Numerical Analysis of Backward Erosion of Soils by Solving the Darcy–Brinkman Equations

Abstract

The backward erosion of soils, which is induced by seepage flows, is numerically simulated. To the end, the following three aspects need to be computed: Water flow fields, onset and speed of erosion and boundary tracking between the soil and the water phases. The authors employ the Darcy–Brinkman equations as the governing equations for the water flow fields around the soils, which easily enable the simultaneous analysis of the seepage flows in the porous media and the water flows in the fluid domain. The onset and the speed of the seepage-induced erosion is predicted by an empirical formula constructed from the flow velocity and the pressure gradient of the seepage water. The boundary tracking scheme based on the phase-field equation is applied for tracking the soil boundary changing with the erosion. This paper shows that the combination of the above three aspects achieves the stable computation of the seepage-induced backward erosion of soils.