Semi‐Analytical Solution for a Lined Non‐Circular Tunnel in Viscoelastic Rock

ABSTRACT Based on the complex variable method and the corresponding principle of viscoelasticity, viscoelastic solutions for the stress and displacement of a lined non‐circular tunnel subjected to in‐situ stresses and internal water pressure is derived. The basic equations for solving the analytic functions are established according to the stress boundary condition along the inner boundary of the lining and the stress and displacement continuity conditions along the rock‐lining interface. The analytic functions are expressed as Laurent series and the Laplace transformation is performed on the basic equation. Herein, the power series method is applied to obtain the linear equations which are expressed by the analytic function coefficients in the Laplace domain. The stress and displacement solutions of tunnel in Laplace domain can be addressed by solving the equations, and then the viscoelastic solutions are obtained through Laplace Inverse transformation. Subsequently, an example for the horseshoe‐shaped tunnel is performed. The example used the generalized Kelvin model to simulate the rheological properties of surrounding rock mass. The obtained solution is compared with the numerical solution. The influences of the lateral pressure coefficient and the internal water pressure on the stresses and displacements of lining are analyzed.