Analysis of pile stabilized slopes based on soil–pile interaction

Computers and Geotechnics 39 (2012) 85–97

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Analysis of pile stabilized slopes based on soil–pile interaction Mohamed Ashour ⇑, Hamed Ardalan Dept. of Civil and Environmental Engineering, University of Alabama in Huntsville, USA

a r t i c l e

i n f o

Article history: Received 13 May 2011 Received in revised form 26 August 2011 Accepted 7 September 2011 Available online 7 October 2011 Keywords: Slope stabilization Soil–pile interaction Pile group Lateral loads Safety factor

a b s t r a c t The paper presents a new procedure for the analysis of slope stabilization using piles. The developed method allows the assessment of soil pressure and its distribution along the pile segment above the slip surface based on soil–pile interaction. The proposed method accounts for the influence of pile spacing on the interaction between the pile and surrounding soils and pile capacity. The paper also studies the effect of soil type, and pile diameter, position and spacing on the safety factor of the stabilized slope. Specific criteria are adopted to evaluate the pile capacity, ultimate soil–pile pressure, development of soil flowaround 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 movements due to slope instability is verified through a number of full scale load tests. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction The use of piles to stabilize active landslides, as a preventive measure in stable slopes, has become one of the important innovative slope reinforcement techniques in last decades. Piles have been used successfully in many situations in order to stabilize slopes or to improve slope stability and numerous methods have been developed for the analysis of piled slopes [1–5]. The piles used in slope stabilization are usually subjected to lateral force by horizontal movements of the surrounding soil and hence they are considered as passive piles. The interaction behavior between pile and soil is a complicated phenomenon due to its 3-dimensional nature and can be influenced by many factors, such as the characteristics of deformation and the strength parameters of both pile and soil. The interaction among piles is complex and depends on soil and pile properties, and the level of soil-induced driving force. Furthermore, the earth pressures applied to the piles are highly dependent upon the relative movement of the soil and the piles. In practical applications, the study of a slope reinforced with piles is usually carried out by extending the methods commonly used for the stability analysis of slopes to incorporate the reaction force exerted on the unstable soil mass by the piles. The characterization of the problem of slope instability and the use of piles to improve the stability of such slopes requires better characterization of the integrated effect of laterally loaded pile behavior, pile-structure-interaction, and the nonlinear behavior of pile materials (steel and/or concrete) on the resultant slope ⇑ Corresponding author. Tel.: +1 256 824 5029; fax: +1 256 824 6724. E-mail address: [email protected] (M. Ashour). 0266-352X/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compgeo.2011.09.001

stability condition. The driving force of the soil mass that acts along the pile segment above the slip surface is transmitted to the lower (stable) soil layers, as shown in Fig. 1. Such a scenario requires representative modeling for the soil–pile interaction above the failure surface that reflects and describes actual distribution for the soil driving force along that particular portion of the pile. In addition, the installation of closely spaced pile row would create an interaction effect (group action) among adjacent piles not only below 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 in NAVFAC [7]. Another alternative is to use the ultimate soil reaction from the traditional p–y curve. Neither of these ultimate resistances was envisioned for sloping ground, and neither considers group interference effects in a fundamental way, certainly not for sloping ground conditions. In addition, flow-around failure of soil around the pile is a significant phenomenon that should be considered in the current practice. It should be noted that the flowaround failure governs the amount of force (PD) acting on the pile above the failure surface. The presented method allows the determination of the mobilized driving soil–pile pressure per unit length of the pile (pD) above the slip surface based on soil–pile interaction in an incremental fashion using the strain wedge (SW) model technique developed by Norris [8] and Ashour et al. [9]. The buildup of pD along the pile segment above the slip surface should be coherent with the variation of stress/strain level that is developed in the resisting soil layers below the slip surface. The mobilized nonuniformly distributed soil pressure (pD) is governed by the soil–pile interaction (i.e. soil and pile properties) and developing flowaround failure above and below the slip surface. In addition, the

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su Slope

rface oil ized s Mobil e (p D) r pressu

g Slidin

mass g soil n i d i l S

e s urfa c

Pile extended into stable soil Soil-pile resistance (p)

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

Slope

Soil-pile resistance (Beam on Elastic Foundation)

mass g s oi l Slidin

surfac

e

soil lized Mobi e (p D) r u s s e pre surfac

Slidin

g

Stable soil

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

presented technique allows the calculation of the post-pile installation safety factor (i.e. stability improvement) for the whole stabilized slope, and the slope portions uphill and downhill the pile. The size of the mobilized passive wedge of sliding soil mass controls the magnitudes and distribution of the soil–pile pressure (pD) and the total amount of the driving force (PD) transferred via an individual pile in a pile row down to the stable soil layers. The presented technique also accounts for the interaction among adjacent piles (group effect) above and below the slip surface. Fig. 2 shows the soil–pile model as employed in the proposed technique. The ability of this method to predict the behavior of piles subject to lateral soil movements due to slope instability is verified through a comparison with two case histories. Also, the efficiency of using stabilizing pile in a slope is discussed by examining the influence of pile location in the slope, pile spacing, and pile diameter and stiffness.

