(asce)gm.1943-5622.0000445

Technical Note

Numerical Study of Slope-Stabilizing Piles in UndrainedClayey Slopes with a Weak Thin Layer

I-Hsuan Ho, M.ASCE1

Abstract: This paper presents a numerical study using three-dimensional (3D) finite-element (FE) analyses for slopes that contain a weak thinlayer and are reinforcedwith piles. The presence of a thinweak layer usually has a negative effect on slope stability. In the FE analysis, a strengthreduction technique is employed using FE software. In the numerical model, an elastic-perfectly plastic withMohr-Coulomb failure criterion isused for the soils. The pile is assumed to be an elastic member, without considering failure. Some of the effective factors, such as the optimal pilelocation and pile length, were verified beforehand using two-dimensional (2D) FE analysis. The spacing effect of the pile, S=D5 4:0 (S is on-center spacing;D is diameter), is found to be comparable for the 3Dmodel in relation to the 2Dmodel. The appropriate length of the pile used inthe 3D analysis is based on the length of piles typically used in engineering practice. It is concluded that proper stabilization can be provided ifapproximately half of the pile length extends below theweak layer and piles are installed in themiddle portion of the slope. The analysismethodsare based on a coupled analysismethod; that is, both slope stability and pile response are considered simultaneously. Also, the 3DFEM is able toovercome the limitations of the 2DFEmodel that lacks proper consideration of the boundary effect, the soilmovement between the piles, and thespacing between the piles. The effectiveness of the pile-stabilized slope depends on the strength of the soil contained in the interbedded layer.Slope stability analysis for a slopewith piles was also performed, whereby three typical failuremechanismswere observed, from translational torotational failure for the differentCu2=Cu1 ratios (Cu1 is the undrained shear strength of the slope soil, andCu2 is the undrained shear strength ofthe soil in a thin layer). The presence of the stabilizing piles in such a slope can change the failure mechanisms and the depth of the slip surface.The restricted conditions applied to the pile head are also found to have similar effects in changing the failuremechanisms in a slope. Fixed-headpiles are found to provide substantially more improvement to slope stability than free-head piles. However, fixed-head piles are not alwaysrecommended, depending on the Cu2=Cu1 ratio and the required factor of safety after being stabilized with piles. This paper also providesa realistic soil–pile interaction model that is subjected to lateral loading on an inclined slope.DOI: 10.1061/(ASCE)GM.1943-5622.0000445.© 2014 American Society of Civil Engineers.

Author keywords: Slope-stabilizing piles; Continuum methods; Elastic-perfectly plastic; Mohr-Coulomb failure criterion; Spacing effect;Coupled analysis.

Introduction

Three types of analysismethods are proposed in this study to analyzethe passive piles used in stabilizing piles. These analysismethods forstabilizing piles are well documented in the literature and can beclassified into three main categories: (1) pressured-based (Ito andMatsui 1975; Hassiotis et al. 1997), (2) displacement-based (Poulos1995; Chow 1996; Jeong et al. 2003; Galli and Prisco 2013), and(3) continuum-based (Goh et al. 1997; Cai andUgai 2000;Won et al.2005; Jenck et al. 2009). The pressure-based method is based on thetheory proposed by Ito and Matsui (1975) that considers passivepiles subjected to lateral soil pressure. This method assumes that thepiles are in a row and rigid and that the length of the piles is infinite.Moreover, only the soil around the piles is considered to deformplastically and in plastic equilibriumwithout taking soil arching into

account (Jeong et al. 2003). This method, therefore, does not reflectthe use of actual finite flexible piles. The second method, thedisplacement-based method, considers the relative displacement be-tween the soil and the pile. Although lateral soil movement can bemeasured directly using inclinometer data, other methods, such ascontinuum approaches or empirical correlations, are required tohelp evaluate the lateral soil movement. The displacement-basedmethod typically includes uncoupled analysis of the pile–soilinteraction, which considers slope stability and pile responseseparately. Usually in such cases, the location of the slip surfacemust be presumed. The last method, the continuum FEM, incor-porates coupled analysis of the pile–soil interaction. No potentialslip surface has to be assumed before the numerical analysis isconducted. The continuummethod not only is able to overcome theshortcomings of the other two methods, but it also provides bettersolutions compared with the limit equilibrium methods.

