径向基函数配点法求解边坡降雨瞬态渗流问题
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摘要
根据土壤水分特征曲线Gardner模式推导线性化非饱和渗流Richard方程,应用无网格法中的多元二次径向基底函数配点法对空间域进行离散,利用龙格库塔法对时间域进行离散.通过离散点满足控制方程式与边界条件,建立求解非饱和渗流问题的数值模型.考虑土层组合以及降雨强度,计算分析非饱和无限边坡降雨入渗的瞬态渗流场的变化情况,得到边坡内不同时刻、不同深度的孔隙水压力.其数值计算结果与解析解相符,较有效地解决了传统数值方法在模拟非饱和土渗流产生的数值病态问题.
Based on the soil water characteristic curve Gardner model,the linearized unsaturated seepage Richard equation is derived. The space domain is discretized by the multiple two radial basis function collocation method in meshless method,and the Runge Kutta method is used to discretize the time domain. The control equation and boundary conditions are satisfied by discrete points,a numerical model for solving the problem of unsaturated seepage is established. Considering the distribution of different soil layers and the intensity of different rainfall,the transient seepage field of unsaturated infinite slope rainfall infiltration is calculated and analyzed,and the pore water pressure at different time and depth is obtained. The numerical results are consistent with the analytical solutions,the problem of numerical pathological problems in the simulation of unsaturated soil seepage is solved.
Based on the soil water characteristic curve Gardner model,the linearized unsaturated seepage Richard equation is derived. The space domain is discretized by the multiple two radial basis function collocation method in meshless method,and the Runge Kutta method is used to discretize the time domain. The control equation and boundary conditions are satisfied by discrete points,a numerical model for solving the problem of unsaturated seepage is established. Considering the distribution of different soil layers and the intensity of different rainfall,the transient seepage field of unsaturated infinite slope rainfall infiltration is calculated and analyzed,and the pore water pressure at different time and depth is obtained. The numerical results are consistent with the analytical solutions,the problem of numerical pathological problems in the simulation of unsaturated soil seepage is solved.
引文
[1]国土资源部.全国地质灾害通报[EB/OL].(2017-02-13)[2017-10-26]. http://www.mlr.gov.cn/zwgk/tjxx/201704/P020170428528974562696.pdf.
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[3]LIM T T,RAHARDJO H,CHANG M F,et al. Effect of rainfall on matric suctions in a residual soil slope[J]. Canadian Geotechnical Journal,1996,33(4):618-628.
[4]LI G,GE J,JIE Y. Free surface seepage analysis based on the element-free method[J]. Mechanics Research Communications,2003,30(1):9-19.
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[6]荣冠,张伟,周创兵.降雨入渗条件下边坡岩体饱和非饱和渗流计算[J].岩土力学,2005,26(10):1545-1550.
[7]张社荣,谭尧升,王超,等.强降雨特性对饱和-非饱和边坡失稳破坏的影响[J].岩石力学与工程学报,2014,33(增刊2):4102-4112.
[8]甘永德,贾仰文,王康,等.考虑空气阻力作用的分层土壤降雨入渗模型[J].水利学报,2015,46(2):164-173.
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[10]秦伶俐,黄文彬,周喆.径向基函数在无单元方法中的应用[J].中国农业大学学报,2004,9(6):80-84.
[11]HARDY R L. Multiquadric equations of topography and other irregular surfaces[J]. Journal of Geophysical Research,1971,76(8):1905-1915.
[12]SARRA S A,KANSA E J. Multiquadric radial basis function approximation methods for the numerical solution of partial differential equations[J]. Advances in Computational Mechanics,2009,2(2):35-57.
[13]苏李君,王全九,秦新强,等.二维非饱和土壤水分运动方程的径向基配点差分法[J].应用数学学报,2013,36(2):337-349.
[14]TRACY F T. Analytical and numerical solutions of Richard’equation with discussions on relative hydraulic conductivity[M].Croatia:INTECH Open Access Publisher,2011:203-222.
[15]周德亮,王焕丽.径向基函数法在地下水模拟中的应用[J].辽宁师范大学学报(自然科学版),2008,31(4):390-392.
[16]詹良通,贾官伟,陈云敏,等.考虑土体非饱和特性的无限长斜坡降雨入渗解析解[J].岩土工程学报,2010,32(8):1214-1220.
[17]李宁,许建聪.无限长均质斜坡降雨入渗解析解[J].岩土工程学报,2012,34(12):2325-2330.
[2]FOURE A B,ROWE D,BLIGHT G E. The effect of in eltration on the stability of the slopes of a dry ash dump[J]. Geotechnique,1999,49(1):1-13.
[3]LIM T T,RAHARDJO H,CHANG M F,et al. Effect of rainfall on matric suctions in a residual soil slope[J]. Canadian Geotechnical Journal,1996,33(4):618-628.
[4]LI G,GE J,JIE Y. Free surface seepage analysis based on the element-free method[J]. Mechanics Research Communications,2003,30(1):9-19.
[5]罗渝,何思明,李新坡,等.圆弧面上的降雨滑坡运动特性研究[J].四川大学学报(工程科学版),2015,47(5):73-77.
[6]荣冠,张伟,周创兵.降雨入渗条件下边坡岩体饱和非饱和渗流计算[J].岩土力学,2005,26(10):1545-1550.
[7]张社荣,谭尧升,王超,等.强降雨特性对饱和-非饱和边坡失稳破坏的影响[J].岩石力学与工程学报,2014,33(增刊2):4102-4112.
[8]甘永德,贾仰文,王康,等.考虑空气阻力作用的分层土壤降雨入渗模型[J].水利学报,2015,46(2):164-173.
[9]CHO S E,LEE S R. Evaluation of surficial stability for homogeneous slopes considering rainfall characteristics[J]. Journal of Geotechnical and Geoenvironmental Engineering,2002,128(9):756-763.
[10]秦伶俐,黄文彬,周喆.径向基函数在无单元方法中的应用[J].中国农业大学学报,2004,9(6):80-84.
[11]HARDY R L. Multiquadric equations of topography and other irregular surfaces[J]. Journal of Geophysical Research,1971,76(8):1905-1915.
[12]SARRA S A,KANSA E J. Multiquadric radial basis function approximation methods for the numerical solution of partial differential equations[J]. Advances in Computational Mechanics,2009,2(2):35-57.
[13]苏李君,王全九,秦新强,等.二维非饱和土壤水分运动方程的径向基配点差分法[J].应用数学学报,2013,36(2):337-349.
[14]TRACY F T. Analytical and numerical solutions of Richard’equation with discussions on relative hydraulic conductivity[M].Croatia:INTECH Open Access Publisher,2011:203-222.
[15]周德亮,王焕丽.径向基函数法在地下水模拟中的应用[J].辽宁师范大学学报(自然科学版),2008,31(4):390-392.
[16]詹良通,贾官伟,陈云敏,等.考虑土体非饱和特性的无限长斜坡降雨入渗解析解[J].岩土工程学报,2010,32(8):1214-1220.
[17]李宁,许建聪.无限长均质斜坡降雨入渗解析解[J].岩土工程学报,2012,34(12):2325-2330.