2. Methods of analysis Ito et al. [1] proposed a limit equilibrium method to deal with the problem of the stability of slopes containing piles. The lateral force 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 considering plastic flow of the soil through the piles. The ultimate soil pressure on the pile segment which is induced by flowing soil depends on the strength properties of the soil, overburden pressure, and spacing between the piles and is independent of pile stiffness as a rigid pile with infinite length. Also, the equations are only valid over a limited range of spacings, since, at large spacing or at very close spacings, the mechanism of flow through the piles postulated by Ito and Matsui [10] is not the critical mode [2]. Large increase in the value of the soil–pile pressure (pD) can be observed by reducing the clear spacing between piles. Hassiotis et al. [11] have extended the friction circle method by defining new expressions for the stability number to incorporate the pile resistance in slope stability analysis using a closed form solution of the beam equation. The ultimate force intensity (soil– pile pressure) is calculated based on the equations proposed by Ito and Matsui [10] assuming a rigid pile. The finite difference method is used to analyze the pile section below the critical surface as a beam on elastic foundations (BEF). However, the safety factor of the slope after inserting the piles is obtained based on the new critical failure surface, which is not necessarily the one before pile installation [11]. Poulos [2] and Lee et al. [12] presented a method of analysis in which a simplified form of boundary element method [13] was employed to study the response of a row of passive piles incorporated in limit equilibrium solutions of slope stability in which the pile is modeled as a simple elastic beam, and the soil as an elastic continuum. The method evaluates the maximum shear force that each pile can provide based on an assumed input free field soil movement and also computes the associated lateral response of the pile. The prescribed soil movements are employed by considering the compatibility of the horizontal movement of the pile and soil at each element. While pile and soil strength and stiffness properties are taken into account to obtain soil–pile pressure in this method, group effects, namely piles spacing, are not considered in the analysis of soil–pile interaction. Poulos [2] recommends the installation of stabilizing piles be located in the center of the failure surface to avoid any slope failure behind or in front of the pile. A constant soil Young’s modulus that varies linearly with depth has been used along with an ultimate lateral pressure, pD. For the practical use, Poulous [2] promoted the flow mode that creates the least damage effect of soil movement on the pile where the soil movement is larger than the pile deflection. Such a slope-pile displacement mechanism coincides with the suggested soil–pile interaction model presented in this paper. Chow [14] presented a numerical approach where the piles are modeled using beam elements as linear elastic materials and soil response at the individual piles is modeled using an average modulus of subgrade reaction. In this method, the sliding soil movement profile are assumed or measured based on the field observation and the problem is analyzed by considering the soil– pile interaction forces acting on the piles and the soil separately and then combining those two by the consideration of equilibrium and compatibility. Ultimate soil pressure acting on the piles in this method for cohesive and cohesionless soils are calculated based on the equations proposed by Viggiani [15] and Broms [6], respectively. These equations are strictly for single piles, while studies such as those by Chen and Poulos [16] shows that the ultimate soil pressure are affected by the pile spacing and group arrangement. The influence of one row of pile groups on the stability of the weathered slope was investigated by Jeong et al. [17] based on an analytical study and a numerical analysis. A model to compute load and deformations of piles subjected to lateral soil movement based on the transfer function approach was presented. In this method, a coupled set of pressure–displacement curves induced

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in the substratum determined either from measured test data or from finite-element analysis is used as input to study the behavior of the piles which can be modeled as a BEF. The study assumes the ultimate soil pressure acting on each pile in a group to be equal to that adopted for the single pile multiplied by the group interaction factor evaluated by performing three-dimensional finite element analysis. Ausilio et al. [18] have used the kinematic approach of limit analysis for the stability of slopes that are reinforced with piles. The case of a slope without piles is first considered where the sliding surface is described by a log-spiral equation, and then a solution is proposed to determine the safety factor of the slope, which is defined as a reduction coefficient for the strength parameters of the soil. Then, the stability of a slope containing piles is analyzed. To account for the presence of the piles, a lateral force and a moment are assumed and applied at the depth of the potential sliding surface. To evaluate the resisting force (FD), which must be provided by the piles in a row to achieve the desired value of the safety factor of the slope, an iterative procedure is used to solve the equation obtained by equating the rate of external work due to soil weight and surcharge boundary loads to the rate of energy dissipation along the potential sliding surface. Nian et al. [19] developed the similar approach to analyze the stability of a slope with reinforcing piles in nonhomogeneous and anisotropic soils. Zeng and Liang [4] presented a limit equilibrium based slope stability analysis technique that would allow the determination of the safety factor (SF) of a slope that is reinforced by drilled shafts. The technique extends the traditional method of slice approach to account for stabilizing shafts by reducing the interslice forces transmitted to the soil slice behind the shafts using a reduction (load transfer) factor obtained from two-dimensional finite element analysis generated load transfer curves. A similar approach presented by Yamin and Liang [20] uses the limit equilibrium method of slices where an interrelationship among the drilled shaft location on the slope, the load transfer factor, and the global SF of the slope/shaft system are derived based on a numerical closed-form solution. Furthermore, to get the required configurations of a single row of drilled shafts to achieve the necessary reduction in the driving forces, a newly generated design charts utilizing three-dimensional finite element are used with 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-structure interaction is modified to evaluate the mobilized non-uniformly distributed soil–pile pressure (pD) along the pile segment above the anticipated failure surface (Fig. 1) assuming a flow mode for soil mass above the slip surface. The presented technique focuses on the calculation of the mobilized soil–pile pressure (pD) based on the interaction between the deflected pile and the sliding mass of soil above the slip surface using the concepts of the SW model. The pile deflection is also controlled by the associated profile of the modulus of subgrade reaction (Es) below the sliding surface (Fig. 2). It should be emphasized that the presented model targets the equilibrium between the soil–pile pressure calculated above and below the slip surface as induced by the progressive soil mass displacement and pile deflection. Such a sophisticated type of equilibrium requires the synchronization among the soil pressure and pile deflection above the failure surface and the accompanying soil–pile resistance (i.e. Es profile) below the slip surface. While pD is governed by the soil–pile interaction and its ultimate value (i.e. soil and pile properties and developing flow-around failure (Ashour and Norris [21]),

