Research on the Critical Mechanical Criterion for Stick‐Slip Instability of Mining‐Affected Normal Faults Based on the Rate‐and‐State Friction Law

Mining‐induced disturbances cause stress imbalance in faults, leading to sudden stick‐slip events that trigger the rapid release of elastic energy and induce dynamic disasters in the surrounding rock. However, the critical criteria for stick‐slip instability in mining‐affected faults remain unclear. In this paper, by constructing a mechanical model of fault slip induced by mining‐disturbed overburden structure instability, and incorporating the rate‐and‐state friction (RSF) law, we propose a critical mechanical criterion for fault stick‐slip instability, revealing the initiation mechanism of such instability. Based on the geological conditions of a specific coal mine, a numerical model was established using FLAC3D to simulate mining in the footwall and hanging wall of a normal fault. The evolution characteristics of key mechanical parameters, such as shear stress and normal stress of the fault rock mass, were analyzed to explore the critical state characteristics of normal fault stick‐slip instability under mining disturbances. The results indicate that under the conditions set in this study, the fault stick‐slip reaches a critical state when the fault pillar support pressure peaks. The fault slip magnitudes are as follows: footwall mining (2438 mm) > hanging wall mining (220.1 mm), suggesting that footwall mining is more prone to inducing slip. The numerical values of the critical mechanical criterion for fault stick‐slip are in good agreement with the shear‐to‐normal stress ratio curves obtained from the numerical simulations, thereby validating the reliability of the theoretical model. This study provides ideas for the early warning of fault‐slip‐induced dynamic disasters in coal mine roadways.