The dynamic response of pile-liquefied soil is a complex problem. Based on the shaking table test test, the vertical bearing characteristics of pile foundation - liquefied soil system under simulated horizontal seismic force are analyzed and studied with the help of MIDAS GTS three-dimensional finite element analysis software. Study the load borne by the pile top under horizontal earthquake with a certain vertical load, different pile spacing and different vibration time, The cumulative coefficient CCPF of pile side friction is introduced. At different vibration times the distribution of CCPF along the pile body of single pile and pile groups with different pile spacing is analyzed, it is concluded that CCPF can intuitively reflect the distribution law of pile side friction during vibration. When the value of CCPF at the pile bottom is equal to 1, it means that the load actually acting on the pile top is equal to the average value of the total load. When CCPF at the pile bottom is less than 1, it means that the load on the pile top is less than the average value of the total load. When CCPF at pile bottom is greater than 1, it indicates the load on the pile top is greater than the average of the total load.
Article
Study on vertical load distribution of pile group-liquefied soil system under horizontal earthquake
https://doi.org/10.21203/rs.3.rs-2224830/v1
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pile - liquefiable soil
seismic load
vertical bearing characteristics
cumulative coefficient of pile side friction
In recent years, earthquakes have occurred frequently all over the world, and the resulting disasters are becoming more and more serious. There are many reasons to cause disasters. However, due to the effect of earthquake force, the disasters caused by the pile foundation damaged, and then the bearing capacity decreases are undoubtedly one of the most important reasons. For this reason, the topic of pile - soil dynamic interaction has been gradually valued and studied by relevant scholars in recent years. However, this subject involves many factors such as pile groups, the properties of soil around piles and the infinity of underlying foundation soil, as well as the cross research of structural dynamics and soil dynamics, which makes the research of this subject very complex, so the relevant research progress is relatively slow.
The study of dynamic interaction between liquefied soil and pile foundation is mainly based on p-y curve. Zhang Chongwen [1], Huang Qunxian [2] and others regard the pile-soil interaction as a nonlinear relationship by using ANSYS analysis software, and use spring elements to simulate the lateral force of pile foundation. Yang Weilin and Chen Guoxing [3] established a one-dimensional wave model to simulate the seismic action, and extended it to two-dimensional and three-dimensional to study the pier-pile group-soil interaction. And the influence of different models on the peak acceleration of pile foundation is obtained. Su Jingbo [4] and others established the nonlinear contact finite element model of pile-soil interaction by using Newmark theory, made relevant numerical simulation research on pile-soil interaction, and obtained the sensitivity calculation formula of different soil parameters to the displacement of liquefiable sand.
In addition, in terms of shaking table research, Wu Xiaoping, Sun Limin and Hu Shide [5] carried out relevant tests on pile-model soil by means of shaking table test, and obtained the response of upper structure and soil properties at different locations to pile body strain. Wang Jianhua and Feng Shilun [6] carried out shaking table tests on pile foundation-saturated sand with different relative densities, obtained p-y curve method for evaluating the horizontal bearing capacity of pile foundation and gave the change trend of hole-pressure ratio. Qi Chunxiang [7] et al. proposed that it is generally assumed that lateral resistance P of soil mass and displacement y of foundation are typical non-linear relationships. Zhao Chenggang [8] and others summarized three different calculation methods for soil liquefaction by referring to the change of pile stress. Li Yurun [9] and others carried out further theoretical research on p-y curve based on shaking table test and put forward an optimized p-y curve method.
Overseas, Amar[10], Paramasivam[11], Al-Isawi[12], Nadarajah[13] and other scholars have carried out relevant research on the dynamic interaction of pile-liquefied soil and reached corresponding conclusions.
