Research ArticleNonlinear Analysis of Flexible Pile near Undrained ClaySlope under Lateral Loading

Chong Jiang Yu Li Lin Liu and Hang Lin

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

Correspondence should be addressed to Lin Liu liulin9358csueducn and Hang Lin linhangabc126com

Received 3 September 2018 Accepted 25 October 2018 Published 21 November 2018

Guest Editor Xihong Zhang

Copyright copy 2018 Chong Jiang et al -is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In this paper a method is developed for nonlinear analysis of laterally loaded long-flexible pile near undrained clay slope-e idealelastic-plastic p-y curve model is used as the basic calculationmodel to study the pile-soil interaction system To consider the slopeeffect on the soil resistance along with pile length related reduction function expressions of soil resistance are selected by assessingthe existing methods A finite difference iteration scheme is proposed to solve the pilersquos deflection curve equations to obtainnonlinear response of pile -e developed method is validated by comparing its results with the existing method which showsa good agreement A number of parameters analyses are carried out and effects of different influence factors on laterally loadedpile are further discussed

1 Introduction

Pile foundations are widely used to support structures suchas bridges high-rise buildings transmission line towersand traffic signs that are frequently constructed near or ina natural or man-made slope [1] -e pile foundations areoften subjected to static lateral loading in many cases Forthe design needs of pile foundations many scholars haveconducted a lot of research on laterally loaded piles inhorizontal ground -e most commonly used theoreticalmethod for laterally loaded pile in the current designapproach is the well-known subgrade reaction methodwhich considers the pile as a beam supported by a series ofnonlinear soil springs -e lateral load transfer curves(ie p-y curves) are often used to describe the load-deformation characteristics of nonlinear soil springsDifferent criteria for developing p-y curves under manycases including soil types soil strength loading conditionspore water pressure conditions in soil etc have beenproposed by several investigators (Matlock [2] Reese et al[3 4] Reese and Welch [5] Gabr et al [6] Fan and Long[7] and some others) mainly through the back analyses oflateral load tests and these typical p-y curves have beenincorporated into the API specification as a reference for

the design of pile foundation structure in offshore engi-neering [8] Subsequently Wang et al [9 10] proposeda new p-y curve method of laterally loaded pile in clay basedon the analyses and calculation of the existing field test datathrough the stress-strain relationship Wang and Yang [11]used the construction parameters to normalize the differentforms of p-y curves in sand and then proposed a hyperbolicmodel An ideal elastic-plastic p-y calculation model forclay was also proposed based on a comprehensive analysisof the measured p-y curves in clay [12] Zhou et al [13]proposed a new empirical formula for the p-y curves ofultralong PHC pipe piles in soft clay based on the analysesof the relationship between ultimate soil resistance andsome geotechnical parameters from lateral pile load test

For laterally loaded pile near slops the stress environ-ment of the pile foundation becomes due to the lack of soilvolume in front of the pile more complex and the lateralload-bearing characteristics and failure model are differentfrom that pile in horizontal ground [14ndash16] -us theexisting theoretical calculation methods for laterally loadedpile in horizontal ground are not suitable for pile near slopesAvailable studies about the lateral loading capacity behaviorof piles in sloped ground mainly focus on model tests andnumerical simulation (Georgiadis [17 18] Muthukkumaran

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 6817362 13 pageshttpsdoiorg10115520186817362

et al [19] Zhang et al [20] Yin et al [21] Gao et al [22])but rare in the theoretical calculations

is paper attempts to present a method for the nonlinearanalysis of laterally loaded long-exible piles near slopedground For the developedmethod the ideal elastic-plastic p-ycurvemodel is used as the basic calculationmodel to study thepile-soil interaction system To consider the slope eect on thesoil resistance along with pile length related reductionfunction expressions of soil resistance are selected by assessingthe existing methods A nite dierence iteration scheme isthen proposed to solve the pilersquos deection curve equations toobtain nonlinear response of pile To validate the developedmethod it is rst compared to pile test and three-dimensionalnumerical nite element analysis results and the results showthat the developedmethod can provide satisfactory predictionof the response of laterally loaded pile near clay slopes enit is applied to analyze the parametric inuence law and thenonlinear response results of pile near clay slope underdierent inuence factors are obtained

2 Method of Analysis

21 Mechanical Analysis Model Currently p-y curvemethods were used by many researchers to study thenonlinear response characteristics of the laterally loaded pilein horizontal ground Zhu [23] conducted extensive analysisof laterally loaded pile in horizontal ground by using theelastic-plastic p-y curve model and suggested that choosingreasonable model parameters can obtain realistic results Insuccession the general calculation form of the ideal elastic-plastic p-y curve method in clay (Figure 1) based on thiswas given by Wang and Yang [12] as follows

p Ky yleyu

pu ygtyu (1)

where K initial slope of the p-y curve y lateral dis-placement of pile pu ultimate soil resistance (per unit pilelength) and yu allowable lateral displacement for soil inelastic state

In order to consider the inuence of slope eects theanalysis model for laterally loaded pile near sloped ground isset up as shown in Figure 2

Where L buried pile length H0 lateral load acting onthe pile top B distance from the pile shaft to the slope crestθ slope angle D pile diameter and e height of the loadabove the clay surface

22 Assumptions To facilitate the establishment of methodassumptions and statements are made in advance

(1) e cross-sectional shape of pile at all depths is equalbesides both the pile and the soil are homogeneousand isotropic materials

(2) e ultimate lateral soil resistance (pu) varies non-linearly with depth

(3) Considering the slope eect the initial stiness (K)and the ultimate lateral soil resistance (pu) should bereduced within a certain depth

(4) Assume that clay slope is stable and the slope de-struction and instability are not taken into consid-eration during the process of calculation

23 p-y Curve Model of Laterally Loaded Pile near SlopeWith the basic assumptions in Section 22 equation (1) isthen modied to obtain the new ideal elastic-plastic p-ycurves as follows

p u(z)Ky yleyu

Psu(θ B z) ygtyu (2)

where μ(z) is the reduction function of the soil lateral initialstiness (K) psu(θ B z) is the ultimate lateral soil resistanceper unit pile length under the condition of pile near slope

Allowable lateral displacement of yu can be obtainedaccording to equation (2)

yu Psu(θ B z)u(z)K

(3)

3 Initial Stiffness K

e problem of choosing the initial stiness of the soil in thep-y curve has always been focused on by investigators Manyscholars believed that the lateral initial stiness K of clayremains constant in all depth is paper adopts the initial

0y

p

pu

K

1 Elastic state

Plastic state

Figure 1 Ideal elastic-plastic p-y curve

BH0

D

z

θ

L

ye

Figure 2 Analysis model denition

2 Advances in Civil Engineering

stiffness recommended by Rajeshree and Sitharam [24] asfollows

Ki 13Ei

1minus v2s

EiD4

EpIp1113888 1113889

112

(4)

where vs EpIp is Poissonrsquos ratio of soil and pile bendingrigidity respectively

According to the Kondner [25] the initial elasticitymodulus can be related to elasticity modulus E50 under the50 failure stress and the elasticity modulus at deviatoricstress can be expressed by

Es Ei 1minusRfσσf

1113888 1113889 (5)

where σ is deviation stress σf is deviatoric failure stress Rf isthe ratio of the deviatoric failure stress over the ultimatedeviatoric stress generally taken as 08 Ei is the initial elasticmodulus and σσf 05

For undrained loading we have vs 05 -e elasticmodulus of the clay is represented by the deformationmodulus E50 under the 50 failure stress of the reaction soiland Ei 167 E50 is satisfied -e above expression can beused to derive the initial stiffness (K) of clay under un-drained conditions

K 3E50E50D

4

EpIp1113888 1113889

112

(6)

4 Reduction Function of Initial Stiffness u(z)

For near-slope laterally loaded pile the initial stiffness of thesoil is also affected by the slope [17 18 22] Georgiadis andGeorgiadis [18] gave the reduction function for the initialstiffness of clay within the shallow foundation under un-drained loading condition

u(z) cos θ +1minus cos θ

6z

D+

B

Dminus 051113874 1113875tan θ1113876 1113877le 1 (7)

5 Ultimate Soil Resistance of Clay psu

Several methods are available for determining the ultimatesoil lateral resistance pu to piles in cohesive soil[2 4ndash6 10 12] It is generally believed that the ultimateresistance (pu) of clay depends mainly on the type of failuremechanism at a certain depth of the soil -e normativeformula in API design code for horizontal ground is given inequation (8)

Np 3 +cprimezcu

+ Jz

Dle 9 (8)

pu NpcuD (9)

where Np is ultimate capacity coefficient of clay cu is un-drained shear strength of clay cprime is effective bulk density ofclay and J is dimensionless experience coefficient its valueranges from 025 to 05

To consider slope effect on the ultimate soil resistancethe following expression proposed by [18] is used to calculatethe ultimate soil resistance Nsp

Nsp

Npuminus Npu minusNp01113872 1113873eminusλ(zD) zle zc

Npuminus Npu minusNpc1113872 1113873eminusλαθ zminuszc( )D zgt zc

⎧⎪⎪⎨

⎪⎪⎩(10)

αθ 1minussin θ(1 + sin θ)

2 (11)

zc 85minus 10log(8minusbD)101113960 1113961D (12)

Npu π + 2Δ + 2 cosΔ + 4 cosΔ2

+ sinΔ2

1113874 1113875 (13)

where zc is the certain critical depth αθ is the parameterrelated to the slope Npu is the ultimate lateral bearing ca-pacity factor Besides Δ sinminus1α and λ 055minus 015α bothare dimensionless coefficients Np0 is the lateral bearingcapacity factor at ground surface Np0 2 + 15 α α is theadhesion coefficient and its value ranges from 0sim1 Npc isthe ultimate soil resistance at a certain critical depth

According to equations (9)ndash(13) the ultimate soil re-sistance of clay psu for undrained conditions can beexpressed as

Psu NspCuD (14)

6 FDM Solution of the Proposed Method

61 Establishment of Calculation Model A simplified cal-culation model can be established as shown in Figure 3

Select a microunit of the pile for force balance analysis Itis stated here that the bending moment is positive in thecounterclockwise rotation direction and the normal of theshear force is positive in the positive direction of the z axis-e shear force is positive in the negative direction of the yaxis -en the equation for the deflection of the pile can bederived as follows

EpIpd4 y

dz4 + p(y z) 0 (15)

where EpIp is the pile bending stiffness p(y z) is the soilresistance distributed along pile length which can be ob-tained from the previous p-y curve and the positive di-rection is positive direction of the y axis

Boundary restrictions must be determined to solve theabove-mentioned deflection differential equation In thispaper the boundary conditions of the pile are determinedthe pile top is free and the pile bottom is fixed and thecorresponding deflection differential equations are asfollows

Free pile head

EpIpyPrime11138681113868111386811138681113868z0

M0

EpIpy11138681113868111386811138681113868z0

H0

⎧⎪⎨

⎪⎩(16)

Fixed pile bottom

Advances in Civil Engineering 3

EpIpyPrime∣∣∣∣∣zL 0

EpIpy∣∣∣∣∣zL 0

(17)

62 Dierential Format Derivation and Solution e nitedierence method principle is used to discrete the buriedsection L into n segments each of which is s Ln e topnode is denoted as 0 and the bottom of the pile is marked asn In order to improve the simplicity of the nite dierenceoperation four virtual nodes minus2 minus1 n + 1 n + 2 are added atthe top of pile and the bottom of the pile respectively edisplacement of the ith node is yi is shown in Figure 4

For a pile there exists (n + 5) dierential equations afterthe discrete division and four extra known dierentialequations can be derived in combination with the boundaryconditions thereby establishing the pile displacement nodevector yi and further solving the pile displacement

Substituting the fourth derivative of pile microelementin equation (15) the dierential equation for each element ofthe pile can be derived

yi+2 minus 4yi+1 + 6yi minus 4yiminus1 + yiminus2 +s4

EpIpp yi z( ) 0 (18)

In combination with equation (2) equation (18) can betransformed into the following two forms according to theallowable displacement yu

(1) yleyu

yi+2 minus 4yi+1 +(6 +mu(z)K)yi minus 4yiminus1 + yiminus2 0

m s4

EpIp

(19)

(2) ygtyu

yi+2 minus 4yi+1 + 6yi minus 4yiminus1 + yiminus2 +mNspCuD 0

m s4

EpIp

(20)

Similarly in terms of equations (16) and (17) the dif-ferential form of the boundary conditions can be derived

y2 minus 2y1 + 2yminus1 minusyminus2 2H0s3

EpIp

y1 minus 2y0 + yminus1 M0s2

EpIp

yn+1 minus 2yn + ynminus1 0

yn+2 minus 2yn+1 + 2ynminus1 minusynminus2 0

(21)

According to the dierential equations from equation(21) of the boundary conditions (n + 1) unknown dier-ential equations are combined to obtain the displacement ofthe pile matrix the corresponding pile displacement solu-tion equations can be expressed as

Kn[ ] y F (22)

where [Kn] is the stiness matrix of pile which is dividedinto two type stiness matrix of [K1] and [K2] according tothe elastic state and plastic state of the soil along the pilelength respectively y is the pile displacement node vectorF is external load vector which is controlled by boundaryconditions and is also divided into two type vector of F1 and F2 correspond to [K1] and [K2] respectively

In most practical projects the maximum bending mo-ment section is regarded as the most dangerous cross section

y

z

s

s

s

s

yi ndash 2

yi ndash 1

yi

yi + 1

yi + 2

s

ndash2

ndash1

0

1

2

n ndash 2

n ndash 1

n

n + 1

n + 2

s

Figure 4 Finite dierence method cell division

y

z z

zl

zi

zj

zn

L

O

H0

Pile

p(yz)

Slopeyl

yi

yj

yn

Displacement of the pile

M0

θ

Figure 3 Simplied calculation model of near-slope pile

4 Advances in Civil Engineering

of the pile design Here the dierential form of the solutionof the bending moment is listed as

Mi yiminus1 minus 2yi + yi+1( )EpIp

s2 (23)

According to the basic solution ideas of equation (22)a MATLAB iterative code is developed to solve the responsebehavior of pile and the ow chart of iterative calculation isshown in Figure 5

7 Validation to Previous Studies

e feasibility of the proposed method is validated in thissection to some previous studies which are well docu-mented in the literatureis method is introduced as inputinto MATLAB to calculate the response of each pile egeometrical characteristics (pile length L pile diameter Ddistance from the pile shaft to the slope crest B bendingstiness of the pile EpIp and slope angleθ) and the soilproperties (undrained shear strength cu secant modulusE50 eective bulk density c or cprime and cohesion coecentcientα) are summarized in Table 1 for each previous studyconsidered

Case 1 e computed pile responses are compared to thepile test results and to the pile responses computed with thesame computer code using as input the Matlock [2] Reeseand Welch [5] Bhushan et al [26] Stevens and Audibert[27] e Shanghai pile tests as shown in Figure 6 reportedby the literature [28] involved lateral loading of piles in levelground It can be seen that despite the small discrepancymeasured and predicted between the proposed p-y curveload-displacement relationships the general shape of thecurves is very similar indicating that the small discrepancymay be due to overestimation of secant modulus E50

Case 2 e results calculated by the proposed method andthe results calculated by Georgiadis and Georgiadis [17]which presented 3D nite-element analyses of pile in slopingground are presented in Figure 7 for comparison purposesis paper selects two dierent slope angles (θ 20deg 40degrespectively) for verication analysis As the slope angleincreases the results of this method are getting closer to theresults of the literature [17]

Case 3 e calculating results given by Georgiadis andGeorgiadis [18] are used as examples for comparisonverication Pile foundation is completely buried in theundrained clay slope us the section of the pile head atground surface only has the initial horizontal forceH0 ispaper selects four dierent pilersquos distance from slope crest(B 03m 06m 12m 24m respectively) for vericationanalysis e H0-y0 curves and H0-maxM curves of pilehead obtained from the proposed method and literature[18] are plotted in Figure 8 A good agreement has beenobserved between the calculating results from the presentstudy and literature results

8 Parametric Study

81 Eect of Slope Angle θ e size of the slope angle di-rectly determines the soil volume in front of the pile toparticipate in the pile-soil interaction In order to bettershow the eect of slope angles the pile head deection ofslope was normalized by dividing the pile head deection ofslope (y0s) by that of horizontal (y0H) Figures 9ndash12 re-spectively show the lateral load-deection curves at pilehead the normalized deection (y0sy0H)-load (H0) curvesat pile head y0 the maximum bending moment (Mmax)-load (H0) curves and the bending moment(M)-depth(z)distribution curves with dierent slope angles of 0deg 10deg 20deg40deg 50deg e relevant calculation parameters here are pilelength L 14m pile diameter D 06m bending stinessof pile EpIp 18449 (MNmiddotm2) normalized distance of pileBD 05 adhesion coecentcient α 1 piles are completelyburied in undrained clay and Poissonrsquos ratio of clay ]s 049 undrained shear strength cu 40 kPa and secantmodulus E50 14MPa

As shown in Figure 9 as the slope angle increases thelateral deection of the pile head increases signicantly and

Determine the number nof pile unit divisions

Start

Input initial lateralload

Input parameters ofpile soil and slope

Calculate the values of K psuiand μ(zi) for each node of the pile

Calculate the allowable displacementvalue of yu for each node of the pile

Calculate pile lateral displacement yi for eachnode by using the elastic matrix of Ki and the

external load vector of Fi

Judge yi gt yu

Resolve by replacing K2 and F2 with Ki and Ficorrespondingly where needed

Output lateral displacement value of yi foreach node and calculate the corresponding

bending moment value of Mi

End

Yes

No

Figure 5 Flowchart of iterative calculation

Advances in Civil Engineering 5

this trend becomes much more obvious with the increase ofthe lateral load It is also observed that when ground surfacechanges from horizontal ground to 10deg slope the behavior ofpile is almost like horizontal ground surface indicating theeect of slope is almost negligible when the slope angle is lt10degFigure 10 further shows the distribution curves of normalizeddeection (y0sy0H) with the lateral load It can be seen thatdierent xed ratios of y0sy0H are almost maintained at lowload levels but as the lateral load continue to increase the

values of y0sy0H start to increase unequally for dierent slopeangle with the increase of load When the lateral load is at750 kN the values of y0sy0H for 40degslope and 50deg slope are1065 2157 respectively indicating that the steeper the slopeangle is the more deection of pile head grows

It can be seen from Figure 11 that the maximum bendingmoment values of the pile also increase as the slope angleincreases but the rate of increase of maximum bendingmoment with lateral load is more moderate

Table 1 Summary of pile load test

Pile testGeometrical characteristics Soil properties

L (m) D (m) B (m) EpIp (kNmiddotm) e (m) θ (deg) cu (kPa) E50 (kPa) c or cprime (kNm3) α1 14 05 0 97900 072 0 30 3000 7 0942 20 10 0 1423534 0 2040 70 14000 18 053 12 06 03 06 12 24 184490 0 45 50 10000 18 073

00

20406080

100120140160180200

10 20 30 40y0 (mm)

H0 (

kN)

50 60 70

Stevens and AudibertBhushan et alMatlock

OrsquoNeill and GaziogluPresent studyPile test

Figure 6 Verication analysis of H0-y0 curves relationship for Shanghai pile tests

Present studyFE analyses (Georgiadis and Georgiadis [18])Present studyFE analyses (Georgiadis and Georgiadis [18])

10000900080007000600050004000300020001000

0

max

M (k

Nmiddotm

)

0306090120150180210240270300

y 0 (m

m)

0 250 500 750 1000 1250 1500 1750 2000 2250 2500H0 (kN)

(a)

Present studyFE analyses (Georgiadis and Georgiadis [18])Present studyFE analyses (Georgiadis and Georgiadis [18])

0 250 500 750 1000 1250 1500 1750 2000 2250 2500H0 (kN)

10000900080007000600050004000300020001000

0

max

M (k

Nmiddotm

)

04080120160200240280320360400

y 0 (m

m)

(b)

Figure 7 Verication analysis of H0-y0 curves relationship for FE analysis (a) θ 20deg (b) θ 40deg

6 Advances in Civil Engineering

Figures 12 and 13 show the bending moment distributionwith depth and the depth of xity (where the maximumbending moment occurs) of the pile for all slope angles witha lateral load at 300 kN and 600 kN respectively It is clear thatthe maximum bending moment of the pile increases with theincrease of slope angle at the same load but the rst zerolocation of bendingmoment curve and depth of xity increasecorrespondingly With the increase of the load the dierencein the maximum bending moment growth at each slope anglebecomes obvious and the rst zero location of bendingmoment curve and depth of xity of the pile also increasemore quickly For example as is shown in Figure 13 the depthof xity for 30deg and 50deg slope angle increased by 446 1734compared with that in horizontal ground at the load of300 kN respectively but the ratio further increases to 11323203 respectively when the load increases to 600 kN It canalso be seen from Figure 13 that the depth of pile xity almostoccurs at a depth of 4sim8D (D diameter of pile)

82 Eect of Normalized Distance of Pile BD Selecting thenormalized distance of pile BD as 05 2 4 6 and considerthe slope angle of 10deg 30deg 50deg respectively as the existingslope conditions e other calculation parameters are thesame as in Section 81

Figures 14ndash16 show the load-deection curve for dif-ferent normalized distance BD of pile head at above threeslope conditions From these gures it is observed that theincrease in normalized distance BD ratio decreases thedeection of pile head When normalized distance BDratio exceeds 6 in all slope angle conditions the deectionat pile head is basically the same as that in horizontalground which means the inuence of the slope eect isalmost negligible in this case It is also observed that theload-deection curves in dierent slope angle conditionshave dierent response results and the increase in slopeangle can increase the discreteness of the curves Figure 17further shows the eect of normalized distance of pile on

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3500

3000

2500

2000

1500

1000

500

0

max

M (k

Nmiddotm

)

0 200 400 600 800 1000H0 (kN)

0

120

240

360

480

600

720

840

y 0 (m

m)

(a)

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3500

3000

2500

2000

1500

1000

500

0

max

M (k

Nmiddotm

)

0

100

200

300

400

500

600

700

y 0 (m

m)

0 200 400 600 800 1000H0 (kN)

(b)

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3000

2500

2000

1500

1000

500

0

max

M (k

Nmiddotm

)

0 200 400 600 800 1000H0 (kN)

0

90

180

270

360

450

540

y 0 (m

m)

(c)

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3000

2500

2000

1500

1000

500

0m

ax M

(kN

middotm)

0 200 400 600 800 1000H0 (kN)

0

80

160

240

320

400

480

y 0 (m

m)

(d)

Figure 8 Verication analysis of H0-y0 curves relationship for LPILE (a) B 03m (b) B 06m (c) B 12m (d) B 24m

Advances in Civil Engineering 7

lateral-load capacity on horizontal ground and slopingground (θ 10deg 30deg 50deg) It can be seen that when thenormalized distance BD of pile changes from 05 to 6 thelateral-load capacity is increased by 227 111 2987on 10deg 30deg 50deg sloping ground respectively indicating thatthe increase in slope angle increases the inuence of BD onthe lateral-load capacity of the pile

Figures 18ndash20 show the bending moment variationalong pile length of the pile for dierent normalized dis-tance BD on horizontal ground and sloping ground(θ 10deg 30deg 50deg) From these gures it is observed that themaximum bending moment increases with the increase inthe normalized distance BD of the pile and the increase inthe applied lateral load Also for the same normalized

distance BD of pile and applied lateral load the increase inslope angle of θ increases the maximum bending momentof pile When ground surface changes from horizontal to10deg 30deg and 50deg sloping ground the maximum bendingmoment of pile in sloping ground is increased by 28126 and 319 respectively under lateral load of 600 kNand normalized distance BD of 05 It is also noted thatwhen the pile is nearer to slope crest the slope angle be-comes a more dominant factor to aect the lateral capacityof the pile especially at a high-load level

0 100 200 300 400 500 600 700 80010

15

20

25

30

Nor

mal

ized

disp

lace

men

t y o

Sy o

H

Lateral load H0 (kN)

θ = 0deg (B = 05D)θ = 10deg (B = 05D)θ = 20deg (B = 05D)

θ = 30deg (B = 05D)θ = 40deg (B = 05D)θ = 50deg (B = 05D)

Figure 10 Normalized deection (y0sy0H)-load (H0) curves fordierent slope angle

ndash200 0 200 400 600 800 1000 1200 1400 1600 18000123456789

101112131415

Dep

th (m

)

Bending moment M (kNmiddotm)

θ = 0deg H0 = 300kNθ = 0deg H0 = 600kNθ = 10deg H0 = 300kNθ = 10deg H0 = 600kNθ = 20deg H0 = 300kNθ = 20deg H0 = 600kN

θ = 30deg H0 = 300kNθ = 30deg H0 = 600kNθ = 40deg H0 = 300kNθ = 40deg H0 = 600kNθ = 50deg H0 = 300kNθ = 50deg H0 = 600kN

Figure 12 Bending moment variation along the depth of pile fordierent slope angle

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Deflection y0 (mm)

θ = 0deg (B = 05D)θ = 10deg (B = 05D)θ = 20deg (B = 05D)

θ = 30deg (B = 05D)θ = 40deg (B = 05D)θ = 50deg (B = 05D)

Figure 9 Lateral load-deection curves for dierent slope angle atpile head

0 400 800 1200 1600 2000 24000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Maximum bending moment Mmax (kNmiddotm)

θ = 0deg (B = 05D)θ = 10deg (B = 05D)θ = 20deg (B = 05D)

θ = 30deg (B = 05D)θ = 40deg (B = 05D)θ = 50deg (B = 05D)

Figure 11 Maximum bending moment-load curves for dierentslope angle

8 Advances in Civil Engineering

83 Eect of Adhesion Coecient α In order to study theeect of adhesion coecentcient α on the lateral behavior of pile insloped ground this paper analyzes the parameter α from 0 to1 with increment of 01 and chooses lateral loadH0 500 kNand the bending momentM0 0 (kNmiddotm) as the xed loadingcondition to calculate and analyze the deection of pile headConsider the slope angle θ as the same in Section 81 andother basic calculation parameters are the same as Section 81

Figures 21 and 22 show pile head deection (y0) and themaximum bending moment (Mmax) of the pile variation withthe adhesion coecentcient α for dierent slope angle re-spectively From these gures it can be seen that increasingthe adhesion coecentcient α at the pile-soil interface can ef-fectively reduce the pile head deection and the maximumbending moment of the pile at the same time Also the in-crease in slope angle almost does not change the corre-sponding curve growth model but will signicantly increase

0 20 40 60 80 100 120 140 160 180 200 220 2400

100

200

300

400

500

600

700

800

Lateral displacement y0 (mm)

BD = 05 (θ = 10deg)BD = 2 (θ = 10deg)

BD = 4 (θ = 10deg)BD = 6 (θ = 10deg)

Late

ral l

oad

H0

(kN

)

Figure 14 Lateral load-deection curves for θ 10deg for dierentnormalized distance of pile at pile head

0 1 2 3 4 5 6

560

580

600

620

640

660

680

700

720

740A

llow

able

pile

capa

city

(kN

)

Normalized distance BD

Level ground (θ = 0deg)θ = 10deg

θ = 30degθ = 50deg

Figure 17 Bearing capacity of pile head for dierent normalizeddistance of pile (corresponding to 200mm)

247

122

247

123

247

126

258

142

274

059

289

9763

6058

3

367

113

376

092

401

397

428

333

476

085

θ = 50degθ = 40degθ = 30degθ = 20degθ = 10deg

H0 = 300kNH0 = 600kN

θ = 0deg00

05

10

15

20

25

30

35

40

45

50

55

Dep

th o

f fix

ity (m

)

Figure 13 Depth of xity variation with dierent slope angle

B = 05D (θ = 30deg)B = 2D (θ = 30deg)

B = 4D (θ = 30deg)B = 6D (θ = 30deg)

0 30 60 90 120 150 180 210 240 270 3000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Lateral displacement y0 (mm)

Figure 15 Lateral load-deection curves for θ 30deg for dierentnormalized distance of pile at pile head

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Lateral displacement y0 (mm)

BD = 05 (θ = 50deg)BD = 2 (θ = 50deg)

BD = 4 (θ = 50deg)BD = 6 (θ = 50deg)

Figure 16 Lateral load-deection curves for θ 50deg for dierentnormalized distance of pile at pile head

Advances in Civil Engineering 9

the pile head deection and maximum bending moment ofthe pile especially when the slope angle exceeds 40deg An ex-ample is used for pile head deection when the value of α isequal to 0 the pile head deection values of pile in slopingground with θ 10deg 30deg 50deg is increased by 74 398137 respectively compared to that in horizontal ground

84 Eect of Undrained Shear Strength cu Here lateral loadH0 500 kN and the initial bending momentM0 0 (kNmiddotm)

were taken as the initial loading conditions choosing un-drained shear strengths cu of 20 kPa 40 kPa 60 80 kPa100 kPa respectively to calculate and analyze Other basiccalculation parameters are the same as in Section 81

Figures 23 and 24 show pile head deection (y0) and themaximum bending moment (Mmax) of the pile variationwith the undrained shear strength cu for dierent slopeangles respectively From the curves given in Figures 23 and24 it is observed that the increase in undrained shearstrength cu decreases the pile head deection and themaximum bending moment is is because of the increasein the strength of soil and the relative stiness of the pile-soilsystem Also it is obvious that the presence of slopes

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

ndash200 0 200 400 600 800 1000 1200 1400 16000123456789

1011121314

Dep

th (m

)

Bending moment M (kNmiddotm)

Figure 19 Bending moment variation along the depth of pile forθ 30deg for dierent slope angle

ndash200 0 200 400 600 800 1000 1200 14000123456789

1011121314

Dep

th (m

)

Bending moment M (kNmiddotm)

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

Figure 18 Bending moment variation along the depth of pile forθ 10deg for dierent slope angle

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

ndash200 0 200 400 600 800 1000 1200 1400 1600 18000123456789

1011121314

Dpe

th (m

)

Bending moment M (kNmiddotm)

Figure 20 Bending moment variation along the depth of pile forθ 50deg for dierent slope angle

ndash01 00 01 02 03 04 05 06 07 08 09 10 116080

100120140160180200220240260

Late

rald

ispla

cem

ent y 0

(mm

)

Adhesion coefficient α

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 21 Pile head deection (y0) variation with adhesion co-ecentcient (α) for dierent slope angle

