Keywords

1 Introduction

As a structure widely used in bridge engineering, pile foundation has the advantages of high bearing capacity, small settlement and not easy to damage. In order to avoid or reduce the loss of life and property caused by earthquake, researchers have carried out a lot of research on the damage or failure of pile foundation in liquefied site due to seismic response. Zheng et al. [1] summarized the earthquake damage of bridge pile foundations in liquefaction sites in several major earthquakes and pointed out that sand liquefaction is one of the important factors leading to the serious damage or even collapse of bridge structures. Ishihara, Yasuda et al. [2] studied the shaking table test of pile-soil group in liquefaction site, and found that soil deformation caused by liquefaction would lead to large bending moments in the middle of pile foundation and pile foundation at the surface. Tokimatsu [3] and Tamura [4] obtained that the bending moment of pile foundation is closely related to the liquefaction of sand by shaking table test. When the sand is liquefied, the bending moment of pile foundation has a significant trend of increase. In addition to carrying out model experiments, the numerical simulation method is also an important means to study the seismic response of pile-soil structures. Based on the two-dimensional finite difference program, Haldar and Sivakumar [5] selected the nonlinear soil constitutive model, and used the strength reduction method to study the failure mechanism of pile foundation in liquefied soil. Uzuoka et al. [6] established a three-dimensional numerical model by referring to the relevant earthquake damage survey data and taking the collapsed buildings in the Hanshin earthquake in Japan as the background. Jiang et al. [7] used FLAC3D finite difference software to discuss the changes of pile bending moment and pile-soil interaction force under earthquake action. Dai et al. [8] analyzed the variation of total stress and effective stress of sand foundation by using finite element numerical method for the seismic problem of pile group foundation in liquefied site.

In general, domestic and foreign scholars have conducted a lot of research on the mechanical response and deformation and failure characteristics of pile foundations in liquefied sites under seismic conditions by using shaking table experiments and numerical simulation methods, and have achieved some guiding results. In this paper, the project from Xiong’an New Area to Beijing Daxing International Airport Express Line is selected as the engineering background. The numerical calculation model of seismic response of bridge pile foundation in liquefied site is established by FLAC3D finite difference program. According to whether the site is liquefied, the dynamic response of soil and pile foundation, the bending moment, shear force and deformation of pile body in dynamic system are compared and analyzed.

2 Project Overview

The express line from Xiong’an New Area to Beijing Daxing International Airport is an important part of the high-speed railway transportation network in the ‘four vertical and two horizontal’ area of Xiong’an New Area. Among them, Xiong’an Station to Bazhou Economic and Technological Development Zone Station crosses the existing Tianjin-Baoding Railway in the form of a bridge between pier C143 # and C146 #, and the angle between the line and the existing railway is 59°. The on-site photos of the cross-Tianjin-Baoding Railway and the elevation map of the cross-Tianjin-Baoding Railway are shown in Fig. 1 and Fig. 2.

Fig. 1.
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On-site photos of the Cross-Tianjin-Baoding Railway

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Fig. 2.
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Elevation drawing of the Cross-Tianjin-Baoding Railway

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3 Numerical Simulation

According to the geological engineering investigation data, the typical geological profile under a borehole can be obtained and the strata under the site are simplified in FLAC3D as shown in Fig. 3, that is, the soil layer is divided into four layers. The size of the calculation model is 40 m × 40 m × 60 m. The soil constitutive model is Mohr-Coulomb model, and the relevant physical and mechanical parameters of the soil used are shown in Table 1.

Fig. 3.
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Initial soil layer model

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Table 1. Relevant soil physical and mechanical parameters
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After the seismic load is applied, considering that the seismic waves will be reflected on the surrounding boundary, in order to reduce the impact of reflection, the free field boundary is used in the dynamic calculation process of numerical simulation. At this time, the free field generated grids are coupled with the main part of the grid, which can better simulate the free field vibration. Figure 4 shows the grid diagram generated by selecting the free field boundaries used.

