Research ArticleEffect of Loading Direction and Slope on Laterally Loaded Pile inSloping Ground

Chong Jiang , Jia-Li He , Lin Liu , and Bo-Wen Sun

School of Resources and Safety Engineering, Central South University, Changsha 410083, Hunan, China

Correspondence should be addressed to Chong Jiang; jiang4107@sohu.com and Lin Liu; liulin9358@csu.edu.cn

Received 11 September 2018; Accepted 25 October 2018; Published 15 November 2018

Guest Editor: Xihong Zhang

Copyright © 2018 Chong Jiang et al. .is is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

A series of three-dimensional finite element analyses were performed to study the behavior of piles in sloping ground underundrained lateral loading conditions. .e analyses have been conducted for slopes with different angles and two loading di-rections. .e obtained results show that as the slope increases, it can cause greater lateral displacement and internal force of thepile. In addition, the increase of the slope ratio will cause the position of the maximum bending moment and soil resistance zeropoint of the pile to move downward, further increasing the pile deflection. Furthermore, when the pile distance from slope crest B< 7D, the displacement and internal force development of the pile under toward loading is more obvious. When the pile distancefrom the slope crest exceeds 7D, the effect of loading direction on the pile can be neglected.

1. Introduction

Pile foundations are widely used to support structures suchas bridges, high-rise buildings, and transmission towers, andthey are often constructed on a natural or artificially con-structed slope. Pile foundations are often subjected to lateralloads caused by wind and earthquakes.When the foundationis built on a slope, the bearing capacity of the foundation willbe significantly reduced, depending on the distance of thefoundation from the slope. .e bearing capacity of thefoundation on the slope is usually calculated by empirical ortheoretical formulas which are based on the limit equilib-rium or the upper boundary plasticity calculation. For thedesign of pile foundations subjected to lateral loads, thelateral response of the piles on the slopes and the interactionof piles with the soil are of great importance.

In order to obtain the design method and related the-oretical guidance of the laterally loaded pile foundation onthe slope site, some scholars have tried to study in theory andput forward some optimization design methods [1–3]. Atpresent, many research scholars have carried out field tests[4–6] and laboratory tests [7, 8] on laterally loaded pilefoundations on slope sites. In order to study the influence of

slope on the pile foundation, Mezazigh and Levacher [9]carried out a centrifuge model test of the laterally loaded pilein the nonadhesive soil foundation. According to the curvedistribution results under different working conditions inthe test, the slope was applied to the shallow nonadhesive soilfoundation. Based on the model test of piles in noncohesivesoil slopes, Muthukkumaran [10] discussed the effects ofslope ratio, soil parameters, loading direction, and pilefoundation position on pile foundation. Nimityongskul et al.[11] carried out a series of full-scale lateral load tests of fullyinstrumented piles in cohesive soils to access the lateralresponse of piles in free field and near a slope condition.

More and more scholars choose numerical simulation toanalyze the problem of actual pile-soil interaction [12–14].Zhang et al. [15] established a three-dimensional calculationmodel based on the actual situation of the slope engineeringin Hong Kong. .rough numerical calculation and analysis,the influence of slope and casing thickness on the perfor-mance of the laterally loaded pile foundation on the slopewas discussed. A large-scale commercial finite elementsoftware was used by Georgiadis and Georgiadis [13] toestablish a three-dimensional model to study the nonlinearresponse behavior of piles in sloping ground under

HindawiAdvances in Civil EngineeringVolume 2018, Article ID 7569578, 12 pageshttps://doi.org/10.1155/2018/7569578

undrained lateral loading conditions. Two parameters ofslope ratio and soil shear strength were selected for sensi-tivity analysis under different working conditions. Based onthe calculation results, the curve in the form of hyperboliccurve is modified to consider the influence of slope ratio andthe cohesion coefficient of the pile-soil cross section. Finally,the feasibility of the proposed method is verified by anexample check. .rough the three-dimensional finite ele-ment model, the influence of the laterally loaded pilefoundation on the bearing performance of the pile foun-dation is studied by Sawant and Shukla [16].

To sum up, the current study on laterally loaded piles onslope sites is mainly based on model tests. Some scholarshave used numerical software to simulate and obtain someresearch results on slope effects. However, there is currentlyno detailed analysis of factors’ impact on slopes. .erefore,this paper will use the finite element software to establish thegeometric calculation model of the laterally loaded pile onthe slope site, calculate, and analyze the deformation of thepile. In the simulation analysis, the influences of slope ratioand loading direction on the displacement of laterally loadedpiles, internal forces, and soil resistance of piles are studied soas to further reveal and summarize the bearing characteristicsof laterally loaded single piles on slope sites and to providereference for practical engineering design and optimization.