10 Advances in Civil Engineering

aggravates the rate of change of pile head deection es-pecially when cu ranges from 20 kPa to 40 kPa and when thevalue of cu exceeds 40 kPa the decrease rate of the deectionof pile head becomes slow and eventually almost becomesat From the results in Figure 23 it is observed that the pilehead deection in the range of 734ndash75 for increase in cu20 kPa to 40 kPa of sloping ground (θ 10deg 20deg 30deg 40deg 50deg)and horizontal ground surfaces from which can concludethat the weaker soil parameters are the more signicantslope eect becomes Besides the curve of the maximumbending moment variation with undrained shear strengthshown in Figure 24 is smoother and the range of themaximum bending moment of the pile with the increase ofthe slope is relatively stable

9 Conclusions

e purpose of this paper is to study the behavior of laterallyloaded long-exible pile in undrained clay sloping groundBased on the basic model of ideal elastic-plastic p-y curvemethod this paper derives the dierential equations of thelaterally loaded single pile in undrained clay sloped groundby introducing the existing related reduction variablefunction and the corresponding nite dierence method forthe pile deection and internal force is obtained A series ofparameters analyses are further performed for slope anglenormalized distance of pile adhesion coecentcient and un-drained shear strength e conclusions obtained from thisstudy are summarized as follows

(1) A nonlinear analysis method for laterally loaded long-exible pile in undrained clay sloped ground isestablished rough the verication of examples thecorrectness and feasibility of the method is proved

(2) Slope angle is the most important factor that aectingthe lateral bearing capacity of the near-slope pile eincrease in slope angle increases the deection and the

rate of increase of deection and this trend becomesmore obvious as the lateral load increased When theslope angle is small enough (θ lt 10o) the eect ofslope is almost negligible Besides the depth of xityof the pile is about 4sim8 times the size of the pilediameter

(3) e distance away from pile to slope crest is also animportant factor that aects the lateral-load capacityof the pile e increase in normalized distance BDof the pile decreases the deection of pile head butincreases the lateral-load capacity and when nor-malized distance BD ratio exceeds 6 the slope eectcan be avoidedWhen laterally loaded pile is closer tothe slope crest the inuence of the slope angle seemsmore dominant

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

ndash01 00 01 02 03 04 05 06 07 08 09 10 11

900

1000

1100

1200

1300

1400

1500

1600

Max

imum

ben

ding

mom

ent

Mm

ax (k

Nmiddotm

)

Adhesion coefficient α

Figure 22 Maximum bending moment (Mmax) variation withadhesion coecentcient (α) for dierent slope angle

0 20 40 60 80 100 1200

50100150200250300350400450500550600

Late

ral d

ispla

cem

ent y 0

(mm

)

Undrained shear strength cu (kPa)

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 23 Pile head deection (y0) variation with undrained shearstrength (cu) for dierent slope angle

0 20 40 60 80 100 1200

300

600

900

1200

1500

1800

2100M

axim

umbe

ndin

gmom

ent M

max

(kN

middotm)

Undrained shear strength cu (kPa)

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 24 Maximum bending moment (Mmax) variation withundrained shear strength (cu) for dierent slope angle

Advances in Civil Engineering 11

(4) -e adhesion coefficient α at the pile-soil interfacecan effectively reduce the pile head deflection and themaximum bending moment of the pile at the sametime -e increase in slope angle will significantlyincrease the pile head deflection and maximumbending moment of the pile especially when theslope angle exceeds 40deg

(5) -e increase in undrained shear strength cu de-creases the pile head deflection and the maximumbending moment of the pile -is is because of theincrease in the strength of soil and the relativestiffness of the pile-soil system Also the presence ofslopes aggravates the rate of change of pile headdeflection especially when the cu is in a mall value(ranges from 20 kPa to 40 kPa) In contrast themaximum bending moment variation with un-drained shear strength affected by the slope effectappears more moderate

(6) -is study researches the lateral bearing behavior ofsingle pile in undrained clay sloping ground Inpractical projects the situation of pile foundationson slope ground surface is not uncommon and thelateral bearing characteristics of pile foundationsare more complicated -erefore the influence ofslope effect on the lateral bearing capacity of pilewhich is on slope ground surface is worth furtherstudy

Data Availability

-e original data for summary of pile load test in Table 1 arefrom Wu et al [28] Georgiadis and Georgiadis [17] andGeorgiadis and Georgiadis [18] respectively -e computedpile responses as shown in Figure 6 are compared to the piletest results (Wu et al [28]) and to the pile responsescomputed with the same computer code using as input theMatlock [2] Reese and Welch [5] Bhushan et al [26]Stevens and Audibert [27] Figures 7 and 8 are calculated bycomputer code MATLAB to compare previous studies(Georgiadis and Georgiadis [17] Georgiadis and Georgiadis[18] respectively) Figures 9ndash24 are calculated by the pro-posedmethod based on the original data mentioned above tostudy parametric analysis In addition all the sharing datawere involved in this paper and there was no redundantdata

Conflicts of Interest

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

Acknowledgments

-is work is supported by the National Natural ScienceFoundation of China (grant nos 51478479 and 51678570)and Hunan Transport Technology Project (grant no201524)

References

[1] N Nimityongskul Y Kawamata D Rayamajhi andS A Ashford ldquoFull-scale tests on effects of slope on lateralcapacity of piles installed in cohesive soilsrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 144 no 1article 04017103 2018

[2] H Matlock ldquoCorrelation for design of laterally loaded piles insoft clayrdquo in Proceedings of the Offshore Technology Confer-ence pp 77ndash94 Houston TX USA April 1970

[3] L C Reese ldquoAnalysis of laterally loaded piles in sandrdquo inProceedings of the Offshore Technical Conference pp 95ndash105Houston TX USA May 1974

[4] L Reese W Cox and F Koop ldquoField testing and analysis oflaterally loaded piles on stiff clayrdquo in Proceedings of theOffshore Technology in Civil Engineering pp 106ndash125 DallasTX USA May 1975

[5] L C Reese and R C Welch ldquoLateral loading of deepfoundations in stiff clayrdquo Journal of Geotechnical and Geo-environmental Engineering vol 101 no 7 pp 633ndash649 1975

[6] M A Gabr T Lunne and J J Powell ldquoP-y analysis of laterallyloaded piles in clay using DMTrdquo Journal of GeotechnicalEngineering vol 120 no 5 pp 816ndash837 1994

[7] C C Fan and J H Long ldquoAssessment of existing methods forpredicting soil response of laterally loaded piles in sandrdquoComputers and Geotechnics vol 32 no 4 pp 274ndash289 2005

[8] G P Yang and Z M Zhang ldquoResearch on P-Y curve oflaterally bearing piles under large displacementrdquo WaterTransportation Engineering vol 342 no 7 pp 40ndash45 2002

[9] C Wang and Z A LU ldquoCalculation of internal forces oflaterally loaded piles by using p-y curverdquo Journal ofChongqing Jiaotong University (Natural Science) vol 4 no 1pp 61ndash65 1958

[10] H C Wang and D Q WU ldquoA new unified approach to thep-y curve of laterally loaded pile in clayrdquo Journal of HohaiUniversity no 1 pp 9ndash17 1991

[11] G C Wang and M Yang ldquoNonlinear analysis of laterallyloaded piles in sandrdquo Rock and Soil Mechanics no 2pp 261ndash267 2011

[12] G CWang andM Yang ldquoCalculation of laterally loaded pilesin clayrdquo Journal of Tongji University (Natural Science) vol 40no 3 pp 373ndash378 2012

[13] T Q Zhou Z A LU and D H Wang ldquoCalculation methodof laterally loaded super-long PHC pilerdquo Port and WaterwayEngineering no 6 pp 155ndash160 2013

[14] L U Cheng X C Xu S X Chen et al ldquoModel test andnumerical simulation of horizontal bearing capacity andimpact factors for foundation piles in sloperdquo Rock and SoilMechanics no 9 pp 2685ndash2691 2014

[15] P YinB H ZhaoM H Zhao et al ldquoStability analysis of pile-column bridge pile considering slope effectrdquo Journal of Hu-nan University (Natural Science) vol 43 no 11 pp 20ndash252016

[16] Y S Deng M H Zhao X J Zhou et al ldquoResearch progress ofbearing characteristics of pile column at steep slope inmountain areasrdquo Journal of Highway and TransportationResearch and Development vol 29 no 6 pp 37ndash45 2012

[17] K Georgiadis and M Georgiadis ldquoUndrained lateral pileresponse in sloping groundrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 136 no 11 pp 1489ndash1500 2010

[18] K Georgiadis and M Georgiadis ldquoDevelopment of p-ycurves for undrained response of piles near slopesrdquo Com-puters and Geotechnics vol 40 no 3 pp 53ndash61 2012

12 Advances in Civil Engineering

[19] K Muthukkumaran R Sundaravadivelu and S R GandhildquoEffect of slope on p-y curves due to surcharge loadrdquo Soils andFoundations vol 48 no 3 pp 353ndash361 2008

[20] L M Zhang C W W Ng and C J Lee ldquoEffects of slope andsleeving on the behavior of laterally loaded pilesrdquo Soils andFoundations vol 44 no 4 pp 99ndash108 2008

[21] B P Yin M H Zhao W He et al ldquoModel test study onidentification of foundation proportional coefficient m inslope groundrdquo Journal of Hunan University (Natural Science)vol 44 no 9 2017

[22] B L Gao C R Zhang and Z X Zhang ldquoModel tests on effectof slopes on lateral resistance of near single piles in sandrdquoRock and Soil Mechanics vol 35 no 11 pp 3191ndash3198 2014

[23] B T Zhu Be Ultimate Resistance and Laterally Loaded PileBehaviors Tongji University School of Civil EngineeringShanghai China 2005

[24] S S Rajashree and T G Sitharam ldquoNonlinear finite-elementmodeling of batter piles under lateral loadrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 127 no 7pp 604ndash612 2001

[25] R L Kondner ldquoHyperbolic stress-strain response cohesivesoilsrdquo Journal of the Soil Mechanics and Foundations Divisionvol 89 no 1 pp 115ndash143 1963

[26] K Bhushan S C Haley and P T Fong ldquoLateral load tests ondrilled piers in stiff claysrdquo Journal of the Geotechnical Engi-neering Division vol 1058 pp 969ndash985 1979

[27] J B Stevens and J M E Audibert ldquoRe-examination of P-Ycurve formulationsrdquo in Proceedings of 11th Offshore Tech-nology Conference pp 397ndash403 Houston TX USA 1980

[28] D Wu B B Broms and V Choa ldquoDesign of laterally loadedpiles in cohesive soils using p-y curvesrdquo Soils and Founda-tions vol 38 no 2 pp 17ndash26 1998

Advances in Civil Engineering 13

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Submit your manuscripts atwwwhindawicom

stiffness recommended by Rajeshree and Sitharam [24] asfollows

Ki 13Ei

1minus v2s

EiD4

EpIp1113888 1113889

112

(4)

where vs EpIp is Poissonrsquos ratio of soil and pile bendingrigidity respectively

According to the Kondner [25] the initial elasticitymodulus can be related to elasticity modulus E50 under the50 failure stress and the elasticity modulus at deviatoricstress can be expressed by

Es Ei 1minusRfσσf

1113888 1113889 (5)

where σ is deviation stress σf is deviatoric failure stress Rf isthe ratio of the deviatoric failure stress over the ultimatedeviatoric stress generally taken as 08 Ei is the initial elasticmodulus and σσf 05

For undrained loading we have vs 05 -e elasticmodulus of the clay is represented by the deformationmodulus E50 under the 50 failure stress of the reaction soiland Ei 167 E50 is satisfied -e above expression can beused to derive the initial stiffness (K) of clay under un-drained conditions

K 3E50E50D

4

EpIp1113888 1113889

112

(6)

4 Reduction Function of Initial Stiffness u(z)

For near-slope laterally loaded pile the initial stiffness of thesoil is also affected by the slope [17 18 22] Georgiadis andGeorgiadis [18] gave the reduction function for the initialstiffness of clay within the shallow foundation under un-drained loading condition

u(z) cos θ +1minus cos θ

6z

D+

B

Dminus 051113874 1113875tan θ1113876 1113877le 1 (7)

5 Ultimate Soil Resistance of Clay psu

Several methods are available for determining the ultimatesoil lateral resistance pu to piles in cohesive soil[2 4ndash6 10 12] It is generally believed that the ultimateresistance (pu) of clay depends mainly on the type of failuremechanism at a certain depth of the soil -e normativeformula in API design code for horizontal ground is given inequation (8)

Np 3 +cprimezcu

+ Jz

Dle 9 (8)

pu NpcuD (9)

where Np is ultimate capacity coefficient of clay cu is un-drained shear strength of clay cprime is effective bulk density ofclay and J is dimensionless experience coefficient its valueranges from 025 to 05

To consider slope effect on the ultimate soil resistancethe following expression proposed by [18] is used to calculatethe ultimate soil resistance Nsp

Nsp

Npuminus Npu minusNp01113872 1113873eminusλ(zD) zle zc

Npuminus Npu minusNpc1113872 1113873eminusλαθ zminuszc( )D zgt zc

⎧⎪⎪⎨

⎪⎪⎩(10)

αθ 1minussin θ(1 + sin θ)

2 (11)

zc 85minus 10log(8minusbD)101113960 1113961D (12)

Npu π + 2Δ + 2 cosΔ + 4 cosΔ2

+ sinΔ2

1113874 1113875 (13)

where zc is the certain critical depth αθ is the parameterrelated to the slope Npu is the ultimate lateral bearing ca-pacity factor Besides Δ sinminus1α and λ 055minus 015α bothare dimensionless coefficients Np0 is the lateral bearingcapacity factor at ground surface Np0 2 + 15 α α is theadhesion coefficient and its value ranges from 0sim1 Npc isthe ultimate soil resistance at a certain critical depth

According to equations (9)ndash(13) the ultimate soil re-sistance of clay psu for undrained conditions can beexpressed as

Psu NspCuD (14)

6 FDM Solution of the Proposed Method

61 Establishment of Calculation Model A simplified cal-culation model can be established as shown in Figure 3

Select a microunit of the pile for force balance analysis Itis stated here that the bending moment is positive in thecounterclockwise rotation direction and the normal of theshear force is positive in the positive direction of the z axis-e shear force is positive in the negative direction of the yaxis -en the equation for the deflection of the pile can bederived as follows

EpIpd4 y

dz4 + p(y z) 0 (15)

where EpIp is the pile bending stiffness p(y z) is the soilresistance distributed along pile length which can be ob-tained from the previous p-y curve and the positive di-rection is positive direction of the y axis

Boundary restrictions must be determined to solve theabove-mentioned deflection differential equation In thispaper the boundary conditions of the pile are determinedthe pile top is free and the pile bottom is fixed and thecorresponding deflection differential equations are asfollows

Free pile head

EpIpyPrime11138681113868111386811138681113868z0

M0

EpIpy11138681113868111386811138681113868z0

H0

⎧⎪⎨

⎪⎩(16)

Fixed pile bottom

Advances in Civil Engineering 3

EpIpyPrime∣∣∣∣∣zL 0

EpIpy∣∣∣∣∣zL 0

(17)

62 Dierential Format Derivation and Solution e nitedierence method principle is used to discrete the buriedsection L into n segments each of which is s Ln e topnode is denoted as 0 and the bottom of the pile is marked asn In order to improve the simplicity of the nite dierenceoperation four virtual nodes minus2 minus1 n + 1 n + 2 are added atthe top of pile and the bottom of the pile respectively edisplacement of the ith node is yi is shown in Figure 4

For a pile there exists (n + 5) dierential equations afterthe discrete division and four extra known dierentialequations can be derived in combination with the boundaryconditions thereby establishing the pile displacement nodevector yi and further solving the pile displacement

Substituting the fourth derivative of pile microelementin equation (15) the dierential equation for each element ofthe pile can be derived

yi+2 minus 4yi+1 + 6yi minus 4yiminus1 + yiminus2 +s4

EpIpp yi z( ) 0 (18)

In combination with equation (2) equation (18) can betransformed into the following two forms according to theallowable displacement yu

(1) yleyu

yi+2 minus 4yi+1 +(6 +mu(z)K)yi minus 4yiminus1 + yiminus2 0

m s4

EpIp

(19)

(2) ygtyu

yi+2 minus 4yi+1 + 6yi minus 4yiminus1 + yiminus2 +mNspCuD 0

m s4

EpIp

(20)

Similarly in terms of equations (16) and (17) the dif-ferential form of the boundary conditions can be derived

y2 minus 2y1 + 2yminus1 minusyminus2 2H0s3

EpIp

y1 minus 2y0 + yminus1 M0s2

EpIp

yn+1 minus 2yn + ynminus1 0

yn+2 minus 2yn+1 + 2ynminus1 minusynminus2 0

(21)

According to the dierential equations from equation(21) of the boundary conditions (n + 1) unknown dier-ential equations are combined to obtain the displacement ofthe pile matrix the corresponding pile displacement solu-tion equations can be expressed as

Kn[ ] y F (22)

where [Kn] is the stiness matrix of pile which is dividedinto two type stiness matrix of [K1] and [K2] according tothe elastic state and plastic state of the soil along the pilelength respectively y is the pile displacement node vectorF is external load vector which is controlled by boundaryconditions and is also divided into two type vector of F1 and F2 correspond to [K1] and [K2] respectively

In most practical projects the maximum bending mo-ment section is regarded as the most dangerous cross section

y

z

s

s

s

s

yi ndash 2

yi ndash 1

yi

yi + 1

yi + 2

s

ndash2

ndash1

0

1

2

n ndash 2

n ndash 1

n

n + 1

n + 2

s

Figure 4 Finite dierence method cell division

y

z z

zl

zi

zj

zn

L

O

H0

Pile

p(yz)

Slopeyl

yi

yj

yn

Displacement of the pile

M0

θ

Figure 3 Simplied calculation model of near-slope pile

4 Advances in Civil Engineering

of the pile design Here the dierential form of the solutionof the bending moment is listed as

Mi yiminus1 minus 2yi + yi+1( )EpIp

s2 (23)

According to the basic solution ideas of equation (22)a MATLAB iterative code is developed to solve the responsebehavior of pile and the ow chart of iterative calculation isshown in Figure 5

7 Validation to Previous Studies

e feasibility of the proposed method is validated in thissection to some previous studies which are well docu-mented in the literatureis method is introduced as inputinto MATLAB to calculate the response of each pile egeometrical characteristics (pile length L pile diameter Ddistance from the pile shaft to the slope crest B bendingstiness of the pile EpIp and slope angleθ) and the soilproperties (undrained shear strength cu secant modulusE50 eective bulk density c or cprime and cohesion coecentcientα) are summarized in Table 1 for each previous studyconsidered

Case 1 e computed pile responses are compared to thepile test results and to the pile responses computed with thesame computer code using as input the Matlock [2] Reeseand Welch [5] Bhushan et al [26] Stevens and Audibert[27] e Shanghai pile tests as shown in Figure 6 reportedby the literature [28] involved lateral loading of piles in levelground It can be seen that despite the small discrepancymeasured and predicted between the proposed p-y curveload-displacement relationships the general shape of thecurves is very similar indicating that the small discrepancymay be due to overestimation of secant modulus E50

Case 2 e results calculated by the proposed method andthe results calculated by Georgiadis and Georgiadis [17]which presented 3D nite-element analyses of pile in slopingground are presented in Figure 7 for comparison purposesis paper selects two dierent slope angles (θ 20deg 40degrespectively) for verication analysis As the slope angleincreases the results of this method are getting closer to theresults of the literature [17]

Case 3 e calculating results given by Georgiadis andGeorgiadis [18] are used as examples for comparisonverication Pile foundation is completely buried in theundrained clay slope us the section of the pile head atground surface only has the initial horizontal forceH0 ispaper selects four dierent pilersquos distance from slope crest(B 03m 06m 12m 24m respectively) for vericationanalysis e H0-y0 curves and H0-maxM curves of pilehead obtained from the proposed method and literature[18] are plotted in Figure 8 A good agreement has beenobserved between the calculating results from the presentstudy and literature results

8 Parametric Study

81 Eect of Slope Angle θ e size of the slope angle di-rectly determines the soil volume in front of the pile toparticipate in the pile-soil interaction In order to bettershow the eect of slope angles the pile head deection ofslope was normalized by dividing the pile head deection ofslope (y0s) by that of horizontal (y0H) Figures 9ndash12 re-spectively show the lateral load-deection curves at pilehead the normalized deection (y0sy0H)-load (H0) curvesat pile head y0 the maximum bending moment (Mmax)-load (H0) curves and the bending moment(M)-depth(z)distribution curves with dierent slope angles of 0deg 10deg 20deg40deg 50deg e relevant calculation parameters here are pilelength L 14m pile diameter D 06m bending stinessof pile EpIp 18449 (MNmiddotm2) normalized distance of pileBD 05 adhesion coecentcient α 1 piles are completelyburied in undrained clay and Poissonrsquos ratio of clay ]s 049 undrained shear strength cu 40 kPa and secantmodulus E50 14MPa

As shown in Figure 9 as the slope angle increases thelateral deection of the pile head increases signicantly and

Determine the number nof pile unit divisions

Start

Input initial lateralload

Input parameters ofpile soil and slope

Calculate the values of K psuiand μ(zi) for each node of the pile

Calculate the allowable displacementvalue of yu for each node of the pile

Calculate pile lateral displacement yi for eachnode by using the elastic matrix of Ki and the

external load vector of Fi

Judge yi gt yu

Resolve by replacing K2 and F2 with Ki and Ficorrespondingly where needed

Output lateral displacement value of yi foreach node and calculate the corresponding

bending moment value of Mi

End

Yes

No

Figure 5 Flowchart of iterative calculation

Advances in Civil Engineering 5

this trend becomes much more obvious with the increase ofthe lateral load It is also observed that when ground surfacechanges from horizontal ground to 10deg slope the behavior ofpile is almost like horizontal ground surface indicating theeect of slope is almost negligible when the slope angle is lt10degFigure 10 further shows the distribution curves of normalizeddeection (y0sy0H) with the lateral load It can be seen thatdierent xed ratios of y0sy0H are almost maintained at lowload levels but as the lateral load continue to increase the

values of y0sy0H start to increase unequally for dierent slopeangle with the increase of load When the lateral load is at750 kN the values of y0sy0H for 40degslope and 50deg slope are1065 2157 respectively indicating that the steeper the slopeangle is the more deection of pile head grows

It can be seen from Figure 11 that the maximum bendingmoment values of the pile also increase as the slope angleincreases but the rate of increase of maximum bendingmoment with lateral load is more moderate

Table 1 Summary of pile load test

Pile testGeometrical characteristics Soil properties

L (m) D (m) B (m) EpIp (kNmiddotm) e (m) θ (deg) cu (kPa) E50 (kPa) c or cprime (kNm3) α1 14 05 0 97900 072 0 30 3000 7 0942 20 10 0 1423534 0 2040 70 14000 18 053 12 06 03 06 12 24 184490 0 45 50 10000 18 073

00

20406080

100120140160180200

10 20 30 40y0 (mm)

H0 (

kN)

50 60 70

Stevens and AudibertBhushan et alMatlock

OrsquoNeill and GaziogluPresent studyPile test

Figure 6 Verication analysis of H0-y0 curves relationship for Shanghai pile tests

Present studyFE analyses (Georgiadis and Georgiadis [18])Present studyFE analyses (Georgiadis and Georgiadis [18])

10000900080007000600050004000300020001000

0

max

M (k

Nmiddotm

)

0306090120150180210240270300

y 0 (m

m)

0 250 500 750 1000 1250 1500 1750 2000 2250 2500H0 (kN)

(a)

Present studyFE analyses (Georgiadis and Georgiadis [18])Present studyFE analyses (Georgiadis and Georgiadis [18])

0 250 500 750 1000 1250 1500 1750 2000 2250 2500H0 (kN)

10000900080007000600050004000300020001000

0

max

M (k

Nmiddotm

)

04080120160200240280320360400

y 0 (m

m)

(b)

Figure 7 Verication analysis of H0-y0 curves relationship for FE analysis (a) θ 20deg (b) θ 40deg

6 Advances in Civil Engineering

Figures 12 and 13 show the bending moment distributionwith depth and the depth of xity (where the maximumbending moment occurs) of the pile for all slope angles witha lateral load at 300 kN and 600 kN respectively It is clear thatthe maximum bending moment of the pile increases with theincrease of slope angle at the same load but the rst zerolocation of bendingmoment curve and depth of xity increasecorrespondingly With the increase of the load the dierencein the maximum bending moment growth at each slope anglebecomes obvious and the rst zero location of bendingmoment curve and depth of xity of the pile also increasemore quickly For example as is shown in Figure 13 the depthof xity for 30deg and 50deg slope angle increased by 446 1734compared with that in horizontal ground at the load of300 kN respectively but the ratio further increases to 11323203 respectively when the load increases to 600 kN It canalso be seen from Figure 13 that the depth of pile xity almostoccurs at a depth of 4sim8D (D diameter of pile)

82 Eect of Normalized Distance of Pile BD Selecting thenormalized distance of pile BD as 05 2 4 6 and considerthe slope angle of 10deg 30deg 50deg respectively as the existingslope conditions e other calculation parameters are thesame as in Section 81

Figures 14ndash16 show the load-deection curve for dif-ferent normalized distance BD of pile head at above threeslope conditions From these gures it is observed that theincrease in normalized distance BD ratio decreases thedeection of pile head When normalized distance BDratio exceeds 6 in all slope angle conditions the deectionat pile head is basically the same as that in horizontalground which means the inuence of the slope eect isalmost negligible in this case It is also observed that theload-deection curves in dierent slope angle conditionshave dierent response results and the increase in slopeangle can increase the discreteness of the curves Figure 17further shows the eect of normalized distance of pile on

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3500

3000

2500

2000

1500

1000

500

0

max

M (k

Nmiddotm

)

0 200 400 600 800 1000H0 (kN)

0

120

240

360

480

600

720

840

y 0 (m

m)

(a)

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3500

3000

2500

2000

1500

1000

500

0

max

M (k

Nmiddotm

)

0

100

200

300

400

500

600

700

y 0 (m

m)

0 200 400 600 800 1000H0 (kN)

(b)

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3000

2500

2000

1500

1000

500

0

max

M (k

Nmiddotm

)

0 200 400 600 800 1000H0 (kN)

0

90

180

270

360

450

540

y 0 (m

m)

(c)

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3000

2500

2000

1500

1000

500

0m

ax M

(kN

middotm)

0 200 400 600 800 1000H0 (kN)

0

80

160

240

320

400

480

y 0 (m

m)

(d)

Figure 8 Verication analysis of H0-y0 curves relationship for LPILE (a) B 03m (b) B 06m (c) B 12m (d) B 24m

Advances in Civil Engineering 7

lateral-load capacity on horizontal ground and slopingground (θ 10deg 30deg 50deg) It can be seen that when thenormalized distance BD of pile changes from 05 to 6 thelateral-load capacity is increased by 227 111 2987on 10deg 30deg 50deg sloping ground respectively indicating thatthe increase in slope angle increases the inuence of BD onthe lateral-load capacity of the pile

Figures 18ndash20 show the bending moment variationalong pile length of the pile for dierent normalized dis-tance BD on horizontal ground and sloping ground(θ 10deg 30deg 50deg) From these gures it is observed that themaximum bending moment increases with the increase inthe normalized distance BD of the pile and the increase inthe applied lateral load Also for the same normalized

distance BD of pile and applied lateral load the increase inslope angle of θ increases the maximum bending momentof pile When ground surface changes from horizontal to10deg 30deg and 50deg sloping ground the maximum bendingmoment of pile in sloping ground is increased by 28126 and 319 respectively under lateral load of 600 kNand normalized distance BD of 05 It is also noted thatwhen the pile is nearer to slope crest the slope angle be-comes a more dominant factor to aect the lateral capacityof the pile especially at a high-load level

0 100 200 300 400 500 600 700 80010

15

20

25

30

Nor

mal

ized

disp

lace

men

t y o

Sy o

H

Lateral load H0 (kN)

θ = 0deg (B = 05D)θ = 10deg (B = 05D)θ = 20deg (B = 05D)

θ = 30deg (B = 05D)θ = 40deg (B = 05D)θ = 50deg (B = 05D)

Figure 10 Normalized deection (y0sy0H)-load (H0) curves fordierent slope angle

ndash200 0 200 400 600 800 1000 1200 1400 1600 18000123456789

101112131415

Dep

th (m

)

Bending moment M (kNmiddotm)

θ = 0deg H0 = 300kNθ = 0deg H0 = 600kNθ = 10deg H0 = 300kNθ = 10deg H0 = 600kNθ = 20deg H0 = 300kNθ = 20deg H0 = 600kN

θ = 30deg H0 = 300kNθ = 30deg H0 = 600kNθ = 40deg H0 = 300kNθ = 40deg H0 = 600kNθ = 50deg H0 = 300kNθ = 50deg H0 = 600kN

Figure 12 Bending moment variation along the depth of pile fordierent slope angle

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Deflection y0 (mm)

θ = 0deg (B = 05D)θ = 10deg (B = 05D)θ = 20deg (B = 05D)

θ = 30deg (B = 05D)θ = 40deg (B = 05D)θ = 50deg (B = 05D)

Figure 9 Lateral load-deection curves for dierent slope angle atpile head

0 400 800 1200 1600 2000 24000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Maximum bending moment Mmax (kNmiddotm)

θ = 0deg (B = 05D)θ = 10deg (B = 05D)θ = 20deg (B = 05D)

θ = 30deg (B = 05D)θ = 40deg (B = 05D)θ = 50deg (B = 05D)

Figure 11 Maximum bending moment-load curves for dierentslope angle

8 Advances in Civil Engineering

83 Eect of Adhesion Coecient α In order to study theeect of adhesion coecentcient α on the lateral behavior of pile insloped ground this paper analyzes the parameter α from 0 to1 with increment of 01 and chooses lateral loadH0 500 kNand the bending momentM0 0 (kNmiddotm) as the xed loadingcondition to calculate and analyze the deection of pile headConsider the slope angle θ as the same in Section 81 andother basic calculation parameters are the same as Section 81

Figures 21 and 22 show pile head deection (y0) and themaximum bending moment (Mmax) of the pile variation withthe adhesion coecentcient α for dierent slope angle re-spectively From these gures it can be seen that increasingthe adhesion coecentcient α at the pile-soil interface can ef-fectively reduce the pile head deection and the maximumbending moment of the pile at the same time Also the in-crease in slope angle almost does not change the corre-sponding curve growth model but will signicantly increase

0 20 40 60 80 100 120 140 160 180 200 220 2400

100

200

300

400

500

600

700

800

Lateral displacement y0 (mm)