the pile capacity is limited to its plastic moment (structural/material failure). The capabilities of the SW model approach have been used to capture the progress in the soil flow-around the pile and the distribution of the induced driving force (PD = R pD) above the slip surface 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 compatible sliding mass displacement and pile deflection for the associated slope factor of safety. As seen in Figs. 1 and 2, the soil–pile model utilizes a lateral driving load (above the failure surface) and lateral resistance from the stable soil (below the failure surface). Shear force and bending moment along the pile are also calculated. Thereafter, the safety factor of the pile-stabilized slope can be re-evaluated. The implemented soil–pile model assumes that the sliding soil mass imposes increasing lateral driving force on the pile as long as the shear resistance along the sliding surface up-slope the pile cannot achieve the desired stability safety factor. As seen in Fig. 3, a mobilized three-dimensional passive wedge of soil will develop into the sliding soil zone above the slip surface (upper passive wedge) with a fixed depth (Hs) and a wedge face of width (BC) that varies with depth (xi) (i.e. soil sublayer and pile segment i).

ðBCÞi ¼ D þ ðHs  xi Þ2ðtan bm Þi ðtan um Þi ðbm Þi ¼ 45 þ

ðum Þi 2

xi 6 H s

ð1Þ ð2Þ

The horizontal size of the upper passive wedge is governed by the mobilized fanning angle (/m), which is a function of the soil stress level (SL) (Fig. 3a). /m in clay is determined based on the effective stress analysis (Ashour et al. [9], Fig. 4). It should be mentioned that the effective stress (ES) analysis is employed with clay soil as well as with sand and C  / soil (Fig. 4) in order to define the three-dimensional strain wedge geometry with mobilized fanning angle (Ashour et al. [9]). To account for the effective stress in clay, the variation of the excess pore water pressure is determined using Skempton’s equation [22] where the water pressure parameter varies with the soil stress level [9]. The sliding mass of soil above the slip surface is assumed in the current analysis to experience lateral displacement larger than pile deflection, (Fig. 5). The mobilized fanning angle, /m, of the upper (driving) passive soil wedge due to the interaction between the moving mass of soil and the embedded portion of the pile (Hs) increases with the progress in soil displacement (i.e. SL in soil). e50 is the normal strain in soil at SL = 0.5 and /m is determined as a function of SL, which is calculated from the constitutive stress–strain model presented by Ashour et al. [9] (Fig. 6). The soil strain (es) in the upper passive wedge (i.e. sliding soil mass) is increasing gradually in an incremental fashion (a step by step loading process). In each loading step, the distribution of pD (Figs. 1 and 2) along the pile length embedded into the sliding soil layer(s) is determined as,

ðpD Þi ¼ ðDrh Þi BC i S1 þ 2si DS2 where PD ¼

i¼n at X slip surface

ð3Þ

pD

i¼1

pD is the soil–pile pressure per unit length of the pile (F/L) at the  3c (i.e. overburden pressure current effective confining pressure r assuming isotropic conditions, K = 1) and soil strain es in the soil sublayer i at depth xi. D is the width of the pile cross section, and BC is the width of the soil passive wedge at depth xi. S1 and S2, on the 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 the pile–soil shear resistance along the side of the pile (Fig. 3a). Drh is

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F1

Real stressed zone

C

τ

A

φm

Pile

Slope surface

Δσh

φm

A

mass g soil Slidin

No shear stress because these are principal stresses

Side shear (τ) that influences the oval shape of the stressed φm zone

e passiv ed soil Mobiliz pper wedge) (u wedge

urface Slip s Lower mobilized wedges

B

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

F1

Soil sublayers

(a) Force equilibrium in a slice of the wedge at depth x. Yo Sublayer 1

Hs

Hi

i-1 i

σV O

x KσVO

Δσh

Sublayer i+1

δ

(c) Mobilized passive soil wedges. βm

(b) Forces at the face of a simplified soil upper passive wedge (Section elevation A-A). Fig. 3. Characterization of the upper soil wedge as employed in the proposed technique.

the deviatoric stress calculated at the current soil strain es in sublay 3c ¼ overburden pressure r  v o ). er i with confining effective stress ðr Therefore, the horizontal stress change at the face of the wedge at depth x becomes,

Drh ¼ SLDrhf

ð4Þ

where

h  u i  v o tan2 45 þ Drhf ¼ r  1 ðsandÞ 2

ð5aÞ

Drhf ¼ 2Su

ð5bÞ

Drhf

ðclayÞ



h  C u i  v o tan2 45 þ ¼ þr  1 ðC  usoilÞ tan u 2

the mobilized friction angle (tan /m) and mobilized cohesion (Cm) in the mobilized wedge. Of course, /s and Cs are limited to the 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 passive pressure (SL = 1) and the flow of soft/loose soil around the pile. It should be noted that pD could reach its ultimate value (i.e. soil starts flowing around the pile) to cease the growth of the upper passive soil wedge and its interaction with the pile segment. Flow-around failure in a soil sublayer i detected via parameter A and its ultimate value Ault.

