Run-out simulation of rock avalanches using a depth-averaged model considering the distance and velocity related frictional weakening effect

The depth-averaged models (DAM) are widely used numerical models for the run-out simulation of flow-like mass movements such as rock avalanches. A constant friction coefficient is usually adopted in the current DAM to consider the friction dissipation of rock avalanches. However, these models cannot reflect the frictional weakening phenomenon of rock avalanches due to factors such as the fragmentation of the rock mass and the thermal effect at the sliding bed. To overcome the limitations of traditional depth-averaged landslide models (DAM), a DAM considering both the velocity-dependent and distance-dependent frictional weakening was developed in this study. The model was validated by two benchmark cases, before being utilized to analyze a real catastrophic rock avalanche that occurred in the Yanjiagou gully, Shanyang County, Shaanxi Province of China. The simulation results of the two benchmark cases, the ideal flume test and a flume experiment of sand flow, agree well with the analytical solutions and the experimental results, respectively. In the simulation of the Yanjiagou rock avalanche, we discussed the impact of the slip-weakening distance (D_c) and the critical sliding velocity (V_c) on the run-out process of the rock avalanche. The results indicate that the parameter D_c mainly affects the acceleration process at landslide initiation, while the parameter V_c primarily influences the average velocity of the landslide motion. In the condition of a larger D_c and a smaller V_c, the distribution of the landslide deposit thickness becomes more uniform. Furthermore, by comparing the simulation results of the friction-weakening model with those of the constant friction coefficient model and the friction-strengthening model (µ(I) rheology), it is shown that, without considering frictional weakening, the initiation of the landslide is overly diffuse, severely overestimating the range of landslide motion. After adopting the friction-weakening model, the range of landslide motion and the thickness of the landslide deposit are more consistent with the results of field investigations. The frictional weakening DAM improves the simulation accuracy of rock avalanches.