# Seismic Interaction Characteristics of an Inclined Straight Alternating Pile Group-Soil in Liquefied Ground

Authors: Desen Kong; Meixu Deng; Zhimin Zhao
Journal: Advances in Civil Engineering
 (2019)

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## Abstract

In this paper, the pile-soil interaction of a low-rise pile cap foundation of an inclined straight alternating pile on two or three layers of a soil liquefaction site under seismic load is studied. By inputting the 0.5 g El Centro seismic wave in FLAC3D, the pile-soil interaction rule of the pile foundation of the inclined and straight pile groups of the low-pile cap under seismic action is simulated. By analyzing the soil acceleration, the pore pressure ratio, the horizontal displacement of the pile body, the vertical displacement, and the pile body bending moment, the law of pile-soil interaction between the pile and soil when the lower part of the pile is embedded in the clay layer is studied, and the low-rise pile cap inclined straight alternating group pile foundation on the two-layer soil and the three-layer soil free field is compared and analyzed. The results show that, under seismic load, the maximum acceleration of soil mass in the two-layer soil and three-layer soil model is discrete, and the pore pressure ratio of sand soil increases from bottom to top. By analyzing the displacement and bending moment of pile body, the bending moment at the joint between the pile cap and the top of pile body is the largest and the most vulnerable to damage. The maximum value of pile displacement and bending moment in the three-layer soil is less than the maximum value of the two-layer soil, indicating that the pile group foundation in the three-layer soil free site model is safer.


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## Body

## 1. Introduction

The inclined straight alternating pile group foundation has been widely used in civil engineering, such as port dock, bridge project, and long-span construction structure. In addition, located between the Pacific seismic belt and the Himalayan-Mediterranean seismic belt, our country is an earthquake-prone country, with the following characteristics: the earthquake distribution range is wide, the intensity is high, and the area with intensity exceeding VII degrees is more than half of the total land area. Moreover, the weakness of the liquefied soil layer is widely distributed in China, and the three urban agglomerations of the Yangtze River Delta, Pearl River Delta, and Beijing-Tianjin-Tangshan in the Bohai Rim Region and many coastal economic developed areas are mostly liquefied soils; as a result, once an earthquake occurs, a large number of pile foundations are likely to be damaged by liquefaction of the site. Therefore, it is urgent to study the seismic response characteristics of the inclined straight alternating pile group-soil in liquefied ground.In recent years, scholars at home and abroad have conducted a series of research studies on the seismic interaction characteristics of pile-soil in liquefied ground, with many research results obtained. Using the vibration table model experiments, Sasaki et al. [1], Tokida et al. [2], and Ohtomo and Hamada [3] had successively studied the influence of the liquefied lateral diffuser of the foundation soil on the seismic response characteristics of pile groups. Shahrour et al. [4] studied the influence of pile inclination and the length/fineness ratio on the seismic response characteristics of a 2 × 2 full inclined pile foundation by establishing a three-dimensional finite element calculation model. Motamed and Towhata [5, 6] studied the lateral diffuser deformation mechanism of a foundation and the influence of a site lateral diffuser on the dynamic response characteristics of a straight pile group using a vibration table model experiment. Dai et al. [7] used the Davidenkov constitutive model and the improved incremental pore pressure model by Byrne; the seismic response characteristics of the group pile foundation in the liquefiable foundation obtained by the total stress method and the effective stress method were compared and analyzed. Liu et al. [8] used the unified constitutive model of sand liquefaction to describe the stress-strain relationship of the soil of liquefiable foundation; on the basis of this model, a three-dimensional numerical calculation model of a 3 × 5 full straight pile group was established to study the dynamic interaction characteristics of the pile and the soil. Sulei et al. [9] used the vibration table model experiment to study the seismic response characteristics of a 2 × 2 full straight pile group with a low-pile cap and a single column pier structure in liquefiable ground. Huang et al. [10] studied the change rule of the pile lateral friction and the pile tip resistance of a straight pile in liquefied ground under a horizontal seismic force. Tang et al. [11] and Ling et al. [12] successively conducted vibration table model experiments to study a pile group with a low-pile cap single-column pier and a high pile cap-single column pier in liquefied ground, and the influence law of the pile cap type on dynamic response characteristics of structural system was analyzed emphatically. However, most of the results obtained at present are aimed at the foundation of a full straight pile or a full inclined pile group, and there are few reports on the seismic interaction characteristics of the inclined straight alternating group pile-soil.In this paper, taking the inclined straight alternating pile group foundation as the research object, the numerical calculation model of the seismic interaction characteristics of the inclined straight alternating pile group is established, and the law of acceleration response and the change law of pore pressure ratio are obtained by calculation and analysis; moreover, the horizontal and vertical displacement of the pile and the bending moment of the pile are obtained. On this basis, the influence law of the soil layer condition on the seismic interaction characteristics of the pile-soil in the liquefied ground is compared and analyzed to provide theoretical and technical support for the improvement of a seismic design method of the straight alternating pile group foundation in liquefaction ground.


## 2. Establishment of Numerical Calculation Model

To study the seismic interaction characteristics of inclined straight alternating pile group-soil in liquefied ground, a numerical calculation model was established for the actual conditions of a project. The foundation of this project is divided into two cases, namely, (1) two layers of soil foundation: the upper soil layer is clay, and the lower soil layer is sand; (2) three layers of soil foundation: the upper and lower soil layers are all clay, and the middle soil layer is sand. The bottom two soil layers are rock in both cases. The pile foundation is 2 × 3 inclined straight alternating pile group. The layout of pile group is shown in Figure1; pile 1 and pile 2 are straight piles, and pile 3, pile 4, pile 5, and pile 6 are inclined piles with outward inclination of 15°. Both straight and inclined piles are reinforced concrete piles. The diameter of piles is 0.8 m, and the height of pile bottom is −11 m (the site existing elevation is 0 m). The pile group foundation is embedded in the 0.5 m of the rectangular pile cap, and the pile cap is in the form of low-pile cap, whose size is 6 m × 4 m × 1 m. The top of the pile cap is a rectangular column with a single column, the cross section of the pier is square, the length is 1 m, the height is 2.5 m, and the bottom of the pier is embedded in the 0.5 m of the pile cap.Figure 1
Layout of the inclined straight alternating pile group.


### 2.1. Establishment of Numerical Model

The two kinds of numerical calculation models of the soil foundation conditions were established according to the actual engineering conditions, as shown in Figures2 and 3. The soil layer distribution and its physical and mechanical parameters of the two-layer and three-layer models are listed in Tables 1 and 2, respectively.Figure 2
Numerical simulation model corresponding to two soil layers.Figure 3
Numerical simulation model corresponding to three soil layers.Table 1
The distribution of soil layers and physical and mechanics parameters of the numerical simulation model corresponding to two soil layers.
Soil
Thickness (m)
Density (t·m−3)
Porosity
Cohesive force (kPa)
Bulk modulus (MPa)
Shear modulus (MPa)
Friction angle (°)
Permeability coefficient (m2/Pa·sec)
①
Clay
2
1.05
0.62
12
14.6
5.7
25
1e − 13
②
Sand
13
1.4
0.45
0
30
11
30
3.56e − 9
④
Rock
1
2.68
/
/
6.7e + 04
3.1e + 4
/
/Table 2
The distribution of soil layers and physical and mechanics parameters of the numerical simulation model corresponding to three soil layers.
Soil
Thickness (m)
Density (t·m−3)
Porosity
Cohesive force (kPa)
Bulk modulus (MPa)
Shear modulus (MPa)
Friction angle (°)
Permeability coefficient (m2/Pa·sec)
①
Clay
2
1.05
0.62
12
14.6
5.7
25
1e − 13
③
Sand
7
1.4
0.45
0
30
11
30
3.56e − 9
Clay
6
1.12
0.58
15
14.6
5.7
25
1e − 13
④
Rock
1
2.68
/
/
6.7e + 04
3.1e + 4
/
/The pile in the pile group model is simulated by the pile structure element. In the two-layer soil model and the three-layer free soil site model with a low-pile cap, the pile contains 7 equal length pile components, and the pile in the pile group extends into the 0.5 m in the pile cap. Using the reinforced concrete pile foundation, the connection property between the pile cap and the pile top node is set as rigid. The Mohr–coulomb model is adopted for the soil constitutive structure, and the elastic model is adopted for the rock constitutive structure. The ground water level is level with the ground, and the sand is completely saturated. The isotropic seepage model is adopted in the soil, and the impervious material model is used in the bottom rock. The flow of water obeys Darcy’s law, and the permeability coefficient and compressibility coefficient of soil are constant.


