Solution for a circular cavity in an elastic half plane under gravity and arbitrary lateral stress

Shallow tunnels excavated in an elastic rock mass can be considered as an elastic half-plane problem. An analytical solution of a circular tunnel with the excavation stress on the tunnel boundary and stress free on the ground surface is presented. The excavation stress in this work can reflect the real condition. The complex variable method and the Laurent series are used in the solving process. The solution is not the exact result but the approximate result with high accuracy can be obtained by taking enough terms of the Laurent series. Based on an example, the effect of the depth and the lateral stress coefficients on the tangential stresses and displacements on the tunnel boundary and the ground surface are discussed.