).

A third soil–pile interaction controlling mechanism would takeplace when pD is equal to (pD)ult in soil sublayer (i) above the slipsurface (i.e. SL = 1).

½ðpDÞult�i ¼ ðDrhf ÞiBCiS1 þ 2ðsf ÞiDS2 ðsandÞ ð10aÞ

½ðpDÞult�i ¼ 10ðSuÞiDS1 þ 2ðSuÞiDS2 ðclayÞ ð10bÞ

In addition, the fixed depth of the upper passive wedge (Hs)would prevent the face of the soil wedge (BC) and pD at that depthfrom growing. In fact, the soil–pile interaction mechanism abovethe slip surface is influenced by the depth of the slip surface atthe pile location (Hs) as presented in the parametric study section.Pile length and bending stiffness (i.e. the pile relative stiffness)have also a significant effect on the pile deflection pattern, and inreturn the soil–pile interaction. The developed (pD) is expressed as

ðpDÞi ¼ AiDesEi ð11Þ

E is the soil Young’s modulus (E = SL Drhf/es).

3.3. Pile row interaction above the failure surface

The number of piles required for slope stabilization is calculatedbased on pile spacing and the interaction among the piles. The pilegroup interaction technique developed by Ashour et al. [24] is usedto estimate the interaction among the piles above and below thesliding surface assuming soil displacement to be larger than piledeflection. The safety factor of the pile-stabilized slope can be re-evaluated based on the distributed lateral force (PD) induced by soilmass and carried by the pile down to the stable soil below the slidesurface.

The fourth soil–pile interaction controlling mechanism adoptedin the presented technique is based on monitoring the horizontalstress overlapping among stabilizing piles above and below the slipsurface. The horizontal growth of the upper mobilized passive soilwedge governs the build up of the soil–pile driving pressure (pD) inany sublayer (i) as a result of adjacent soil wedge overlapping. Theupper soil wedges developed into the up-slope portion of the slid-ing soil mass overlap according to the pile spacing and level of soilstress (Fig. 7). Consequently, the stresses into adjacent soil inten-sify (compared to the case of isolated pile) until pD reaches its ulti-mate value or the flow-around failure takes place.

The current study utilizes the technique presented by Ashouret al. [24] that was developed to assess the lateral interactionamong the piles in a group based on soil and pile properties and

Overlap of stresses based on elastic theory

Adjusted uniform stress at the face of the soil wedge

eliPeliPUniform pile face movement

Soil wedge Soil wedge

r BC

Fig. 7. Horizontal passive soil wedge overlap among adjacent piles.

pile spacing using the SW model. The SW model is used to accountfor the effect of neighboring piles (one row) on the characterizationof the soil–pile pressure above and below the slip surface (pD andp), respectively. The average stress level in a soil layer due topassive wedge overlap (SLg) is evaluated based on the followingrelationship (Ashour et al. [24]),

ðSLgÞi ¼ SLið1þX

RjÞ1:5 6 1 ð12Þ

where j is the number of neighboring passive wedges in soil layer ithat overlap the wedge of the pile in question (j = 2 for a single pilerow). R is the ratio between the length of the overlapped portion ofthe face of the passive wedge (r) and the width of the face of thepassive wedge (BC) (Fig. 7). R (which is less than 1) is determinedfor both sides of the pile overlap.

SLg and the associated soil strain (eg) will be assessed for eachsoil sublayer. eg is Pe of the isolated pile (no group effect) and isdetermined based on the stress–strain relationship (r vs. e) pre-sented by Ashour et al. [9] (Fig. 6). The angles and dimensions(geometry) of the passive wedge (/m, bm, and BC) obtained fromEqs. (1) and (2) would be modified for the group effect accordingto the calculated value of SLg and eg. The average value of deviatoricstress (Drh)g developed at the face of the passive wedge in a par-ticular soil sublayer i is

ðDrhÞg ¼ SLgDrhf ð13Þ

The soil Young’s modulus Eg and the soil–pile pressure (pD) due tosoil wedge overlap are determined as follows,

Eg ¼SLgDrhf

egwhere Eg 6 E of isolated pile case ð14Þ

ðpDÞg ¼ ðAgÞiDðegÞiðEgÞi ð15Þ

Compared to the isolated pile, the soil mass in contact with thepile row maintains a softer response (i.e. less pD at the same y) as aresult of pile interaction (soil wedge overlap effect). To avoidrepetition, the interaction among adjacent piles in a pile row belowthe slip surface and the resulting modulus of subgrade reaction(Es)g profile are determined as presented by Ashour et al. [24].