Two-dimensional (2D) finite-element (FE) analysis has beenwidely used and applied to geotechnical engineering applications overthe past several decades. Because of the computational limitationsof three-dimensional (3D) analysis, 2D FE techniques have beenadopted for solving problems in engineering and geotechnical engi-neering. However, in reality, slope failures are actually 3D in nature(Nian et al. 2012).Furthermore, 2Danalysis results have been found tobe more conservative than 3D analysis results, according to previousstudies (Chen and Chameau 1985; Griffiths andMarquez 2007). Thefactor of safety for 2D slope stability analysis is usually smaller thanthat obtained from 3D FE analysis. Hence, the 2D results of slope

1Assistant Professor, Harold Hamm School of Geology and GeologicalEngineering, Univ. of North Dakota, 217 Leonard Hall, Grand Forks, ND58202; formerly, Clinical Assistant Professor, Dept. of Civil and Environ-mental Engineering, Washington State Univ., 27 Sloan Hall, Pullman, WA99163. E-mail: [email protected]

Note. This manuscript was submitted on December 15, 2012; approvedon September 2, 2014; published online on October 23, 2014. Discussionperiod open until March 23, 2015; separate discussions must be submittedfor individual papers. This technical note is part of the International Journalof Geomechanics, © ASCE, ISSN 1532-3641/06014025(12)/$25.00.

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stability analysis are considered to be more conservative than 3Dresults (Griffiths andMarquez 2007; Nian et al. 2012). In engineeringapplications, conservative design solutions generally imply highercosts. 3D FE analysis provides rigorous solutions by consideringconditions of the third dimension, such as slopedimensions, boundaryconditions, and the realistic geometry of the slope. Hence, compu-tational accuracy can be improved using 3D FE analysis.

However, in certain cases, 2D solutions are still viable if thelimitations of the 2D model, such as the complexity of the dimen-sions and boundary conditions, can be determined and taken intoaccount. In such cases, 2D FEMs are still considered to be efficient.Furthermore, significant differences between 2D and 3D models inmany slope stability–related analyses have not been found (Griffithsand Marquez 2007). Hence, substantial benefits of 3D FE analysishave not yet been fully revealed.

Nonetheless, 3D FE analysis has been found to provide moreaccurate solutions than 2D FE analysis because it properly considersthe boundary conditions in the third dimension. That is, the modelbecomes more realistic by considering the dimensions, geometry,and fixity of the boundaries in the third dimension. Particularly inmodeling problems related to pile-stabilized slopes, 3D FE analysisconsiders the large deformations of the soil between the piles, whichmay be ignored in 2D FE analysis because the spacing effect of thepiles is not considered in 2D FE models. The analysis is more rig-orous because it does not just simplify the pile-slope problem intoa plane-strain problem. In addition, the soil and pile that are modeledusing a FE technique will provide proper assessment of the soil–structure interaction (Reul 2004). The pile response in a slopesubjected to lateral loading is different from that of a pile ina horizontal ground surface (Muthukkumaran 2013). Furthermore,the presence of a weak interlayer usually plays an adverse role inslope stability because of its low strength (Huang et al. 2013).

This paper presents a numerical study using 3D FE analysis ofa slope containing a weak thin layer reinforced with piles. The slopestability of a slope without piles is determined using a 3D FEmodel,and the results are comparable to those obtained from 2D FE anal-ysis. The piles are then used to stabilize a slope containing a thinlayer, and 3D FE analysis is performed using ABAQUS 6.12. It iswell documented that the elastic-perfectly plastic soil constitutivemodel is independent of the construction sequence. The advantagesof using 3D FE analysis are provided in this paper. A FE analysismethod coupledwith the strength reductionmethod (SRM) is used toconsider both slope stability and pile responses simultaneously. Thedepth of the slip surface changes because of the presence of sta-bilizing piles. Some influential factors, such as the optimal pilelocation and the length of the pile verified earlier using 2D FEanalysis, are applied in the 3D analysis. Moreover, although free-head piles generally are used in engineering practice, the restrictionson the pile head are considered to mitigate the effectiveness of thestabilizing piles. The effect of the pile head conditions, the failuremechanisms that are affected, and the pile responses in a pile-stabilized slope are discussed herein.

