A physical model predicting instability of rock slopes with locked segments along a potential slip surface
Predicting the occurrence of landslides is important to prevent or reduce loss of lives and property. The stability of rock slopes is often dominated by one or more locked segments along a potential slip surface; these segments have relatively high strength and accumulate strain energy. Locked segments can be preliminarily classified into three categories: "rock bridge", "retaining wall" and "sustaining arch." Coupling a one-dimensional renormalization group model with the strain-softening constitutive relation of geo-materials considering the Weibull's distribution, a physical model for predicting the instability of slopes with locked segments is established. It is found that the ratio of the strain or displacement at the peak strength point to that at the volume dilation point for a locked segment is exclusively dependent on the Weibull's shape parameter m, and is approximately constant at 1.48. A corresponding accelerating displacement increment (tertiary creep) of the slope can be observed from the onset of the volume dilation of the locked segment due to its unsteady cracking. For a slope with multiple locked segments, one can predict its critical instability displacement value according to the accelerating displacement onset corresponding to the volume dilation point of the first locked segment and the number of locked segments. The back-analysis of two typical cases, the Yanchihe rockslide in China and the wedge rockslide, Libby Dam, USA, shows that their evolutionary processes, dominated respectively by one and two locked segments, follow this model, confirming the reliability of the proposed model.