## 4 Results and Analysis
### Acceleration Response of Tunnel Lining  
The acceleration responses of the tunnel under SV-waves with different incidence directions and angles were calculated and analyzed. Note that, since the longitudinal seismic response of the tunnel is the object of concern, the longitudinal envelope of the acceleration response is presented and analyzed herein. As a matter of fact, the seismic responses at all the outer element nodes at the arch vault, arch bottom, left arch, and right arch along the tunnel model were extracted, and then the envelopes of the seismic response for the arch vault, arch bottom, left arch, and right arch were obtained and are displayed in Figures 8-11, respectively. According to Tables 5 and 6, the propagation and vibration directions of the various waves in the site for incidence angles = 11.31\({}^{\circ}\) and 33.69\({}^{\circ}\) are drawn in Figures 12 and 13, respectively, to facilitate a relevant analysis. Figure 7: Displacement contour under incident SV–wave for (**a**) plain site and left-side incidence at t = 0.27 s; (**b**) plain–mountain site and left–side incidence at t = 0.27 s; (**c**) plain site and right–side incidence at t = 0.36 s; and (**d**) plain–mountain site and right-side incidence at t = 0.36 s. (Unit: m). Figure 8: Seismic response at the arch vault of the tunnel: (**a**) acceleration response in the horizontal direction; and (**b**) acceleration response in the vertical direction. Figure 10: Seismic response at the left arch of the tunnel: (**a**) acceleration response in the horizontal direction; and (**b**) acceleration response in the vertical direction. Figure 11: Seismic response at the right arch of the tunnel: (**a**) acceleration response in the horizontal direction; and (**b**) acceleration response in the vertical direction. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{**Incidence Angle/\({}^{\circ}\)**} & \multicolumn{1}{c}{
\begin{tabular}{c} **Angle between Incident Wave** \\ **and Normal Direction of** \\ **Soil–Rock Interface/\({}^{\circ}\)** \\ \end{tabular} } & \multicolumn{1}{c}{**Reflected Angle of**} & \multicolumn{1}{c}{**Reflected Angle of**} & \multicolumn{1}{c}{**Transmitted Angle of**} \\ \multicolumn{1}{c}{\multirow{-2}{*}{**Incidence Angle/\({}^{\circ}\)**}} & **Soil–Rock Interface/\({}^{\circ}\)** & **SV-Wave/\({}^{\circ}\)** & **Converted P-Wave/\({}^{\circ}\)** & **SV- or P-Wave/\({}^{\circ}\)** \\ \hline
33.69 & 66.31 & 66.31 & & \\
25.67 & 74.33 & 74.33 & No reflected converted & \\
18.43 & 81.57 & 81.57 & P-wave & No transmitted wave \\
11.31 & 88.69 & 88.69 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Angles of the reflected SV- and P-waves at the soil–rock interface for a right-side-incident SV-wave. Figure 12: Diagram of the wave field for (**a**) left-side-incident SV-wave and (**b**) right-side-incident SV-wave with an incidence angle = \(11.31^{\circ}\) in the plain–mountain site. Figures 8-11 show that the acceleration response at the arch vault, arch bottom, left arch, and right arch of the tunnel's lining in the vertical direction are ultimately lower than those in the horizontal direction. This can be attributed to the fact that the vibration direction of the SV-wave is perpendicular to the propagation direction, and the incidence angles taken into consideration are lower than 45\({}^{\circ}\), and, thus, the vertical component of motion is smaller. As the incidence angle increases, the horizontal component of the acceleration response of the lining decreases, while the vertical component increases gradually, because, as the incidence angle increases, the horizontal component of the incident SV-wave decreases, whereas the vertical component increases. The above-mentioned results are in agreement with theoretical knowledge, which verifies the validity of this study to some extent.