A large number of literatures have studied the pile-soil dynamic interaction based on the horizontal dynamic characteristics, but few studies on the vertical bearing capacity of pile foundation under dynamic load. The two-stage analysis method in the current standard is applicable to low pile cap. The two-stage refers to that the pile foundation checking calculation is divided into two stages: earthquake stage and post earthquake stage. In the earthquake stage, the pile body is affected by the earthquake force, and there is already a liquefaction area in the soil. According to the fact that most of the water spraying and gushing lag behind the earthquake, it is generally considered that the liquefaction area has not developed near the pile top at this stage, considering that the impact on the transverse bearing capacity is not large, the liquefaction impact can be ignored in the seismic calculation, and the checking of the bearing capacity of the pile foundation is the same as that of the non liquefied soil. Pile body does not act on seismic force in post-earthquake stage. Vertical bearing capacity of pile foundation after liquefaction is checked under static load. It is almost impossible to determine the bearing capacity of pile foundation at different times of vibration by model test. Based on the laboratory model test [14], through comprehensive understanding and analysis of relevant research at home and abroad, this paper establishes intuitive and clear mathematical model by using the three-dimensional finite element analysis software MIDAS GTS of geotechnical engineering specialty, and selects reasonable numerical simulation parameters. The vertical bearing characteristics of pile foundation under simulated seismic force under similar conditions are analyzed and tested in laboratory.
1.1 Constitutive relationship of soil mass
The constitutive relation of soil mass under dynamic action is very complex, and it is different under different conditions. It is impossible to establish a universal constitutive relation. At present, the dynamic non-linear constitutive relation of saturated soils under cyclic loading can be divided into two categories: one is viscoelastic theoretical model and the other is elastic-plastic theoretical model [15]. For this research, D-P model based on elastic-plastic theory is selected as the constitutive model of soil in numerical analysis, which provides an important theoretical basis for the analysis of soil properties in concrete pile-saturated sand system.
1.2 Model boundary conditions
In the numerical model, different action forms have different boundary treatment methods. The theory and control of boundary conditions under dynamic loads are very complex and are hot and difficult issues in current research. The viscoelastic artificial boundary proposed by Deesk[16] basically solves this problem and can accurately simulate the radiation damping of soil at the boundary and the elastic recovery of foundation. This method is realized by adding parallel linear springs and viscous dampers to the boundary to absorb the waves scattered on the interface. In this study, viscoelastic artificial boundary is used.
The shear wave velocity of the upper soil is set as 60m / s, and the P wave velocity is set as 130m / s, The shear wave velocity of the lower soil is set at 280m / s and the P-wave velocity is set at 700m / s. Select the nodes on the model boundary, and set springs and dampers on the nodes onthe model boundary to generate the viscoelastic boundary as shown in Fig. 1.
1.3 Damping setting
In the MIDAS-GTS program, damping types are mass-proportional, stiffness-proportional and Rayleigh-type. Rayleigh damping is often used in entity analysis, so Rayleigh damping is used in calculation model. The mass and stiffness factors are a0 = 0.026 and a1 = 0.401[17] respectively.
1.4 Contact unit selection
The structure in the soil studied in this paper is pile and cap. The rigidity of pile and cap is much higher than that of soil. Under the action of external force, when the soil is in the plastic state, the pile and cap are still in the elastic stage. And this paper mainly studies the dynamic vertical bearing characteristics of pile foundation system, without considering the damage in the horizontal direction, so it is reasonable to adopt the linear elastic model for the pile and the cap, that is, to meet the test requirements, and the convergence speed of the calculation can be greatly improved.
In the model analysis, there will be incongruous deformation between the two materials at the contact surface of different materials (there are obvious differences in stiffness). In addition, soil is a typical nonlinear material, which will show obvious nonlinearity even if there is small deformation. Therefore, on the contact surface between pile and soil, due to the inconsistent deformation, it is impossible for the pile to transmit all the force to the soil, so that part of the energy is lost. In order to correctly reflect the interaction of pile-soil system under dynamic action, Goodman contact unit surface which can generate individual deformation is set between pile, soil and bearing cap. In this paper, the modified Goodman element is adopted and the damping factor is considered, which can further simulate the energy loss on the contact surface of pile, soil and cushion cap. Relevant parameters of contact unit are set in Table 1.
