黄土沟壑区坡面入渗-产流方程推导及数值解法
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摘要
从修正的Green-Ampt方程出发,通过数学推导将常微分形式的Green-Ampt入渗方程转化为超越方程求解,从而简化了Creen-Ampt方程的计算过程;对坡面流运动波方程,给出了推导过程和四点隐式差分求解方法.简化为超越形式的入渗方程经牛顿迭代和四阶龙格-库塔算法求解,可以保证解的收敛和稳定,牛顿迭代相比龙格-库塔方法计算精度更高;在坡面土槽进行恒降雨强度的3场降雨冲刷试验,利用三维激光扫描仪获取生成的DEM数据,检验在l mm网格精度下的入渗和产流模拟结果,结果表明坡面流过程的模拟计算结果与实测资料符合良好,可用于模拟坡面入渗和产流过程,入渗误差可控制在12%以内,流量误差在13.1%以内,模拟的入渗率和流量均比实测值偏大,且模拟入渗率误差与流量误差呈正相关.
From the modified Green- Ampt infiltration equation,the differential form of the equation was changed into transcendental equation solution by the mathematical derivation,therefore,the calculation process was simplified.Considering the slope movement wave equation,the derivation process and four implicit difference solution methods were provided.The simplified transcendental infiltration equation was calculated by Newton iteration and fourth order runge- kutta algorithm,and the convergence and stability of the equation was guaranteed,when the accuracy of the Newton iterative calculation is higher than the runge- kutta method.Three rainfall scouring experiments with the constant rainfall intensity were carried out to vahdate the simulation on infiltration,and the flow with a grid precision of 1 mm was generated by the DEM data obtained from the Lidar.The results show that the simulation results of slope surface flow process are in good agreement with the measured data,and infiltration errors can be controlled within 12%,while the flow rate error can be widiin 13.1%.The simulated infiltration rate and the flow rate are larger dian diat in the measured results,and the simulated infiltration rate error and flow rate error are positively correlated.
From the modified Green- Ampt infiltration equation,the differential form of the equation was changed into transcendental equation solution by the mathematical derivation,therefore,the calculation process was simplified.Considering the slope movement wave equation,the derivation process and four implicit difference solution methods were provided.The simplified transcendental infiltration equation was calculated by Newton iteration and fourth order runge- kutta algorithm,and the convergence and stability of the equation was guaranteed,when the accuracy of the Newton iterative calculation is higher than the runge- kutta method.Three rainfall scouring experiments with the constant rainfall intensity were carried out to vahdate the simulation on infiltration,and the flow with a grid precision of 1 mm was generated by the DEM data obtained from the Lidar.The results show that the simulation results of slope surface flow process are in good agreement with the measured data,and infiltration errors can be controlled within 12%,while the flow rate error can be widiin 13.1%.The simulated infiltration rate and the flow rate are larger dian diat in the measured results,and the simulated infiltration rate error and flow rate error are positively correlated.
引文
[1]Green W H,Ampt G A.Studies on soils physics-Part1:The flow of air and water through soils[J].Journal of Agricultural Science,1911(4):1-24.
[2]雷志栋,杨诗秀,谢森传.土壤水动力学[M].北京:清华大学出版社,1988.
[3]Mein R G,Larson C L.Modeling infiltration during a steady rain[J].Water Resour Res,1973,9(2):384-394.
[4]张光辉,邵明安.用土壤物理特性推求Green-Ampt入渗模型中吸力参数S_f[J].土壤学报,2000,37(4):553-557.Zhang Guanghui,Shao Ming'an.Using soil physical properties to determine the absorptive parameter S_f in Green-Ampt infiltration model[J].Acta Pedologica Sinica,2000,37(4):553-557.(in Chinese)
[5]陈力,刘青泉,李家春.坡面降雨入渗产流规律的数值模拟研究[J].泥沙研究,2001,26(4):61-67.Chen Li,Liu Qingquan,Li Jiachun.Study on the runoff generation process on the slope with numerical method[J].Journal of Sediment Research,2001,26(4):61-67.(in Chinese)
[6]王全九,邵明安,汪志荣,等.Green-Ampt公式在层状土入渗模拟计算中的应用[J].土壤侵蚀与水土保持学报,1999,5(4):66-70.Wang Quanjiu,Shao Ming'an,Wang Zhirong,et al.Application of Green-Ampt equation during infiltration in layered soil[J].Journal of Soil and Water Conservation,1999,5(4):66-70.(in Chinese)
[7]王文焰,汪志荣,王全九,等.黄土中Green-Ampt入渗模型的改进与验证[J].水利学报,2003,34(5):30-34.Wang Wenyan,Wang Zhirong,Wang Quanjiu,et al.Improvement and evaluation of the Green-Ampt model in loess soil[J].Journal of Hydraulic Engineering,2003,34(5):30-34.(in Chinese)
[8]毛丽丽,雷廷武.用修正的Green-Ampt模型确定土壤入渗性能的速算方法[J].农业工程学报,2010,26(12):53-57.Mao Lili,Lei Tingwu.Fast method for estimating soil infiltrability with modified Green-Ampt model[J].Transactions of the CSAE,2010,26(12):53-57.(in Chinese)
[9]彭振阳,黄介生,伍靖伟,等.基于分层假设的Green-Ampt模型改进[J].水科学进展,2012,23(1):59-66.Peng Zhenyang,Huang Jiesheng,Wu Jingwei,et al.Modification of Green-Ampt model based on the stratification hypothesis[J].Advances in Water Science,2012,23(1):59-66.(in Chinese)
[10]汤立群,陈国祥.小流域产流产沙动力学模型[J].水动力学研究与进展,1997,12(2):164-174.Tang Liqun,Chen Guoxiang.A dynamic model of runoff and sediment yield from small watershed[J].Chinese Journal of Hydrodynamics,1997,12(2):164-174.(in Chinese)
[11]杨具瑞,成自勇,张炜.小流域坡面产流汇流模拟研究[J].甘肃农业大学学报,2000,35(1):75-78.Yang Jurui,Cheng Ziyong,Zhang Wei.Analog study on slope run-off and afflux of small basin[J].Journal of Gansu Agricultural University,2000,35(1):75-78.(in Chinese)
[12]李占斌,鲁克新.透水坡面降雨径流过程的运动波近似解析解[J].水利学报,2003,34(6):8-21.Li Zhanbin,Lu Kexin.Approximate analytical solution of rainfall runoff process on permeable slope[J].Journal of Hydraulic Engineering,2003,34(6):8-21.(in Chinese)
[13]Woolhiser D A,Ligget J A.Unsteady one dimension flow over a plane—The rising hydrograph[J].Water Resources Research,1967,3(3):753-771.