2. Numerical Simulation

2.1. Finite Element Model. A circular pile foundation witha length of 12m and a diameter of 1m was located near theslope. In order to avoid the influence of size effect on thecalculation results, the length of the slope top and the wholewidth of the model were 20 times the pile diameter. .eheight of the slope was 12m, and the total height of themodel was 2 times the length of the pile. It was assumed thatthe pile foundation and soil are isotropic homogeneousmaterials, and Poisson’s ratio and elastic modulus did notchange with the load. .e top boundary of the model wasfree. .e four vertical sides of the model set the radialdisplacement constraint; that is, U2 � 0 was set on the frontand back sides and U1 � 0 was set on the left and right sides..e bottom surface of the model was set as the fixedboundary, whereas the top surface of the pile remained free.In the mesh generation of this model, the eight-nodehexahedron linear reduced element was used to simulatethe pile foundation and soil. .e grid around the contactsurface between pile foundation and soil should be sub-divided, and the grid setting proportion away from thecontact surface gradually evacuated. .e grid of the pilefoundation and soil mass in the slope calculation model isshown in Figure 1.

.e main process of numerical modeling is as follows:

(1) In order to balance the initial stress, the model ofa pile foundation in a slope was established, and theoriginal soil at the pile hole was preserved. A gravityvalue of −10 in the Z direction was applied to theentire soil model (opposite to the Z-axis direction)..e geostatic automatic stress balance method was

used to calculate the original initial stress field of theslope.

(2) After the initial stress calculation of the slope soil wascompleted, the “model change” function was used tokill the soil at the pile hole, and the pile foundationcomponent was modified into a living unit toreactivate the pile foundation.

(3) A contact pair was added to the contact faces of thepile body, the pile end, and the soil body, re-spectively. .en, the self-weight value of −10 in the Zdirection was applied to the pile foundation so thatthe pile foundation interacted with the slope soilunder the action of self-weight until equilibrium.

Different loading steps were established to apply lateralloads on the pile head step by step.

2.2. Verification of the Numerical Model. Georgiadis andGeorgiadis [13] performed three-dimensional finite elementanalyses to study the behavior of piles in sloping groundunder undrained lateral loading conditions. .e numericalsimulation results of the model in this paper were comparedwith those in the literature to verify the rationality of themodel. .e pile foundation parameters were set as follows:pile length L � 12m, pile diameterD � 1m, and slope angle �

30°. .e soil and pile properties of the three-dimensionalfinite element model are shown in Table 1.

In the contact setting, the normal behavior was set to the“hard” contact mode, and the tangential behavior was in theform of “penalty” friction. .e “penalty” friction coefficientvalue μ was generally 0.36 (tan(0.75φ)), and the case wherethe contact surface of the pile and soil was completely roughwas considered, so μ � 1. In particular, the stability of slopemust be ensured before the three-dimensional calculation ofthe laterally loaded piles in sloping ground. .e stability ofthe slope is not taken into consideration, and the pilefoundation does not play the role of an antislide pile butserves to the bearing structure. .erefore, according to thesoil and pile properties, the slope stability calculation for-mula and chart given by Taylor were used for analysis [17]..e slope safety factor of the model was calculated to exceed1.08, which proved that the slope was stable.

.e comparative results of the model in this paper andthe 3D finite element analyses are shown in Figure 2. A goodcompatibility could be seen between the present simulationmodel and the results of published data..emaximum erroris 9.2%, which is within the reasonable error range. It alsoproves the correctness of the modeling method.

2.3. Type of Analysis. A series of numerical models wereperformed for various slope angles and loading directions.According to the geological environment conditions in theactual project, the clay will adopt the common c-φ hard clayin the subsequent analysis model. .e pile foundation pa-rameters were set as follows: pile length L � 12m, pile di-ameter D � 0.6m, and the material was C30 concrete. .eschematic of the model analyzed is presented in Figure 3.

2 Advances in Civil Engineering

Soil and pile properties used in the �nite element analysesare summarized in Table 2.

3. Results and Discussion

3.1. E�ect of Slope Ratio. e slope ratio of di�erent modelswas set as 1V :1H, 2V : 3H, 1V : 2H, and 1V : 4H,

respectively, with the pile distance from slope crest B/D � 1.Figure 4 shows the contours of lateral displacement of thepile and soil for the 1V :1H slope when the lateral loadapplied on the slope model is 500 kN and 1000 kN, re-spectively. It can be seen from the �gure that both thede�ection of the pile and the deformation of the soil beforethe pile increase with the increase of lateral load. Moreover,the displacement �eld of the soil in the shallow foundation isdistributed in the shape of wedge, which is in good agree-ment with the assumed shape of the strain wedge modelproposed by Xu et al. [18]. e de�ection of the pile and thedisplacement of the wedge mainly occur above a criticalposition of the pile. Below the critical depth, the pile has an“insertion e�ect” and the embedded position decreases withthe increase of the lateral load.

e pile head load-displacement curves are shown inFigure 5 for di�erent slope ratios. As expected, under thesame lateral load H0, the pile head displacement increaseswith the increase in the slope ratio. It is clear that the

(a) (b)

Figure 1: Typical mesh for three-dimensional �nite element analyses. (a) Mesh for soil. (b) Mesh for pile.

