Seismic response of a deep circular tunnel subjected to axial shear and axial bending

Abstract

Significant attention has been devoted to investigate the seismic performance of tunnels when shear waves intersect in a direction perpendicular to the tunnel axis with motion perpendicular to the tunnel axis, thereby causing the tunnel to respond transversely. In contrast, the effects of shear waves that cause the tunnel to respond longitudinally have received less attention. This paper provides two analytical solutions to capture the longitudinal response of a deep circular tunnel and its surrounding ground when a shear wave intersects the tunnel: (i) in a direction perpendicular to the tunnel axis with motion parallel to the tunnel axis (axial shear); and (ii) in a direction parallel to the tunnel axis with motion perpendicular to the tunnel axis (axial bending). The assumptions used to develop the solutions are that: (i) a static analysis may be sufficient; (ii) the tunnel is deep and very long and has a circular cross section; (iii) the ground and the support are homogeneous, isotropic, and elastic; (iv) the ground-liner interface is tied; and (v) the wavelength of the ground motion is much larger than the radius of the tunnel. The solutions are applicable to both drained and undrained loading. 3D numerical simulations are carried out to verify the analytical solutions. The results show a good agreement between the analytical and numerical solutions.