3.4. Iteration in the proposed model

To clarify the procedure employed in the suggested model, theflowchart presented in Fig. 8 demonstrates the calculation and iter-ation process as implemented in the current model. A small initialvalue of soil strain above and below the slip surface (es and e,respectively) is assumed to determine (1) pD as summarized inEq. (11) and related equations for A and E; and (2) Es profile belowthe slip surface [24]. The current pile head deflection (Yo) is evalu-ated using the SW model procedure [24] to obtain (Yo)SWM that iscompared to the pile head deflection (Yo)BEF calculated from theBEF analysis using current pD distribution and Es profile. If (Yo)SWM

is larger than (Yo)BEF, es is adjusted (increased) till acceptable con-vergence between (Yo)SWM and (Yo)BEF is achieved. On the otherside, e will be increased if (Yo)SWM is less than (Yo)BEF. It shouldbe noted that adjusting es (i.e. pD) will also affect the Es profile asa result of changing the dimensions of the lower wedges (i.e. softerEs profile). Therefore, es is always increased in slower rate com-pared to e in order to capture the desired convergence of pile headdeflection. The next increment of loading will be followed byincreasing es and adjusting (increasing) e of soil below the slip sur-face (i.e. new Es profile) to calculate (Yo)SWM and (Yo)BEF. The pre-sented methodology aims at the state of soil–pile equilibriumwhere the deflected pile would interact with surrounding soils toinduce balanced driving (pD) and resisting (p) soil pressure aboveand below the slip surface. Practically, there is only a single pile

Apply the SW model concepts/Eqns (1 thr. 7) to do the following:

1. Use εs to calculate Δσh = σd, SL, ϕm, BC, E, and pD for sublayers above slip surface. The depth of the upper passive wedge is always equal to the depth of slipping mass (Hs).

2. Use ε to calculate Δσh = σd, SL, ϕm, BC, E, and Es for sublayers

below slip surface [9] (i.e. Es profile along the pile for current ε). 3. Check soil wedge geometry and overlap above/below the slip surface.4. Use Eqns 12 and 13 to adjust εs and ε for group action [24].

5. Repeat step 1 and 2 for adjusted εs and ε.6. Detemine the pile-head deflection (Yo)SWM based on the SW model [9].

1. Use Es profile to solve the pile problem as a BEF under driving soil pressure pD acting on the pile segment above the slip surface.2. Obtain the pile head deflection, (Yo)BEF, from the BEF analysis.

1. Accepted loading increment, pD and p above and below the slip surface, Yo and Es profile.2. Calculate bending deflection, moment, shear Force, distribution of driving forces (pD), and safety factor.

3. Current driving force (PD) = Σ(pD)i above the slip surface.

Increase the value of εs by Δε

STOP

INPUT DATASoil properties, slope profile, pile propertiesand desired safety factor of supported portion

Calculate the driving force (FD) along the slip surface of the upslope (supported) part of theslope that is needed to acheive the desired safety factor of the supported portion.

IF PD < FD

Yes

No

Perform slope stability analysis (modified Bishop) with no piles.

1. Divide soil layers into thin sublayers (i) with thichness Hi.

2. Calculate effective vertical stress (σvo) for each sublayer.

3. Assume an initial small soil strain εs in soil above the slip surface.

4. Assume a very small soil strain (ε) in soil layers below the slip surface.

IF(Yo)SWM = (Yo)BEF

No

Yes

IF(Yo)SWM > (Yo)BEF Increase εs

IF(Yo)SWM < (Yo)BEF Increase ε

Fig. 8. Flowchart for the analysis of pile-stabilized slopes.

