Analytical Solution for Stress and Displacement of the Arbitrary‐Shaped Shallow Tunnel Excavated in Orthotropic Rock

ABSTRACT Excavating tunnels in anisotropic rock induces greater stress concentrations at the excavation boundary compared to isotropic rock. However, existing analytical solutions for the shallow tunnel are founded on the simplifying assumption of isotropic rock masses. To clarify the deformation mechanism and mechanical behavior of the shallow tunnel, we proposed an analytical method for solving stress and displacement of the arbitrary‐shaped shallow tunnel excavated in orthotropic rock mass, incorporating the effects of body forces and anisotropy of rock mass. Proposing the specific forms of the analytical functions for the shallow tunnel in anisotropic rock, which can reflect body forces and the anisotropy of the rock mass. A linear equation system, derived from stress boundary conditions at the surface and tunnel excavation, is solved by the boundary collocation method. In the solution process, conformal transformation techniques are employed to construct three polar coordinate systems, which aid in resolving boundary conditions. Subsequently, we analyzed the effects of tunnel depth and anisotropic parameters on the stress and displacement of a horseshoe‐shaped tunnel and verified the correctness of the results through ANSYS software.