边坡降雨入渗与坡面径流耦合数学模型及有限元模拟

A Coupled Mathematic Model and Finite Element Modeling for Slope Rainfall Infiltration and Sheet Flow

降雨,特别是强降雨时边坡渗流和坡面径流过程是研究许多工程问题的基础。本文采用Richards方程描述非饱和渗流过程;运动波方程描述坡面径流。先推导了Richards方程的积分弱解格式;然后将坡面水深作为运动波方程的控制变量,并用运动波方程表示入渗率;再将这一表达式融入Richards方程的积分弱解格式,从而构建同时描述边坡渗流和径流的积分弱解格式的数学方程。该方程不再包含入渗率这一未知量。采用Galerkin有限元法实现方程的有限元模拟。算例表明,所建有限元模拟方法可以用于模拟边坡渗流和坡面径流过程。

The slope infiltration and sheet flow processes during rainfall especially heavy rainfall are the origin of many engineering issues. The paper has used Richards equation to describe unsaturated infiltration process and kinematic wave equation for sheet flow process. Firstly has deduced Richards equation integral weak solution scheme, then taken the slope sheet water depth as control variable of kinematic wave equation, and indicated infiltration rate through kinematic wave equation;and then taken the expression integrated into Richards equation integral weak solution scheme, so as to establish and describe synchronously both slope infiltration and sheet flow integral weak solution scheme mathematical equation. The equation has no longer included infiltration rate the unknown. Through Galerkin finite element method realized equation finite element modeling. The examples have shown that the established finite element modeling method can be used to simulate slope infiltration and sheet flow processes.