M. Ashour, H. Ardalan / Computers and Geotechnics 39 (2012) 85–97 91

deflection pattern that could maintain the state of equilibriumbetween the pile and surrounding soil above and below the slipsurface. The analysis stops indicating pile failure when themoment in the pile reaches its ultimate value (plastic moment).

3.5. Input data

One of the main advantages of the SW model approach is thesimplicity of the required soil and pile properties. Those propertiesrepresent basic and most common properties of soil and pile, such

as the effective unit weight, angle of internal friction (/), un-drained shear strength (Su) and pile geometry, bending stiffnessand plastic moment. Boundaries of soil layers in addition to thelocation of the driven pile need to be also identified. The soil profileis divided into thin sublayers (0.5 or 1 ft thick) and each sublayer istreated as an independent entity with its own properties. In thisfashion, the variation in soil properties (such as e50 and / in thecase of sand, or Su in the case of clay) of each sublayer of soil canbe explored. e50 is obtained from the charts presented in [9]. Thecomputer software (PSSLOPE), which is written in Visual Basicand FORTRAN, has been developed to implement the presentedtechnique for pile stabilized slopes including the slope stabilityanalysis (with no piles) using the modified Bishop method.

3.6. Safety factor

As mentioned in the previous section, the modified Bishopmethod of slices is used to analyze the slope stability. The safetyfactor before installing the stabilizing pile is defined as

FS ¼ Frs

Fdð16Þ

where Frs and Fd are the resisting and driving force of soil mass(along the critical or potential failure surface) which are determinedby the method of slices in the slope stability analysis of landslide asshown in Fig. 9a. In this method, the safety factor of the whole pile-stabilized slope is calculated by including the total resistance pro-vided by piles for one unit length of the slope (Frp) as follows:

FS ¼ Fr

Fd¼ ðFrs þ FrpÞ

Fdð17Þ

Also, the safety factor of supported and unsupported portion of thestabilized slope is obtained in current study as follows (Fig. 9b):

FSðsupportedÞ ¼Fr

Fd¼ ðFrsðsupportedÞ þ FrpÞ

FdðsupportedÞð18Þ

FSðunsupportedÞ ¼Fr

Fd

¼ FrsðunsupportedÞ

FdðunsupportedÞ þ ½ðFdðsupportedÞ � FrsðsupportedÞÞ � Frp�ð19Þ

where Frs(supported) and Fd(supported) are the resisting and driving forceof soil mass along the supported portion of the critical failure sur-face. The resisting and driving force of soil mass along the unsup-ported portion of critical failure surface Frs(unsupported) andFd(unsupported) are also calculated using the slope stability methodof slices as shown in Fig. 9b. Frp in Eqs. (17) and (19) is calculatedfrom Eq. (18) after the desired safety factor of the supported (up-slope) portion of the slope (FS(supported)) is identified. By calculatingFrp, the targeted load carried by each pile in the pile row can be eval-uated (FD = Frp � S). FS(supported) needs to be identified with a mini-mum value of unity.

The achievement of the minimum factor of safety(FS(supported) = 1) indicates that the stabilizing pile is able to provideenough interaction with the sliding mass of soil in order to take aforce equal to the difference between the driving and resistingforces along the slip surface of the supported portion of the slope(Frp = Fd(supported) � Frs(supported)). As a result, the second term ofthe denominator in Eq. (19) would be zero. However, the minimumsafety factor may not be achieved as a result of reaching the ulti-mate soil–pile interaction as presented in the previous section.Therefore, the rest of driving force (the second term of the denom-inator in Eq. (19)) will be delivered (flow) to the lower segment ofthe slope (the unsupported portion).

Table 1Pile properties.

Unit weight (kN/m3) 23Diameter (m) 1.2Elastic modulus (kPa) 2.6 � 107

Compressive strength of concrete (kPa) 3.0 � 104

Plastic moment (kN-m) 5000Yield strength of the rebar (kPa) 4.14 � 105

Fd

Frs

Critical Failure Surface

(a) Slope stability under driving and resistance forces.

Frs(unsupported)

Fd(unsupported)

Frp

(b) Forces acting on a pile-stabilized slope.

Fig. 9. Slope stability pre- and post-pile installation.

