An analytical solution for stresses and deformations of tunnels in a non-uniform stress field based on strain-softening model and Mogi-Coulomb criterion

Abstract In this study, a mechanical model for tunnels excavated in a non-uniform stress field is developed. A new strain-softening model simultaneously considers the weakening of cohesion and internal friction angle is proposed. Then, an analytical solution for the post-peak region radii, stresses, and displacements is deduced. Taking a tunnel in Taoyuan coal mine as an engineering example, the post-peak region radii, surface displacement, and stresses distribution are determined. The effects of the horizontal-to-vertical stress ratio, intermediate principal stress, residual cohesion, and residual internal friction angle on tunnel deformations are discussed. The results show that the post-peak region radii and stresses distribution around the tunnel varies with direction due to the non-uniform stress field. The post-peak region radii and surface displacement are larger with consideration of intermediate principal stress. Tunnels surrounded by rock masses with a higher residual cohesion and internal friction angle experience lower post-peak region radii and surface displacement.