|
Pile-soil |
Cap-soil |
Pile-cap |
|
|---|---|---|---|
|
Normal stiffness Kn (kPa) |
8000 |
8000 |
10000 |
|
Shear stiffness Ks (kPa) |
1400 |
283 |
1500 |
|
Internal friction angle (o) |
29 |
29 |
— |
|
Cohesion (kPa) |
78 |
17 |
— |
1.5 Seepage Theory and Soil Consolidation
This simulation uses Biot consolidation theory. Soil unit in Fig. 2. The momentum equation is as follows:
The relationship among total stress, pore pressure and effective stress is analyzed according to the principle of effective stress
$$\left\{\sigma \right\}=\left\{{\sigma }^{{\prime }}\right\}+\left\{p\right\}$$ 2
The stress-strain relationship can usually be expressed as
$$\left\{d{\sigma }^{{\prime }}\right\}=\left[{D}^{ep}\right]\left\{d\epsilon \right\}$$ 3
\(\left[{D}^{ep}\right]\) is the elastic-plastic matrix of soil and the strain increment of soil skeleton.
1.6 Power input
Considering the consistency with the indoor shaking table model test, the numerical simulation also uses sine wave, and the input peak acceleration and frequency are the same as those of the indoor test, i.e., a = 0.372g, f = 4.313Hz. See Fig. 3.
1.7 Geometric models and parameters
The sizes of piles and supporting plates are basically the same as those of our indoor shaking table model tests. Limited by the size and load of the shaking table, a 10mm thick polyethylene plate was affixed to the box walls on both sides in the direction of vibration to simulate the boundary conditions of the free site. Although the errors caused by boundary conditions can be reduced, there are still some errors compared with free sites. In order to reduce the errors caused by boundary conditions, the numerical simulation model further extends the calculation boundary from the pile reinforced soil area by 2 m. The thickness of bearing layer increases to 0.5m. The liquefied soil layer is sandy soil and the bearing layer is silty clay. Material parameters are shown in Table 2. Relevant physical parameters are in agreement with those of shaking table tests. Other parameters are obtained from reference [18]. The dimensions and spacing of the piles are shown in Table 3.
The geometric model is shown in Fig. 4.
|
Physical variable |
Liquefiable soil (sand) |
Bearing layer soil (silty clay) |
Cushion cap |
Pile |
|---|---|---|---|---|
|
Constitutive model |
D-P |
D-P |
Elastic |
Elastic |
|
Elastic modulus (kPa) |
50000 |
75000 |
200000 |
200000 |
|
Poisson's ratio |
0.33 |
0.32 |
0.3 |
0.3 |
|
Density (g/cm3) |
1.88 |
1.43 |
2.5 |
2.5 |
|
Cohesion (kPa) |
6 |
12.8 |
— |
— |
|
Internal friction angle (o) |
22 |
16 |
— |
— |
|
Vertical and horizontal seepage coefficients (m/s) |
1×10-3 |
1×10-5 |
— |
— |
Table 3 Model size
|
Pile |
Cushion cap |
||
|
Cross section (cm ) |
2.7×2.7 |
Size (mm) |
Distance between outer sides of side pile plus 15 |
|
Pile length (cm) |
60 |
Thickness (mm) |
30 |
|
Spacing |
3D, 3.5D, 4D, 5D, 6D |
|
|
The following assumptions apply to saturated soils：
(1) The soil was completely saturated with water. The water flow in the soil follows Darcy's law.
(2) Pore water and soil particles are incompressible.
(3) Permeability and compressibility do not change with consolidation.
(4) Vertical relative displacement between pile and soil is small.
(5) Lateral deformation of soil is not considered.
Before seismic loading is applied, initial stress and initial pore water pressure (the latter is used to solve the excess static pore water pressure) need to be applied in two steps in the analysis software. Firstly, the initial head and drainage boundary around and below the model are set as shown in Fig. 5. The boundary conditions and gravity field with degree of freedom of constraint are applied and the initial seepage flow field of the model is obtained by using the seepage analysis solver. Then, using the solution module of consolidation analysis in the program, the initial consolidation stress field is obtained when the D-P model reaches equilibrium under gravity. In this way, the initial soil stress and the initial pore water pressure of the foundation in the calculation model are formed. The calculation method of the interaction coupling between solid and fluid is referred to as "fluid structure coupling calculation" in numerical analysis. The same as the indoor test, measurement and control points are set at - 5cm, - 30cm and - 50cm below the soil surface.
