Stress Analysis of Circular Tunnel with Void behind the Lining

Tunnels in Japan, which is especially constructed by the conventional tunneling method, often have voids behind the lining, that is, they have partial discontinuity between the lining and the ground. These defects may induce undesirable deformation and stress to the tunnel lining. However, there are only a few studies to evaluate the effect of a void to tunnel lining. In this paper, analytical solutions for a circular tunnel with a void behind the lining in the ground subject to external pressure are presented. The surrounding ground is taken as an infinite, homogeneous, isotropic, and linear elastic medium and the lining is treated as a linear elastic shell. Traction-free boundary condition is imposed on the place where there is a void behind the lining and no-slip boundary condition is imposed on the place where there is no void behind the lining. Numerical results show that the stress states of the lining is greatly affected by the presence of a void for isotropic compression and is a little affected for shear-type loading. The circumferential stress of the lining becomes higher in proportion to the extent of the void because of the decrease in the ground reaction. However, the circumferential stress of the lining becomes smaller when the extent of the void exceeds a certain range because the influence of the decrease in traction from the ground to lining is larger than that of the decrease in the ground reaction.