## Numerical Simulations  
### Finite Element Models  
The prototype substation used in this study is selected from Urban underground substation design rule (2005, China) [25]. The main plant of the underground substation is a three-story, four-bay reinforced concrete shear wall structure, as shown in Figures 1-4. The dimensions of the main plant are 50 m by 25 m, and floor heights from the bottom to top are 4.4 m, 4.8 m, and 5.2 m respectively. Figure 3: Long cross-section. Figure 2: Dimensions of the floor and wall. Figure 1: Plan of the second floor. The exterior wall of the main plant structure is made of a reinforced concrete wall, 0.45 m in width. The dimensions of the main beams are 600 \(\times\) 1300 mm\({}^{2}\), 500 \(\times\) 1400 mm\({}^{2}\), 500 \(\times\) 1000 mm\({}^{2}\) separately, and the cross-sectional dimension of the transverse beams is 400 \(\times\) 1000 mm\({}^{2}\). The thicknesses of the first, second, third, and roof slabs are 900 mm, 400 mm, 400 mm, and 600 mm respectively. The total weight of the plant is approximately 27,530 kN. Ten sets of electrical equipment, shown in Figure 5, are installed on the second floor, the dimensions of which are 6.0 m (length), 2.0 m (width) and 3.5 m (height). The total weight of the equipment is approximately 964 kN, which corresponds to 3.5% of the plant weight. The plant was designed by Chinese loading Code for Design of Building Structures (2012, [26]), in which gravity loads are selected as 1.8 kN/m\({}^{2}\) for floors and 3.5 kN/m\({}^{2}\) for the roof. Live loads are selected as 2.5 kN/m\({}^{2}\) for floors and 2.0 kN/m\({}^{2}\) for the roof. The gravity load of equipment is 8.0 kN/m\({}^{2}\). The seismic design of the substation is allowed according to Chinese Code for Seismic Design of Buildings (2010, [27]) and Chinese Code for Seismic Design of Electrical Installations (2013, [28]). The underground substation is assumed to be located in Xi'an, China, where the design basis acceleration associated with 10% probability exceedance in 50 years is 0.2 g (g denotes the coefficient of gravitational acceleration). The compressive strength of concrete and the yield strength of steel are taken as \(f_{c}\) = 30 MPa, and \(f_{y}\) = 400 MPa, respectively. According to the first eigen-frequency, the factor \(\beta\) is shown in Equation (6). \[\beta=\frac{2\xi_{1}}{\omega_{1}} \tag{6}\]  
Based on a natural frequency extraction analysis of the interaction system, the first eigen-frequency is 0.39 rad/s. Therefore, \(\beta\) is 0.179 s.  
Figure 4: Short cross-section. Figure 5: Electrical equipment. The models were developed and analyzed in ABAQUS (2006, [29]). The beams and columns are modeled in three-dimensional beam elements, the floors and concrete walls are modeled in shell elements, and the equipment is modeled in pipe elements, as shown in Figure 6. The three-dimensional finite element electrical equipment model is shown in Figure 7. The concrete plastic-damage model is used for the constitutive properties of concrete material and the double linear dynamic reinforcement model is used for rebar. Druker-Prager, a generalized Mises yield criterion, is adopted in soil dilation. The effect of hydrostatic pressure on yield and strength is used as the constitutive model of soil ([PERSON] et al., 2006, [30]). The physical and mechanical parameters of soil, as determined by the penetration test and consolidation test, are listed in Table 1. Based on the artificial constrained boundary, the boundary element is used to simulate the infinite field of soil, and the horizontal reaction forces on the lateral boundary are determined by static analysis. According to the literature ([PERSON] et al., 2006 [31]; [PERSON] et al., 2010 [32]), the coupling analysis method is used in the soil boundary condition.