In order to easily read the results of model calculation and to study the seismic resistance of pile foundation, a series of control points of measuring units are set on the model. The measuring and control units can be divided into two categories according to the measuring characteristics: the measuring and control points of excess pore water pressure at specified positions in soil mass and the measuring and control points of pile stress (stress is only analyzed in this paper). As the direction of seismic wave propagation in this study is unidirectional, the functions of piles in different locations under earthquake may be different, see Figure 6. Initially, it can be divided into four categories: corner pile JZ1, JZ2, JZ3, JZ4; Middle Pile ZZ1; And two side piles are BZ1,BZ2 and DBZ1,DBZ2 respectively. Detailed arrangement of measuring and control points is shown in Table 4.
Table 4 Position of monitoring point
|
Stress control point |
Excess pore water pressure control point |
||
|
Number |
Position |
Number |
Position |
|
ZZ1 |
Entire pile |
P1 |
-5cm |
|
JZ1 |
Entire pile |
P2 |
-30cm |
|
BZ1 |
Entire pile |
P3 |
-50cm |
|
DBZ1 |
Entire pile |
|
|
The vertical bearing capacity of friction-type pile foundation is provided by the side friction resistance and the end friction resistance of the pile. Under the vertical load, the soil around the pile exerts its side friction resistance from top to bottom. The development of side friction resistance is related to the nature of the soil around the pile and the load on the top of the pile. The axial force of the vertical compressed pile body decreases gradually from top to bottom along the pile body. The reduction of axial force of pile body is due to the exertion of friction resistance on the side of the pile. The soil around the pile with higher friction resistance will change the axial force of the corresponding pile body greatly. After the friction resistance along the side of the pile body has been fully exerted, the axial force transmitted to the bottom of the pile is borne by the bearing layer soil at the end of the pile. Finally, the force of the pile body is balanced by the coordination of the friction resistance at the side of the pile and the friction resistance at the end of the pile. Therefore, the vertical bearing capacity of the pile is equal to the sum of the side friction resistance and the end friction resistance of the pile. As a result, the variation rule of pile side friction resistance can be reflected by the distribution of axial force (stress) of pile body. The relationship between axial force of pile body and side friction resistance is shown in Figure 7.
A large number of studies show that in pile group foundation, each foundation pile bears different loads transmitted from the bearing platform plate, and the soil around the foundation pile at different positions also has different effects on the pile, so it is difficult to compare and analyze them. In this section, the foundation pile ZZ1 at a specific location is selected for the analysis of the vertical bearing characteristics of the pile during vibration. To facilitate analysis, the cumulative coefficient of pile side friction resistance CCPF is introduced in this paper.
The pile is divided into n sections, Ni+1 and Ni are the axial forces at section i and i+1 of the pile body respectively, and P foundation represents the sum of the side friction resistance of the pile under equivalent load Q. P0=Q-Nmin，9 pile is adopted in the model, so Q takes 1/9 of the load on the bearing cap and Nmin is the axial force at the bottom of the pile (considered as the resistance at the end of the pile).
The number of CCPF reflects the distribution of soil friction around the pile along the side of the pile, the change of CCPF reflects the change of side friction resistance. In liquefied sites, liquefaction of the soil layer under horizontal seismic forces will lead to a decrease in shear strength of the soil, which will naturally reduce the friction on the side of the pile provided. The axial force of pile body will inevitably change with the change of pile side friction. Such change trend and law can be reflected in the change of cumulative coefficient of pile side friction.