92 M. Ashour, H. Ardalan / Computers and Geotechnics 39 (2012) 85–97

To reach the ultimate safety factor of the stabilized slope, anincreasing value of the safety factor of the supported portion ofthe slope should be used (i.e. transferring more soil pressurethrough the piles) until maximum interaction between the pilesand surrounding soil is observed. However, the stabilizing pilesmay fail under plastic moment before reaching the ultimate soil–pile interaction.

4. Parameters affecting the SF of pile-stabilized slopes

There are several parameters that could affect the slope-pileinteraction and the amount of resistance that the stabilizing pilecan provide to increase the safety factor of the stabilized slope.Some of these influencing factors can be outlined as the geometryand material properties of the pile, soil properties, pile position inthe slope (i.e. the depth of slip surface at pile location), and thespacing of adjacent piles.

To examine the effect of the above mentioned parameters onslopes stabilized by one row of piles, two slopes (Cases I and II)with the same geometry but different soil properties are studied(Fig. 10). The slopes are 10 m high with an inclination angle withthe horizontal ground surface of 30�. A weathered rock deposit is

10 m

4 m

30o

C = 7.5 kPaϕ = 17O

γ = 19 kN/m3

C = 700 kPaϕ = 0O

γ = 20 kN/m3

LLx

Hs

Firm Layer (Weathered Rock)

(Case I)

(a)

Fig. 10. Illustrative examples

located at 4 m below the ground surface at the slope toe. For bothcases, the soil is assumed to be a C � / soil such as a silty or clayeysand. The safety factor of both slopes before stabilization is about1.03 obtained by performing slope stability analysis using themodified Bishop method and the corresponding critical failure sur-faces are shown in Fig 10. As depicted in Fig. 10, the critical failuresurface for Case II is deeper than that of Case I because of the dif-ferent soil properties in both cases (Case II is more cohesive andless frictional compared to Case I).

One row of 1.2-m diameter reinforced concrete piles with theproperties summarized in Table 1 has been installed to increasethe stability of the slopes. In order to carry out this study, the pilesare assumed to have enough embedment into the weathered rock.The pile head maintains free head conditions (free rotation and dis-placement), which is very common in practice. The parametricstudy carried out is based on the pile properties listed in Table 1unless otherwise stated. Pile analysis results showed that stressescaused by the moment in the piles are more critical than thosecaused by shear. Therefore, in the following study the ratio of thepile maximum moment to its plastic moment (Mmax/Mp) is consid-ered as an indication of pile structural stability (i.e. pile materialfailure).

4.1. Effect of pile position

The effect of pile position on the safety factor of pile-stabilizedslopes is illustrated in Fig. 11. A constant center-to-center pilespacing versus pile diameter ratio (S/D) of 2.5 is maintained inthe analysis. For both slopes, the most effective pile position islocated between the middle and the crest of the slope as foundby Hassiotis et al. [11], Jeong et al. [17], and also Lee et al. [12]for the two-layered soil slope case where the upper soft layer isunderlain by a stiff layer. This optimum position of the pile rowis also influenced by the pile characteristic length that is embeddedinto the unstable and stable regions. Compared to Case I, a largerforce carried by the pile (Frp) (Fig. 11a) and less safety factor(Fig. 11b) can be observed in Case II due to the deeper slip surfaceat the pile position and larger associated driving force (Fd). Itshould be mentioned that the Hs/D ratio has a significant effect

10 m

4 m

30o

C = 14 kPaϕ = 10O

γ = 18 kN/m3

C = 700 kPaϕ = 0O

γ = 20 kN/m3

LLx

H s

Firm Layer (Weathered Rock)

(Case II)

(b)

of pile stabilized slopes.

0.2 0.4 0.6 0.8 1

Lx/L

200

400

600

800

1000R

esis

tanc

e de

velo

ped

by e

ach

pile

(PD),

kN

Case ICase II

S/D = 2.5

(a)

0.2 0.4 0.6 0.8 1

Lx/L

1.2

1.4

1.6

SF(W

hole

slo

pe)

Case ICase II

S/D = 2.5

(b)

Fig. 11. Effect of pile position on the load carried by the pile and SF of the slope.