BD = 05 (θ = 10deg)BD = 2 (θ = 10deg)

BD = 4 (θ = 10deg)BD = 6 (θ = 10deg)

Late

ral l

oad

H0

(kN

)

Figure 14 Lateral load-deection curves for θ 10deg for dierentnormalized distance of pile at pile head

0 1 2 3 4 5 6

560

580

600

620

640

660

680

700

720

740A

llow

able

pile

capa

city

(kN

)

Normalized distance BD

Level ground (θ = 0deg)θ = 10deg

θ = 30degθ = 50deg

Figure 17 Bearing capacity of pile head for dierent normalizeddistance of pile (corresponding to 200mm)

247

122

247

123

247

126

258

142

274

059

289

9763

6058

3

367

113

376

092

401

397

428

333

476

085

θ = 50degθ = 40degθ = 30degθ = 20degθ = 10deg

H0 = 300kNH0 = 600kN

θ = 0deg00

05

10

15

20

25

30

35

40

45

50

55

Dep

th o

f fix

ity (m

)

Figure 13 Depth of xity variation with dierent slope angle

B = 05D (θ = 30deg)B = 2D (θ = 30deg)

B = 4D (θ = 30deg)B = 6D (θ = 30deg)

0 30 60 90 120 150 180 210 240 270 3000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Lateral displacement y0 (mm)

Figure 15 Lateral load-deection curves for θ 30deg for dierentnormalized distance of pile at pile head

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Lateral displacement y0 (mm)

BD = 05 (θ = 50deg)BD = 2 (θ = 50deg)

BD = 4 (θ = 50deg)BD = 6 (θ = 50deg)

Figure 16 Lateral load-deection curves for θ 50deg for dierentnormalized distance of pile at pile head

Advances in Civil Engineering 9

the pile head deection and maximum bending moment ofthe pile especially when the slope angle exceeds 40deg An ex-ample is used for pile head deection when the value of α isequal to 0 the pile head deection values of pile in slopingground with θ 10deg 30deg 50deg is increased by 74 398137 respectively compared to that in horizontal ground

84 Eect of Undrained Shear Strength cu Here lateral loadH0 500 kN and the initial bending momentM0 0 (kNmiddotm)

were taken as the initial loading conditions choosing un-drained shear strengths cu of 20 kPa 40 kPa 60 80 kPa100 kPa respectively to calculate and analyze Other basiccalculation parameters are the same as in Section 81

Figures 23 and 24 show pile head deection (y0) and themaximum bending moment (Mmax) of the pile variationwith the undrained shear strength cu for dierent slopeangles respectively From the curves given in Figures 23 and24 it is observed that the increase in undrained shearstrength cu decreases the pile head deection and themaximum bending moment is is because of the increasein the strength of soil and the relative stiness of the pile-soilsystem Also it is obvious that the presence of slopes

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

ndash200 0 200 400 600 800 1000 1200 1400 16000123456789

1011121314

Dep

th (m

)

Bending moment M (kNmiddotm)

Figure 19 Bending moment variation along the depth of pile forθ 30deg for dierent slope angle

ndash200 0 200 400 600 800 1000 1200 14000123456789

1011121314

Dep

th (m

)

Bending moment M (kNmiddotm)

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

Figure 18 Bending moment variation along the depth of pile forθ 10deg for dierent slope angle

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

ndash200 0 200 400 600 800 1000 1200 1400 1600 18000123456789

1011121314

Dpe

th (m

)

Bending moment M (kNmiddotm)

Figure 20 Bending moment variation along the depth of pile forθ 50deg for dierent slope angle

ndash01 00 01 02 03 04 05 06 07 08 09 10 116080

100120140160180200220240260

Late

rald

ispla

cem

ent y 0

(mm

)

Adhesion coefficient α

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 21 Pile head deection (y0) variation with adhesion co-ecentcient (α) for dierent slope angle

10 Advances in Civil Engineering

aggravates the rate of change of pile head deection es-pecially when cu ranges from 20 kPa to 40 kPa and when thevalue of cu exceeds 40 kPa the decrease rate of the deectionof pile head becomes slow and eventually almost becomesat From the results in Figure 23 it is observed that the pilehead deection in the range of 734ndash75 for increase in cu20 kPa to 40 kPa of sloping ground (θ 10deg 20deg 30deg 40deg 50deg)and horizontal ground surfaces from which can concludethat the weaker soil parameters are the more signicantslope eect becomes Besides the curve of the maximumbending moment variation with undrained shear strengthshown in Figure 24 is smoother and the range of themaximum bending moment of the pile with the increase ofthe slope is relatively stable

9 Conclusions

e purpose of this paper is to study the behavior of laterallyloaded long-exible pile in undrained clay sloping groundBased on the basic model of ideal elastic-plastic p-y curvemethod this paper derives the dierential equations of thelaterally loaded single pile in undrained clay sloped groundby introducing the existing related reduction variablefunction and the corresponding nite dierence method forthe pile deection and internal force is obtained A series ofparameters analyses are further performed for slope anglenormalized distance of pile adhesion coecentcient and un-drained shear strength e conclusions obtained from thisstudy are summarized as follows

(1) A nonlinear analysis method for laterally loaded long-exible pile in undrained clay sloped ground isestablished rough the verication of examples thecorrectness and feasibility of the method is proved

(2) Slope angle is the most important factor that aectingthe lateral bearing capacity of the near-slope pile eincrease in slope angle increases the deection and the

rate of increase of deection and this trend becomesmore obvious as the lateral load increased When theslope angle is small enough (θ lt 10o) the eect ofslope is almost negligible Besides the depth of xityof the pile is about 4sim8 times the size of the pilediameter

(3) e distance away from pile to slope crest is also animportant factor that aects the lateral-load capacityof the pile e increase in normalized distance BDof the pile decreases the deection of pile head butincreases the lateral-load capacity and when nor-malized distance BD ratio exceeds 6 the slope eectcan be avoidedWhen laterally loaded pile is closer tothe slope crest the inuence of the slope angle seemsmore dominant

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

ndash01 00 01 02 03 04 05 06 07 08 09 10 11

900

1000

1100

1200

1300

1400

1500

1600

Max

imum

ben

ding

mom

ent

Mm

ax (k

Nmiddotm

)

Adhesion coefficient α

Figure 22 Maximum bending moment (Mmax) variation withadhesion coecentcient (α) for dierent slope angle

0 20 40 60 80 100 1200

50100150200250300350400450500550600

Late

ral d

ispla

cem

ent y 0

(mm

)

Undrained shear strength cu (kPa)

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 23 Pile head deection (y0) variation with undrained shearstrength (cu) for dierent slope angle

0 20 40 60 80 100 1200

300

600

900

1200

1500

1800

2100M

axim

umbe

ndin

gmom

ent M

max

(kN

middotm)

Undrained shear strength cu (kPa)

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 24 Maximum bending moment (Mmax) variation withundrained shear strength (cu) for dierent slope angle

Advances in Civil Engineering 11

(4) -e adhesion coefficient α at the pile-soil interfacecan effectively reduce the pile head deflection and themaximum bending moment of the pile at the sametime -e increase in slope angle will significantlyincrease the pile head deflection and maximumbending moment of the pile especially when theslope angle exceeds 40deg

(5) -e increase in undrained shear strength cu de-creases the pile head deflection and the maximumbending moment of the pile -is is because of theincrease in the strength of soil and the relativestiffness of the pile-soil system Also the presence ofslopes aggravates the rate of change of pile headdeflection especially when the cu is in a mall value(ranges from 20 kPa to 40 kPa) In contrast themaximum bending moment variation with un-drained shear strength affected by the slope effectappears more moderate

(6) -is study researches the lateral bearing behavior ofsingle pile in undrained clay sloping ground Inpractical projects the situation of pile foundationson slope ground surface is not uncommon and thelateral bearing characteristics of pile foundationsare more complicated -erefore the influence ofslope effect on the lateral bearing capacity of pilewhich is on slope ground surface is worth furtherstudy

Data Availability

-e original data for summary of pile load test in Table 1 arefrom Wu et al [28] Georgiadis and Georgiadis [17] andGeorgiadis and Georgiadis [18] respectively -e computedpile responses as shown in Figure 6 are compared to the piletest results (Wu et al [28]) and to the pile responsescomputed with the same computer code using as input theMatlock [2] Reese and Welch [5] Bhushan et al [26]Stevens and Audibert [27] Figures 7 and 8 are calculated bycomputer code MATLAB to compare previous studies(Georgiadis and Georgiadis [17] Georgiadis and Georgiadis[18] respectively) Figures 9ndash24 are calculated by the pro-posedmethod based on the original data mentioned above tostudy parametric analysis In addition all the sharing datawere involved in this paper and there was no redundantdata

Conflicts of Interest

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

Acknowledgments

-is work is supported by the National Natural ScienceFoundation of China (grant nos 51478479 and 51678570)and Hunan Transport Technology Project (grant no201524)

References

[1] N Nimityongskul Y Kawamata D Rayamajhi andS A Ashford ldquoFull-scale tests on effects of slope on lateralcapacity of piles installed in cohesive soilsrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 144 no 1article 04017103 2018

[2] H Matlock ldquoCorrelation for design of laterally loaded piles insoft clayrdquo in Proceedings of the Offshore Technology Confer-ence pp 77ndash94 Houston TX USA April 1970

[3] L C Reese ldquoAnalysis of laterally loaded piles in sandrdquo inProceedings of the Offshore Technical Conference pp 95ndash105Houston TX USA May 1974

[4] L Reese W Cox and F Koop ldquoField testing and analysis oflaterally loaded piles on stiff clayrdquo in Proceedings of theOffshore Technology in Civil Engineering pp 106ndash125 DallasTX USA May 1975

[5] L C Reese and R C Welch ldquoLateral loading of deepfoundations in stiff clayrdquo Journal of Geotechnical and Geo-environmental Engineering vol 101 no 7 pp 633ndash649 1975

[6] M A Gabr T Lunne and J J Powell ldquoP-y analysis of laterallyloaded piles in clay using DMTrdquo Journal of GeotechnicalEngineering vol 120 no 5 pp 816ndash837 1994

[7] C C Fan and J H Long ldquoAssessment of existing methods forpredicting soil response of laterally loaded piles in sandrdquoComputers and Geotechnics vol 32 no 4 pp 274ndash289 2005

[8] G P Yang and Z M Zhang ldquoResearch on P-Y curve oflaterally bearing piles under large displacementrdquo WaterTransportation Engineering vol 342 no 7 pp 40ndash45 2002

[9] C Wang and Z A LU ldquoCalculation of internal forces oflaterally loaded piles by using p-y curverdquo Journal ofChongqing Jiaotong University (Natural Science) vol 4 no 1pp 61ndash65 1958

[10] H C Wang and D Q WU ldquoA new unified approach to thep-y curve of laterally loaded pile in clayrdquo Journal of HohaiUniversity no 1 pp 9ndash17 1991

[11] G C Wang and M Yang ldquoNonlinear analysis of laterallyloaded piles in sandrdquo Rock and Soil Mechanics no 2pp 261ndash267 2011

[12] G CWang andM Yang ldquoCalculation of laterally loaded pilesin clayrdquo Journal of Tongji University (Natural Science) vol 40no 3 pp 373ndash378 2012

[13] T Q Zhou Z A LU and D H Wang ldquoCalculation methodof laterally loaded super-long PHC pilerdquo Port and WaterwayEngineering no 6 pp 155ndash160 2013

[14] L U Cheng X C Xu S X Chen et al ldquoModel test andnumerical simulation of horizontal bearing capacity andimpact factors for foundation piles in sloperdquo Rock and SoilMechanics no 9 pp 2685ndash2691 2014

[15] P YinB H ZhaoM H Zhao et al ldquoStability analysis of pile-column bridge pile considering slope effectrdquo Journal of Hu-nan University (Natural Science) vol 43 no 11 pp 20ndash252016

[16] Y S Deng M H Zhao X J Zhou et al ldquoResearch progress ofbearing characteristics of pile column at steep slope inmountain areasrdquo Journal of Highway and TransportationResearch and Development vol 29 no 6 pp 37ndash45 2012

[17] K Georgiadis and M Georgiadis ldquoUndrained lateral pileresponse in sloping groundrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 136 no 11 pp 1489ndash1500 2010

[18] K Georgiadis and M Georgiadis ldquoDevelopment of p-ycurves for undrained response of piles near slopesrdquo Com-puters and Geotechnics vol 40 no 3 pp 53ndash61 2012

12 Advances in Civil Engineering

[19] K Muthukkumaran R Sundaravadivelu and S R GandhildquoEffect of slope on p-y curves due to surcharge loadrdquo Soils andFoundations vol 48 no 3 pp 353ndash361 2008

[20] L M Zhang C W W Ng and C J Lee ldquoEffects of slope andsleeving on the behavior of laterally loaded pilesrdquo Soils andFoundations vol 44 no 4 pp 99ndash108 2008

[21] B P Yin M H Zhao W He et al ldquoModel test study onidentification of foundation proportional coefficient m inslope groundrdquo Journal of Hunan University (Natural Science)vol 44 no 9 2017

[22] B L Gao C R Zhang and Z X Zhang ldquoModel tests on effectof slopes on lateral resistance of near single piles in sandrdquoRock and Soil Mechanics vol 35 no 11 pp 3191ndash3198 2014

[23] B T Zhu Be Ultimate Resistance and Laterally Loaded PileBehaviors Tongji University School of Civil EngineeringShanghai China 2005

[24] S S Rajashree and T G Sitharam ldquoNonlinear finite-elementmodeling of batter piles under lateral loadrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 127 no 7pp 604ndash612 2001

[25] R L Kondner ldquoHyperbolic stress-strain response cohesivesoilsrdquo Journal of the Soil Mechanics and Foundations Divisionvol 89 no 1 pp 115ndash143 1963

[26] K Bhushan S C Haley and P T Fong ldquoLateral load tests ondrilled piers in stiff claysrdquo Journal of the Geotechnical Engi-neering Division vol 1058 pp 969ndash985 1979

[27] J B Stevens and J M E Audibert ldquoRe-examination of P-Ycurve formulationsrdquo in Proceedings of 11th Offshore Tech-nology Conference pp 397ndash403 Houston TX USA 1980

[28] D Wu B B Broms and V Choa ldquoDesign of laterally loadedpiles in cohesive soils using p-y curvesrdquo Soils and Founda-tions vol 38 no 2 pp 17ndash26 1998

Advances in Civil Engineering 13

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EpIpyPrime∣∣∣∣∣zL 0

EpIpy∣∣∣∣∣zL 0

(17)

62 Dierential Format Derivation and Solution e nitedierence method principle is used to discrete the buriedsection L into n segments each of which is s Ln e topnode is denoted as 0 and the bottom of the pile is marked asn In order to improve the simplicity of the nite dierenceoperation four virtual nodes minus2 minus1 n + 1 n + 2 are added atthe top of pile and the bottom of the pile respectively edisplacement of the ith node is yi is shown in Figure 4

For a pile there exists (n + 5) dierential equations afterthe discrete division and four extra known dierentialequations can be derived in combination with the boundaryconditions thereby establishing the pile displacement nodevector yi and further solving the pile displacement

Substituting the fourth derivative of pile microelementin equation (15) the dierential equation for each element ofthe pile can be derived

yi+2 minus 4yi+1 + 6yi minus 4yiminus1 + yiminus2 +s4

EpIpp yi z( ) 0 (18)

In combination with equation (2) equation (18) can betransformed into the following two forms according to theallowable displacement yu

(1) yleyu

yi+2 minus 4yi+1 +(6 +mu(z)K)yi minus 4yiminus1 + yiminus2 0

m s4

EpIp

(19)

(2) ygtyu

yi+2 minus 4yi+1 + 6yi minus 4yiminus1 + yiminus2 +mNspCuD 0

m s4

EpIp

(20)

Similarly in terms of equations (16) and (17) the dif-ferential form of the boundary conditions can be derived

y2 minus 2y1 + 2yminus1 minusyminus2 2H0s3

EpIp

y1 minus 2y0 + yminus1 M0s2

EpIp

yn+1 minus 2yn + ynminus1 0

yn+2 minus 2yn+1 + 2ynminus1 minusynminus2 0

(21)

According to the dierential equations from equation(21) of the boundary conditions (n + 1) unknown dier-ential equations are combined to obtain the displacement ofthe pile matrix the corresponding pile displacement solu-tion equations can be expressed as

Kn[ ] y F (22)

where [Kn] is the stiness matrix of pile which is dividedinto two type stiness matrix of [K1] and [K2] according tothe elastic state and plastic state of the soil along the pilelength respectively y is the pile displacement node vectorF is external load vector which is controlled by boundaryconditions and is also divided into two type vector of F1 and F2 correspond to [K1] and [K2] respectively

In most practical projects the maximum bending mo-ment section is regarded as the most dangerous cross section

y

z

s

s

s

s

yi ndash 2

yi ndash 1

yi

yi + 1

yi + 2

s

ndash2

ndash1

0

1

2

n ndash 2

n ndash 1

n

n + 1

n + 2

s

Figure 4 Finite dierence method cell division

y

z z

zl

zi

zj

zn

L

O

H0

Pile

p(yz)

Slopeyl

yi

yj

yn

Displacement of the pile

M0

θ

Figure 3 Simplied calculation model of near-slope pile

4 Advances in Civil Engineering

of the pile design Here the dierential form of the solutionof the bending moment is listed as

Mi yiminus1 minus 2yi + yi+1( )EpIp

s2 (23)

According to the basic solution ideas of equation (22)a MATLAB iterative code is developed to solve the responsebehavior of pile and the ow chart of iterative calculation isshown in Figure 5

7 Validation to Previous Studies

e feasibility of the proposed method is validated in thissection to some previous studies which are well docu-mented in the literatureis method is introduced as inputinto MATLAB to calculate the response of each pile egeometrical characteristics (pile length L pile diameter Ddistance from the pile shaft to the slope crest B bendingstiness of the pile EpIp and slope angleθ) and the soilproperties (undrained shear strength cu secant modulusE50 eective bulk density c or cprime and cohesion coecentcientα) are summarized in Table 1 for each previous studyconsidered

Case 1 e computed pile responses are compared to thepile test results and to the pile responses computed with thesame computer code using as input the Matlock [2] Reeseand Welch [5] Bhushan et al [26] Stevens and Audibert[27] e Shanghai pile tests as shown in Figure 6 reportedby the literature [28] involved lateral loading of piles in levelground It can be seen that despite the small discrepancymeasured and predicted between the proposed p-y curveload-displacement relationships the general shape of thecurves is very similar indicating that the small discrepancymay be due to overestimation of secant modulus E50

Case 2 e results calculated by the proposed method andthe results calculated by Georgiadis and Georgiadis [17]which presented 3D nite-element analyses of pile in slopingground are presented in Figure 7 for comparison purposesis paper selects two dierent slope angles (θ 20deg 40degrespectively) for verication analysis As the slope angleincreases the results of this method are getting closer to theresults of the literature [17]

Case 3 e calculating results given by Georgiadis andGeorgiadis [18] are used as examples for comparisonverication Pile foundation is completely buried in theundrained clay slope us the section of the pile head atground surface only has the initial horizontal forceH0 ispaper selects four dierent pilersquos distance from slope crest(B 03m 06m 12m 24m respectively) for vericationanalysis e H0-y0 curves and H0-maxM curves of pilehead obtained from the proposed method and literature[18] are plotted in Figure 8 A good agreement has beenobserved between the calculating results from the presentstudy and literature results

8 Parametric Study

81 Eect of Slope Angle θ e size of the slope angle di-rectly determines the soil volume in front of the pile toparticipate in the pile-soil interaction In order to bettershow the eect of slope angles the pile head deection ofslope was normalized by dividing the pile head deection ofslope (y0s) by that of horizontal (y0H) Figures 9ndash12 re-spectively show the lateral load-deection curves at pilehead the normalized deection (y0sy0H)-load (H0) curvesat pile head y0 the maximum bending moment (Mmax)-load (H0) curves and the bending moment(M)-depth(z)distribution curves with dierent slope angles of 0deg 10deg 20deg40deg 50deg e relevant calculation parameters here are pilelength L 14m pile diameter D 06m bending stinessof pile EpIp 18449 (MNmiddotm2) normalized distance of pileBD 05 adhesion coecentcient α 1 piles are completelyburied in undrained clay and Poissonrsquos ratio of clay ]s 049 undrained shear strength cu 40 kPa and secantmodulus E50 14MPa

As shown in Figure 9 as the slope angle increases thelateral deection of the pile head increases signicantly and

Determine the number nof pile unit divisions

Start

Input initial lateralload

Input parameters ofpile soil and slope

Calculate the values of K psuiand μ(zi) for each node of the pile

Calculate the allowable displacementvalue of yu for each node of the pile

Calculate pile lateral displacement yi for eachnode by using the elastic matrix of Ki and the

external load vector of Fi

Judge yi gt yu

Resolve by replacing K2 and F2 with Ki and Ficorrespondingly where needed

Output lateral displacement value of yi foreach node and calculate the corresponding

bending moment value of Mi

End

Yes

No

Figure 5 Flowchart of iterative calculation

Advances in Civil Engineering 5

this trend becomes much more obvious with the increase ofthe lateral load It is also observed that when ground surfacechanges from horizontal ground to 10deg slope the behavior ofpile is almost like horizontal ground surface indicating theeect of slope is almost negligible when the slope angle is lt10degFigure 10 further shows the distribution curves of normalizeddeection (y0sy0H) with the lateral load It can be seen thatdierent xed ratios of y0sy0H are almost maintained at lowload levels but as the lateral load continue to increase the

values of y0sy0H start to increase unequally for dierent slopeangle with the increase of load When the lateral load is at750 kN the values of y0sy0H for 40degslope and 50deg slope are1065 2157 respectively indicating that the steeper the slopeangle is the more deection of pile head grows

It can be seen from Figure 11 that the maximum bendingmoment values of the pile also increase as the slope angleincreases but the rate of increase of maximum bendingmoment with lateral load is more moderate

Table 1 Summary of pile load test

Pile testGeometrical characteristics Soil properties

L (m) D (m) B (m) EpIp (kNmiddotm) e (m) θ (deg) cu (kPa) E50 (kPa) c or cprime (kNm3) α1 14 05 0 97900 072 0 30 3000 7 0942 20 10 0 1423534 0 2040 70 14000 18 053 12 06 03 06 12 24 184490 0 45 50 10000 18 073

00

20406080

100120140160180200

10 20 30 40y0 (mm)

H0 (

kN)

50 60 70

Stevens and AudibertBhushan et alMatlock

OrsquoNeill and GaziogluPresent studyPile test

Figure 6 Verication analysis of H0-y0 curves relationship for Shanghai pile tests

Present studyFE analyses (Georgiadis and Georgiadis [18])Present studyFE analyses (Georgiadis and Georgiadis [18])

10000900080007000600050004000300020001000

0

max

M (k

Nmiddotm

)

0306090120150180210240270300

y 0 (m

m)

0 250 500 750 1000 1250 1500 1750 2000 2250 2500H0 (kN)

(a)

Present studyFE analyses (Georgiadis and Georgiadis [18])Present studyFE analyses (Georgiadis and Georgiadis [18])

0 250 500 750 1000 1250 1500 1750 2000 2250 2500H0 (kN)

10000900080007000600050004000300020001000

0

max

M (k

Nmiddotm

)

04080120160200240280320360400

y 0 (m

m)

(b)

Figure 7 Verication analysis of H0-y0 curves relationship for FE analysis (a) θ 20deg (b) θ 40deg

6 Advances in Civil Engineering

Figures 12 and 13 show the bending moment distributionwith depth and the depth of xity (where the maximumbending moment occurs) of the pile for all slope angles witha lateral load at 300 kN and 600 kN respectively It is clear thatthe maximum bending moment of the pile increases with theincrease of slope angle at the same load but the rst zerolocation of bendingmoment curve and depth of xity increasecorrespondingly With the increase of the load the dierencein the maximum bending moment growth at each slope anglebecomes obvious and the rst zero location of bendingmoment curve and depth of xity of the pile also increasemore quickly For example as is shown in Figure 13 the depthof xity for 30deg and 50deg slope angle increased by 446 1734compared with that in horizontal ground at the load of300 kN respectively but the ratio further increases to 11323203 respectively when the load increases to 600 kN It canalso be seen from Figure 13 that the depth of pile xity almostoccurs at a depth of 4sim8D (D diameter of pile)

82 Eect of Normalized Distance of Pile BD Selecting thenormalized distance of pile BD as 05 2 4 6 and considerthe slope angle of 10deg 30deg 50deg respectively as the existingslope conditions e other calculation parameters are thesame as in Section 81

Figures 14ndash16 show the load-deection curve for dif-ferent normalized distance BD of pile head at above threeslope conditions From these gures it is observed that theincrease in normalized distance BD ratio decreases thedeection of pile head When normalized distance BDratio exceeds 6 in all slope angle conditions the deectionat pile head is basically the same as that in horizontalground which means the inuence of the slope eect isalmost negligible in this case It is also observed that theload-deection curves in dierent slope angle conditionshave dierent response results and the increase in slopeangle can increase the discreteness of the curves Figure 17further shows the eect of normalized distance of pile on

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3500

3000

2500

2000

1500

1000

500

0

max

M (k

Nmiddotm

)

0 200 400 600 800 1000H0 (kN)

0

120

240

360

480

600

720

840

y 0 (m

m)

(a)

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3500

3000

2500

2000

1500

1000

500

0

max

M (k

Nmiddotm

)

0

100

200

300

400

500

600

700

y 0 (m

m)

0 200 400 600 800 1000H0 (kN)

(b)

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3000

2500

2000

1500

1000

500

0

max

M (k

Nmiddotm

)

0 200 400 600 800 1000H0 (kN)

0

90

180

270

360

450

540

y 0 (m

m)

(c)

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3000

2500

2000

1500

1000

500

0m

ax M

(kN

middotm)

0 200 400 600 800 1000H0 (kN)

0

80

160

240

320

400

480

y 0 (m

m)

(d)

Figure 8 Verication analysis of H0-y0 curves relationship for LPILE (a) B 03m (b) B 06m (c) B 12m (d) B 24m

Advances in Civil Engineering 7

lateral-load capacity on horizontal ground and slopingground (θ 10deg 30deg 50deg) It can be seen that when thenormalized distance BD of pile changes from 05 to 6 thelateral-load capacity is increased by 227 111 2987on 10deg 30deg 50deg sloping ground respectively indicating thatthe increase in slope angle increases the inuence of BD onthe lateral-load capacity of the pile

Figures 18ndash20 show the bending moment variationalong pile length of the pile for dierent normalized dis-tance BD on horizontal ground and sloping ground(θ 10deg 30deg 50deg) From these gures it is observed that themaximum bending moment increases with the increase inthe normalized distance BD of the pile and the increase inthe applied lateral load Also for the same normalized

distance BD of pile and applied lateral load the increase inslope angle of θ increases the maximum bending momentof pile When ground surface changes from horizontal to10deg 30deg and 50deg sloping ground the maximum bendingmoment of pile in sloping ground is increased by 28126 and 319 respectively under lateral load of 600 kNand normalized distance BD of 05 It is also noted thatwhen the pile is nearer to slope crest the slope angle be-comes a more dominant factor to aect the lateral capacityof the pile especially at a high-load level

0 100 200 300 400 500 600 700 80010

15

20

25

30

Nor

mal

ized

disp

lace

men

t y o

Sy o

H

Lateral load H0 (kN)

θ = 0deg (B = 05D)θ = 10deg (B = 05D)θ = 20deg (B = 05D)

θ = 30deg (B = 05D)θ = 40deg (B = 05D)θ = 50deg (B = 05D)

Figure 10 Normalized deection (y0sy0H)-load (H0) curves fordierent slope angle

ndash200 0 200 400 600 800 1000 1200 1400 1600 18000123456789

101112131415

Dep

th (m

)

Bending moment M (kNmiddotm)

θ = 0deg H0 = 300kNθ = 0deg H0 = 600kNθ = 10deg H0 = 300kNθ = 10deg H0 = 600kNθ = 20deg H0 = 300kNθ = 20deg H0 = 600kN

θ = 30deg H0 = 300kNθ = 30deg H0 = 600kNθ = 40deg H0 = 300kNθ = 40deg H0 = 600kNθ = 50deg H0 = 300kNθ = 50deg H0 = 600kN

Figure 12 Bending moment variation along the depth of pile fordierent slope angle

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Deflection y0 (mm)

θ = 0deg (B = 05D)θ = 10deg (B = 05D)θ = 20deg (B = 05D)

θ = 30deg (B = 05D)θ = 40deg (B = 05D)θ = 50deg (B = 05D)

Figure 9 Lateral load-deection curves for dierent slope angle atpile head

0 400 800 1200 1600 2000 24000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Maximum bending moment Mmax (kNmiddotm)

θ = 0deg (B = 05D)θ = 10deg (B = 05D)θ = 20deg (B = 05D)

θ = 30deg (B = 05D)θ = 40deg (B = 05D)θ = 50deg (B = 05D)

Figure 11 Maximum bending moment-load curves for dierentslope angle

8 Advances in Civil Engineering

83 Eect of Adhesion Coecient α In order to study theeect of adhesion coecentcient α on the lateral behavior of pile insloped ground this paper analyzes the parameter α from 0 to1 with increment of 01 and chooses lateral loadH0 500 kNand the bending momentM0 0 (kNmiddotm) as the xed loadingcondition to calculate and analyze the deection of pile headConsider the slope angle θ as the same in Section 81 andother basic calculation parameters are the same as Section 81

Figures 21 and 22 show pile head deection (y0) and themaximum bending moment (Mmax) of the pile variation withthe adhesion coecentcient α for dierent slope angle re-spectively From these gures it can be seen that increasingthe adhesion coecentcient α at the pile-soil interface can ef-fectively reduce the pile head deection and the maximumbending moment of the pile at the same time Also the in-crease in slope angle almost does not change the corre-sponding curve growth model but will signicantly increase

0 20 40 60 80 100 120 140 160 180 200 220 2400

100

200

300

400

500

600

700

800

Lateral displacement y0 (mm)

BD = 05 (θ = 10deg)BD = 2 (θ = 10deg)

BD = 4 (θ = 10deg)BD = 6 (θ = 10deg)

Late

ral l

oad

H0

(kN

)

Figure 14 Lateral load-deection curves for θ 10deg for dierentnormalized distance of pile at pile head

0 1 2 3 4 5 6

560

580

600

620

640

660

680

700

720

740A

llow

able

pile

capa

city

(kN

)

