Stress Analytical Solution for Shallow Buried Lined Circular Tunnel Under the Deformation of Surrounding Rock Inner Edge

Abstract

In this article, an analytical solution is presented for an elastic shallow buried lined tunnel, which consider a certain surrounding rock deformation at the inner boundary. Concrete lining and the surrounding rock was assumed as linearly elastic materials. The solution uses Muskhelishvili complex potential functions combined with conformal mapping method to determine stress components within concrete lining and the surrounding rock mass. The coefficient of Laurent series expansion of the stress functions is determined by a combination of analytical and numerical computations. As an example, the case of a uniform radial displacement of surrounding rock inner edge is considered in some detail. The solution was verified by FEM through an example, very good agreement was demonstrated between analytical solution and numerical solution. Through numerical examples, the effect of elasticity modular and the ratio of the diameter to buried depth on the stresses component were assessed.