0.5 0.6 0.7 0.8 0.9 1Lx/L

1

2

3

4

5

6

7

SF (U

nsup

porte

d po

rtion

)

Case ICase II

S/D = 2.5

Fig. 12. Effect of pile location on SF of the unsupported portion of the slope.

0.2 0.4 0.6 0.8 1Lx/L

0

0.2

0.4

0.6

0.8

1

1.2

Mm

ax/M

P

Case ICase II

S/D = 2.5

Fig. 13. Variation of pile efficiency ratio (Mmax/MP) versus pile position.

M. Ashour, H. Ardalan / Computers and Geotechnics 39 (2012) 85–97 93

on the soil–pile interaction and the amount of force transferred bythe pile down to the stable soil layer. Thus, designers should notrely on just a general position ratio (Lx/L) for pile installation tocapture the largest safety factor. The desired pile location is influ-

enced by the shape of the failure surface (i.e. soil properties) andpile properties.

Fig. 12 also presents the variation of the safety factor of theunsupported portion of the slope versus the pile position. It shouldbe emphasized that the safety factor of the unsupported portion ofthe slope should not be less than the desired safety factor of thewhole slope as determined from Eq. (17). Such a scenario could takeplace when the stabilizing pile is installed close to the crest of theslope. For example, if the pile is located at Lx /L > 0.8 andLx/L > 0.9 in Cases I and II, respectively, the safety factor of the unsup-ported part would be less than the safety factor of the whole slope.

Fig. 13 shows the efficiency ratio (Mmax/Mp) of the stabilizingpiles with respect to their position in the slope (Lx/L). Mmax andMP are maximum and plastic moment, respectively. From Fig. 13,it can be noticed that for Case II at Lx/L > 0.6 the safety factor is con-trolled by the strength of pile materials (i.e. structural failure andthe formation of a plastic hinge where Mmax = MP) while for otherpile positions in Case II and the entire slope of Case I the maximumsafety factor of the stabilized slope is obtained based on the ulti-mate interaction between the pile and sliding mass of soil.

4.2. Effect of pile spacing

The effect of pile spacing on the factor of safety of the slopes isexpressed via the relationship of the factor of safety versus S/D ra-tio. Fig. 14 shows the effect of pile spacing (i.e. group action amongneighboring piles) on the factor of safety assessed at the ultimatestate of soil–pile interaction in Cases I and II at a particular pile po-sition Lx/L = 0.7. The factor of safety of the slopes, as expected, isdecreasing by increasing the pile spacing. It is significant to notethat the closer the pile spacing the larger the interaction amongthe piles below the slip surface. Therefore, larger pile deflectionis anticipated.

4.3. Effect of soil type

Fig. 15 shows the soil pressure per unit length of the pile (pD)above the slip surface for piles located at Lx/L = 0.5 in Cases I and IIwhere the values of Hs are 3.8 and 5.5 m, respectively. The distribu-tion of pD in both cases corresponds to the ultimate slope-pile inter-action. In order to avoid the pile material failure in Case II beforereaching the ultimate interaction of the pile with surrounding soil,Lx /L < 0.6 has been used. More soil–pile interaction should beexpected with less soil plasticity (i.e. soils with higher / and less C).

1 2 3 4 5S/D

1.2

1.4

1.6

1.8

2SF

(Who

le s

lope

)

Case ICase II

Lx/L = 0.7

Fig. 14. Effect of pile spacing (adjacent pile interaction) on slope stability.

0 40 80 120 160 200

Soil-pile pressure (pD), kN/m

7

6

5

4

3

2

1

0

Dep

th, m

Case ICase II

Slip surface for Case I

Slip surface for Case II

Lx/L = 0.5

Fig. 15. pD Along the pile segment above the slip surface.

0.6 0.8 1 1.2 1.4 1.6 1.8D, m

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

SF(W

hole

slo

pe)

Case ICase II

Lx/L = 0.7S = 3 m

Fig. 16. Effect of pile diameter on the slope safety factor using a constant spacing of3 m.

