Research ArticleNumerical Simulation Study on Lateral Displacement of PileFoundation and Construction Process under Stacking Loads

Yan-yan Cai,1,2 Bing-xiong Tu,1 Jin Yu ,1 Yao-liang Zhu,1 and Jian-feng Zhou1

1Fujian Engineering Technology Research Center for Tunneling and Urban Underground Space, Huaqiao University,Xiamen 361021, China2State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology,Chengdu 610059, China

Correspondence should be addressed to Jin Yu; bugyu0717@163.com

Received 16 January 2018; Accepted 18 February 2018; Published 21 March 2018

Academic Editor: Changzhi Wu

Copyright © 2018 Yan-yan Cai et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Lateral displacement of pile foundation is crucial to the safety of an overall structure. In this study, a numerical simulation on thelateral displacement of pile foundation under stacking loads was conducted to determine its relation with different influencingfactors. Simulation results demonstrated that stacking loads at the pile side mostly influence the lateral displacement of pilefoundation. The lateral displacement of pile foundation increases by one order of magnitude when the stacking loads increasefrom 100 kPa to 300 kPa. Other influencing factors are less important than stacking loads. Lateral displacements of the pile bodyand at the pile top can be reduced effectively by increasing the deformation modulus of surface soil mass, reducing the thickness ofsoft soil, and expanding pile diameter. Our analysis indicates that a nonlinear relationship exists between the lateral displacement atthe pile top and the pile diameter. The lateral resistance of the pile body can be enhanced by coupling the stacking load along pilesand the axial force at the pile top. An actual large-scale engineering project was chosen to simulate the effects of postconstructedembankment on lateral displacement and axial force of bridge pile foundation under different construction conditions and to obtainthe lateral displacement of the pile body and the negative frictional resistance caused by soft soil compression under stacking loads.On the basis of the calculated results, engineering safety and stability were evaluated, and a guide for the design and constructionwas proposed.

1. Introduction

Pile foundations in bridge, housing construction, and wharfconstruction engineering mainly bear axial loads. However,pile foundation is inevitably affected by the lateral movementof soil mass in actual construction and use due to excavation,current scouring, adjacent stacking loads, or other reasons,according to Liang et al. [1] and Poulos [2]. Engineering acci-dents might occur if such influences are not considered thor-oughly.Moreover, the expected goal cannot be achieved if thehorizontal resistance of pile foundation, which is set to main-tain soil stability in some high embankment or slope engi-neering, is inadequate. Such problems show that studying theresponses of pile foundation under lateral movement of soilmass is important. To discuss these problems, scholars haveconducted numerous theoretical and experimental studies

and applied breakthroughs in engineering. For example, theslope stability problem can be designed by the ultimateequilibrium method proposed by Ito et al. [3]. Horizontalforce applied on pile foundation was calculated by usingthe theoretical equation deduced by Ito and Matsui [4] onthe basis of plastic displacement theory. Considering thecomplexity and diversity of actual engineering, scholars havereported many studies on the horizontal resistance of pilefoundation. Chen andPoulos [5] studied the responses of ver-tical piles under horizontal movement of soil mass by usingthe simplified boundary element. Goh et al. [6] analyzedthe responses of single pile to embankment-induced lateralmovement of soil mass. Ashour and Norris [7] analyzed theeffects of the bending rigidity of pile body, pile section shape,pile interval, and soil layers on the lateral resistance of pilefoundation by using the stress wedge model formula. On the

HindawiComplexityVolume 2018, Article ID 2128383, 17 pageshttps://doi.org/10.1155/2018/2128383

2 Complexity

basis of the flexural differential equation of elastic piles andthe pile-soil interaction spring model of Winkler, Liang etal. [1] proposed a simplified analysis approach by combiningthe two-stage method, which was used to solve the effectsof lateral displacement of soil on pile. LeBlanc et al. [8], DeSanctis and Russo [9], and Kitiyodom and Matsumoto [10]have conducted corresponding studies that mainly focusedon the behaviors of piles under pure transverse loads. How-ever, loads on pile foundation might occur in inclined orcombined forms in actual service. Karthigeyan et al. [11],Chien et al. [12], Lee et al. [13], and Mu et al. [14] have foundthat pile responses under combined loads differ significantlyfrom those under pure vertical or pure horizontal loads.Mu et al. [15] studied the responses of a single pile underthe combined effect of vertical and transverse loads througha series of experiments and found that vertical loads canincrease the horizontal resistance of a single pile. Thesestudies did not consider the soil masses surrounding the pile.Considering actual layering conditions in depth range of pilefoundation, Goh et al. [6], Ashour et al. [16], and Yang andBoris [17] evaluated the lateral behaviors of piles with twosoil layers. Jing et al. [18] studied the lateral displacement andbendingmoment of deepmixed pile at different embankmentpositions by using the slope failure mode and found that themaximum bending moment always occurs in the soft-hardsoil interface. These studies considered few soil layers andmainly two soil layers (soft and hard soil layers), which isapparently different from actual engineering. Moreover, theydid not consider the relative thickness of the soft and hardsoil layers. Hence, further studies should be conducted. Thekey to studying horizontal resistance of pile foundation isto determine the lateral displacement of the pile. The mostaccurate method of determining the lateral displacementof pile is through an in situ test or experimental study, asproposed by Chien et al. [12], Guo and Ghee [19], and Reddyand Ayothiraman [20]. However, the method is difficult toapply in actual engineering.The empirical approach andfiniteelement method are widely used. The empirical approachwas developed from the accumulation of many engineeringprojects and is applied to certain cases only. In specialsituations, the empirical approach might cause large errors.With the improvement of the performance of computers,large finite element software has been applied to analyzeengineering problems, which could obtain accurate results.Yang and Boris [17], Hazzar et al. [21], Zhang et al. [22, 23],Souri et al. [24], and Chen andHsu [25] studied the behaviorsof pile under transverse load by using the finite elementmethod. Subsequently, Karthigeyan et al. [11] discussed theeffects of axial load on the lateral resistance of pile foundationthrough a numerical simulation. Zhang and Li [26] studiedthe bending features of pile under the combined effect of axialload and lateral displacement of piles by using the 3D non-linear elastoplasticity finite element method. Choi et al. [27]studied the influence of bed rock depth on load-displacementcurve, displacement, and bending moment of pile body byusing the FLAC3D finite difference analysis program. Tocombine analysis results and practices, Poulos [2] studiedground displacement caused by excavation by establishing a2D model and using the FLAC software. Karimm et al. [28]

studied the combination of 2D and 3D analysis approachesin influences of postconstructed embankment on the originalpiles.

Currently, few studies focus on multilayer soil mass andnegative frictional resistance surrounding piles caused bystacking loads. To further discuss the effects of lateral move-ment of soil mass on pile under complex terrain conditions,this paper discussed the effects of lateral displacement of soilmass on pile by using finite element numerical simulationand studied the lateral resistances of pile foundation understacking loads in different construction stages in actualengineering.

