## 4 Results and Analysis  
### Analysis of Wave Field  
Figure 6 presents the diagrams of the wave field in the mountain-plain site for the SV-wave. Based on [PERSON]'s law, the incidence angle, and the wave velocities in soil and rock, the angles of the transmitted SV- and P-waves at the soil-rock interface for the left-side-incident SV-wave are shown in Table 4, and the angles of the reflected waves for right-side incidence are in Table 5. Under the considered incidence angles, total reflection would occur on the left or right interface between soil and rock for left- or right-side-incident SV-waves. Since the right side of the mountain was inclined, total reflection was more likely to show up on the right side of the mountain under the right-side incidence of the wave. In the subsequent text, if lacking a special statement, the interface stands for the soil-rock interface on the right side of the mountain. Moreover, based on [PERSON]'s law, the  
Figure 5: Simulated ground motions: (**a**) acceleration time–history; (**b**) velocity time–history; (**c**) displacement time–history; and (**d**) the PSD of the simulated ground motion. incidence angles considered herein, and the wave velocities in soil and rock, the critical angle that reflected P-wave can show up is 35.26\({}^{\circ}\) on the interface; however, the angle between the incident SV-wave and the normal direction of the interface was beyond the above-mentioned critical angle, and, thus, no reflected P-wave could be produced on the interface. Additionally, for the left-side-incident SV-wave, the tunnel was subjected to the incident wave, the transmitted converted waves coming from the rock mountain side, and the reflected converted waves from the site's surface. For the right-side-incident SV-wave, the tunnel was mainly subjected to the incident wave, the reflected SV-wave on the soil-rock interface after total reflection, the reflected converted waves coming from the site's surface, and the subsequent reflected waves. Due to the obstacle induced by total reflection, part of the waves could not go into the rock mountain from the soil, and, thus, multiple reflections would occur in the soil for right-side incidence. Taking all the above-mentioned information into consideration and based on Figure 6, it can be found that, for both left-side incidence and right-side incidence, the tunnel's lining may be subjected to multiple waves pointing to the tunnel, and an inclined subsurface geometry focuses both left-side and right-side obliquely incident waves. Figure 7 displays the displacement contour of the site for the SV-wave with an incidence angle = 33.69\({}^{\circ}\), where the left, bottom region of Figure 7b is enlarged to show the wave's front. Note that the observation time instant during which the incident wave just passes through the rock mountain has been chosen to observe the propagation direction of the transmitted wave. Firstly, it can be seen that the displacement contour is obliquely layered, and this demonstrates that the waves are, indeed, obliquely incident to the site. Secondly, as shown in the enlarged zone in Figure 7b, as the wave propagates, the inclined angle of the wave's front, near the soil-rock interface on the left side of the mountain, increases gradually, and this might suggest that, when arriving at the interface between soil and rock, waves encounter some obstacles. The wave's front tends to up-warp at the  
Figure 6: Wave propagation diagram for SV-waves: (a) left-side incidence; and (b) right-side incidence. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Incidence Angle/\({}^{\circ}\)**} & **Angle between Incident Wave and** & **Transmitted Angle** & **Transmitted Angle of** \\  & **Normal Direction of Soil–Rock Interface/\({}^{\circ}\)** & **of SV-Wave/\({}^{\circ}\)** & **Converted P-Wave/\({}^{\circ}\)** \\ \hline
33.69 & 46.31 & 13.01 & 22.95 \\
25.67 & 54.33 & 14.65 & 25.98 \\
18.43 & 61.57 & 15.89 & 28.31 \\
11.31 & 68.69 & 16.86 & 30.16 \\ \hline \hline \end{tabular}
\end{table}