Table 1: Soil and pile properties for veri�cation.

E(Pa) μ ρ(kg/m3) C(Pa) φ(°) ψ(°)Pile 2.9 × 1010 0.1 2500 — — —Clay 1 × 107 0.49 1800 5 × 104 0 0

–0.05 0.00 0.05 0.10 0.15 0.20 0.25

0

2

4

6

8

10

12

z/D

y/D

H0 = 500kN (Abaqus)H0 = 1000kN (Abaqus)H0 = 1500kN (Abaqus)H0 = 500kN (data by Georgiadis [13])H0 = 1000kN (data by Georgiadis [13])H0 = 1500kN (data by Georgiadis [13])

Figure 2: Displacement curve for comparison.

Lθ

V

D

H

B

Figure 3: Schematic of the model.

Table 2: Soil and pile properties for modeling.

E(Pa) μ ρ(kg/m3) C(Pa) φ(°) ψ(°)Pile 3.0 × 1010 0.1 2500 — — —Clay 1.2 × 107 0.4 1800 3.0 × 104 35 5

Advances in Civil Engineering 3

increase in pile head displacement due to slope ratio is largerat higher lateral load.

In order to re�ect the e�ect of the slope ratio on thedisplacement of the pile head more intuitively, the load-displacement curves in Figure 5 were normalized to obtainthe relationship between the normalized displacementy0,slope/y0,level and the lateral load H0 for di�erent sloperatios. e dimensionless parameter y0,slope/y0,level is de�nedas the ratio of the displacement of the pile head in slopingground to the displacement of the same pile head in levelground at the same load levels.

As shown in Figure 6, the normalized displacement valuey0,slope/y0,level continues to increase with the increase oflateral load, but the growth rate of y0,slope/y0,level changes asthe slope ratio increases. Before the third-stage load, thegrowth of y0,slope/y0,level is relatively stable for slope ratios of1V : 4H, 1V : 2H, and 2V : 3H, which is basically between 1.14and 1.31. However, the growth rate of y0,slope/y0,level increasesslowly after the third-level load. e corresponding growthrates in the whole loading process are 14.9%, 36.4%, and52.7% for slope ratios of 1V : 4H, 1V : 2H, and 2V : 3H,

respectively. In contrast, y0,slope/y0,level increases at a fast ratefor the 1V :1H slope ratio throughout the whole loadingprocess, varying from 1.29568 (�rst-stage load) to 2.52214(tenth-order load), which increases 94.66%. It indicates thatthe e�ect of slope on lateral pile displacement is much largeras the slope gets steeper.

Figures 7 and 8 show the variation of lateral pile de-�ection with depth for di�erent slope ratios at lateral loads of500 kN and 1000 kN, respectively. e �ndings from Fig-ures 7 and 8 can be listed as follows:

(1) e e�ect of slope ratio is to increase pile de�ectionat the same load level, and the growth rate of the pilede�ection for the 1V :1H slope ratio is the fastest.Moreover, the increase of pile de�ection will becomegreater as the load level increases.

(2) e pile de�ection will increase as the lateral loadlevel increases, which is more obvious in shallow soillayers. Below the position of the �rst displacementzero point, the pile de�ection no longer changes,which is called the “insertion e�ect.”

U, U1+7.958e – 02+7.281e – 02+6.604e – 02+5.928e – 02+5.251e – 02+4.574e – 02+3.897e – 02+3.220e – 02+2.544e – 02+1.867e – 02+1.190e – 02+5.132e – 03–1.636e – 03

(a)

U, U1+3.047e – 01+2.789e – 01+2.530e – 01+2.272e – 01+2.013e – 01+1.755e – 01+1.496e – 01+1.237e – 01+9.789e – 02+7.203e – 02+4.618e – 02+2.032e – 02–5.538e – 03

(b)

Figure 4: Lateral displacement �eld at di�erent lateral loads for the 1V :1H slope. (a) Lateral loadH0 � 500 kN. (b) Lateral loadH0 � 1000 kN.

0 25 50 75 100 125 150 175 200 225 250 275 300 3250

100200300400500600700800900

10001100

H0 (

kN)

y0 (mm)

1V:1H2V:3H1V:2H

1V:4HLevel ground

Figure 5: Pile head load-displacement curves for di�erent slope ratios.

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1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

y 0,sl

ope/y

0,le

vel

1V:1H2V:3H

1V:2H1V:4H

H0 (kN)

Figure 6: Curves of normalized displacement and lateral load fordi�erent slope ratios.

4 Advances in Civil Engineering

(3) e increase of the slope ratio will cause the �rstdisplacement zero points of the pile to movedownward. For example, when the lateral load H0 �500 kN, the �rst displacement zero points for theslope ratios of 1V :1H, 2V : 3H, 1V : 2H, and 1V : 4Hand the level ground appear at 6.5m, 6.1m, 5.9m,5.86m, and 5.5m below the ground surface,respectively.