2. Principle of MIDAS/GTS Finite ElementMethod and Numerical Model

2.1. Principle of MIDAS/GTS Finite Element Method. In thisstudy, the large commercial finite element software MIDAS(Geotechnical and Tunnel Analysis System) was applied fornumerical simulation analysis. MIDAS organically combinesthe universal finite element analysis core and professionalrequirements of rock tunnel structure. MIDAS integratesthe advantages of existing rock tunnel analysis softwareand solves the displacement field and stress field of thewhole structure well, including displacement distribution,size, positions of stress concentration, area, and scope ofplastic region. The operation process mainly includes thedefinition of attributes, establishment of geometric model,meshing, setting of analysis conditions, analysis, and resultexamination. Six calculation steps are performed.(1) Discretization of structure: in the discretization ofstructure, the calculation object is viewed as a continuumand then divided into finite elements. Next, nodes are set atappointed points of elements. The adjacent elements connectmutually at nodes only. The shape, materials, load, andboundary conditions of the discretized structure are the sameas those of the original structure.(2) Selection of shape function: in accordance with thechosen shape function, the relation formula that expressesnode displacement at any point in the formula can bededuced. The matrix form is

{𝜔} = [𝑁] {𝛿}𝑒 , (1)

where {𝜔} = [𝜔𝑥, 𝜔𝑧]𝑇 is the displacement component arrayat any point and {𝛿}𝑒 = [𝜔𝑥𝑖, 𝜔𝑧𝑖, 𝜔𝑥𝑗, 𝜔𝑧𝑗, 𝜔𝑥𝑚, 𝜔𝑧𝑚]𝑇 isthe displacement array at element nodes 𝑖, 𝑗, and 𝑚. Theshape function matrix [𝑁] = [𝑁𝑖 0 𝑁𝑗 0 𝑁𝑚 00 𝑁𝑖 0 𝑁𝑗 0 𝑁𝑚

] is thefunction of the node coordinates.With respect to the triangleelement with three nodes, a linearmode can be hypothesized.Therefore, (1) can be rewritten as

𝜔𝑥 (𝑥, 𝑧) = 𝑁𝑖 (𝑥, 𝑧) 𝜔𝑥𝑖 + 𝑁𝑗 (𝑥, 𝑧) 𝜔𝑥𝑗+ 𝑁𝑚 (𝑥, 𝑧) 𝜔𝑥𝑚,

𝜔𝑧 (𝑥, 𝑧) = 𝑁𝑖 (𝑥, 𝑧) 𝜔𝑧𝑖 + 𝑁𝑗 (𝑥, 𝑧) 𝜔𝑧𝑗+ 𝑁𝑚 (𝑥, 𝑧) 𝜔𝑧𝑚.

(2)

Complexity 3

(3) Establishment of the relationship between elementstress and nodal displacement: the relation formula thatexpresses element strain by nodal displacement, known asgeometric equation, can be deduced from the geometricequation and (1):

{𝜀} = [𝐵] {𝛿}𝑒 , (3)

where {𝜀} = {𝜀𝑥, 𝜀𝑧, 𝛾𝑥𝑧}𝑇 is the strain array of any points inelements in the 𝑥 and 𝑧 planes. [𝐵] is the strain matrix,

[𝐵] =[[[[[[[[

𝜕𝑁𝑖𝜕𝑥 0 𝜕𝑁𝑗𝜕𝑥 0 𝜕𝑁𝑚𝜕𝑥 0

0 𝜕𝑁𝑖𝜕𝑧 0 𝜕𝑁𝑗𝜕𝑧 0 𝜕𝑁𝑚𝜕𝑧𝜕𝑁𝑖𝜕𝑧

𝜕𝑁𝑖𝜕𝑥𝜕𝑁𝑗𝜕𝑧

𝜕𝑁𝑗𝜕𝑥

𝜕𝑁𝑚𝜕𝑧𝜕𝑁𝑚𝜕𝑥

]]]]]]]]

. (4)

The relation formula of element stress can be deducedfrom the physical equation and (3) and is the physicalequation

{𝜎} = [𝐷] [𝐵] {𝛿}𝑒 , (5)

where {𝜎} is the stress array at any point in the element,and [𝐷] is the elasticity matrix or the elastoplasticity matrixrelated to thematerial properties of the element. For the planestrain elasticity problem, the equation is

[𝐷] = 𝐸 (1 − ])(1 + ]) (1 − 2]) =

[[[[[[

1 ]1 − ]

0]

1 − ]1 0

0 0 1 − 2]2 (1 − ])

]]]]]], (6)

where 𝐸 is the deformation modulus and ] is Poisson’s ratio.(4) Establishment of the relationship between node forceand nodal displacement on the element: on the basis of theprinciple of virtual work, the relation between node forceand nodal displacement on element can be expressed as anequilibrium equation of the element:

{𝐹}𝑒 = [𝑘]𝑒 {𝛿}𝑒 , (7)

where {𝐹}𝑒 is the equivalent node force array of element.Each node (𝑖, 𝑗, and 𝑚) of any element has two com-ponent forces along the 𝑋 and 𝑍 directions. Therefore,{𝐹}𝑒 = [𝐹𝑥𝑖, 𝐹𝑧𝑖, 𝐹𝑥𝑗, 𝐹𝑧𝑗, 𝐹𝑥𝑚, 𝐹𝑧𝑚]. [𝑘]𝑒 is the element stiffnessmatrix. {𝐹}𝑒 and [𝑘]𝑒 are

{𝐹}𝑒 = ∬[𝐵]𝑇 [𝜎] 𝑑𝑥 𝑑𝑧,{𝑘}𝑒 = ∬[𝐵]𝑇 [𝐷] [𝐵] 𝑑𝑥 𝑑𝑧.

(8)

(5) Establishment of the overall equilibrium equation: theoverall stiffnessmatrix of the structure [𝐾] can be obtained bycombining the stiffness matrixes of all elements. Meanwhile,the equivalent node force arrays of different elements are

combined, forming the overall load array [𝑅]. As a result, theequilibrium equation of the whole structure is

[𝐾] {𝛿} = {𝑅} . (9)

(6) The unknown nodal displacement and element stressare solved.

