Derivation of Bed-load Formula from a View Point of Continuum Body

Abstract

It is emphasized that there are no significant differences between the dynamics of debris flow and bed load so far as bed shear stress is large enough for forming a grain sheet flow. The constitutive equation, which is developed for debris flows, is applied in order to discuss the characteristics of bed-load such as the depth of bed-load layer h_s, particle-concentration c (z) and velocity-distribution of bed-load layer u (z). A bed-load formula is developed by integrating the product of u (z) and c (z) from 0 to h_s. According to this, non- dimensionmal bed-load rate is proportional to τ^5/2_*.