### 2.2. Boundary Condition and Material Parameter Setting

The free site parameters of the two-layer and three-layer soil foundation conditions are listed in Tables1 and 2, respectively. The two layers of soil case correspond to ①, ②, and ④, and the three layers of soil case correspond to ①, ③, and ④. By using free boundary conditions, 4 two-dimensional plane grids and 4 one-dimensional cylindrical meshes are generated around the free site model. The plane grid corresponds to the cylindrical mesh on the boundary of the model one by one, and the column grid is equivalent to the free boundary of the plane free field grid. The dynamic calculation model after the free boundary is generated is shown in Figure 4.Figure 4
Model of the dynamic calculation.Dynamic analysis of the numerical model of a pile foundation with a low-rise pile cap inclined straight alternating group is mainly divided into three steps: Step 1 is to establish the free site model, set the parameters, fluid model parameters, initial hole pressure field conditions, and boundary conditions, close the fluid mode and dynamic mode, and set the fluid modulus to 0 to achieve static balance under gravity. Step 2 is to clear the velocity field displacement field, open the mechanical calculation module, close the fluid calculation module, excavate the soil body, set the pile cap, establish the contact surface between the pile cap and the soil body, and set the parameters. Then, the model of pile and column pier is built in the model, and the model parameters are set for the initial balance calculation. Step 3 is to open the mechanical and fluid calculation mode, set the dynamic hole pressure model, set the boundary conditions and mechanical damping, set the monitoring point, input the acceleration at the bottom of the model, and then conduct the dynamic calculation.The critical damping ratio of pile cap and rock layer was 0.05, the damping ratio of clay was 0.1, and the damping ratio of sand and soil was 0.15. The local damping coefficients of pile cap, rock layer, clay, and sand soil were 0.1572, 0.1572, 0.3142, and 0.4713, respectively. The parameters of pile element are shown in Table3. The piers of the inclined straight pile group foundation have a diameter of 1 m and a height of 2.5 m. In the numerical model, the beam element in FLAC3D is adopted to simulate the column pier, including four equal length beam members. The bottom end of the pier extends into the pile cap for 0.5 m, and the connection property of the bottom end node of the beam element is set as rigid. The foundation of the bridge is a simply supported beam system, and 400-t mass blocks can be set on the pier to simulate the superstructure; this approach can reduce calculation, improve operation efficiency, and meet the requirements of engineering precision.Table 3
Parameters of piles.
Name
Angle (°)
Length (m)
Elasticity modulus (GPa)
Poisson’s ratio
Tangential coupling spring stiffness (GPa)
Tangential coupling spring adhesive strength (kPa)
Normal coupled spring stiffness (GPa)
Normal coupling spring adhesive strength (kPa)
Straight pile
0
10
40
0.3
23.4
97
2.34
97
Inclined pile
15
10.35
40
0.3
23.4
97
2.34
97In the pile group foundation, the elastic modulus of the pier is 40 GPa, the Poisson ratio is 0.3, and the density is 2400 kg m−3. The pile cap of the inclined straight alternating pile group is 6 m × 4 m × 1 m and is built by solid units and divided into a cube grid of 8 nodes of 1 m × 1 m × 1 m. In the pile group model of low-rise pile cap, 5 contact surfaces were established on 5 surfaces of contact between the bearing platform and the soil body; the parameters of the contact surfaces are listed in Table 4. The constitutive model of pile cap adopts the isotropic elastic model and impervious model.Table 4
Parameters of interfaces.
Name
Normal stiffness (MPa)
Tangential stiffness (MPa)
Friction angle (°)
Cohesive force (kPa)
Contact surface
100
100
14
8


### 2.3. Seismic Wave Selection

In this paper, the 0.5 g El Centro seismic wave is selected as the dynamic load to simulate the seismic load. The implementation is to enter the acceleration directly at the bottom of the model. The El Centro seismic wave is a real seismic wave recorded by a human and is widely used in seismic research. Kuhlemeyer and Lysmer [13] have shown that, to accurately describe the propagation of seismic waves in the model, the mesh size must be less than 1/8∼1/10 of the wavelength corresponding to the highest frequency of the input waveform, i.e,(1)Δl≤18∼110λ,where λ is the wavelength corresponding to the highest frequency.


### 2.4. Initial Equilibrium Analysis

The layer at the bottom of the model with a thickness of 1 m is a rigid foundation. The modely and z directions are fixed, the x direction is free, and seismic waves are input along the x direction. The hole pressure model adopts the Finn dynamic hole pressure model. The pore water pressure distribution of the model in the initial equilibrium calculation is shown in Figure 5(a). The figure shows that the pore water pressure increases from top to bottom. The bottom pore water pressure is zero because the bottom layer of the model is an impervious layer. The maximum pore water pressure is at the height of 29 m, and the maximum pore water pressure is 0.15 MPa.Figure 5
Contour of the pore water pressure and the Z-stress.
(a)
(b)The vertical stress distribution of the initial equilibrium calculation of the model after the mass block is set at the top of the pier is shown in Figure5(b). The figure shows that high stress zones are formed at the bottom of pile. The stress of the soil under the base of the inclined straight group pile is higher than that of the outer soil with the same depth; this difference is caused by the direct transfer of the load to the soil among the piles. Moreover, the vertical stress distribution in the lateral soil of the inclined pile is lower than that of the other soil at the same depth because the load under which the soil under the pile body is pressed and the soil in the upper part of the pile is less stressed.


## 2.1. Establishment of Numerical Model

The two kinds of numerical calculation models of the soil foundation conditions were established according to the actual engineering conditions, as shown in Figures2 and 3. The soil layer distribution and its physical and mechanical parameters of the two-layer and three-layer models are listed in Tables 1 and 2, respectively.Figure 2
Numerical simulation model corresponding to two soil layers.Figure 3
Numerical simulation model corresponding to three soil layers.Table 1
The distribution of soil layers and physical and mechanics parameters of the numerical simulation model corresponding to two soil layers.
Soil
Thickness (m)
Density (t·m−3)
Porosity
Cohesive force (kPa)
Bulk modulus (MPa)
Shear modulus (MPa)
Friction angle (°)
Permeability coefficient (m2/Pa·sec)
①
Clay
2
1.05
0.62
12
14.6
5.7
25
1e − 13
②
Sand
13
1.4
0.45
0
30
11
30
3.56e − 9
④
Rock
1
2.68
/
/
6.7e + 04
3.1e + 4
/
/Table 2
The distribution of soil layers and physical and mechanics parameters of the numerical simulation model corresponding to three soil layers.
Soil
Thickness (m)
Density (t·m−3)
Porosity
Cohesive force (kPa)
Bulk modulus (MPa)
Shear modulus (MPa)
Friction angle (°)
Permeability coefficient (m2/Pa·sec)
①
Clay
2
1.05
0.62
12
14.6
5.7
25
1e − 13
③
Sand
7
1.4
0.45
0
30
11
30
3.56e − 9
Clay
6
1.12
0.58
15
14.6
5.7
25
1e − 13
④
Rock
1
2.68
/
/
6.7e + 04
3.1e + 4
/
/The pile in the pile group model is simulated by the pile structure element. In the two-layer soil model and the three-layer free soil site model with a low-pile cap, the pile contains 7 equal length pile components, and the pile in the pile group extends into the 0.5 m in the pile cap. Using the reinforced concrete pile foundation, the connection property between the pile cap and the pile top node is set as rigid. The Mohr–coulomb model is adopted for the soil constitutive structure, and the elastic model is adopted for the rock constitutive structure. The ground water level is level with the ground, and the sand is completely saturated. The isotropic seepage model is adopted in the soil, and the impervious material model is used in the bottom rock. The flow of water obeys Darcy’s law, and the permeability coefficient and compressibility coefficient of soil are constant.