0.6 0.8 1 1.2 1.4 1.6 1.8D, m

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

SF(W

hole

slo

pe)

Case ICase II

Lx/L = 0.7S/D = 2.5

Fig. 17. Effect of pile diameter on the slope safety factor for a constant S/D of 2.5.

94 M. Ashour, H. Ardalan / Computers and Geotechnics 39 (2012) 85–97

4.4. Effect of pile diameter

The effect of pile diameter on the safety factor (SF) of the slopehas been studied for a constant center-to-center pile spacing of3.0 m and Lx/L = 0.7, where pile stiffness and strength propertiesare taken into account (Fig. 16). As expected, the safety factor ofthe stabilized slopes increases as pile diameter increases from0.9 m to 1.6 m. However, a slow increase in the safety factor canbe observed beyond pile diameter 1.0 m and 1.4 m in Cases I andII, respectively, as a result of decreasing Hs/D ratio. It should be alsonoted that increasing the pile diameter within the constant pilespacing (3.0 m) would increase the interaction among adjacentpiles above and below the slip surface.

Fig. 17 shows the effect of pile diameter on the safety factor ofstabilized slopes using S/D = 2.5 (i.e. varying D and S with a con-stant ratio of S/D) at the same pile location (Lx/L = 0.7). As observedin Fig. 17, the safety factor (SF) of the slope is governed by the pilestrength (i.e. pile failure) and grows by the increase of pile diame-ter until SF reaches its optimum value at a certain pile diameter.Thereafter, the safety factor is decreasing by the increase of pilediameter (i.e. no pile failure) due to the decrease of Hs /D ratio.Consequently, the safety factor of the stabilized slope is not only

dependent on the S/D ratio, but also is a function of Hs /D ratioand soil properties. In practice, it is an important issue to chooseappropriate pile spacing and diameter to provide adequate pileresistance and avoid high construction costs that may be associ-ated with large diameter piles.

5. Case studies

5.1. Reinforced concrete piles used to stabilize a railway embankment

Instrumented discrete reinforced concrete piles were used tostabilize an 8-m high railway embankment of Weald Clay atHildenborough, Kent, UK (Smethurst and Powerie [25]) (Fig. 18).Remediation of the embankment was carried out to solve long-term serviceability problems, including excessive side slope dis-placements and track settlements. Stability calculations carriedout after an initial site investigation showed the north slopes ofthe embankment to be close to failure. A 3.5 m high rockfill bermwas constructed at the toe of the embankment, and 200 piles wereinstalled along two lengths of the embankment at a spacing of2.4 m to increase the factor of safety of the whole slope to the re-quired value of 1.3. Smethurst and Powerie [25] estimated the soildriving (shear) force required to achieve the desired safety factor

10 m 6.0m

1.0 mcess

Ballast

4.5 m

3.5 m

Weathered Weald Clay

Weald Clayembankment fill

Rockfill24o

30o

Design failure surfaceIntact Weald Clay

Fig. 18. Embankment profile after the construction platform had been regraded[25].

0 5 10 15 20 25 30 35 40Displacement, mm

10

9

8

7

6

5

4

3

2

1

0

Dep

th b

elow

gro

und

leve

l, m

Average slope displacement, day 42 Average slope displacement, day 1345 Average pile displacement, day 42Average pile displacement, day 1345

Uncracked sectionCracked section

Rockfill

Embankment fill

Intact weatheredand unweatheredWeald Clay

Measured [25]

Proposed Method

Fig. 19. Measured and computed pile displacements.

-100 0 100 200Bending moment, kN-m

10

8

6

4

2

0

Dep

th, m

Measured [25] Proposed method - Uncracked sectionProposed method - Cracked section

Fig. 20. Measured and computed bending moment along pile C.

M. Ashour, H. Ardalan / Computers and Geotechnics 39 (2012) 85–97 95

and transferred by the pile to be 60 kN. Soil strength parametersreported by Smethurst and Powerie [25] and also used in currentanalysis are based on data from the site investigation and associ-ated triaxial tests (Table 2).

