Simulation study on dynamic rill erosion processes: mathematical models and FEM formulation

A series of mathematical models were formulated for the dynamic simulation of the hill slope rill erosion of homogeneous soil body under concentrated flow. The models include the following components: the continuation equation of water flow in rills of variable width based on mass conservation; the hydrodynamic equation of rill flow based upon momentum conservation; the sediment transportation equation based on mass conservation; soil detachment equation based on the probability of turbulent bursts; as well as the equation of sediment deposition of the first order. The model takes into accounts of the interdependent feed back loop of rill morphology, hydrodynamics, soil erosion, and sediment deposition. Numerical formula with finite element method for the hydrodynamic and sedimentation processes were given for sequential solution to the model equations. The simulation procedures were outlined.