5.1 CCPF distribution law and characteristics of single pile system along the pile body
Firstly, single pile system is selected as the research object. By analyzing the distribution rule and characteristics of CCPF along the pile body, the change of vertical bearing capacity of single pile during earthquake is further analyzed to verify whether CCPF can reflect the common action mechanism of pile and soil comprehensively and reasonably. Vibration time points are 0s, 15s, 25s and 35s. Pile stress is picked up every 5cm along the pile body. According to the stress, the axial force can be obtained, and then the side friction resistance of each section of soil around the pile can be obtained. In the laboratory test, 750N load is applied before vibration of pile group foundation of 9 piles. Therefore, 1/9 of pile group, i.e. 83.33N, is applied to single pile. From the model calculation, the stress of the pile body is obtained directly, and then the curve of CCPF along the pile body at different specific moment of earthquake action is obtained by further calculation. See Fig. 8, the corresponding changing values are shown in Table 5. In addition, for the purpose of analysis, static load tests are carried out on the pile-soil system at different times of vibration, and the corresponding Q-S curve is obtained as shown in Fig. 9, the relevant values are shown in Table 6.
|
shaking time(s) |
Longitudinal depth of pile(cm) |
||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
0 |
-5 |
-10 |
-15 |
-20 |
-25 |
-30 |
-35 |
-40 |
-45 |
-50 |
-55 |
-60 |
|
|
0 |
0 |
5 |
11 |
17 |
28 |
39 |
49 |
61 |
70 |
79 |
85 |
93 |
100 |
|
15 |
0 |
0 |
1 |
6 |
12 |
18 |
27 |
36 |
54 |
70 |
81 |
91 |
98 |
|
25 |
0 |
0 |
0 |
1 |
2 |
4 |
9 |
16 |
28 |
37 |
59 |
75 |
90 |
|
35 |
0 |
0 |
0 |
0 |
1 |
2 |
3 |
5 |
10 |
21 |
32 |
51 |
75 |
|
shaking time(s) |
Vertical force(N) |
|||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
80 |
100 |
120 |
140 |
160 |
180 |
200 |
220 |
240 |
260 |
280 |
300 |
|
|
0 |
0 |
-0.7 |
-1.4 |
-1.9 |
-2.6 |
-3.9 |
-6.2 |
-8.4 |
-12.3 |
-22.1 |
-37 |
-48.2 |
|
15 |
-1.3 |
-3.8 |
-6.2 |
-9.1 |
-12.7 |
-17.8 |
-21.9 |
-35 |
-46 |
---- |
---- |
---- |
|
25 |
-2.2 |
-6.7 |
-11.4 |
-16.3 |
-24.1 |
-35 |
-47 |
---- |
---- |
---- |
---- |
---- |
|
35 |
-3.5 |
-10.4 |
-18.1 |
-29.8 |
-39.1 |
---- |
---- |
---- |
---- |
---- |
---- |
---- |
As can be seen from Fig. 8, with the duration of vibration, the CCPF increases rapidly at the same vibration time within the range of 0 ~ − 40cm along the pile, but the longer the vibration time, the CCPF of the same pile decreases significantly. In the range of -40~-60, at 0s and 15s, CCPF maintains the same growth rate as at 0~-40cm, but at 25s and 35s, the growth rate of CCPF significantly slows down. Moreover, it can be seen that the CCPF at the bottom of the pile is reduced from 100–74% at 0s. Based on the analysis of Fig. 9, it can be seen from the Q-S curve that the curve steepens and the ultimate bearing capacity gradually decreases with the duration of vibration. The ultimate bearing capacity of single pile is about 220N at 0s, 150N at 15s and 120N at 25s. The curve drops sharply at the beginning of 35S and the bearing capacity is lower. Combined with the CCPF and Q-S curves, it can be shown that when the vibration time is short (within 15s), the soil has not been liquefied and the CCPF = 1 at the bottom of the pile indicates that the actual load acting on the top of the pile in a short time is equal to the applied load. As the time of vibration increases continuously, the soil around the pile begins to liquefy from top to bottom. The liquefied soil layer not only reduces the friction resistance on the side of the pile, but also finds that the actual load acting on the top of the pile is less than the load applied on the top of the pile. Thus, the phenomenon that CCPF at the bottom of pile is less than 1 at 25s and 35S appears.
The above analysis shows that CCPF can more intuitively reflect the distribution rule of accumulated pile side friction resistance along the pile body during earthquake. By comparing the value of CCPF at the bottom of pile with that of 1, the change of actual load on the top of pile during vibration can be clearly analyzed.