Objective and Scope

The 2D FEM, as it is applied to slope stability analysis, is consideredto be more conservative than the 3D FEM, as mentioned previously.However, the results of 2D and 3D slope stability analyses do notalways differ significantly. In many cases, the boundary condition inthe third dimension is an important consideration. Especially fora pile-slope system, some key factors, such as large soil movementbetween piles and the spacing between piles, may be ignored or hardto justify in a 2D FE model. Furthermore, both pressure-based anddisplacement-based methods have shortcomings. Hence, a 3D FE

analysis technique is used in this study to analyze the stability ofa slope containing a weak thin layer. A slope that consists of clayeysoil with an average undrained shear strength Cu1 and a weak thininterbedded layer with undrained shear strength Cu2 are considered.The proposed method is able to overcome the limitations of the 2Dmodel. To validate the results of the slope stability analysis, theauthor has adopted the case study presented in a paper by Griffithsand Lane (1999). The soil properties and the cases of the slope aresummarized in Table 1. The geometry of the 3D slope is shown inFig. 1. Fig. 1 shows a slope on a foundation layer of undrained clay.The slope includes a thin layer that initially runs parallel to the slope,then runs horizontally in the foundation, and finally outcrops at anangle of 45� beyond the toe.

Parametric Study

The strength ratiosCu2=Cu1 5 0:2, 0:4, 0:6, 0:8, and 1:0 are analyzedusing the FEM found inABAQUSwith 3D stress elements and eight-node linearity with reduced integration (C3D8R). Because the pile isassumed to be a linear element, only soil failure is considered in thepile-slope system. The pile members also are modeled usingC3D8R. In ABAQUS, the element type and mesh must avoid ir-regular shapes to increase the accuracy of the computational results.

The same parameters are used in the 2D FE models for com-parison. The elastic-perfectly plastic Mohr-Coulomb failure crite-rion is used in the constitutive model of the soil in the analyses.Because clayey soils are assumed to be undrained, the Young’smodulus (E) and Poisson’s ratio (y) of both layers of soils default to100 MPa and 0.5 in the elastic part, respectively. The dilation anglein the model is assumed and taken as zero because of the saturatedclay. The factors of safety discussed are based on the three strengthratios obtained: Cu2=Cu1 5 0:2, 0:6, and 1:0. These three strengthratios are found to govern three critical types of failure in thetransition of the failure mechanism in the slope stability analysis.The boundary conditions on both sides in the third dimension areregarded as important influencing factors in the 3D slope stabilityanalysis.

Table 1. Soil Properties of Slope

Property Value

Cu1 (kPa) 102f (�) 0.001g (kN=m3) 20Cu2 (kPa)

Cu2=Cu1 5 1:0 100Cu2=Cu1 5 0:6 60Cu2=Cu1 5 0:2 20

Fig. 1. Clayey slope containing a thin layer

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According to Griffiths and Marquez (2007), the boundary canbe assumed in terms of three typical types: (1) smooth-smooth,(2) rough-smooth, and (3) rough-rough. In this paper, rollers wereapplied to both z-planes, which are defined as smooth-smooth bound-aries (horizontal deformation, Uz 5 0) in the studies by Griffiths andMarquez (2007) and Ho (2014). In addition, the pile model is in-corporated into the numerical models to be analyzed. The effect of thewidth-to-height ratio, L=H, is examined by analyzing ratios of L=Hfrom 1.0 to 12 based on the Cu2=Cu1 5 0:2 case. Here, H representsthe height of the slope, excluding the foundation beneath the slope,and L is the width of the slope in the third dimension (z-axis).

3D Slope Stability Analysis

The results of the slope stability analysis using 3D models aresummarized in Table 2. A higher factor of safety is presented in the3D analysis than in the 2D FE analysis using the same materials andboundary conditions. The difference in the factor of safety betweenthe 3D and 2D models is approximately 30–40% when L=H5 1:0.The 2D analysis results are relatively conservative. Fig. 2 presentsthe results of the slope stability analysis that compares the 2D and 3Danalyses by changing the L=H ratio. The factor of safety is seen todecrease as the L=H ratio increases. The results show that when theL=H ratio is larger than 10, the factors of safety between the 3D and2D analyses are very close. The deformation contour in the 3Dmodels is shown in Fig. 3 for the strength ratio of soils, Cu2=Cu1

5 0:2. The failure takes place in the weak layer based on theequivalent plastic strain contour (PEEQ) in the 3D analysis.