As reported by Smethurst and Powerie [25], the 0.6-m diameterand 10-m long bored concrete piles were constructed at a spacingof 2.4 m. Each pile contains six (high tensile) T25 reinforcementbars over their full length, and six T32 bars over the bottom 7 m,giving an estimated ultimate bending moment capacity (plasticmoment, MP) of 250 kN-m over the top 3 m, and 520 kN-m overthe bottom part of the pile.

After pile construction, the granular rockfill material was re-graded into a two-stage slope with the suggested failure surfaceshown in Fig. 18. The reported pile bending stiffness (EI) was187 � 103 kN-m2 for the lower 7 m of the pile and 171 � 103

kN-m2 for the top 3 m. EI of 171 � 103 kN-m2 is taken to be theEI of the whole pile in linear analysis. EI = 115 � 103 kN-m2 is con-sidered in current analysis to be the bending stiffness of the par-tially cracked section (2/3 of the initial EI).

Strain gauges were installed in three adjacent piles to measurethe bending moments induced in the pile by slope movements.Displacement data for the soil and piles were obtained from theinclinometer tubes in the slope midway between the piles andthe inclinometer tubes in Piles.

The average pile and soil displacements for 42 days, shortlyafter the rockfill on the slope surface had been regraded, and1345 days are shown in Fig. 19 [25]. Using the soil parameterspresented in Table 2, the Modified Bishop method is applied inthe current procedure to study the stability of the given slopewithout piles. A safety factor of 1.176 is obtained. No specificslope safety factor value was reported by Smethurst and Powerie[25]. It should be noted that the slope safety factor is verysensitive toward any slight change in the slip surfacecoordinates.

Table 2Design soil parameters [24].

Soil type Unit weight, c (kN/m3)

Weald Clay embankment fill 19Softened Weald Clay embankment fill 19Weathered Weald Clay 19Weald Clay 20Rockfill 19

Figs. 19 and 20 show the calculated pile lateral response in com-parison with the measured data. The computed results are basedon 89 kN of shear force transferred by the pile which is larger thanthe shear force (60 kN) anticipated by Smethurst and Powerie [25].In addition, the negative moment measured in the upper portion ofthe pile affects and reduces the lower peak of the positive moment(Fig. 20). This could be referred to the top rock-fill layer displace-ment, which is less than the pile deflection as shown in Fig. 19.

Friction angle, /0

(degrees) Effective cohesion, c0

(kPa)

25 20.919 20.925 20.930 104.435 0

0 20 40 60 80

Soil-pile pressure (pD), kN/m

4

3

2

1

0

Dep

th, m

Weald Clay embankment fill

Rockfill

Fig. 21. Soil–pile pressure (pD) along the pile segment above the critical surface.

20 30 40 50Horizental distance, m

10

20

30

40

Verti

cal d

ista

nce,

m

Failure surface

Soil No. 1 (Sand)

Soil No. 2 (Sand)

Rock

Pile

G.W.T

Fig. 22. Soil–pile profile of the test site at Tygart Lake [26].

0 10 20 30 40 50 60 70Displacement, mm

10

9

8

7

6

5

4

3

2

1

0

Dep

th, m

Pile 4 [26]Pile 5 [26]Proposed method

Fig. 23. Measured and computed pile deflection of the Tygart Lake Test.

96 M. Ashour, H. Ardalan / Computers and Geotechnics 39 (2012) 85–97

The distribution of bending moment with depth from the two setsof gauges in Pile C is shown for day 1345 in Fig. 20.

Fig. 21 exhibits the variation of mobilized pD along the pile seg-ment embedded into two different types of soils above the slip sur-face. The current method provides 89 kN of shear force (

PpD in

Fig. 21) transferred by the pile which is larger than the initially cal-culated shear force (60 kN) and smaller than the shear force(110 kN) that was back-calculated from the strain gauge data after1345 ‘s by Smethurst and Powerie [25]. Substantial amount of thedriving force is caused by the interaction between the pile and therockfill layer compared to the underlying clay fill. As presented inFig. 21, the proposed technique allows the assessment of the mobi-lized soil–pile pressure based on soil and pile properties assumingsoil movement larger than pile deflection.