[14]Van Genuchten M Th,Leij F J,Yates S R.The RETC Code for Quantifying the Hydraulic Functions of Unsaturated Soils[M].California:Agricultural Research Service Riverside,1991:9-17.
[15]Bouwer H.Infiltration of water into non-uniform soil[J].Journal of Irrigation and Drainage Engineering,1969,95(4):451-462.
[16]Brooks R H,Corey A T.Hydraulic Properties of Porous Media[M].Colorado:Colorado State University,1964.
[2]雷志栋,杨诗秀,谢森传.土壤水动力学[M].北京:清华大学出版社,1988.
[3]Mein R G,Larson C L.Modeling infiltration during a steady rain[J].Water Resour Res,1973,9(2):384-394.
[4]张光辉,邵明安.用土壤物理特性推求Green-Ampt入渗模型中吸力参数S_f[J].土壤学报,2000,37(4):553-557.Zhang Guanghui,Shao Ming'an.Using soil physical properties to determine the absorptive parameter S_f in Green-Ampt infiltration model[J].Acta Pedologica Sinica,2000,37(4):553-557.(in Chinese)
[5]陈力,刘青泉,李家春.坡面降雨入渗产流规律的数值模拟研究[J].泥沙研究,2001,26(4):61-67.Chen Li,Liu Qingquan,Li Jiachun.Study on the runoff generation process on the slope with numerical method[J].Journal of Sediment Research,2001,26(4):61-67.(in Chinese)
[6]王全九,邵明安,汪志荣,等.Green-Ampt公式在层状土入渗模拟计算中的应用[J].土壤侵蚀与水土保持学报,1999,5(4):66-70.Wang Quanjiu,Shao Ming'an,Wang Zhirong,et al.Application of Green-Ampt equation during infiltration in layered soil[J].Journal of Soil and Water Conservation,1999,5(4):66-70.(in Chinese)
[7]王文焰,汪志荣,王全九,等.黄土中Green-Ampt入渗模型的改进与验证[J].水利学报,2003,34(5):30-34.Wang Wenyan,Wang Zhirong,Wang Quanjiu,et al.Improvement and evaluation of the Green-Ampt model in loess soil[J].Journal of Hydraulic Engineering,2003,34(5):30-34.(in Chinese)
[8]毛丽丽,雷廷武.用修正的Green-Ampt模型确定土壤入渗性能的速算方法[J].农业工程学报,2010,26(12):53-57.Mao Lili,Lei Tingwu.Fast method for estimating soil infiltrability with modified Green-Ampt model[J].Transactions of the CSAE,2010,26(12):53-57.(in Chinese)
[9]彭振阳,黄介生,伍靖伟,等.基于分层假设的Green-Ampt模型改进[J].水科学进展,2012,23(1):59-66.Peng Zhenyang,Huang Jiesheng,Wu Jingwei,et al.Modification of Green-Ampt model based on the stratification hypothesis[J].Advances in Water Science,2012,23(1):59-66.(in Chinese)
[10]汤立群,陈国祥.小流域产流产沙动力学模型[J].水动力学研究与进展,1997,12(2):164-174.Tang Liqun,Chen Guoxiang.A dynamic model of runoff and sediment yield from small watershed[J].Chinese Journal of Hydrodynamics,1997,12(2):164-174.(in Chinese)
[11]杨具瑞,成自勇,张炜.小流域坡面产流汇流模拟研究[J].甘肃农业大学学报,2000,35(1):75-78.Yang Jurui,Cheng Ziyong,Zhang Wei.Analog study on slope run-off and afflux of small basin[J].Journal of Gansu Agricultural University,2000,35(1):75-78.(in Chinese)
[12]李占斌,鲁克新.透水坡面降雨径流过程的运动波近似解析解[J].水利学报,2003,34(6):8-21.Li Zhanbin,Lu Kexin.Approximate analytical solution of rainfall runoff process on permeable slope[J].Journal of Hydraulic Engineering,2003,34(6):8-21.(in Chinese)
[13]Woolhiser D A,Ligget J A.Unsteady one dimension flow over a plane—The rising hydrograph[J].Water Resources Research,1967,3(3):753-771.
[14]Van Genuchten M Th,Leij F J,Yates S R.The RETC Code for Quantifying the Hydraulic Functions of Unsaturated Soils[M].California:Agricultural Research Service Riverside,1991:9-17.
[15]Bouwer H.Infiltration of water into non-uniform soil[J].Journal of Irrigation and Drainage Engineering,1969,95(4):451-462.
[16]Brooks R H,Corey A T.Hydraulic Properties of Porous Media[M].Colorado:Colorado State University,1964.