Pseudo-static simplified analytical solution for seismic response of deep tunnels with arbitrary cross-section shapes

Abstract

Tunnels located in seismic active areas must support not only static loads exerted by the ground under gravity but also seismic loads from earthquake events. Current analytical solutions for seismic analysis of tunnel structures are limited to circular or rectangular tunnels but not available for tunnels with other complex cross-section shapes, such as straight-wall-arch-shaped or semi-rectangular-shaped tunnels. This paper presents a unified simplified analytical solution for deep tunnels with arbitrary cross-section shapes subjected to seismic loading. Since the cross-section dimension of tunnels is normally much smaller than the wavelength of ground peak velocities, the structure can be designed using the pseudo-static approach. The ground and the tunnel liner are assumed to be elastic, homogeneous, and isotropic in plane strain condition. Two different contact conditions, no-slip and full-slip conditions, are considered at the liner-ground interface. The complex variable theory combined with the conformal mapping technique are employed to obtain closed-form solutions for tunnel deformation and stresses. The proposed solution is verified by providing comparisons between its results and those from the finite element program ABAQUS. Furthermore, parametric analyses are carried out to investigate the influence of soil-structure relative stiffness ratio, cross-section shape, height-span ratio and thickness of middle wall on tunnel responses.