Normalized distance BD

Level ground (θ = 0deg)θ = 10deg

θ = 30degθ = 50deg

Figure 17 Bearing capacity of pile head for dierent normalizeddistance of pile (corresponding to 200mm)

247

122

247

123

247

126

258

142

274

059

289

9763

6058

3

367

113

376

092

401

397

428

333

476

085

θ = 50degθ = 40degθ = 30degθ = 20degθ = 10deg

H0 = 300kNH0 = 600kN

θ = 0deg00

05

10

15

20

25

30

35

40

45

50

55

Dep

th o

f fix

ity (m

)

Figure 13 Depth of xity variation with dierent slope angle

B = 05D (θ = 30deg)B = 2D (θ = 30deg)

B = 4D (θ = 30deg)B = 6D (θ = 30deg)

0 30 60 90 120 150 180 210 240 270 3000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Lateral displacement y0 (mm)

Figure 15 Lateral load-deection curves for θ 30deg for dierentnormalized distance of pile at pile head

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Lateral displacement y0 (mm)

BD = 05 (θ = 50deg)BD = 2 (θ = 50deg)

BD = 4 (θ = 50deg)BD = 6 (θ = 50deg)

Figure 16 Lateral load-deection curves for θ 50deg for dierentnormalized distance of pile at pile head

Advances in Civil Engineering 9

the pile head deection and maximum bending moment ofthe pile especially when the slope angle exceeds 40deg An ex-ample is used for pile head deection when the value of α isequal to 0 the pile head deection values of pile in slopingground with θ 10deg 30deg 50deg is increased by 74 398137 respectively compared to that in horizontal ground

84 Eect of Undrained Shear Strength cu Here lateral loadH0 500 kN and the initial bending momentM0 0 (kNmiddotm)

were taken as the initial loading conditions choosing un-drained shear strengths cu of 20 kPa 40 kPa 60 80 kPa100 kPa respectively to calculate and analyze Other basiccalculation parameters are the same as in Section 81

Figures 23 and 24 show pile head deection (y0) and themaximum bending moment (Mmax) of the pile variationwith the undrained shear strength cu for dierent slopeangles respectively From the curves given in Figures 23 and24 it is observed that the increase in undrained shearstrength cu decreases the pile head deection and themaximum bending moment is is because of the increasein the strength of soil and the relative stiness of the pile-soilsystem Also it is obvious that the presence of slopes

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

ndash200 0 200 400 600 800 1000 1200 1400 16000123456789

1011121314

Dep

th (m

)

Bending moment M (kNmiddotm)

Figure 19 Bending moment variation along the depth of pile forθ 30deg for dierent slope angle

ndash200 0 200 400 600 800 1000 1200 14000123456789

1011121314

Dep

th (m

)

Bending moment M (kNmiddotm)

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

Figure 18 Bending moment variation along the depth of pile forθ 10deg for dierent slope angle

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

ndash200 0 200 400 600 800 1000 1200 1400 1600 18000123456789

1011121314

Dpe

th (m

)

Bending moment M (kNmiddotm)

Figure 20 Bending moment variation along the depth of pile forθ 50deg for dierent slope angle

ndash01 00 01 02 03 04 05 06 07 08 09 10 116080

100120140160180200220240260

Late

rald

ispla

cem

ent y 0

(mm

)

Adhesion coefficient α

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 21 Pile head deection (y0) variation with adhesion co-ecentcient (α) for dierent slope angle

10 Advances in Civil Engineering

aggravates the rate of change of pile head deection es-pecially when cu ranges from 20 kPa to 40 kPa and when thevalue of cu exceeds 40 kPa the decrease rate of the deectionof pile head becomes slow and eventually almost becomesat From the results in Figure 23 it is observed that the pilehead deection in the range of 734ndash75 for increase in cu20 kPa to 40 kPa of sloping ground (θ 10deg 20deg 30deg 40deg 50deg)and horizontal ground surfaces from which can concludethat the weaker soil parameters are the more signicantslope eect becomes Besides the curve of the maximumbending moment variation with undrained shear strengthshown in Figure 24 is smoother and the range of themaximum bending moment of the pile with the increase ofthe slope is relatively stable

9 Conclusions

e purpose of this paper is to study the behavior of laterallyloaded long-exible pile in undrained clay sloping groundBased on the basic model of ideal elastic-plastic p-y curvemethod this paper derives the dierential equations of thelaterally loaded single pile in undrained clay sloped groundby introducing the existing related reduction variablefunction and the corresponding nite dierence method forthe pile deection and internal force is obtained A series ofparameters analyses are further performed for slope anglenormalized distance of pile adhesion coecentcient and un-drained shear strength e conclusions obtained from thisstudy are summarized as follows

(1) A nonlinear analysis method for laterally loaded long-exible pile in undrained clay sloped ground isestablished rough the verication of examples thecorrectness and feasibility of the method is proved

(2) Slope angle is the most important factor that aectingthe lateral bearing capacity of the near-slope pile eincrease in slope angle increases the deection and the

rate of increase of deection and this trend becomesmore obvious as the lateral load increased When theslope angle is small enough (θ lt 10o) the eect ofslope is almost negligible Besides the depth of xityof the pile is about 4sim8 times the size of the pilediameter

(3) e distance away from pile to slope crest is also animportant factor that aects the lateral-load capacityof the pile e increase in normalized distance BDof the pile decreases the deection of pile head butincreases the lateral-load capacity and when nor-malized distance BD ratio exceeds 6 the slope eectcan be avoidedWhen laterally loaded pile is closer tothe slope crest the inuence of the slope angle seemsmore dominant

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

ndash01 00 01 02 03 04 05 06 07 08 09 10 11

900

1000

1100

1200

1300

1400

1500

1600

Max

imum

ben

ding

mom

ent

Mm

ax (k

Nmiddotm

)

Adhesion coefficient α

Figure 22 Maximum bending moment (Mmax) variation withadhesion coecentcient (α) for dierent slope angle

0 20 40 60 80 100 1200

50100150200250300350400450500550600

Late

ral d

ispla

cem

ent y 0

(mm

)

Undrained shear strength cu (kPa)

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 23 Pile head deection (y0) variation with undrained shearstrength (cu) for dierent slope angle

0 20 40 60 80 100 1200

300

600

900

1200

1500

1800

2100M

axim

umbe

ndin

gmom

ent M

max

(kN

middotm)

Undrained shear strength cu (kPa)

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 24 Maximum bending moment (Mmax) variation withundrained shear strength (cu) for dierent slope angle

Advances in Civil Engineering 11

(4) -e adhesion coefficient α at the pile-soil interfacecan effectively reduce the pile head deflection and themaximum bending moment of the pile at the sametime -e increase in slope angle will significantlyincrease the pile head deflection and maximumbending moment of the pile especially when theslope angle exceeds 40deg

(5) -e increase in undrained shear strength cu de-creases the pile head deflection and the maximumbending moment of the pile -is is because of theincrease in the strength of soil and the relativestiffness of the pile-soil system Also the presence ofslopes aggravates the rate of change of pile headdeflection especially when the cu is in a mall value(ranges from 20 kPa to 40 kPa) In contrast themaximum bending moment variation with un-drained shear strength affected by the slope effectappears more moderate

(6) -is study researches the lateral bearing behavior ofsingle pile in undrained clay sloping ground Inpractical projects the situation of pile foundationson slope ground surface is not uncommon and thelateral bearing characteristics of pile foundationsare more complicated -erefore the influence ofslope effect on the lateral bearing capacity of pilewhich is on slope ground surface is worth furtherstudy

Data Availability

-e original data for summary of pile load test in Table 1 arefrom Wu et al [28] Georgiadis and Georgiadis [17] andGeorgiadis and Georgiadis [18] respectively -e computedpile responses as shown in Figure 6 are compared to the piletest results (Wu et al [28]) and to the pile responsescomputed with the same computer code using as input theMatlock [2] Reese and Welch [5] Bhushan et al [26]Stevens and Audibert [27] Figures 7 and 8 are calculated bycomputer code MATLAB to compare previous studies(Georgiadis and Georgiadis [17] Georgiadis and Georgiadis[18] respectively) Figures 9ndash24 are calculated by the pro-posedmethod based on the original data mentioned above tostudy parametric analysis In addition all the sharing datawere involved in this paper and there was no redundantdata

Conflicts of Interest

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

Acknowledgments

-is work is supported by the National Natural ScienceFoundation of China (grant nos 51478479 and 51678570)and Hunan Transport Technology Project (grant no201524)

References

[1] N Nimityongskul Y Kawamata D Rayamajhi andS A Ashford ldquoFull-scale tests on effects of slope on lateralcapacity of piles installed in cohesive soilsrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 144 no 1article 04017103 2018

[2] H Matlock ldquoCorrelation for design of laterally loaded piles insoft clayrdquo in Proceedings of the Offshore Technology Confer-ence pp 77ndash94 Houston TX USA April 1970

[3] L C Reese ldquoAnalysis of laterally loaded piles in sandrdquo inProceedings of the Offshore Technical Conference pp 95ndash105Houston TX USA May 1974

[4] L Reese W Cox and F Koop ldquoField testing and analysis oflaterally loaded piles on stiff clayrdquo in Proceedings of theOffshore Technology in Civil Engineering pp 106ndash125 DallasTX USA May 1975

[5] L C Reese and R C Welch ldquoLateral loading of deepfoundations in stiff clayrdquo Journal of Geotechnical and Geo-environmental Engineering vol 101 no 7 pp 633ndash649 1975

[6] M A Gabr T Lunne and J J Powell ldquoP-y analysis of laterallyloaded piles in clay using DMTrdquo Journal of GeotechnicalEngineering vol 120 no 5 pp 816ndash837 1994

[7] C C Fan and J H Long ldquoAssessment of existing methods forpredicting soil response of laterally loaded piles in sandrdquoComputers and Geotechnics vol 32 no 4 pp 274ndash289 2005

[8] G P Yang and Z M Zhang ldquoResearch on P-Y curve oflaterally bearing piles under large displacementrdquo WaterTransportation Engineering vol 342 no 7 pp 40ndash45 2002

[9] C Wang and Z A LU ldquoCalculation of internal forces oflaterally loaded piles by using p-y curverdquo Journal ofChongqing Jiaotong University (Natural Science) vol 4 no 1pp 61ndash65 1958

[10] H C Wang and D Q WU ldquoA new unified approach to thep-y curve of laterally loaded pile in clayrdquo Journal of HohaiUniversity no 1 pp 9ndash17 1991

[11] G C Wang and M Yang ldquoNonlinear analysis of laterallyloaded piles in sandrdquo Rock and Soil Mechanics no 2pp 261ndash267 2011

[12] G CWang andM Yang ldquoCalculation of laterally loaded pilesin clayrdquo Journal of Tongji University (Natural Science) vol 40no 3 pp 373ndash378 2012

[13] T Q Zhou Z A LU and D H Wang ldquoCalculation methodof laterally loaded super-long PHC pilerdquo Port and WaterwayEngineering no 6 pp 155ndash160 2013

[14] L U Cheng X C Xu S X Chen et al ldquoModel test andnumerical simulation of horizontal bearing capacity andimpact factors for foundation piles in sloperdquo Rock and SoilMechanics no 9 pp 2685ndash2691 2014

[15] P YinB H ZhaoM H Zhao et al ldquoStability analysis of pile-column bridge pile considering slope effectrdquo Journal of Hu-nan University (Natural Science) vol 43 no 11 pp 20ndash252016

[16] Y S Deng M H Zhao X J Zhou et al ldquoResearch progress ofbearing characteristics of pile column at steep slope inmountain areasrdquo Journal of Highway and TransportationResearch and Development vol 29 no 6 pp 37ndash45 2012

[17] K Georgiadis and M Georgiadis ldquoUndrained lateral pileresponse in sloping groundrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 136 no 11 pp 1489ndash1500 2010

[18] K Georgiadis and M Georgiadis ldquoDevelopment of p-ycurves for undrained response of piles near slopesrdquo Com-puters and Geotechnics vol 40 no 3 pp 53ndash61 2012

12 Advances in Civil Engineering

[19] K Muthukkumaran R Sundaravadivelu and S R GandhildquoEffect of slope on p-y curves due to surcharge loadrdquo Soils andFoundations vol 48 no 3 pp 353ndash361 2008

[20] L M Zhang C W W Ng and C J Lee ldquoEffects of slope andsleeving on the behavior of laterally loaded pilesrdquo Soils andFoundations vol 44 no 4 pp 99ndash108 2008

[21] B P Yin M H Zhao W He et al ldquoModel test study onidentification of foundation proportional coefficient m inslope groundrdquo Journal of Hunan University (Natural Science)vol 44 no 9 2017

[22] B L Gao C R Zhang and Z X Zhang ldquoModel tests on effectof slopes on lateral resistance of near single piles in sandrdquoRock and Soil Mechanics vol 35 no 11 pp 3191ndash3198 2014

[23] B T Zhu Be Ultimate Resistance and Laterally Loaded PileBehaviors Tongji University School of Civil EngineeringShanghai China 2005

[24] S S Rajashree and T G Sitharam ldquoNonlinear finite-elementmodeling of batter piles under lateral loadrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 127 no 7pp 604ndash612 2001

[25] R L Kondner ldquoHyperbolic stress-strain response cohesivesoilsrdquo Journal of the Soil Mechanics and Foundations Divisionvol 89 no 1 pp 115ndash143 1963

[26] K Bhushan S C Haley and P T Fong ldquoLateral load tests ondrilled piers in stiff claysrdquo Journal of the Geotechnical Engi-neering Division vol 1058 pp 969ndash985 1979

[27] J B Stevens and J M E Audibert ldquoRe-examination of P-Ycurve formulationsrdquo in Proceedings of 11th Offshore Tech-nology Conference pp 397ndash403 Houston TX USA 1980

[28] D Wu B B Broms and V Choa ldquoDesign of laterally loadedpiles in cohesive soils using p-y curvesrdquo Soils and Founda-tions vol 38 no 2 pp 17ndash26 1998

Advances in Civil Engineering 13

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of the pile design Here the dierential form of the solutionof the bending moment is listed as

Mi yiminus1 minus 2yi + yi+1( )EpIp

s2 (23)

According to the basic solution ideas of equation (22)a MATLAB iterative code is developed to solve the responsebehavior of pile and the ow chart of iterative calculation isshown in Figure 5

7 Validation to Previous Studies

e feasibility of the proposed method is validated in thissection to some previous studies which are well docu-mented in the literatureis method is introduced as inputinto MATLAB to calculate the response of each pile egeometrical characteristics (pile length L pile diameter Ddistance from the pile shaft to the slope crest B bendingstiness of the pile EpIp and slope angleθ) and the soilproperties (undrained shear strength cu secant modulusE50 eective bulk density c or cprime and cohesion coecentcientα) are summarized in Table 1 for each previous studyconsidered

Case 1 e computed pile responses are compared to thepile test results and to the pile responses computed with thesame computer code using as input the Matlock [2] Reeseand Welch [5] Bhushan et al [26] Stevens and Audibert[27] e Shanghai pile tests as shown in Figure 6 reportedby the literature [28] involved lateral loading of piles in levelground It can be seen that despite the small discrepancymeasured and predicted between the proposed p-y curveload-displacement relationships the general shape of thecurves is very similar indicating that the small discrepancymay be due to overestimation of secant modulus E50

Case 2 e results calculated by the proposed method andthe results calculated by Georgiadis and Georgiadis [17]which presented 3D nite-element analyses of pile in slopingground are presented in Figure 7 for comparison purposesis paper selects two dierent slope angles (θ 20deg 40degrespectively) for verication analysis As the slope angleincreases the results of this method are getting closer to theresults of the literature [17]

Case 3 e calculating results given by Georgiadis andGeorgiadis [18] are used as examples for comparisonverication Pile foundation is completely buried in theundrained clay slope us the section of the pile head atground surface only has the initial horizontal forceH0 ispaper selects four dierent pilersquos distance from slope crest(B 03m 06m 12m 24m respectively) for vericationanalysis e H0-y0 curves and H0-maxM curves of pilehead obtained from the proposed method and literature[18] are plotted in Figure 8 A good agreement has beenobserved between the calculating results from the presentstudy and literature results

8 Parametric Study

81 Eect of Slope Angle θ e size of the slope angle di-rectly determines the soil volume in front of the pile toparticipate in the pile-soil interaction In order to bettershow the eect of slope angles the pile head deection ofslope was normalized by dividing the pile head deection ofslope (y0s) by that of horizontal (y0H) Figures 9ndash12 re-spectively show the lateral load-deection curves at pilehead the normalized deection (y0sy0H)-load (H0) curvesat pile head y0 the maximum bending moment (Mmax)-load (H0) curves and the bending moment(M)-depth(z)distribution curves with dierent slope angles of 0deg 10deg 20deg40deg 50deg e relevant calculation parameters here are pilelength L 14m pile diameter D 06m bending stinessof pile EpIp 18449 (MNmiddotm2) normalized distance of pileBD 05 adhesion coecentcient α 1 piles are completelyburied in undrained clay and Poissonrsquos ratio of clay ]s 049 undrained shear strength cu 40 kPa and secantmodulus E50 14MPa

As shown in Figure 9 as the slope angle increases thelateral deection of the pile head increases signicantly and

Determine the number nof pile unit divisions

Start

Input initial lateralload

Input parameters ofpile soil and slope

Calculate the values of K psuiand μ(zi) for each node of the pile

Calculate the allowable displacementvalue of yu for each node of the pile

Calculate pile lateral displacement yi for eachnode by using the elastic matrix of Ki and the

external load vector of Fi

Judge yi gt yu

Resolve by replacing K2 and F2 with Ki and Ficorrespondingly where needed

Output lateral displacement value of yi foreach node and calculate the corresponding

bending moment value of Mi

End

Yes

No

Figure 5 Flowchart of iterative calculation

Advances in Civil Engineering 5

this trend becomes much more obvious with the increase ofthe lateral load It is also observed that when ground surfacechanges from horizontal ground to 10deg slope the behavior ofpile is almost like horizontal ground surface indicating theeect of slope is almost negligible when the slope angle is lt10degFigure 10 further shows the distribution curves of normalizeddeection (y0sy0H) with the lateral load It can be seen thatdierent xed ratios of y0sy0H are almost maintained at lowload levels but as the lateral load continue to increase the

values of y0sy0H start to increase unequally for dierent slopeangle with the increase of load When the lateral load is at750 kN the values of y0sy0H for 40degslope and 50deg slope are1065 2157 respectively indicating that the steeper the slopeangle is the more deection of pile head grows

It can be seen from Figure 11 that the maximum bendingmoment values of the pile also increase as the slope angleincreases but the rate of increase of maximum bendingmoment with lateral load is more moderate

Table 1 Summary of pile load test

Pile testGeometrical characteristics Soil properties

L (m) D (m) B (m) EpIp (kNmiddotm) e (m) θ (deg) cu (kPa) E50 (kPa) c or cprime (kNm3) α1 14 05 0 97900 072 0 30 3000 7 0942 20 10 0 1423534 0 2040 70 14000 18 053 12 06 03 06 12 24 184490 0 45 50 10000 18 073

00

20406080

100120140160180200

10 20 30 40y0 (mm)

H0 (

kN)

50 60 70

Stevens and AudibertBhushan et alMatlock

OrsquoNeill and GaziogluPresent studyPile test

Figure 6 Verication analysis of H0-y0 curves relationship for Shanghai pile tests

Present studyFE analyses (Georgiadis and Georgiadis [18])Present studyFE analyses (Georgiadis and Georgiadis [18])

10000900080007000600050004000300020001000

0

max

M (k

Nmiddotm

)

0306090120150180210240270300

y 0 (m

m)

0 250 500 750 1000 1250 1500 1750 2000 2250 2500H0 (kN)

(a)

Present studyFE analyses (Georgiadis and Georgiadis [18])Present studyFE analyses (Georgiadis and Georgiadis [18])

0 250 500 750 1000 1250 1500 1750 2000 2250 2500H0 (kN)

10000900080007000600050004000300020001000

0

max

M (k

Nmiddotm

)

04080120160200240280320360400

y 0 (m

m)

(b)

Figure 7 Verication analysis of H0-y0 curves relationship for FE analysis (a) θ 20deg (b) θ 40deg

6 Advances in Civil Engineering

Figures 12 and 13 show the bending moment distributionwith depth and the depth of xity (where the maximumbending moment occurs) of the pile for all slope angles witha lateral load at 300 kN and 600 kN respectively It is clear thatthe maximum bending moment of the pile increases with theincrease of slope angle at the same load but the rst zerolocation of bendingmoment curve and depth of xity increasecorrespondingly With the increase of the load the dierencein the maximum bending moment growth at each slope anglebecomes obvious and the rst zero location of bendingmoment curve and depth of xity of the pile also increasemore quickly For example as is shown in Figure 13 the depthof xity for 30deg and 50deg slope angle increased by 446 1734compared with that in horizontal ground at the load of300 kN respectively but the ratio further increases to 11323203 respectively when the load increases to 600 kN It canalso be seen from Figure 13 that the depth of pile xity almostoccurs at a depth of 4sim8D (D diameter of pile)

82 Eect of Normalized Distance of Pile BD Selecting thenormalized distance of pile BD as 05 2 4 6 and considerthe slope angle of 10deg 30deg 50deg respectively as the existingslope conditions e other calculation parameters are thesame as in Section 81

Figures 14ndash16 show the load-deection curve for dif-ferent normalized distance BD of pile head at above threeslope conditions From these gures it is observed that theincrease in normalized distance BD ratio decreases thedeection of pile head When normalized distance BDratio exceeds 6 in all slope angle conditions the deectionat pile head is basically the same as that in horizontalground which means the inuence of the slope eect isalmost negligible in this case It is also observed that theload-deection curves in dierent slope angle conditionshave dierent response results and the increase in slopeangle can increase the discreteness of the curves Figure 17further shows the eect of normalized distance of pile on

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3500

3000

2500

2000

1500

1000

500

0

max

M (k

Nmiddotm

)

0 200 400 600 800 1000H0 (kN)

0

120

240

360

480

600

720

840

y 0 (m

m)

(a)

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3500

3000

2500

2000

1500

1000

500

0

max

M (k

Nmiddotm

)

0

100

200

300

400

500

600

700

y 0 (m

m)

0 200 400 600 800 1000H0 (kN)

(b)

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3000

2500

2000

1500

1000

500

0

max

M (k

Nmiddotm

)

0 200 400 600 800 1000H0 (kN)

0

90

180

270

360

450

540

y 0 (m

m)

(c)

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3000

2500

2000

1500

1000

500

0m

ax M

(kN

middotm)

0 200 400 600 800 1000H0 (kN)

0

80

160

240

320

400

480

y 0 (m

m)

(d)

Figure 8 Verication analysis of H0-y0 curves relationship for LPILE (a) B 03m (b) B 06m (c) B 12m (d) B 24m

Advances in Civil Engineering 7

lateral-load capacity on horizontal ground and slopingground (θ 10deg 30deg 50deg) It can be seen that when thenormalized distance BD of pile changes from 05 to 6 thelateral-load capacity is increased by 227 111 2987on 10deg 30deg 50deg sloping ground respectively indicating thatthe increase in slope angle increases the inuence of BD onthe lateral-load capacity of the pile

Figures 18ndash20 show the bending moment variationalong pile length of the pile for dierent normalized dis-tance BD on horizontal ground and sloping ground(θ 10deg 30deg 50deg) From these gures it is observed that themaximum bending moment increases with the increase inthe normalized distance BD of the pile and the increase inthe applied lateral load Also for the same normalized

distance BD of pile and applied lateral load the increase inslope angle of θ increases the maximum bending momentof pile When ground surface changes from horizontal to10deg 30deg and 50deg sloping ground the maximum bendingmoment of pile in sloping ground is increased by 28126 and 319 respectively under lateral load of 600 kNand normalized distance BD of 05 It is also noted thatwhen the pile is nearer to slope crest the slope angle be-comes a more dominant factor to aect the lateral capacityof the pile especially at a high-load level

0 100 200 300 400 500 600 700 80010

15

20

25

30

Nor

mal

ized

disp

lace

men

t y o

Sy o

H

Lateral load H0 (kN)

θ = 0deg (B = 05D)θ = 10deg (B = 05D)θ = 20deg (B = 05D)

θ = 30deg (B = 05D)θ = 40deg (B = 05D)θ = 50deg (B = 05D)

Figure 10 Normalized deection (y0sy0H)-load (H0) curves fordierent slope angle

ndash200 0 200 400 600 800 1000 1200 1400 1600 18000123456789

101112131415

Dep

th (m

)

Bending moment M (kNmiddotm)

θ = 0deg H0 = 300kNθ = 0deg H0 = 600kNθ = 10deg H0 = 300kNθ = 10deg H0 = 600kNθ = 20deg H0 = 300kNθ = 20deg H0 = 600kN

θ = 30deg H0 = 300kNθ = 30deg H0 = 600kNθ = 40deg H0 = 300kNθ = 40deg H0 = 600kNθ = 50deg H0 = 300kNθ = 50deg H0 = 600kN

Figure 12 Bending moment variation along the depth of pile fordierent slope angle

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Deflection y0 (mm)

θ = 0deg (B = 05D)θ = 10deg (B = 05D)θ = 20deg (B = 05D)

θ = 30deg (B = 05D)θ = 40deg (B = 05D)θ = 50deg (B = 05D)

Figure 9 Lateral load-deection curves for dierent slope angle atpile head

0 400 800 1200 1600 2000 24000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Maximum bending moment Mmax (kNmiddotm)

θ = 0deg (B = 05D)θ = 10deg (B = 05D)θ = 20deg (B = 05D)

θ = 30deg (B = 05D)θ = 40deg (B = 05D)θ = 50deg (B = 05D)

Figure 11 Maximum bending moment-load curves for dierentslope angle

8 Advances in Civil Engineering

83 Eect of Adhesion Coecient α In order to study theeect of adhesion coecentcient α on the lateral behavior of pile insloped ground this paper analyzes the parameter α from 0 to1 with increment of 01 and chooses lateral loadH0 500 kNand the bending momentM0 0 (kNmiddotm) as the xed loadingcondition to calculate and analyze the deection of pile headConsider the slope angle θ as the same in Section 81 andother basic calculation parameters are the same as Section 81

Figures 21 and 22 show pile head deection (y0) and themaximum bending moment (Mmax) of the pile variation withthe adhesion coecentcient α for dierent slope angle re-spectively From these gures it can be seen that increasingthe adhesion coecentcient α at the pile-soil interface can ef-fectively reduce the pile head deection and the maximumbending moment of the pile at the same time Also the in-crease in slope angle almost does not change the corre-sponding curve growth model but will signicantly increase

0 20 40 60 80 100 120 140 160 180 200 220 2400

100

200

300

400

500

600

700

800

Lateral displacement y0 (mm)

BD = 05 (θ = 10deg)BD = 2 (θ = 10deg)

BD = 4 (θ = 10deg)BD = 6 (θ = 10deg)

Late

ral l

oad

H0

(kN

)

Figure 14 Lateral load-deection curves for θ 10deg for dierentnormalized distance of pile at pile head

0 1 2 3 4 5 6

560

580

600

620

640

660

680

700

720

740A

llow

able

pile

capa

city

(kN

)

Normalized distance BD

Level ground (θ = 0deg)θ = 10deg

θ = 30degθ = 50deg

Figure 17 Bearing capacity of pile head for dierent normalizeddistance of pile (corresponding to 200mm)

247

122

247

123

247

126

258

142

274

059

289

9763

6058

3

367

113

376

092

401

397

428

333

476

085

θ = 50degθ = 40degθ = 30degθ = 20degθ = 10deg

H0 = 300kNH0 = 600kN

θ = 0deg00

05

10

15

20

25

30

35

40

45

50

55

Dep

th o

f fix

ity (m

)

Figure 13 Depth of xity variation with dierent slope angle

B = 05D (θ = 30deg)B = 2D (θ = 30deg)

B = 4D (θ = 30deg)B = 6D (θ = 30deg)

0 30 60 90 120 150 180 210 240 270 3000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Lateral displacement y0 (mm)

Figure 15 Lateral load-deection curves for θ 30deg for dierentnormalized distance of pile at pile head

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Lateral displacement y0 (mm)

BD = 05 (θ = 50deg)BD = 2 (θ = 50deg)

BD = 4 (θ = 50deg)BD = 6 (θ = 50deg)

Figure 16 Lateral load-deection curves for θ 50deg for dierentnormalized distance of pile at pile head

Advances in Civil Engineering 9

the pile head deection and maximum bending moment ofthe pile especially when the slope angle exceeds 40deg An ex-ample is used for pile head deection when the value of α isequal to 0 the pile head deection values of pile in slopingground with θ 10deg 30deg 50deg is increased by 74 398137 respectively compared to that in horizontal ground

84 Eect of Undrained Shear Strength cu Here lateral loadH0 500 kN and the initial bending momentM0 0 (kNmiddotm)

were taken as the initial loading conditions choosing un-drained shear strengths cu of 20 kPa 40 kPa 60 80 kPa100 kPa respectively to calculate and analyze Other basiccalculation parameters are the same as in Section 81

Figures 23 and 24 show pile head deection (y0) and themaximum bending moment (Mmax) of the pile variationwith the undrained shear strength cu for dierent slopeangles respectively From the curves given in Figures 23 and24 it is observed that the increase in undrained shearstrength cu decreases the pile head deection and themaximum bending moment is is because of the increasein the strength of soil and the relative stiness of the pile-soilsystem Also it is obvious that the presence of slopes

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

ndash200 0 200 400 600 800 1000 1200 1400 16000123456789

1011121314

Dep

th (m

)

Bending moment M (kNmiddotm)

Figure 19 Bending moment variation along the depth of pile forθ 30deg for dierent slope angle

ndash200 0 200 400 600 800 1000 1200 14000123456789

1011121314

Dep

th (m

)

Bending moment M (kNmiddotm)

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

Figure 18 Bending moment variation along the depth of pile forθ 10deg for dierent slope angle

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

ndash200 0 200 400 600 800 1000 1200 1400 1600 18000123456789

1011121314

Dpe

th (m

)

Bending moment M (kNmiddotm)

Figure 20 Bending moment variation along the depth of pile forθ 50deg for dierent slope angle

ndash01 00 01 02 03 04 05 06 07 08 09 10 116080

100120140160180200220240260

Late

rald

ispla

cem

ent y 0

(mm

)

Adhesion coefficient α

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 21 Pile head deection (y0) variation with adhesion co-ecentcient (α) for dierent slope angle

