© 2016, Springer-Verlag Berlin Heidelberg.Differential weathering is a primary cause of secondary toppling failures of rock slopes. Using the Taibaiyan cliff in the Three Gorges Reservoir as a case study, the evolution of an overhanging slope was numerically investigated using fracture mechanics. A displacement discontinuity method (DDM)-based computer program, which incorporated joint elements, was developed. In addition, a factor of safety was defined for the slope failure analysis. The progressive failure process was simulated by analyzing the propagation and coalescence of cracks through rock bridges. The influence of the joint geometry parameters was investigated based on the defined factor of safety and the calculated stress intensity factor (SIF). The weathering rate in the Three Gorges Reservoir was quantitatively estimated using field measurements. The relationship between the factor of safety and the undercutting depth was studied, and the critical undercutting depth associated with a factor of safety of 1 was determined. The approach for predicting the failure time of an overhanging slope subject to weathering processes was presented based on time-dependent weathering and the critical undercutting depth. The results show that the failure mechanism of an overhanging slope is tensile-shear fracturing and that the failure processes can be identified as weathering, undercutting, stress concentration, crack initiation and crack propagation, and coalescence.