模拟排水孔列渗流行为的以沟代孔列延长渗径法研究
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摘要
排水孔是降低岩土体中地下水位和减小渗透压力的重要设施。因排水孔孔径小、排列密集,研究排水孔列的简化模拟方法对减小渗流数值计算规模,提高计算效率十分必要。基于流量等效原理的以沟代井列的延长渗径法,因其概念清晰、实现简便,在承压含水层井列的渗流场模拟中应用广泛。现有以沟代井列的延长渗径法中附加渗径计算公式与井深和含水层厚度息息相关,使得该方法应用于多层和有自由面的问题困难重重。针对现有延长渗径法的局限性,提出适用于有自由面的各向异性多种介质中排水孔列渗流问题的延长渗径法,附加渗径长度的确定不再受到孔深和含水层厚度的影响。采用该方法对几个典型的溢流型、逸出型和复合型排水孔列进行渗流场有限元分析,并与排水孔直接模拟的结果进行对比。结果表明,延长渗径法得到的排水孔的流量与排水孔直接模拟法的流量相差很小,且两种方法获得的自由面基本吻合。因此,提出的延长渗径法是模拟排水孔列渗流行为的简单而有效的方法。
The installation of drainage holes is one of the important practical measures to decrease the seepage pressure and groundwater table in rock and soil masses. Owing to its clear concept and simplicity, the extended seepage tracking method for slot instead of well curtain, which is based on the theory of equivalent discharge, is widely used in the seepage simulation for the well curtain in confined aquifer. The additional seepage tracking in the existing extended seepage tracking method is closely related to the thickness of the aquifer and the depth of the wells, which makes it difficult to be used in the situation containing multilayers and free surface. To remove the limitation of this method, an improved method for seepage problems with drainage holes curtains in multilayered anisotropic mass containing free surface is developed in this paper, in which the formulation of the additional seepage tracking is no longer related to the depth of a drainage hole and the thickness of aquifer. Finite element analyses of several typical drainage holes curtains in the overflow, escape flow and composite flow situations are given by this method. The solutions are compared with the solutions of every drainage hole directly modeled. The results show that the differences between the fluxes by the extended seepage tracking method and those by direct modeling method are very small; and the free surfaces from these two methods are similar. It also shown that the proposed extended seepage tracking method is a simple and effective method to simulate the seepage behaviors of drainage holes curtains.
The installation of drainage holes is one of the important practical measures to decrease the seepage pressure and groundwater table in rock and soil masses. Owing to its clear concept and simplicity, the extended seepage tracking method for slot instead of well curtain, which is based on the theory of equivalent discharge, is widely used in the seepage simulation for the well curtain in confined aquifer. The additional seepage tracking in the existing extended seepage tracking method is closely related to the thickness of the aquifer and the depth of the wells, which makes it difficult to be used in the situation containing multilayers and free surface. To remove the limitation of this method, an improved method for seepage problems with drainage holes curtains in multilayered anisotropic mass containing free surface is developed in this paper, in which the formulation of the additional seepage tracking is no longer related to the depth of a drainage hole and the thickness of aquifer. Finite element analyses of several typical drainage holes curtains in the overflow, escape flow and composite flow situations are given by this method. The solutions are compared with the solutions of every drainage hole directly modeled. The results show that the differences between the fluxes by the extended seepage tracking method and those by direct modeling method are very small; and the free surfaces from these two methods are similar. It also shown that the proposed extended seepage tracking method is a simple and effective method to simulate the seepage behaviors of drainage holes curtains.
引文
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[10]佘成学,刘先珊,叶查贵.改进的排水孔解析解和有限元耦合计算方法[J].岩土力学,2002,23(5):601-603.SHE Cheng-xue,LIU Xian-shan,YE Cha-gui.Improved coupling method of analytical solution for drainage hole and FEM[J].Rock and Soil Mechanics,2002,23(5):601-603.
