The unifed theory of debris flow initiation by using homogenization theory

Abstract

We attempt to find the unified theory for the prediction of the initiation of debris-flow by using homogenization theory. In this study, we show the leading order solution, which is the first step of this derivation of unified theory. The derivation started in the microscopic scale in the soil. The representative elementary volume (REV) in the soil is set to be one order larger than the scale of porosity. Solids in the REV are assumed to be rigid and adhesion-less. The liquid velocity in the porosity is slow. By the noslip boundary condition and periodicity of REV, we could obtain the microscopic flow conditions. Using the assemble average with time dependence taken into account, we obtain the macroscopic relation of water content with the spatial and time variables from the microscopic flow conditions. This macroscopic equation could be validated by the Richards’ equation.