## 2.2. Boundary Condition and Material Parameter Setting

The free site parameters of the two-layer and three-layer soil foundation conditions are listed in Tables1 and 2, respectively. The two layers of soil case correspond to ①, ②, and ④, and the three layers of soil case correspond to ①, ③, and ④. By using free boundary conditions, 4 two-dimensional plane grids and 4 one-dimensional cylindrical meshes are generated around the free site model. The plane grid corresponds to the cylindrical mesh on the boundary of the model one by one, and the column grid is equivalent to the free boundary of the plane free field grid. The dynamic calculation model after the free boundary is generated is shown in Figure 4.Figure 4
Model of the dynamic calculation.Dynamic analysis of the numerical model of a pile foundation with a low-rise pile cap inclined straight alternating group is mainly divided into three steps: Step 1 is to establish the free site model, set the parameters, fluid model parameters, initial hole pressure field conditions, and boundary conditions, close the fluid mode and dynamic mode, and set the fluid modulus to 0 to achieve static balance under gravity. Step 2 is to clear the velocity field displacement field, open the mechanical calculation module, close the fluid calculation module, excavate the soil body, set the pile cap, establish the contact surface between the pile cap and the soil body, and set the parameters. Then, the model of pile and column pier is built in the model, and the model parameters are set for the initial balance calculation. Step 3 is to open the mechanical and fluid calculation mode, set the dynamic hole pressure model, set the boundary conditions and mechanical damping, set the monitoring point, input the acceleration at the bottom of the model, and then conduct the dynamic calculation.The critical damping ratio of pile cap and rock layer was 0.05, the damping ratio of clay was 0.1, and the damping ratio of sand and soil was 0.15. The local damping coefficients of pile cap, rock layer, clay, and sand soil were 0.1572, 0.1572, 0.3142, and 0.4713, respectively. The parameters of pile element are shown in Table3. The piers of the inclined straight pile group foundation have a diameter of 1 m and a height of 2.5 m. In the numerical model, the beam element in FLAC3D is adopted to simulate the column pier, including four equal length beam members. The bottom end of the pier extends into the pile cap for 0.5 m, and the connection property of the bottom end node of the beam element is set as rigid. The foundation of the bridge is a simply supported beam system, and 400-t mass blocks can be set on the pier to simulate the superstructure; this approach can reduce calculation, improve operation efficiency, and meet the requirements of engineering precision.Table 3
Parameters of piles.
Name
Angle (°)
Length (m)
Elasticity modulus (GPa)
Poisson’s ratio
Tangential coupling spring stiffness (GPa)
Tangential coupling spring adhesive strength (kPa)
Normal coupled spring stiffness (GPa)
Normal coupling spring adhesive strength (kPa)
Straight pile
0
10
40
0.3
23.4
97
2.34
97
Inclined pile
15
10.35
40
0.3
23.4
97
2.34
97In the pile group foundation, the elastic modulus of the pier is 40 GPa, the Poisson ratio is 0.3, and the density is 2400 kg m−3. The pile cap of the inclined straight alternating pile group is 6 m × 4 m × 1 m and is built by solid units and divided into a cube grid of 8 nodes of 1 m × 1 m × 1 m. In the pile group model of low-rise pile cap, 5 contact surfaces were established on 5 surfaces of contact between the bearing platform and the soil body; the parameters of the contact surfaces are listed in Table 4. The constitutive model of pile cap adopts the isotropic elastic model and impervious model.Table 4
Parameters of interfaces.
Name
Normal stiffness (MPa)
Tangential stiffness (MPa)
Friction angle (°)
Cohesive force (kPa)
Contact surface
100
100
14
8


## 2.3. Seismic Wave Selection

In this paper, the 0.5 g El Centro seismic wave is selected as the dynamic load to simulate the seismic load. The implementation is to enter the acceleration directly at the bottom of the model. The El Centro seismic wave is a real seismic wave recorded by a human and is widely used in seismic research. Kuhlemeyer and Lysmer [13] have shown that, to accurately describe the propagation of seismic waves in the model, the mesh size must be less than 1/8∼1/10 of the wavelength corresponding to the highest frequency of the input waveform, i.e,(1)Δl≤18∼110λ,where λ is the wavelength corresponding to the highest frequency.


## 2.4. Initial Equilibrium Analysis

The layer at the bottom of the model with a thickness of 1 m is a rigid foundation. The modely and z directions are fixed, the x direction is free, and seismic waves are input along the x direction. The hole pressure model adopts the Finn dynamic hole pressure model. The pore water pressure distribution of the model in the initial equilibrium calculation is shown in Figure 5(a). The figure shows that the pore water pressure increases from top to bottom. The bottom pore water pressure is zero because the bottom layer of the model is an impervious layer. The maximum pore water pressure is at the height of 29 m, and the maximum pore water pressure is 0.15 MPa.Figure 5
Contour of the pore water pressure and the Z-stress.
(a)
(b)The vertical stress distribution of the initial equilibrium calculation of the model after the mass block is set at the top of the pier is shown in Figure5(b). The figure shows that high stress zones are formed at the bottom of pile. The stress of the soil under the base of the inclined straight group pile is higher than that of the outer soil with the same depth; this difference is caused by the direct transfer of the load to the soil among the piles. Moreover, the vertical stress distribution in the lateral soil of the inclined pile is lower than that of the other soil at the same depth because the load under which the soil under the pile body is pressed and the soil in the upper part of the pile is less stressed.


## 3. Analysis of the Calculation Results

### 3.1. Analysis of Calculation Results of the Two Layers of Soil

#### 3.1.1. Analysis of the Soil Acceleration

The propagation of and variation in seismic waves in the soil body model can be obtained by analyzing the acceleration time-history curve of the soil body of the model on the basis of inclined straight piles of the low-rise pile cap in the two-layer soil liquefaction site. The acceleration of soil under the action of the 0.5 g El Centro seismic wave is compared and analyzed to study the effect of a seismic wave on soil acceleration. The locations of soil body monitoring points J1-J8 in the model are shown in Figure2, and the specific information of these points is provided in Table 5. The acceleration of soil under the action of the alternating pile group foundation and the acceleration of soil mass outside the pile foundation are collected. Monitoring points J1 and J5 are located at the interface between the rock layer and the sand layer, and the other 6 monitoring points are in the sand layer. The time-history curve of soil acceleration under the action of seismic waves is shown in Figure 6. The maximum acceleration in the time-history curve of soil acceleration from monitoring points J1, J2, J3, and J4 was 8.10 m/s2, 9.95 m/s2, 7.793 m/s2, and 3.27 m/s2, respectively. The maximum acceleration in the time-history curve of soil acceleration from monitoring points J5, J6, J7, and J8 was 8.88 m/s2, 10.41 m/s2, 6.25 m/s2, and 5.06 m/s2, respectively. The maximum acceleration of soil mass monitoring point is greater than the maximum value of the input seismic load; this observation fully shows the amplification effect of soil mass on the acceleration load. The amplification effect of sand layer on seismic load increases first and then decreases from the bottom to the top, and there is no obvious regularity in the propagation of seismic waves along the soil layer.Table 5
Information of monitoring location.
Name
Coordinates
Name
Coordinates
J4
(0, 0, −3)
J8
(10, 0, −3)
J3
(0, 0, −7)
J7
(10, 0, −7)
J2
(0, 0, −11)
J6
(10, 0, −11)
J1
(0, 0, −15)
J5
(10, 0, −15)Figure 6
Acceleration of soil under the 0.5 g El Centro seismic wave.


#### 3.1.2. Analysis of the Pore Pressure Ratio

Five monitoring points in the model were selected for analysis. The location is shown in Figure2. In the 5 monitoring points, 2 of the soil masses are under the action of inclined straight pile alternating group foundation, and the remaining 3 soil masses are outside the pile group foundation. These 5 monitoring points are all located in the liquefiable sand soil layer, and the value of the pore pressure ratio of each monitoring point is listed in Table 6. The time-history curve of the hole pressure ratio at each monitoring point under the action of seismic waves is shown in Figure 7. The overall time-history curve of the hole pressure ratio at the monitoring point fluctuates. The time-history curve of the hole pressure ratio at the KJ2 monitoring point presents a fluctuating upward trend, and the hole pressure ratio exceeds 0.8 after 13 s. The hole pressure ratios at monitoring points KJ1 and KJ5 are lower than those at the same buried depth at KJ2 and KJ4, indicating that the pile group foundation can still inhibit the liquefaction of sand and soil under the pile group foundation during seismic action, and the pile group foundation is still strengthened. The pore pressure ratio of KJ2 exceeds 0.8, indicating that the liquefaction depth of the sand and soil layer under the earthquake is large. The time-history curve of the pore pressure ratio at KJ4 is concentrated near 1 and moves forward in a wavy manner because the liquefaction of the lower soil has a seismic isolation effect on the upper sand layer.Table 6
Information of monitoring location.
Name
Coordinates
Name
Coordinates
KJ1
(0, 0, −7.5)
KJ3
(10, 0, −5.5)
KJ2
(10, 0, −7.5)
KJ4
(10, 0, −2.5)
KJ5
(0, 0, −2.5)
/
/Figure 7
Time-history curves of the pore pressure ratio.


