Stress analysis for an arbitrary-shaped tunnel in orthotropic rock masses based on a simple mapping function

摘要

? 2023 Elsevier LtdMost natural rock masses are anisotropic, but there is no simple and effective method to quickly and accurately calculate the stress at any point in the tunnel with an arbitrary shape in orthotropic rock masses. In this paper, first, the hole shapes of the z1- and z2-planes are calculated from the hole shapes of the z-plane, and then the outer regions of these two planes are mapped to the ζ1- and ζ2-planes, respectively, and an efficient algorithm to determine the mapping function is provided. After mapping, the stress boundary conditions originally expressed by z as the independent variable are transformed into ζ1 and ζ2 as the independent variables, posing new difficulties to the solution of the stress boundary condition. To solve the stress boundary conditions, in this paper, the power series solution and the boundary collocation method are proposed, and two complex potential functions expressed by series are obtained. The stress and displacement of each point on and outside the hole can be easily calculated because the form of the two mapping functions is simple. Finally, the correctness of this method is evaluated by comparing the stress calculated using this method with the stress calculated using the previous methods and numerical simulation software.