中梁水库岩溶水流数值模型及渗漏量计算
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摘要
回顾了岩溶区地下水流运动数值模拟的发展历程，概述了岩溶水运动的基本理论，系统全面地总结了国内外有关岩溶区地下水运动数值模拟方法，分析比较了各种计算方法的优缺点，在此基础上给出了各种计算方法的适用条件。
在仔细分析中梁水利水电工程库区水文地质条件的基础上，结合地表水测流资料、水化学分析资料及示踪连通试验资料，得出水库区岩溶渗漏条件，并在此基础上提出水库渗漏概念模型，采用水均衡法计算出库区的岩溶水渗漏量。
结合库区具体水文地质条件，讨论了三种岩溶区地下水流数值模型：线性渗流模型，非线性渗流模型和线性—非线性渗流模型。
线性渗流模型结合了中梁水库库区水文地质条件，重点进行正反问题的计算分析，利用研究区若干观测孔资料，采用有限单元法反演库区的水文地质参数，并预测了库区岩溶水渗漏量。
推导出整体坐标系下岩溶管道区非线性渗流模型渗透张量计算公式，基于Galerkin有限元法，导出了地下水非线性渗流的有限元方程，在此基础上编制了计算程序KARCON.FOR，将该程序用于典型模型的计算分析，结果表明该方法是合理的。
考虑到岩溶区渗流往往都是线性流与非线性流并存，首次提出了基于区域分解法理论的线性—非线性渗流模型，利用该方法模拟出理想模型中的水流运动，并编制了计算程序DAR-NONDAR.FOR，然后将该成果应用于中梁水利水电工程中，预测出库区岩溶水渗漏量。
在上述三种计算库区岩溶水渗漏量的模型中，由于线性—非线性渗流模型同时考虑了与中梁水库区实际情况相符合的达西流和非达西流区域并存的地下水运动，因此，利用该模型计算出的库区岩溶水渗漏量更合理。
On basis of the history of research on the development of groundwater modeling in the area of karst, this paper presents the summary of basic theory of karst water movement. The main concerned methods used to model the movement of karst groundwater are summarized systematically and comprehensively. The advantages and disadvantages of every calculation methods are analyzed and compared, based on the analysis, the adaptability of these methods are clarified.
On the basis of anatomizing the condition of hydrogeology with Zhongliang water resources and power engineering, combined with the data analysis of flux with surface water, aquatic chemistry, and experiment of tracing, the condition of karst leakage in the region of reservoir is educed. The concept of reservoir leakage with these information is put forward, the leakage quantity of karst water in the region of reservoir with the method of water equilibrium is applied.
Considering the practical status of the condition of hydrogeology in the region of reservior, This paper discuss the numerical model of linear seepage, nonlinear seepage, and linear-nonlinear seepage in karst groundwater.
Combing the linear seepage model with hydrogeology in the region of Zhong-liang reservior, the analysis of the problem of positive and negative is emphasized. Make use of With some observing information of boreholes in this region, adverse seeking the hydrogeology of the reservoir in the region with finite element method, the leakage quatity of karst water in the region of reservoir is forecasted..
The calculation formula of seepage tensor to the model of non-linear seepage with the area of karst conduit in the whole coordinate axis is deduced. On the basis of Galerkin finite element method, the equation of finite element with the non-linear seepage of groundwater is educed, on the foundation of this information, the program of KARCON.FOR is compiled. As this program to a typical model with calculation and analysis is applied, the results indicate the method is reasonable.
Considering the seepage of linear and the seepage of non-linear in the karst area are always coexisting, the model of linear seepage and non-linear seepage is put forward firstly on the basis of domain decomposition method. The movement of groundwater in an ideal model is simulated with this method, and the program of DAR-NONDAR.FOR is compiled. Then these results are applied to Zhongliang water resources and power engineering, the leakage quantity of karst water is calculated.
In the three models of calculating the leakage quantity of karst water, on account of the linear and non-linear seepage model are accord with the movement of darcy flow and non-darcy flow coexists with the practical instances in Zhong-liang reseviour, so the calculation result of leakage quantity of karst groundwater with this model is more reasonable.