Ai ¼ ð5cÞ

The side shear stress, si, is determined as

si ¼ ðr v o Þi tanðus Þi where tan us ¼ 2 tan um and tan us 6 tan u ðsandÞ

ð6aÞ

si ¼ ðSLt Þi ðsult Þi where sult is a function of Su ðclayÞ

ð6bÞ

si ¼ ðr v o Þi tanðus Þi þ 2Cs where tan /s ¼ 2 tan /m and C s ¼ 2C m ðC  u SoilÞ

ð6cÞ

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

ðpD Þi =D BC i S1 2 s i S2 ¼ þ ð Dr h Þ i D ðDrh Þi

ð7Þ

The progress in soil mass displacement (i.e. pD and soil–pileinteraction) continues until the targeted slope safety factor is achieved or the pile fails to interact with sliding soil mass. Therefore, no additional soil driving force is transferred to the stable soil layer(s) below the failure surface. The SW model is applied to assess the modulus of subgrade reaction profile (Es) along the pile length below the slip surface (i.e. p) as shown in Fig. 2). Ashour et al. [9] presents detailed information on the assessment of the Es profile below the slip surface as employed in the current analysis for the BEF. 3.2. Failure criteria and ultimate soil–pile pressure above the slip surface The presented technique accounts for different failure mechanisms that include pile and soil failure and limiting values for

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Shear Stress (τ)

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Displacement SL =

ϕ

Δσ h tan 2 (45 + ϕ m / 2) − 1 = Δσ hf tan 2 (45 + ϕ / 2) − 1

Soil movement Deflected pile

(σ vo )1 (σ vo ) 2 (σ vo )3

(σ vo ) 4

Depth below ground level

ϕm

Normal Stress (σ)

(a) Sand Lab total stress (or field total stress minus static pore water pressure) Δσ h

Undrained excess pore water pressure

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

σ vo + Δσ h − Δu Δu

σ vo σ vo

Failure surface

_

σ vo − Δu

Shear Stress (τ)

=

ϕ ϕm

SL Su σ vo + Δσ h

σ vo − Δu

σ vo

σ vo + Δσ h − Δu

Normal Stress (σ)

Shear Stress (τ)

(b) Clay

ϕ ϕm

Normal Stress (σ)

(Ci ) m

σ vo

σ vo + Δσ h

σ vo + Δσ hf

(c) C-ϕ soil Fig. 4. Mobilized effective friction angle with the variation of soil stress as employed in current study.

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

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

embedment into the stable soil (i.e. less flexural deformation). MP is determined from the moment–curvature relationship of the pile cross section. The second failure mechanism reflects the development of a flow-around failure when parameter A reaches its ultimate value (Ault). The assessment of Ault in sand was initially developed by Reese [23] and modified by Norris [8].

ðAult Þi ¼

ðK a Þi ½ðK p Þ4i  1 þ ðK o Þi ðK p Þ2i tan ui ðK p Þi  1

ð8Þ

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

ðAult Þi ¼

ðpult Þi D

ðDrhf Þi

¼

ðpult Þi ¼ 5S1 þ S2 D2ðSu Þi

ð9Þ

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

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slipping sublayer of soil. As a result, no additional soil pressure is transferred via the pile segment embedded into that soil sublayer (i). A third soil–pile interaction controlling mechanism would take place when pD is equal to (pD)ult in soil sublayer (i) above the slip surface (i.e. SL = 1).

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

½ðpD Þult i ¼ ðDrhf Þi BC i S1 þ 2ðsf Þi DS2

ð10aÞ

ðSLg Þi ¼ SLi ð1 þ

ð10bÞ

where j is the number of neighboring passive wedges in soil layer i that overlap the wedge of the pile in question (j = 2 for a single pile row). R is the ratio between the length of the overlapped portion of the face of the passive wedge (r) and the width of the face of the passive wedge (BC) (Fig. 7). R (which is less than 1) is determined for both sides of the pile overlap. SLg and the associated soil strain (eg) will be assessed for each soil sublayer. eg is Pe of the isolated pile (no group effect) and is determined based on the stress–strain relationship (r vs. e) presented by Ashour et al. [9] (Fig. 6). The angles and dimensions (geometry) of the passive wedge (/m, bm, and BC) obtained from Eqs. (1) and (2) would be modified for the group effect according to the calculated value of SLg and eg. The average value of deviatoric stress (Drh)g developed at the face of the passive wedge in a particular soil sublayer i is

½ðpD Þult i ¼ 10ðSu Þi DS1 þ 2ðSu Þi DS2

ðsandÞ ðclayÞ

In addition, the fixed depth of the upper passive wedge (Hs) would prevent the face of the soil wedge (BC) and pD at that depth from growing. In fact, the soil–pile interaction mechanism above the slip surface is influenced by the depth of the slip surface at the 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 in return the soil–pile interaction. The developed (pD) is expressed as

ðpD Þi ¼ Ai Des Ei

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 calculated based on pile spacing and the interaction among the piles. The pile group interaction technique developed by Ashour et al. [24] is used to estimate the interaction among the piles above and below the sliding surface assuming soil displacement to be larger than pile deflection. The safety factor of the pile-stabilized slope can be reevaluated based on the distributed lateral force (PD) induced by soil mass and carried by the pile down to the stable soil below the slide surface. The fourth soil–pile interaction controlling mechanism adopted in the presented technique is based on monitoring the horizontal stress overlapping among stabilizing piles above and below the slip surface. The horizontal growth of the upper mobilized passive soil wedge governs the build up of the soil–pile driving pressure (pD) in any sublayer (i) as a result of adjacent soil wedge overlapping. The upper soil wedges developed into the up-slope portion of the sliding soil mass overlap according to the pile spacing and level of soil stress (Fig. 7). Consequently, the stresses into adjacent soil intensify (compared to the case of isolated pile) until pD reaches its ultimate value or the flow-around failure takes place. The current study utilizes the technique presented by Ashour et al. [24] that was developed to assess the lateral interaction among the piles in a group based on soil and pile properties and

Adjusted uniform stress at the face of the soil wedge

r Soil wedge

BC Soil wedge

Pile

Pile Uniform pile face movement

Overlap of stresses based on elastic theory Fig. 7. Horizontal passive soil wedge overlap among adjacent piles.