Factor of Safety

The 3D FE analysis is used to examine slope stability based on thestrength reduction factor (SRF). Unlike limit equilibrium meth-ods, FE analysis is unable to output a global factor of safety di-rectly. An equivalent factor of safety, i.e., the SRF using the SRM(Zienkiewicz, et al. 1975; Cai andUgai 2000; Ho 2014) is adopted.

The SRF is applied to reduce the strength of the soil to the point offailure. The maximum SRF is regarded as the factor that is equiva-lent to the factor of safety in limit equilibrium analysis. If the totalstrength parameters of the soil are c andf, the cf andff are the totalstrength parameters that will bring the slope to failure, which can bedefined as

cf ¼ cfSRF

(1)

ff ¼ arctan

�tanff

SRF

�(2)

In the application of the SRM in FE analyses, successive increases inSRF are applied to themodel until the solution cannot converge. Thecomputation will continue and the SRF will keep increasing in thenext iteration if the solution continues to converge. When excessivedistortion occurs, the computational solution will become uncon-verged. Then the computation will stop. The unconverged solutionis regarded as the failure of the slope in the numerical model. In thispaper, the SRF can be determined from the transition point where thedisplacement of any selected node increases dramatically, as shownin Fig. 4. The highest SRF that leads to this unconverged solution isdefined as the factor of safety used in the limit equilibrium method.The factor of safety concept is introduced to explicitly describe theeffectiveness of stabilizing piles. To illustrate the effectiveness ofa stabilizing pile in a slope, a stability improvement ratio (Npi) isproposed to quantify the slope stability after being improved bystabilizing piles. Npi is defined as follows:

Npi ¼ Fp2Fs

Fsp 100% (3)

whereFp 5minimum factor of safety for the pile-slope system; andFs 5 minimum factor of safety for the slope stability analysiswithout piles.

Pile-Stabilized Slope Analysis Using 3DABAQUS Model

Before the 3D FE model was created, the 2D model was developedto verify several influencing factors associated with pile perfor-mance. These factors include the optimal pile location on the slopeand the appropriate range of the pile length. The lateral view of themodel is shown in Fig. 5 and illustrates the location of the pile, the

Table 2. Factor of Safety versus Cu2=Cu1, L=H5 1:0

Cu2=Cu1 ABAQUS 2D ABAQUS 3D

0.2 0.59 0.850.6 1.4 1.651 1.49 1.7

Fig. 2. Comparisons of 3D and 2D FE analysis, Cu2=Cu1 5 0:2

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dimensions of the pile-slope system, and the presence of the thin layer.The parameters used in the model also are defined: X is the horizontaldistance between the crest and the toe of the slope, and Xp representsthe pile location away from the toe. To explain and determine the bestlocation to install the pile, the dimensionless ratio Xp=X is introducedto indicate its position. The pile is placed at the toe if Xp=X5 0,whereas Xp=X5 1:0 means the pile presents at the crest. The re-lationship between the factor of safety and the Xp=X ratio is presentedin Fig. 6 for free-head pile cases. From the results, it is concluded thatthe middle portion of the slope is the optimal location for a stabilizingpile, and the peak factor of safety values are found atXp=X5 0:5 in allcases of Cu2=Cu1. The results of similar analyses using fixed-headpiles are summarized in Fig. 7. The optimal pile location is also shownas themiddle portion of the slope, regardless of theCu2=Cu1 ratio. Theresults indicate that the recommended optimal pile location in the 3DFE analysis is Xp=X5 0:5.

Although very few studies have addressed the appropriate lengthof the pile, case studies are available that summarize the length ofstabilizing piles used in practice and define a ratio that considers thepile length above the slip surface in terms of the entire length of the

pile. The ratios were found to be at approximately 0.45 to 0.55(Fukumoto 1972). The data associated with pile length using 2D FEanalysis are summarized in Tables 3 and 4. In terms of the factor ofsafety, lengths of piles between 24 and 25m in a slope result in higherfactors of safety for all cases. In terms of ratio, Lz=L is introduced,where Lz is the pile length above the potential slip surface and L is thetotal length of the pile; a length ratio Lz=L between 0.48 and 0.52 isdetermined to be the most effective with regard to slope stability. Theanalysis can also support and validate the finding that approximatelyhalf of the pile length can be extended below the weak layer.Therefore, it is reasonable to extend the pile length by approximatelyhalf the length of the pile below the weak layer in the 3D FE models.