5.2 Distribution regularity and characteristics of CCPF along pile body of pile group system
The same analysis is carried out for piles in group piles foundation by means of CCPF. When the spacing between piles is 3D, 3.5D, 4D, 5D and 6D respectively, the CCPF curve of ZZ1 piles at different times of seismic action is shown in Fig. 10. The relationship between vertical force and settlement of 3D, 3.5D, 4D, 5D and 6D working conditions at different specific shaking times are shown in Table7, Table8, Table9, Table10, Table11.
|
shaking time(s) |
Longitudinal depth of pile(cm) |
||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
0 |
-5 |
-10 |
-15 |
-20 |
-25 |
-30 |
-35 |
-40 |
-45 |
-50 |
-55 |
-60 |
|
|
0 |
0 |
5 |
8 |
13 |
18 |
24 |
29 |
35 |
41 |
52 |
60 |
67 |
75 |
|
15 |
0 |
4 |
6 |
9 |
13 |
18 |
23 |
30 |
40 |
51 |
63 |
75 |
86 |
|
25 |
0 |
2 |
4 |
5 |
7 |
10 |
14 |
20 |
34 |
52 |
71 |
85 |
100 |
|
35 |
0 |
0 |
1 |
3 |
6 |
9 |
10 |
14 |
26 |
40 |
62 |
86 |
118 |
|
shaking time(s) |
Longitudinal depth of pile(cm) |
||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
0 |
-5 |
-10 |
-15 |
-20 |
-25 |
-30 |
-35 |
-40 |
-45 |
-50 |
-55 |
-60 |
|
|
0 |
0 |
4 |
7 |
12 |
16 |
23 |
29 |
33 |
38 |
45 |
54 |
62 |
70 |
|
15 |
0 |
3 |
5 |
9 |
12 |
17 |
21 |
26 |
32 |
40 |
52 |
64 |
81 |
|
25 |
0 |
1 |
3 |
6 |
9 |
10 |
13 |
18 |
27 |
39 |
58 |
79 |
94 |
|
35 |
0 |
0 |
1 |
2 |
4 |
7 |
10 |
15 |
24 |
43 |
61 |
85 |
111 |
|
shaking time(s) |
Longitudinal depth of pile(cm) |
||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
0 |
-5 |
-10 |
-15 |
-20 |
-25 |
-30 |
-35 |
-40 |
-45 |
-50 |
-55 |
-60 |
|
|
0 |
0 |
3 |
6 |
10 |
15 |
20 |
26 |
31 |
38 |
43 |
51 |
58 |
65 |
|
15 |
0 |
1 |
2 |
4 |
8 |
12 |
17 |
24 |
31 |
42 |
53 |
64 |
78 |
|
25 |
0 |
0 |
1 |
3 |
5 |
7 |
10 |
14 |
18 |
25 |
43 |
64 |
89 |
|
35 |
0 |
0 |
0 |
2 |
3 |
5 |
7 |
9 |
14 |
20 |
34 |
61 |
94 |
|
shaking time(s) |
Longitudinal depth of pile(cm) |
||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
0 |
-5 |
-10 |
-15 |
-20 |
-25 |
-30 |
-35 |
-40 |
-45 |
-50 |
-55 |
-60 |
|
|
0 |
0 |
2 |
5 |
10 |
15 |
20 |
26 |
31 |
38 |
43 |
50 |
57 |
63 |
|
15 |
0 |
1 |
2 |
4 |
8 |
12 |
17 |
24 |
31 |
42 |
53 |
64 |
79 |
|
25 |
0 |
0 |
1 |
2 |
5 |
7 |
10 |
15 |
20 |
29 |
42 |
63 |
90 |
|
35 |
0 |
0 |
0 |
1 |
3 |
7 |
11 |
15 |
18 |
24 |
33 |
58 |
92 |
|
shaking time(s) |
Longitudinal depth of pile(cm) |
||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
0 |
-5 |
-10 |
-15 |
-20 |
-25 |
-30 |
-35 |
-40 |
-45 |
-50 |
-55 |
-60 |
|
|
0 |
0 |
2 |
4 |
9 |
14 |
19 |
25 |
30 |
37 |
44 |
51 |
57 |
62 |
|
15 |
0 |
1 |
2 |
4 |
8 |
11 |
15 |
22 |
29 |
40 |
50 |
64 |
75 |
|
25 |
0 |
0 |
1 |
2 |
5 |
7 |
12 |
15 |
20 |
29 |
42 |
63 |
86 |
|
35 |
0 |
0 |
0 |
1 |
3 |
7 |
10 |
16 |
19 |
25 |
35 |
59 |
92 |
By analyzing 3D working conditions, the CCPF value at the same position of pile body decreases gradually with the extension of vibration time in the range of 0 to -50cm and increases gradually in the range of -50cm to -60cm. The distribution curve of CCPF at each moment intersects at -40 ~ 50cm of the pile body, and the maximum value of CCPF occurs at the bottom of the pile at each moment of vibration. From 0.75 at 0s to 1.28 at 35s, and the maximum CCPF of 0s and 15s is less than 1. Based on previous research [14], no liquefaction occurs in soil around the pile before 20s of vibration, which indicates that the actual load on the top of ZZ1 pile is less than the average of