X

Rj Þ1:5 6 1

ðDrh Þg ¼ SLg Drhf

ð12Þ

ð13Þ

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

Eg ¼

SLg Drhf

eg

where Eg 6 E of isolated pile case

ðpD Þg ¼ ðAg Þi Dðeg Þi ðEg Þi

ð14Þ ð15Þ

Compared to the isolated pile, the soil mass in contact with the pile row maintains a softer response (i.e. less pD at the same y) as a result of pile interaction (soil wedge overlap effect). To avoid repetition, the interaction among adjacent piles in a pile row below the 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, the flowchart presented in Fig. 8 demonstrates the calculation and iteration process as implemented in the current model. A small initial value of soil strain above and below the slip surface (es and e, respectively) is assumed to determine (1) pD as summarized in Eq. (11) and related equations for A and E; and (2) Es profile below the slip surface [24]. The current pile head deflection (Yo) is evaluated using the SW model procedure [24] to obtain (Yo)SWM that is compared to the pile head deflection (Yo)BEF calculated from the BEF analysis using current pD distribution and Es profile. If (Yo)SWM is larger than (Yo)BEF, es is adjusted (increased) till acceptable convergence between (Yo)SWM and (Yo)BEF is achieved. On the other side, e will be increased if (Yo)SWM is less than (Yo)BEF. It should be noted that adjusting es (i.e. pD) will also affect the Es profile as a result of changing the dimensions of the lower wedges (i.e. softer Es profile). Therefore, es is always increased in slower rate compared to e in order to capture the desired convergence of pile head deflection. The next increment of loading will be followed by increasing es and adjusting (increasing) e of soil below the slip surface (i.e. new Es profile) to calculate (Yo)SWM and (Yo)BEF. The presented methodology aims at the state of soil–pile equilibrium where the deflected pile would interact with surrounding soils to induce balanced driving (pD) and resisting (p) soil pressure above and below the slip surface. Practically, there is only a single pile

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

INPUT DATA Soil properties, slope profile, pile properties and desired safety factor of supported portion

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

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

1. Divide soil layers into thin sublayers (i) with thichness Hi. 2. Calculate effective vertical stress (σvo) for each sublayer.

91

as the effective unit weight, angle of internal friction (/), undrained shear strength (Su) and pile geometry, bending stiffness and plastic moment. Boundaries of soil layers in addition to the location of the driven pile need to be also identified. The soil profile is divided into thin sublayers (0.5 or 1 ft thick) and each sublayer is treated as an independent entity with its own properties. In this fashion, the variation in soil properties (such as e50 and / in the case of sand, or Su in the case of clay) of each sublayer of soil can be explored. e50 is obtained from the charts presented in [9]. The computer software (PSSLOPE), which is written in Visual Basic and FORTRAN, has been developed to implement the presented technique for pile stabilized slopes including the slope stability analysis (with no piles) using the modified Bishop method. 3.6. Safety factor

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.

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 (H s). 2. Use ε to calculate Δσh = σd, SL, ϕm, BC, E, and Es for sublayers below slip surface [9] (i.e. E s 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 (Y o)SWM based on the SW model [9].

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

FS ¼

F r ðF rs þ F rp Þ ¼ Fd Fd

No

IF(Yo)SWM > (Yo)BEF Increase εs IF(Yo)SWM < (Yo)BEF Increase ε

Yes

F r ðF rsðsupportedÞ þ F rp Þ ¼ Fd F dðsupportedÞ

FSðunsupportedÞ ¼ ¼

1. Accepted loading increment, p D and p above and below the slip surface, Yo and Es profile. 2. Calculate bending deflection, moment, shear Force, distribution of driving forces (p D), and safety factor. 3. Current driving force (P D) = Σ(pD)i above the slip surface.

IF PD < FD

Yes

Increase the value of εs by Δε

No STOP Fig. 8. Flowchart for the analysis of pile-stabilized slopes.

deflection pattern that could maintain the state of equilibrium between the pile and surrounding soil above and below the slip surface. The analysis stops indicating pile failure when the moment in the pile reaches its ultimate value (plastic moment). 3.5. Input data One of the main advantages of the SW model approach is the simplicity of the required soil and pile properties. Those properties represent basic and most common properties of soil and pile, such

ð17Þ

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

FSðsupportedÞ ¼ IF (Yo)SWM = (Yo)BEF

ð16Þ

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

FS ¼ 1. Use Es profile to solve the pile problem as a BEF under driving soil pressure p D acting on the pile segment above the slip surface. 2. Obtain the pile head deflection, (Y o) BEF, from the BEF analysis.

F rs Fd

ð18Þ

Fr Fd F rsðunsupportedÞ F dðunsupportedÞ þ ½ðF dðsupportedÞ  F rsðsupportedÞ Þ  F rp  ð19Þ

where Frs(supported) and Fd(supported) are the resisting and driving force of soil mass along the supported portion of the critical failure surface. The resisting and driving force of soil mass along the unsupported portion of critical failure surface Frs(unsupported) and Fd(unsupported) are also calculated using the slope stability method of slices as shown in Fig. 9b. Frp in Eqs. (17) and (19) is calculated from Eq. (18) after the desired safety factor of the supported (upslope) portion of the slope (FS(supported)) is identified. By calculating Frp, the targeted load carried by each pile in the pile row can be evaluated (FD = Frp  S). FS(supported) needs to be identified with a minimum value of unity. The achievement of the minimum factor of safety (FS(supported) = 1) indicates that the stabilizing pile is able to provide enough interaction with the sliding mass of soil in order to take a force equal to the difference between the driving and resisting forces along the slip surface of the supported portion of the slope (Frp = Fd(supported)  Frs(supported)). As a result, the second term of the denominator in Eq. (19) would be zero. However, the minimum safety factor may not be achieved as a result of reaching the ultimate soil–pile interaction as presented in the previous section. Therefore, the rest of driving force (the second term of the denominator in Eq. (19)) will be delivered (flow) to the lower segment of the slope (the unsupported portion).