Fig. 8 presents the analysis results of a 3D slope with two pilesplaced symmetrically. The sidewidth of the slope in this case is set at10m to control S=D5 4:0 in the 3D FE analysis. The factor of safetyis identified as independent of the width of the slope in the analysisfor the pile-slope system but not for the S=D ratios. According toa previous study (Ho 2009), the middle portion is the optimal po-sition to place the pile for this type of slope. Hence, the two sym-metric piles are located in the middle of the slope in the model toexamine other influential factors.

Because of the undrained conditions of the soils for both layers,Poisson’s ratio is assumed as 0.45 for both layers. The properties ofthe piles are selected as 2.5m in diameter for the circular pilewith themodulus of elasticity of 25,000 MPa and Poisson’s ratio of 0.2. Thebending rigidity (EI) of the piles in the 3D model is 15:34 MN ×m2,whereas the equivalent EI is adopted in the 2D model. The di-mensions of the pile are adjusted to fit the parameters used in the3D model. The length of each pile in the 3D FE model is 25 m. Thepiles’ elements are meshed using C3D8R 3D stress continuumelements built in ABAQUS. The interface element between the soillayers and the pile elements is defined as penalty, with the frictioncoefficient of 0.51 in the tangent direction, and the hard contactdefaulted to normal contact behavior.

Implications of 3D Analysis

The 3D FE analysis provides slightly different outcomes comparedwith the 2D analysis. The ratio S=D is used to normalize the spacingbetween the piles, where S is the on-center distance between the

Fig. 3. (Color) Slope failure contour (PEEQ) in 3D ABAQUS model, Cu2=Cu1 5 0:2

Fig. 4. Example for SRF determination

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Fig. 5. Pile-slope system model in ABAQUS (Xp=X5 0:50, L5 25 m)

Fig. 6. (Color) Factor of safety versus Xp=X, free-head piles

Fig. 7. (Color) Factor of safety versus Xp=X, fixed-head piles

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piles, andD is the diameter of the piles. The relationship between thefactor of safety and S=D is shown in Fig. 9. The results indicate thata smaller S=D ratio results in a factor of safety that is higher in the 3DFE analysis than in the 2D FE analysis. In the 3D FE model,S=D5 4:0 is found to obtain a factor of safety close to that in the 2DFE model. If the spacing ratio gradually increases, the given factor ofsafety approaches that of the unstabilized cases. Hence, the 3D pile-slope system in this study adopts the S=D5 4:0 ratio to compare theresults with those obtained from 2D analysis. The results also suggestthat 2D analysis could replace 3D analysis if the spacing ratio of the2D model is too conservative (i.e., smaller than 4.0). The spacingeffect cannot be considered in 2Danalysis. Therefore, according to theresults shown in Fig. 9, the factor of safety could be overestimated fora S=D that is greater than 4.0. In terms of percentages, the differencecould be as high as 60%.Hence, if a S=D other than 4.0 is considered,the 3D FE model needs to be used to provide better solutions.However, S=D5 4:0 has been found to be themost cost-effective pilespacing according to Kourkoulis et al. (2011).

Failure Mechanisms of Slopes

Five different strength ratios, Cu2=Cu1 5 0:2, 0:4, 0:6, 0:8, and 1:0,are used to investigate the failure mechanism in the 3D pile-slopesystem. In previous studies (Griffiths and Lane 1999; Ho 2009,2014), three typical failure types are identified in terms of threedifferent strength ratios: Cu2=Cu1 5 0:2, 0:6, and 1:0, respectively.In the case ofCu2=Cu1 5 0:2, the undrained shear strength of the soilis relatively low in the thin layer compared with the soil in the slope.Hence, the weak layer governs the failure mechanism; the failureoccurs along the weak interbedded zone. As for Cu2=Cu1 5 1:0, theslope is actually homogeneous. The potential slip surface is tangentto the stiff layer, which is at the bottom of the boundary in themodel;thus, the failure mechanism is governed by a greater circular base.Another failure mechanism is regarded as the transition mechanismbetween these two cases, transitioning from a noncircular slipsurface to a circular base failuremechanism.Both the thinweak layerand the circular base control the slope failure mechanism ifCu2=Cu1 5 0:6. In this case, the two types of failure mechanismappear in the slope simultaneously. The three critical ratios(Cu2=Cu1) that correspond to the failure mechanisms are determinedas 0.2, 0.6, and 1.0. The case of Cu2=Cu1 5 1:0 is actually a ho-mogeneous slope. No particular slip surface can be found in theslope, and a large circle tangent to the base is evident.

