Mechanism and stability of unloading fracture in rock slopes containing trailing edge cracks in open pit mines

Based on the real structural characteristics of slopes and using the theory of fracture mechanics, the formulas for calculating the stress intensity factor and the critical instability height of trailing edge crack tip under unloading are deduced, Considering the extension length of branch cracks, the mechanical model for crack expansion in slope rock mass is established, and the method for the stability coefficient of slopes is put forward, and is verified through an engineering example. The results show that: (1) The stronger the unloading effects, the greater the intensity factor of compound stress at the tip of the trailing edge crack, and the worse the stability of the slope. (2) The larger the inclination angle of the trailing edge crack, the smaller the critical expansion height and the larger the crack initiation angle. The larger the average height, the smaller the critical expansion height, and the larger the crack initiation angle. The crack is more and more deviating from the slope expansion, and the crack length has no effects on the critical propagation height and the initiation angle. (3) The factor of safety of the slope increases with the increase of the crack inclination angle, average height and fracture toughness, and decreases with the increase of the crack length, lower crack angle and unloading tensile stress. The research results may provide some theoretical reference for understanding and controlling the collapse and landslide disasters of rock slopes with trailing edge cracks induced by excavation unloading.