(4) e shape of pile de�ection curves does not change dueto the slope e�ect. However, as the slope ratio in-creases, the decrease of the soil resistance around thepile will increase the pile de�ection at the same depth.

e variation of bending moment with depth for dif-ferent slope ratios at lateral loads of 500 kN and 1000 kN ispresented in Figures 9 and 10, respectively. From Figures 9and 10, three �ndings can be drawn:

(1) e slope e�ect does not a�ect the shape of thebending moment curves of the pile. e bendingmoment grows rapidly from 0 on the ground surfaceto the maximum value and then decreases.ere willbe two zero points in the bending moment curves ofthe pile.

(2) e lateral load level a�ects the position of themaximum bending moment of the pile. When thelateral load H0 � 500 kN, the positions of maximumbending moment for the slope ratios of 1V :1H, 2V :3H, 1V : 2H, and 1V : 4H and the level ground appearat 3.25m, 3.01m, 2.92m, 2.79m, and 2.71m belowthe ground surface, respectively. When the lateralload increases to 1000 kN, the corresponding posi-tions of maximum bending moment appear at4.28m, 3.61m, 3.48m, 3.25m, and 2.98m below theground surface, respectively. It can be seen that as theload increases, the position of maximum bendingmoment of the pile will move downward.

(3) e bending moment of the pile increases with theincrease of the slope ratio at the same depth. Itdemonstrates that the elastic deformation range ofthe pile body is larger and the �exural properties ofthe pile are more fully developed as the slope ratioincreases.

Figure 11 shows the variation in maximum bendingmoment with the applied lateral load for di�erent sloperatios. In the initial stage of loading, the maximum bendingmoment is almost the same, indicating that the resistance ofthe soil around the pile at the stage of elastic deformation issu¤cient to balance the maximum bending moment of thepile. When the load exceeds 200 kN, the maximum bendingmoment of the pile for di�erent slope ratios increases rapidlyat di�erent rates. When the lateral load H0 � 1000 kN, themaximum bending moment of the pile for the slope ratios of2V : 3H, 1V : 2H, and 1V : 4H is 15.75%, 28.2%, and 38.76%,respectively, higher than that for level ground. e maxi-mum bending moment of the pile for the slope ratio of 1V :1H is 69.6% higher than that for level ground, which is muchhigher than the corresponding increase rate for other sloperatios. It indicates that the growth rate of maximum bendingmoment is much larger with the increase of lateral load asthe slope gets steeper.

In order to analyze the e�ect of slope on the lateral soilresistance, the “free body cut” postprocessing function fromthe �nite element software was used to obtain the data ofshear force (Q) of the pile varying with depth. A sixth-orderpolynomial function has been chosen for the curve �tting inorder to reduce the error:

Q(z) � az6 + bz5 + cz4 + dz3 + ez2 + fz + g. (1)

Based on Equation (2), the shear force (Q) versus depth(z) �gures were di�erentiated to give �gures of lateral soil

13

1V:1H2V:3H1V:2H

1V:4HLevel ground

121110

9876543210

0–10 10 20 30 40y (mm)

z (m

)

50 60 70 80 90

Figure 7: Pile de�ection versus depth relationships of di�erentslope ratios for H0 � 500 kN.

–50 –25 0 25 50 75 100 125 150 175 200 225 250 275 300 3250123456789

10111213

z (m

)

y (mm)

1V:1H2V:3H1V:2H

1V:4HLevel ground

Figure 8: Pile de�ection versus depth relationships of di�erentslope ratios for H0 � 1000 kN.

Advances in Civil Engineering 5

resistance (p) versus depth (z) for di�erent values of pilehead load H0, such as those presented in Figures 12 and 13:

p(z) �dQ(z)dz

. (2)

e �ndings from Figures 12 and 13 can be listed asfollows:

(1) e shape of the lateral soil resistance curves of thepile in sloping ground is similar to that in levelground. e soil resistance increases from a certainvalue on the ground surface to the maximum valueand then decreases. After reaching the position of the

�rst soil resistance zero point, it increases to themaximum value in the opposite direction. ecompressive stress occurs in the soil before the pileabove the �rst soil resistance zero point, while thetensile stress appears in the soil below the point, whichis consistent with the direction of the pile de�ection.

(2) On the ground surface, the soil resistance will de-crease as the slope ratio increases. e soil re-sistance on the ground surface under level groundcondition is the largest. As it was mentioned, thepile head displacement will increase as the sloperatio increases. It can be inferred that when the pileis in level ground and with small slope ratio, the soilresistance is larger in the shallower ground because

0 100 200 300 400 500 600 700 800 900 1000 11000

250

500

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1750

2000

2250

2500

Mm

ax (k

N·m

)

H (kN)

1V:1H1V:1H1V:1H

1V:1HLevel ground

Figure 11: E�ect of slope ratio on maximum bending moment.