10 Advances in Civil Engineering

aggravates the rate of change of pile head deection es-pecially when cu ranges from 20 kPa to 40 kPa and when thevalue of cu exceeds 40 kPa the decrease rate of the deectionof pile head becomes slow and eventually almost becomesat From the results in Figure 23 it is observed that the pilehead deection in the range of 734ndash75 for increase in cu20 kPa to 40 kPa of sloping ground (θ 10deg 20deg 30deg 40deg 50deg)and horizontal ground surfaces from which can concludethat the weaker soil parameters are the more signicantslope eect becomes Besides the curve of the maximumbending moment variation with undrained shear strengthshown in Figure 24 is smoother and the range of themaximum bending moment of the pile with the increase ofthe slope is relatively stable

9 Conclusions

e purpose of this paper is to study the behavior of laterallyloaded long-exible pile in undrained clay sloping groundBased on the basic model of ideal elastic-plastic p-y curvemethod this paper derives the dierential equations of thelaterally loaded single pile in undrained clay sloped groundby introducing the existing related reduction variablefunction and the corresponding nite dierence method forthe pile deection and internal force is obtained A series ofparameters analyses are further performed for slope anglenormalized distance of pile adhesion coecentcient and un-drained shear strength e conclusions obtained from thisstudy are summarized as follows

(1) A nonlinear analysis method for laterally loaded long-exible pile in undrained clay sloped ground isestablished rough the verication of examples thecorrectness and feasibility of the method is proved

(2) Slope angle is the most important factor that aectingthe lateral bearing capacity of the near-slope pile eincrease in slope angle increases the deection and the

rate of increase of deection and this trend becomesmore obvious as the lateral load increased When theslope angle is small enough (θ lt 10o) the eect ofslope is almost negligible Besides the depth of xityof the pile is about 4sim8 times the size of the pilediameter

(3) e distance away from pile to slope crest is also animportant factor that aects the lateral-load capacityof the pile e increase in normalized distance BDof the pile decreases the deection of pile head butincreases the lateral-load capacity and when nor-malized distance BD ratio exceeds 6 the slope eectcan be avoidedWhen laterally loaded pile is closer tothe slope crest the inuence of the slope angle seemsmore dominant

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

ndash01 00 01 02 03 04 05 06 07 08 09 10 11

900

1000

1100

1200

1300

1400

1500

1600

Max

imum

ben

ding

mom

ent

Mm

ax (k

Nmiddotm

)

Adhesion coefficient α

Figure 22 Maximum bending moment (Mmax) variation withadhesion coecentcient (α) for dierent slope angle

0 20 40 60 80 100 1200

50100150200250300350400450500550600

Late

ral d

ispla

cem

ent y 0

(mm

)

Undrained shear strength cu (kPa)

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 23 Pile head deection (y0) variation with undrained shearstrength (cu) for dierent slope angle

0 20 40 60 80 100 1200

300

600

900

1200

1500

1800

2100M

axim

umbe

ndin

gmom

ent M

max

(kN

middotm)

Undrained shear strength cu (kPa)

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 24 Maximum bending moment (Mmax) variation withundrained shear strength (cu) for dierent slope angle

Advances in Civil Engineering 11

(4) -e adhesion coefficient α at the pile-soil interfacecan effectively reduce the pile head deflection and themaximum bending moment of the pile at the sametime -e increase in slope angle will significantlyincrease the pile head deflection and maximumbending moment of the pile especially when theslope angle exceeds 40deg

(5) -e increase in undrained shear strength cu de-creases the pile head deflection and the maximumbending moment of the pile -is is because of theincrease in the strength of soil and the relativestiffness of the pile-soil system Also the presence ofslopes aggravates the rate of change of pile headdeflection especially when the cu is in a mall value(ranges from 20 kPa to 40 kPa) In contrast themaximum bending moment variation with un-drained shear strength affected by the slope effectappears more moderate

(6) -is study researches the lateral bearing behavior ofsingle pile in undrained clay sloping ground Inpractical projects the situation of pile foundationson slope ground surface is not uncommon and thelateral bearing characteristics of pile foundationsare more complicated -erefore the influence ofslope effect on the lateral bearing capacity of pilewhich is on slope ground surface is worth furtherstudy

Data Availability

-e original data for summary of pile load test in Table 1 arefrom Wu et al [28] Georgiadis and Georgiadis [17] andGeorgiadis and Georgiadis [18] respectively -e computedpile responses as shown in Figure 6 are compared to the piletest results (Wu et al [28]) and to the pile responsescomputed with the same computer code using as input theMatlock [2] Reese and Welch [5] Bhushan et al [26]Stevens and Audibert [27] Figures 7 and 8 are calculated bycomputer code MATLAB to compare previous studies(Georgiadis and Georgiadis [17] Georgiadis and Georgiadis[18] respectively) Figures 9ndash24 are calculated by the pro-posedmethod based on the original data mentioned above tostudy parametric analysis In addition all the sharing datawere involved in this paper and there was no redundantdata

Conflicts of Interest

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

Acknowledgments

-is work is supported by the National Natural ScienceFoundation of China (grant nos 51478479 and 51678570)and Hunan Transport Technology Project (grant no201524)

References

[1] N Nimityongskul Y Kawamata D Rayamajhi andS A Ashford ldquoFull-scale tests on effects of slope on lateralcapacity of piles installed in cohesive soilsrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 144 no 1article 04017103 2018

[2] H Matlock ldquoCorrelation for design of laterally loaded piles insoft clayrdquo in Proceedings of the Offshore Technology Confer-ence pp 77ndash94 Houston TX USA April 1970

[3] L C Reese ldquoAnalysis of laterally loaded piles in sandrdquo inProceedings of the Offshore Technical Conference pp 95ndash105Houston TX USA May 1974

[4] L Reese W Cox and F Koop ldquoField testing and analysis oflaterally loaded piles on stiff clayrdquo in Proceedings of theOffshore Technology in Civil Engineering pp 106ndash125 DallasTX USA May 1975

[5] L C Reese and R C Welch ldquoLateral loading of deepfoundations in stiff clayrdquo Journal of Geotechnical and Geo-environmental Engineering vol 101 no 7 pp 633ndash649 1975

[6] M A Gabr T Lunne and J J Powell ldquoP-y analysis of laterallyloaded piles in clay using DMTrdquo Journal of GeotechnicalEngineering vol 120 no 5 pp 816ndash837 1994

[7] C C Fan and J H Long ldquoAssessment of existing methods forpredicting soil response of laterally loaded piles in sandrdquoComputers and Geotechnics vol 32 no 4 pp 274ndash289 2005

[8] G P Yang and Z M Zhang ldquoResearch on P-Y curve oflaterally bearing piles under large displacementrdquo WaterTransportation Engineering vol 342 no 7 pp 40ndash45 2002

[9] C Wang and Z A LU ldquoCalculation of internal forces oflaterally loaded piles by using p-y curverdquo Journal ofChongqing Jiaotong University (Natural Science) vol 4 no 1pp 61ndash65 1958

[10] H C Wang and D Q WU ldquoA new unified approach to thep-y curve of laterally loaded pile in clayrdquo Journal of HohaiUniversity no 1 pp 9ndash17 1991

[11] G C Wang and M Yang ldquoNonlinear analysis of laterallyloaded piles in sandrdquo Rock and Soil Mechanics no 2pp 261ndash267 2011

[12] G CWang andM Yang ldquoCalculation of laterally loaded pilesin clayrdquo Journal of Tongji University (Natural Science) vol 40no 3 pp 373ndash378 2012

[13] T Q Zhou Z A LU and D H Wang ldquoCalculation methodof laterally loaded super-long PHC pilerdquo Port and WaterwayEngineering no 6 pp 155ndash160 2013

[14] L U Cheng X C Xu S X Chen et al ldquoModel test andnumerical simulation of horizontal bearing capacity andimpact factors for foundation piles in sloperdquo Rock and SoilMechanics no 9 pp 2685ndash2691 2014

[15] P YinB H ZhaoM H Zhao et al ldquoStability analysis of pile-column bridge pile considering slope effectrdquo Journal of Hu-nan University (Natural Science) vol 43 no 11 pp 20ndash252016

[16] Y S Deng M H Zhao X J Zhou et al ldquoResearch progress ofbearing characteristics of pile column at steep slope inmountain areasrdquo Journal of Highway and TransportationResearch and Development vol 29 no 6 pp 37ndash45 2012

[17] K Georgiadis and M Georgiadis ldquoUndrained lateral pileresponse in sloping groundrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 136 no 11 pp 1489ndash1500 2010

[18] K Georgiadis and M Georgiadis ldquoDevelopment of p-ycurves for undrained response of piles near slopesrdquo Com-puters and Geotechnics vol 40 no 3 pp 53ndash61 2012

12 Advances in Civil Engineering

[19] K Muthukkumaran R Sundaravadivelu and S R GandhildquoEffect of slope on p-y curves due to surcharge loadrdquo Soils andFoundations vol 48 no 3 pp 353ndash361 2008

[20] L M Zhang C W W Ng and C J Lee ldquoEffects of slope andsleeving on the behavior of laterally loaded pilesrdquo Soils andFoundations vol 44 no 4 pp 99ndash108 2008

[21] B P Yin M H Zhao W He et al ldquoModel test study onidentification of foundation proportional coefficient m inslope groundrdquo Journal of Hunan University (Natural Science)vol 44 no 9 2017

[22] B L Gao C R Zhang and Z X Zhang ldquoModel tests on effectof slopes on lateral resistance of near single piles in sandrdquoRock and Soil Mechanics vol 35 no 11 pp 3191ndash3198 2014

[23] B T Zhu Be Ultimate Resistance and Laterally Loaded PileBehaviors Tongji University School of Civil EngineeringShanghai China 2005

[24] S S Rajashree and T G Sitharam ldquoNonlinear finite-elementmodeling of batter piles under lateral loadrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 127 no 7pp 604ndash612 2001

[25] R L Kondner ldquoHyperbolic stress-strain response cohesivesoilsrdquo Journal of the Soil Mechanics and Foundations Divisionvol 89 no 1 pp 115ndash143 1963

[26] K Bhushan S C Haley and P T Fong ldquoLateral load tests ondrilled piers in stiff claysrdquo Journal of the Geotechnical Engi-neering Division vol 1058 pp 969ndash985 1979

[27] J B Stevens and J M E Audibert ldquoRe-examination of P-Ycurve formulationsrdquo in Proceedings of 11th Offshore Tech-nology Conference pp 397ndash403 Houston TX USA 1980

[28] D Wu B B Broms and V Choa ldquoDesign of laterally loadedpiles in cohesive soils using p-y curvesrdquo Soils and Founda-tions vol 38 no 2 pp 17ndash26 1998

Advances in Civil Engineering 13

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this trend becomes much more obvious with the increase ofthe lateral load It is also observed that when ground surfacechanges from horizontal ground to 10deg slope the behavior ofpile is almost like horizontal ground surface indicating theeect of slope is almost negligible when the slope angle is lt10degFigure 10 further shows the distribution curves of normalizeddeection (y0sy0H) with the lateral load It can be seen thatdierent xed ratios of y0sy0H are almost maintained at lowload levels but as the lateral load continue to increase the

values of y0sy0H start to increase unequally for dierent slopeangle with the increase of load When the lateral load is at750 kN the values of y0sy0H for 40degslope and 50deg slope are1065 2157 respectively indicating that the steeper the slopeangle is the more deection of pile head grows

It can be seen from Figure 11 that the maximum bendingmoment values of the pile also increase as the slope angleincreases but the rate of increase of maximum bendingmoment with lateral load is more moderate

Table 1 Summary of pile load test

Pile testGeometrical characteristics Soil properties

L (m) D (m) B (m) EpIp (kNmiddotm) e (m) θ (deg) cu (kPa) E50 (kPa) c or cprime (kNm3) α1 14 05 0 97900 072 0 30 3000 7 0942 20 10 0 1423534 0 2040 70 14000 18 053 12 06 03 06 12 24 184490 0 45 50 10000 18 073

00

20406080

100120140160180200

10 20 30 40y0 (mm)

H0 (

kN)

50 60 70

Stevens and AudibertBhushan et alMatlock

OrsquoNeill and GaziogluPresent studyPile test

Figure 6 Verication analysis of H0-y0 curves relationship for Shanghai pile tests

Present studyFE analyses (Georgiadis and Georgiadis [18])Present studyFE analyses (Georgiadis and Georgiadis [18])

10000900080007000600050004000300020001000

0

max

M (k

Nmiddotm

)

0306090120150180210240270300

y 0 (m

m)

0 250 500 750 1000 1250 1500 1750 2000 2250 2500H0 (kN)

(a)

Present studyFE analyses (Georgiadis and Georgiadis [18])Present studyFE analyses (Georgiadis and Georgiadis [18])

0 250 500 750 1000 1250 1500 1750 2000 2250 2500H0 (kN)

10000900080007000600050004000300020001000

0

max

M (k

Nmiddotm

)

04080120160200240280320360400

y 0 (m

m)

(b)

Figure 7 Verication analysis of H0-y0 curves relationship for FE analysis (a) θ 20deg (b) θ 40deg

6 Advances in Civil Engineering

Figures 12 and 13 show the bending moment distributionwith depth and the depth of xity (where the maximumbending moment occurs) of the pile for all slope angles witha lateral load at 300 kN and 600 kN respectively It is clear thatthe maximum bending moment of the pile increases with theincrease of slope angle at the same load but the rst zerolocation of bendingmoment curve and depth of xity increasecorrespondingly With the increase of the load the dierencein the maximum bending moment growth at each slope anglebecomes obvious and the rst zero location of bendingmoment curve and depth of xity of the pile also increasemore quickly For example as is shown in Figure 13 the depthof xity for 30deg and 50deg slope angle increased by 446 1734compared with that in horizontal ground at the load of300 kN respectively but the ratio further increases to 11323203 respectively when the load increases to 600 kN It canalso be seen from Figure 13 that the depth of pile xity almostoccurs at a depth of 4sim8D (D diameter of pile)

82 Eect of Normalized Distance of Pile BD Selecting thenormalized distance of pile BD as 05 2 4 6 and considerthe slope angle of 10deg 30deg 50deg respectively as the existingslope conditions e other calculation parameters are thesame as in Section 81

Figures 14ndash16 show the load-deection curve for dif-ferent normalized distance BD of pile head at above threeslope conditions From these gures it is observed that theincrease in normalized distance BD ratio decreases thedeection of pile head When normalized distance BDratio exceeds 6 in all slope angle conditions the deectionat pile head is basically the same as that in horizontalground which means the inuence of the slope eect isalmost negligible in this case It is also observed that theload-deection curves in dierent slope angle conditionshave dierent response results and the increase in slopeangle can increase the discreteness of the curves Figure 17further shows the eect of normalized distance of pile on

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3500

3000

2500

2000

1500

1000

500

0

max

M (k

Nmiddotm

)

0 200 400 600 800 1000H0 (kN)

0

120

240

360

480

600

720

840

y 0 (m

m)

(a)

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3500

3000

2500

2000

1500

1000

500

0

max

M (k

Nmiddotm

)

0

100

200

300

400

500

600

700

y 0 (m

m)

0 200 400 600 800 1000H0 (kN)

(b)

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3000

2500

2000

1500

1000

500

0

max

M (k

Nmiddotm

)

0 200 400 600 800 1000H0 (kN)

0

90

180

270

360

450

540

y 0 (m

m)

(c)

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3000

2500

2000

1500

1000

500

0m

ax M

(kN

middotm)

0 200 400 600 800 1000H0 (kN)

0

80

160

240

320

400

480

y 0 (m

m)

(d)

Figure 8 Verication analysis of H0-y0 curves relationship for LPILE (a) B 03m (b) B 06m (c) B 12m (d) B 24m

Advances in Civil Engineering 7

lateral-load capacity on horizontal ground and slopingground (θ 10deg 30deg 50deg) It can be seen that when thenormalized distance BD of pile changes from 05 to 6 thelateral-load capacity is increased by 227 111 2987on 10deg 30deg 50deg sloping ground respectively indicating thatthe increase in slope angle increases the inuence of BD onthe lateral-load capacity of the pile

Figures 18ndash20 show the bending moment variationalong pile length of the pile for dierent normalized dis-tance BD on horizontal ground and sloping ground(θ 10deg 30deg 50deg) From these gures it is observed that themaximum bending moment increases with the increase inthe normalized distance BD of the pile and the increase inthe applied lateral load Also for the same normalized

distance BD of pile and applied lateral load the increase inslope angle of θ increases the maximum bending momentof pile When ground surface changes from horizontal to10deg 30deg and 50deg sloping ground the maximum bendingmoment of pile in sloping ground is increased by 28126 and 319 respectively under lateral load of 600 kNand normalized distance BD of 05 It is also noted thatwhen the pile is nearer to slope crest the slope angle be-comes a more dominant factor to aect the lateral capacityof the pile especially at a high-load level

0 100 200 300 400 500 600 700 80010

15

20

25

30

Nor

mal

ized

disp

lace

men

t y o

Sy o

H

Lateral load H0 (kN)

θ = 0deg (B = 05D)θ = 10deg (B = 05D)θ = 20deg (B = 05D)

θ = 30deg (B = 05D)θ = 40deg (B = 05D)θ = 50deg (B = 05D)

Figure 10 Normalized deection (y0sy0H)-load (H0) curves fordierent slope angle

ndash200 0 200 400 600 800 1000 1200 1400 1600 18000123456789

101112131415

Dep

th (m

)

Bending moment M (kNmiddotm)

θ = 0deg H0 = 300kNθ = 0deg H0 = 600kNθ = 10deg H0 = 300kNθ = 10deg H0 = 600kNθ = 20deg H0 = 300kNθ = 20deg H0 = 600kN

θ = 30deg H0 = 300kNθ = 30deg H0 = 600kNθ = 40deg H0 = 300kNθ = 40deg H0 = 600kNθ = 50deg H0 = 300kNθ = 50deg H0 = 600kN

Figure 12 Bending moment variation along the depth of pile fordierent slope angle

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Deflection y0 (mm)

θ = 0deg (B = 05D)θ = 10deg (B = 05D)θ = 20deg (B = 05D)

θ = 30deg (B = 05D)θ = 40deg (B = 05D)θ = 50deg (B = 05D)

Figure 9 Lateral load-deection curves for dierent slope angle atpile head

0 400 800 1200 1600 2000 24000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Maximum bending moment Mmax (kNmiddotm)

θ = 0deg (B = 05D)θ = 10deg (B = 05D)θ = 20deg (B = 05D)

θ = 30deg (B = 05D)θ = 40deg (B = 05D)θ = 50deg (B = 05D)

Figure 11 Maximum bending moment-load curves for dierentslope angle

8 Advances in Civil Engineering

83 Eect of Adhesion Coecient α In order to study theeect of adhesion coecentcient α on the lateral behavior of pile insloped ground this paper analyzes the parameter α from 0 to1 with increment of 01 and chooses lateral loadH0 500 kNand the bending momentM0 0 (kNmiddotm) as the xed loadingcondition to calculate and analyze the deection of pile headConsider the slope angle θ as the same in Section 81 andother basic calculation parameters are the same as Section 81

Figures 21 and 22 show pile head deection (y0) and themaximum bending moment (Mmax) of the pile variation withthe adhesion coecentcient α for dierent slope angle re-spectively From these gures it can be seen that increasingthe adhesion coecentcient α at the pile-soil interface can ef-fectively reduce the pile head deection and the maximumbending moment of the pile at the same time Also the in-crease in slope angle almost does not change the corre-sponding curve growth model but will signicantly increase

0 20 40 60 80 100 120 140 160 180 200 220 2400

100

200

300

400

500

600

700

800

Lateral displacement y0 (mm)

BD = 05 (θ = 10deg)BD = 2 (θ = 10deg)

BD = 4 (θ = 10deg)BD = 6 (θ = 10deg)

Late

ral l

oad

H0

(kN

)

Figure 14 Lateral load-deection curves for θ 10deg for dierentnormalized distance of pile at pile head

0 1 2 3 4 5 6

560

580

600

620

640

660

680

700

720

740A

llow

able

pile

capa

city

(kN

)

Normalized distance BD

Level ground (θ = 0deg)θ = 10deg

θ = 30degθ = 50deg

Figure 17 Bearing capacity of pile head for dierent normalizeddistance of pile (corresponding to 200mm)

247

122

247

123

247

126

258

142

274

059

289

9763

6058

3

367

113

376

092

401

397

428

333

476

085

θ = 50degθ = 40degθ = 30degθ = 20degθ = 10deg

H0 = 300kNH0 = 600kN

θ = 0deg00

05

10

15

20

25

30

35

40

45

50

55

Dep

th o

f fix

ity (m

)

Figure 13 Depth of xity variation with dierent slope angle

B = 05D (θ = 30deg)B = 2D (θ = 30deg)

B = 4D (θ = 30deg)B = 6D (θ = 30deg)

0 30 60 90 120 150 180 210 240 270 3000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Lateral displacement y0 (mm)

Figure 15 Lateral load-deection curves for θ 30deg for dierentnormalized distance of pile at pile head

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Lateral displacement y0 (mm)

BD = 05 (θ = 50deg)BD = 2 (θ = 50deg)

BD = 4 (θ = 50deg)BD = 6 (θ = 50deg)

Figure 16 Lateral load-deection curves for θ 50deg for dierentnormalized distance of pile at pile head

Advances in Civil Engineering 9

the pile head deection and maximum bending moment ofthe pile especially when the slope angle exceeds 40deg An ex-ample is used for pile head deection when the value of α isequal to 0 the pile head deection values of pile in slopingground with θ 10deg 30deg 50deg is increased by 74 398137 respectively compared to that in horizontal ground

84 Eect of Undrained Shear Strength cu Here lateral loadH0 500 kN and the initial bending momentM0 0 (kNmiddotm)

were taken as the initial loading conditions choosing un-drained shear strengths cu of 20 kPa 40 kPa 60 80 kPa100 kPa respectively to calculate and analyze Other basiccalculation parameters are the same as in Section 81

Figures 23 and 24 show pile head deection (y0) and themaximum bending moment (Mmax) of the pile variationwith the undrained shear strength cu for dierent slopeangles respectively From the curves given in Figures 23 and24 it is observed that the increase in undrained shearstrength cu decreases the pile head deection and themaximum bending moment is is because of the increasein the strength of soil and the relative stiness of the pile-soilsystem Also it is obvious that the presence of slopes

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

ndash200 0 200 400 600 800 1000 1200 1400 16000123456789

1011121314

Dep

th (m

)

Bending moment M (kNmiddotm)

Figure 19 Bending moment variation along the depth of pile forθ 30deg for dierent slope angle

ndash200 0 200 400 600 800 1000 1200 14000123456789

1011121314

Dep

th (m

)

Bending moment M (kNmiddotm)

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

Figure 18 Bending moment variation along the depth of pile forθ 10deg for dierent slope angle

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

ndash200 0 200 400 600 800 1000 1200 1400 1600 18000123456789

1011121314

Dpe

th (m

)

Bending moment M (kNmiddotm)

Figure 20 Bending moment variation along the depth of pile forθ 50deg for dierent slope angle

ndash01 00 01 02 03 04 05 06 07 08 09 10 116080

100120140160180200220240260

Late

rald

ispla

cem

ent y 0

(mm

)

Adhesion coefficient α

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 21 Pile head deection (y0) variation with adhesion co-ecentcient (α) for dierent slope angle

10 Advances in Civil Engineering

aggravates the rate of change of pile head deection es-pecially when cu ranges from 20 kPa to 40 kPa and when thevalue of cu exceeds 40 kPa the decrease rate of the deectionof pile head becomes slow and eventually almost becomesat From the results in Figure 23 it is observed that the pilehead deection in the range of 734ndash75 for increase in cu20 kPa to 40 kPa of sloping ground (θ 10deg 20deg 30deg 40deg 50deg)and horizontal ground surfaces from which can concludethat the weaker soil parameters are the more signicantslope eect becomes Besides the curve of the maximumbending moment variation with undrained shear strengthshown in Figure 24 is smoother and the range of themaximum bending moment of the pile with the increase ofthe slope is relatively stable

9 Conclusions

e purpose of this paper is to study the behavior of laterallyloaded long-exible pile in undrained clay sloping groundBased on the basic model of ideal elastic-plastic p-y curvemethod this paper derives the dierential equations of thelaterally loaded single pile in undrained clay sloped groundby introducing the existing related reduction variablefunction and the corresponding nite dierence method forthe pile deection and internal force is obtained A series ofparameters analyses are further performed for slope anglenormalized distance of pile adhesion coecentcient and un-drained shear strength e conclusions obtained from thisstudy are summarized as follows

(1) A nonlinear analysis method for laterally loaded long-exible pile in undrained clay sloped ground isestablished rough the verication of examples thecorrectness and feasibility of the method is proved

(2) Slope angle is the most important factor that aectingthe lateral bearing capacity of the near-slope pile eincrease in slope angle increases the deection and the

rate of increase of deection and this trend becomesmore obvious as the lateral load increased When theslope angle is small enough (θ lt 10o) the eect ofslope is almost negligible Besides the depth of xityof the pile is about 4sim8 times the size of the pilediameter

(3) e distance away from pile to slope crest is also animportant factor that aects the lateral-load capacityof the pile e increase in normalized distance BDof the pile decreases the deection of pile head butincreases the lateral-load capacity and when nor-malized distance BD ratio exceeds 6 the slope eectcan be avoidedWhen laterally loaded pile is closer tothe slope crest the inuence of the slope angle seemsmore dominant

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

ndash01 00 01 02 03 04 05 06 07 08 09 10 11

900

1000

1100

1200

1300

1400

1500

1600

Max

imum

ben

ding

mom

ent

Mm

ax (k

Nmiddotm

)

Adhesion coefficient α

Figure 22 Maximum bending moment (Mmax) variation withadhesion coecentcient (α) for dierent slope angle

0 20 40 60 80 100 1200

50100150200250300350400450500550600

Late

ral d

ispla

cem

ent y 0

(mm

)

Undrained shear strength cu (kPa)

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 23 Pile head deection (y0) variation with undrained shearstrength (cu) for dierent slope angle

0 20 40 60 80 100 1200

300

600

900

1200

1500

1800

2100M

axim

umbe

ndin

gmom

ent M

max

(kN

middotm)

Undrained shear strength cu (kPa)

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 24 Maximum bending moment (Mmax) variation withundrained shear strength (cu) for dierent slope angle

Advances in Civil Engineering 11

(4) -e adhesion coefficient α at the pile-soil interfacecan effectively reduce the pile head deflection and themaximum bending moment of the pile at the sametime -e increase in slope angle will significantlyincrease the pile head deflection and maximumbending moment of the pile especially when theslope angle exceeds 40deg

(5) -e increase in undrained shear strength cu de-creases the pile head deflection and the maximumbending moment of the pile -is is because of theincrease in the strength of soil and the relativestiffness of the pile-soil system Also the presence ofslopes aggravates the rate of change of pile headdeflection especially when the cu is in a mall value(ranges from 20 kPa to 40 kPa) In contrast themaximum bending moment variation with un-drained shear strength affected by the slope effectappears more moderate

(6) -is study researches the lateral bearing behavior ofsingle pile in undrained clay sloping ground Inpractical projects the situation of pile foundationson slope ground surface is not uncommon and thelateral bearing characteristics of pile foundationsare more complicated -erefore the influence ofslope effect on the lateral bearing capacity of pilewhich is on slope ground surface is worth furtherstudy

Data Availability

-e original data for summary of pile load test in Table 1 arefrom Wu et al [28] Georgiadis and Georgiadis [17] andGeorgiadis and Georgiadis [18] respectively -e computedpile responses as shown in Figure 6 are compared to the piletest results (Wu et al [28]) and to the pile responsescomputed with the same computer code using as input theMatlock [2] Reese and Welch [5] Bhushan et al [26]Stevens and Audibert [27] Figures 7 and 8 are calculated bycomputer code MATLAB to compare previous studies(Georgiadis and Georgiadis [17] Georgiadis and Georgiadis[18] respectively) Figures 9ndash24 are calculated by the pro-posedmethod based on the original data mentioned above tostudy parametric analysis In addition all the sharing datawere involved in this paper and there was no redundantdata

Conflicts of Interest

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

Acknowledgments

-is work is supported by the National Natural ScienceFoundation of China (grant nos 51478479 and 51678570)and Hunan Transport Technology Project (grant no201524)

References

[1] N Nimityongskul Y Kawamata D Rayamajhi andS A Ashford ldquoFull-scale tests on effects of slope on lateralcapacity of piles installed in cohesive soilsrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 144 no 1article 04017103 2018

[2] H Matlock ldquoCorrelation for design of laterally loaded piles insoft clayrdquo in Proceedings of the Offshore Technology Confer-ence pp 77ndash94 Houston TX USA April 1970

[3] L C Reese ldquoAnalysis of laterally loaded piles in sandrdquo inProceedings of the Offshore Technical Conference pp 95ndash105Houston TX USA May 1974

[4] L Reese W Cox and F Koop ldquoField testing and analysis oflaterally loaded piles on stiff clayrdquo in Proceedings of theOffshore Technology in Civil Engineering pp 106ndash125 DallasTX USA May 1975

[5] L C Reese and R C Welch ldquoLateral loading of deepfoundations in stiff clayrdquo Journal of Geotechnical and Geo-environmental Engineering vol 101 no 7 pp 633ndash649 1975

[6] M A Gabr T Lunne and J J Powell ldquoP-y analysis of laterallyloaded piles in clay using DMTrdquo Journal of GeotechnicalEngineering vol 120 no 5 pp 816ndash837 1994

[7] C C Fan and J H Long ldquoAssessment of existing methods forpredicting soil response of laterally loaded piles in sandrdquoComputers and Geotechnics vol 32 no 4 pp 274ndash289 2005

[8] G P Yang and Z M Zhang ldquoResearch on P-Y curve oflaterally bearing piles under large displacementrdquo WaterTransportation Engineering vol 342 no 7 pp 40ndash45 2002

[9] C Wang and Z A LU ldquoCalculation of internal forces oflaterally loaded piles by using p-y curverdquo Journal ofChongqing Jiaotong University (Natural Science) vol 4 no 1pp 61ndash65 1958

[10] H C Wang and D Q WU ldquoA new unified approach to thep-y curve of laterally loaded pile in clayrdquo Journal of HohaiUniversity no 1 pp 9ndash17 1991

[11] G C Wang and M Yang ldquoNonlinear analysis of laterallyloaded piles in sandrdquo Rock and Soil Mechanics no 2pp 261ndash267 2011

