Mass conservation equations for a debris]flow body and bed sediment as well as an equation of motion constitute the governing equations for debris flow. The erosion rate equation is generally added to close the governing equation system. The entrainment coefficient of the existing erosion rate equation is derived on the basis of only the balance between the riverbed gradient and the sediment concentration or the balance between the sediment concentration and the riverbed gradient. This set of equations can produce good results under the condition where the riverbed gradient changes gradually. However, some problems occurred when we applied this equation set to highly unsteady conditions, such as those in the upstream area of the sabo dam and the riverbed evolution with the change in the channel width. Therefore, a non]entrainment erosion rate equation is proposed. Numerical simulations of debris flow are performed by using an existing model along with our model. The results for the condition where the riverbed gradient changes gradually show that both models indicate similar tendencies. Further, our model can yield clear results for the highly unsteady conditions, such as those in the formation of the convex upward deposition shape caused by the sudden change in the riverbed gradient from steep to low and those in the riverbed evolution with the change of the channel width. These results were experimentally confirmed in past studies. Further, in the upstream area of the sabo dam, the results given by our model indicate that many sediments are deposited as low as the scale of debris flow. These results seem to clearly explain the actual phenomena..

Key wordsFdebris flow, numerical simulation, non]entrainment erosion rate equation