A finite element model for simulating surface run-off and unsaturated seepage flow in the shallow subsurface

摘要

This work introduces water-air two-phase flow into integrated surface-subsurface flow by simulating rainfall infiltration and run-off production on a soil slope with the finite element method. The numerical model is formulated by partial differential equations for hydrostatic shallow flow and water-air two-phase flow in the shallow subsurface. Finite element computing formats and solution strategies are presented to obtain a numerical solution for the coupled model. An unsaturated seepage flow process is first simulated by water-air two-phase flow under the atmospheric pressure boundary condition to obtain the rainfall infiltration rate. Then, the rainfall infiltration rate is used as an input parameter to solve the surface run-off equations and determine the value of the surface run-off depth. In the next iteration, the pressure boundary condition of unsaturated seepage flow is adjusted by the surface run-off depth. The coupling process is achieved by updating the rainfall infiltration rate and surface run-off depth sequentially until the convergence criteria are reached in a time step. A well-conducted surface run-off experiment and traditional surface-subsurface model are used to validate the new model. Comparisons with the traditional surface-subsurface model show that the initiation time of surface run-off calculated by the proposed model is earlier and that the water depth is larger, thus providing values that are closer to the experimental results.