Depth-averaged mixture model for development processes of debris flows over a steep unsaturated mobile bed

As water flow erodes bed sediment in a steep channel, a partly saturated debris flow, which has an unsaturated layer in its upper part, develops while interacting with a subsurface flow in the bed sediment; however, this interaction remains unclear. This study developed a numerical model that links the shallow water equation representing surface flows (i.e., fully and partly saturated, hyperconcentrated, and turbulent flows) with the depth-averaged Richards equation representing subsurface flows. The shallow water equation incorporates a new resistance equation, which accurately reproduces previous experimental results on steady uniform fully and partly saturated flows. The numerical model successfully replicated our experimental results on the evolution of a partly saturated flow. The sensitivity analysis of the numerical model demonstrated that the front velocity of a debris flow over the 4.0-m-thick bed is 28% smaller than that over the 0.6-m-thick bed and that over the unsaturated bed sediment is 22% smaller than that over bed sediment saturated through the entire layer. The decreases in front velocities are due to water seeping through the bed surface. Additionally, the analysis revealed that water infiltrating through a bed surface triggers the transition of a debris flow front from fully to partly saturated flow when the channel gradient ranges from 18 to 19°. We concluded that the interaction between the process of infiltration in the bed sediment and the development of a debris flow should be considered for accurate prediction of debris flow development processes in a steep channel.