Table 3. FS versus Cu2=Cu1 with Free-Head Piles

Pile Cu2=Cu1 versus FS (free-head, free-tip)

Length (m) Ratio (Lz=L) 0.2 0.4 0.6 0.8 1.0

16 0.78 1.09 1.17 1.45 1.56 1.6018 0.69 1.15 1.23 1.48 1.58 1.6219 0.66 1.23 1.29 1.55 1.61 1.6520 0.63 1.35 1.40 1.59 1.63 1.6622 0.57 1.49 1.51 1.63 1.65 1.6824 0.52 1.63 1.65 1.70 1.68 1.7026 0.48 1.59 1.63 1.72 1.70 1.74

Table 4. FS versus Cu2=Cu1 with Fixed-Head Piles

Pile Cu2=Cu1 versus FS (free-head, free-tip)

Length (m) Ratio (Lz=L) 0.2 0.4 0.6 0.8 1.0

16 0.78 1.20 1.32 1.52 1.63 1.6718 0.69 1.32 1.46 1.60 1.65 1.7119 0.66 1.43 1.58 1.65 1.74 1.8220 0.63 1.49 1.66 1.69 1.80 1.9022 0.57 1.60 1.70 1.73 1.92 2.0124 0.52 1.70 1.77 1.78 2.06 2.1226 0.48 1.71 1.80 1.85 2.18 2.29

Fig. 8. Geometry of slope reinforced with piles in 3D model

Fig. 9. Comparisons of 2D and 3D analyses for pile-slope systems

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In this study, changes in the failure mechanisms for pile-stabilized slopes also were observed. Depending on the restric-tions of a given pile head, the failure mechanisms are affected bythe pile head conditions. Two pile head conditions are applied:free-head and fixed-head. Figs. 10–12 present the free-head pilesplaced in Cu2=Cu1 ratios of 0.2, 0.6, and 1.0, respectively. InFig. 10, the PEEQ indicates that the main slope movement occursalong the weak layer. However, the pile reduces the movement in

the downslope. The failure mechanism of this piled slope is stilldetermined by the weak layer. The Cu2=Cu1 5 0:4 condition alsoexhibits a similar failure mechanism. The lower portion of the pileis inserted into a relatively stiff layer and behaves like a cantileverbeam. In Fig. 11, the largest movement can still be seen along theweak layer, but the soil below the thin layer tends to form a circularpotential slip surface. The pile in this type of slope behavessomewhat similarly to a simple beam. Although the behavior of the

Fig. 10. (Color) PEEQ for 3D pile-stabilized slope (Cu2=Cu1 5 0:2, free-head)

Fig. 11. (Color) PEEQ for 3D pile-stabilized slope (Cu2=Cu1 5 0:6, free-head)

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pile in the case of Cu2=Cu1 5 1:0 (homogeneous slope) is like thatof a simple beam, the greatest amount of potential soil movementdoes not concentrate locally. The potential failure surface is a greatcircle that is tangent to the boundary and can be seen in Fig. 12 asa plastic strain contour. Hence, global stability is considered witha higher Cu2=Cu1 ratio, whereas local failure must be consideredwith a lower Cu2=Cu1 ratio. The fundamental types of failure arealso consistent with the three categories of failure found in theunstabilized (Cu2=Cu1 5 0:2, 0:6, and 1:0) cases according to thedeformation of piles subjected to soil movement.

Figs. 13–15 show cases of fixed-head piles in slopes in terms oflateral soil movement in themodel. The piles in these three cases also

behave like cantilever beams, where the fixed ends (no displacementand rotation) are applied in the pile head, and the free ends (freedisplacement and rotation) are in the pile tips. All three figures areexpressed using the lateral movement contours (U1, displacement inthe x direction). In the case ofCu2=Cu1 5 0:2, the pile tip is restrictedsomewhat by the stiff layer. Thus, the largest amount ofmovement inthe piles takes place at the middle portion of the piles, which issubject to the soil mass sliding along theweaker layer.Moreover, thepresence of the piles is found to decrease the upslope movement. Inthe case ofCu2=Cu1 5 0:6, the largest lateral movement of the piles isfound to be close to the pile tip, because the failure of the pile-slopesystem is governed by the global stability. The potential failure