[11]许桂生,冯学敏,陈胜宏.渗流分析中排水孔和不连续面模拟的复合单元法[J].岩石力学与工程学报,2006,25(增刊2):3714-3718.XU Gui-sheng,FENG Xue-min,CHEN Sheng-hong.Cmposite element method for simulation of discontinuous subface and drainage hole in seepage analysis[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(Supp.2):3714-3718.
[12]CHEN S H,XUE L L,XU G S,et al.Composite element method for the seepage analysis of rock masses containing fractures and drainage holes[J].International Journal of Rock Mechanics and Mining Sciences,2010,47(5):762-770.
[13]李斌,张俊霞.数值计算中以沟代井列的附加单元法[J].水利学报,1996,(3):51-56.LI Bin,ZHANG Jun-xia.An additional element used in numerical analysis for slot instead of well curtain[J].Journal of Hydraulic Engineering,1996,(3):51-56.
[14]毛昶熙.井孔与井列的渗流数值计算[J].岩土力学,2002,23(3):257-262.MAO Chang-xi.Numerical computation of seepage flow for wells and well row[J].Rock and Soil Mechanics,2002,23(3):257-262.
[15]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 Xiao-ping,XU Qing,CHEN Sheng-hong.An air element method for overflow boundary problem in seepage analysis[J].Rock and Soil Mechanics,2015,36(8):2345-2351.
[16]吴梦喜,高莲士.饱和-非饱和土体非稳定渗流数值分析[J].水利学报,1999,(12):38-42.WU Meng-xi,GAO Lian-shi.Saturated-unsaturated unsteady seepage numerical analysis[J].Journal of Hydraulic Engineering,1999,(12):38-42.
[17]WU M X.A finite-element algorithm for modeling variably saturated flows[J].Journal of Hydrology,2010,394(3-4):315-323.
[18]毛昶熙.渗流计算分析与控制(第二版)[M].北京:中国水利水电出版社,2003.MAO Chang-xi.Seepage computation analysis&control(2rd)[M].Beijing:China Water Power Press,2003.
[19]MILLER C T,WILLIAMS G A,KELLEY C T,et al.Robust solution of Richards’equation for non-uniform porous media[J].Water Resources Research,1998,34(10):2599-2610.
[20]PETERS R R,KLAVETTER E A.A continuum model for water movement in an unsaturated fractured rock mass[J].Water Resources Research,1988,24(3):416-430.
[2]朱岳民,张燎军.渗流场求解的改进排水子结构法[J].岩土工程学报,1997,19(2):69-76.ZHU Yue-ming,ZHANG Liao-jun.Solution to seepage field problem with the technique of improved drainage substructure[J].Chinese Jounral of Geotechnical Engineering,1997,19(2):69-76.
[3]朱军,刘光廷,陆述远.被自由面穿过排水孔的数值模拟方法[J].武汉大学学报(工学版),2001,34(2):10-13.ZHU Jun,LIU Guang-ting,LU Shu-yuan.Numerical simulation for drainage crossed by free surface[J].Engineering Journal of Wuhan University,2001,34(2):10-13.
[4]CHEN Y F,HU R,ZHOU C B,et al.A new parabolic variational inequality formulation of signorini’s consition for non-steady seepage problem with complex seepage control systems[J].International Journal for Numerical and Analytical Methods in Geomechanics,2011,35(9):1034-1035.
[5]王恩志,王洪涛,邓旭东.“以管代孔”--排水孔模拟方法探讨[J].岩石力学与工程学报,2001,20(3):346-349.WANG En-zhi,WANG Hong-tao,DENG Xu-dong.Pipe to represent hole-numerical method for simulating single drainage hole in rock-masses[J].Chinese Journal of Rock Mechanics and Engineering,2001,20(3):346-349.
