Elasto-plastic solution for shallow tunnel in semi-infinite space

This study focuses on a novel approach to develop an elasto-plastic solution for surrounding rocks around a shallow tunnel in an elasto-plastic semi-infinite space that incorporates the gravitational effect based on the bipolar coordinate system. A shallow circular tunnel was excavated in continuous, isotropic, and homogeneous rock masses. The solution for the surrounding rock in semi-infinite space was regarded as a semi-infinite plane problem, and the semi-infinite plane was partitioned along the curve trajectories of the bipolar coordinate. Based on the Mohr-Coulomb failure criterion and considering the gravitational effect, the closed-form solutions for the stress distribution of the surrounding rock were proposed. Furthermore, novel approaches for the calculation of the shape of the plastic zone around the tunnel and the critical internal support pressure were obtained. These presented approaches were validated by comparing the results of finite element method and the published literature. Using the numerical method, the sensitivity of gravity and the influences of the geological strength index, internal support pressure, surface loading, and buried depth of the tunnel on the plastic radius, shape of the plastic zone, and stress distribution of the surrounding rocks around the shallow circular tunnel were discussed.