接触面单元计算土石坝渗流逸出点的效果分析
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摘要
为研究利用接触面单元方法计算渗流逸出点的处理技巧及其效果,针对2个渗流算例进行计算,其中对浸润线穿越的单元用蒙特卡罗积分方法计算其复合渗透系数。在渗透系数相差较大的材料之间设置2层接触面单元,利用接触面的渗流矩阵建立材料间的水力联系,通过迭代得到浸润线位置。选择较薄的接触面单元厚度(比如相邻单元厚度的1/4),把计算误差控制在局部范围内,而对整体没有太大影响。分析结果表明,选择合适的接触面渗透系数或透水率,能够得到接近于常规方法的计算结果。
In the calculation of seepage or consolidation, if there is a large difference in seepage coefficient of two adjacent materials, the release point, as well as the phreatic line, should be determined by iterations. However, if we set interface elements between two materials, reasonable results of release point can be captured without iterations. In this paper, two seepage cases are investigated, and the composite seepage coefficient of the elements, which are intersected by the phreatic line, is calculated with the Monte Carlo integration method. Two interface elements are set between two materials with great difference in seepage coefficient. The hydraulic relationship between two materials is built based on the seepage matrices of the interface elements, while the location of the phreatic line is then calculated by iterations. Choosing a thin thickness for the interface element(e.g., 1/4 of the thickness of the adjacent element) could localize the error of calculation, which has little impact to the whole area at the same time. By choosing an appropriate seepage coefficient or permeability rate of the interface element, results close to those obtained through the traditional methods can be acquired, which shows the applicability of the proposed method.
In the calculation of seepage or consolidation, if there is a large difference in seepage coefficient of two adjacent materials, the release point, as well as the phreatic line, should be determined by iterations. However, if we set interface elements between two materials, reasonable results of release point can be captured without iterations. In this paper, two seepage cases are investigated, and the composite seepage coefficient of the elements, which are intersected by the phreatic line, is calculated with the Monte Carlo integration method. Two interface elements are set between two materials with great difference in seepage coefficient. The hydraulic relationship between two materials is built based on the seepage matrices of the interface elements, while the location of the phreatic line is then calculated by iterations. Choosing a thin thickness for the interface element(e.g., 1/4 of the thickness of the adjacent element) could localize the error of calculation, which has little impact to the whole area at the same time. By choosing an appropriate seepage coefficient or permeability rate of the interface element, results close to those obtained through the traditional methods can be acquired, which shows the applicability of the proposed method.
引文
[ 1 ] LI Guangxin,GE Jinhong,JIE Yuxin.Free surface seepage analysis based on the element-free method[J].Mechanics Research Communications,2003,30(1):9-19.
[ 2 ] 介玉新,刘岩.基于蒙特卡罗积分的无网格伽辽金法及其在渗流分析中的应用[J].岩土工程学报,2007,29(12):1794-1799.(JIE Yuxin,LIU Yan.Element-free Galerkin method based on Monte Carlo integration and its application in seepage analysis[J].Chinese Journal of Geotechnical Engineering,2007,29(12):1794-1799.(in Chinese))
[ 3 ] JIE Yuxin,LIU Lizhen,XU Wenjie,et al.Application of NEM in seepage analysis with a free surface[J].Mathematics and Computers in Simulation,2013,89:23-37.
[ 4 ] 张有天,陈平,王镭.有自由面渗流分析的初流量法[J].水利学报,1988,19(8):18-26.(ZHANG Youtian,CHEN Ping,WANG Lei.Initial flow method for seepage analysis with free surface[J].Journal of Hydraulic Engineering,1988,19(8):18-26.(in Chinese))
[ 5 ] BATHE K J,KHOSHGOFTAAR M R.Finite element free surface seepage analysis without mesh iteration[J].International Journal for Numerical and Analytical Methods in Geomechanics,1979,3(1):13-22.
