# Effect of Subsequent Subgrade on Seismic Response of the High-Speed Railway Track-Bridge System
## 4 Earthquake Input  
Seismic waves contain three elements: peak, spectrum, and hold time [28,29]. Each of them affects the response of the structure under seismic action. Even under the action of seismic waves with the same peak ground acceleration, the calculation results can be very different due to differences in spectrum and holding time. The ground vibration input method used in this study is ground vibration acceleration time-range, which is used to analyze the nonlinear time-range of two bridge models, BMCS and BMWS, respectively.  
Since there are no historical earthquake records for the bridge and the site type is classified as Category II with a seismic fortification intensity of VII, the design acceleration response spectrum was selected as the reference seismic acceleration response spectrum curve in this study [30,31]. As shown in Figure 4, the damping ratio of HSRTBS is assumed to be 0.05, with the bridge's characteristic seismic period set at 0.25 s, and a dynamic amplification factor of the seismic spectrum at 2.25. Concurrently, this study generated three artificial seismic acceleration time histories, fitted to the reference seismic acceleration response spectrum curve, to be used as seismic inputs. From these, the highest value among the trio of seismic response datasets is selected as the definitive seismic response result [32,33].  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Interlayer Component** & **F0** & **D0** & **k0** & **k1** \\ \hline Fastener & 8.66 & 2.00 \(\times\) 10\({}^{-3}\) & 4.33 \(\times\) 10\({}^{3}\) & 0 \\ \hline CA layer & 4.50 \(\times\) 10\({}^{1}\) & 5.00 \(\times\) 10\({}^{-4}\) & 9.00 \(\times\) 10\({}^{4}\) & 0 \\ \hline Sliding layer & 6 & 5.00 \(\times\) 10\({}^{-4}\) & 1.20 \(\times\) 10\({}^{4}\) & 0 \\ \hline Fixed bearing & 5.16 \(\times\) 10\({}^{3}\) & 2.00 \(\times\) 10\({}^{-3}\) & 2.58 \(\times\) 10\({}^{6}\) & 2.58 \(\times\) 10\({}^{4}\) \\ \hline Sliding bearing & - & - & 2.58 \(\times\) 10\({}^{4}\) & 2.58 \(\times\) 10\({}^{4}\) \\ \hline Lateral block & 6 & 5.00 \(\times\) 10\({}^{-4}\) & 1.20 \(\times\) 10\({}^{4}\) & 0 \\ \hline Sheer teeth & 1.20 \(\times\) 10\({}^{5}\) & 1.20 \(\times\) 10\({}^{-4}\) & 1.00 \(\times\) 10\({}^{9}\) & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Longitudinal stiffness of interlayer components (unit: kN, m).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Component** & **Material** & **Elastic Modulus (N - mm -2)** & **Density(kg - m -3)** & **Poisson Ratio** \\ \hline Main beam & C50 & 3.85 \(\times\) 10\({}^{4}\) & 2400 & 0.2 \\ \hline Bridge pier & C30 & 3.05 \(\times\) 10\({}^{4}\) & 2400 & 0.2 \\ \hline Base plate & C35 & 3.25 \(\times\) 10\({}^{4}\) & 2400 & 0.2 \\ \hline Track slab & C55 & 4.05 \(\times\) 10\({}^{4}\) & 2400 & 0.2 \\ \hline Rail & CHN60 & 2.1 \(\times\) 10\({}^{5}\) & 7850 & 0.3 \\ \hline Friction plate & C30 & 3.05 \(\times\) 10\({}^{4}\) & 2400 & 0.2 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Material properties of critical components.  
In this study, the selected load combination is a combination of longitudinal direction and vertical direction [34; 35]. For analyzing the differences in the seismic response of HSTRBS under normal earthquakes, design earthquakes, and rare earthquakes, the peak ground acceleration (PGA) of three artificial seismic acceleration time histories can be taken as 0.1 g, 0.2 g, and 0.4 g, respectively. In this way, the seismic response of each critical component of the two bridge models, BMCS and BMWS, is obtained under three different seismic IM (intensity measure) levels. The proportional coefficients of seismic load components are shown in Table 3. This study includes a total of 18 conditions.