Fig. 12. (Color) PEEQ for 3D pile-stabilized slope (Cu2=Cu1 5 1:0, free-head)

Fig. 13. (Color) Displacement contour in 3D FE model for pile-stabilized slope (Cu2=Cu1 5 0:2, fixed-head)

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surface in this case is tangent to the bottom boundary. As for the caseof Cu2=Cu1 5 1:0, which is similar to the case of Cu2=Cu1 5 0:6, thedisplacement contour indicates that a deeper circular rotation planewill form and that the stability also is dominated by a global factor ofsafety.

Fig. 16 compares the factor of safety that is improved usingdifferent pile heads in the 2D and 3D analyses. The improvementof the stability of the piled slopes is hard to quantify unless theevaluation is based on Npi. This ratio provides a reasonable

illustration of the improvement of the stabilizing piles in a stabilizedslope by comparing the results to the slope stability analysis resultsfor an unstabilized slope. In terms of Npi, the presence of piles isproven to increase the stability of unstable slopes, as indicated bythe positive number shown in the results. Particularly in comparisonwith the relatively weak soil in the thin layer, such as Cu2=Cu1

5 0:2 or 0:4, the improvement in slope stability is remarkable.Fig. 17 also presents comparisons of the stability improvement ratiosin the 3D and 2D analyses. The fixed-head pile shows a better

Fig. 14. (Color) Displacement contour in 3D FE model for pile-stabilized slope (Cu2=Cu1 5 0:6, fixed-head)

Fig. 15. (Color) Displacement contour in 3D FE model for pile-stabilized slope (Cu2=Cu1 5 1:0, fixed-head)

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stability improvement ratio in both the 2D and 3D analyses than thefree-head pile. Because of the relatively conservative outcome givenin the 2D FE analysis, the stability improvement ratio seems rela-tively high compared with the results from the 3D FE analysis.Regardless of whether 2D or 3D analysis is performed, the im-provement in the stability for piled slopes ofCu2=Cu1 5 0:6 or higherseems to reduce the effectiveness, especially for free-head piles. Thisoutcome is because the failure mechanism is for either a slope witha higher Cu2=Cu1 value or a homogeneous slope, depending on theglobally circular base plane. If the pile is not long enough to extendacross the potential slip surface, which can be determined beforeplacing the stabilizing piles in the model, then the increase in sta-bility for this type of slope is limited. As far as the pile condition isconcerned, both fixed- and free-head piles are shown to improve thestability of piled slopes, particularly for fixed-head piles in a slopethat is close to homogeneous.

The results of the analyses show that stabilizing piles do con-tribute to the stabilization of a slope. For a slope containing a weaklayer, both free-head and fixed-head piles can be used to stabilize theslope successfully. For homogeneous slopes, fixed-head piles areshown to be more effective than free-head piles. Unless the

undrained shear strength of the homogeneous, or close to homo-geneous, slope is low, or the unstabilized slope has a factor of safetylower than 1.0, fixed-head piles are the better option. In other cases,free-head piles will be more commonly adopted.

Pile Responses

Figs. 18 and 19 show the calculated responses of the slope-stabilizing piles in a slope with different Cu2=Cu1 ratios for free-head and fixed-head conditions, respectively. The strength ratiosCu2=Cu1 5 0:2, 0:4, 0:6, 0:8, and 1:0 are all presented in these twofigures.

Regarding the soil–pile interaction, Fig. 18(a) presents the dis-placement of the free-head pile subjected to soil movement. Forcases of Cu2=Cu1 5 0:6 or smaller, the piles are inserted into a rel-atively firm layer. The unstable soils are the mass above the weaklayer. The piles deflect because of the soil movement above theweakzone. Hence, the pile head exhibits a larger displacement than thepile tip. For cases of Cu2=Cu1 5 0:8 and 1:0, the middle portion ofthe pile exhibits a larger deflection because the potential slip surface