92

M. Ashour, H. Ardalan / Computers and Geotechnics 39 (2012) 85–97 Table 1 Pile properties.

Critical Failure Surface

Unit weight (kN/m3) Diameter (m) Elastic modulus (kPa) Compressive strength of concrete (kPa) Plastic moment (kN-m) Yield strength of the rebar (kPa)

Fd Frs

(a) Slope stability under driving and resistance forces.

Frp Fd(unsupported) Frs(unsupported)

(b) Forces acting on a pile-stabilized slope. Fig. 9. Slope stability pre- and post-pile installation.

To reach the ultimate safety factor of the stabilized slope, an increasing value of the safety factor of the supported portion of the slope should be used (i.e. transferring more soil pressure through the piles) until maximum interaction between the piles and surrounding soil is observed. However, the stabilizing piles may 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-pile interaction and the amount of resistance that the stabilizing pile can provide to increase the safety factor of the stabilized slope. Some of these influencing factors can be outlined as the geometry and material properties of the pile, soil properties, pile position in the slope (i.e. the depth of slip surface at pile location), and the spacing of adjacent piles. To examine the effect of the above mentioned parameters on slopes 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 with the horizontal ground surface of 30°. A weathered rock deposit is

30o

C = 7.5 kPa ϕ = 17O γ = 19 kN/m3

Lx

Firm Layer (Weathered Rock)

Hs

23 1.2 2.6  107 3.0  104 5000 4.14  105

located at 4 m below the ground surface at the slope toe. For both cases, the soil is assumed to be a C  / soil such as a silty or clayey sand. The safety factor of both slopes before stabilization is about 1.03 obtained by performing slope stability analysis using the modified Bishop method and the corresponding critical failure surfaces are shown in Fig 10. As depicted in Fig. 10, the critical failure surface for Case II is deeper than that of Case I because of the different soil properties in both cases (Case II is more cohesive and less frictional compared to Case I). One row of 1.2-m diameter reinforced concrete piles with the properties summarized in Table 1 has been installed to increase the stability of the slopes. In order to carry out this study, the piles are assumed to have enough embedment into the weathered rock. The pile head maintains free head conditions (free rotation and displacement), which is very common in practice. The parametric study carried out is based on the pile properties listed in Table 1 unless otherwise stated. Pile analysis results showed that stresses caused by the moment in the piles are more critical than those caused by shear. Therefore, in the following study the ratio of the pile maximum moment to its plastic moment (Mmax/Mp) is considered as an indication of pile structural stability (i.e. pile material failure).

4.1. Effect of pile position The effect of pile position on the safety factor of pile-stabilized slopes is illustrated in Fig. 11. A constant center-to-center pile spacing versus pile diameter ratio (S/D) of 2.5 is maintained in the analysis. For both slopes, the most effective pile position is located between the middle and the crest of the slope as found by 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 is underlain by a stiff layer. This optimum position of the pile row is also influenced by the pile characteristic length that is embedded into the unstable and stable regions. Compared to Case I, a larger force carried by the pile (Frp) (Fig. 11a) and less safety factor (Fig. 11b) can be observed in Case II due to the deeper slip surface at the pile position and larger associated driving force (Fd). It should be mentioned that the Hs /D ratio has a significant effect

10 m

30o

Hs

C = 14 kPa ϕ = 10O γ = 18 kN/m3

4m

4m L

L Lx

C = 700 kPa ϕ = 0O γ = 20 kN/m3

(Case I)

10 m

(a)

C = 700 kPa ϕ = 0O γ = 20 kN/m3

(Case II)

(b) Fig. 10. Illustrative examples of pile stabilized slopes.

Firm Layer (Weathered Rock)

93

1.2

1000

(a)

S/D = 2.5

1

800 0.8

Mmax/MP

Resistance developed by each pile (PD), kN

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

600

S/D = 2.5

400

0.4

0.2

Case I Case II

200 0.2

0.4

0.6

0.6

0.8

1

0 0.2

Case I Case II 0.4

0.6

0.8

1

Lx/L

Lx /L

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

SF(Whole slope)

1.6

(b)

1.4

S/D = 2.5

1.2

Case I Case II

0.2

0.4

0.6

0.8

1

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

enced by the shape of the failure surface (i.e. soil properties) and pile properties. Fig. 12 also presents the variation of the safety factor of the unsupported portion of the slope versus the pile position. It should be emphasized that the safety factor of the unsupported portion of the slope should not be less than the desired safety factor of the whole slope as determined from Eq. (17). Such a scenario could take place when the stabilizing pile is installed close to the crest of the slope. For example, if the pile is located at Lx /L > 0.8 and Lx/L > 0.9 in Cases I and II, respectively, the safety factor of the unsupported part would be less than the safety factor of the whole slope. Fig. 13 shows the efficiency ratio (Mmax/Mp) of the stabilizing piles with respect to their position in the slope (Lx/L). Mmax and MP 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 controlled by the strength of pile materials (i.e. structural failure and the formation of a plastic hinge where Mmax = MP) while for other pile positions in Case II and the entire slope of Case I the maximum safety factor of the stabilized slope is obtained based on the ultimate interaction between the pile and sliding mass of soil.

7 S/D = 2.5

4.2. Effect of pile spacing

SF (Unsupported portion)

6

The effect of pile spacing on the factor of safety of the slopes is expressed via the relationship of the factor of safety versus S/D ratio. Fig. 14 shows the effect of pile spacing (i.e. group action among neighboring piles) on the factor of safety assessed at the ultimate state of soil–pile interaction in Cases I and II at a particular pile position Lx /L = 0.7. The factor of safety of the slopes, as expected, is decreasing by increasing the pile spacing. It is significant to note that the closer the pile spacing the larger the interaction among the piles below the slip surface. Therefore, larger pile deflection is anticipated.

