中文摘要：

运用断裂力学分析危岩中的倾倒变形破坏，基于岩石拉剪断裂试验，研究裂纹在载荷作用下起裂、扩展规律，探索断裂过程中裂纹的扩展行为，并探讨裂纹长度、宽度、倾角与荷载位置对危岩失稳模式与稳定性的影响。以重庆万州太白岩危岩为例，利用有限元软件ANSYS计算不同裂纹条件下裂纹尖端的应力状态，并讨论其与联合断裂应力强度因子的关系，模拟裂纹扩展的动态过程。结果表明，拉剪倾倒型危岩在受力破坏过程中，裂纹尖端出现拉应力集中，危岩的开裂从张拉破坏开始，下部出现压剪破坏，危岩稳定性的影响因子敏感性从大到小依次为：荷载位置、裂纹长度、裂纹倾角、裂纹宽度。

英文摘要：

Toppling failure of unstable rocks was analyzed using fracture mechanics. Based on tensile-shear fracture tests of rock samples, fracture initiation and propagation mechanisms under loading were analyzed, and crack propagation during the fracture process was investigated. The effects of the crack length, width, and inclination angle as well as the loading point on the failure mode and stability of unstable rocks were discussed. An overhanging rock, the Taibaiyan unstable rock in Wanzhou District of Chongqing City was used as a case study. The stress state of crack tips under different cracking conditions was calculated using the finite element software ANSYS, the relationship between the complex breaking stress intensity factor and stress state was discussed, and the dynamic process of crack propagation was simulated. Results show that, during the processes of tension, shear, and toppling failures of unstable rocks, tensile stresses were concentrated at creak tips, unstable rock cracking was first induced by tension failures, and shear-compression failures occurred at the bottom. The sensibilities of the factors to the instability of unstable rocks were ranked in an descending order as follows ： the loading position, crack length, crack inclination angle, and crack width.