In recent ten years, with the increase in the number of underground projects and the frequent occurrence of earthquake damage to underground structures, especially inspired by the Kobe earthquake, people have a new understanding of the seismic capacity of underground structures and strengthened the research on the theory and method of establishing seismic design of underground structures.
Great earthquakes in history show that soft soil will amplify the destructive effect of earthquakes, so it is more meaningful to study the analysis theory and design method of subway seismic design in Shanghai area with soft soil layer thickness of 250~300m m. Zhang Xiong [1] and others studied the three-dimensional seismic response of soil-underground structure interaction system in time domain; AKIRA[2] studied the seismic response of underground structures by static finite element method. Domestic scholars have also strengthened the research on the seismic performance of underground structures. Ma Xianfeng [3] and others investigated the earthquake damage of underground structures in detail earlier in China, which provided a basis for establishing the theory and method of seismic calculation of underground structures. Chen Guoxing [4] used substructure method to analyze the earthquake of subway station structure; Zhang Hong [5] and others analyzed the nonlinear seismic response of subway tunnels.
Professor Yang Linde conducted shaking table model tests on typical subway station structures in Shanghai soft soil area. The model test includes two parts: free field shaking table model test and typical subway station structure shaking table model test. The former is mainly used to simulate the seismic response of soil layer in free site, determine the working performance of model box, and provide preconditions for shaking table model test of typical subway station structure. The latter is mainly used to understand the laws and characteristics of ground motion response when subway stations interact with soil. According to the model test results, Yang Chao [6] and Liu Qijian [7] studied the calculation method of seismic response of subway station structure in Shanghai soft soil area based on plane strain assumption. In this paper, a three-dimensional calculation model is established for the shaking table model test of free field, and its three-dimensional numerical fitting analysis is carried out, which lays the foundation for establishing a numerical calculation method for the three-dimensional seismic response of Shanghai soft soil.
1 free field shaking table model test
1. 1 test overview
The free-field shaking table model test [8] is shown in figure 1, and the model box device is a three-electro-hydraulic servo-driven earthquake simulation shaking table produced by MTS company in the United States. The mesa size is 4.0m×4.0m；; Maximum bearing capacity15t; The vibration mode is six degrees of freedom in x, y and z directions; The frequency range is 0.1~ 50hz; The maximum acceleration of the workbench is 1.2g in X direction, 0.8g in Y direction and 0.7g in Z direction. The model box is a hollow cuboid with a height of 1.2m, a clear length of 3.0m along the vibration direction and a clear width of 2.5m perpendicular to the vibration direction. The height of soil in the box is1m.
There are 16 acceleration sensors on the surface and middle of the model soil, denoted by a (Figure 2). Four dynamic earth pressure sensors are arranged on the contact surface between the model soil and the box wall, denoted by P. The information collected in the experiment is the acceleration value and the contact pressure value between the model soil and the box.
Selection and preparation of 1.2 model soil
The performance of model soil is difficult to be similar to that of undisturbed soil in all aspects, so we try to make model soil similar to undisturbed soil in two aspects: the maximum dynamic shear modulus and the change law of dynamic shear modulus and dynamic strain relationship curve.
The material used to make model soil in this experiment is brown silty clay. The main reasons are as follows: (1) This kind of clay is ubiquitous in the shallow layer of Shanghai and easy to obtain; (2) This kind of clay has high strength when it is dry, and it will soften quickly when it meets water. By adjusting its water content and compactness, it is easy to make its characteristics meet the requirements of model soil preparation.
2 calculation model
2. 1 Determination of calculation area
The range of the calculation area is consistent with the size of the model box. The model soil is 3.35m long (excitation direction, including foam plastic plates with thickness of 175mm on both sides), 2.5m wide and 1.0m deep. The model soil and plastic plate are divided into three-dimensional finite difference grids by solid elements, as shown in Figure 3.