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101112

z (m

)

P (kN·m)

1V:1H2V:3H1V:2H

1V:4HLevel ground

Figure 12: Lateral soil resistance versus depth relationships ofdi�erent slope ratios for H0 � 500 kN.

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123456789

101112

z (m

)M (kN·m)

1V:1H2V:3H1V:2H

1V:4HLevel ground

Figure 9: Bending moment of the pile versus depth relationships ofdi�erent slope ratios for H0 � 500 kN.

–250 0 250 500 750 1000 1250 1500 1750 2000 2250 25000123456789

101112

z (m

)

M (kN·m)

1V:1H2V:3H1V:2H

1V:4HLevel ground

Figure 10: Bending moment of the pile versus depth relationshipsof di�erent slope ratios for H0 � 1000 kN.

6 Advances in Civil Engineering

it is under larger con�nement and exposed bysmaller pile displacement.

(3) e slope ratio a�ects the position of the soil re-sistance zero point of the pile. When the lateral loadH0 � 500 kN, the position of the soil resistance zeropoint of the pile for the level ground appears at4.36m below the ground surface, while that for theslope ratio of 1V :1H appears at 5.09m. More soil isneeded to provide lateral soil resistance to balancethe interaction between pile and soil due to thereduction of soil volume in front of the pile.

(4) e soil resistance increases in the opposite directionnear the bottom of the pile for higher load levels.iscould be due to the fact that the large deformation ofthe pile makes the embedded part of the pile to causea certain lateral displacement and separate from thesoil around the pile, resulting in tension stress of soil.In addition, the soil resistance will increase in theopposite direction near the bottom of the pile as theslope ratio increases for the same load level.

3.2. E�ect of Loading Direction. For the pile adjacent to theslope under lateral load, the conditions of soil in front of thepile and the soil behind the pile will directly a�ect thebearingmechanism of the pile.e conditions of soil in frontof the pile and the soil behind the pile are asymmetrical. elack of soil mass on the slope side of the pile tends to reducethe bearing capacity of the pile. erefore, the loading di-rections (toward loading and reverse loading) have di�erente�ects on the pile bearing mechanism (Figure 14).

In order to study the bearing mechanism of the pileunder di�erent loading directions, the pile distance fromslope crest B/D of di�erent models was set as 1, 3, 5, 7, and∞(level ground), respectively, with the slope ratio of 1V :1H.

Toward lateral load and reverse lateral load were applied onthe models for comparative analysis. To simplify the pre-sentation of results, TL is toward loading in short and RL isreverse loading in short. e pile displacement, bendingmoment, and lateral soil resistance for reverse loading are allpositive values.

Figure 15 shows the contours of lateral displacement ofthe pile and soil for the 1V :1H slope at a lateral load of1000 kN with di�erent loading directions. It can be seenfrom the �gure that the loading directions (toward loadingand reverse loading) a�ect the lateral displacement �eld ofthe soil before the pile. e displacement �eld of the soil inthe shallow foundation for forward loading is distributed inthe shape of wedge, while that for reverse loading is dis-tributed in the U-shaped area. e maximum displacementfor forward loading is much larger than that for reverseloading, which indicates that the loading direction hasa great in�uence on the bearing mechanism of the pileadjacent to a slope.

e pile head load-displacement curves are shown inFigure 16 under di�erent loading directions for the 1V :1Hslope. It can be seen that, with the increase of lateral load, thepile head displacement increases rapidly. e curves fortoward loading are quite di�erent, while the curves forreverse loading are very similar. It indicates that the pilehead displacement is signi�cantly a�ected by the pile dis-tance from slope crest under toward loading. On the con-trary, the pile distance from slope crest under reverse loadinghas little e�ect on the pile head displacement.e maximumpile head displacement is 298.813mm under toward lateralloading of 1000 kN, while the maximum pile head dis-placement is only 118.543mm under reverse lateral loadingof the same load level, which demonstrates that reverseloading is not conducive to the development of pile headdisplacement.

Figures 17 and 18 show the variation of lateral pilede�ection with depth for the 1V :1H slope under di�erentloading directions at lateral loads of 500 kN and 1000 kN,respectively. e �ndings from Figures 17 and 18 can belisted as follows:

(1) When H0 � 500 kN, the maximum pile displacementunder reverse lateral loading increases by 6.61% fromB/D � 7 to B/D � 1. In the meanwhile, the position ofthe �rst displacement zero point moves downwardfrom 5.49m to 6.01m with the decrease of piledistance from slope crest. is is because thecritical load values are di�erent for soil around thepile with di�erent B/D to change from elasticdeformation to plastic deformation at lower ap-plied load levels. e soil that �rst enters the plasticdeformation causes the pile to have a larger de-�ection and also expands the plastic zone into thedeeper foundation soil.