2.2. Constitutive Model of Soil Mass. When defining materialattributes, the selection of a constitutive model of soil massis crucial to the results. Currently, common yield criteriain the geotechnical engineering world include Tresca yieldcriterion, von Mises yield criterion, Drucker–Prager yieldcriterion, Mohr–Coulomb yield criterion, and double-shearstress yield criterion. All these yield criteria have certainadaptive norms. The Mohr–Coulomb yield criterion modelcan reflect the strength difference effect (S-D effect) ofsoil mass with different levels of compressive strength andsensitivity to hydrostatic pressure.The yield has the followingthree expressions:

The Mohr–Coulomb yield criterion is expressed as

𝜏𝑛 = 𝜎𝑛𝑡𝑔𝜑 + 𝑐. (10)

Yield condition is expressed by principle stress:

𝜎1 − 𝜎3 = (𝜎1 + 𝜎3) sin𝜑 + 2𝑐 cos𝜑. (11)

If expressed by invariants,

𝑓 = −13𝐼1 sin𝜑 + √𝐽2 sin(𝜃𝜎 +𝜋3 )

− 1√3√𝐽2 cos(𝜃𝜎 +

𝜋3 ) sin𝜑 − 𝑐 cos𝜑 = 0,

𝐼1 = 𝜎11 + 𝜎22 + 𝜎33,𝐽2 = −𝑆11𝑆22 − 𝑆22𝑆33 − 𝑆33𝑆11 + 𝑆122 + 𝑆232 + 𝑆312,

(12)

where 𝜏𝑛 is the ultimate shear stress,𝜎𝑛 is the ultimate positivestress, 𝜑 is the internal frictional angle of material, 𝑐 is thecohesion of materials, 𝜎1, 𝜎3 are the principal stress, 𝐼1 is thefirst principal invariant of the tensor of stress, 𝐽2 is the secondinvariant of the deviation tensor of stress, and 𝜃𝜎 is the localangle that ranges between (−𝜋/6, 𝜋/6).

Rock material is a granular material and mainly bearsload through frictions of particles. The displacement andfailure of rock materials are influenced by friction. Particlesovercome frictions and cause relative slippage failure as aresult of the combined effects of shear stress and verticalstress. Therefore, the Mohr–Coulomb yield criterion is rel-atively applicable to rock mass. In the principal stress space,the Mohr–Coulomb yield surface considering influences ofhydrostatic pressure is an irregular pyramid surface witha hexagonal section and is projected into a hexagon withunequal angles in the 𝜋 plane (Figure 1). Compared with theother criteria, the Mohr–Coulomb yield criterion model hasbetter comparability and requires relatively less parameterinformation. The needed cohesion (𝑐) and internal frictionangle (𝜑) can be tested by conducting a conventional test,which has important roles in engineering practice and hasbeen widely applied.

4 Complexity

Table 1: Information of soil.

Name Thickness of soilDeformationmodulus𝐸 (MPa)

Poisson’s ratio ] Unit weight𝛾 (kN/m3) Cohesive𝑐 (kPa) Internal frictionangle 𝜑

Filling 𝐻1 = 5m 10 0.35 18 15 15Mucky soil 𝐻2 = 5m 9 0.43 16.4 25 14.5Clay 𝐻3 = 10m 60 0.25 18 35 25Pile ℎ = 14m 40000 0.2 25

1

2

3

Figure 1: Mohr–Coulomb yield surface.

2.3. Numerical Model. The finite element model is shown inFigure 2. 𝐻1 is filling, 𝐻2 is soft soil, and 𝐻3 is clay. Pilefoundation selects the linear elastic model and uses beamelements. In order to consider the interaction of pile and soil,the key of modeling is to ensure that the element node of thepile is coincident with the element node of soil, and the meshsize of the soil and the pile is 1m. Poisson’s ratio, unit weightof soil, and elasticity modulus are set to 0.2, 25 kN/m3, and40GPa, respectively. To study the effect of pile size on lateraldisplacement, pile diameter is set to 0.8, 1.0, and 1.2m. Themature Mohr–Coulomb model is chosen for rock and soilmasses. Solid elements are used. Initial deformationmodulus,Poisson’s ratio, cohesion, and specific parameters are listed inTable 1.

3. Parameter Analysis and Discussions

3.1. Stacking Loads. Vertical and lateral (𝑥-axis direction)displacements cloud charts of soil mass under 100 kPa stack-ing load are shown in Figure 3. Figure 3(a) shows that,under stacking loads, a 18mm downward displacement isgenerated on the soil surface. However, soil displacement thatsurrounds pile foundation is relatively smaller than that ofsurrounding areas due to pile-soil friction. Figure 3(b) showsthat soil mass generates displacement toward two sides bycentering at the stacking load, whereas the lateral displace-ment mainly occurs in the second soft soil layer. Figure 4shows that the lateral displacement of pile increases with theincrease in stacking load, and the maximum displacement isat the pile top.Themaximum lateral displacement is 6.14mmwhen the stacking load is 100 kPa and increases to 5.55 cmwhen the stacking load is 300 kPa, showing an order of

growth magnitude. By comparing with the results of otherfactors, we can find that stacking load is mostly important tothe lateral displacement of pile. Figure 5 shows that, with theincrease in stacking load, lateral displacement caused by thelateral displacement of soil mass basically achieves a lineargrowth and reaches themaximumat the top layer.The growthrate of lateral displacement increases continuously.

3.2. Deformation Modulus of the Surface Soil (𝐸1). As isshown in Figures 6-7, we can find that, with the increase inthe deformation modulus of surface soil, the lateral displace-ments of pile body and at pile top decline gradually, whichreflects that the elasticity modulus of surface soil at the piletop is positively related to the lateral restraint of soil mass tothe pile. In Figure 6, themaximum lateral displacement of thepile body is 6.14mm when the deformation modulus of soilmass is 10MPa. When the deformation modulus increasesto 30MPa, the maximum displacement is decreased by 50%to 2.67mm. A comparison among the calculated results inSection 3.1 shows that the deformation modulus of surfacesoil mass is not as important as stacking loads at the pile side.Figure 7 shows that no evident linear relationship is foundbetween the displacement at the pile top and the deformationmodulus of the surface soil. Moreover, the increase of theconstraint effect decreases with the increase of the surfacesoil’s deformation modulus.

3.3. Pile Diameter. The lateral displacement distributioncloud chart of the pile body under different pile diametersis shown in Figure 8. Combining the calculated results inFigure 9 shows that the lateral displacements of the pilebody and the pile top decrease gradually with the increase inpile diameter. However, the reduction degree varies. Whenthe pile diameter increases from 0.8m to 1.0m, the lateraldisplacements of the pile body and the pile top changeslightly. The lateral displacements of the pile body and thepile top decrease from 6.62mm to 6.14mm only. However,the maximum lateral displacement at the pile top droppedsharply to 3.41mm when the pile diameter increased to1.2m, thus apparently showing a nonlinear relationship. Thelinear relationship is developed gradually at different types ofsoil interface (Figure 10), which could be interpreted fromtwo aspects. On the one hand, the dead load of the pilebody increases nonlinearly with the increase in pile diameter,which is beneficial to the increase in the lateral resistanceof the pile body. On the other hand, increased pile diam-eter expands the pile-soil contact area (linear relationshipbetween pile-soil contact area and pile diameter). As a result

Complexity 5

p Location of pile Pile

d

Pile

h

1Ｇ

H1

H2

H3

(a) Profile of the soil mode

p

Pile

X

Z

Y

H1

H2

H3

(b) Three-dimensional model of soil

Figure 2: Numerical model of pile and soil.

