## 4 Numerical Example
### The Selection of Ground Motion Records  
Ground motion records for this study are primarily determined based on the site classification. According to the National Earthquake Hazards Reduction Program (NEHRP) guidelines ([PERSON] et al., 2018), the shear wave velocity (\(V_{\mathrm{s}}\)30) of the site where the Daikai station is located ranges from 180 m/s to 360 m/s. This categorizes the site as a Class D location. In terms of the number of ground motion records to be selected, the work by [PERSON] and [PERSON] (2018) suggests that a range of 10 to 20 records provides an adequate representation of ground motion randomness. Additionally, it has been observed that pulse-like ground motions, which contain numerous low-frequency components, induce significant structural dynamic responses. These responses manifest as variations in the internal force within the central column, lateral deformation of the soil layer, and displacement of the side walls. These effects are notably more pronounced compared to non-pulse motions ([PERSON] et al., 2018; [PERSON] and [PERSON], 2018). Therefore, 18 pulse-like ground motion records were chosen for this study based on the multi-component velocity pulse identification method proposed by [PERSON] and [PERSON] (2018). These records were sourced from the NGA-West2 strong earthquake database, part of the Pacific Earthquake Engineering Research (PEER) Ground Motion Database ([PERSON] and [PERSON], 2018). All selected records correspond to a Class D site, as detailed in Table 3. To comprehensively capture the structure's dynamic response, from elastic behavior through to elastic-plastic and finally to collapse during IDA, these 18 ground motion records were subject to amplitude modulation. Preliminary calculations showed initial amplitude modulations of PGA at 0.03 g, 0.06 g, and 0.1 g. These amplitudes were then incrementally adjusted up to 0.8 g in steps of 0.05 g.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Verify Indicators**} & \multicolumn{2}{c}{**Horizontal**} & \multirow{2}{*}{\begin{tabular}{c} **Maximum Axial** \\ **Contal Column (cm)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Maximum Shear** \\ **Force (kN)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Static Axial Force (kN)** \\ \end{tabular} } \\  & & & & & \\ \hline Results of [PERSON] et al. (2018) & 3.8 & 4900 & 730 & 3700 \\ Results of this study & 3.41 & 4762.05 & 689.97 & 3205.68 \\ Deviation (\%) & 10.26 & 2.82 & 5.48 & 13.36 \\ \hline \end{tabular}
\end{table}
Table 2: Verification of the finite element model of Daikai subway station.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Event**} & \multirow{2}{*}{**Station**} & \multirow{2}{*}{\begin{tabular}{c} **Mag.** \\ **(M\({}_{\text{W}}\))** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **R** \\ **(km)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Pulse** \\ **(s)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **\(V_{\mathrm{s}}\)30** \\ **(m/s)** \\ \end{tabular} } & \multirow{2}{*}{**Direction**} & \multirow{2}{*}{\
\begin{tabular}{c} **PGA** \\ **(g)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **PGV** \\ **(cm/s)** \\ \end{tabular} } \\ \hline
1 & Imperial Valley-06, 1979 & El Centro Array \#10 & 6.53 & 8.60 & 4.515 & 202.85 & E10320 & 0.23 & 46.25 \\
2 & Superstition Hills-02, 1987 & Parachute Test Site & 6.54 & 0.95 & 2.394 & 348.69 & PTS225 & 0.43 & 134.81 \\
3 & Loma Prieta, 1989 & Saratoga-W Valley & & 6.93 & 8.48 & 5.649 & 347.9 & WVC270 & 0.33 & 64.94 \\
4 & Kobe, Japan, 1995 & Takazuka & 6.9 & 0 & 1.806 & 312.00 & TAZ090 & 0.61 & 86.27 \\
5 & Northridge-01, 1994 & Parde-SCE & 6.69 & 5.54 & 1.232 & 325.67 & PAR–T & 0.30 & 53.97 \\
6 & Kobe, Japan, 1995 & Takatori & 6.9 & 1.46 & 1.554 & 256.00 & TAK090 & 0.67 & 123.14 \\ \hline \end{tabular}
\end{table}
Table 3: Eighteen pulse-like ground motion records.