(2) When the lateral load increases to 1000 kN, themaximum pile displacement under reverse lateralloading only increases by 4.24% from B/D � 7 to B/D� 1. In addition, the position of the �rst displacementzero point for di�erent B/D is about 6.01m below the

–200 –150 –100 –50 0 50 100 150 200 250 300 350 4000123456789

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z (m

)

P (kN·m)

1V:1H2V:3H1V:2H

1V:4HLevel ground

Figure 13: Lateral soil resistance versus depth relationships ofdi�erent slope ratios for H0 � 1000 kN.

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ground surface. It indicates that when the lateral loadincreases to a certain critical value, the soil aroundthe pile for di�erent B/D has completely entered the

stage of plastic deformation and pile displacementgradually increases to the maximum value and nolonger changes.

θ

Passivewedge

Activewedge

H0

45 – ϕ/2 45 + ϕ/2

Pile

(a)

θ

Passivewedge

Activewedge

H0

45 – ϕ/245 + ϕ/2

Pile

(b)

Figure 14: Failure mechanism of a pile in sloping ground. (a) Toward loading. (b) Reverse loading.

+3.047e – 01U, U1

+2.789e – 01+2.530e – 01+2.272e – 01+2.013e – 01+1.755e – 01+1.496e – 01+1.237e – 01+9.789e – 02+7.203e – 02+4.618e – 02+2.032e – 02–5.538e – 03

(a)

+3.135e – 03U, U1

–7.005e – 03–1.715e – 02–2.728e – 02–3.742e – 02–4.756e – 02–5.770e – 02–6.784e – 02–7.798e – 02–8.812e – 02–9.826e – 02–1.084e – 01–1.185e – 01

(b)

Figure 15: Lateral displacement �eld at H0 � 1000 kN for the 1V :1H slope. (a) Toward loading. (b) Reverse loading.

0 10 20 30 40 50 60 70 80 90 100 110 120 1300

100200300400500600700800900

10001100

H0 (

kN)

y0 (mm)

B/D = 1-RLB/D = 3-RL

B/D = 5-RLB/D = 7-RL

(a)

H0 (

kN)

y0 (mm)0 25 50 75 100 125 150 175 200 225 250 275 300 325

0100200300400500600700800900

10001100

B/D = 1-TLB/D = 3-TL

B/D = 5-TLB/D = 7-TL

(b)

Figure 16: Pile head load-displacement curves under di�erent loading directions for the 1V :1H slope. (a) Reverse loading. (b) Towardloading.

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(3) e pile de�ection is greatly a�ected by the piledistance from slope crest. Moreover, the increase ofpile de�ection will become greater as the load levelincreases.

e variation of bending moment with depth for the 1V :1H slope under di�erent loading directions with di�erentB/D is presented in Figure 19. From Figure 19, these �ndingscan be drawn:

(1) As the lateral load increases, the bending moment ofthe pile under di�erent loading directions increases.However, the bending moment of the pile for reverse

loading is lower than that for toward loading underthe same condition. It indicates that the bearingcapacity of the pile for reverse loading is better thanthat for toward loading due to the fact that thepassive wedge for toward loading is near the slope.

(2) With the increase of pile distance from slope crest, thebending moment of the pile for reverse loadinggradually approaches the bending moment of the pilefor toward loading. Moreover, when the pile distancefrom slope crest increases to a critical value, the e�ectof loading direction on the bending moment of the

–5 0 5 10 15 20 25 30 35 40 45 500123456789

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z (m

)y (mm)

B/D = 1-RLB/D = 3-RL

B/D = 5-RLB/D = 7-RL

(a)

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10111213

z (m

)

y (mm)

B/D = 1-TLB/D = 3-TL

B/D = 5-TLB/D = 7-TL

(b)

Figure 17: Pile de�ection versus depth relationships under di�erent loading directions for the 1V :1H slope at H0 � 500 kN. (a) Reverseloading. (b) Toward loading.

–20 –10 0 10 20 30 40 50 60 70 80 90 100 110 120 1300123456789

10111213

B/D = 1-RLB/D = 3-RL

B/D = 5-RLB/D = 7-RL

z (m

)

y (mm)

(a)

–50 –25 0 25 50 75 100 125 150 175 200 225 250 275 300 3250123456789

10111213

B/D = 1-TLB/D = 3-TL

B/D = 5-TLB/D = 7-TL

z (m

)

y (mm)

(b)

Figure 18: Pile de�ection versus depth relationships under di�erent loading directions for the 1V :1H slope at H0 � 1000 kN. (a) Reverseloading. (b) Toward loading.

Advances in Civil Engineering 9

pile can be neglected. At an applied loadH0 � 800 kN,the maximum bending moment of the pile for reverseloading is 40.32% lower than that for toward loadingwith B/D � 1. When the pile distance from slope crestB/D increases to 7, the maximum bending moment ofthe pile for reverse loading is only 2.5% lower thanthat for toward loading.

(3) e position of the maximum bending moment ofthe pile for reverse loading is higher than that fortoward loading at the same load level with small B/D.

e e�ect of loading direction on the position of thebending moment of the pile becomes smaller as thepile distance from slope crest increases. When thepile distance from slope crest B/D increases to 7, thepositions of the bending moment of the pile fordi�erent loading directions are the same.