2.2 Selection of material constitutive model
The dynamic test of remolded soil [9] shows that the dynamic stress-strain relationship of Shanghai soft soil follows the law of "strain softening": the dynamic shear modulus decreases with the increase of shear strain, and the damping ratio increases with the increase of shear strain, and the relationship can be described by Davidenco's model as follows.
Where: a, b and γr are fitting constants; γr is also the reference shear strain, and γd is the instantaneous dynamic shear strain; Gd and λ are instantaneous dynamic shear modulus and damping ratio; Gmax and λmax are the maximum dynamic shear modulus and the maximum damping ratio.
In this experiment, brown silty clay was selected as the raw material for making model soil. The parameters of Davidenkov model are determined by experiments [8], as shown in table 1. Its Poisson's ratio is 0.4 and its density is 1760kg/m3. According to the test [8], the dynamic elastic modulus of the foamed plastic board is 4. 13MPa, the density is 15kg/m3, and Poisson's ratio is 0.4, so the foamed plastic board is selected as the elastic model.
2.3 boundary conditions
Due to the large stiffness of the model box during vibration excitation, its deformation can be ignored, and it can be considered that the acceleration of the lateral and bottom boundaries in the horizontal direction is always consistent with the test wave input by the shaking table. Therefore, the dynamic boundary conditions used in the calculation are as follows: (1) simultaneously applying acceleration boundaries consistent with the input acceleration of the shaking table on the four sides and the bottom of the model along the excitation direction; The bottom of the model is a vertically fixed boundary; The top surface is a freely deformable boundary.
2.4 Load input
Three kinds of seismic waves are selected as the input waves of the shaking table, and the loading system of the test is shown in Table 2. The experiment adopts one-way input excitation, and the mesa wave is input at the bottom of the model.
3 Calculation results and analysis
In the free-field shaking table model test, the sensors used to receive the excitation response information are mainly acceleration sensors, so this paper only analyzes the acceleration response law.
3. 1 acceleration amplification factor
The ratio of the peak acceleration response of the measuring point to the input peak of the shaking table is defined as the acceleration response amplification factor. Under various load conditions, the 2D [6] and 3D numerical simulation results of measuring points A3 and A25 on the soil surface are shown in Table 3 and Table 4, and the arrangement of measuring points is shown in Figure 2.
It can be seen from Tables 3 and 4 that the three-dimensional calculation results are in good agreement with the two-dimensional calculation results and the test results under most working conditions, and the relative errors are all within 10%, which shows that the proposed calculation method can well simulate the dynamic response law of model soil. Only under the two working conditions of El-9 and SH- 10, there are some errors between the two-dimensional and three-dimensional calculation results and the experimental results. The reason may be that the input peak of ground motion is too large and the shear modulus of soil is greatly attenuated, which makes the actual stress-strain relationship curve of soil deviate greatly from the curve of Davidenkov model used in the test. In addition, it can be seen that the three-dimensional calculation result is greater than the two-dimensional calculation result, and the two-dimensional calculation result is greater than the experiment.
3.2 acceleration response time history and Fourier spectrum
Figs. 4 and 5 show the acceleration time-history curve of measuring point A25 and the calculation and measurement results of its Fourier spectrum under SH-3 condition. It can be seen from the figure that the waveform and amplitude of the calculated results are basically consistent with the experimental results, and their frequency components are basically the same in all frequency bands, which also shows that the calculation method in this paper can well simulate the acceleration response law of model soil.
4 conclusion
In this paper, based on the shaking table model test of Shanghai subway station structure in soft soil area, a three-dimensional calculation model is established, and the three-dimensional numerical fitting analysis is carried out through the shaking table model test, and the acceleration response law of the model soil and the dynamic soil pressure between the model soil and the model box are obtained. The calculated results are in good agreement with the measured results and the calculated results of the two-dimensional model, which shows that the three-dimensional calculation model established in this paper can simulate the dynamic characteristics of the model soil well and lay the foundation for establishing the three-dimensional seismic response calculation method of Shanghai soft soil. The research of three-dimensional calculation method will be introduced in another article.
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