DisplacementTZ, m

25.2%45.7%14.0%

3.9%

0.8%

5.4%

3.1%

0.7%0.8%0.3%0.0%0.1%

−1.47524e − 002

−1.79314e − 002−1.63419e − 002

−1.31629e − 002−1.15734e − 002−9.98389e − 003−8.39438e − 003−6.80488e − 003−5.21358e − 003−3.62587e − 003−2.03637e − 003−4.46866e − 004+1.14264e − 003

X

Z

Y

(a) Soil displacement (𝑍 direction)

DisplacementTX, m

1.3%3.4%3.6%

5.1%

59.3%

4.8%

5.1%

6.4%4.8%3.9%2.0%0.4%

−1.41625e − 003

−2.35808e − 003

−1.88716e − 003

−9.45331e − 004

−4.74414e − 004

−3.49776e − 004

+4.67419e − 004

+9.38336e − 004

+1.40925e − 003

+1.88017e − 003

+2.35109e − 003

+2.82200e − 003

+3.29292e − 003

X

ZY

(b) Soil displacement (𝑋 direction)

Figure 3: Soil displacement under 100 kPa of stacking loads.

of the frictional force between pile body and soil mass, thelateral displacement of soil mass will cause lateral stress onthe pile body and thereby cause lateral displacement of thepile body. The final variation law of lateral displacement ofpile body is used to determine which between the dead loador lateral friction of piles takes the dominant role. The deadload takes the dominant role in this case.

3.4. Thickness of Soft Soil. To discuss the effects of relativethickness of soft soil, the deformation modulus of surfacesoil in the model is determined to be twice the deformationmodulus of soft soil. Figures 11 and 12 show that the lateraldisplacement of the pile body increases with the increase inthe relative thickness of soft soil. The lateral displacement ofthe pile body increases from 3.92mm to 6.63mm as the softsoil thickness increases from 5m to 10m (two soil layers).

Figure 12 shows an apparent linear relationship between thepile displacement and the relative thickness of soft soil. Effectsof relative thickness of soft soil on the lateral displacement ofpile are basically consistent with the deformation modulus ofsurface soil in Section 3.2.When the deformationmodulus ofthe soil mass that surrounds the pile top decreases, the lateralconstraint to the pile top is weakened, thereby increasing piledisplacement under lateral displacement or forces. On thebasis of the computational analysis, given the thick soft soillayer, the replacement thickness can be determined accordingto the displacement limit and properties of filling soils, whichavoids unnecessary excessive filling.

3.5. Effects of 𝐸1/𝐸2. The effects of deformation modulusratio of the adjacent hard soft layer and soft soil layer(𝐸1/𝐸2) on the lateral displacement of the pile body are

6 Complexity

E1 = 10－０；

E2 = 9－０；

p = 100 Ｅ０；

p = 200 Ｅ０；

p = 300 Ｅ０；

10 20 30 40 50 600Lateral displacement of pile body (mm)

14

12

10

8

6

4

2

0D

epth

(m)

Figure 4: Relationship between lateral displacement of pile andstacking loads.

The top of pileInterface of layers 1 and 2Interface of layers 2 and 3

0

10

20

30

40

50

60

Late

ral d

ispla

cem

ent (

mm

)

200 300100Stacking loads (kPa)

Figure 5: Relationship between lateral displacement and stackingloads at different positions.

shown in Figures 13 and 14. With the increase of 𝐸1/𝐸2, themaximum lateral displacement of the pile body decreasesgradually. However, the reduction amplitude varies. When𝐸1/𝐸2 increases from 1 to 2, the total reduction amplitudeis 40%. When 𝐸1/𝐸2 increases to 3, the total reductionamplitude is 56%, and the relative reduction amplitude isonly 16%, which indicates that increasing 𝐸1/𝐸2 can preventand solve the lateral displacement of the pile body effectively.However, 𝐸1/𝐸2 (2 in this case) can have a significant effectin a certain range. The effect will become insignificant when

p = 100 Ｅ０；

E1 = 10－０；

E1 = 20－０；

E1 = 30－０；

1 2 3 4 5 6 70Lateral displacement of pile body (mm)

14

12

10

8

6

4

2

0

Dep

th (m

)Figure 6: Relationship between lateral displacement of pile and 𝐸1.

20 3010Deformation modulus of layer 1 (MPa)

1

2

3

4

5

6

Late

ral d

ispla

cem

ent (

mm

)

The top of pileInterface of layers 1 and 2Interface of layers 2 and 3

Figure 7: Relationship between lateral displacement and 𝐸1 atdifferent positions.

the value is exceeded. In specific engineering, finite elementsoftware can be used to simulate the lateral displacements ofpile body under different 𝐸1/𝐸2, when foundation processingof surface soil mass and increasing deformation modulus areneeded, thus enabling the appropriate foundation processingto be determined and the lateral resistance demands of thepile body to be met.

3.6. Coupling Effect of Stacking Load and Axial Force at PileTop. On the basis of Section 3.1, an axial load of 7000 kN isapplied on the top of the pile.The result is shown in Figures 15

Complexity 7

1.3%3.4%3.6%

5.1%

59.3%

4.8%

5.1%

6.4%4.8%3.9%2.0%0.4%

DisplacementTX (m)

+1.10396e − 003

+5.51978e − 004

+1.65593e − 003

+2.20791e − 003

+2.75989e − 003

+3.31187e − 003

+4.41582e − 003

+3.85984e − 003

+4.95780e − 003

+5.51970e − 003

+6.07175e − 003

+6.62373e − 003

+0.00000e − 000

(a) 𝑟 = 0.8m

3.6%7.1%

7.1%

0.0%

7.1%

7.1%

7.1%7.1%14.2%7.1%25%

7.1%

DisplacementTX (m)

+0.00000e − 000

+1.02436e − 003

+5.12180e − 004

+1.53654e − 003

+2.04872e − 003

+2.56090e − 003

+3.07308e − 003

+4.09744e − 003

+3.58526e − 003

+4.60962e − 003

+5.12179e − 003

+5.68897e − 003

+6.14615e − 003

(b) 𝑟 = 1.0m

3.6%7.1%

7.1%

7.1%

7.1%

7.1%

7.1%7.1%7.1%7.1%25%

7.1%

DisplacementTX (m)

+0.00000e − 000

+5.68712e − 004

+2.84356e − 004

+8.53069e − 004

+1.13742e − 003

+1.42178e − 003

+1.70614e − 003

+2.27485e − 003

+1.99049e − 003

+2.55921e − 003

+2.84356e − 003

+3.12792e − 003

+3.41227e − 003

(c) 𝑟 = 1.2m

Figure 8: The lateral displacement distribution cloud chart of pile body under different pile diameters.

E1 = 10－０；E2 = 9－０；

p = 100 Ｅ０；

d = 0.8d = 1.0d = 1.2

1 2 3 4 5 6 70Lateral displacement of pile body (mm)

14

12

10

8

6

4

2

0

Dep

th (m

)

Figure 9: Relationship between lateral displacement of pile and pilediameters.

and 16.The lateral displacements of the pile body decrease by58.8%, 57.5%, and 44.9% respectively, compared to Figure 4.This result indicates that the load at the pile top can reducethe lateral displacement of the pile body significantly becauseapplying axial force at the pile top is equivalent to applyingone constraint. Therefore, the free displacement at the piletop is transformed into constrained displacement and limitsdisplacement at the pile top to some extent.