[6]王恩志,王洪涛,王慧明.“以缝代井列”--排水孔幕模拟方法探讨[J].岩石力学与工程学报,2002,21(1):98-101.WANG En-zhi,WANG Hong-tao,WANG Hui-ming.“Fissure to represent line of holes”-numerical method for simulating the drainage hole curtain in rock masses[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(1):98-101.
[7]朱伯芳,李玥,许平,等.渗流场分析的夹层代孔列法[J].水利水电技术,2007,38(10):24-28.ZHU Bo-fang,LI Yue,XU Ping,et al.Substitution of the curtain of drainage holes by a seeping layer in the three dimensional finite element analysis of seepage field[J].Water Resources and Hydropower Engineering,2007,38(10):24-28.
[8]ZHAN M L,SU B Y.New method of simulating concentrated drain hole in seepage control analysis[J].Journal of Hydrodynamics(Ser.B),1999,(3):27-35.
[9]詹美礼,速宝玉,刘俊勇.渗流控制分析中密集排水孔模拟的新方法[J].水力发电,2000,(4):23-25.ZHAN Mei-li,SU Bao-yu,LIU Jun-yong.A new method of close drainage hole simulation in the seepage control analysis[J].Water Power,2000,(4):23-25.
[10]佘成学,刘先珊,叶查贵.改进的排水孔解析解和有限元耦合计算方法[J].岩土力学,2002,23(5):601-603.SHE Cheng-xue,LIU Xian-shan,YE Cha-gui.Improved coupling method of analytical solution for drainage hole and FEM[J].Rock and Soil Mechanics,2002,23(5):601-603.
[11]许桂生,冯学敏,陈胜宏.渗流分析中排水孔和不连续面模拟的复合单元法[J].岩石力学与工程学报,2006,25(增刊2):3714-3718.XU Gui-sheng,FENG Xue-min,CHEN Sheng-hong.Cmposite element method for simulation of discontinuous subface and drainage hole in seepage analysis[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(Supp.2):3714-3718.
[12]CHEN S H,XUE L L,XU G S,et al.Composite element method for the seepage analysis of rock masses containing fractures and drainage holes[J].International Journal of Rock Mechanics and Mining Sciences,2010,47(5):762-770.
[13]李斌,张俊霞.数值计算中以沟代井列的附加单元法[J].水利学报,1996,(3):51-56.LI Bin,ZHANG Jun-xia.An additional element used in numerical analysis for slot instead of well curtain[J].Journal of Hydraulic Engineering,1996,(3):51-56.
[14]毛昶熙.井孔与井列的渗流数值计算[J].岩土力学,2002,23(3):257-262.MAO Chang-xi.Numerical computation of seepage flow for wells and well row[J].Rock and Soil Mechanics,2002,23(3):257-262.
[15]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 Xiao-ping,XU Qing,CHEN Sheng-hong.An air element method for overflow boundary problem in seepage analysis[J].Rock and Soil Mechanics,2015,36(8):2345-2351.
[16]吴梦喜,高莲士.饱和-非饱和土体非稳定渗流数值分析[J].水利学报,1999,(12):38-42.WU Meng-xi,GAO Lian-shi.Saturated-unsaturated unsteady seepage numerical analysis[J].Journal of Hydraulic Engineering,1999,(12):38-42.
[17]WU M X.A finite-element algorithm for modeling variably saturated flows[J].Journal of Hydrology,2010,394(3-4):315-323.
[18]毛昶熙.渗流计算分析与控制(第二版)[M].北京:中国水利水电出版社,2003.MAO Chang-xi.Seepage computation analysis&control(2rd)[M].Beijing:China Water Power Press,2003.
[19]MILLER C T,WILLIAMS G A,KELLEY C T,et al.Robust solution of Richards’equation for non-uniform porous media[J].Water Resources Research,1998,34(10):2599-2610.
[20]PETERS R R,KLAVETTER E A.A continuum model for water movement in an unsaturated fractured rock mass[J].Water Resources Research,1988,24(3):416-430.