Fig. 4.
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Setting up free-field boundaries

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Fig. 5.
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Acceleration time history curve for vibratory load

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4 Simulation Analysis of Seismic Response of Pile Foundation in Liquefaction Site

In this paper, in order to compare and analyze, the site conditions are treated differently in the calculation, and the site is divided into two conditions: liquefaction and non-liquefaction. One is the PL-Finn model [9], which uses the pore water pressure accumulation of the soil under dynamic conditions to cause liquefaction. The other uses the Mohr-Coulomb model without considering the pore pressure accumulation. The input vibration waveform at the bottom of the model is consistent, and the peak acceleration reaches 0.2 g within 2 s. The acceleration time history curve of the vibration load is shown in Fig. 5.

4.1 Dynamic Analysis

In order to facilitate the analysis of the numerical simulation results, the monitoring points p1, p2 and p3 are set from near to far away from the pile foundation, as shown in Fig. 6. Under the action of vibration load, the time history curves of pore pressure ratio of sand layer under three measuring points are shown in Fig. 7. It can be seen that the pore pressure is constantly changing under the influence of the peak acceleration of the earthquake, and the overall trend of the calculated value at each monitoring point is roughly the same. In the initial stage, the pore pressure ratio increases in an uneven and irregular trend, reaching a peak around 0.5 s, and then maintaining a certain range for a period of time. From the change frequency and the change peak, it can be analyzed that the farther the measuring point from the pile foundation, the smaller the change range of the excess pore pressure ratio and the more stable it is.

Fig. 6.
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Horizontal monitoring point deployment diagram

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Fig. 7.
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Time history curve graph for excess pore pressure ratio

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4.2 Comparative Analysis of Liquefaction and Non-liquefaction Site Conditions

Figure 8 shows the bending moment envelope diagram of pile foundation under liquefied and non-liquefied conditions. It can be seen from the Fig that the bending moment of pier body increases first and then decreases, and the changing trend is the same. However, for the non-liquefied site, the bending moment of the pile reaches an extreme value of 335 kN·m at a distance of 40 m from the pile top, while for the liquefied site, the bending moment reaches an extreme value of 883 kN·m at a distance of 43 pm from the pile top. It can be seen that the bending moment effect of the pile increases due to liquefaction. In the liquefied soil layer, due to the lack of effective lateral support of the pile body caused by liquefaction, the bending moment of the pile body increases faster than that of the non-liquefied soil layer. As can be seen from the slope of the corresponding curve in the figure, the pile body is also most likely to withstand bending moments beyond the ultimate bending resistance of the pile itself in this liquefaction area, resulting in bending failure. This is consistent with the macro-seismic damage of the liquefied lateral expansion pile foundation obtained by other scholars [10].

Fig. 8.
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Enveloping diagram of the bending moment for pile foundation

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Figure 9 shows the enveloping diagram of axial force for pile foundation in liquefied and non-liquefied state. It can be seen from the Fig that the axial force of pile body increases gradually. The variation trend of the axial force envelope curve is consistent, but for the non-liquefied site, due to the influence of the friction resistance of the soil layer on the pile side, the axial force reaches a peak of 6612 kN at 45 m from the pile top, and continues to increase after a short decrease. For the liquefiable site, after the liquefaction of the liquefied soil layer, as the pore water pressure dissipates, the foundation consolidation settlement is caused, and the pile body is affected by the lateral negative friction resistance of the soil, resulting in the increase of the axial force of the liquefied pile in the site compared with the extreme axial force of the non-liquefied site. It can be seen from the Fig that the axial force of the pile foundation in the liquefied site reaches an extreme value of 7780 kN. However, in general, the influence of soil liquefaction on the axial force of pile foundation is relatively small.

Fig. 9.
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Enveloping diagram of axial force for pile foundation

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5 Conclusion

In this paper, through the numerical simulation analysis of pile foundation in liquefied and non-liquefied sites under earthquake action, the following results can be obtained:

Under site liquefaction condition, the bending moment of pile body increases first and then decreases, and the extreme value of bending moment is also greater than that of non-liquefied conditions. The position of the peak bending moment of the pile is near the 45 m below the surface (the junction of liquefied layer and non-liquefied layer), so it can be concluded that this position is the main location for pile body failure and the main location for seismic design of pile foundation. The variation trend of axial force envelope curve of pile foundation in liquefied site and non-liquefied site is consistent, but the extreme value of axial force in liquefied site is larger, and the influence of soil liquefaction on axial force of pile foundation is relatively small. On the whole, the liquefaction of the site has a great impact on the pile foundation, which will reduce the bearing capacity of the pile, and the impact should be considered in the actual design.