#### 3.1.3. Displacement Analysis of the Pile Body

(1) Analysis of the Horizontal Displacement of the Pile Body. The six piles in the inclined straight pile group foundation are symmetric about the xOz plane, the seismic waves are input along the x direction, and the x direction displacement of the 1#, 3#, and 5# piles is taken for analysis, as shown in Figure 8. The figure shows that, under the earthquake action, the pile foundation of inclined straight alternating group moves towards the horizontal direction. The pile cap of the pile foundation was moved 0.0391 m under the seismic action of inclined straight alternating group piles, and the connecting line of each point was curved, indicating that the pile body had buckled. All three piles in the pile group foundation of inclined piles are inclined to different degrees, and the degree of incline of the piles is greater than that of straight piles, primarily because the straight pile is subjected to soil pressure on the pile side, whereas the inclined pile is subjected to overburden pressure and soil support on the lower side. The pile body of the 3# pile is inclined in the positive direction of x, the slope of the 5# pile foundation is high, and the displacement difference between pile top and pile bottom is 0.14 m.Figure 8
Horizontal displacement of the pile.(2) Vertical Displacement Analysis of the Pile Body. Under the seismic action of the liquefaction site, the pile foundation of the inclined straight alternating group moves downward as a whole. The vertical displacement of the pile top is different, and the pile foundation pile cap is inclined. Under seismic action, the displacement of pile top of pile 3# is greater than that of pile 1#; the displacement difference between the tops of the 3# pile and the 5# pile is 0.0473 m, and the vertical displacement of all points of 1# pile is almost the same because the liquefaction sand layer under the earthquake is thicker, the bottom end of pile is under less stress, and the pile body moves down. Figure 9 shows that the vertical displacement of the top of the inclined pile is different from that of the pile bottom via the inclination of the inclined pile. The maximum vertical displacement difference between pile top and pile bottom is for the 5# pile, with a difference of 0.0377 m, indicating that the 5# pile has a large tilt; this result is the same as the horizontal displacement analysis result. The vertical displacement at the top of the 1# pile is 0.3454 m.Figure 9
Vertical displacement of the pile.


#### 3.1.4. Analysis of the Bending Moment of the Pile Body

The bending moments of the pile bodies of the 1#, 3#, and 5# piles were taken for analysis, as shown in Figure10. Under seismic load, the maximum bending moment was generated at the junction of the pile top and the pile cap of the 5# pile, and the maximum value was 5710 kN m, whereas the bending moment at the top of the 3# pile is the smallest, with a bending moment of 3060 kN m. During strong earthquakes, the enveloping line of pile bending moments decreases sharply at a buried depth of 9 m, and the enveloping line of the bending moment above 9 m is a smooth curve because of the large liquefaction thickness of the sand and soil layer. The maximum value of the bending moment at each point of piles 1# and 5# is positive, and the maximum value of the bending moment at each point of pile 3# is negative because the horizontal displacement direction of the 1# and 5# piles is the same; this result is the same as the analysis result of the horizontal displacement of the pile body. The maximum bending moment of 3 piles in the foundation of inclined straight alternating group piles is produced in the connection between the pile body and the pile cap, indicating that the connection of the pile and the pile cap under seismic load is the most likely to cause foundation damage.Figure 10
Moment envelope of the pile.


### 3.2. Analysis of the Results of Three Layers of Soil

#### 3.2.1. Analysis of Soil Acceleration

The information of the 8 monitoring points is consistent with Section2.1. The thickness of the sand soil layer in the three-layer free site model is 7 m, that is, there are 4 monitoring points in the sand soil layer, and the remaining monitoring points are in the clay layer. Since the lower part of the model is the lithosphere, the acceleration input in the soil layer is equal to the acceleration of the monitoring point at the buried depth of 15 m. The time-history curve of soil acceleration is shown in Figure 11.Figure 11
Acceleration of soil under the 0.5 g El Centro seismic wave.The time-history curve of acceleration at monitoring points J1 and J4 is equivalent to the time history of acceleration input in soil. The maximum acceleration in the acceleration time curve of the monitoring point is greater than that of the input acceleration time curve. The maximum acceleration at monitoring points J1, J2, J3, and J4 was 10.61 m/s2, 13.13 m/s2, 11.55 m/s2, and 6.35 m/s2, respectively. The maximum acceleration at monitoring points J5, J6, J7, and J8 was 9.66 m/s2, 12.55 m/s2, 10.42 m/s2, and 7.29 m/s2, respectively. The maximum acceleration at the monitoring point increases and then decreases from the bottom up because the maximum acceleration of the soil body decreases via the liquefaction of the upper sand and soil layer. When the maximum acceleration of the soil body appears, it is discrete, and the discreteness of the maximum acceleration of the sand soil layer is obviously greater than that of the clay layer.


#### 3.2.2. Analysis of Pore Pressure Ratio

The monitoring point information is consistent with Section3.1.2, as shown in Table 6. Under seismic load, the time-history curve of the hole pressure ratio at the soil monitoring points is shown in Figure 12. The maximum hole pressure ratio of KJ2 reaches 1, indicating that the liquefaction depth of sand and soil layer is large. The maximum hole pressure ratio of KJ3 also reaches 1 and then fluctuates around 0.9. The hole pressure ratio of KJ1 is less than that of KJ2 at the same buried depth. The hole pressure ratio at KJ5 is smaller than that at KJ4 at the same buried depth; this result fully demonstrates the reinforcement effect of the pile foundation on the sand and soil layer. The hole pressure ratios of the monitoring points fluctuates greatly with time, the time-history curve of the hole pressure ratio of sand soil exhibits fluctuation, and the hole pressure of each monitoring point does not dissipate.Figure 12
Time-history curves of the pore pressure ratio.


#### 3.2.3. Analysis of Pile Displacement

(1) Horizontal Displacement Analysis of the Pile Body. Piles 1#, 3#, and 5# were taken for horizontal displacement analysis of the pile body. The displacement lines in the x direction of each point of the pile body are shown in Figure 13. Under the seismic action, the pile cap of the pile foundation of the inclined straight alternating pile group moved horizontally, the pile cap moved 0.0077 m in the negative direction of x, the pile body of pile 3# is inclined in the positive direction of the x-axis, and pile 1#, and pile 5# are inclined in the negative direction of x. The slope of the pile body of the 5# pile is the largest, and the horizontal displacement difference between the pile top and the bottom is 0.0668 m.Figure 13
Horizontal displacement of the pile.(2) Vertical Displacement Analysis of the Pile Body. The vertical displacement lines of the pile monitoring points of piles 1#, 3#, and 5# are shown in Figure 14. The figure shows that the vertical displacement of each point of the pile body is not the same, indicating that pile body is inclined. If each point of the pile is connected in a straight line, then no buckling occurs; if it is not a straight line, then the pile body is bent and deformed. Figure 14 shows that pile body has been bent under seismic load. The displacement at the joint of pile top and pile cap is not the same, indicating that the pile cap is inclined. The pile cap of the inclined straight alternating pile group inclines to the negative x direction. The difference of vertical displacement between the top of pile 3# and pile 5# is 0.0031 m. The embedding of the bottom part of the pile body in the clay layer can effectively prevent the downward movement of the pile foundation with inclined straight alternating group; the vertical displacement of the pile top of 1# pile is 0.2006 m.Figure 14
Vertical displacement of the pile.


#### 3.2.4. Analysis of the Bending Moment of the Pile Body

For the analysis of pile bending moments of the 1#, 3#, and 5# piles, the maximum bending moment of each monitoring point is drawn, as shown in Figure15. As shown in the figure, the maximum bending moment of pile body is at the junction of pile top and pile cap. The bending moment values of the pile tip and the bearing joints of pile 1#, pile 3#, and pile 5# are 3130 kN m, 4080 kN m, and 3690 kN m, respectively. The bending moment at the top of the 3# pile is the largest. Under earthquake load, the connecting line of the maximum bending moment of each monitoring point is a smooth curve. The maximum bending moments of piles 1# and 3# are negative, whereas the maximum bending moment of each monitoring point of pile 5# is positive.Figure 15
Bending moment envelope of the pile.


