Modeling the evolution of natural cliffs subject to weathering: 1. Limit analysis approach

Retrogressive landsliding evolution of natural slopes subjected to weathering has been modeled by assuming Mohr‐Coulomb material behavior and by using an analytical method. The case of weathering‐limited slope conditions, with complete erosion of the accumulated debris, has been modeled. The limit analysis upper‐bound method is used to study slope instability induced by a homogeneous decrease of material strength in space and time. The only assumption required in the model concerns the degree of weathering within the slope, and for this we assumed and tested different weathering laws. By means of this method, the evolution of cliffs subject to strong weathering conditions (weathering‐limited conditions) was predicted. The discrete succession of failures taking place was modeled taking into account the geometry assumed by slopes as a consequence of previous mass movements. The results have been compared with published data from long‐term slope monitoring and show a good match between experimental observations and analytical predictions. The retrogressive evolution of the slope occurs with decreasing size of the unstable blocks, following a logarithmic volume‐frequency relationship. A nonlinear relationship is found between mass flux and average slope gradient. A set of normalized solutions is presented both by nomograms and tables for different values of slope angle, cohesion, and internal friction angle.