Analytical method for elastic-brittle-plastic analysis of a circular tunnel in a non-hydrostatic in-situ stress field considering the unified strength criterion

Abstract

Based on the unified strength criterion, an analytical solution is proposed to explore the variation law of the impact of tunnel axial stress on the development of failure zone around a circular tunnel. The proposed method aims to deal with the non-axisymmetric problem under a high and complex three-dimensional stress condition. The mechanical behavior of the rock mass is considered to follow an elastic-brittle-plastic model. The conformal transformation is used to deal with the mathematical difficulties caused by the non-circular nature of the boundary. The procedure enables the quantitative representation of the unknown elastoplastic boundary through an undetermined mapping function. The differential-evolution algorithm is used to determine the boundary from the perspective of positive analysis. The presented solution is compared with published analytical solutions. The results show that the solution in this paper covers the first two solutions and is more reasonable than the last one, reflecting the reliability and generality of the new extended method. The parametric study is implemented to discuss the development of failure zone affected by various parameters.