4. Case Study

In this section, the lateral displacement of the pile bodyand the negative frictional resistance of soft soil caused by

The top of pileInterface of layers 1 and 2Interface of layers 1 and 3

0.8 1.21.0Pile diameter (m)

1

2

3

4

5

6

7La

tera

l disp

lace

men

t (m

m)

Figure 10: Relationship between lateral displacement and pilediameters at different positions.

stacking loads under different working conditions in differentconstruction stages are discussed by combining a real engi-neering case. The engineering case is a newly constructedembankment with a height of approximately 6-7m and runsthrough an existing bridge project. To avoid adverse impactsof the new embankment on the running safety of the originalbridge structure, the embankment body applied a U-type-reinforced concrete integrated section, which runs throughthe whole section in a span of one bridge. To eliminatethe compressive displacement of the foundation soil layerby the upper embankment load, the pile foundation wasprocessed by using a small single-tube high-pressure jet

8 Complexity

Table 2: Information of soil and pile.

Name Thickness of soil(m)

Deformationmodulus𝐸 (MPa)

Poisson’s ratio ] Unit weight𝛾 (kN/m3) Cohesive𝑐 (kPa) Internal frictionangle 𝜑

(1) Filling 0–2 10 0.35 18 15 15(2) Silty clay 0.4–3.9 18 0.38 19.1 25 14.5(3) Coarse sand 0.5–4 20 0.25 18 0 25(4) Sand and gravel 4–6 21 0.28 21 0 35(5) Sludge 4.5–5.0 9.25 0.43 16.4 11 1.5

(6) Completelyweathered 0.5–8 60 0.27 18.6 90 25

(7) Intenseweathering 30 200 0.23 19.5 180 35

(8) Embankmentbackfill 6-7 20 0.25 18 0 25

(9) Jet-grouted pilefoundation 5 400 0.3 20 450 30

(10) Pile/column 20/20 40000 0.2 25

(11) U-shapedconcrete tank 40000 0.2 25

E1/E2 = 2 : 1p = 100 Ｅ０；

H2 = 5Ｇ

H2 = 8Ｇ

H2 = 10Ｇ

1 2 3 4 5 6 70Lateral displacement of pile body (mm)

14

12

10

8

6

4

2

0

Dep

th (m

)

Figure 11: Relationship between lateral displacement of pile andrelative thickness of soft soil.

grouting pile with simple equipment and small disturbanceto the basic soil layer. The geological distribution is shownin Figure 17, the soil parameters are shown in Table 2,and the calculation model is shown in Figure 18. The axialload on the pile foundation is taken as the design bearingcapacity of a single pile at 7000 kN, and the diameter of thebridge pile is 1.8m. Numerical simulation analysis mainlyconsiders five construction conditions based on initial rocksoil solidification simulation.

The top of pileAt the depth of 5Ｇ

At the depth of 10Ｇ

6 7 8 9 105The thickness of soft soil (m)

0

1

2

3

4

5

6

7

Late

ral d

ispla

cem

ent (

mm

)

Figure 12: Lateral displacement at different positions.

(1)WorkingCondition 1.Mulanxi bridge pile construction andbridge pile construction are finished.

(2) Working Condition 2. Jet-grouted pile foundation con-struction is finished.

(3) Working Condition 3. U-shaped concrete pit and surfacefilling outside the pit are finished.

(4) Working Condition 4. Embankment filling in U-shapedconcrete pit is finished.

Complexity 9

E2 = 9－０；

p = 100 Ｅ０；

E1/E2 = 1

E1/E2 = 2

E1/E2 = 3

1 2 3 4 5 6 70Lateral displacement of pile body (mm)

14

12

10

8

6

4

2

0

Dep

th (m

)

Figure 13: Relationship between lateral displacement of pile and𝐸1/𝐸2.

The top of pileInterface of layers 1 and 2Interface of layers 2 and 3

0

1

2

3

4

5

6

7

Late

ral d

ispla

cem

ent (

mm

)

2 31E1/E2

Figure 14: Relationship between lateral displacement and 𝐸1/𝐸2 atdifferent positions.

(5) Working Condition 5. Embankment pavement is rununder overloads (30 kPa).

4.1. Lateral Displacement of Bridge Piles and Bridge Columns(𝑥-Axis). The lateral displacements of the bridge pile andpile column under different working conditions are shown inFigure 19. Small lateral displacements, with a size of 3.6mm,are found at the bridge column top under working conditions1 and 2. The lateral displacement under working condition 3increases to some extent and shows displacement expansion

E2 = 9－０；

N = 7000 ＋．E1 = 10－０；

p = 100 Ｅ０；

p = 200 Ｅ０；

p = 300 Ｅ０；

5 10 15 20 25 30 350Lateral displacement of pile body (mm)

14

12

10

8

6

4

2

0

Dep

th (m

)Figure 15: Lateral displacement of pile under coupling effect ofstacking load and axial force.

The top of pileInterface of layers 1 and 2Interface of layers 2 and 3

0

5

10

15

20

25

30

35

Late

ral d

ispla

cem

ent (

mm

)

200 300100Stacking loads (kPa)

Figure 16: Lateral displacement of pile at different positions undercoupling effect.

toward two sides. The displacement of the left pile is higherthan that of the right pile and has a size of 10mm.The lateraldisplacement under working condition 4 increases sharply.The lateral displacement of the left pile reaches 21.3mm, andthe lateral displacement of the right pile is 13.0mm. Thelateral displacement under working condition 5 continues toincrease. The lateral displacements of the left and right pilesreach 22.9 and 16.9mm, respectively.

The lateral displacement of the pile along the depth isshown in Figure 20. The lateral displacement under working

10 Complexity

Embankmentbackfill

6

Bridge piles and columnsBridge piles and columns

U-shaped concrete tank

Jet-grouted pilefoundation

112

34

5

7

24 4

5 56

Figure 17: Soil layer distribution and calculation model.

21

60

X

Z

Y62.5

Figure 18: Numerical simulation of postconstructed embankment(m).

condition 4 increases dramatically, and the displacement ofthe right pile is smaller than that of the left pile, mainlybecause the rock-socketed depth of the left pile is approxi-mately 4m, whereas the rock-socketed depth of the right pileis approximately 11m. In the pile region of 28–36m, the lateraldisplacement of the right pile is significantly smaller than thatof the left pile, thereby resulting in the small inclination of thepile body. Consequently, the lateral displacement at the piletop is relatively small.

The profiles of the lateral displacement under workingcondition 5 are shown in Figure 21. Soil mass generateslateral compressional displacement in the depth range ofapproximately 8m below the surface close to the bridge piles,

thus weakening lateral constraint to the piles. If bridge pileshave to be reinforced in the construction process, then doingso can reinforce soil mass in the passive region outside thebridge piles.

