Impact of incident angles of earthquake shear (S) waves on 3-D non-linear seismic responses of long lined tunnels

The incident direction of earthquake waves has significance on the seismic responses of long lined tunnels. In this study, based on the equivalent node force method and together with the viscous-spring artificial boundary, the 3-D input method of SV and SH-waves with arbitrary incident angles is studied firstly. The input method is introduced within the framework of ABAQUS software and is verified by two numerical examples. Consequently, the proposed input method is employed to investigate the impact of the incident angles of SV and SH-waves on the seismic responses of a long lined tunnel. The numerical results indicate that the non-linear seismic responses of long lined tunnels are highly affected by the incident angles of S-waves. As the incident directions of SV and SH-waves being not perpendicular to the tunnel longitude, non-uniform motions appear along the tunnel longitude, as well as the longitudinal internal forces. The plastic deformation and strain components along the tunnel cross-section are also influenced by the incident angles of SV and SH-waves. It is thus important to include the incident angles of earthquake waves in mapping the seismic risk of tunnels.