Seismic analysis of underground tunnels subjected to 3D oblique incident P and SV waves by 2.5D approach

This paper presents, for the first time, the consideration of three-dimensional (3D) oblique incident P and SV waves in calculating the 3D seismic response of a lined tunnel embedded in a half-space by the 2.5D finite/infinite element method (FIEM). Firstly, the applicability of the 2.5D FIEM for 3D seismic analysis is summarized. With the exact solutions obtained for the free field in the Appendix, the equivalent seismic forces are rationally computed for the near-field boundary, considering the horizontal and vertical excitations of the Chi-Chi Earthquake. By performing seismic analysis of the half space embedded with a tunnel using the 2.5D FIEM, the time-domain responses of the tunnel are obtained. The accuracy of the present solutions is verified against those of de Barros and Luco. Conclusions drawn from the parametric study include: (1) Stress concentration for the principal stress under oblique incident seismic waves occurs at the polar angles of $0^{°}$ (vault), ${90}^{°}$, ${180}^{°}$ (inverted arch), and ${270}^{°}$ of the lining wall. (2) The vault and inverted arch are the weakest parts of the tunnel during earthquakes. (3) The accelerations of the tunnel during earthquakes can be regarded as of the rigid body type. (4) The responses of the tunnel lining caused by SV waves of an earthquake are much more critical than those by P waves. (5) For arbitrary seismic waves, the maximum longitudinal acceleration $a_{zmax}$ is of the same order of magnitude as the maximum horizontal acceleration $a_{xmax}$.