4.2. Lateral Displacement of Bridge Piles and Bridge Columns(𝑦-Axis). Limited by article length and actual calculationresults, only vertical displacements (𝑦-axis direction) ofbridge piles and bridge column under working conditions1 and 5 were introduced in this study (Figure 22). The soilmass did not result in a noticeable lateral displacement inthe length range of embankment (𝑦-axis direction) becausethe postconstructed embankment and pedestrian loads weredistributed along the 𝑦-axis direction. Therefore, loads canslightly influence the longitudinal displacement of the bridgepile and the bridge column. Figure 22 shows that themaximum lateral displacement of the bridge column underworking condition 5 is only 0.25mm, which is also observedin the right bridge column. The longitudinal displacementof the left bridge column is smaller because of the differentpositions of coupling beams at the left and right sides. Onecoupling beam at the top of the left side connects two pilesand enhances the lateral resistance of 𝑦-axis displacementsignificantly.

4.3. Lateral Displacement of Bridge Piles and Bridge Columns(𝑧-Axis). To understand the effects of stacking load on thevertical displacement of bridge piles and columns, the verticaldisplacements of working conditions 1 and 5 of bridge pilesand columns were extracted (Figure 23). The extra axialloads with vertical sedimentation under stacking loads aregenerated and applied onto the pile top, resulting in themaximum axial loads at the pile top. As a result of pile-soilfriction, the extra axial loads distribute to the pile end along

Complexity 11

14.6%12.7%11.46%

7.6%

5.1%

11.7%

5.1%

6.3%3.8%5.1%5.1%5.7%

DisplacementTX, m

−6.59093e − 003

−4.88589e − 003

−5.73841e − 003

−4.03337e − 003

−3.18085e − 003

−2.32883e − 003

−1.47581e − 003

+2.29223e − 004

−6.23296e − 004

+1.08174e − 003

+1.93426e − 003

+2.78678e − 003

+3.93930e − 003

(a) Working condition 2

14.6%12.7%11.46%

7.6%

5.1%

11.7%

5.1%

6.3%3.8%5.1%5.1%5.7%

DisplacementTX, m

−1.00438e − 002

−7.69266e − 003

−8.86823e − 003

−6.51709e − 003

−5.34152e − 003

−4.16595e − 003

−2.99038e − 003

−6.39236e − 004

−1.81481e − 003

+5.36335e − 004

+1.71191e − 003

+2.88748e − 003

+4.06305e − 003

(b) Working condition 3

9.5%

10.1%

10.1%

19.0%

5.1%

7.6%

6.3%

6.3%

6.3%

6.3%

6.3%

7.0%

DisplacementTX, m

−2.12870e − 002

−1.55685e − 002

−1.84277e − 002

−1.27092e − 002

−9.84998e − 003

−6.99073e − 003

−4.13149e − 003

+1.58700e − 004

−1.27225e − 004

+4.44624e − 003

+7.30549e − 003

+1.01647e − 002

+1.30240e − 002

(c) Working condition 4

8.2%

8.9%

8.9%

11.4%

5.1%

7.6%

15.2%

6.3%

7.6%

6.3%

7.6%

7.0%

DisplacementTX, m

−2.28864e − 002

−1.62618e − 002

−1.95741e − 002

−1.29494e − 002

−9.63712e − 003

−6.32480e − 003

−3.01248e − 003

+3.61216e − 003

+2.99841e − 004

+6.92448e − 003

+1.02368e − 002

+1.35491e − 002

+1.68614e − 002

(d) Working condition 5

Figure 19: Lateral displacement of bridge piles and columns under different working condition.

the pile top and decrease gradually.The vertical displacementof the bridge pile reaches the maximum at the op accordingto mechanics knowledge of materials but declines graduallywith the increase in depth.These findings are consistent withthe cloud chart in Figure 23. The maximum displacementsunder working conditions 1 and 5 are 3.81 and 4.31mm,respectively. Compared with the length of the pile column,the vertical displacement of bridge columns is insignificantunder most unfavorable construction working conditions ofthe project, and the effects can be neglected.

4.4. Axial Forces of Bridge Piles and Columns. Variations ofaxial forces of bridge piles and columns under five workingconditions are shown in Figure 24. Spinning pile treatmentwas performed for foundation construction after bridgepile construction. The axial force of the pile body basicallyremains the same but increases to some extent along the pile

body because the model calculation considers the effects ofgravity. The axial force of the bridge piles under workingconditions 3, 4, and 5 increases sharply compared with thatof working condition 2. However, the axial force of bridgepiles under working condition 5 is slightly higher than thatof working condition 4. Figure 24 shows that the axial forceof the pile body increases continuously as it proceeds deeply.The slopes of the curve changes of axial forces in workingconditions 3, 4, and 5 are smaller than those of the firsttwo working conditions, indicating that considerable drop-down loads are generated along piles. Combining Figures23(b) and 25, the vertical displacement of the pile body is ata millimeter level, and significant displacement of soil massis basically at a centimeter level. The vertical sediment of thesoil mass surrounding the bridge piles is larger than that ofthe vertical displacement of the piles, thus creating frictionalresistance on the piles downward and generating downward

12 Complexity

−25 −20 −15 −10 −5 0 5 10 15 20

Workingcondition 5

Workingcondition 4

Workingcondition 3

Workingcondition 1

Workingcondition 1

Workingcondition 2

Workingcondition 2

Workingcondition 3

Workingcondition 4

Workingcondition 5

The left pile

Lateral displacement of pile body (mm)

The right pile

40

35

30

25

20

15

10

5

0

Dep

th (m

)

Figure 20: Lateral displacement of left and right bridge piles and columns.

0.1%0.2%0.4%

2.6%

34.3%

1.4%

5.6%

31.9%13.2%6.4%2.8%0.8%0.2%0.0%0.0%0.0%

DisplacementTX, m

+7.21369e − 003

−1.63694e − 002−1.45553e − 002

−9.11304e − 003

−5.48488e − 003−3.67080e − 003−1.85672e − 003−4.26361e − 003

+5.39961e − 003

+9.02777e − 003+1.08419e − 002+1.26559e − 002

+1.77145e − 003+3.58553e − 003

−1.09271e − 002

−7.29896e − 003

−1.27412e − 002

Figure 21: Profiles of bridge pile columns and lateral displacement of foundation soil-working condition 5.

