Influence of stress path on excavation unloading response

• A theoretical model was applied to characterise unloading responses under different paths.
• The propagation of unloading perturbation was represented in 3D contour maps.
• Numerical simulation was performed for the 2D unloading responses under different paths.
• Results of numerical simulation were consistent with the mathematical physical model.
• The effects of unloading rate and path were studied on excavation unloading responses.

The unloading process of rock mass is critical to the research of excavation disturbances of tunnels in deep mines, and the dynamic effects induced by the release of in situ stress cannot be ignored. In this study, a mathematical physics model was applied to characterise the unloading mechanisms of brittle rock under different stress paths in two dimensions using the universal discrete element code PFC2D for numerical simulations. The excavation relaxation method was employed to control forces applied to the tunnel internal surface to investigate the influence of various in situ stresses, the unloading rate and path on the dynamic effects. Longer unloading time can mitigate the dynamic effects within a certain time range. Nonlinear unloading paths prevail over the linear path in releasing kinetic energy. Furthermore, the exponential path that represents “slow followed by fast” unloading induces the most peripheral displacement, while the cosine path that represents “fast followed by slow” unloading yields the most cracks around the tunnel. The results also indicated that increasing the ratio of horizontal and vertical in situ stresses can exacerbate the dynamic effects. The proposed model agreed well with the theoretical solution and provided a basis for understanding the evolution of the unloading response around the tunnel.