在仔细分析中梁水利水电工程库区水文地质条件的基础上，结合地表水测流资料、水化学分析资料及示踪连通试验资料，得出水库区岩溶渗漏条件，并在此基础上提出水库渗漏概念模型，采用水均衡法计算出库区的岩溶水渗漏量。
结合库区具体水文地质条件，讨论了三种岩溶区地下水流数值模型：线性渗流模型，非线性渗流模型和线性—非线性渗流模型。
线性渗流模型结合了中梁水库库区水文地质条件，重点进行正反问题的计算分析，利用研究区若干观测孔资料，采用有限单元法反演库区的水文地质参数，并预测了库区岩溶水渗漏量。
推导出整体坐标系下岩溶管道区非线性渗流模型渗透张量计算公式，基于Galerkin有限元法，导出了地下水非线性渗流的有限元方程，在此基础上编制了计算程序KARCON.FOR，将该程序用于典型模型的计算分析，结果表明该方法是合理的。
考虑到岩溶区渗流往往都是线性流与非线性流并存，首次提出了基于区域分解法理论的线性—非线性渗流模型，利用该方法模拟出理想模型中的水流运动，并编制了计算程序DAR-NONDAR.FOR，然后将该成果应用于中梁水利水电工程中，预测出库区岩溶水渗漏量。
在上述三种计算库区岩溶水渗漏量的模型中，由于线性—非线性渗流模型同时考虑了与中梁水库区实际情况相符合的达西流和非达西流区域并存的地下水运动，因此，利用该模型计算出的库区岩溶水渗漏量更合理。
On basis of the history of research on the development of groundwater modeling in the area of karst, this paper presents the summary of basic theory of karst water movement. The main concerned methods used to model the movement of karst groundwater are summarized systematically and comprehensively. The advantages and disadvantages of every calculation methods are analyzed and compared, based on the analysis, the adaptability of these methods are clarified.
On the basis of anatomizing the condition of hydrogeology with Zhongliang water resources and power engineering, combined with the data analysis of flux with surface water, aquatic chemistry, and experiment of tracing, the condition of karst leakage in the region of reservoir is educed. The concept of reservoir leakage with these information is put forward, the leakage quantity of karst water in the region of reservoir with the method of water equilibrium is applied.
Considering the practical status of the condition of hydrogeology in the region of reservior, This paper discuss the numerical model of linear seepage, nonlinear seepage, and linear-nonlinear seepage in karst groundwater.
Combing the linear seepage model with hydrogeology in the region of Zhong-liang reservior, the analysis of the problem of positive and negative is emphasized. Make use of With some observing information of boreholes in this region, adverse seeking the hydrogeology of the reservoir in the region with finite element method, the leakage quatity of karst water in the region of reservoir is forecasted..
The calculation formula of seepage tensor to the model of non-linear seepage with the area of karst conduit in the whole coordinate axis is deduced. On the basis of Galerkin finite element method, the equation of finite element with the non-linear seepage of groundwater is educed, on the foundation of this information, the program of KARCON.FOR is compiled. As this program to a typical model with calculation and analysis is applied, the results indicate the method is reasonable.
Considering the seepage of linear and the seepage of non-linear in the karst area are always coexisting, the model of linear seepage and non-linear seepage is put forward firstly on the basis of domain decomposition method. The movement of groundwater in an ideal model is simulated with this method, and the program of DAR-NONDAR.FOR is compiled. Then these results are applied to Zhongliang water resources and power engineering, the leakage quantity of karst water is calculated.
In the three models of calculating the leakage quantity of karst water, on account of the linear and non-linear seepage model are accord with the movement of darcy flow and non-darcy flow coexists with the practical instances in Zhong-liang reseviour, so the calculation result of leakage quantity of karst groundwater with this model is more reasonable.
