Transition mechanism of debris flows over rigid bed to over erodible bed

In debris flows over erodible beds, the kinematic conditions at the bed surface, such as velocity and velocity gradient, are determined by the dynamic condition that the driving force must be equal to the yield stress at the bed surface. In debris flows over rigid beds, on the other hand, kinematic quantities depend on such conditions as bed slope, sediment discharge rate, static friction angle of sediment and friction angle of grain to the bed surface. In the present study, the differences between debris flows over erodible and rigid beds as well as the transition between the two are analyzed theoretically by solving for velocity and sediment concentration profiles. An important difference between the two lies in the shear stress distributions near the bed. The velocity gradient takes a finite value in the case of a rigid bed, and zero in the case of an erodible bed, which causes several different features in the profiles of velocity, and sediment concentration, and correspondingly in the flow resistance. The theoretical results are verified by flume data.