基于数值流形法的降雨入渗与坡面径流耦合算法研究  

A Coupling Analysis of Rainfall Infiltration and Slope Surface Runoff Based on the Numerical Manifold Method

作　　者：陈远强 郑宏 屈新 CHEN Yuanqiang;ZHENG Hong;QU Xin(School of Civil Engineering,Hunan University of Science and Technology,Xiangtan,Hunan 411201,P.R.China;Key Laboratory of Urban Security and Disaster Engineering,Ministry of Education,Beijing University of Technology,Beijing 100124,P.R.China;School of Civil and Architectural Engineering,Anyang Institute of Technology,Anyang,Henan 455000,P.R.China)

机构地区：[1]湖南科技大学土木工程学院,湖南湘潭411201 [2]北京工业大学城市与工程安全减灾教育部重点实验室,北京100124 [3]安阳工学院土木与建筑工程学院,河南安阳455000

出　　处：《应用数学和力学》2023年第12期1499-1511,共13页Applied Mathematics and Mechanics

基　　金：国家自然科学基金项目(42107195);湖南省教育厅科研项目(21C0317)。

摘　　要：降雨时坡地的入渗-产流分析,是降雨型滑坡、泥石流等地质灾害机理研究中的重要课题之一.为实现边坡降雨-入渗-产流的全过程数值模拟,进一步提高计算效率,考虑将降雨入渗面视作坡面径流与坡体渗流的内部域,基于一维运动波方程和二维压力水头格式的Richards方程建立耦合模型,并推导出其总体控制方程,采用数值流形法(numerical manifold method, NMM)实现其数值求解,通过编制相应的计算程序分析了边坡降雨产流过程.数值分析结果表明:所建模型的计算结果与试验数据及前人模拟结果吻合良好,验证了该文模型及计算方法的有效性与可靠性;降雨强度越大,产流时间越早,坡面积水深度越大,对坡体内的水分分布影响范围越广.研究表明,所建模型能真实反映边坡降雨-入渗-产流全过程,可为降雨诱发的各类地质灾害分析提供计算依据.The infiltration-runoff processes of slopes during rainfall were of significance in the mechanism study of rainfall-induced landslides,debris flows,and other geological disasters.To realize the numerical simulation of the whole rainfall infiltration-runoff process and further improve the computation efficiency,a coupling mod-el and its total governing equations were derived from the 1D kinematic wave equation and the 2D h-based Rich-ards’equation,with the rainfall infiltration surface deemed as the internal domain of the runoff and the seep-age.Then the numerical manifold method(NMM)was used to solve the total governing equations,and the computation program was compiled to simulate the rainfall infiltration-runoff processes of slopes.The numerical analysis results showed that,the coupling model solution is in good agreement with the experimental data and previous results,verifying the validity and reliability of the proposed model.The higher the rainfall intensity is,the earlier the runoff producing time will be;the deeper the ponding depth is,and the wider the influence range on the water distribution within the slope will be.The proposed model can truly reflect the whole rainfall infil-tration-runoff process of the slope,and provides a calculation basis for the analysis of various geological disas-ters induced by rainfall.

关 键 词：降雨入渗 坡面径流 饱和-非饱和渗流 数值流形法 

分 类 号：O241[理学—计算数学] TV139.14[理学—数学]