Elastic solutions for circular tunnel with void behind lining

Tunnels in Japan, many of which had been constructed using conventional tunneling methods, often have partial separations, or voids, between the lining and the ground. These defects may induce undesirable deformation and stress in the lining. In this paper, two-dimensional elastic solutions for a deep circular tunnel with a void behind the lining and under far-field static loading are presented. The plane strain condition is assumed at the cross-section of the tunnel. The void is treated as a partially non-contact boundary between the lining and the ground. The substructure method and the point matching method are used to derive the solutions. Numerical results show the presence of a void causes the stress state of the lining to change from axial thrust to bending moment. As a result, under isotropic compression, the lining is in a state of stress where axial thrust dominates and bending moment is low, the presence of a void leads to large stress concentration on the lining and in turn causes undesirable deformation and stress in the lining. In contrast, under shear-type loading, where the stress state of the lining is low axial thrust and high bending moment, the presence of a void does not lead to a large stress concentration on the lining.