A physical model predicting instability of rock slopes with locked segments along a potential slip surface

Better understanding the evolutionary mechanism of landslides is very important to predict their occurrence based on firm scientific grounds. The stability of a rock slope is often dominated by one or more locked segments along a potential slip surface with a large bearing capacity to resist instability. We propose three preliminary categories for locked segments and develop a physical model for predicting the instability of rock slopes with locked segments, by coupling a one-dimensional renormalization group model with a strain-softening constitutive model, based on the Weibull distribution. We found that the ratio of the strain at the peak strength point of a locked segment to the strain at its volume dilation point is exclusively dependent on the Weibull shape parameter m and is approximately constant at 1.48. The accelerating displacement of the slope can be observed from the volume dilation point of the locked segment due to unstable fracture propagation. The physical model for slopes with multiple locked segments is only related to the displacement corresponding to the volume dilation point of the first locked segment and the number of locked segments. Applying this model to two typical cases, the Yanchihe rockslide in China and the wedge rockslide in Libby Dam, USA, the results are in agreement with field records. This work will help to better understand the failure mechanism of slopes with locked segments and may provide guidelines for disaster mitigation and prevention.