[12] G CWang andM Yang ldquoCalculation of laterally loaded pilesin clayrdquo Journal of Tongji University (Natural Science) vol 40no 3 pp 373ndash378 2012

[13] T Q Zhou Z A LU and D H Wang ldquoCalculation methodof laterally loaded super-long PHC pilerdquo Port and WaterwayEngineering no 6 pp 155ndash160 2013

[14] L U Cheng X C Xu S X Chen et al ldquoModel test andnumerical simulation of horizontal bearing capacity andimpact factors for foundation piles in sloperdquo Rock and SoilMechanics no 9 pp 2685ndash2691 2014

[15] P YinB H ZhaoM H Zhao et al ldquoStability analysis of pile-column bridge pile considering slope effectrdquo Journal of Hu-nan University (Natural Science) vol 43 no 11 pp 20ndash252016

[16] Y S Deng M H Zhao X J Zhou et al ldquoResearch progress ofbearing characteristics of pile column at steep slope inmountain areasrdquo Journal of Highway and TransportationResearch and Development vol 29 no 6 pp 37ndash45 2012

[17] K Georgiadis and M Georgiadis ldquoUndrained lateral pileresponse in sloping groundrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 136 no 11 pp 1489ndash1500 2010

[18] K Georgiadis and M Georgiadis ldquoDevelopment of p-ycurves for undrained response of piles near slopesrdquo Com-puters and Geotechnics vol 40 no 3 pp 53ndash61 2012

12 Advances in Civil Engineering

[19] K Muthukkumaran R Sundaravadivelu and S R GandhildquoEffect of slope on p-y curves due to surcharge loadrdquo Soils andFoundations vol 48 no 3 pp 353ndash361 2008

[20] L M Zhang C W W Ng and C J Lee ldquoEffects of slope andsleeving on the behavior of laterally loaded pilesrdquo Soils andFoundations vol 44 no 4 pp 99ndash108 2008

[21] B P Yin M H Zhao W He et al ldquoModel test study onidentification of foundation proportional coefficient m inslope groundrdquo Journal of Hunan University (Natural Science)vol 44 no 9 2017

[22] B L Gao C R Zhang and Z X Zhang ldquoModel tests on effectof slopes on lateral resistance of near single piles in sandrdquoRock and Soil Mechanics vol 35 no 11 pp 3191ndash3198 2014

[23] B T Zhu Be Ultimate Resistance and Laterally Loaded PileBehaviors Tongji University School of Civil EngineeringShanghai China 2005

[24] S S Rajashree and T G Sitharam ldquoNonlinear finite-elementmodeling of batter piles under lateral loadrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 127 no 7pp 604ndash612 2001

[25] R L Kondner ldquoHyperbolic stress-strain response cohesivesoilsrdquo Journal of the Soil Mechanics and Foundations Divisionvol 89 no 1 pp 115ndash143 1963

[26] K Bhushan S C Haley and P T Fong ldquoLateral load tests ondrilled piers in stiff claysrdquo Journal of the Geotechnical Engi-neering Division vol 1058 pp 969ndash985 1979

[27] J B Stevens and J M E Audibert ldquoRe-examination of P-Ycurve formulationsrdquo in Proceedings of 11th Offshore Tech-nology Conference pp 397ndash403 Houston TX USA 1980

[28] D Wu B B Broms and V Choa ldquoDesign of laterally loadedpiles in cohesive soils using p-y curvesrdquo Soils and Founda-tions vol 38 no 2 pp 17ndash26 1998

Advances in Civil Engineering 13

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Submit your manuscripts atwwwhindawicom

Figures 12 and 13 show the bending moment distributionwith depth and the depth of xity (where the maximumbending moment occurs) of the pile for all slope angles witha lateral load at 300 kN and 600 kN respectively It is clear thatthe maximum bending moment of the pile increases with theincrease of slope angle at the same load but the rst zerolocation of bendingmoment curve and depth of xity increasecorrespondingly With the increase of the load the dierencein the maximum bending moment growth at each slope anglebecomes obvious and the rst zero location of bendingmoment curve and depth of xity of the pile also increasemore quickly For example as is shown in Figure 13 the depthof xity for 30deg and 50deg slope angle increased by 446 1734compared with that in horizontal ground at the load of300 kN respectively but the ratio further increases to 11323203 respectively when the load increases to 600 kN It canalso be seen from Figure 13 that the depth of pile xity almostoccurs at a depth of 4sim8D (D diameter of pile)

82 Eect of Normalized Distance of Pile BD Selecting thenormalized distance of pile BD as 05 2 4 6 and considerthe slope angle of 10deg 30deg 50deg respectively as the existingslope conditions e other calculation parameters are thesame as in Section 81

Figures 14ndash16 show the load-deection curve for dif-ferent normalized distance BD of pile head at above threeslope conditions From these gures it is observed that theincrease in normalized distance BD ratio decreases thedeection of pile head When normalized distance BDratio exceeds 6 in all slope angle conditions the deectionat pile head is basically the same as that in horizontalground which means the inuence of the slope eect isalmost negligible in this case It is also observed that theload-deection curves in dierent slope angle conditionshave dierent response results and the increase in slopeangle can increase the discreteness of the curves Figure 17further shows the eect of normalized distance of pile on

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3500

3000

2500

2000

1500

1000

500

0

max

M (k

Nmiddotm

)

0 200 400 600 800 1000H0 (kN)

0

120

240

360

480

600

720

840

y 0 (m

m)

(a)

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3500

3000

2500

2000

1500

1000

500

0

max

M (k

Nmiddotm

)

0

100

200

300

400

500

600

700

y 0 (m

m)

0 200 400 600 800 1000H0 (kN)

(b)

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3000

2500

2000

1500

1000

500

0

max

M (k

Nmiddotm

)

0 200 400 600 800 1000H0 (kN)

0

90

180

270

360

450

540

y 0 (m

m)

(c)

Present studyLPILE (Georgiadis and Georgiadis [18])Present studyLPILE (Georgiadis and Georgiadis [18])

3000

2500

2000

1500

1000

500

0m

ax M

(kN

middotm)

0 200 400 600 800 1000H0 (kN)

0

80

160

240

320

400

480

y 0 (m

m)

(d)

Figure 8 Verication analysis of H0-y0 curves relationship for LPILE (a) B 03m (b) B 06m (c) B 12m (d) B 24m

Advances in Civil Engineering 7

lateral-load capacity on horizontal ground and slopingground (θ 10deg 30deg 50deg) It can be seen that when thenormalized distance BD of pile changes from 05 to 6 thelateral-load capacity is increased by 227 111 2987on 10deg 30deg 50deg sloping ground respectively indicating thatthe increase in slope angle increases the inuence of BD onthe lateral-load capacity of the pile

Figures 18ndash20 show the bending moment variationalong pile length of the pile for dierent normalized dis-tance BD on horizontal ground and sloping ground(θ 10deg 30deg 50deg) From these gures it is observed that themaximum bending moment increases with the increase inthe normalized distance BD of the pile and the increase inthe applied lateral load Also for the same normalized

distance BD of pile and applied lateral load the increase inslope angle of θ increases the maximum bending momentof pile When ground surface changes from horizontal to10deg 30deg and 50deg sloping ground the maximum bendingmoment of pile in sloping ground is increased by 28126 and 319 respectively under lateral load of 600 kNand normalized distance BD of 05 It is also noted thatwhen the pile is nearer to slope crest the slope angle be-comes a more dominant factor to aect the lateral capacityof the pile especially at a high-load level

0 100 200 300 400 500 600 700 80010

15

20

25

30

Nor

mal

ized

disp

lace

men

t y o

Sy o

H

Lateral load H0 (kN)

θ = 0deg (B = 05D)θ = 10deg (B = 05D)θ = 20deg (B = 05D)

θ = 30deg (B = 05D)θ = 40deg (B = 05D)θ = 50deg (B = 05D)

Figure 10 Normalized deection (y0sy0H)-load (H0) curves fordierent slope angle

ndash200 0 200 400 600 800 1000 1200 1400 1600 18000123456789

101112131415

Dep

th (m

)

Bending moment M (kNmiddotm)

θ = 0deg H0 = 300kNθ = 0deg H0 = 600kNθ = 10deg H0 = 300kNθ = 10deg H0 = 600kNθ = 20deg H0 = 300kNθ = 20deg H0 = 600kN

θ = 30deg H0 = 300kNθ = 30deg H0 = 600kNθ = 40deg H0 = 300kNθ = 40deg H0 = 600kNθ = 50deg H0 = 300kNθ = 50deg H0 = 600kN

Figure 12 Bending moment variation along the depth of pile fordierent slope angle

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Deflection y0 (mm)

θ = 0deg (B = 05D)θ = 10deg (B = 05D)θ = 20deg (B = 05D)

θ = 30deg (B = 05D)θ = 40deg (B = 05D)θ = 50deg (B = 05D)

Figure 9 Lateral load-deection curves for dierent slope angle atpile head

0 400 800 1200 1600 2000 24000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Maximum bending moment Mmax (kNmiddotm)

θ = 0deg (B = 05D)θ = 10deg (B = 05D)θ = 20deg (B = 05D)

θ = 30deg (B = 05D)θ = 40deg (B = 05D)θ = 50deg (B = 05D)

Figure 11 Maximum bending moment-load curves for dierentslope angle

8 Advances in Civil Engineering

83 Eect of Adhesion Coecient α In order to study theeect of adhesion coecentcient α on the lateral behavior of pile insloped ground this paper analyzes the parameter α from 0 to1 with increment of 01 and chooses lateral loadH0 500 kNand the bending momentM0 0 (kNmiddotm) as the xed loadingcondition to calculate and analyze the deection of pile headConsider the slope angle θ as the same in Section 81 andother basic calculation parameters are the same as Section 81

Figures 21 and 22 show pile head deection (y0) and themaximum bending moment (Mmax) of the pile variation withthe adhesion coecentcient α for dierent slope angle re-spectively From these gures it can be seen that increasingthe adhesion coecentcient α at the pile-soil interface can ef-fectively reduce the pile head deection and the maximumbending moment of the pile at the same time Also the in-crease in slope angle almost does not change the corre-sponding curve growth model but will signicantly increase

0 20 40 60 80 100 120 140 160 180 200 220 2400

100

200

300

400

500

600

700

800

Lateral displacement y0 (mm)

BD = 05 (θ = 10deg)BD = 2 (θ = 10deg)

BD = 4 (θ = 10deg)BD = 6 (θ = 10deg)

Late

ral l

oad

H0

(kN

)

Figure 14 Lateral load-deection curves for θ 10deg for dierentnormalized distance of pile at pile head

0 1 2 3 4 5 6

560

580

600

620

640

660

680

700

720

740A

llow

able

pile

capa

city

(kN

)

Normalized distance BD

Level ground (θ = 0deg)θ = 10deg

θ = 30degθ = 50deg

Figure 17 Bearing capacity of pile head for dierent normalizeddistance of pile (corresponding to 200mm)

247

122

247

123

247

126

258

142

274

059

289

9763

6058

3

367

113

376

092

401

397

428

333

476

085

θ = 50degθ = 40degθ = 30degθ = 20degθ = 10deg

H0 = 300kNH0 = 600kN

θ = 0deg00

05

10

15

20

25

30

35

40

45

50

55

Dep

th o

f fix

ity (m

)

Figure 13 Depth of xity variation with dierent slope angle

B = 05D (θ = 30deg)B = 2D (θ = 30deg)

B = 4D (θ = 30deg)B = 6D (θ = 30deg)

0 30 60 90 120 150 180 210 240 270 3000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Lateral displacement y0 (mm)

Figure 15 Lateral load-deection curves for θ 30deg for dierentnormalized distance of pile at pile head

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Lateral displacement y0 (mm)

BD = 05 (θ = 50deg)BD = 2 (θ = 50deg)

BD = 4 (θ = 50deg)BD = 6 (θ = 50deg)

Figure 16 Lateral load-deection curves for θ 50deg for dierentnormalized distance of pile at pile head

Advances in Civil Engineering 9

the pile head deection and maximum bending moment ofthe pile especially when the slope angle exceeds 40deg An ex-ample is used for pile head deection when the value of α isequal to 0 the pile head deection values of pile in slopingground with θ 10deg 30deg 50deg is increased by 74 398137 respectively compared to that in horizontal ground

84 Eect of Undrained Shear Strength cu Here lateral loadH0 500 kN and the initial bending momentM0 0 (kNmiddotm)

were taken as the initial loading conditions choosing un-drained shear strengths cu of 20 kPa 40 kPa 60 80 kPa100 kPa respectively to calculate and analyze Other basiccalculation parameters are the same as in Section 81

Figures 23 and 24 show pile head deection (y0) and themaximum bending moment (Mmax) of the pile variationwith the undrained shear strength cu for dierent slopeangles respectively From the curves given in Figures 23 and24 it is observed that the increase in undrained shearstrength cu decreases the pile head deection and themaximum bending moment is is because of the increasein the strength of soil and the relative stiness of the pile-soilsystem Also it is obvious that the presence of slopes

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

ndash200 0 200 400 600 800 1000 1200 1400 16000123456789

1011121314

Dep

th (m

)

Bending moment M (kNmiddotm)

Figure 19 Bending moment variation along the depth of pile forθ 30deg for dierent slope angle

ndash200 0 200 400 600 800 1000 1200 14000123456789

1011121314

Dep

th (m

)

Bending moment M (kNmiddotm)

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

Figure 18 Bending moment variation along the depth of pile forθ 10deg for dierent slope angle

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

ndash200 0 200 400 600 800 1000 1200 1400 1600 18000123456789

1011121314

Dpe

th (m

)

Bending moment M (kNmiddotm)

Figure 20 Bending moment variation along the depth of pile forθ 50deg for dierent slope angle

ndash01 00 01 02 03 04 05 06 07 08 09 10 116080

100120140160180200220240260

Late

rald

ispla

cem

ent y 0

(mm

)

Adhesion coefficient α

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 21 Pile head deection (y0) variation with adhesion co-ecentcient (α) for dierent slope angle

10 Advances in Civil Engineering

aggravates the rate of change of pile head deection es-pecially when cu ranges from 20 kPa to 40 kPa and when thevalue of cu exceeds 40 kPa the decrease rate of the deectionof pile head becomes slow and eventually almost becomesat From the results in Figure 23 it is observed that the pilehead deection in the range of 734ndash75 for increase in cu20 kPa to 40 kPa of sloping ground (θ 10deg 20deg 30deg 40deg 50deg)and horizontal ground surfaces from which can concludethat the weaker soil parameters are the more signicantslope eect becomes Besides the curve of the maximumbending moment variation with undrained shear strengthshown in Figure 24 is smoother and the range of themaximum bending moment of the pile with the increase ofthe slope is relatively stable

9 Conclusions

e purpose of this paper is to study the behavior of laterallyloaded long-exible pile in undrained clay sloping groundBased on the basic model of ideal elastic-plastic p-y curvemethod this paper derives the dierential equations of thelaterally loaded single pile in undrained clay sloped groundby introducing the existing related reduction variablefunction and the corresponding nite dierence method forthe pile deection and internal force is obtained A series ofparameters analyses are further performed for slope anglenormalized distance of pile adhesion coecentcient and un-drained shear strength e conclusions obtained from thisstudy are summarized as follows

(1) A nonlinear analysis method for laterally loaded long-exible pile in undrained clay sloped ground isestablished rough the verication of examples thecorrectness and feasibility of the method is proved

(2) Slope angle is the most important factor that aectingthe lateral bearing capacity of the near-slope pile eincrease in slope angle increases the deection and the

rate of increase of deection and this trend becomesmore obvious as the lateral load increased When theslope angle is small enough (θ lt 10o) the eect ofslope is almost negligible Besides the depth of xityof the pile is about 4sim8 times the size of the pilediameter

(3) e distance away from pile to slope crest is also animportant factor that aects the lateral-load capacityof the pile e increase in normalized distance BDof the pile decreases the deection of pile head butincreases the lateral-load capacity and when nor-malized distance BD ratio exceeds 6 the slope eectcan be avoidedWhen laterally loaded pile is closer tothe slope crest the inuence of the slope angle seemsmore dominant

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

ndash01 00 01 02 03 04 05 06 07 08 09 10 11

900

1000

1100

1200

1300

1400

1500

1600

Max

imum

ben

ding

mom

ent

Mm

ax (k

Nmiddotm

)

Adhesion coefficient α

Figure 22 Maximum bending moment (Mmax) variation withadhesion coecentcient (α) for dierent slope angle

0 20 40 60 80 100 1200

50100150200250300350400450500550600

Late

ral d

ispla

cem

ent y 0

(mm

)

Undrained shear strength cu (kPa)

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 23 Pile head deection (y0) variation with undrained shearstrength (cu) for dierent slope angle

0 20 40 60 80 100 1200

300

600

900

1200

1500

1800

2100M

axim

umbe

ndin

gmom

ent M

max

(kN

middotm)

Undrained shear strength cu (kPa)

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 24 Maximum bending moment (Mmax) variation withundrained shear strength (cu) for dierent slope angle

Advances in Civil Engineering 11

(4) -e adhesion coefficient α at the pile-soil interfacecan effectively reduce the pile head deflection and themaximum bending moment of the pile at the sametime -e increase in slope angle will significantlyincrease the pile head deflection and maximumbending moment of the pile especially when theslope angle exceeds 40deg

(5) -e increase in undrained shear strength cu de-creases the pile head deflection and the maximumbending moment of the pile -is is because of theincrease in the strength of soil and the relativestiffness of the pile-soil system Also the presence ofslopes aggravates the rate of change of pile headdeflection especially when the cu is in a mall value(ranges from 20 kPa to 40 kPa) In contrast themaximum bending moment variation with un-drained shear strength affected by the slope effectappears more moderate

(6) -is study researches the lateral bearing behavior ofsingle pile in undrained clay sloping ground Inpractical projects the situation of pile foundationson slope ground surface is not uncommon and thelateral bearing characteristics of pile foundationsare more complicated -erefore the influence ofslope effect on the lateral bearing capacity of pilewhich is on slope ground surface is worth furtherstudy

Data Availability

-e original data for summary of pile load test in Table 1 arefrom Wu et al [28] Georgiadis and Georgiadis [17] andGeorgiadis and Georgiadis [18] respectively -e computedpile responses as shown in Figure 6 are compared to the piletest results (Wu et al [28]) and to the pile responsescomputed with the same computer code using as input theMatlock [2] Reese and Welch [5] Bhushan et al [26]Stevens and Audibert [27] Figures 7 and 8 are calculated bycomputer code MATLAB to compare previous studies(Georgiadis and Georgiadis [17] Georgiadis and Georgiadis[18] respectively) Figures 9ndash24 are calculated by the pro-posedmethod based on the original data mentioned above tostudy parametric analysis In addition all the sharing datawere involved in this paper and there was no redundantdata

Conflicts of Interest

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

Acknowledgments

-is work is supported by the National Natural ScienceFoundation of China (grant nos 51478479 and 51678570)and Hunan Transport Technology Project (grant no201524)

References

[1] N Nimityongskul Y Kawamata D Rayamajhi andS A Ashford ldquoFull-scale tests on effects of slope on lateralcapacity of piles installed in cohesive soilsrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 144 no 1article 04017103 2018

[2] H Matlock ldquoCorrelation for design of laterally loaded piles insoft clayrdquo in Proceedings of the Offshore Technology Confer-ence pp 77ndash94 Houston TX USA April 1970

[3] L C Reese ldquoAnalysis of laterally loaded piles in sandrdquo inProceedings of the Offshore Technical Conference pp 95ndash105Houston TX USA May 1974

[4] L Reese W Cox and F Koop ldquoField testing and analysis oflaterally loaded piles on stiff clayrdquo in Proceedings of theOffshore Technology in Civil Engineering pp 106ndash125 DallasTX USA May 1975

[5] L C Reese and R C Welch ldquoLateral loading of deepfoundations in stiff clayrdquo Journal of Geotechnical and Geo-environmental Engineering vol 101 no 7 pp 633ndash649 1975

[6] M A Gabr T Lunne and J J Powell ldquoP-y analysis of laterallyloaded piles in clay using DMTrdquo Journal of GeotechnicalEngineering vol 120 no 5 pp 816ndash837 1994

[7] C C Fan and J H Long ldquoAssessment of existing methods forpredicting soil response of laterally loaded piles in sandrdquoComputers and Geotechnics vol 32 no 4 pp 274ndash289 2005

[8] G P Yang and Z M Zhang ldquoResearch on P-Y curve oflaterally bearing piles under large displacementrdquo WaterTransportation Engineering vol 342 no 7 pp 40ndash45 2002

[9] C Wang and Z A LU ldquoCalculation of internal forces oflaterally loaded piles by using p-y curverdquo Journal ofChongqing Jiaotong University (Natural Science) vol 4 no 1pp 61ndash65 1958

[10] H C Wang and D Q WU ldquoA new unified approach to thep-y curve of laterally loaded pile in clayrdquo Journal of HohaiUniversity no 1 pp 9ndash17 1991

[11] G C Wang and M Yang ldquoNonlinear analysis of laterallyloaded piles in sandrdquo Rock and Soil Mechanics no 2pp 261ndash267 2011

[12] G CWang andM Yang ldquoCalculation of laterally loaded pilesin clayrdquo Journal of Tongji University (Natural Science) vol 40no 3 pp 373ndash378 2012

[13] T Q Zhou Z A LU and D H Wang ldquoCalculation methodof laterally loaded super-long PHC pilerdquo Port and WaterwayEngineering no 6 pp 155ndash160 2013

[14] L U Cheng X C Xu S X Chen et al ldquoModel test andnumerical simulation of horizontal bearing capacity andimpact factors for foundation piles in sloperdquo Rock and SoilMechanics no 9 pp 2685ndash2691 2014

[15] P YinB H ZhaoM H Zhao et al ldquoStability analysis of pile-column bridge pile considering slope effectrdquo Journal of Hu-nan University (Natural Science) vol 43 no 11 pp 20ndash252016

[16] Y S Deng M H Zhao X J Zhou et al ldquoResearch progress ofbearing characteristics of pile column at steep slope inmountain areasrdquo Journal of Highway and TransportationResearch and Development vol 29 no 6 pp 37ndash45 2012

[17] K Georgiadis and M Georgiadis ldquoUndrained lateral pileresponse in sloping groundrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 136 no 11 pp 1489ndash1500 2010

[18] K Georgiadis and M Georgiadis ldquoDevelopment of p-ycurves for undrained response of piles near slopesrdquo Com-puters and Geotechnics vol 40 no 3 pp 53ndash61 2012

12 Advances in Civil Engineering

[19] K Muthukkumaran R Sundaravadivelu and S R GandhildquoEffect of slope on p-y curves due to surcharge loadrdquo Soils andFoundations vol 48 no 3 pp 353ndash361 2008

[20] L M Zhang C W W Ng and C J Lee ldquoEffects of slope andsleeving on the behavior of laterally loaded pilesrdquo Soils andFoundations vol 44 no 4 pp 99ndash108 2008

[21] B P Yin M H Zhao W He et al ldquoModel test study onidentification of foundation proportional coefficient m inslope groundrdquo Journal of Hunan University (Natural Science)vol 44 no 9 2017

[22] B L Gao C R Zhang and Z X Zhang ldquoModel tests on effectof slopes on lateral resistance of near single piles in sandrdquoRock and Soil Mechanics vol 35 no 11 pp 3191ndash3198 2014

[23] B T Zhu Be Ultimate Resistance and Laterally Loaded PileBehaviors Tongji University School of Civil EngineeringShanghai China 2005

[24] S S Rajashree and T G Sitharam ldquoNonlinear finite-elementmodeling of batter piles under lateral loadrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 127 no 7pp 604ndash612 2001

[25] R L Kondner ldquoHyperbolic stress-strain response cohesivesoilsrdquo Journal of the Soil Mechanics and Foundations Divisionvol 89 no 1 pp 115ndash143 1963

[26] K Bhushan S C Haley and P T Fong ldquoLateral load tests ondrilled piers in stiff claysrdquo Journal of the Geotechnical Engi-neering Division vol 1058 pp 969ndash985 1979

[27] J B Stevens and J M E Audibert ldquoRe-examination of P-Ycurve formulationsrdquo in Proceedings of 11th Offshore Tech-nology Conference pp 397ndash403 Houston TX USA 1980

[28] D Wu B B Broms and V Choa ldquoDesign of laterally loadedpiles in cohesive soils using p-y curvesrdquo Soils and Founda-tions vol 38 no 2 pp 17ndash26 1998

Advances in Civil Engineering 13

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

lateral-load capacity on horizontal ground and slopingground (θ 10deg 30deg 50deg) It can be seen that when thenormalized distance BD of pile changes from 05 to 6 thelateral-load capacity is increased by 227 111 2987on 10deg 30deg 50deg sloping ground respectively indicating thatthe increase in slope angle increases the inuence of BD onthe lateral-load capacity of the pile

Figures 18ndash20 show the bending moment variationalong pile length of the pile for dierent normalized dis-tance BD on horizontal ground and sloping ground(θ 10deg 30deg 50deg) From these gures it is observed that themaximum bending moment increases with the increase inthe normalized distance BD of the pile and the increase inthe applied lateral load Also for the same normalized

distance BD of pile and applied lateral load the increase inslope angle of θ increases the maximum bending momentof pile When ground surface changes from horizontal to10deg 30deg and 50deg sloping ground the maximum bendingmoment of pile in sloping ground is increased by 28126 and 319 respectively under lateral load of 600 kNand normalized distance BD of 05 It is also noted thatwhen the pile is nearer to slope crest the slope angle be-comes a more dominant factor to aect the lateral capacityof the pile especially at a high-load level

0 100 200 300 400 500 600 700 80010

15

20

25

30

Nor

mal

ized

disp

lace

men

t y o

Sy o

H

Lateral load H0 (kN)

θ = 0deg (B = 05D)θ = 10deg (B = 05D)θ = 20deg (B = 05D)

θ = 30deg (B = 05D)θ = 40deg (B = 05D)θ = 50deg (B = 05D)

Figure 10 Normalized deection (y0sy0H)-load (H0) curves fordierent slope angle

ndash200 0 200 400 600 800 1000 1200 1400 1600 18000123456789

101112131415

Dep

th (m

)

Bending moment M (kNmiddotm)

θ = 0deg H0 = 300kNθ = 0deg H0 = 600kNθ = 10deg H0 = 300kNθ = 10deg H0 = 600kNθ = 20deg H0 = 300kNθ = 20deg H0 = 600kN

θ = 30deg H0 = 300kNθ = 30deg H0 = 600kNθ = 40deg H0 = 300kNθ = 40deg H0 = 600kNθ = 50deg H0 = 300kNθ = 50deg H0 = 600kN

Figure 12 Bending moment variation along the depth of pile fordierent slope angle

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Deflection y0 (mm)

θ = 0deg (B = 05D)θ = 10deg (B = 05D)θ = 20deg (B = 05D)

θ = 30deg (B = 05D)θ = 40deg (B = 05D)θ = 50deg (B = 05D)

Figure 9 Lateral load-deection curves for dierent slope angle atpile head

0 400 800 1200 1600 2000 24000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Maximum bending moment Mmax (kNmiddotm)

θ = 0deg (B = 05D)θ = 10deg (B = 05D)θ = 20deg (B = 05D)

θ = 30deg (B = 05D)θ = 40deg (B = 05D)θ = 50deg (B = 05D)

Figure 11 Maximum bending moment-load curves for dierentslope angle

8 Advances in Civil Engineering

83 Eect of Adhesion Coecient α In order to study theeect of adhesion coecentcient α on the lateral behavior of pile insloped ground this paper analyzes the parameter α from 0 to1 with increment of 01 and chooses lateral loadH0 500 kNand the bending momentM0 0 (kNmiddotm) as the xed loadingcondition to calculate and analyze the deection of pile headConsider the slope angle θ as the same in Section 81 andother basic calculation parameters are the same as Section 81

Figures 21 and 22 show pile head deection (y0) and themaximum bending moment (Mmax) of the pile variation withthe adhesion coecentcient α for dierent slope angle re-spectively From these gures it can be seen that increasingthe adhesion coecentcient α at the pile-soil interface can ef-fectively reduce the pile head deection and the maximumbending moment of the pile at the same time Also the in-crease in slope angle almost does not change the corre-sponding curve growth model but will signicantly increase

0 20 40 60 80 100 120 140 160 180 200 220 2400

100

200

300

400

500

600

700

800

Lateral displacement y0 (mm)

BD = 05 (θ = 10deg)BD = 2 (θ = 10deg)

BD = 4 (θ = 10deg)BD = 6 (θ = 10deg)

Late

ral l

oad

H0

(kN

)

Figure 14 Lateral load-deection curves for θ 10deg for dierentnormalized distance of pile at pile head

0 1 2 3 4 5 6

560

580

600

620

640

660

680

700

720

740A

llow

able

pile

capa

city

(kN

)

Normalized distance BD

Level ground (θ = 0deg)θ = 10deg

θ = 30degθ = 50deg

Figure 17 Bearing capacity of pile head for dierent normalizeddistance of pile (corresponding to 200mm)

247

122

247

123

247

126

258

142

274

059

289

9763

6058

3

367

113

376

092

401

397

428

333

476

085

θ = 50degθ = 40degθ = 30degθ = 20degθ = 10deg

H0 = 300kNH0 = 600kN

θ = 0deg00

05

10

15

20

25

30

35

40

45

50

55

Dep

th o

f fix

ity (m

)

Figure 13 Depth of xity variation with dierent slope angle

B = 05D (θ = 30deg)B = 2D (θ = 30deg)

B = 4D (θ = 30deg)B = 6D (θ = 30deg)

0 30 60 90 120 150 180 210 240 270 3000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Lateral displacement y0 (mm)

Figure 15 Lateral load-deection curves for θ 30deg for dierentnormalized distance of pile at pile head

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Lateral displacement y0 (mm)

BD = 05 (θ = 50deg)BD = 2 (θ = 50deg)

BD = 4 (θ = 50deg)BD = 6 (θ = 50deg)

Figure 16 Lateral load-deection curves for θ 50deg for dierentnormalized distance of pile at pile head

Advances in Civil Engineering 9

the pile head deection and maximum bending moment ofthe pile especially when the slope angle exceeds 40deg An ex-ample is used for pile head deection when the value of α isequal to 0 the pile head deection values of pile in slopingground with θ 10deg 30deg 50deg is increased by 74 398137 respectively compared to that in horizontal ground