[ 6 ] 朱军,刘光廷.改进的单元渗透矩阵调整法求解无压渗流场[J].水利学报,2001,26(8):49-52.(ZHU Jun,LIU Guangting.An improved method for calculating unconfined seepage with changing element conductivity matrix[J].Journal of Hydraulic Engineering,2001,26(8):49-52.(in Chinese))
[ 7 ] 舒仲英,邓建霞,李龙国.加密Gauss点单元传导矩阵调整法在有自由面渗流分析中的应用[J].四川大学学报(自然科学版),2007,39(1):48-52.(SHU Zhongying,DENG Jianxia,LI Longguo.Application of element conduct matrix regulative method by encrypting Gauss point in seepage analysis with free surface[J].Journal of Sichuan University(Science and Technology),2007,39(1):48-52.(in Chinese))
[ 8 ] 周创兵,熊文林,梁业国.求解无压渗流场的一种新方法[J].水动力学研究与进展,1996,11(5):528-534.(ZHOU Chuangbing,XIONG Wenlin,LIANG Yeguo.A new method for the solution of unconfined seepage field[J].Journal of Hydrodynamics,1996,11(5):528-534.(in Chinese))
[ 9 ] 介玉新.引用Monte Carlo法的自由面渗流分析[J].清华大学学报(自然科学版),2009,49(12):1944-1947.(JIE Yuxin.Seepage analysis with free surface using a Monte Carlo model[J].Journal of Tsinghua University(Science and Technology),2009,49(12):1944-1947.(in Chinese))
[10] JIANG Bin.A priori error analysis of the mortar finite element method for variational inequalities[J].Numerical Methods for Partial Differential Equations,2008,24(2):476-503.
[11] FUKUCHI T.Numerical analyses of steady-state seepage problems using the interpolation finite difference method[J].Soils and Foundations,2016,56(4):608-626.
[12] 吴梦喜,张雪勤.有自由面渗流分析的虚单元法[J].水利学报,1994,34(8):67-71.(WU Mengxi,ZHANG Xueqin.Imaginary element method for numerical analysis of seepage with free surface[J].Journal of Hydraulic Engineering,1994,34(8):67-71.(in Chinese))
[13] 侯兴民,孙伟建.基于实域总势能计算渗流溢出点位置[J].岩土工程学报,2018,40(4):612-617.(HOU Xingmin,SUN Weijian.Calculation of seepage spill point position based on total potential energy in real domain[J].Chinese Journal of Geotechnical Engineering,2018,40(4):612-617.(in Chinese))
[14] 侯晓萍,徐青,陈胜宏.用空气单元法求解渗流场的逸出边界问题[J].岩土力学,2015,36(8):2345-2351.(HOU Xiaoping,XU Qing,CHEN Shenghong.An air element method for overflow boundary problem in seepage analysis[J].Rock and Soil Mechanics,2015,36(8):2345-2351.(in Chinese))
[15] 胡静,陈胜宏.渗流分析中排水孔模拟的空气单元法[J].岩土力学,2003,24(2):281-284.(HU Jing,CHEN Shenghong.Air element method for modeling drainage holes in seepage analysis[J].Rock and Soil Mechanics,2003,24(2):281-284.(in Chinese))
[16] WU Mengxi,YANG Lianzhi,YU Ting.Simulation procedure of unconfined seepage with an inner seepage face in a heterogeneous field[J].Science China Physics,Mechanics and Astronomy,2013,56(6):1139-1147.