the total load. After 20 seconds of vibration, the soil begins to liquefy, which is approximately equal to 1 at 25 seconds, indicating that the load on the top of the pile is approximately equal to the average of the total load. More than 1 at 35S indicates that with the continuous liquefaction of soil from top to bottom, the bearing load of soil between piles decreases gradually due to group pile effect, and the bearing load of each foundation pile increases accordingly, which indicates that the bearing load on top of ZZ1 pile is greater than the average of total load.
Under 3.5D working conditions, the change curves of CCPF values at different times of vibration are similar. According to the analysis of 3D working condition, only when the vibration is 35s, the load on the top of the pile is greater than the average value, and other times are less than the average value. From the CCPF distribution curve, it can be seen that the intersection point moves down a little along the pile body compared with the 3D condition, about − 50cm.
The distribution characteristics of CCPF curves under 4D, 5D and 6D conditions are the same. At each vibration moment, the value of CCPF at the bottom of pile is less than 1, which means that the load at the top of pile is less than the average value of the total load at each time. The steepness of CCPF curve reflects the change degree of friction resistance along the side of the pile body at each moment of vibration. Because the actual load on the pile top varies with the liquefaction degree at each moment of vibration, the CCPF value can not reflect the friction resistance on the side of the pile at each time and there is no comparability. The intersection points are all concentrated at -50cm, which continues to decline compared with 3.5D conditions.
The variation curve of CCPF at the bottom of middle pile (ZZ1) in pile group foundation with vibration time is shown in Fig. 11. The relevant data see the Table 12.
|
different time |
Pile spacing(D) |
||||
|---|---|---|---|---|---|
|
3 |
3.5 |
4 |
5 |
6 |
|
|
0s |
75 |
70 |
65 |
63 |
64 |
|
15s |
86 |
81 |
78 |
79 |
78.5 |
|
25s |
100 |
94 |
89 |
90 |
87.8 |
|
35s |
118 |
111 |
94 |
92 |
91.5 |
Figure 11 shows that under certain pile spacing, the value of CCPF gradually increases with the duration of vibration, which indicates that the actual load on the top of ZZ1 pile increases with the increase of vibration time. The same vibration time of different spacing between piles decreases with the increase of spacing between piles, which indicates that the actual load on the top of piles decreases with the increase of spacing between piles.
The cumulative coefficient of pile side friction resistance CCPF is introduced. Through the distribution of foundation piles (middle piles) in single pile and group piles with different pile spacing along the CCPF of pile body, it can be concluded that CCPF can more intuitively reflect the distribution rule of accumulated pile side friction resistance along the pile body during earthquake. When the value of CCPF at the bottom of the pile is equal to 1, the actual load on the top of the pile is equal to the average value of the total load, and when the CCPF at the bottom of the pile is less than 1, the load on the top of the pile is less than the average value of the total load. When CCPF at the bottom of the pile is greater than 1, the load at the top of the pile is greater than the average of the total load.
