Elastic–plastic response of a deep tunnel excavated in 3D Hoek–Brown rock mass considering different approaches for obtaining the out-of-plane stress

Abstract

The difficulty in the 3D analysis of a circular tunnel excavation lies in the selection of a reasonable softening equation for the out-of-plane stress (σz) in the plastic zone. This study developed and compared the semi-analytical solutions of a circular opening considering different approaches for obtaining σz, and the results were verified by the numerical results (1) The elastic approaches (e.g., generalized Hooke's law). cannot accurately reflect the mechanical properties of rock in the plastic zone and the results exhibit large differences compared with numerical results. (2) Plastic approaches demonstrate that the in-site axis stress (q) has a limited effect on the stability of surrounding rock, whereas the elastic approach-based results exhibit severe dependence on q. (3) The excavation responses based on the GZZ strength criterion and Hoek–Brown strength criteria have significant differences, reflecting the obvious effect of σz (σ2) on the stability of rock mass, and an unreasonable criterion may result in inappropriate support measures (4) Different post-peak behaviors of rock mass (e.g., constitutive model, residual strength, dilatancy, etc.). significantly affect the surrounding rock stresses, and the applicability of elastic theories and shallow tunnel experiences need to be further considered in deep tunnel where the plastic zone is widely distributed.