细沟侵蚀动态过程模拟数学模型和有限元计算方法

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

建立了集中水流作用下均质土壤坡面上细沟侵蚀动态模拟数学模型。模型包括根据质量守恒原理推导而得到的变沟宽水流连续性方程和泥沙运移方程;根据动量守恒方程推得到的水流动力学方程;由紊流冲击分布概率来确定的土壤剥离方程;过量泥沙采用沉积的一阶沉积方程。模型还考虑了沟床形态、水流动力、土壤侵蚀与泥沙沉积形成相互依赖的反馈环,具有表达细沟的空间变化和时间演变的能力。给出了利用有限元方法对水动力学方程及泥沙运移连续方程进行顺序求解的数值计算公式以及模型数值求解的具体步骤。

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.