Study on Crack Propagation and Dynamic Characteristic Evolution of Cantilevered Unstable Rock Masses Based on XFEM

Cantilevered unstable rock masses constitute a prevalent geological hazard, with their stability intrinsically governed by the depth of trailing edge cracks. Traditional stability assessment methods, which largely rely on static calculations or displacement monitoring, often suffer from poor timeliness and insufficient early warning capabilities. To address these limitations, this study employs the Extended Finite Element Method (XFEM) to simulate the natural crack propagation trajectory and investigate the associated dynamic response characteristics under loading. The simulation results demonstrate that XFEM effectively captures the natural “vertical-to-oblique” fracture morphology, overcoming the limitations of pre-defined crack models. A critical correlation is established between crack evolution and natural frequency: the first-order natural frequency exhibits a staged decline, characterized by a precipitous drop of approximately 7 Hz during the late stage of fracture development (80–97% depth). Consequently, a “crack evolution–frequency response” model is proposed. This model confirms that natural frequency is a significantly more sensitive indicator of internal damage than displacement, providing a novel theoretical foundation and technical pathway for the early identification and dynamic evaluation of rock mass stability.