0.0%0.0%0.0%

0.1%

0.3%

0.1%

0.2%

0.5%98.3%0.3%0.2%0.1%0.1%0.0%0.0%0.0%

DisplacementTY, m

−3.57636e − 005

−5.72217e − 005

−5.00690e − 005

−4.29163e − 005

−2.14582e − 005

−2.86109e − 005

−1.43054e − 005

−7.15272e − 006

−9.73874e − 015

+7.15272e − 006

+2.14582e − 005

+1.43054e − 005

+2.86109e − 005

+4.29163e − 005

+5.00690e − 005

+5.72217e − 005

+3.57636e − 005

(a) Working condition 1

0.0%0.0%0.0%

0.0%

0.1%

0.0%

0.0%

99.3%0.5%0.1%0.0%0.0%0.0%0.0%0.0%0.0%

DisplacementTY, m

−2.50217e − 004

−2.19238e − 004

−1.88260e − 004

−1.57281e − 004

−9.53244e − 005

−1.26303e − 004

−6.43460e − 005

−3.33675e − 005

−2.38901e − 006

+2.85895e − 005

+9.05464e − 005

+5.95679e − 005

+1.21525e − 004

+1.83482e − 004

+2.14460e − 004

+2.45439e − 004

+1.52503e − 004

(b) Working condition 5

Figure 22: Longitudinal displacement of bridge piles.

Complexity 13

0.1%0.2%0.3%

0.5%

0.7%

0.4%

0.6%

96.8%0.1%0.0%0.0%0.0%0.0%0.0%0.0%0.0%

DisplacementTZ, m

−3.09207e − 003

−2.61636e − 003

−2.85422e − 003

−2.37851e − 003

−2.14066e − 003

−1.90281e − 003

−1.66496e − 003

−1.18926e − 003

−1.42711e − 003

−9.51405e − 004

−4.75703e − 004

−2.37851e − 004

+0.00000e − 000

−7.13554e − 004

−3.80562e − 003

−3.56777e − 003

−3.32992e − 003

(a) Working condition 1

0.1%0.2%0.2%

0.4%

0.6%

0.3%

0.5%

0.7%96.8%0.1%0.0%0.0%0.0%0.0%0.0%0.0%

DisplacementTZ, m

−4.31250e − 003

−4.04297e − 003

−3.77344e − 003

−3.50391e − 003

−2.96484e − 003

−3.26437e − 003

−2.69531e − 003

−2.42578e − 003

−2.15625e − 003

−1.88672e − 003

−1.34766e − 003

−1.61719e − 003

−1.07812e − 003

−5.39062e − 004

−2.69531e − 004

+0.00000e − 000

−8.08594e − 004

(b) Working condition 5

Figure 23: Vertical displacement of bridge piles and columns.

8 9 10 11 12 13 14 15 16 177Axial forces (103 Ｅ．)

40

35

30

25

20

15

10

5

0

Dep

th (m

)

Working condition 1Working condition 2Working condition 3

Working condition 4Working condition 5

Figure 24: Axial forces of bridge piles and columns.

load. Consequently, the axial force of the pile body increaseswith the increase in depth.

4.5. Jet-Grouted Pile Processing against Foundation Settlement.According to calculation results, a large lateral displacementwill be generated under the postconstructed embankmentand pedestrian loads. To ensure the safety of a bridge struc-ture, spinning pile processing was adopted by combining theparameter analysis results in Section 3. Spinning pile process-ing can increase the strength of the soil mass surroundingthe pile top and thereby restrict the lateral displacement of

32.0%13.1%9.2%

4.1%

3.6%

6.6%

3.0%

4.4%11.1%2.3%2.2%2.3%2.0%1.7%1.5%1.0%

DisplacementTZ, m

−1.84913e − 002

−9.86203e − 002−9.24565e − 002−8.62928e − 002−8.01290e − 002

−6.16377e − 002−5.54739e − 002−4.93102e − 002−4.31464e − 002

−3.08188e − 002−3.96826e − 002

−2.46551e − 002

−1.23275e − 002−6.16377e − 003+0.00000e − 000

−7.39652e − 002−6.78015e − 002

Figure 25: Vertical sedimentation of bridge pile and columns.

the pile body. Table 2 shows that the deformation modu-lus of the processed foundation increases to 400MPa. InFigure 19(b), the lateral displacement at the pile top afterthe processing is only 3.6mm. Moreover, the processingcan increase the vertical bearing capacity of the soil massand transmit the upper load uniformly, thus resulting ina uniform contribution of overall soil settlement. Verticalsettlements of processed soil mass under working conditions2 to 5 are shown in Figure 26. Settlement displacement ismaintained at 53mm after foundation processing and theoverall settlement became relatively uniform, thereby causinguniform stress of the bridge pile foundation and ensuringstructural safety.

4.6. Plastic Displacement of Foundation Soil. Soil mass willgenerate lateral displacement under stacking loads, and pilesgenerate lateral displacement due to pile-soil interaction.However, soil mass surrounding piles is restricted by piles

14 Complexity

85.7%3.0%2.4%

1.4%

0.9%

1.7%

1.2%

0.8%0.7%0.6%0.5%0.4%0.3%0.2%0.2%0.1%

DisplacementTZ, m

−1.72038e − 003−1.68450e − 003−1.64863e − 003−1.61275e − 003

−1.54099e − 003−1.57687e − 003

−1.50512e − 003−1.46924e − 003−1.43336e − 003−1.39748e − 003

−1.32573e − 003−1.36161e − 003

−1.28985e − 003

−1.21810e − 003−1.18222e − 003−1.14634e − 003

−1.25398e − 003

(a) Working condition 2

80.5%2.1%2.0%

1.7%

1.6%

1.9%

1.6%

1.4%1.3%1.2%1.1%1.0%0.9%0.7%0.6%0.3%

DisplacementTZ, m

−2.01730e − 002−1.98094e − 002−1.94457e − 002−1.90820e − 002

−1.83546e − 002−1.87183e − 002

−1.79910e − 002−1.76273e − 002−1.72636e − 002−1.68999e − 002

−1.61726e − 002−1.65363e − 002

−1.58089e − 002

−1.50815e − 002−1.47179e − 002−1.43542e − 002

−1.54452e − 002

(b) Working condition 3

80.2%2.0%2.1%

1.7%

1.7%

1.9%

1.6%

1.5%1.5%1.2%1.1%1.0%0.9%0.8%0.6%0.3%

DisplacementTZ, m

−4.79144e − 002

−4.72172e − 002−4.75658e − 002

−4.68687e − 002−4.65201e − 002−4.61715e − 002−4.58229e − 002

−4.51257e − 002−4.54743e − 002

−4.47772e − 002

−4.40800e − 002−4.37314e − 002−4.33828e − 002

−4.44268e − 002

−4.89602e − 002−4.86116e − 002−4.82630e − 002

(c) Working condition 4

0.1%0.1%0.2%

2.5%

2.2%

85.9%

2.7%

1.7%1.3%1.0%0.7%0.5%0.4%0.3%0.2%0.1%

DisplacementTZ, m

−5.28446e − 002−5.29363e − 002

−5.27529e − 002−5.26613e − 002−5.25696e − 002−5.24780e − 002

−5.22947e − 002−5.23863e − 002

−5.22030e − 002

−5.20197e − 002−5.19280e − 002−5.18364e − 002

−5.21113e − 002

−5.33029e − 002−5.32112e − 002−5.31196e − 002−5.30279e − 002

(d) Working condition 5

Figure 26: Vertical settlement of foundation after spinning pile processing.

from free displacement. The lateral displacement of piles (𝑥-axis direction) causes the soilmass in front of piles to generateactive earth pressure and the soil mass behind piles to gener-ate passive earth pressure. Plastic displacement is generatedwhen the earth pressure exceeds the strength of soil mass.The maximum principal plastic strain of soil mass underfive working conditions is shown in Figure 27. The lateraldisplacements of the pile body under working conditions 1and 2 are relatively small. Moreover, no plastic zones areformed in the foundation soil.The lateral displacement of thepile body increases with the increase of working condition 3,and the soilmass range in the accessories section surroundingpiles develops a plastic zone. The range and depth of theplastic zone increase gradually from working conditions 1 to5, which is in agreement with the lateral displacement of thepile body in Figure 19.