## 3.1. Analysis of Calculation Results of the Two Layers of Soil

### 3.1.1. Analysis of the Soil Acceleration

The propagation of and variation in seismic waves in the soil body model can be obtained by analyzing the acceleration time-history curve of the soil body of the model on the basis of inclined straight piles of the low-rise pile cap in the two-layer soil liquefaction site. The acceleration of soil under the action of the 0.5 g El Centro seismic wave is compared and analyzed to study the effect of a seismic wave on soil acceleration. The locations of soil body monitoring points J1-J8 in the model are shown in Figure2, and the specific information of these points is provided in Table 5. The acceleration of soil under the action of the alternating pile group foundation and the acceleration of soil mass outside the pile foundation are collected. Monitoring points J1 and J5 are located at the interface between the rock layer and the sand layer, and the other 6 monitoring points are in the sand layer. The time-history curve of soil acceleration under the action of seismic waves is shown in Figure 6. The maximum acceleration in the time-history curve of soil acceleration from monitoring points J1, J2, J3, and J4 was 8.10 m/s2, 9.95 m/s2, 7.793 m/s2, and 3.27 m/s2, respectively. The maximum acceleration in the time-history curve of soil acceleration from monitoring points J5, J6, J7, and J8 was 8.88 m/s2, 10.41 m/s2, 6.25 m/s2, and 5.06 m/s2, respectively. The maximum acceleration of soil mass monitoring point is greater than the maximum value of the input seismic load; this observation fully shows the amplification effect of soil mass on the acceleration load. The amplification effect of sand layer on seismic load increases first and then decreases from the bottom to the top, and there is no obvious regularity in the propagation of seismic waves along the soil layer.Table 5
Information of monitoring location.
Name
Coordinates
Name
Coordinates
J4
(0, 0, −3)
J8
(10, 0, −3)
J3
(0, 0, −7)
J7
(10, 0, −7)
J2
(0, 0, −11)
J6
(10, 0, −11)
J1
(0, 0, −15)
J5
(10, 0, −15)Figure 6
Acceleration of soil under the 0.5 g El Centro seismic wave.


### 3.1.2. Analysis of the Pore Pressure Ratio

Five monitoring points in the model were selected for analysis. The location is shown in Figure2. In the 5 monitoring points, 2 of the soil masses are under the action of inclined straight pile alternating group foundation, and the remaining 3 soil masses are outside the pile group foundation. These 5 monitoring points are all located in the liquefiable sand soil layer, and the value of the pore pressure ratio of each monitoring point is listed in Table 6. The time-history curve of the hole pressure ratio at each monitoring point under the action of seismic waves is shown in Figure 7. The overall time-history curve of the hole pressure ratio at the monitoring point fluctuates. The time-history curve of the hole pressure ratio at the KJ2 monitoring point presents a fluctuating upward trend, and the hole pressure ratio exceeds 0.8 after 13 s. The hole pressure ratios at monitoring points KJ1 and KJ5 are lower than those at the same buried depth at KJ2 and KJ4, indicating that the pile group foundation can still inhibit the liquefaction of sand and soil under the pile group foundation during seismic action, and the pile group foundation is still strengthened. The pore pressure ratio of KJ2 exceeds 0.8, indicating that the liquefaction depth of the sand and soil layer under the earthquake is large. The time-history curve of the pore pressure ratio at KJ4 is concentrated near 1 and moves forward in a wavy manner because the liquefaction of the lower soil has a seismic isolation effect on the upper sand layer.Table 6
Information of monitoring location.
Name
Coordinates
Name
Coordinates
KJ1
(0, 0, −7.5)
KJ3
(10, 0, −5.5)
KJ2
(10, 0, −7.5)
KJ4
(10, 0, −2.5)
KJ5
(0, 0, −2.5)
/
/Figure 7
Time-history curves of the pore pressure ratio.


### 3.1.3. Displacement Analysis of the Pile Body

(1) Analysis of the Horizontal Displacement of the Pile Body. The six piles in the inclined straight pile group foundation are symmetric about the xOz plane, the seismic waves are input along the x direction, and the x direction displacement of the 1#, 3#, and 5# piles is taken for analysis, as shown in Figure 8. The figure shows that, under the earthquake action, the pile foundation of inclined straight alternating group moves towards the horizontal direction. The pile cap of the pile foundation was moved 0.0391 m under the seismic action of inclined straight alternating group piles, and the connecting line of each point was curved, indicating that the pile body had buckled. All three piles in the pile group foundation of inclined piles are inclined to different degrees, and the degree of incline of the piles is greater than that of straight piles, primarily because the straight pile is subjected to soil pressure on the pile side, whereas the inclined pile is subjected to overburden pressure and soil support on the lower side. The pile body of the 3# pile is inclined in the positive direction of x, the slope of the 5# pile foundation is high, and the displacement difference between pile top and pile bottom is 0.14 m.Figure 8
Horizontal displacement of the pile.(2) Vertical Displacement Analysis of the Pile Body. Under the seismic action of the liquefaction site, the pile foundation of the inclined straight alternating group moves downward as a whole. The vertical displacement of the pile top is different, and the pile foundation pile cap is inclined. Under seismic action, the displacement of pile top of pile 3# is greater than that of pile 1#; the displacement difference between the tops of the 3# pile and the 5# pile is 0.0473 m, and the vertical displacement of all points of 1# pile is almost the same because the liquefaction sand layer under the earthquake is thicker, the bottom end of pile is under less stress, and the pile body moves down. Figure 9 shows that the vertical displacement of the top of the inclined pile is different from that of the pile bottom via the inclination of the inclined pile. The maximum vertical displacement difference between pile top and pile bottom is for the 5# pile, with a difference of 0.0377 m, indicating that the 5# pile has a large tilt; this result is the same as the horizontal displacement analysis result. The vertical displacement at the top of the 1# pile is 0.3454 m.Figure 9
Vertical displacement of the pile.


### 3.1.4. Analysis of the Bending Moment of the Pile Body

The bending moments of the pile bodies of the 1#, 3#, and 5# piles were taken for analysis, as shown in Figure10. Under seismic load, the maximum bending moment was generated at the junction of the pile top and the pile cap of the 5# pile, and the maximum value was 5710 kN m, whereas the bending moment at the top of the 3# pile is the smallest, with a bending moment of 3060 kN m. During strong earthquakes, the enveloping line of pile bending moments decreases sharply at a buried depth of 9 m, and the enveloping line of the bending moment above 9 m is a smooth curve because of the large liquefaction thickness of the sand and soil layer. The maximum value of the bending moment at each point of piles 1# and 5# is positive, and the maximum value of the bending moment at each point of pile 3# is negative because the horizontal displacement direction of the 1# and 5# piles is the same; this result is the same as the analysis result of the horizontal displacement of the pile body. The maximum bending moment of 3 piles in the foundation of inclined straight alternating group piles is produced in the connection between the pile body and the pile cap, indicating that the connection of the pile and the pile cap under seismic load is the most likely to cause foundation damage.Figure 10
Moment envelope of the pile.


## 3.1.1. Analysis of the Soil Acceleration

The propagation of and variation in seismic waves in the soil body model can be obtained by analyzing the acceleration time-history curve of the soil body of the model on the basis of inclined straight piles of the low-rise pile cap in the two-layer soil liquefaction site. The acceleration of soil under the action of the 0.5 g El Centro seismic wave is compared and analyzed to study the effect of a seismic wave on soil acceleration. The locations of soil body monitoring points J1-J8 in the model are shown in Figure2, and the specific information of these points is provided in Table 5. The acceleration of soil under the action of the alternating pile group foundation and the acceleration of soil mass outside the pile foundation are collected. Monitoring points J1 and J5 are located at the interface between the rock layer and the sand layer, and the other 6 monitoring points are in the sand layer. The time-history curve of soil acceleration under the action of seismic waves is shown in Figure 6. The maximum acceleration in the time-history curve of soil acceleration from monitoring points J1, J2, J3, and J4 was 8.10 m/s2, 9.95 m/s2, 7.793 m/s2, and 3.27 m/s2, respectively. The maximum acceleration in the time-history curve of soil acceleration from monitoring points J5, J6, J7, and J8 was 8.88 m/s2, 10.41 m/s2, 6.25 m/s2, and 5.06 m/s2, respectively. The maximum acceleration of soil mass monitoring point is greater than the maximum value of the input seismic load; this observation fully shows the amplification effect of soil mass on the acceleration load. The amplification effect of sand layer on seismic load increases first and then decreases from the bottom to the top, and there is no obvious regularity in the propagation of seismic waves along the soil layer.Table 5
Information of monitoring location.
Name
Coordinates
Name
Coordinates
J4
(0, 0, −3)
J8
(10, 0, −3)
J3
(0, 0, −7)
J7
(10, 0, −7)
J2
(0, 0, −11)
J6
(10, 0, −11)
J1
(0, 0, −15)
J5
(10, 0, −15)Figure 6
Acceleration of soil under the 0.5 g El Centro seismic wave.


