Elastoplastic semi-analytical investigation on a deep circular tunnel incorporating generalized Zhang–Zhu rock mass strength

Abstract

The semi-analytical method based on finite difference method is widely used in the study of the mechanical response of surrounding rocks in a circular tunnel. The core of the three-dimensional (3D) mechanical analysis of the plastic zone is to solve nonlinear equations with a complex yield criterion, which leads to a long iterative solution time and low accuracy. In this study, a new 3D semi-analytical method is proposed for a circular tunnel excavation. The method is based on the finite difference method, wherein a linear equation is used to replace the complex yield surface equation. This significantly reduces the iterative solution process and effectively improves the calculation rate. The accuracy of the proposed method is verified using conventional and 3D numerical methods. The two-dimensional (2D) generalized Hoek–Brown criterion (GHB), 3D generalized Pan–Hudson criterion (GPH), and 3D generalized Zhang–Zhu criterion (GZZ) are used to analyze the applicability of the proposed method. The mechanical properties of a circular tunnel excavation are studied using these criteria. Our results show that the calculation rate of the plastic zone response of the proposed method (based on the GZZ criterion) is 12,000 times higher than that of the conventional iterative method. The overall calculation rate is increased by a factor of 65, and the calculation error is smaller than that of the conventional method. The GHB does not consider the intermediate principal stress, and the GPH cannot reflect the mechanical properties of rock masses with different tensile and compressive strengths, although it considers the intermediate principal stress. The convergence–constraint characteristics of the surrounding rock of the GHB and GPH are significantly different from those of the GZZ. There is an optimal initial axial stress value qopt that yields the smallest deformation of the surrounding rock and the best stability. The internal support pressure and residual strength of the rock mass have a significant effect on the mechanical response of the surrounding rock. The proposed method has acceptable applicability to elastic–brittle and elastic–perfectly plastic rock masses. Additionally, it can be used in the study of deep-buried tunnel excavation at high geo-stresses.