84 Eect of Undrained Shear Strength cu Here lateral loadH0 500 kN and the initial bending momentM0 0 (kNmiddotm)

were taken as the initial loading conditions choosing un-drained shear strengths cu of 20 kPa 40 kPa 60 80 kPa100 kPa respectively to calculate and analyze Other basiccalculation parameters are the same as in Section 81

Figures 23 and 24 show pile head deection (y0) and themaximum bending moment (Mmax) of the pile variationwith the undrained shear strength cu for dierent slopeangles respectively From the curves given in Figures 23 and24 it is observed that the increase in undrained shearstrength cu decreases the pile head deection and themaximum bending moment is is because of the increasein the strength of soil and the relative stiness of the pile-soilsystem Also it is obvious that the presence of slopes

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

ndash200 0 200 400 600 800 1000 1200 1400 16000123456789

1011121314

Dep

th (m

)

Bending moment M (kNmiddotm)

Figure 19 Bending moment variation along the depth of pile forθ 30deg for dierent slope angle

ndash200 0 200 400 600 800 1000 1200 14000123456789

1011121314

Dep

th (m

)

Bending moment M (kNmiddotm)

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

Figure 18 Bending moment variation along the depth of pile forθ 10deg for dierent slope angle

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

ndash200 0 200 400 600 800 1000 1200 1400 1600 18000123456789

1011121314

Dpe

th (m

)

Bending moment M (kNmiddotm)

Figure 20 Bending moment variation along the depth of pile forθ 50deg for dierent slope angle

ndash01 00 01 02 03 04 05 06 07 08 09 10 116080

100120140160180200220240260

Late

rald

ispla

cem

ent y 0

(mm

)

Adhesion coefficient α

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 21 Pile head deection (y0) variation with adhesion co-ecentcient (α) for dierent slope angle

10 Advances in Civil Engineering

aggravates the rate of change of pile head deection es-pecially when cu ranges from 20 kPa to 40 kPa and when thevalue of cu exceeds 40 kPa the decrease rate of the deectionof pile head becomes slow and eventually almost becomesat From the results in Figure 23 it is observed that the pilehead deection in the range of 734ndash75 for increase in cu20 kPa to 40 kPa of sloping ground (θ 10deg 20deg 30deg 40deg 50deg)and horizontal ground surfaces from which can concludethat the weaker soil parameters are the more signicantslope eect becomes Besides the curve of the maximumbending moment variation with undrained shear strengthshown in Figure 24 is smoother and the range of themaximum bending moment of the pile with the increase ofthe slope is relatively stable

9 Conclusions

e purpose of this paper is to study the behavior of laterallyloaded long-exible pile in undrained clay sloping groundBased on the basic model of ideal elastic-plastic p-y curvemethod this paper derives the dierential equations of thelaterally loaded single pile in undrained clay sloped groundby introducing the existing related reduction variablefunction and the corresponding nite dierence method forthe pile deection and internal force is obtained A series ofparameters analyses are further performed for slope anglenormalized distance of pile adhesion coecentcient and un-drained shear strength e conclusions obtained from thisstudy are summarized as follows

(1) A nonlinear analysis method for laterally loaded long-exible pile in undrained clay sloped ground isestablished rough the verication of examples thecorrectness and feasibility of the method is proved

(2) Slope angle is the most important factor that aectingthe lateral bearing capacity of the near-slope pile eincrease in slope angle increases the deection and the

rate of increase of deection and this trend becomesmore obvious as the lateral load increased When theslope angle is small enough (θ lt 10o) the eect ofslope is almost negligible Besides the depth of xityof the pile is about 4sim8 times the size of the pilediameter

(3) e distance away from pile to slope crest is also animportant factor that aects the lateral-load capacityof the pile e increase in normalized distance BDof the pile decreases the deection of pile head butincreases the lateral-load capacity and when nor-malized distance BD ratio exceeds 6 the slope eectcan be avoidedWhen laterally loaded pile is closer tothe slope crest the inuence of the slope angle seemsmore dominant

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

ndash01 00 01 02 03 04 05 06 07 08 09 10 11

900

1000

1100

1200

1300

1400

1500

1600

Max

imum

ben

ding

mom

ent

Mm

ax (k

Nmiddotm

)

Adhesion coefficient α

Figure 22 Maximum bending moment (Mmax) variation withadhesion coecentcient (α) for dierent slope angle

0 20 40 60 80 100 1200

50100150200250300350400450500550600

Late

ral d

ispla

cem

ent y 0

(mm

)

Undrained shear strength cu (kPa)

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 23 Pile head deection (y0) variation with undrained shearstrength (cu) for dierent slope angle

0 20 40 60 80 100 1200

300

600

900

1200

1500

1800

2100M

axim

umbe

ndin

gmom

ent M

max

(kN

middotm)

Undrained shear strength cu (kPa)

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 24 Maximum bending moment (Mmax) variation withundrained shear strength (cu) for dierent slope angle

Advances in Civil Engineering 11

(4) -e adhesion coefficient α at the pile-soil interfacecan effectively reduce the pile head deflection and themaximum bending moment of the pile at the sametime -e increase in slope angle will significantlyincrease the pile head deflection and maximumbending moment of the pile especially when theslope angle exceeds 40deg

(5) -e increase in undrained shear strength cu de-creases the pile head deflection and the maximumbending moment of the pile -is is because of theincrease in the strength of soil and the relativestiffness of the pile-soil system Also the presence ofslopes aggravates the rate of change of pile headdeflection especially when the cu is in a mall value(ranges from 20 kPa to 40 kPa) In contrast themaximum bending moment variation with un-drained shear strength affected by the slope effectappears more moderate

(6) -is study researches the lateral bearing behavior ofsingle pile in undrained clay sloping ground Inpractical projects the situation of pile foundationson slope ground surface is not uncommon and thelateral bearing characteristics of pile foundationsare more complicated -erefore the influence ofslope effect on the lateral bearing capacity of pilewhich is on slope ground surface is worth furtherstudy

Data Availability

-e original data for summary of pile load test in Table 1 arefrom Wu et al [28] Georgiadis and Georgiadis [17] andGeorgiadis and Georgiadis [18] respectively -e computedpile responses as shown in Figure 6 are compared to the piletest results (Wu et al [28]) and to the pile responsescomputed with the same computer code using as input theMatlock [2] Reese and Welch [5] Bhushan et al [26]Stevens and Audibert [27] Figures 7 and 8 are calculated bycomputer code MATLAB to compare previous studies(Georgiadis and Georgiadis [17] Georgiadis and Georgiadis[18] respectively) Figures 9ndash24 are calculated by the pro-posedmethod based on the original data mentioned above tostudy parametric analysis In addition all the sharing datawere involved in this paper and there was no redundantdata

Conflicts of Interest

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

Acknowledgments

-is work is supported by the National Natural ScienceFoundation of China (grant nos 51478479 and 51678570)and Hunan Transport Technology Project (grant no201524)

References

[1] N Nimityongskul Y Kawamata D Rayamajhi andS A Ashford ldquoFull-scale tests on effects of slope on lateralcapacity of piles installed in cohesive soilsrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 144 no 1article 04017103 2018

[2] H Matlock ldquoCorrelation for design of laterally loaded piles insoft clayrdquo in Proceedings of the Offshore Technology Confer-ence pp 77ndash94 Houston TX USA April 1970

[3] L C Reese ldquoAnalysis of laterally loaded piles in sandrdquo inProceedings of the Offshore Technical Conference pp 95ndash105Houston TX USA May 1974

[4] L Reese W Cox and F Koop ldquoField testing and analysis oflaterally loaded piles on stiff clayrdquo in Proceedings of theOffshore Technology in Civil Engineering pp 106ndash125 DallasTX USA May 1975

[5] L C Reese and R C Welch ldquoLateral loading of deepfoundations in stiff clayrdquo Journal of Geotechnical and Geo-environmental Engineering vol 101 no 7 pp 633ndash649 1975

[6] M A Gabr T Lunne and J J Powell ldquoP-y analysis of laterallyloaded piles in clay using DMTrdquo Journal of GeotechnicalEngineering vol 120 no 5 pp 816ndash837 1994

[7] C C Fan and J H Long ldquoAssessment of existing methods forpredicting soil response of laterally loaded piles in sandrdquoComputers and Geotechnics vol 32 no 4 pp 274ndash289 2005

[8] G P Yang and Z M Zhang ldquoResearch on P-Y curve oflaterally bearing piles under large displacementrdquo WaterTransportation Engineering vol 342 no 7 pp 40ndash45 2002

[9] C Wang and Z A LU ldquoCalculation of internal forces oflaterally loaded piles by using p-y curverdquo Journal ofChongqing Jiaotong University (Natural Science) vol 4 no 1pp 61ndash65 1958

[10] H C Wang and D Q WU ldquoA new unified approach to thep-y curve of laterally loaded pile in clayrdquo Journal of HohaiUniversity no 1 pp 9ndash17 1991

[11] G C Wang and M Yang ldquoNonlinear analysis of laterallyloaded piles in sandrdquo Rock and Soil Mechanics no 2pp 261ndash267 2011

[12] G CWang andM Yang ldquoCalculation of laterally loaded pilesin clayrdquo Journal of Tongji University (Natural Science) vol 40no 3 pp 373ndash378 2012

[13] T Q Zhou Z A LU and D H Wang ldquoCalculation methodof laterally loaded super-long PHC pilerdquo Port and WaterwayEngineering no 6 pp 155ndash160 2013

[14] L U Cheng X C Xu S X Chen et al ldquoModel test andnumerical simulation of horizontal bearing capacity andimpact factors for foundation piles in sloperdquo Rock and SoilMechanics no 9 pp 2685ndash2691 2014

[15] P YinB H ZhaoM H Zhao et al ldquoStability analysis of pile-column bridge pile considering slope effectrdquo Journal of Hu-nan University (Natural Science) vol 43 no 11 pp 20ndash252016

[16] Y S Deng M H Zhao X J Zhou et al ldquoResearch progress ofbearing characteristics of pile column at steep slope inmountain areasrdquo Journal of Highway and TransportationResearch and Development vol 29 no 6 pp 37ndash45 2012

[17] K Georgiadis and M Georgiadis ldquoUndrained lateral pileresponse in sloping groundrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 136 no 11 pp 1489ndash1500 2010

[18] K Georgiadis and M Georgiadis ldquoDevelopment of p-ycurves for undrained response of piles near slopesrdquo Com-puters and Geotechnics vol 40 no 3 pp 53ndash61 2012

12 Advances in Civil Engineering

[19] K Muthukkumaran R Sundaravadivelu and S R GandhildquoEffect of slope on p-y curves due to surcharge loadrdquo Soils andFoundations vol 48 no 3 pp 353ndash361 2008

[20] L M Zhang C W W Ng and C J Lee ldquoEffects of slope andsleeving on the behavior of laterally loaded pilesrdquo Soils andFoundations vol 44 no 4 pp 99ndash108 2008

[21] B P Yin M H Zhao W He et al ldquoModel test study onidentification of foundation proportional coefficient m inslope groundrdquo Journal of Hunan University (Natural Science)vol 44 no 9 2017

[22] B L Gao C R Zhang and Z X Zhang ldquoModel tests on effectof slopes on lateral resistance of near single piles in sandrdquoRock and Soil Mechanics vol 35 no 11 pp 3191ndash3198 2014

[23] B T Zhu Be Ultimate Resistance and Laterally Loaded PileBehaviors Tongji University School of Civil EngineeringShanghai China 2005

[24] S S Rajashree and T G Sitharam ldquoNonlinear finite-elementmodeling of batter piles under lateral loadrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 127 no 7pp 604ndash612 2001

[25] R L Kondner ldquoHyperbolic stress-strain response cohesivesoilsrdquo Journal of the Soil Mechanics and Foundations Divisionvol 89 no 1 pp 115ndash143 1963

[26] K Bhushan S C Haley and P T Fong ldquoLateral load tests ondrilled piers in stiff claysrdquo Journal of the Geotechnical Engi-neering Division vol 1058 pp 969ndash985 1979

[27] J B Stevens and J M E Audibert ldquoRe-examination of P-Ycurve formulationsrdquo in Proceedings of 11th Offshore Tech-nology Conference pp 397ndash403 Houston TX USA 1980

[28] D Wu B B Broms and V Choa ldquoDesign of laterally loadedpiles in cohesive soils using p-y curvesrdquo Soils and Founda-tions vol 38 no 2 pp 17ndash26 1998

Advances in Civil Engineering 13

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

83 Eect of Adhesion Coecient α In order to study theeect of adhesion coecentcient α on the lateral behavior of pile insloped ground this paper analyzes the parameter α from 0 to1 with increment of 01 and chooses lateral loadH0 500 kNand the bending momentM0 0 (kNmiddotm) as the xed loadingcondition to calculate and analyze the deection of pile headConsider the slope angle θ as the same in Section 81 andother basic calculation parameters are the same as Section 81

Figures 21 and 22 show pile head deection (y0) and themaximum bending moment (Mmax) of the pile variation withthe adhesion coecentcient α for dierent slope angle re-spectively From these gures it can be seen that increasingthe adhesion coecentcient α at the pile-soil interface can ef-fectively reduce the pile head deection and the maximumbending moment of the pile at the same time Also the in-crease in slope angle almost does not change the corre-sponding curve growth model but will signicantly increase

0 20 40 60 80 100 120 140 160 180 200 220 2400

100

200

300

400

500

600

700

800

Lateral displacement y0 (mm)

BD = 05 (θ = 10deg)BD = 2 (θ = 10deg)

BD = 4 (θ = 10deg)BD = 6 (θ = 10deg)

Late

ral l

oad

H0

(kN

)

Figure 14 Lateral load-deection curves for θ 10deg for dierentnormalized distance of pile at pile head

0 1 2 3 4 5 6

560

580

600

620

640

660

680

700

720

740A

llow

able

pile

capa

city

(kN

)

Normalized distance BD

Level ground (θ = 0deg)θ = 10deg

θ = 30degθ = 50deg

Figure 17 Bearing capacity of pile head for dierent normalizeddistance of pile (corresponding to 200mm)

247

122

247

123

247

126

258

142

274

059

289

9763

6058

3

367

113

376

092

401

397

428

333

476

085

θ = 50degθ = 40degθ = 30degθ = 20degθ = 10deg

H0 = 300kNH0 = 600kN

θ = 0deg00

05

10

15

20

25

30

35

40

45

50

55

Dep

th o

f fix

ity (m

)

Figure 13 Depth of xity variation with dierent slope angle

B = 05D (θ = 30deg)B = 2D (θ = 30deg)

B = 4D (θ = 30deg)B = 6D (θ = 30deg)

0 30 60 90 120 150 180 210 240 270 3000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Lateral displacement y0 (mm)

Figure 15 Lateral load-deection curves for θ 30deg for dierentnormalized distance of pile at pile head

0 50 100 150 200 250 300 350 400 450 5000

100

200

300

400

500

600

700

800

Late

ral l

oad

H0

(kN

)

Lateral displacement y0 (mm)

BD = 05 (θ = 50deg)BD = 2 (θ = 50deg)

BD = 4 (θ = 50deg)BD = 6 (θ = 50deg)

Figure 16 Lateral load-deection curves for θ 50deg for dierentnormalized distance of pile at pile head

Advances in Civil Engineering 9

the pile head deection and maximum bending moment ofthe pile especially when the slope angle exceeds 40deg An ex-ample is used for pile head deection when the value of α isequal to 0 the pile head deection values of pile in slopingground with θ 10deg 30deg 50deg is increased by 74 398137 respectively compared to that in horizontal ground

84 Eect of Undrained Shear Strength cu Here lateral loadH0 500 kN and the initial bending momentM0 0 (kNmiddotm)

were taken as the initial loading conditions choosing un-drained shear strengths cu of 20 kPa 40 kPa 60 80 kPa100 kPa respectively to calculate and analyze Other basiccalculation parameters are the same as in Section 81

Figures 23 and 24 show pile head deection (y0) and themaximum bending moment (Mmax) of the pile variationwith the undrained shear strength cu for dierent slopeangles respectively From the curves given in Figures 23 and24 it is observed that the increase in undrained shearstrength cu decreases the pile head deection and themaximum bending moment is is because of the increasein the strength of soil and the relative stiness of the pile-soilsystem Also it is obvious that the presence of slopes

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

ndash200 0 200 400 600 800 1000 1200 1400 16000123456789

1011121314

Dep

th (m

)

Bending moment M (kNmiddotm)

Figure 19 Bending moment variation along the depth of pile forθ 30deg for dierent slope angle

ndash200 0 200 400 600 800 1000 1200 14000123456789

1011121314

Dep

th (m

)

Bending moment M (kNmiddotm)

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

Figure 18 Bending moment variation along the depth of pile forθ 10deg for dierent slope angle

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

ndash200 0 200 400 600 800 1000 1200 1400 1600 18000123456789

1011121314

Dpe

th (m

)

Bending moment M (kNmiddotm)

Figure 20 Bending moment variation along the depth of pile forθ 50deg for dierent slope angle

ndash01 00 01 02 03 04 05 06 07 08 09 10 116080

100120140160180200220240260

Late

rald

ispla

cem

ent y 0

(mm

)

Adhesion coefficient α

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 21 Pile head deection (y0) variation with adhesion co-ecentcient (α) for dierent slope angle

10 Advances in Civil Engineering

aggravates the rate of change of pile head deection es-pecially when cu ranges from 20 kPa to 40 kPa and when thevalue of cu exceeds 40 kPa the decrease rate of the deectionof pile head becomes slow and eventually almost becomesat From the results in Figure 23 it is observed that the pilehead deection in the range of 734ndash75 for increase in cu20 kPa to 40 kPa of sloping ground (θ 10deg 20deg 30deg 40deg 50deg)and horizontal ground surfaces from which can concludethat the weaker soil parameters are the more signicantslope eect becomes Besides the curve of the maximumbending moment variation with undrained shear strengthshown in Figure 24 is smoother and the range of themaximum bending moment of the pile with the increase ofthe slope is relatively stable

9 Conclusions

e purpose of this paper is to study the behavior of laterallyloaded long-exible pile in undrained clay sloping groundBased on the basic model of ideal elastic-plastic p-y curvemethod this paper derives the dierential equations of thelaterally loaded single pile in undrained clay sloped groundby introducing the existing related reduction variablefunction and the corresponding nite dierence method forthe pile deection and internal force is obtained A series ofparameters analyses are further performed for slope anglenormalized distance of pile adhesion coecentcient and un-drained shear strength e conclusions obtained from thisstudy are summarized as follows

(1) A nonlinear analysis method for laterally loaded long-exible pile in undrained clay sloped ground isestablished rough the verication of examples thecorrectness and feasibility of the method is proved

(2) Slope angle is the most important factor that aectingthe lateral bearing capacity of the near-slope pile eincrease in slope angle increases the deection and the

rate of increase of deection and this trend becomesmore obvious as the lateral load increased When theslope angle is small enough (θ lt 10o) the eect ofslope is almost negligible Besides the depth of xityof the pile is about 4sim8 times the size of the pilediameter

(3) e distance away from pile to slope crest is also animportant factor that aects the lateral-load capacityof the pile e increase in normalized distance BDof the pile decreases the deection of pile head butincreases the lateral-load capacity and when nor-malized distance BD ratio exceeds 6 the slope eectcan be avoidedWhen laterally loaded pile is closer tothe slope crest the inuence of the slope angle seemsmore dominant

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

ndash01 00 01 02 03 04 05 06 07 08 09 10 11

900

1000

1100

1200

1300

1400

1500

1600

Max

imum

ben

ding

mom

ent

Mm

ax (k

Nmiddotm

)

Adhesion coefficient α

Figure 22 Maximum bending moment (Mmax) variation withadhesion coecentcient (α) for dierent slope angle

0 20 40 60 80 100 1200

50100150200250300350400450500550600

Late

ral d

ispla

cem

ent y 0

(mm

)

Undrained shear strength cu (kPa)

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 23 Pile head deection (y0) variation with undrained shearstrength (cu) for dierent slope angle

0 20 40 60 80 100 1200

300

600

900

1200

1500

1800

2100M

axim

umbe

ndin

gmom

ent M

max

(kN

middotm)

Undrained shear strength cu (kPa)

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 24 Maximum bending moment (Mmax) variation withundrained shear strength (cu) for dierent slope angle

Advances in Civil Engineering 11

(4) -e adhesion coefficient α at the pile-soil interfacecan effectively reduce the pile head deflection and themaximum bending moment of the pile at the sametime -e increase in slope angle will significantlyincrease the pile head deflection and maximumbending moment of the pile especially when theslope angle exceeds 40deg

(5) -e increase in undrained shear strength cu de-creases the pile head deflection and the maximumbending moment of the pile -is is because of theincrease in the strength of soil and the relativestiffness of the pile-soil system Also the presence ofslopes aggravates the rate of change of pile headdeflection especially when the cu is in a mall value(ranges from 20 kPa to 40 kPa) In contrast themaximum bending moment variation with un-drained shear strength affected by the slope effectappears more moderate

(6) -is study researches the lateral bearing behavior ofsingle pile in undrained clay sloping ground Inpractical projects the situation of pile foundationson slope ground surface is not uncommon and thelateral bearing characteristics of pile foundationsare more complicated -erefore the influence ofslope effect on the lateral bearing capacity of pilewhich is on slope ground surface is worth furtherstudy

Data Availability

-e original data for summary of pile load test in Table 1 arefrom Wu et al [28] Georgiadis and Georgiadis [17] andGeorgiadis and Georgiadis [18] respectively -e computedpile responses as shown in Figure 6 are compared to the piletest results (Wu et al [28]) and to the pile responsescomputed with the same computer code using as input theMatlock [2] Reese and Welch [5] Bhushan et al [26]Stevens and Audibert [27] Figures 7 and 8 are calculated bycomputer code MATLAB to compare previous studies(Georgiadis and Georgiadis [17] Georgiadis and Georgiadis[18] respectively) Figures 9ndash24 are calculated by the pro-posedmethod based on the original data mentioned above tostudy parametric analysis In addition all the sharing datawere involved in this paper and there was no redundantdata

Conflicts of Interest

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

Acknowledgments

-is work is supported by the National Natural ScienceFoundation of China (grant nos 51478479 and 51678570)and Hunan Transport Technology Project (grant no201524)

References

[1] N Nimityongskul Y Kawamata D Rayamajhi andS A Ashford ldquoFull-scale tests on effects of slope on lateralcapacity of piles installed in cohesive soilsrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 144 no 1article 04017103 2018

[2] H Matlock ldquoCorrelation for design of laterally loaded piles insoft clayrdquo in Proceedings of the Offshore Technology Confer-ence pp 77ndash94 Houston TX USA April 1970

[3] L C Reese ldquoAnalysis of laterally loaded piles in sandrdquo inProceedings of the Offshore Technical Conference pp 95ndash105Houston TX USA May 1974

[4] L Reese W Cox and F Koop ldquoField testing and analysis oflaterally loaded piles on stiff clayrdquo in Proceedings of theOffshore Technology in Civil Engineering pp 106ndash125 DallasTX USA May 1975

[5] L C Reese and R C Welch ldquoLateral loading of deepfoundations in stiff clayrdquo Journal of Geotechnical and Geo-environmental Engineering vol 101 no 7 pp 633ndash649 1975

[6] M A Gabr T Lunne and J J Powell ldquoP-y analysis of laterallyloaded piles in clay using DMTrdquo Journal of GeotechnicalEngineering vol 120 no 5 pp 816ndash837 1994

[7] C C Fan and J H Long ldquoAssessment of existing methods forpredicting soil response of laterally loaded piles in sandrdquoComputers and Geotechnics vol 32 no 4 pp 274ndash289 2005

[8] G P Yang and Z M Zhang ldquoResearch on P-Y curve oflaterally bearing piles under large displacementrdquo WaterTransportation Engineering vol 342 no 7 pp 40ndash45 2002

[9] C Wang and Z A LU ldquoCalculation of internal forces oflaterally loaded piles by using p-y curverdquo Journal ofChongqing Jiaotong University (Natural Science) vol 4 no 1pp 61ndash65 1958

[10] H C Wang and D Q WU ldquoA new unified approach to thep-y curve of laterally loaded pile in clayrdquo Journal of HohaiUniversity no 1 pp 9ndash17 1991

[11] G C Wang and M Yang ldquoNonlinear analysis of laterallyloaded piles in sandrdquo Rock and Soil Mechanics no 2pp 261ndash267 2011

[12] G CWang andM Yang ldquoCalculation of laterally loaded pilesin clayrdquo Journal of Tongji University (Natural Science) vol 40no 3 pp 373ndash378 2012

[13] T Q Zhou Z A LU and D H Wang ldquoCalculation methodof laterally loaded super-long PHC pilerdquo Port and WaterwayEngineering no 6 pp 155ndash160 2013

[14] L U Cheng X C Xu S X Chen et al ldquoModel test andnumerical simulation of horizontal bearing capacity andimpact factors for foundation piles in sloperdquo Rock and SoilMechanics no 9 pp 2685ndash2691 2014

[15] P YinB H ZhaoM H Zhao et al ldquoStability analysis of pile-column bridge pile considering slope effectrdquo Journal of Hu-nan University (Natural Science) vol 43 no 11 pp 20ndash252016

[16] Y S Deng M H Zhao X J Zhou et al ldquoResearch progress ofbearing characteristics of pile column at steep slope inmountain areasrdquo Journal of Highway and TransportationResearch and Development vol 29 no 6 pp 37ndash45 2012

[17] K Georgiadis and M Georgiadis ldquoUndrained lateral pileresponse in sloping groundrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 136 no 11 pp 1489ndash1500 2010

[18] K Georgiadis and M Georgiadis ldquoDevelopment of p-ycurves for undrained response of piles near slopesrdquo Com-puters and Geotechnics vol 40 no 3 pp 53ndash61 2012

12 Advances in Civil Engineering

[19] K Muthukkumaran R Sundaravadivelu and S R GandhildquoEffect of slope on p-y curves due to surcharge loadrdquo Soils andFoundations vol 48 no 3 pp 353ndash361 2008

[20] L M Zhang C W W Ng and C J Lee ldquoEffects of slope andsleeving on the behavior of laterally loaded pilesrdquo Soils andFoundations vol 44 no 4 pp 99ndash108 2008

[21] B P Yin M H Zhao W He et al ldquoModel test study onidentification of foundation proportional coefficient m inslope groundrdquo Journal of Hunan University (Natural Science)vol 44 no 9 2017

[22] B L Gao C R Zhang and Z X Zhang ldquoModel tests on effectof slopes on lateral resistance of near single piles in sandrdquoRock and Soil Mechanics vol 35 no 11 pp 3191ndash3198 2014

[23] B T Zhu Be Ultimate Resistance and Laterally Loaded PileBehaviors Tongji University School of Civil EngineeringShanghai China 2005

[24] S S Rajashree and T G Sitharam ldquoNonlinear finite-elementmodeling of batter piles under lateral loadrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 127 no 7pp 604ndash612 2001

[25] R L Kondner ldquoHyperbolic stress-strain response cohesivesoilsrdquo Journal of the Soil Mechanics and Foundations Divisionvol 89 no 1 pp 115ndash143 1963

[26] K Bhushan S C Haley and P T Fong ldquoLateral load tests ondrilled piers in stiff claysrdquo Journal of the Geotechnical Engi-neering Division vol 1058 pp 969ndash985 1979

[27] J B Stevens and J M E Audibert ldquoRe-examination of P-Ycurve formulationsrdquo in Proceedings of 11th Offshore Tech-nology Conference pp 397ndash403 Houston TX USA 1980

[28] D Wu B B Broms and V Choa ldquoDesign of laterally loadedpiles in cohesive soils using p-y curvesrdquo Soils and Founda-tions vol 38 no 2 pp 17ndash26 1998

Advances in Civil Engineering 13

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the pile head deection and maximum bending moment ofthe pile especially when the slope angle exceeds 40deg An ex-ample is used for pile head deection when the value of α isequal to 0 the pile head deection values of pile in slopingground with θ 10deg 30deg 50deg is increased by 74 398137 respectively compared to that in horizontal ground

84 Eect of Undrained Shear Strength cu Here lateral loadH0 500 kN and the initial bending momentM0 0 (kNmiddotm)

were taken as the initial loading conditions choosing un-drained shear strengths cu of 20 kPa 40 kPa 60 80 kPa100 kPa respectively to calculate and analyze Other basiccalculation parameters are the same as in Section 81

Figures 23 and 24 show pile head deection (y0) and themaximum bending moment (Mmax) of the pile variationwith the undrained shear strength cu for dierent slopeangles respectively From the curves given in Figures 23 and24 it is observed that the increase in undrained shearstrength cu decreases the pile head deection and themaximum bending moment is is because of the increasein the strength of soil and the relative stiness of the pile-soilsystem Also it is obvious that the presence of slopes

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

ndash200 0 200 400 600 800 1000 1200 1400 16000123456789

1011121314

Dep

th (m

)

Bending moment M (kNmiddotm)

Figure 19 Bending moment variation along the depth of pile forθ 30deg for dierent slope angle

ndash200 0 200 400 600 800 1000 1200 14000123456789

1011121314

Dep

th (m

)

Bending moment M (kNmiddotm)

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

Figure 18 Bending moment variation along the depth of pile forθ 10deg for dierent slope angle

BD = 05 H0 = 300kNBD = 05 H0 = 600kNBD = 2 H0 = 300kNBD = 2 H0 = 600kNBD = 4 H0 = 300kN

BD = 4 H0 = 600kNBD = 6 H0 = 300kNBD = 6 H0 = 600kNLevel ground H0 = 300kNLevel ground H0 = 600kN

ndash200 0 200 400 600 800 1000 1200 1400 1600 18000123456789

1011121314

Dpe

th (m

)

Bending moment M (kNmiddotm)

Figure 20 Bending moment variation along the depth of pile forθ 50deg for dierent slope angle

ndash01 00 01 02 03 04 05 06 07 08 09 10 116080

100120140160180200220240260

Late

rald

ispla

cem

ent y 0

(mm

)

Adhesion coefficient α

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 21 Pile head deection (y0) variation with adhesion co-ecentcient (α) for dierent slope angle

10 Advances in Civil Engineering

aggravates the rate of change of pile head deection es-pecially when cu ranges from 20 kPa to 40 kPa and when thevalue of cu exceeds 40 kPa the decrease rate of the deectionof pile head becomes slow and eventually almost becomesat From the results in Figure 23 it is observed that the pilehead deection in the range of 734ndash75 for increase in cu20 kPa to 40 kPa of sloping ground (θ 10deg 20deg 30deg 40deg 50deg)and horizontal ground surfaces from which can concludethat the weaker soil parameters are the more signicantslope eect becomes Besides the curve of the maximumbending moment variation with undrained shear strengthshown in Figure 24 is smoother and the range of themaximum bending moment of the pile with the increase ofthe slope is relatively stable

