## 4 Results and Analysis
### Damage Assessment of Tunnel Lining
To verify this statement, the deformation of tunnel lining in the profile for longitudinal distance = 105 m at time interval = 6.0 s under right-side-incident SV-wave was observed, as shown in Figure 16. It can be obviously found that at the same time interval the deformation modes of lining under right-side-incident SV-wave with predefined various incidence angles are significantly different, and when the incidence angle = 33.69\({}^{\circ}\), the shape of deformed lining tends to be rectangular. This demonstrates that the lining may be subjected to multi-directional deformation. Figure 14: Tensile damage of tunnel lining under right-side-incident SV-wave: (**a**) incidence angle = 33.69\({}^{\circ}\) and t = 2.25 s; (**b**) incidence angle = 33.69\({}^{\circ}\) and t = 20 s; (**c**) incidence angle = 26.57\({}^{\circ}\) and t = 2.31 s; (**d**) incidence angle = 26.57\({}^{\circ}\) and t = 20 s; (**e**) incidence angle = 18.43\({}^{\circ}\) and t = 2.26 s; (**f**) incidence angle = 18.43\({}^{\circ}\) and t = 20 s; (**g**) incidence angle = 11.31\({}^{\circ}\) and t = 2.21 s; and (**h**) incidence angle = 11.31\({}^{\circ}\) and t = 20 s.  
Figure 15: Tunnel lining deformation at the time when damage initially shows up for right-side-incident SV-wave with the following incidence angles: (**a**) 33.69\({}^{\circ}\); (**b**) 26.57\({}^{\circ}\); (**c**) 18.43\({}^{\circ}\); and (**d**) 11.31\({}^{\circ}\) (scaling factor = 300; unit: m). The tensile damage contours in the longitudinal view of the tunnel's lining under left-side-incident SV-waves for the different incidence angles considered and different time intervals are shown in Figure 17. The deformation of the lining under left-side-incident SV-waves with different incidence angles at the moment when damage first appears is shown in Figure 18. Similar to the cases with right-side incidence, the part of lining that is initially subjected to severe tension gradually changes from the vault to the hance with varying incidence angles in the cases with left-side incidence. However, what is different  
Figure 16: Tunnel lining deformation at t = 6.0 s for right-side-incident SV-wave with the following incidence angles: (**a**) 33.69\({}^{\circ}\); (**b**) 26.57\({}^{\circ}\); (**c**) 18.43\({}^{\circ}\); and (**d**) 11.31\({}^{\circ}\) (scaling factor = 300; unit: m). from the right-side cases is that, in all four cases of left-side incidence, the tunnel lining displays damage in multiple directions. As shown in Table 5, the transmitted angle of the SV- and P-waves at the soil-rock interface varies slightly with varying incidence angles, meaning that the propagation direction of the transmitted SV- and P-waves is always significantly different from that of the incident waves (see Figures 12 and 13). Therefore, for all the incidence angles considered, the tunnel lining always experiences compression in multiple directions. Thus, the damage distribution of the lining for the cases with left incidence is always multi-directional. Figure 17: Tensile damage of tunnel lining under left-side-incident SV-wave: **(a)** incidence angle = 33.69\({}^{\circ}\) and t = 2.25 s; **(b)** incidence angle = 33.69\({}^{\circ}\) and t = 20 s; **(c)** incidence angle = 26.57\({}^{\circ}\) and t = 2.31 s; **(d)** incidence angle  
Figure 18: Tunnel lining deformation at the time when damage initially shows up for left-side-incident SV-wave with the following incidence angles: (**a**) 33.69\({}^{\circ}\); (**b**) 26.57\({}^{\circ}\); (**c**) 18.43\({}^{\circ}\); and (**d**) 11.31\({}^{\circ}\) (scaling factor = 300; unit m).