# Effect of Subsequent Subgrade on Seismic Response of the High-Speed Railway Track-Bridge System
## 5 Seismic Response Analysis of Each Critical Component in HSTRBS
### Seismic Response Analysis of Main Beam  
The main beam is a crucial component of the railway track-bridge system, with its displacement and deformation having a direct impact on the smoothness of the overlying track structure and, by extension, the safety of rail traffic. To assess this, we analyzed the longitudinal and vertical displacements of the main beam under varying peak ground accelerations for the two bridge models, BMCS and BMWS. The comparative results of these displacements are meticulously presented in Figures 5 and 6. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Object** & **Impact Parameters** & **U1, mm** & **U2, mm** & **Px, kN** & **V2, kN** & **V3, kN** & **M3, kN\(\cdot\)m** \\ \hline Main beam & \(\Delta\) & \(-\) & / & \(\dots\) & \(\dots\) & \(\dots\) & \(\dots\) \\  & \(\Delta\)max & \(-5.1\) & \(1.7\) & \(\dots\) & \(\dots\) & \(\dots\) & \(\dots\) \\ \hline \multirow{4}{*}{Bearings} & \(\Delta\) & \(+\) & / & \(+\) & \(+\) & \(+\) & \(\dots\) \\  & \(\Delta\)max & \(-3.9\) & \(-0.2\) & \(-227\) & \(-139\) & \(-14\) & \(\dots\) \\  & \(\varepsilon\) & \(\dots\) & \(\dots\) & \(-\) & \(+\) & \(-\) & \(\dots\) \\  & \(\varepsilon\)max & \(\dots\) & \(\dots\) & \(18.7\%\) & \(-5.5\%\) & \(-17.4\%\) & \(\dots\) \\ \hline \multirow{4}{*}{Left pier (1\(\sharp\))} & \(\Delta\) & \(+\) & / & \(+\) & \(+\) & \(+\) & \(+\) \\  & \(\Delta\)max & \(-1.7\) & \(-0.02\) & \(459\) & \(-1513\) & \(-7\) & \(-15,\)106 \\  & \(\varepsilon\) & \(\dots\) & \(\dots\) & \(+\) & \(+\) & \(+\) & \(+\) \\  & \(\varepsilon\)max & \(\dots\) & \(\dots\) & \(8.6\%\) & \(-43.1\%\) & \(-8.7\%\) & \(-47.2\%\) \\ \hline \multirow{4}{*}{Fixed pier (2\(\#\))} & \(\Delta\) & \(+\) & / & \(+\) & \(+\) & \(+\) & \(+\) \\  & \(\Delta\)max & \(-1.4\) & \(-0.03\) & \(1311\) & \(-1476\) & \(-24\) & \(-16,\)187 \\  & \(\varepsilon\) & \(\dots\) & \(\dots\) & \(+\) & \(+\) & \(+\) & \(+\) \\  & \(\varepsilon\)max & \(\dots\) & \(\dots\) & \(21.0\%\) & \(-14.7\%\) & \(-5.7\%\) & \(-25.5\%\) \\ \hline \multirow{4}{*}{Non-fixed pier (3\(\#\))} & \(\Delta\) & \(+\) & / & \(+\) & \(+\) & \(+\) & \(+\) \\  & \(\Delta\)max & \(-1.4\) & \(-0.01\) & \(1466\) & \(-586\) & \(-9\) & \(-4227\) \\  & \(\varepsilon\) & \(\dots\) & \(\dots\) & \(+\) & \(+\) & \(+\) & \(+\) \\  & \(\varepsilon\)max & \(\dots\) & \(\dots\) & \(18.3\%\) & \(-8.61\%\) & \(-6.9\%\) & \(-8.8\%\) \\ \hline \multirow{4}{*}{Right pier (4\(\#\))} & \(\Delta\) & \(+\) & / & \(+\) & \(+\) & \(+\) & \(+\) \\  & \(\Delta\)max & \(-1.8\) & \(-0.01\) & \(502\) & \(-1009\) & \(-6\) & \(-10,\)298 \\  & \(\varepsilon\) & \(\dots\) & \(\dots\) & \(+\) & \(+\) & \(+\) & \(+\) \\  & \(\varepsilon\)max & \(\dots\) & \(\dots\) & \(7.8\%\) & \(-44.28\%\) & \(-7.0\%\) & \(-45.4\%\) \\ \hline \multirow{4}{*}{Foundation piles} & \(\Delta\) & \(\dots\) & \(\dots\) & \(+\) & \(+\) & \(+\) & \(+\) \\  & \(\Delta\)max & \(\dots\) & \(\dots\) & \(-1176\) & \(-223\) & \(-13\) & \(-341\) \\  & \(\varepsilon\) & \(\dots\) & \(\dots\) & / & / & / & / \\  & \(\varepsilon\)max & \(\dots\) & \(-24.6\%\) & \(-25.9\%\) & \(-26.3\%\) & \(-27.4\%\) \\ \hline \hline \end{tabular} Note: “\(\star\)”: \(\Delta\) or \(\varepsilon\) gradually increases with the increase in the peak ground acceleration (PGA); “\(\dash\)”: \(\Delta\) or \(\varepsilon\) gradually decreases with the increase in the PGA; “\(\dash\)”: no significant change in \(\Delta\) or \(\varepsilon\) with the increase in the PGA; “\(\dots\)”: the results are not relevant to the research and will not be studied in this paper; “U1”: longitudinal displacement or longitudinal deformation; “U2”: lateral displacement or lateral deformation; “PX”: vertical axial force; “V2”: longitudinal shear; “V3”: transverse shear; M33 transverse bending moment.  
\end{table} 
Table 4: Comparison result of the seismic response of the two bridge models. Figure 5: Longitudinal displacement of the main beam under varying PGA.