Theoretical study on dynamic stress redistribution around circular tunnel with different unloading paths

This study presents a solution for stress redistribution induced by dynamic excavation of a rock tunnel in hydrostatic and non-hydrostatic stress states. Considering rock as an elastic medium, the analytical solution of dynamic excavation unloading was derived in the Laplace transform space utilizing the wave function expansion method and mode decomposition, and transformed into the time domain using the approximate numerical inversion method. The effects of the unloading path (linear, cosine, and exponential), unloading rate, and initial stress state on stress redistribution were analyzed. The analytical results indicated that a high unloading rate led to a high stress concentration and oscillations around the tunnel, and instantaneous dynamic unloading caused 20–30% stress concentration. When dynamic unloading is complete, the stress state around the tunnel converges to the Kirsch solution. The 3D numerical results indicated that deformation of the tunnel boring face increased as the initial stress increased. Moreover, the accumulation and release of strain energy and stress state change paths were analyzed and discussed. The results of this study provide a theoretical basis for understanding the stress adjustment and failure of surrounding rock induced by excavation of deep-buried openings in hydrostatic and non-hydrostatic stress states.