The data availability statement：
The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.
Fund
The Foundation of Key Laboratory for Comprehensive Energy Saving of Cold Regions Architecture of Ministry of Education (JLZHKF022021002);
- Zhang C.W., Zhao J.M., Zhang S.R. Dynamic nonlinear finite layer-element method for pile-soil interaction analysis.Chinese Journal of Geotechnical Engineering. 1996, 18(4): 1–10. (in chinese)
- Huang Q.X., Lin J.H. Finite element analysis of the pile in foundation of laterally extending liquefaction.Journal of Huaqiao University (Natural Science). 2004, 25(3): 328–330. (in chinese)
- Yang W.L., Chen G.X., Wang Z.H. 2D and 3D seismic response analyses of supergian bridge pier-group piles-soil interaction system on deep overburden layers.Journal of Earthquake Engineering and Engineering Vibration. 2003, 23(6): 124–132. (in chinese)
- Su J.B., Shao G.J., Liu N. Nonlinear finite element analysis of piles under lateral load based on P-Y curves. Rock and Soil Mechanics. 2006, 27 (10): 1781–1785. (in chinese)
- Wu X.P., Sun L.M., Hu S.D. Development of laminar shear box used in shaking table test .Journal of Tongji University. 2002, 30(7): 781–785. (in chinese)
- Wang J.H., Feng S.L. Research on lateral resistance of pile foundation in liquefaction strata.Rock and Soil Mechanics. 2005, 26(10): 1597–1601. (in chinese)
- Qi C.X., Wang J.H. Studies on dynamic p-y curve of laterally loaded piles in liquefied soil.China Offshore Platform. 2007, 22(3): 1–7. (in chinese)
- Zhao C.G., Long C.L. Liquefaction and strength steady state.China Civil Engineering Journal. 2001, 34(3): 90–96. (in chinese)
- Li Y.R., Yuan X.M., Liang Y. Analysis for p-y curves of liquefied soil-pile interaction. Journal of Earthquake Engineering and Engineering Vibration. 2008, 28(3): 165–171. (in chinese)
- Amar S.P., Dilip K. B. Dynamic analysis of pile foundation embedded in homogeneous soil using cone model. Journal of Geotechnical and Geoenvironmental Engineering. 2018; 144(8): 06018007. DOI:10.1061/(ASCE)GT.1943-5606.0001927
- Paramasivam B., Dashti S., Liel A. Centrifuge investigation of the effects of liquefiable soil interlayering and structural strength on the seismic performance of soil-structure systems. Earthquake Engineering and Soil Dynamics. Geo-Congress 2019 GSP 308. 66–75.
- Al-Isawi A.T., Collins P.E.F., Cashell K.A. Fully non-linear numerical simulation of a shaking table test of dynamic soil-pile-structure interactions in soft clay using ABAQUS. Earthquake Engineering and Soil Dynamics. Geo-Congress 2019 GSP 308. 252–265.
- Nadarajah R., H. K. Shada. Dynamic response of pile foundation in partially saturated soils. Advances in Analysis, Modeling & Design. GeoFlorida 2010 GSP 199. 3009–3018. DOI:10.1061/41095(365)307
- Huang Z.F., Bai X.H. Study of seismic response of pile-liquefiable sandy Soil foundation based on shaking table model test. Vibration and Shock. 2013; 32(18): 153–158. (in chinese)
- Akira.A, Noda.T, Yamada.E, et al. An elasto-plastic description of two distinct volume change mechanisms of soils. Soils and Foundation, 2002, 42(5).
- Deeks.A.J, M.F.R and olph.Axisvmmetrie time-domain transmitting boundaries. Jonrnal of Engineering Mechanies, 1991.1–25.
- Xia D.Z., He Y.B., Liu J.H. Study of damping property and seismic action effect for soil-Xia D.Z., He Y.B., Liu J.H. Study of damping property and seismic action effect for soil- structure dynamic interaction system. Rock and Soil Mechanics，2009. 30(10). 10-30.
- 《Code for Design of Building Foundation》GB50007-2011. China Construction Industry Press. 2011. (in chinese)
No competing interests reported.