## 3.1.2. Analysis of the Pore Pressure Ratio

Five monitoring points in the model were selected for analysis. The location is shown in Figure2. In the 5 monitoring points, 2 of the soil masses are under the action of inclined straight pile alternating group foundation, and the remaining 3 soil masses are outside the pile group foundation. These 5 monitoring points are all located in the liquefiable sand soil layer, and the value of the pore pressure ratio of each monitoring point is listed in Table 6. The time-history curve of the hole pressure ratio at each monitoring point under the action of seismic waves is shown in Figure 7. The overall time-history curve of the hole pressure ratio at the monitoring point fluctuates. The time-history curve of the hole pressure ratio at the KJ2 monitoring point presents a fluctuating upward trend, and the hole pressure ratio exceeds 0.8 after 13 s. The hole pressure ratios at monitoring points KJ1 and KJ5 are lower than those at the same buried depth at KJ2 and KJ4, indicating that the pile group foundation can still inhibit the liquefaction of sand and soil under the pile group foundation during seismic action, and the pile group foundation is still strengthened. The pore pressure ratio of KJ2 exceeds 0.8, indicating that the liquefaction depth of the sand and soil layer under the earthquake is large. The time-history curve of the pore pressure ratio at KJ4 is concentrated near 1 and moves forward in a wavy manner because the liquefaction of the lower soil has a seismic isolation effect on the upper sand layer.Table 6
Information of monitoring location.
Name
Coordinates
Name
Coordinates
KJ1
(0, 0, −7.5)
KJ3
(10, 0, −5.5)
KJ2
(10, 0, −7.5)
KJ4
(10, 0, −2.5)
KJ5
(0, 0, −2.5)
/
/Figure 7
Time-history curves of the pore pressure ratio.


## 3.1.3. Displacement Analysis of the Pile Body

(1) Analysis of the Horizontal Displacement of the Pile Body. The six piles in the inclined straight pile group foundation are symmetric about the xOz plane, the seismic waves are input along the x direction, and the x direction displacement of the 1#, 3#, and 5# piles is taken for analysis, as shown in Figure 8. The figure shows that, under the earthquake action, the pile foundation of inclined straight alternating group moves towards the horizontal direction. The pile cap of the pile foundation was moved 0.0391 m under the seismic action of inclined straight alternating group piles, and the connecting line of each point was curved, indicating that the pile body had buckled. All three piles in the pile group foundation of inclined piles are inclined to different degrees, and the degree of incline of the piles is greater than that of straight piles, primarily because the straight pile is subjected to soil pressure on the pile side, whereas the inclined pile is subjected to overburden pressure and soil support on the lower side. The pile body of the 3# pile is inclined in the positive direction of x, the slope of the 5# pile foundation is high, and the displacement difference between pile top and pile bottom is 0.14 m.Figure 8
Horizontal displacement of the pile.(2) Vertical Displacement Analysis of the Pile Body. Under the seismic action of the liquefaction site, the pile foundation of the inclined straight alternating group moves downward as a whole. The vertical displacement of the pile top is different, and the pile foundation pile cap is inclined. Under seismic action, the displacement of pile top of pile 3# is greater than that of pile 1#; the displacement difference between the tops of the 3# pile and the 5# pile is 0.0473 m, and the vertical displacement of all points of 1# pile is almost the same because the liquefaction sand layer under the earthquake is thicker, the bottom end of pile is under less stress, and the pile body moves down. Figure 9 shows that the vertical displacement of the top of the inclined pile is different from that of the pile bottom via the inclination of the inclined pile. The maximum vertical displacement difference between pile top and pile bottom is for the 5# pile, with a difference of 0.0377 m, indicating that the 5# pile has a large tilt; this result is the same as the horizontal displacement analysis result. The vertical displacement at the top of the 1# pile is 0.3454 m.Figure 9
Vertical displacement of the pile.


## 3.1.4. Analysis of the Bending Moment of the Pile Body

The bending moments of the pile bodies of the 1#, 3#, and 5# piles were taken for analysis, as shown in Figure10. Under seismic load, the maximum bending moment was generated at the junction of the pile top and the pile cap of the 5# pile, and the maximum value was 5710 kN m, whereas the bending moment at the top of the 3# pile is the smallest, with a bending moment of 3060 kN m. During strong earthquakes, the enveloping line of pile bending moments decreases sharply at a buried depth of 9 m, and the enveloping line of the bending moment above 9 m is a smooth curve because of the large liquefaction thickness of the sand and soil layer. The maximum value of the bending moment at each point of piles 1# and 5# is positive, and the maximum value of the bending moment at each point of pile 3# is negative because the horizontal displacement direction of the 1# and 5# piles is the same; this result is the same as the analysis result of the horizontal displacement of the pile body. The maximum bending moment of 3 piles in the foundation of inclined straight alternating group piles is produced in the connection between the pile body and the pile cap, indicating that the connection of the pile and the pile cap under seismic load is the most likely to cause foundation damage.Figure 10
Moment envelope of the pile.


## 3.2. Analysis of the Results of Three Layers of Soil

### 3.2.1. Analysis of Soil Acceleration

The information of the 8 monitoring points is consistent with Section2.1. The thickness of the sand soil layer in the three-layer free site model is 7 m, that is, there are 4 monitoring points in the sand soil layer, and the remaining monitoring points are in the clay layer. Since the lower part of the model is the lithosphere, the acceleration input in the soil layer is equal to the acceleration of the monitoring point at the buried depth of 15 m. The time-history curve of soil acceleration is shown in Figure 11.Figure 11
Acceleration of soil under the 0.5 g El Centro seismic wave.The time-history curve of acceleration at monitoring points J1 and J4 is equivalent to the time history of acceleration input in soil. The maximum acceleration in the acceleration time curve of the monitoring point is greater than that of the input acceleration time curve. The maximum acceleration at monitoring points J1, J2, J3, and J4 was 10.61 m/s2, 13.13 m/s2, 11.55 m/s2, and 6.35 m/s2, respectively. The maximum acceleration at monitoring points J5, J6, J7, and J8 was 9.66 m/s2, 12.55 m/s2, 10.42 m/s2, and 7.29 m/s2, respectively. The maximum acceleration at the monitoring point increases and then decreases from the bottom up because the maximum acceleration of the soil body decreases via the liquefaction of the upper sand and soil layer. When the maximum acceleration of the soil body appears, it is discrete, and the discreteness of the maximum acceleration of the sand soil layer is obviously greater than that of the clay layer.


### 3.2.2. Analysis of Pore Pressure Ratio

The monitoring point information is consistent with Section3.1.2, as shown in Table 6. Under seismic load, the time-history curve of the hole pressure ratio at the soil monitoring points is shown in Figure 12. The maximum hole pressure ratio of KJ2 reaches 1, indicating that the liquefaction depth of sand and soil layer is large. The maximum hole pressure ratio of KJ3 also reaches 1 and then fluctuates around 0.9. The hole pressure ratio of KJ1 is less than that of KJ2 at the same buried depth. The hole pressure ratio at KJ5 is smaller than that at KJ4 at the same buried depth; this result fully demonstrates the reinforcement effect of the pile foundation on the sand and soil layer. The hole pressure ratios of the monitoring points fluctuates greatly with time, the time-history curve of the hole pressure ratio of sand soil exhibits fluctuation, and the hole pressure of each monitoring point does not dissipate.Figure 12
Time-history curves of the pore pressure ratio.


### 3.2.3. Analysis of Pile Displacement

(1) Horizontal Displacement Analysis of the Pile Body. Piles 1#, 3#, and 5# were taken for horizontal displacement analysis of the pile body. The displacement lines in the x direction of each point of the pile body are shown in Figure 13. Under the seismic action, the pile cap of the pile foundation of the inclined straight alternating pile group moved horizontally, the pile cap moved 0.0077 m in the negative direction of x, the pile body of pile 3# is inclined in the positive direction of the x-axis, and pile 1#, and pile 5# are inclined in the negative direction of x. The slope of the pile body of the 5# pile is the largest, and the horizontal displacement difference between the pile top and the bottom is 0.0668 m.Figure 13
Horizontal displacement of the pile.(2) Vertical Displacement Analysis of the Pile Body. The vertical displacement lines of the pile monitoring points of piles 1#, 3#, and 5# are shown in Figure 14. The figure shows that the vertical displacement of each point of the pile body is not the same, indicating that pile body is inclined. If each point of the pile is connected in a straight line, then no buckling occurs; if it is not a straight line, then the pile body is bent and deformed. Figure 14 shows that pile body has been bent under seismic load. The displacement at the joint of pile top and pile cap is not the same, indicating that the pile cap is inclined. The pile cap of the inclined straight alternating pile group inclines to the negative x direction. The difference of vertical displacement between the top of pile 3# and pile 5# is 0.0031 m. The embedding of the bottom part of the pile body in the clay layer can effectively prevent the downward movement of the pile foundation with inclined straight alternating group; the vertical displacement of the pile top of 1# pile is 0.2006 m.Figure 14
Vertical displacement of the pile.