[17] 岑威钧,和浩楠,温朗昇.防渗土工膜的缺陷特性与缺陷渗漏研究进展[J].河海大学学报(自然科学版),2017,45(1):36-44.(CEN Weijun,HE Haonan,WEN Langsheng.Research progress on defect property and defect-induced leakage of impermeable geomembrane[J].Journal of Hohai University (Natural Sciences),2017,45(1):36-44.(in Chinese))
[18] 岑威钧,和浩楠,李邓军.土工膜缺陷对土石坝渗流特性的影响及控制措施[J].水利水电科技进展,2017,37(3):61-65.(CEN Weijun,HE Haonan,LI Dengjun.Influence of geomembrane defect on seepage property of earth-rock dams and measures of seepage control[J].Advances in Science and Technology of Water Resources,2017,37(3):61-65.(in Chinese))
[19] 白广明,张守杰,卢建旗,等.流场法探测堤坝渗漏数值模拟及分析[J].河海大学学报(自然科学版),2018,46(1):52-58.(BAI Guangming,ZHANG Shoujie,LU Jianqi,et al.Numerical modelling and verification of the dam leakage detection using the quasi-flowing field method[J].Journal of Hohai University (Natural Sciences),2018,46(1):52-58.(in Chinese))
[20] 李明远,周志芳,杨蕴,等.新干航电枢纽工程右岸浸没评价与控制[J].河海大学学报(自然科学版),2018,46(3):203-210.(LI Mingyuan,ZHOU Zhifang,YANG Yun,et al.Immersion assessment and control of the right bank of Xingan Navigation and Power Junction[J].Journal of Hohai University (Natural Sciences),2018,46(3):203-210.(in Chinese))
[21] 介玉新,许延春,李广信.固结计算中接触面渗流问题的模拟[J].工程力学,2007,24(增刊1):104-107.(JIE Yuxin,XU Yanchun,LI Guangxin.Simulating seepage through interface in consolidation analysis[J].Engineering Mechanics,2007,24(Sup1):104-107.(in Chinese))
[22] 介玉新,李广信.有限元计算中土工合成材料渗流问题的处理[J].水利水电科技进展,2009,29(6):42-43,62.(JIE Yuxin,LI Guangxin.FEM calculation of seepage through geosynthetics[J].Advances in Science and Technology of Water Resources,2009,29(6):42-43,62.(in Chinese))
[ 2 ] 介玉新,刘岩.基于蒙特卡罗积分的无网格伽辽金法及其在渗流分析中的应用[J].岩土工程学报,2007,29(12):1794-1799.(JIE Yuxin,LIU Yan.Element-free Galerkin method based on Monte Carlo integration and its application in seepage analysis[J].Chinese Journal of Geotechnical Engineering,2007,29(12):1794-1799.(in Chinese))
[ 3 ] JIE Yuxin,LIU Lizhen,XU Wenjie,et al.Application of NEM in seepage analysis with a free surface[J].Mathematics and Computers in Simulation,2013,89:23-37.
[ 4 ] 张有天,陈平,王镭.有自由面渗流分析的初流量法[J].水利学报,1988,19(8):18-26.(ZHANG Youtian,CHEN Ping,WANG Lei.Initial flow method for seepage analysis with free surface[J].Journal of Hydraulic Engineering,1988,19(8):18-26.(in Chinese))
[ 5 ] BATHE K J,KHOSHGOFTAAR M R.Finite element free surface seepage analysis without mesh iteration[J].International Journal for Numerical and Analytical Methods in Geomechanics,1979,3(1):13-22.
[ 6 ] 朱军,刘光廷.改进的单元渗透矩阵调整法求解无压渗流场[J].水利学报,2001,26(8):49-52.(ZHU Jun,LIU Guangting.An improved method for calculating unconfined seepage with changing element conductivity matrix[J].Journal of Hydraulic Engineering,2001,26(8):49-52.(in Chinese))
[ 7 ] 舒仲英,邓建霞,李龙国.加密Gauss点单元传导矩阵调整法在有自由面渗流分析中的应用[J].四川大学学报(自然科学版),2007,39(1):48-52.(SHU Zhongying,DENG Jianxia,LI Longguo.Application of element conduct matrix regulative method by encrypting Gauss point in seepage analysis with free surface[J].Journal of Sichuan University(Science and Technology),2007,39(1):48-52.(in Chinese))
[ 8 ] 周创兵,熊文林,梁业国.求解无压渗流场的一种新方法[J].水动力学研究与进展,1996,11(5):528-534.(ZHOU Chuangbing,XIONG Wenlin,LIANG Yeguo.A new method for the solution of unconfined seepage field[J].Journal of Hydrodynamics,1996,11(5):528-534.(in Chinese))
[ 9 ] 介玉新.引用Monte Carlo法的自由面渗流分析[J].清华大学学报(自然科学版),2009,49(12):1944-1947.(JIE Yuxin.Seepage analysis with free surface using a Monte Carlo model[J].Journal of Tsinghua University(Science and Technology),2009,49(12):1944-1947.(in Chinese))
[10] JIANG Bin.A priori error analysis of the mortar finite element method for variational inequalities[J].Numerical Methods for Partial Differential Equations,2008,24(2):476-503.
