A post-peak dilatancy model for soft rock and its application in deep tunnel excavation

The dilation angle is the most commonly used parameter to study nonlinear post-peak dilatancy (PPD) behavior and simulate surrounding rock deformation; however, simplified or constant dilatancy models are often used in numerical calculations owing to their simple mathematical forms. This study developed a PPD model for rocks (rock masses) based on the Alejano–Alonso (A–A) dilatancy model. The developed model comprehensively reflects the influences of confining pressure (σ3) and plastic shear strain (γp), with the advantages of a simple mathematical form, while requiring fewer parameters and demonstrating a clear physical significance. The overall fitting accuracy of the PPD model for 11 different rocks was found to be higher than that of the A–A model, particularly for Witwatersrand quartzite and jointed granite. The applicability and reliability of the PPD model to jointed granites and different scaled Moura coals were also investigated, and the model was found to be more suitable for the soft and large-scale rocks, e.g. deep rock mass. The PPD model was also successfully applied in studying the mechanical response of a circular tunnel excavated in strain-softening rock mass, and the developed semi-analytical solution was compared and verified with existing analytical solutions. The sensitivities of the rock dilatancy to γp and σ3 showed significant spatial variabilities along the radial direction of the surrounding rock, and the dilation angle did not exhibit a monotonical increasing or decreasing law from the elastic–plastic boundary to the tunnel wall, thereby presenting the σ3-or γp-dominated differential effects of rock dilatancy. Tunnel deformation parabolically or exponentially increased with increasing in situ stress (buried depth). The developed PPD model is promising to conduct refined numerical and analytical analyses for deep tunneling, which produces extensive plastic deformation and exhibits significant nonlinear post-peak behavior.