To understand the plastic region size of soil mass, thevertical and plane views of the maximum principal plasticstrain of soil mass under working condition 5 are shown inFigures 28 and 29. The plastic zone of the left bridge pilecovers a 1.5m radius away from the bridge pile and a depthof approximately 8m. The plastic zone of the right bridge

pile covers a 1.0m radius away from the bridge pile and adepth of approximately 6m. Similar to that in Section 4.1,the rock-socketed depth of the left pile is smaller than thatof the right pile, resulting in different lateral displacements ofthe right and left piles, as well as different active and passiveearth pressures on soil mass in the front and back of the piles.Therefore, the plastic zones of soil mass have different ranges.

On the basis of the above numerical analysis, attentionis given to the monitoring of lateral displacement and axialforce of bridge columns in actual construction to ensure thesafety and stability of the original bridge pile foundation.The construction shall be stopped immediately if the lateraldisplacement of pile columns is too large, the displacementrate is high, or the displacement exceeds a certain value. Thecauses of such occurrences shall be analyzed. Considering theanalysis results for the lateral displacement of the pile body inSection 3, the following emergency measures can be adoptedas necessary:(1) Piling pressure is applied at the external side of thebridge pile.(2) Soil mass in a certain range outside the bridge pile isreinforced.

Complexity 15

0.0%0.0%0.0%

0.0%

0.0%

0.0%

0.0%

0.0%0.0%0.0%0.0%0.0%0.0%0.0%0.0%100%

X

Z

Y

3D element strainsoil PE1 center

+0.00000e − 000+0.00000e − 000+0.00000e − 000+0.00000e − 000+0.00000e − 000+0.00000e − 000+0.00000e − 000+0.00000e − 000+0.00000e − 000+0.00000e − 000+0.00000e − 000+0.00000e − 000+0.00000e − 000

+0.00000e − 000+0.00000e − 000

+0.00000e − 000+0.00000e − 000

(a) Working conditions 1, 2

0.0%0.0%0.0%

0.1%

0.1%

0.1%

0.1%

0.2%0.2%0.3%0.3%0.5%0.6%0.8%1.0%95.7%

X

Z

Y

3D element strainsoil PE1 center

+0.00000e − 000+4.84809e − 004+9.69617e − 004+1.45443e − 003+1.93923e − 003+2.42404e − 003+2.90885e − 003+3.39366e − 003+3.87847e − 003+4.36328e − 003+4.84809e − 003+5.33290e − 003+5.81770e − 003+6.30251e − 003+6.78732e − 003+7.27213e − 003+7.75694e − 003

(b) Working condition 3

0.1%0.1%0.0%

0.1%

0.2%

0.1%

0.1%

0.2%0.4%0.5%0.6%0.8%

3D element strainsoil PE1 center

1.0%1.4%2.0%92.6%

X

Z

Y

+3.66735e − 003+4.88980e − 003+6.11225e − 003+7.33470e − 003+8.55715e − 003+9.77960e − 003+1.10020e − 002+1.22245e − 002+1.34469e − 002+1.46694e − 002+1.58918e − 002+1.71143e − 002+1.83367e − 002+1.95592e − 002

+0.00000e − 000+1.22245e − 003+2.44490e − 003

(c) Working condition 4

0.1%0.1%0.0%

0.1%

0.2%

0.1%

0.1%

0.2%0.4%0.6%0.7%1.0%1.3%1.7%2.2%91.3%

X

Z

Y

3D element strainsoil PE1 center

+0.00000e − 000+1.37503e − 003+2.75007e − 003+4.12510e − 003+5.50013e − 003+6.87516e − 003+8.25020e − 003+9.62523e − 003+1.10003e − 002+1.23753e − 002+1.37503e − 002+1.51254e − 002+1.65004e − 002+1.78754e − 002+1.92505e − 002+2.06255e − 002+2.20005e − 002

(d) Working condition 5

Figure 27: Maximum principal plastic strain of foundation soil under different working conditions.

Figure 28: Maximum principal plastic strain of foundation soil-vertical view.

Figure 29: Maximum principal plastic strain of foundation soil-plane view.

16 Complexity

(3)One to three cast-in-place piles connected with bridgepiles by coupling beams are set at a certain interval along theconstruction direction of bridge outside the bridge pile.

5. Conclusions

(1) The lateral displacement of a pile foundation understacking load is studied usingMIDAS finite element software.Our findings showed that the lateral displacement of thepile foundation is positively correlated with stacking pressureand soft soil thickness but is negatively correlated withthe deformation modulus of surface soil, the deformationmodulus ratio of hard and soft soils, the pile diameter, andthe axial force at the pile top. Lateral displacement has asignificant nonlinear relationship with pile diameter and alinear relationship with the relative thickness of soft soil,which basically shows linear relations with other factors.(2) Lateral displacement and axial force of bridge pilefoundation in an actual engineering project during excava-tion and stacking loads are simulated by using finite elementsoftware. Numerical simulation results demonstrate that thelateral displacement resistance of the pile foundation ispositively related to the rock-socketed depth of hard rock(soil). The lateral displacement of the pile foundation underdifferent working conditions varies significantly. Stackingloads along piles not only causes lateral displacement ofthe pile body and the pile top but may also generate extra-negative frictional resistance due to the compression of soilmass, thus increasing the axial force of the column bottom.Consequently, stacking loads along piles might cause piledamage, which deserves utmost attention. As a result of thelateral displacement of the pile body, soil mass along pilesis damaged by compression, thereby causing a plastic zone,which weakens the lateral constraint of piles.(3) With respect to large-scale actual engineering, anumerical simulation of complicated problems is conductedby using finite element software.The late construction is con-ducted according to the calculated values, which can achieveideal results. In comparison with the empirical method andthe in situ test, the proposed method exhibits outstandingspeed, convenience, and accuracy. Therefore, the proposedmethod can be applied widely in actual engineering.

Conflicts of Interest

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

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (51679093 and 51774147), the OpeningFund of State Key Laboratory of Geohazard Preventionand Geoenvironment Protection (Chengdu University ofTechnology), China (SKLGP2018K008), the Natural ScienceFoundation of Fujian Province of China (2017J01094), andthe Promotion Program for Young andMiddle-Aged Teacherin Science and Technology Research of Huaqiao University,China (ZQN-PY112 and ZQN-PY311).

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