## 4 Discussion
### Seismic Response of the PSC Girder Bridge According to the Wave Passage Effect  
Assuming the bedrock shear wave velocity of Seismic Load 4 as 500 m/s, 571 m/s, 667 m/s, 800 m/s, 1000 m/s, 1333 m/s, 2500 m/s, and 4000 m/s, and applying wave passage effect as 0.08 s, 0.07 s, 0.06 s, 0.05 s, 0.04 s, 0.03 s, 0.02 s, and 0.01 s, respectively, the seismic response of the bridge was compared, as shown in Figure 14 and Table 6. We observed that insignificant differences appeared in the maximum bending moment during the increase in the wave passage effect from 0.00 s to 0.05 s. However, after 0.06 s, the maximum bending moment dramatically increased, and it was confirmed that the maximum bending moment increased by ~150% at 0.08 s compared to 0.06 s.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Wave Passage Effect**} & \multirow{2}{*}{**Peaked Acceleration**} & \multicolumn{3}{c}{**Spectral Acceleration**} & \multicolumn{1}{c}{**Max. Bending**} \\ \cline{3-6}  & & **1 st Mode** & **2 nd Mode** & **3 rd Mode** & **Moment (kN\(\cdot\)m)** \\ \hline \(\Delta\)T: 0.00 s & 0.836 & 3.954 & 1.762 & 0.880 & 3561.83 \\ \(\Delta\)T: 0.01 s & 0.835 & 3.950 & 1.757 & 0.879 & 3605.90 \\ \(\Delta\)T: 0.02 s & 0.830 & 3.917 & 1.729 & 0.873 & 3638.98 \\ \(\Delta\)T: 0.03 s & 0.833 & 3.936 & 1.746 & 0.877 & 3626.76 \\ \(\Delta\)T: 0.04 s & 0.803 & 3.748 & 1.588 & 0.848 & 3635.79 \\ \(\Delta\)T: 0.05 s & 0.782 & 3.614 & 1.479 & 0.828 & 3637.15 \\ \(\Delta\)T: 0.06 s & 0.758 & 3.448 & 1.347 & 0.803 & 4009.57 \\ \(\Delta\)T: 0.07 s & 0.730 & 3.253 & 1.196 & 0.773 & 4675.18 \\ \(\Delta\)T: 0.08 s & 0.698 & 3.029 & 1.028 & 0.739 & 5344.66 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of peaked acceleration, spectral acceleration, and maximum bending moment of the PSC girder bridge.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Seismic Load**} & \multirow{2}{*}{**Peaked Acceleration**} & \multirow{2}{*}{**Ratio (\%)**} & \multicolumn{3}{c}{**Spectral Acceleration**} & \multicolumn{1}{c}{**Maximum**} \\ \cline{3-6}  & & & **1 st** & **Ratio** & **2 nd** & **Ratio** & **3 rd** & **Ratio** \\  & & & **Mode** & **(\%)** & **Mode** & **(\%)** & **Mode** & **(\%)** & **Moment (kN\(\cdot\)m)** \\ \hline El Centro & 0.609 & 170.588 & 3.387 & 462.705 & 1.268 & 171.583 & 0.615 & 109.626 & 2683.60 \\ Initial Artificial & 0.549 & 183.000 & 3.275 & 488.806 & 1.499 & 182.139 & 0.658 & 113.253 & 2308.36 \\ Time–History & 0.782 & 260.667 & 3.302 & 380.854 & 1.955 & 225.230 & 0.826 & 126.107 & 3223.90 \\ Applied Soil & 0.836 & 205.911 & 3.954 & 391.873 & 1.762 & 242.033 & 0.880 & 189.655 & 3561.83 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of peaked acceleration, spectral acceleration, and maximum bending moment of the PSC girder bridge.  
The response spectrum calculated from the response acceleration of the bridge shows small differences in the 1 st, 2 nd, and 3 rd modes of the bridge, until 0.04 s of the wave passage effect. However, from 0.05 s, the response spectrum began to decrease in the major mode of the bridge, and in the 2 nd mode of 0.08 s of the wave passage effect it reduced by \(\sim\)58% compared to the 2 nd mode of 0.00 s. This is because even if identical seismic loads act on the bridge, the acceleration in the opposite direction acts on the two piers due to the wave passage effect, as can be confirmed by the displacement shape of the deck of the bridge shown in Figure 14c. Based on the above results, to ensure the stability of the bridge under seismic loads, the wave passage effect should be considered under a shear wave velocity of bedrock of 1000 m/s (\(\Delta t\): 0.05 s) in the area where the bridge is constructed.