## Numerical Simulations
### Finite Element Models
Meanwhile, it is suggested from literature ([PERSON] et al., 1999 [33]; [PERSON] et al., 2000 [34]) that five times the width of the structure can be defined as the width of the computational area of soil in order to reduce the motion reflection on the boundary. Following this rule, five times the width of the structure is selected as the soil width in the finite element model. Therefore, the soil size of the finite element is \(250\:\mathrm{m}\times 132.5\:\mathrm{m}\times 50\:\mathrm{m}\) and the size of the entire soil is \(500\:\mathrm{m}\times 265\:\mathrm{m}\times 50\:\mathrm{m}\). The arbitrary Lagrangian Eulerian (ALE) adaptive meshing method is used to maintain a high-qualified meshing system for soil, which allows the meshes to move independently when large deformation of liquefied soils occurs. The soil element meshes are shown in Figure 8, in which the finite element of soil is simulated by unit C3 DBR. In order to simulate the most realistic condition of soil and simplify some less salient factors in this paper, the following basic assumptions are advised in analysis ([PERSON] [35], 2015; [PERSON] [36], 1972). 1. Each layer of soil is homogeneous, and extends infinitely in the horizontal direction;
2. There is no relative sliding among different layers of soil;
3. Earthquake excitations are supposed from the bottom of the foundation;
4. The movement of each point on the bottom of the foundation is consistent without a traveling motion effect. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multirow{2}{*}{**Name of Soil**} & **Density** & **Elastic Modulus** & **Poisson** & **Cohesion** & **Internal Friction** & **Soil** \\  & & **(kg/m\({}^{3}\))** & **(MPa)** & **Ratio** & **(kPa)** & **Angle (\({}^{\circ}\))** & **Depth (m)** \\ \hline
1 & Plain fill & 1720 & 5.0 & 0.39 & 22 & 15 & 4.30 \\
2 & New loess & 1600 & 12.0 & 0.30 & 28 & 18 & 6.20 \\
3 & Silty clay & 1950 & 15.0 & 0.30 & 45 & 15 & 1.70 \\
4 & Pebble bed & 2250 & 55.0 & 0.15 & 0 & 45 & 2.10 \\
5 & Silty clay & 1950 & 15.0 & 0.30 & 45 & 15 & 27.0 \\
6 & Coarse ands & 1920 & 40.0 & 0.26 & 0 & 35 & 4.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The physical and mechanical soil parameters. Figure 6: Finite element model of a substation. According to the classification of site type and seismic fortification intensity, three earthquake records--El-Centro record, Taft record and Lanzhou record--were derived from the registered seismic data. Moreover, in order to obtain earthquake motions, three earthquake records were back-calculated to the bottom of the foundation level by the SHAKE91 procedure ([PERSON] et al., 1992 [37]). According to the finite element division of the soil layer, soil properties such as density, shear velocity, shear modulus of elasticity, etc., were taken into account in earthquake motion inversion. Time-histories and spectra of these records after inversion are shown in Figures 9-14. Figure 8: Finite element model of soil. Figure 7: Finite element model of equipment. Figure 9: El-Centro motion in the horizontal direction after inversion. Figure 11: Taft motion in the horizontal direction after inversion. Figure 12: Taft motion in the vertical direction after inversion. Figure 10: El-Centro motion in the vertical direction after inversion. Figure 13: Lanzhou motion in the horizontal direction after inversion.