Dynamic Responses of U-Shaped Caverns under Transient Stress Waves in Deep Rock Engineering

Deep caverns are frequently subjected to transient loading, resulting in different failure characteristics in the surrounding rock compared to those in shallow caverns. Previous research has rarely focused on the transient responses of non-circular caverns. To address this gap, a theoretical solution for the dynamic stress concentration factor around a U-shaped cavern under transient stress waves was derived based on elasto-dynamic theory and conformal mapping. The theoretical results were validated through simulations using the discrete element software PFC2D 7.0 (Particle Flow Code in two dimensions). Additionally, the energy evolution and failure pattern of the surrounding rock under coupled static-dynamic loading were investigated. The results indicated that, when the stress wave was horizontally incident, rockburst failure was more likely to be observed in the cavern floor, while dynamic tensile failure was prone to occur in the incident sidewall. Furthermore, when the incident direction of the stress wave aligned with the maximum principal stress, more violent rockburst occurred. Moreover, when the rising time of the stress wave was greater than 6.0 ms, the peak dynamic stress concentration factor converged to a stable value, and the surrounding rock could be considered to be in a quasi-static loading state. These findings provide insight into the failure mechanisms of deep caverns and could guide the design of cavern supporting structures.