粒度分布を考慮した砂質土における非定常浸透流の基礎方程式とその抵抗則

Abstract

Applying local volume-averaging method to the microscopic continuity and Navier-Stokes equations, the macroscopic continuity equation and equations of motion of flow through porous media of sandy soil are derived. From the order estimation of each term in the derived equations, the simplified macroscopic basic equations for unsteady flow through porous media is obtained under the periodic boundary condition.The resistance law of flow in porous media is derived by assuming the log-normal grain size distribution and modeling the pore system of porous media by series of capillary tube, in which relation between the grain size and the pore size is considered. The proposed capillary tube model is applied to evaluation of the total resistance of flow in the real porous media, in which permeability is expressed as a function of the grain size distribution and porosity. The evaluated permeability by the capillary tube model is in good agreement with experiments by Takeuchi (1971) and Loudon (1952).