### 3.2.4. Analysis of the Bending Moment of the Pile Body

For the analysis of pile bending moments of the 1#, 3#, and 5# piles, the maximum bending moment of each monitoring point is drawn, as shown in Figure15. As shown in the figure, the maximum bending moment of pile body is at the junction of pile top and pile cap. The bending moment values of the pile tip and the bearing joints of pile 1#, pile 3#, and pile 5# are 3130 kN m, 4080 kN m, and 3690 kN m, respectively. The bending moment at the top of the 3# pile is the largest. Under earthquake load, the connecting line of the maximum bending moment of each monitoring point is a smooth curve. The maximum bending moments of piles 1# and 3# are negative, whereas the maximum bending moment of each monitoring point of pile 5# is positive.Figure 15
Bending moment envelope of the pile.


## 3.2.1. Analysis of Soil Acceleration

The information of the 8 monitoring points is consistent with Section2.1. The thickness of the sand soil layer in the three-layer free site model is 7 m, that is, there are 4 monitoring points in the sand soil layer, and the remaining monitoring points are in the clay layer. Since the lower part of the model is the lithosphere, the acceleration input in the soil layer is equal to the acceleration of the monitoring point at the buried depth of 15 m. The time-history curve of soil acceleration is shown in Figure 11.Figure 11
Acceleration of soil under the 0.5 g El Centro seismic wave.The time-history curve of acceleration at monitoring points J1 and J4 is equivalent to the time history of acceleration input in soil. The maximum acceleration in the acceleration time curve of the monitoring point is greater than that of the input acceleration time curve. The maximum acceleration at monitoring points J1, J2, J3, and J4 was 10.61 m/s2, 13.13 m/s2, 11.55 m/s2, and 6.35 m/s2, respectively. The maximum acceleration at monitoring points J5, J6, J7, and J8 was 9.66 m/s2, 12.55 m/s2, 10.42 m/s2, and 7.29 m/s2, respectively. The maximum acceleration at the monitoring point increases and then decreases from the bottom up because the maximum acceleration of the soil body decreases via the liquefaction of the upper sand and soil layer. When the maximum acceleration of the soil body appears, it is discrete, and the discreteness of the maximum acceleration of the sand soil layer is obviously greater than that of the clay layer.


## 3.2.2. Analysis of Pore Pressure Ratio

The monitoring point information is consistent with Section3.1.2, as shown in Table 6. Under seismic load, the time-history curve of the hole pressure ratio at the soil monitoring points is shown in Figure 12. The maximum hole pressure ratio of KJ2 reaches 1, indicating that the liquefaction depth of sand and soil layer is large. The maximum hole pressure ratio of KJ3 also reaches 1 and then fluctuates around 0.9. The hole pressure ratio of KJ1 is less than that of KJ2 at the same buried depth. The hole pressure ratio at KJ5 is smaller than that at KJ4 at the same buried depth; this result fully demonstrates the reinforcement effect of the pile foundation on the sand and soil layer. The hole pressure ratios of the monitoring points fluctuates greatly with time, the time-history curve of the hole pressure ratio of sand soil exhibits fluctuation, and the hole pressure of each monitoring point does not dissipate.Figure 12
Time-history curves of the pore pressure ratio.


## 3.2.3. Analysis of Pile Displacement

(1) Horizontal Displacement Analysis of the Pile Body. Piles 1#, 3#, and 5# were taken for horizontal displacement analysis of the pile body. The displacement lines in the x direction of each point of the pile body are shown in Figure 13. Under the seismic action, the pile cap of the pile foundation of the inclined straight alternating pile group moved horizontally, the pile cap moved 0.0077 m in the negative direction of x, the pile body of pile 3# is inclined in the positive direction of the x-axis, and pile 1#, and pile 5# are inclined in the negative direction of x. The slope of the pile body of the 5# pile is the largest, and the horizontal displacement difference between the pile top and the bottom is 0.0668 m.Figure 13
Horizontal displacement of the pile.(2) Vertical Displacement Analysis of the Pile Body. The vertical displacement lines of the pile monitoring points of piles 1#, 3#, and 5# are shown in Figure 14. The figure shows that the vertical displacement of each point of the pile body is not the same, indicating that pile body is inclined. If each point of the pile is connected in a straight line, then no buckling occurs; if it is not a straight line, then the pile body is bent and deformed. Figure 14 shows that pile body has been bent under seismic load. The displacement at the joint of pile top and pile cap is not the same, indicating that the pile cap is inclined. The pile cap of the inclined straight alternating pile group inclines to the negative x direction. The difference of vertical displacement between the top of pile 3# and pile 5# is 0.0031 m. The embedding of the bottom part of the pile body in the clay layer can effectively prevent the downward movement of the pile foundation with inclined straight alternating group; the vertical displacement of the pile top of 1# pile is 0.2006 m.Figure 14
Vertical displacement of the pile.


## 3.2.4. Analysis of the Bending Moment of the Pile Body

For the analysis of pile bending moments of the 1#, 3#, and 5# piles, the maximum bending moment of each monitoring point is drawn, as shown in Figure15. As shown in the figure, the maximum bending moment of pile body is at the junction of pile top and pile cap. The bending moment values of the pile tip and the bearing joints of pile 1#, pile 3#, and pile 5# are 3130 kN m, 4080 kN m, and 3690 kN m, respectively. The bending moment at the top of the 3# pile is the largest. Under earthquake load, the connecting line of the maximum bending moment of each monitoring point is a smooth curve. The maximum bending moments of piles 1# and 3# are negative, whereas the maximum bending moment of each monitoring point of pile 5# is positive.Figure 15
Bending moment envelope of the pile.


## 4. Analysis of the Effect of Soil Layer Conditions on the Seismic Interaction between the Pile and the Soil in an Inclined Straight Alternating Group

### 4.1. Comparison and Analysis of Soil Acceleration

By comparing the contents provided in Sections2.1 and 3.2.1, it is found that, under the action of seismic load, the acceleration of the bottom clay layer of the lower pile foundation in the low-pile cap model of the three-layer soil free site is slightly greater than the acceleration of the sand soil layer at the same position in the low-rise pile cap model of the two-layer soil free site. The maximum acceleration of soil mass is discrete in the low-rise pile cap model of the two-layer soil free site and the low-rise pile cap model of three-layer soil free site. The maximum acceleration dispersion of the soil mass of the two-layer soil free site model is greater than that of the three-layer soil free site model. This result is observed because of the 6 m thick clay layer at the lower part of the three-layer soil free site model. The discreteness of the maximum acceleration of the clay layer is less than the discreteness of the maximum acceleration of the sand soil layer.


### 4.2. Comparative Analysis of the Hole Pressure Ratio

By comparing the contents provided in Sections3.1.2 and 3.2.2, it is found that the hole pressure ratio of the monitoring point in the three-layer free site model is significantly higher than that of the two-layer model under the seismic load. The pore pressure ratio in the three-layer of soil reaches the maximum value at 2.3 s, after which, the pore pressure ratio fluctuates less. The hole pressure ratio at the monitoring point in the two-layer soil free site model fluctuates greatly with time. The hole pressure ratio of KJ2 in the two-layer of soil free site increases continuously and then tends to be stable after 25 s. In the three-layer soil free site model, the KJ3 reaches the maximum hole pressure ratio at 3.3 s, and its value is 1.006; KJ2 reaches the maximum hole pressure ratio of 1.036 at 5.5 s. The liquefaction degree of sandy soil layer in the three-layer free site model is much higher than that of the two-layer free site model.


### 4.3. Comparative Analysis of Pile Displacement

#### 4.3.1. Comparative Analysis of the Horizontal Displacement of the Pile Body

As shown in Figure16, in the two-layer soil free site model and the three-layer soil free site model, the pile body is inclined in the same direction under the earthquake, the pile body of 1# and 5# is inclined in the negative direction of the X-axis, and the pile body of 3# is inclined in the positive direction of the X-axis. The horizontal displacement of the pile foundation pile cap in the three-layer soil free site model is much less than that of two layers of soil; this difference is caused by the embedding of the pile foundation bottom in the clay layer. In the analysis of the two-layer soil and three-layer soil models, the horizontal displacement difference of the pile body of the 5# pile is 0.14 m and 0.0668 m, respectively. The group pile foundation of the two-layer soil free site model is more likely to be damaged than that of the three-layer soil free site model; this result shows that the lower clay layer of the three-layer soil free site model has an obvious embedding effect on the pile foundation.Figure 16
Comparison of the horizontal displacement for different soil layers.


#### 4.3.2. Comparative Analysis of the Vertical Displacement of the Pile Body

As shown in Figure17, the slope degree of the pile cap in the three-layer soil free site model is less than that of the two-layer soil free site model. The vertical displacement of the top of the 1# pile in the two-layer soil is 0.3454 m; the vertical displacement of the 1# pile top in the three-layer soil is 0.2006 m. The vertical displacement of the top of pile 1# in three layers of soil is less than that of pile 1# in two layers of soil, indicating that the vertical displacement of the pile foundation in three layers of soil is less than that of the pile foundation in two layers of soil. This difference is caused by the consolidation of the pile foundation by the clay layer at the bottom of the three-layer free site model.Figure 17
Comparison of the vertical displacements for different soil layers.


