## 3 Finite Element Model Analysis
### Earthquake Input  
In order to simulate the real damage situation of the Dakai subway station underground, this paper adopted a combination of acceleration loading and resonance force loading. The acceleration time-history curves of the two earthquakes were input from the bottom of the model in the vertical direction, and the equivalent resonant force of the two earthquakes was loaded on one side of the structure in the horizontal direction; the force of the underground station during the earthquake is shown in Figure 12. The horizontal and vertical acceleration time curves in the Kobe earthquake were recorded based on the data from the earthquake observation station set up near the Dakai station, and the horizontal and vertical acceleration time-history curves of the Kobe earthquake are shown in Figures 13a and 14a. The El Centro earthquake was also chosen as a reference. The horizontal and vertical acceleration time-history curves of the El Centro earthquake are shown in Figures 13b and 14b. As shown in Figure 15, the vertical bandwidth of Kobe and El Centro earthquakes contain the vertical self-oscillation frequency of the structure. This indicates that the both earthquakes can effectively cause structural vibration. The frequency of the resonant force was taken as the main frequency of the two earthquakes, and the peak value of the resonant force was calculated according to the seismic active earth pressure formula mentioned in the Chinese Standard (NB 35047-2015) [35]. Figure 11: Bearing arrangement diagram: (**a**) friction pendulum bearing arrangement, (**b**) ring spring bearing arrangement, and (**c**) ring spring–friction pendulum support arrangement. Figure 12: The stress diagram of the underground station in an earthquake. Figure 13: Horizontal acceleration time history curve: (**a**) Kobe earthquake and (**b**) El Centro earthquake. The seismic active earth pressure is calculated using the following equation:  
\[F_{E}=[q_{0}\frac{\cos\psi_{1}}{\cos(\psi_{1}-\psi_{2})}+\frac{1}{2}\gamma H^{2}] (1+\xi q_{\
u}/g)C_{e} \tag{9}\]  
The structure was designed according to the seismic fortification intensity of 7 degrees under rare earthquakes, and the representative value of the horizontal design seismic acceleration av was 310 cm/s\({}^{2}\). According to the formula in the Chinese Standards, \(C_{e}\) can be calculated as 0.426, \(F_{E}\) as 295.3 kN/m, the axial length of the three-section station structure is 10.5 m, and then the active earth pressure acting on one side of the structure is \(3.1\times 10^{6}\)N. The horizontal acceleration time curves of the Kobe and El Centro earthquakes were Fourier-transformed to obtain the Fourier spectra shown in Figure 16, from which it can be seen that the main frequency of the Kobe earthquake wave was 1.16 Hz and the main frequency of the El Centro earthquake was 1.45 Hz. In order to be more realistic, the horizontal equivalent resonance force of the Kobe earthquake was amplitude-modulated. From Figure 12a, it can be seen that the Kobe earthquake reached its seismic peak at about 8.06 s, so the horizontal equivalent resonant force of the Kobe earthquake from 0 s to 4.3 s was adjusted to 1/3 of the seismic active earth pressure and the peak from 4.3 s to 8.6 s was adjusted to 2/3 of the seismic active earth pressure; the El Centro earthquake reached its seismic peak at about 2.12 s, so there was no need for amplitude modulation. The equivalent resonant force curves of the two earthquakes are shown in Figure 17.  
Figure 14: Vertical acceleration time–history curve: (**a**) Kobe earthquake and (**b**) El Centro earthquake. Figure 15: Fourier spectrum of vertical acceleration: (**a**) Kobe earthquake and (**b**) El Centro earthquake. The finite element simulation was divided into two analysis steps.