5

4

3

Case I Case II

2

1 0.5

4.3. Effect of soil type 0.6

0.7

0.8

0.9

1

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

on the soil–pile interaction and the amount of force transferred by the pile down to the stable soil layer. Thus, designers should not rely on just a general position ratio (Lx/L) for pile installation to capture the largest safety factor. The desired pile location is influ-

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 II where the values of Hs are 3.8 and 5.5 m, respectively. The distribution of pD in both cases corresponds to the ultimate slope-pile interaction. In order to avoid the pile material failure in Case II before reaching the ultimate interaction of the pile with surrounding soil, Lx /L < 0.6 has been used. More soil–pile interaction should be expected with less soil plasticity (i.e. soils with higher / and less C).

94

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

1.7

2 Lx /L = 0.7

1.5

SF(Whole slope)

SF(Whole slope)

1.8

1.6

1.4 1.3 1.2

1.4

1

2

Case I Case II

1.1

Case I Case II 1.2

Lx/L = 0.7 S=3m

1.6

3

4

1 0.6

5

0.8

1

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

40

80

120

160

1.6

1.8

1.7

200

L x/L = 0.7 S/D = 2.5

1.6 L x /L = 0.5

1

3 Slip surface for Case I

4

SF(Whole slope)

1.5

2

Depth, m

1.4

Fig. 16. Effect of pile diameter on the slope safety factor using a constant spacing of 3 m.

Soil-pile pressure (p D), kN/m 0 0

1.2

D, m

S/D

1.4 1.3 1.2

5 Slip surface for Case II

6

Case I Case II

1 0.6

4.4. Effect of pile diameter The effect of pile diameter on the safety factor (SF) of the slope has been studied for a constant center-to-center pile spacing of 3.0 m and Lx /L = 0.7, where pile stiffness and strength properties are taken into account (Fig. 16). As expected, the safety factor of the stabilized slopes increases as pile diameter increases from 0.9 m to 1.6 m. However, a slow increase in the safety factor can be observed beyond pile diameter 1.0 m and 1.4 m in Cases I and II, respectively, as a result of decreasing Hs/D ratio. It should be also noted that increasing the pile diameter within the constant pile spacing (3.0 m) would increase the interaction among adjacent piles above and below the slip surface. Fig. 17 shows the effect of pile diameter on the safety factor of stabilized slopes using S/D = 2.5 (i.e. varying D and S with a constant ratio of S/D) at the same pile location (Lx/L = 0.7). As observed in Fig. 17, the safety factor (SF) of the slope is governed by the pile strength (i.e. pile failure) and grows by the increase of pile diameter until SF reaches its optimum value at a certain pile diameter. Thereafter, the safety factor is decreasing by the increase of pile diameter (i.e. no pile failure) due to the decrease of Hs /D ratio. Consequently, the safety factor of the stabilized slope is not only

0.8

1

1.2

1.4

1.6

1.8

D, m

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

Case I Case II

1.1

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

dependent on the S/D ratio, but also is a function of Hs /D ratio and soil properties. In practice, it is an important issue to choose appropriate pile spacing and diameter to provide adequate pile resistance and avoid high construction costs that may be associated 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 to stabilize an 8-m high railway embankment of Weald Clay at Hildenborough, Kent, UK (Smethurst and Powerie [25]) (Fig. 18). Remediation of the embankment was carried out to solve longterm serviceability problems, including excessive side slope displacements and track settlements. Stability calculations carried out after an initial site investigation showed the north slopes of the embankment to be close to failure. A 3.5 m high rockfill berm was constructed at the toe of the embankment, and 200 piles were installed along two lengths of the embankment at a spacing of 2.4 m to increase the factor of safety of the whole slope to the required value of 1.3. Smethurst and Powerie [25] estimated the soil driving (shear) force required to achieve the desired safety factor

95

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

1.0 m cess

Displacement, mm 10 m

6.0m

0

5

10

15

20

25

30

35

40

0 Ballast

Rockfill

4.5 m

3.5 m

Rockfill

Depth below ground level, m

1 24 o

Weald Clay embankment fill

30 o

Weathered Weald Clay

Intact Weald Clay

Design failure surface

2 Embankment fill

3 4

Intact weathered and unweathered Weald Clay

5 6

Measured [25]

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

7 8

Proposed Method

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

Uncracked section Cracked section

10

Fig. 19. Measured and computed pile displacements.

Bending moment, kN-m -100

0

100

200

0

2

4

Depth, m

and transferred by the pile to be 60 kN. Soil strength parameters reported by Smethurst and Powerie [25] and also used in current analysis are based on data from the site investigation and associated triaxial tests (Table 2). As reported by Smethurst and Powerie [25], the 0.6-m diameter and 10-m long bored concrete piles were constructed at a spacing of 2.4 m. Each pile contains six (high tensile) T25 reinforcement bars over their full length, and six T32 bars over the bottom 7 m, giving an estimated ultimate bending moment capacity (plastic moment, MP) of 250 kN-m over the top 3 m, and 520 kN-m over the bottom part of the pile. After pile construction, the granular rockfill material was regraded into a two-stage slope with the suggested failure surface shown in Fig. 18. The reported pile bending stiffness (EI) was 187  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 the EI of the whole pile in linear analysis. EI = 115  103 kN-m2 is considered in current analysis to be the bending stiffness of the partially cracked section (2/3 of the initial EI). Strain gauges were installed in three adjacent piles to measure the bending moments induced in the pile by slope movements. Displacement data for the soil and piles were obtained from the inclinometer tubes in the slope midway between the piles and the inclinometer tubes in Piles. The average pile and soil displacements for 42 days, shortly after the rockfill on the slope surface had been regraded, and 1345 days are shown in Fig. 19 [25]. Using the soil parameters presented in Table 2, the Modified Bishop method is applied in the current procedure to study the stability of the given slope without piles. A safety factor of 1.176 is obtained. No specific slope safety factor value was reported by Smethurst and Powerie [25]. It should be noted that the slope safety factor is very sensitive toward any slight change in the slip surface coordinates.