### 4.4. Comparative Analysis of the Bending Moment of the Pile Body

As shown in Figure18, the maximum bending moment of pile body of both models is generated at the junction of the pile top and the pile cap. Under earthquake action, the maximum bending moment of the connecting part between the top of the pile and the cap is 5710 kN·m in the two-layer soil free site model, and the maximum bending moment of the three-layer soil is 4080 kN m. The bending moment of the three-layer soil is less than the moment of the two-layer soil. This observation indicates that the low-pile cap inclined straight alternating pile group foundation in the three-layer soil free site model is better than the two-layer soil group pile foundation in resisting the earthquake load.Figure 18
Comparison of the bending moments for different soil layers.


## 4.1. Comparison and Analysis of Soil Acceleration

By comparing the contents provided in Sections2.1 and 3.2.1, it is found that, under the action of seismic load, the acceleration of the bottom clay layer of the lower pile foundation in the low-pile cap model of the three-layer soil free site is slightly greater than the acceleration of the sand soil layer at the same position in the low-rise pile cap model of the two-layer soil free site. The maximum acceleration of soil mass is discrete in the low-rise pile cap model of the two-layer soil free site and the low-rise pile cap model of three-layer soil free site. The maximum acceleration dispersion of the soil mass of the two-layer soil free site model is greater than that of the three-layer soil free site model. This result is observed because of the 6 m thick clay layer at the lower part of the three-layer soil free site model. The discreteness of the maximum acceleration of the clay layer is less than the discreteness of the maximum acceleration of the sand soil layer.


## 4.2. Comparative Analysis of the Hole Pressure Ratio

By comparing the contents provided in Sections3.1.2 and 3.2.2, it is found that the hole pressure ratio of the monitoring point in the three-layer free site model is significantly higher than that of the two-layer model under the seismic load. The pore pressure ratio in the three-layer of soil reaches the maximum value at 2.3 s, after which, the pore pressure ratio fluctuates less. The hole pressure ratio at the monitoring point in the two-layer soil free site model fluctuates greatly with time. The hole pressure ratio of KJ2 in the two-layer of soil free site increases continuously and then tends to be stable after 25 s. In the three-layer soil free site model, the KJ3 reaches the maximum hole pressure ratio at 3.3 s, and its value is 1.006; KJ2 reaches the maximum hole pressure ratio of 1.036 at 5.5 s. The liquefaction degree of sandy soil layer in the three-layer free site model is much higher than that of the two-layer free site model.


## 4.3. Comparative Analysis of Pile Displacement

### 4.3.1. Comparative Analysis of the Horizontal Displacement of the Pile Body

As shown in Figure16, in the two-layer soil free site model and the three-layer soil free site model, the pile body is inclined in the same direction under the earthquake, the pile body of 1# and 5# is inclined in the negative direction of the X-axis, and the pile body of 3# is inclined in the positive direction of the X-axis. The horizontal displacement of the pile foundation pile cap in the three-layer soil free site model is much less than that of two layers of soil; this difference is caused by the embedding of the pile foundation bottom in the clay layer. In the analysis of the two-layer soil and three-layer soil models, the horizontal displacement difference of the pile body of the 5# pile is 0.14 m and 0.0668 m, respectively. The group pile foundation of the two-layer soil free site model is more likely to be damaged than that of the three-layer soil free site model; this result shows that the lower clay layer of the three-layer soil free site model has an obvious embedding effect on the pile foundation.Figure 16
Comparison of the horizontal displacement for different soil layers.


### 4.3.2. Comparative Analysis of the Vertical Displacement of the Pile Body

As shown in Figure17, the slope degree of the pile cap in the three-layer soil free site model is less than that of the two-layer soil free site model. The vertical displacement of the top of the 1# pile in the two-layer soil is 0.3454 m; the vertical displacement of the 1# pile top in the three-layer soil is 0.2006 m. The vertical displacement of the top of pile 1# in three layers of soil is less than that of pile 1# in two layers of soil, indicating that the vertical displacement of the pile foundation in three layers of soil is less than that of the pile foundation in two layers of soil. This difference is caused by the consolidation of the pile foundation by the clay layer at the bottom of the three-layer free site model.Figure 17
Comparison of the vertical displacements for different soil layers.


## 4.3.1. Comparative Analysis of the Horizontal Displacement of the Pile Body

As shown in Figure16, in the two-layer soil free site model and the three-layer soil free site model, the pile body is inclined in the same direction under the earthquake, the pile body of 1# and 5# is inclined in the negative direction of the X-axis, and the pile body of 3# is inclined in the positive direction of the X-axis. The horizontal displacement of the pile foundation pile cap in the three-layer soil free site model is much less than that of two layers of soil; this difference is caused by the embedding of the pile foundation bottom in the clay layer. In the analysis of the two-layer soil and three-layer soil models, the horizontal displacement difference of the pile body of the 5# pile is 0.14 m and 0.0668 m, respectively. The group pile foundation of the two-layer soil free site model is more likely to be damaged than that of the three-layer soil free site model; this result shows that the lower clay layer of the three-layer soil free site model has an obvious embedding effect on the pile foundation.Figure 16
Comparison of the horizontal displacement for different soil layers.


## 4.3.2. Comparative Analysis of the Vertical Displacement of the Pile Body

As shown in Figure17, the slope degree of the pile cap in the three-layer soil free site model is less than that of the two-layer soil free site model. The vertical displacement of the top of the 1# pile in the two-layer soil is 0.3454 m; the vertical displacement of the 1# pile top in the three-layer soil is 0.2006 m. The vertical displacement of the top of pile 1# in three layers of soil is less than that of pile 1# in two layers of soil, indicating that the vertical displacement of the pile foundation in three layers of soil is less than that of the pile foundation in two layers of soil. This difference is caused by the consolidation of the pile foundation by the clay layer at the bottom of the three-layer free site model.Figure 17
Comparison of the vertical displacements for different soil layers.


## 4.4. Comparative Analysis of the Bending Moment of the Pile Body

As shown in Figure18, the maximum bending moment of pile body of both models is generated at the junction of the pile top and the pile cap. Under earthquake action, the maximum bending moment of the connecting part between the top of the pile and the cap is 5710 kN·m in the two-layer soil free site model, and the maximum bending moment of the three-layer soil is 4080 kN m. The bending moment of the three-layer soil is less than the moment of the two-layer soil. This observation indicates that the low-pile cap inclined straight alternating pile group foundation in the three-layer soil free site model is better than the two-layer soil group pile foundation in resisting the earthquake load.Figure 18
Comparison of the bending moments for different soil layers.


## 5. Conclusion

FLAC3D was used to establish the numerical model of the low platform inclined straight alternating group pile foundation with two layers and three layers of soil liquefaction. The dynamic analysis was conducted using the 0.5 g El Centro seismic wave, and the soil acceleration, the pore pressure ratio, the pile body level, the vertical displacement, and the pile body bending moment were obtained. Based on the results obtained, the conclusions of this paper are as follows:(1)
The acceleration of the clay layer under a three-layer soil pile foundation is slightly greater than that of the sand layer at the same position of the two-layer soil. The maximum acceleration of the soil mass in the two-layer soil model and the three-layer soil model is discrete without obvious law, and the maximum acceleration of the soil in the two layers is more discrete than that of the three-layer soil.(2)
The hole pressure ratio of the monitoring points in the model of a three-layer soil free site under seismic action is significantly higher than that of a two-layer soil site. The hole pressure ratio of sand soil increases from bottom to top, indicating that the pile group foundation has a certain strengthening effect on the sand soil layer. The liquefaction soil in the lower part has a certain seismic isolation effect on the upper part of the soil.(3)
A pile foundation tilts and has horizontal displacement under seismic load, and the horizontal displacement of the pile caps on three layers of soil is slightly smaller than that on two layers of soil. The pile foundation pile cap is inclined, and the slope degree and the vertical displacement of the three-layer soil pile foundation bearing platform are less than those of the two-layer soil because the clay at the bottom of the model has immobilization effect on the pile foundation. The maximum bending moment at the joint between the pile cap and the top of the pile body indicates that the joint between the pile body and the pile body is the most vulnerable in the liquefaction site. The maximum bending moment of the three-layer soil pile is less than the maximum value of the two-layer soil, indicating that the group pile foundation in the three-layer soil free site model is safer.



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*Source: 3758286-2019-03-05.xml*