[11] FUKUCHI T.Numerical analyses of steady-state seepage problems using the interpolation finite difference method[J].Soils and Foundations,2016,56(4):608-626.
[12] 吴梦喜,张雪勤.有自由面渗流分析的虚单元法[J].水利学报,1994,34(8):67-71.(WU Mengxi,ZHANG Xueqin.Imaginary element method for numerical analysis of seepage with free surface[J].Journal of Hydraulic Engineering,1994,34(8):67-71.(in Chinese))
[13] 侯兴民,孙伟建.基于实域总势能计算渗流溢出点位置[J].岩土工程学报,2018,40(4):612-617.(HOU Xingmin,SUN Weijian.Calculation of seepage spill point position based on total potential energy in real domain[J].Chinese Journal of Geotechnical Engineering,2018,40(4):612-617.(in Chinese))
[14] 侯晓萍,徐青,陈胜宏.用空气单元法求解渗流场的逸出边界问题[J].岩土力学,2015,36(8):2345-2351.(HOU Xiaoping,XU Qing,CHEN Shenghong.An air element method for overflow boundary problem in seepage analysis[J].Rock and Soil Mechanics,2015,36(8):2345-2351.(in Chinese))
[15] 胡静,陈胜宏.渗流分析中排水孔模拟的空气单元法[J].岩土力学,2003,24(2):281-284.(HU Jing,CHEN Shenghong.Air element method for modeling drainage holes in seepage analysis[J].Rock and Soil Mechanics,2003,24(2):281-284.(in Chinese))
[16] WU Mengxi,YANG Lianzhi,YU Ting.Simulation procedure of unconfined seepage with an inner seepage face in a heterogeneous field[J].Science China Physics,Mechanics and Astronomy,2013,56(6):1139-1147.
[17] 岑威钧,和浩楠,温朗昇.防渗土工膜的缺陷特性与缺陷渗漏研究进展[J].河海大学学报(自然科学版),2017,45(1):36-44.(CEN Weijun,HE Haonan,WEN Langsheng.Research progress on defect property and defect-induced leakage of impermeable geomembrane[J].Journal of Hohai University (Natural Sciences),2017,45(1):36-44.(in Chinese))
[18] 岑威钧,和浩楠,李邓军.土工膜缺陷对土石坝渗流特性的影响及控制措施[J].水利水电科技进展,2017,37(3):61-65.(CEN Weijun,HE Haonan,LI Dengjun.Influence of geomembrane defect on seepage property of earth-rock dams and measures of seepage control[J].Advances in Science and Technology of Water Resources,2017,37(3):61-65.(in Chinese))
[19] 白广明,张守杰,卢建旗,等.流场法探测堤坝渗漏数值模拟及分析[J].河海大学学报(自然科学版),2018,46(1):52-58.(BAI Guangming,ZHANG Shoujie,LU Jianqi,et al.Numerical modelling and verification of the dam leakage detection using the quasi-flowing field method[J].Journal of Hohai University (Natural Sciences),2018,46(1):52-58.(in Chinese))
[20] 李明远,周志芳,杨蕴,等.新干航电枢纽工程右岸浸没评价与控制[J].河海大学学报(自然科学版),2018,46(3):203-210.(LI Mingyuan,ZHOU Zhifang,YANG Yun,et al.Immersion assessment and control of the right bank of Xingan Navigation and Power Junction[J].Journal of Hohai University (Natural Sciences),2018,46(3):203-210.(in Chinese))
[21] 介玉新,许延春,李广信.固结计算中接触面渗流问题的模拟[J].工程力学,2007,24(增刊1):104-107.(JIE Yuxin,XU Yanchun,LI Guangxin.Simulating seepage through interface in consolidation analysis[J].Engineering Mechanics,2007,24(Sup1):104-107.(in Chinese))
[22] 介玉新,李广信.有限元计算中土工合成材料渗流问题的处理[J].水利水电科技进展,2009,29(6):42-43,62.(JIE Yuxin,LI Guangxin.FEM calculation of seepage through geosynthetics[J].Advances in Science and Technology of Water Resources,2009,29(6):42-43,62.(in Chinese))