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
宋秋明
摘要(Abstract)：
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。
关键词(KeyWords)： 边坡渗流;坡面径流;数值模拟;有限元
基金项目(Foundation):
作者(Author): 宋秋明
参考文献(References)：
- [1]Richards L A. Capillary conduction of liquids in porous mediums[J]. Physics,1931,1:318-333.
- [2]M J Lighthill,G B Whitham. On Kinematic Waves. I. Flood Movement in Long Rivers[J]. Proceedings of the Royal Society of London. Series A,Mathematical and Physical Sciences,1955,229(1178):281-316.
- [3]Panday S,Huyakorn PS. A fully-coupled physically-based spatially distributed model for evaluating surface/subsurface flow[J]. Advances in Water Resources,2004,27(4):361-382.
- [4]张培文,刘德富,郑宏,等.降雨条件下坡面径流和入渗耦合的数值模拟[J].岩土力学,2004,25(1):109-113.ZHANG Pei-wen,LIU De-fu,ZHENG Hong,et al. Coupling numerical simulation of slope runoff and infiltration under rainfall conditions[J].Rock and Soil Mechanics,2004,25(1):109-113.
- [5]Shokri A,Bardsley W E. Development,testing and application of DrainFlow:A fully distributed integrated surface-subsurface flow model for drainage study[J]. Advances in Water Resources,2016,92:299-315.
- [6]KOLLET S J,MAXWELL R M. Integrated surface-groundwater flow modeling:A free-surface overland flow boundary condition in a parallel groundwater flow model[J]. Advances in Water Resources,2006,29:945-958.
- [7]童富果,田斌,刘德富.改进的斜坡降雨入渗与坡面径流耦合算法研究[J].岩土力学,2008,29(4):1035-1040.TONG Fu-guo,TIAN Bin,LIU De-fu. A coupling analysis of slope runoff and infiltration under rainfall[J]. Rock and Soil Mechanics,2008,29(4):1035-1040.
- [8]Tian D F,Liu D F. A new integrated surface and subsurface flows model and its verification[J]. Applied Mathematical Modelling,2011,35:3574-3586.
- [9]Tian D F,Zheng h,Liu D F. A 2D integrated FEM model for surface water–groundwater flow of slopes under rainfall condition[J].Landslide,2017,14:577-593.
- [10]SON PHI,WILLIA M C,LING Li. Labboratory and numerical investigations of hillslope soil saturation development and runoff generation over rainfall events[J]. Journal of Hodrology,2013,493:1-15.