6

8

10

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

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

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

Table 2 Design soil parameters [24]. 0

0

Soil type

Unit weight, c (kN/m3)

Friction angle, / (degrees)

Effective cohesion, c (kPa)

Weald Clay embankment fill Softened Weald Clay embankment fill Weathered Weald Clay Weald Clay Rockfill

19 19 19 20 19

25 19 25 30 35

20.9 20.9 20.9 104.4 0

96

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

40

Soil-pile pressure (pD), kN/m 0

20

40

60

80

Vertical distance, m

0

Rockfill

Depth, m

1

2

G.W.T

30

Soil No. 1 (Sand)

20

Soil No. 2 (Sand)

Weald Clay embankment fill

Pile

Rock

3

10

20

Failure surface

30

40

50

Horizental distance, m 4

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

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

Displacement, mm

The distribution of bending moment with depth from the two sets of gauges in Pile C is shown for day 1345 in Fig. 20. Fig. 21 exhibits the variation of mobilized pD along the pile segment embedded into two different types of soils above the slip surP face. The current method provides 89 kN of shear force ( pD in Fig. 21) transferred by the pile which is larger than the initially calculated shear force (60 kN) and smaller than the shear force (110 kN) that was back-calculated from the strain gauge data after 1345 ‘s by Smethurst and Powerie [25]. Substantial amount of the driving force is caused by the interaction between the pile and the rockfill layer compared to the underlying clay fill. As presented in Fig. 21, the proposed technique allows the assessment of the mobilized soil–pile pressure based on soil and pile properties assuming soil movement larger than pile deflection.

0

10

20

30

40

50

60

70

0 1 2

Depth, m

3 4 5 6 7

5.2. Tygart lake slope stabilization using H-piles

8

Richardson [26] conducted full scale load tests on pilestabilized slopes at the Tygart Lake site, West Virginia. The slope movement at that site has occurred periodically for a number of years. As reported by Richardson [26], ten test holes were made and soil and rock samples were collected for laboratory testing. In five of the test holes, slope inclinometer casing was installed and monitoring wells were installed in the other five test holes. Based on the data collected in the test holes, the bedrock at the site dipped and ranged from 6.7 to 9 m from the ground surface near the road edge to 11 to 15.5 m below the ground surface downslope. After about a year of slope monitoring, test piles were installed near the test holes giving the most movement. Test holes 2 and 6 were the first to show signs of a similar slip plane. Holes of 18-inch diameters were augured to accommodate the HP 10  42 test piles that were lowered in place and filled with grout at 1.22 m pile spacing. The results of this case study are based on a section cut between Test Borings 2 and 6. Detailed information about the test site and monitoring and soil description is provided by Richardson [26].

9

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

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

The failure surface suggested in Fig. 22 is given based on the slope stability analysis of the profile. The soil strength parameters (Table 3) used in the slope stability analysis were back-calculated based on impending failure. The sand peak friction angle is determined from the SPT-N (blowcounts) (NAVFAC [27]), and the rock strength is obtained from unconfined compression tests [26]. Pile movement under working conditions was collected via inclinometer data as presented by Richardson [26]. Table 3 presents (1) the disturbed cohesion and residual friction angle of the soil along the impending failure surface for slope stability analysis; and (2) the undisturbed cohesion and full friction angle of the soil along the length of the pile. The failure surface coordinates shown in Fig. 22 and the soil properties presented in

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

Soil type

Unit weight (kN/ m3)

Average SPT-N

Disturbed cohesion, Cd (kPa)

Residual friction angle, /r (degree)

Undisturbed cohesion, Cu (kPa)

Peak friction angle, / (degree)

1 2 3

Sand Sand Rock

17.3 20.4 20.4

14 37 –

0 0 2068

19 30 0

0 0 2068

35 42 30

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

Moment, kN-m -50

0

50

100

150

200

0

97

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

1

References

2

Depth, m

3 4 5 6 7 8 9

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

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

Table 3 yield a slope safety factor of 0.976 using the modified Bishop method. A comparison between measured (piles 4 and 5) and calculated deflection and moment is presented in Figs. 23 and 24. Good agreement between measured and computed pile deflection and bending moment can be observed. 6. Conclusions An approach has been developed to predict the behavior and safety factors of pile-stabilized slopes considering the interaction between the pile and surrounding soil assuming soil displacement larger than pile deflection. The lateral soil pressure acting on the pile segment above the slip surface is determined based on soil and pile properties (i.e. soil–pile interaction). The developed technique accounts for the effect of pile diameter and position and the center-to-center pile spacing on the mobilized soil–pile pressure (pD). The development of the ultimate interaction between the pile and sliding mass of soil is determined via the consideration of the strength of pile material, soil flow-around failure, soil resistance, and pile interaction with adjacent piles. The study also shows that the position of the pile into the slope, the depth of the failure surface at the pile position, soil type, pile diameter and pile spacings have a combined effect on the maximum driving force that the pile can transfer down to the stable soil. The presented case studies exhibit the capabilities of the current technique via the comparison with measured results and the prediction of the soil–pile pressure above the slip surface. Acknowledgment This research was sponsored by the West Virginia Division of Highways (WVDOH, Project RP-213) and the University Transpor-

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