Figures 20 and 21 show the curves of lateral soil re-sistance under di�erent loading directions for the 1V :1Hslope at H0 � 500 kN and H0 � 1000 kN, respectively. It canbe seen that the soil resistance on the ground surface for

–200 0 200 400 600 800 1000 1200 1400 16000123456789

101112

M (kN·m)

H0 = 200kN-RLH0 = 400kN-RLH0 = 600kN-RLH0 = 800kN-RL

H0 = 200kN-TLH0 = 400kN-TLH0 = 600kN-TLH0 = 800kN-TL

z (m

)

(a)

H0 = 200kN-RLH0 = 400kN-RLH0 = 600kN-RLH0 = 800kN-RL

H0 = 200kN-TLH0 = 400kN-TLH0 = 600kN-TLH0 = 800kN-TL

M (kN·m)–200 0 200 400 600 800 1000 1200

0123456789

101112

z (m

)(b)

M (kN·m)

H0 = 200kN-RLH0 = 400kN-RLH0 = 600kN-RLH0 = 800kN-RL

H0 = 200kN-TLH0 = 400kN-TLH0 = 600kN-TLH0 = 800kN-TL

–100 0 100 200 300 400 500 600 700 800 900 1000 11000123456789

101112

z (m

)

(c)

H0 = 200kN-RLH0 = 400kN-RLH0 = 600kN-RLH0 = 800kN-RL

H0 = 200kN-TLH0 = 400kN-TLH0 = 600kN-TLH0 = 800kN-TL

M (kN·m)–100 0 100 200 300 400 500 600 700 800 900 1000 1100

0123456789

101112

z (m

)

(d)

Figure 19: Bending moment of the pile versus depth relationships under di�erent loading directions for the 1V :1H slope. (a) B/D � 1. (b)B/D � 3. (c) B/D � 5. (d) B/D � 7.

10 Advances in Civil Engineering

reverse loading is higher than that for toward loading at thesame load level and B/D. In addition, the soil resistancevalues for reverse loading are almost the same, while thosefor toward loading are very obvious. It indicates that theslope has little e�ect on the soil resistance for reverse loadingbecause of the integrity of soil in front of the pile for reverseloading.

e position of the soil resistance zero point of the pilefor reverse loading is higher than that for toward loading atthe same load level. When the lateral load H0 � 500 kN, theposition of the soil resistance zero point of the pile forreverse loading appears at 4.29∼4.33m below the groundsurface, while that for toward loading appears at 4.35∼5.1m.e pile de�ection becomes greater when the position of thesoil resistance zero point of the pile gets deeper. erefore,the pile under reverse loading is safer than the pile undertoward loading under the same conditions.

4. Conclusions

In order to further explore the bearing mechanism of thelaterally loaded single pile in clay slope under di�erentworking conditions, this paper uses the �nite elementsoftware to establish the laterally loaded pile in slopingground considering the slope ratio and loading direction.Based on the results of �nite element calculation fromdi�erent numerical models, the following main conclusionscan be drawn:

(1) According to the data from previous works, a three-dimensional �nite element veri�cation model of theundrained lateral pile in sloping ground wasestablished. By comparing the �nite element resultswith the theoretical calculation results, the correct-ness of the three-dimensional �nite element mod-eling method was proved.

(2) e slope causes greater pile de�ection and internalforce compared with level ground.e growth rate ofpile head displacement and maximum bendingmoment is much larger with the increase of lateralload as the slope gets steeper. In the meanwhile, theincrease of the slope ratio will also cause the positionof maximum bending moment and soil resistancezero point of the pile to move downward, furtherincreasing the pile de�ection.

(3) When the pile distance from slope crest B < 7D,regardless of the loading direction, the compressivesoil in front of piles is a�ected by the slope e�ect, thusa�ecting the bearing characteristics of the pilefoundation. e displacement and internal forcedevelopment of the pile under toward loading ismore obvious. Moreover, when the pile distancefrom slope crest exceeds 7D, the e�ect of loadingdirection on the pile can be neglected.

Data Availability

Readers can get the data from the numerical simulationmentioned in this paper. Finite element models were

created with appropriate model sizes, and reasonablemodel parameters were assigned for numerical calcula-tions. From the calculation results, the data in the softwarewere extracted, which were processed by the softwareOrigin to obtain diagrams in the paper. Because the dataextracted from the software were useful, there were nounavailable data. In addition, the data used to support the�ndings of this study are available from the correspondingauthor upon request.

–75 –50 –25 0 25 50 75 100 125 150 175 200 225 2500123456789

101112

z (m

)

P (kN·m)

B/D = 1-RLB/D = 3-RLB/D = 5-RLB/D = 7-RL

B/D = 1-TLB/D = 3-TLB/D = 5-TLB/D = 7-TL

Figure 20: Lateral soil resistance versus depth relationships underdi�erent loading directions for the 1V :1H slope at H0 � 500 kN.