5.2. Tygart lake slope stabilization using H-piles

Richardson [26] conducted full scale load tests on pile-stabilized slopes at the Tygart Lake site, West Virginia. The slopemovement at that site has occurred periodically for a number ofyears. As reported by Richardson [26], ten test holes were madeand soil and rock samples were collected for laboratory testing.In five of the test holes, slope inclinometer casing was installedand monitoring wells were installed in the other five test holes.

Based on the data collected in the test holes, the bedrock at thesite dipped and ranged from 6.7 to 9 m from the ground surfacenear the road edge to 11 to 15.5 m below the ground surface down-slope. After about a year of slope monitoring, test piles were in-stalled near the test holes giving the most movement. Test holes2 and 6 were the first to show signs of a similar slip plane. Holesof 18-inch diameters were augured to accommodate the HP10 � 42 test piles that were lowered in place and filled with groutat 1.22 m pile spacing. The results of this case study are based on asection cut between Test Borings 2 and 6. Detailed informationabout the test site and monitoring and soil description is providedby Richardson [26].

Table 3Soil properties input data utilized in current study based on reported data.

Soilnumber

Soiltype

Unit weight (kN/m3)

AverageSPT-N

Disturbed cohesion, Cd

(kPa)Re(de

1 Sand 17.3 14 0 192 Sand 20.4 37 0 303 Rock 20.4 – 2068 0

The failure surface suggested in Fig. 22 is given based on theslope stability analysis of the profile. The soil strength parameters(Table 3) used in the slope stability analysis were back-calculatedbased on impending failure. The sand peak friction angle is deter-mined from the SPT-N (blowcounts) (NAVFAC [27]), and the rockstrength is obtained from unconfined compression tests [26]. Pilemovement under working conditions was collected via inclinome-ter data as presented by Richardson [26].

Table 3 presents (1) the disturbed cohesion and residual frictionangle of the soil along the impending failure surface for slope sta-bility analysis; and (2) the undisturbed cohesion and full frictionangle of the soil along the length of the pile. The failure surfacecoordinates shown in Fig. 22 and the soil properties presented in

sidual friction angle, /r

gree)Undisturbed cohesion, Cu

(kPa)Peak friction angle, /(degree)

0 350 422068 30

-50 0 50 100 150 200

Moment, kN-m

10

9

8

7

6

5

4

3

2

1

0D

epth

, m

Pile 4 [26]Pile 5 [26]Proposed method

Fig. 24. Measured and computed pile moment of the Tygart Lake Test.

M. Ashour, H. Ardalan / Computers and Geotechnics 39 (2012) 85–97 97

Table 3 yield a slope safety factor of 0.976 using the modifiedBishop method. A comparison between measured (piles 4 and 5)and calculated deflection and moment is presented in Figs. 23and 24. Good agreement between measured and computed piledeflection and bending moment can be observed.

6. Conclusions

An approach has been developed to predict the behavior andsafety factors of pile-stabilized slopes considering the interactionbetween the pile and surrounding soil assuming soil displacementlarger than pile deflection. The lateral soil pressure acting on thepile segment above the slip surface is determined based on soiland pile properties (i.e. soil–pile interaction). The developed tech-nique accounts for the effect of pile diameter and position and thecenter-to-center pile spacing on the mobilized soil–pile pressure(pD). The development of the ultimate interaction between the pileand sliding mass of soil is determined via the consideration of thestrength of pile material, soil flow-around failure, soil resistance,and pile interaction with adjacent piles. The study also shows thatthe position of the pile into the slope, the depth of the failure sur-face at the pile position, soil type, pile diameter and pile spacingshave a combined effect on the maximum driving force that the pilecan transfer down to the stable soil. The presented case studiesexhibit the capabilities of the current technique via the comparisonwith measured results and the prediction of the soil–pile pressureabove the slip surface.

Acknowledgment

This research was sponsored by the West Virginia Division ofHighways (WVDOH, Project RP-213) and the University Transpor-

tation Center of Alabama (UTCA). The authors would also like tothank Mr. Joseph (Joe) Carte, Mr. Lawrence (Larry) Douglas,Mr. Jim Fisher and Mr. Mark Nettleton for their support and valu-able feedback.

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