9 Conclusions

e purpose of this paper is to study the behavior of laterallyloaded long-exible pile in undrained clay sloping groundBased on the basic model of ideal elastic-plastic p-y curvemethod this paper derives the dierential equations of thelaterally loaded single pile in undrained clay sloped groundby introducing the existing related reduction variablefunction and the corresponding nite dierence method forthe pile deection and internal force is obtained A series ofparameters analyses are further performed for slope anglenormalized distance of pile adhesion coecentcient and un-drained shear strength e conclusions obtained from thisstudy are summarized as follows

(1) A nonlinear analysis method for laterally loaded long-exible pile in undrained clay sloped ground isestablished rough the verication of examples thecorrectness and feasibility of the method is proved

(2) Slope angle is the most important factor that aectingthe lateral bearing capacity of the near-slope pile eincrease in slope angle increases the deection and the

rate of increase of deection and this trend becomesmore obvious as the lateral load increased When theslope angle is small enough (θ lt 10o) the eect ofslope is almost negligible Besides the depth of xityof the pile is about 4sim8 times the size of the pilediameter

(3) e distance away from pile to slope crest is also animportant factor that aects the lateral-load capacityof the pile e increase in normalized distance BDof the pile decreases the deection of pile head butincreases the lateral-load capacity and when nor-malized distance BD ratio exceeds 6 the slope eectcan be avoidedWhen laterally loaded pile is closer tothe slope crest the inuence of the slope angle seemsmore dominant

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

ndash01 00 01 02 03 04 05 06 07 08 09 10 11

900

1000

1100

1200

1300

1400

1500

1600

Max

imum

ben

ding

mom

ent

Mm

ax (k

Nmiddotm

)

Adhesion coefficient α

Figure 22 Maximum bending moment (Mmax) variation withadhesion coecentcient (α) for dierent slope angle

0 20 40 60 80 100 1200

50100150200250300350400450500550600

Late

ral d

ispla

cem

ent y 0

(mm

)

Undrained shear strength cu (kPa)

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 23 Pile head deection (y0) variation with undrained shearstrength (cu) for dierent slope angle

0 20 40 60 80 100 1200

300

600

900

1200

1500

1800

2100M

axim

umbe

ndin

gmom

ent M

max

(kN

middotm)

Undrained shear strength cu (kPa)

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 24 Maximum bending moment (Mmax) variation withundrained shear strength (cu) for dierent slope angle

Advances in Civil Engineering 11

(4) -e adhesion coefficient α at the pile-soil interfacecan effectively reduce the pile head deflection and themaximum bending moment of the pile at the sametime -e increase in slope angle will significantlyincrease the pile head deflection and maximumbending moment of the pile especially when theslope angle exceeds 40deg

(5) -e increase in undrained shear strength cu de-creases the pile head deflection and the maximumbending moment of the pile -is is because of theincrease in the strength of soil and the relativestiffness of the pile-soil system Also the presence ofslopes aggravates the rate of change of pile headdeflection especially when the cu is in a mall value(ranges from 20 kPa to 40 kPa) In contrast themaximum bending moment variation with un-drained shear strength affected by the slope effectappears more moderate

(6) -is study researches the lateral bearing behavior ofsingle pile in undrained clay sloping ground Inpractical projects the situation of pile foundationson slope ground surface is not uncommon and thelateral bearing characteristics of pile foundationsare more complicated -erefore the influence ofslope effect on the lateral bearing capacity of pilewhich is on slope ground surface is worth furtherstudy

Data Availability

-e original data for summary of pile load test in Table 1 arefrom Wu et al [28] Georgiadis and Georgiadis [17] andGeorgiadis and Georgiadis [18] respectively -e computedpile responses as shown in Figure 6 are compared to the piletest results (Wu et al [28]) and to the pile responsescomputed with the same computer code using as input theMatlock [2] Reese and Welch [5] Bhushan et al [26]Stevens and Audibert [27] Figures 7 and 8 are calculated bycomputer code MATLAB to compare previous studies(Georgiadis and Georgiadis [17] Georgiadis and Georgiadis[18] respectively) Figures 9ndash24 are calculated by the pro-posedmethod based on the original data mentioned above tostudy parametric analysis In addition all the sharing datawere involved in this paper and there was no redundantdata

Conflicts of Interest

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

Acknowledgments

-is work is supported by the National Natural ScienceFoundation of China (grant nos 51478479 and 51678570)and Hunan Transport Technology Project (grant no201524)

References

[1] N Nimityongskul Y Kawamata D Rayamajhi andS A Ashford ldquoFull-scale tests on effects of slope on lateralcapacity of piles installed in cohesive soilsrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 144 no 1article 04017103 2018

[2] H Matlock ldquoCorrelation for design of laterally loaded piles insoft clayrdquo in Proceedings of the Offshore Technology Confer-ence pp 77ndash94 Houston TX USA April 1970

[3] L C Reese ldquoAnalysis of laterally loaded piles in sandrdquo inProceedings of the Offshore Technical Conference pp 95ndash105Houston TX USA May 1974

[4] L Reese W Cox and F Koop ldquoField testing and analysis oflaterally loaded piles on stiff clayrdquo in Proceedings of theOffshore Technology in Civil Engineering pp 106ndash125 DallasTX USA May 1975

[5] L C Reese and R C Welch ldquoLateral loading of deepfoundations in stiff clayrdquo Journal of Geotechnical and Geo-environmental Engineering vol 101 no 7 pp 633ndash649 1975

[6] M A Gabr T Lunne and J J Powell ldquoP-y analysis of laterallyloaded piles in clay using DMTrdquo Journal of GeotechnicalEngineering vol 120 no 5 pp 816ndash837 1994

[7] C C Fan and J H Long ldquoAssessment of existing methods forpredicting soil response of laterally loaded piles in sandrdquoComputers and Geotechnics vol 32 no 4 pp 274ndash289 2005

[8] G P Yang and Z M Zhang ldquoResearch on P-Y curve oflaterally bearing piles under large displacementrdquo WaterTransportation Engineering vol 342 no 7 pp 40ndash45 2002

[9] C Wang and Z A LU ldquoCalculation of internal forces oflaterally loaded piles by using p-y curverdquo Journal ofChongqing Jiaotong University (Natural Science) vol 4 no 1pp 61ndash65 1958

[10] H C Wang and D Q WU ldquoA new unified approach to thep-y curve of laterally loaded pile in clayrdquo Journal of HohaiUniversity no 1 pp 9ndash17 1991

[11] G C Wang and M Yang ldquoNonlinear analysis of laterallyloaded piles in sandrdquo Rock and Soil Mechanics no 2pp 261ndash267 2011

[12] G CWang andM Yang ldquoCalculation of laterally loaded pilesin clayrdquo Journal of Tongji University (Natural Science) vol 40no 3 pp 373ndash378 2012

[13] T Q Zhou Z A LU and D H Wang ldquoCalculation methodof laterally loaded super-long PHC pilerdquo Port and WaterwayEngineering no 6 pp 155ndash160 2013

[14] L U Cheng X C Xu S X Chen et al ldquoModel test andnumerical simulation of horizontal bearing capacity andimpact factors for foundation piles in sloperdquo Rock and SoilMechanics no 9 pp 2685ndash2691 2014

[15] P YinB H ZhaoM H Zhao et al ldquoStability analysis of pile-column bridge pile considering slope effectrdquo Journal of Hu-nan University (Natural Science) vol 43 no 11 pp 20ndash252016

[16] Y S Deng M H Zhao X J Zhou et al ldquoResearch progress ofbearing characteristics of pile column at steep slope inmountain areasrdquo Journal of Highway and TransportationResearch and Development vol 29 no 6 pp 37ndash45 2012

[17] K Georgiadis and M Georgiadis ldquoUndrained lateral pileresponse in sloping groundrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 136 no 11 pp 1489ndash1500 2010

[18] K Georgiadis and M Georgiadis ldquoDevelopment of p-ycurves for undrained response of piles near slopesrdquo Com-puters and Geotechnics vol 40 no 3 pp 53ndash61 2012

12 Advances in Civil Engineering

[19] K Muthukkumaran R Sundaravadivelu and S R GandhildquoEffect of slope on p-y curves due to surcharge loadrdquo Soils andFoundations vol 48 no 3 pp 353ndash361 2008

[20] L M Zhang C W W Ng and C J Lee ldquoEffects of slope andsleeving on the behavior of laterally loaded pilesrdquo Soils andFoundations vol 44 no 4 pp 99ndash108 2008

[21] B P Yin M H Zhao W He et al ldquoModel test study onidentification of foundation proportional coefficient m inslope groundrdquo Journal of Hunan University (Natural Science)vol 44 no 9 2017

[22] B L Gao C R Zhang and Z X Zhang ldquoModel tests on effectof slopes on lateral resistance of near single piles in sandrdquoRock and Soil Mechanics vol 35 no 11 pp 3191ndash3198 2014

[23] B T Zhu Be Ultimate Resistance and Laterally Loaded PileBehaviors Tongji University School of Civil EngineeringShanghai China 2005

[24] S S Rajashree and T G Sitharam ldquoNonlinear finite-elementmodeling of batter piles under lateral loadrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 127 no 7pp 604ndash612 2001

[25] R L Kondner ldquoHyperbolic stress-strain response cohesivesoilsrdquo Journal of the Soil Mechanics and Foundations Divisionvol 89 no 1 pp 115ndash143 1963

[26] K Bhushan S C Haley and P T Fong ldquoLateral load tests ondrilled piers in stiff claysrdquo Journal of the Geotechnical Engi-neering Division vol 1058 pp 969ndash985 1979

[27] J B Stevens and J M E Audibert ldquoRe-examination of P-Ycurve formulationsrdquo in Proceedings of 11th Offshore Tech-nology Conference pp 397ndash403 Houston TX USA 1980

[28] D Wu B B Broms and V Choa ldquoDesign of laterally loadedpiles in cohesive soils using p-y curvesrdquo Soils and Founda-tions vol 38 no 2 pp 17ndash26 1998

Advances in Civil Engineering 13

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

aggravates the rate of change of pile head deection es-pecially when cu ranges from 20 kPa to 40 kPa and when thevalue of cu exceeds 40 kPa the decrease rate of the deectionof pile head becomes slow and eventually almost becomesat From the results in Figure 23 it is observed that the pilehead deection in the range of 734ndash75 for increase in cu20 kPa to 40 kPa of sloping ground (θ 10deg 20deg 30deg 40deg 50deg)and horizontal ground surfaces from which can concludethat the weaker soil parameters are the more signicantslope eect becomes Besides the curve of the maximumbending moment variation with undrained shear strengthshown in Figure 24 is smoother and the range of themaximum bending moment of the pile with the increase ofthe slope is relatively stable

9 Conclusions

e purpose of this paper is to study the behavior of laterallyloaded long-exible pile in undrained clay sloping groundBased on the basic model of ideal elastic-plastic p-y curvemethod this paper derives the dierential equations of thelaterally loaded single pile in undrained clay sloped groundby introducing the existing related reduction variablefunction and the corresponding nite dierence method forthe pile deection and internal force is obtained A series ofparameters analyses are further performed for slope anglenormalized distance of pile adhesion coecentcient and un-drained shear strength e conclusions obtained from thisstudy are summarized as follows

(1) A nonlinear analysis method for laterally loaded long-exible pile in undrained clay sloped ground isestablished rough the verication of examples thecorrectness and feasibility of the method is proved

(2) Slope angle is the most important factor that aectingthe lateral bearing capacity of the near-slope pile eincrease in slope angle increases the deection and the

rate of increase of deection and this trend becomesmore obvious as the lateral load increased When theslope angle is small enough (θ lt 10o) the eect ofslope is almost negligible Besides the depth of xityof the pile is about 4sim8 times the size of the pilediameter

(3) e distance away from pile to slope crest is also animportant factor that aects the lateral-load capacityof the pile e increase in normalized distance BDof the pile decreases the deection of pile head butincreases the lateral-load capacity and when nor-malized distance BD ratio exceeds 6 the slope eectcan be avoidedWhen laterally loaded pile is closer tothe slope crest the inuence of the slope angle seemsmore dominant

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

ndash01 00 01 02 03 04 05 06 07 08 09 10 11

900

1000

1100

1200

1300

1400

1500

1600

Max

imum

ben

ding

mom

ent

Mm

ax (k

Nmiddotm

)

Adhesion coefficient α

Figure 22 Maximum bending moment (Mmax) variation withadhesion coecentcient (α) for dierent slope angle

0 20 40 60 80 100 1200

50100150200250300350400450500550600

Late

ral d

ispla

cem

ent y 0

(mm

)

Undrained shear strength cu (kPa)

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 23 Pile head deection (y0) variation with undrained shearstrength (cu) for dierent slope angle

0 20 40 60 80 100 1200

300

600

900

1200

1500

1800

2100M

axim

umbe

ndin

gmom

ent M

max

(kN

middotm)

Undrained shear strength cu (kPa)

θ = 0deg (BD = 05)θ = 10deg (BD = 05)θ = 20deg (BD = 05)

θ = 30deg (BD = 05)θ = 40deg (BD = 05)θ = 50deg (BD = 05)

Figure 24 Maximum bending moment (Mmax) variation withundrained shear strength (cu) for dierent slope angle

Advances in Civil Engineering 11

(4) -e adhesion coefficient α at the pile-soil interfacecan effectively reduce the pile head deflection and themaximum bending moment of the pile at the sametime -e increase in slope angle will significantlyincrease the pile head deflection and maximumbending moment of the pile especially when theslope angle exceeds 40deg

(5) -e increase in undrained shear strength cu de-creases the pile head deflection and the maximumbending moment of the pile -is is because of theincrease in the strength of soil and the relativestiffness of the pile-soil system Also the presence ofslopes aggravates the rate of change of pile headdeflection especially when the cu is in a mall value(ranges from 20 kPa to 40 kPa) In contrast themaximum bending moment variation with un-drained shear strength affected by the slope effectappears more moderate

(6) -is study researches the lateral bearing behavior ofsingle pile in undrained clay sloping ground Inpractical projects the situation of pile foundationson slope ground surface is not uncommon and thelateral bearing characteristics of pile foundationsare more complicated -erefore the influence ofslope effect on the lateral bearing capacity of pilewhich is on slope ground surface is worth furtherstudy

Data Availability

-e original data for summary of pile load test in Table 1 arefrom Wu et al [28] Georgiadis and Georgiadis [17] andGeorgiadis and Georgiadis [18] respectively -e computedpile responses as shown in Figure 6 are compared to the piletest results (Wu et al [28]) and to the pile responsescomputed with the same computer code using as input theMatlock [2] Reese and Welch [5] Bhushan et al [26]Stevens and Audibert [27] Figures 7 and 8 are calculated bycomputer code MATLAB to compare previous studies(Georgiadis and Georgiadis [17] Georgiadis and Georgiadis[18] respectively) Figures 9ndash24 are calculated by the pro-posedmethod based on the original data mentioned above tostudy parametric analysis In addition all the sharing datawere involved in this paper and there was no redundantdata

Conflicts of Interest

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

Acknowledgments

-is work is supported by the National Natural ScienceFoundation of China (grant nos 51478479 and 51678570)and Hunan Transport Technology Project (grant no201524)

References

[1] N Nimityongskul Y Kawamata D Rayamajhi andS A Ashford ldquoFull-scale tests on effects of slope on lateralcapacity of piles installed in cohesive soilsrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 144 no 1article 04017103 2018

[2] H Matlock ldquoCorrelation for design of laterally loaded piles insoft clayrdquo in Proceedings of the Offshore Technology Confer-ence pp 77ndash94 Houston TX USA April 1970

[3] L C Reese ldquoAnalysis of laterally loaded piles in sandrdquo inProceedings of the Offshore Technical Conference pp 95ndash105Houston TX USA May 1974

[4] L Reese W Cox and F Koop ldquoField testing and analysis oflaterally loaded piles on stiff clayrdquo in Proceedings of theOffshore Technology in Civil Engineering pp 106ndash125 DallasTX USA May 1975

[5] L C Reese and R C Welch ldquoLateral loading of deepfoundations in stiff clayrdquo Journal of Geotechnical and Geo-environmental Engineering vol 101 no 7 pp 633ndash649 1975

[6] M A Gabr T Lunne and J J Powell ldquoP-y analysis of laterallyloaded piles in clay using DMTrdquo Journal of GeotechnicalEngineering vol 120 no 5 pp 816ndash837 1994

[7] C C Fan and J H Long ldquoAssessment of existing methods forpredicting soil response of laterally loaded piles in sandrdquoComputers and Geotechnics vol 32 no 4 pp 274ndash289 2005

[8] G P Yang and Z M Zhang ldquoResearch on P-Y curve oflaterally bearing piles under large displacementrdquo WaterTransportation Engineering vol 342 no 7 pp 40ndash45 2002

[9] C Wang and Z A LU ldquoCalculation of internal forces oflaterally loaded piles by using p-y curverdquo Journal ofChongqing Jiaotong University (Natural Science) vol 4 no 1pp 61ndash65 1958

[10] H C Wang and D Q WU ldquoA new unified approach to thep-y curve of laterally loaded pile in clayrdquo Journal of HohaiUniversity no 1 pp 9ndash17 1991

[11] G C Wang and M Yang ldquoNonlinear analysis of laterallyloaded piles in sandrdquo Rock and Soil Mechanics no 2pp 261ndash267 2011

[12] G CWang andM Yang ldquoCalculation of laterally loaded pilesin clayrdquo Journal of Tongji University (Natural Science) vol 40no 3 pp 373ndash378 2012

[13] T Q Zhou Z A LU and D H Wang ldquoCalculation methodof laterally loaded super-long PHC pilerdquo Port and WaterwayEngineering no 6 pp 155ndash160 2013

[14] L U Cheng X C Xu S X Chen et al ldquoModel test andnumerical simulation of horizontal bearing capacity andimpact factors for foundation piles in sloperdquo Rock and SoilMechanics no 9 pp 2685ndash2691 2014

[15] P YinB H ZhaoM H Zhao et al ldquoStability analysis of pile-column bridge pile considering slope effectrdquo Journal of Hu-nan University (Natural Science) vol 43 no 11 pp 20ndash252016

[16] Y S Deng M H Zhao X J Zhou et al ldquoResearch progress ofbearing characteristics of pile column at steep slope inmountain areasrdquo Journal of Highway and TransportationResearch and Development vol 29 no 6 pp 37ndash45 2012

[17] K Georgiadis and M Georgiadis ldquoUndrained lateral pileresponse in sloping groundrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 136 no 11 pp 1489ndash1500 2010

[18] K Georgiadis and M Georgiadis ldquoDevelopment of p-ycurves for undrained response of piles near slopesrdquo Com-puters and Geotechnics vol 40 no 3 pp 53ndash61 2012

12 Advances in Civil Engineering

[19] K Muthukkumaran R Sundaravadivelu and S R GandhildquoEffect of slope on p-y curves due to surcharge loadrdquo Soils andFoundations vol 48 no 3 pp 353ndash361 2008

[20] L M Zhang C W W Ng and C J Lee ldquoEffects of slope andsleeving on the behavior of laterally loaded pilesrdquo Soils andFoundations vol 44 no 4 pp 99ndash108 2008

[21] B P Yin M H Zhao W He et al ldquoModel test study onidentification of foundation proportional coefficient m inslope groundrdquo Journal of Hunan University (Natural Science)vol 44 no 9 2017

[22] B L Gao C R Zhang and Z X Zhang ldquoModel tests on effectof slopes on lateral resistance of near single piles in sandrdquoRock and Soil Mechanics vol 35 no 11 pp 3191ndash3198 2014

[23] B T Zhu Be Ultimate Resistance and Laterally Loaded PileBehaviors Tongji University School of Civil EngineeringShanghai China 2005

[24] S S Rajashree and T G Sitharam ldquoNonlinear finite-elementmodeling of batter piles under lateral loadrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 127 no 7pp 604ndash612 2001

[25] R L Kondner ldquoHyperbolic stress-strain response cohesivesoilsrdquo Journal of the Soil Mechanics and Foundations Divisionvol 89 no 1 pp 115ndash143 1963

[26] K Bhushan S C Haley and P T Fong ldquoLateral load tests ondrilled piers in stiff claysrdquo Journal of the Geotechnical Engi-neering Division vol 1058 pp 969ndash985 1979

[27] J B Stevens and J M E Audibert ldquoRe-examination of P-Ycurve formulationsrdquo in Proceedings of 11th Offshore Tech-nology Conference pp 397ndash403 Houston TX USA 1980

[28] D Wu B B Broms and V Choa ldquoDesign of laterally loadedpiles in cohesive soils using p-y curvesrdquo Soils and Founda-tions vol 38 no 2 pp 17ndash26 1998

Advances in Civil Engineering 13

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

(4) -e adhesion coefficient α at the pile-soil interfacecan effectively reduce the pile head deflection and themaximum bending moment of the pile at the sametime -e increase in slope angle will significantlyincrease the pile head deflection and maximumbending moment of the pile especially when theslope angle exceeds 40deg

(5) -e increase in undrained shear strength cu de-creases the pile head deflection and the maximumbending moment of the pile -is is because of theincrease in the strength of soil and the relativestiffness of the pile-soil system Also the presence ofslopes aggravates the rate of change of pile headdeflection especially when the cu is in a mall value(ranges from 20 kPa to 40 kPa) In contrast themaximum bending moment variation with un-drained shear strength affected by the slope effectappears more moderate

(6) -is study researches the lateral bearing behavior ofsingle pile in undrained clay sloping ground Inpractical projects the situation of pile foundationson slope ground surface is not uncommon and thelateral bearing characteristics of pile foundationsare more complicated -erefore the influence ofslope effect on the lateral bearing capacity of pilewhich is on slope ground surface is worth furtherstudy

Data Availability

-e original data for summary of pile load test in Table 1 arefrom Wu et al [28] Georgiadis and Georgiadis [17] andGeorgiadis and Georgiadis [18] respectively -e computedpile responses as shown in Figure 6 are compared to the piletest results (Wu et al [28]) and to the pile responsescomputed with the same computer code using as input theMatlock [2] Reese and Welch [5] Bhushan et al [26]Stevens and Audibert [27] Figures 7 and 8 are calculated bycomputer code MATLAB to compare previous studies(Georgiadis and Georgiadis [17] Georgiadis and Georgiadis[18] respectively) Figures 9ndash24 are calculated by the pro-posedmethod based on the original data mentioned above tostudy parametric analysis In addition all the sharing datawere involved in this paper and there was no redundantdata

Conflicts of Interest

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

Acknowledgments

-is work is supported by the National Natural ScienceFoundation of China (grant nos 51478479 and 51678570)and Hunan Transport Technology Project (grant no201524)

References

[1] N Nimityongskul Y Kawamata D Rayamajhi andS A Ashford ldquoFull-scale tests on effects of slope on lateralcapacity of piles installed in cohesive soilsrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 144 no 1article 04017103 2018

[2] H Matlock ldquoCorrelation for design of laterally loaded piles insoft clayrdquo in Proceedings of the Offshore Technology Confer-ence pp 77ndash94 Houston TX USA April 1970

[3] L C Reese ldquoAnalysis of laterally loaded piles in sandrdquo inProceedings of the Offshore Technical Conference pp 95ndash105Houston TX USA May 1974

[4] L Reese W Cox and F Koop ldquoField testing and analysis oflaterally loaded piles on stiff clayrdquo in Proceedings of theOffshore Technology in Civil Engineering pp 106ndash125 DallasTX USA May 1975

[5] L C Reese and R C Welch ldquoLateral loading of deepfoundations in stiff clayrdquo Journal of Geotechnical and Geo-environmental Engineering vol 101 no 7 pp 633ndash649 1975

[6] M A Gabr T Lunne and J J Powell ldquoP-y analysis of laterallyloaded piles in clay using DMTrdquo Journal of GeotechnicalEngineering vol 120 no 5 pp 816ndash837 1994

[7] C C Fan and J H Long ldquoAssessment of existing methods forpredicting soil response of laterally loaded piles in sandrdquoComputers and Geotechnics vol 32 no 4 pp 274ndash289 2005

[8] G P Yang and Z M Zhang ldquoResearch on P-Y curve oflaterally bearing piles under large displacementrdquo WaterTransportation Engineering vol 342 no 7 pp 40ndash45 2002

[9] C Wang and Z A LU ldquoCalculation of internal forces oflaterally loaded piles by using p-y curverdquo Journal ofChongqing Jiaotong University (Natural Science) vol 4 no 1pp 61ndash65 1958

[10] H C Wang and D Q WU ldquoA new unified approach to thep-y curve of laterally loaded pile in clayrdquo Journal of HohaiUniversity no 1 pp 9ndash17 1991

[11] G C Wang and M Yang ldquoNonlinear analysis of laterallyloaded piles in sandrdquo Rock and Soil Mechanics no 2pp 261ndash267 2011

[12] G CWang andM Yang ldquoCalculation of laterally loaded pilesin clayrdquo Journal of Tongji University (Natural Science) vol 40no 3 pp 373ndash378 2012

[13] T Q Zhou Z A LU and D H Wang ldquoCalculation methodof laterally loaded super-long PHC pilerdquo Port and WaterwayEngineering no 6 pp 155ndash160 2013

[14] L U Cheng X C Xu S X Chen et al ldquoModel test andnumerical simulation of horizontal bearing capacity andimpact factors for foundation piles in sloperdquo Rock and SoilMechanics no 9 pp 2685ndash2691 2014

[15] P YinB H ZhaoM H Zhao et al ldquoStability analysis of pile-column bridge pile considering slope effectrdquo Journal of Hu-nan University (Natural Science) vol 43 no 11 pp 20ndash252016

[16] Y S Deng M H Zhao X J Zhou et al ldquoResearch progress ofbearing characteristics of pile column at steep slope inmountain areasrdquo Journal of Highway and TransportationResearch and Development vol 29 no 6 pp 37ndash45 2012

[17] K Georgiadis and M Georgiadis ldquoUndrained lateral pileresponse in sloping groundrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 136 no 11 pp 1489ndash1500 2010

[18] K Georgiadis and M Georgiadis ldquoDevelopment of p-ycurves for undrained response of piles near slopesrdquo Com-puters and Geotechnics vol 40 no 3 pp 53ndash61 2012

12 Advances in Civil Engineering

[19] K Muthukkumaran R Sundaravadivelu and S R GandhildquoEffect of slope on p-y curves due to surcharge loadrdquo Soils andFoundations vol 48 no 3 pp 353ndash361 2008

[20] L M Zhang C W W Ng and C J Lee ldquoEffects of slope andsleeving on the behavior of laterally loaded pilesrdquo Soils andFoundations vol 44 no 4 pp 99ndash108 2008

[21] B P Yin M H Zhao W He et al ldquoModel test study onidentification of foundation proportional coefficient m inslope groundrdquo Journal of Hunan University (Natural Science)vol 44 no 9 2017

[22] B L Gao C R Zhang and Z X Zhang ldquoModel tests on effectof slopes on lateral resistance of near single piles in sandrdquoRock and Soil Mechanics vol 35 no 11 pp 3191ndash3198 2014

[23] B T Zhu Be Ultimate Resistance and Laterally Loaded PileBehaviors Tongji University School of Civil EngineeringShanghai China 2005

[24] S S Rajashree and T G Sitharam ldquoNonlinear finite-elementmodeling of batter piles under lateral loadrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 127 no 7pp 604ndash612 2001

[25] R L Kondner ldquoHyperbolic stress-strain response cohesivesoilsrdquo Journal of the Soil Mechanics and Foundations Divisionvol 89 no 1 pp 115ndash143 1963

[26] K Bhushan S C Haley and P T Fong ldquoLateral load tests ondrilled piers in stiff claysrdquo Journal of the Geotechnical Engi-neering Division vol 1058 pp 969ndash985 1979

[27] J B Stevens and J M E Audibert ldquoRe-examination of P-Ycurve formulationsrdquo in Proceedings of 11th Offshore Tech-nology Conference pp 397ndash403 Houston TX USA 1980

[28] D Wu B B Broms and V Choa ldquoDesign of laterally loadedpiles in cohesive soils using p-y curvesrdquo Soils and Founda-tions vol 38 no 2 pp 17ndash26 1998

Advances in Civil Engineering 13

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

[19] K Muthukkumaran R Sundaravadivelu and S R GandhildquoEffect of slope on p-y curves due to surcharge loadrdquo Soils andFoundations vol 48 no 3 pp 353ndash361 2008

[20] L M Zhang C W W Ng and C J Lee ldquoEffects of slope andsleeving on the behavior of laterally loaded pilesrdquo Soils andFoundations vol 44 no 4 pp 99ndash108 2008

[21] B P Yin M H Zhao W He et al ldquoModel test study onidentification of foundation proportional coefficient m inslope groundrdquo Journal of Hunan University (Natural Science)vol 44 no 9 2017

[22] B L Gao C R Zhang and Z X Zhang ldquoModel tests on effectof slopes on lateral resistance of near single piles in sandrdquoRock and Soil Mechanics vol 35 no 11 pp 3191ndash3198 2014

[23] B T Zhu Be Ultimate Resistance and Laterally Loaded PileBehaviors Tongji University School of Civil EngineeringShanghai China 2005

[24] S S Rajashree and T G Sitharam ldquoNonlinear finite-elementmodeling of batter piles under lateral loadrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 127 no 7pp 604ndash612 2001

[25] R L Kondner ldquoHyperbolic stress-strain response cohesivesoilsrdquo Journal of the Soil Mechanics and Foundations Divisionvol 89 no 1 pp 115ndash143 1963

[26] K Bhushan S C Haley and P T Fong ldquoLateral load tests ondrilled piers in stiff claysrdquo Journal of the Geotechnical Engi-neering Division vol 1058 pp 969ndash985 1979

[27] J B Stevens and J M E Audibert ldquoRe-examination of P-Ycurve formulationsrdquo in Proceedings of 11th Offshore Tech-nology Conference pp 397ndash403 Houston TX USA 1980

[28] D Wu B B Broms and V Choa ldquoDesign of laterally loadedpiles in cohesive soils using p-y curvesrdquo Soils and Founda-tions vol 38 no 2 pp 17ndash26 1998

Advances in Civil Engineering 13

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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