B/D = 1-RLB/D = 3-RLB/D = 5-RLB/D = 7-RL

B/D = 1-TLB/D = 3-TLB/D = 5-TLB/D = 7-TL

–200–150–100 –50 0 50 100 150 200 250 300 350 400 4500123456789

101112

z (m

)P (kN·m)

Figure 21: Lateral soil resistance versus depth relationships underdi�erent loading directions for the 1V :1H slope at H0 � 1000 kN.

Advances in Civil Engineering 11

Conflicts of Interest

.e authors declare that there are no conflicts of interestregarding the publication of this paper.

Acknowledgments

.is work was supported by the National Natural ScienceFoundation of China (Grant Nos. 51478479 and 51678570)and Hunan Transport Technology Project (Grant No.201524).

References

[1] K. Georgiadis, M. Georgiadis, and C. Anagnostopoulos,“Lateral bearing capacity of rigid piles near clay slopes,” Soilsand Foundations, vol. 53, no. 1, pp. 144–154, 2013.

[2] L. C. Reese, W. M. Isenhower, and S. T. Wang, Analysis andDesign of Shallow and Deep Foundations, Blackwell SciencePublishing, Hoboken, NJ, USA, 2006.

[3] D. P. Stewart, “Reduction of undrained lateral pile capacity inclay due to an adjacent slope,” Australian Geomechanics,vol. 34, no. 4, pp. 17–23, 1999.

[4] K. Bhushan, S. C. Haley, and P. T. Fong, “Lateral load tests ondrilled piers in stiff clays,” Journal of the Geotechnical Engi-neering Division-ASCE, vol. 105, no. 8, pp. 969–985, 1979.

[5] A. D. Mirzoyan and K. M. Rollins, “Full scale tests to evaluatelateral pile resistance at the edge of a slope,” in Proceedings of32nd Annual Conference on Deep Foundations, DFI, ColoradoSprings, CO, USA, 2007.

[6] A. D. Mirzoyan, “Lateral resistance of piles at the crest of slopein sand,” M. S. thesis, Brigham Young University, Provo,Utah, 2007.

[7] H. G. Poulos, “Behavior of laterally loaded piles near a cut orslope,” Australian Geomechanics Journal, vol. 6, no. 1,pp. 6–12, 1976.

[8] S. V. Sivapriya and S. R. Gandhi, “Experimental and numericalstudy on pile behavior under lateral load in clayey slope,”Indian Geotechnical Journal, vol. 43, no. 1, pp. 105–114, 2013.

[9] S. Mezazigh and D. Levacher, “Laterally loaded piles in sand:slope effect on P-Y reaction curves,” Canadian GeotechnicalJournal, vol. 35, no. 3, pp. 433–441, 1998.

[10] K. Muthukkumaran, “Effect of slope and loading direction onlaterally loaded piles in cohesionless soil,” InternationalJournal of Geomechanics, vol. 14, no. 1, pp. 1–7, 2014.

[11] N. Nimityongskul, Y. Kawamata, D. Rayamajhi, andS. A. Ashford, “Full-scale tests on effects of slope on lateralcapacity of piles installed in cohesive soils,” Journal of Geo-technical and Geoenvironmental Engineering, vol. 144, no. 1,article 4017103, 2018.

[12] D. A. Brown and C.-F. Shie, “Some numerical experimentswith a three dimensional finite element model of a laterallyloaded pile,” Computers and Geotechnics, vol. 12, no. 2,pp. 149–162, 1991.

[13] K. Georgiadis and M. Georgiadis, “Undrained lateral pileresponse in sloping ground,” Journal of Geotechnical andGeoenvironmental Engineering, vol. 136, no. 11, pp. 1489–1500, 2010.

[14] C.W.W. Ng and L. M. Zhang, “.ree-dimensional analysis ofperformance of laterally loaded sleeved piles in slopingground,” Journal of Geotechnical and Geoenvironmental En-gineering, vol. 127, no. 6, pp. 499–509, 2001.

[15] L. M. Zhang, C. W. W. Ng, and C. J. Lee, “Effects of slope andsleeving on the behavior of laterally loaded piles,” Soils andFoundations, vol. 44, no. 4, pp. 99–108, 2004.

[16] V. A. Sawant and S. K. Shukla, “Effect of edge distance fromthe slope crest on the response of a laterally loaded pile insloping ground,” Geotechnical and Geological Engineering,vol. 32, no. 1, pp. 197–204, 2014.

[17] R. Baker, “A second look at Taylor’s stability chart,” Journal ofGeotechnical and Geoenvironmental Engineering, vol. 129,no. 12, pp. 1102–1108, 2003.

[18] L.-Y. Xu, F. Cai, G.-X.Wang, and K. Ugai, “Nonlinear analysisof laterally loaded single piles in sand using modified strainwedge model,” Computers and Geotechnics, vol. 51, pp. 60–71,2013.

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