It is necessary to deal with transitional flow from debris flow through sheet flow to bedload flow for estimating the effect of debris flows on downstream area. Previously, numerical simulations were conducted using a model combining each type's flow model simply. In regard to riverbed shear stress, Manning's theory is applied in bedload region, an empirical formula is applied in sheet flow region, and existing theory of debris flow is applied in debris flow region. In regard to equilibrium sediment concentration, existing bedload discharge formula is applied in bedload region, an experimental formula is applied in sheet flow region, and existing theory of debris flow is applied in debris flow region. However, in this type numerical simulation, the calculated riverbed shear stress and equilibrium sediment concentration often discontinuously transit at transition boundaries because physical background of each flow model is different. These discontinuities may cause unreasonable simulation results and numerical oscillation. Therefore, a serially]connected model was developed in this study. In our model, riverbed shear stress formula was developed by applying existing theory of debris flow to the sediment layer and Manning's theory to the water layer. Also, we proposed a new method for determining transitional condition of sediment transport region to be continuous transition of equilibrium concentration. Numerical simulations were performed by using an existing model along with our model. The results for the condition where the riverbed gradient changes gradually showed that existing model caused irregular deposition deformation. Moreover, simulation results of flow depth and sediment concentration oscillated around transition boundaries. When discontinuities of riverbed shear stress and equilibrium sediment concentration coincided, numerical oscillation became larger. Our model could yield smooth and stable simulation results without these problems. Overflow sites and flooding area may be underrated or overrated using existing model, therefore, our model is effective.

Key wordsFdebris flow, bedload, numerical simulation, continuity around transition boundary