Fig. 16. (Color) Factor of safety versus Cu2=Cu1 for fixed- and free-head piles

Fig. 17. (Color) Npi versus Cu2=Cu1 of pile-slope system in 2D and 3D analyses

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is no longer in the weak zone. The coupled effect of both the pile andthe slope brings the potential slip to a deeper position in the slope.The change in the failure mechanism from a low Cu2=Cu1 ratio toa higher value also can be identified in Fig. 18(b). The weak layergoverns the failure mode in the slope of a lower Cu2=Cu1 ratio; thus,peak shear is evident in the position of the sliding zone. The shearforce of the tip is also high because the tip is held in a stiff zone and,thus, behaves like a hinged tip. A slope with a higher Cu2=Cu1 ratiohas a higher shear force on the tip than on the head. In response toconclusionsmade earlier, piles with slopes ofCu2=Cu15 0:8 and 1:0deform like a simple beam, so the bending moments on both endsare zero, according to Fig. 18(c). The other three cases (Cu2=Cu1

5 0:2, 0:4, and 0:6) are not zero, which means the restriction is notfully free because of the stiff layer. The maximum bending momenttakes place near the middle of the pile.

Fig. 19 shows the pile responses, including the displacement,shear force, and bending moment, for the piles with fixed heads.Fig. 19(a) shows that the maximum displacement appears some-where in the stiff layer, but not exactly at the tip in the case ofCu2=Cu1 5 0:2 because the tip is constrained at the pile tip by the stifflayer. In terms of the shear force, shown in Fig. 19(b), the maximumshear stress appears on the restricted pile heads in all cases. Thepotential slip surface of the piled slope is found to form at a deeperposition with the increase inCu2=Cu1 ratios (Cu2=Cu1 $ 0:6). Hence,

Fig. 18. (Color) (a) Displacement, (b) shear force, and (c) bending moment diagrams for free-head pile at critical state in different strength ratios

Fig. 19. (Color) (a) Displacement, (b) shear force, and (c) bending moment diagrams for fixed head pile at critical state in different strength ratios

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the potential slip surface and the largest soil movement are expectedto take place close to the base in the cases of Cu2=Cu1 5 0:6e1:0. Inaddition, the largest bending moment in each case is found to be ator close to the middle point of the pile depending on the Cu2=Cu1

ratio (i.e., Cu2=Cu1 5 0:2 and 0:4 for the midpoint of the pile orCu2=Cu1 5 0:6, 0:8, and 1:0 for close to the midpoint of the pile).Furthermore, the largest bending moment among all five casescorresponds to the case that has the largest pile deflection(i.e., Cu2=Cu1 5 1:0). A comparison of the results is shown inFig. 19(c). The pile responses are found to be relative to the failuremechanism of the pile-stabilized slopes. Because the cases ofCu2=Cu1 5 0:6, 0:8, or 1:0 have deeper potential slip surfaces tan-gent to the base boundaries, the failure mechanisms are governedby these deeper slip surfaces. Consequently, the largest amount ofsoil movement is found to take place at the locations close to thepile tips.

Summary and Conclusions

In this study, 3D FE analysis that incorporates a strength reductiontechnique was performed to verify and validate slope stability withthe presence of piles. The pile responses and the slope stabilitywere considered simultaneously in the so-called coupled analysis.The failure mechanisms before and after pile installation werecompared. Based on the analysis, the presence of piles is shown tochange the failure mechanism and the depth of the slip surface,particularly for the cases presented in this paper. The restriction ofthe pile head also is shown to alter the failure mechanism of a piledslope. Based on the analysis results, the following conclusions aredrawn:1. The middle portion of the slope is the optimal pile position in

the type of slope investigated in this study, and the length of thepile should be 40–60% across the potential slip surface, asdetermined by slope stability analysis.

2. 3D FE analysis provides a rigorous solution for slopes rein-forced with piles. The selection of the spacing-to-diameterratio, S=D, is important and affects the analysis results.However, for a S=D ratio that is equal to or greater than4.0, 2D analysis results are found to be comparable to 3Danalysis results based on the SRF. To provide better stabili-zation using piles, the S=D should be smaller than 4.0.Therefore, 3D FE analysis is recommended over 2D analysisin this case.

3. The pile length is recommended as Lz=L5 0:5, which meansthat the pile should be extended halfway below the weaklayer.

4. The use of fixed-head piles also increases the effectiveness ofstabilizing piles compared with free-head piles. Particularlyfor slopes with aCu2=Cu1 ratio that is lower than 0.6, the effectof the pile head condition is found to be significant. The pilehead condition is also found to change both the failuremechanism and the depth of slip surface.

References

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