Multiple-stage dynamic responses and failure behaviors of surrounding rocks subjected to development blasting: Exponential and triangular paths

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During the development blasting of circular tunnels, the detonation of multiple blastholes arranged on concentric circles induces a complex dynamic response in the surrounding rocks. This process involves multiple blast loadings, static stress unloadings, and stress redistributions. In this study, the dynamic stresses of the surrounding rocks during development blasting, considering multiple blasting-unloading stages with exponential paths and triangular paths (linear simplified paths of exponential paths), are solved based on the dynamic theory and the Fourier transform method. Then, a corresponding discrete element model is established using particle flow code (PFC). The multiple-stage dynamic stress and fracture distribution under different in situ stress levels and lateral coefficients are investigated. Theoretical results indicate that the peak compressive stresses in the surrounding rocks induced by both triangular and exponential paths are equal, while the triangular path generates greater additional dynamic tensile stresses, particularly in the circumferential direction, compared to the exponential path. Numerical results show that the exponential path causes less dynamic circumferential tensile damage and forms fewer radial fractures than the triangular path in the first few blast stages; conversely, it exacerbates the damage and instability in the final blast unloading stage and forms more circumferential fractures. Furthermore, the in situ stress determines which of the two opposite effects is dominant. Therefore, when using overly simplified triangular paths to evaluate the stability of surrounding rocks, potential overestimation or underestimation caused by different failure mechanisms should be considered. Specifically, under high horizontal and vertical stresses, the static stress redistribution with layer-by-layer blasting suppresses dynamic circumferential tensile and radial compressive damage. The damage evolution of surrounding rocks in multi-stage blasting under different in situ stresses is summarized and classified according to the damage mechanism and characteristics, which can guide blasting and support design.