引文
[1] 袁道先主编．岩溶学词典．地质出版社，1988．
[2] 邹成杰．水利水电工程岩溶地质．水利水电出版社，1994．
[3] 任美锷等．岩溶学概论．商务印书馆，1983．
[4] Howard. A.D. and C. G. Groves. Early development of karst systems: 2. Turblent flow. Water Resourse Research. Vol. 31,No.4,1995
[5] 中国科学院地质研究所岩溶研究组．中国岩溶研究．科学出版社，1979
[6] 丁士群，傅瑞金．琅琊山抽水蓄能电站上水库副坝地段岩溶发育特征及渗漏分析[J]．中国岩溶，1997，16(1)：75-81
[7] 赖苗，赵坚．岩溶地下水渗流计算方法综述．水电能源科学[J]，2002，Vol．20，(4)，44-47
[8] Lomize G M.Groundwater in fractured[M].Gosenergoizdat, Moscow.1951
[9] Breaker R J.Liquid flow in fractured rocks[A].Proc.1 Vth Intern.Petrol.Congr. Well drilling and petroleum and gas production[M].Gostoptekhizdat, Moscow.1956
[10] Bocker T.Karstic water research in Hungary[A].Bull.OF the Inter.Assoc.of Sci.Hydrology[C], 1969, XIV4-12, 7～20
[11] Huitt J L.Fluid flow in simulated fractures[J].A.I.CH.E.Jour.1956, 2(2), 259～264
[12] Babushkin V D, Boker T, Borevsky B V, Kovalevsky V S.Regime of subterranean water flows in karst region.in Hydrogeology of karstic terrains[M].Paris:Inter.Union of Geol.Sci.B, 1975
[13] Borelli M, Pavlinz B.Approach to the problem of underground water leakage from the storages in karst regions[A].Hydrologie des Roches Fissures, Proc.Of the Dubrovnik Symposium[M], AIME, 1965, 32～62
[14] Pankow J F, Johoson R L, Hewetson J P, Cherry J A.An evaluation of contaminant migration patterns at two waste disposal on fractured porous media in terms of the porous medium(EMP) model[J].Journal of Contaminant Hydrology. 1986, 1(1), 65～86
[15] 夏日元，郭纯青．岩溶地下水系统单元网络数学模拟方法研究[J]．中国岩溶，1992，11(4)：267-276
[16] 陈崇希．岩溶管道-裂隙-孔隙三重介质地下水流模型及模拟方法研究[J]．地球科学，1995，20(4)：361-366
[17] 陈建梅，陈崇希．广西北山岩溶管道-裂隙-孔隙地下水流数值模拟初探[J]．水文地质工程地质，1998(4)：50-54
[18] M.M.斯维婷．喀斯特水和喀斯特水文学．地貌译丛，1978，第3号．
[19] 卢耀如．中国喀斯特地貌的演化模式．地理研究，1986．
[20] 铁道部第二勘测设计院．岩溶工程地质．中国铁道出版社，1984．
[21] 袁道先．岩溶环境学．重庆出版社，1988．
[22] 张英骏等．应用岩溶学与洞穴学．贵州人民出版社，1985．
[23] 邹成杰．岩溶管道水汇流理论研究．中国岩溶，1992(2)
[24] 郭东屏．地下水动力学．陕西科学技术出版社，1994．
[25] 代群力．地下水非线性流动模拟．水文地质工程地质，2000，(2)：50-51
[26] 重庆大宁河中梁水利水电工程地质报告．国电公司中南水利水电勘测设计研究院，2001
[27] Bear J.Hydraulics of Groundwater. New York:McGraw-Hill, 1979.
[28] 金光炎，汪家权．地下水计算参数的测定与估计．水科学进展，1997，8(1)：16-24
[29] 李炜，徐孝平．水力学[M]．武汉水利电力大学出版社．2000
[30] 柴军瑞．地下水非达西渗流分析．勘察科学技术．2002，(1)：25-27
[31] 梁昆淼．数学物理方法．高等教育出版社，北京，1996
[32] B.Li, V. K. Garga, M. H. Davies.Relationship for no-darcy flow in rockfill. Journal of Hydraulic Engineering. 1998, 124 (2): 206-212
[33] B.Li, V. K. Garga. Theorectical solution for seepage flow in overtopped rockfill. Journal of Hydraulic Engineering. 1998, 124(2):213-217
[34] Bear J. Dynamics of Fluids in Porous Media. New York: Elsevier, 1979
[35] 芮孝芳．产汇流理论．水利水电出版设，1995．
[36] 雒文生．河流水文学．水利水电出版设，1992．
[37] 范文生，王大齐．水资源水文学．水利水电出版社，1996．
[38] 任树梅，朱仲元．工程水文学．中国农业大学出版设，2001．
[39] 中国水文年鉴．1996，vol(5)
[40] 张顺联．地下水资源评价与计算．水利水电出版社，1992．
[41] 陆地水文学．成都水利水电学校主编．水利水电出版社，1979．
[42] 陈雨孙．地下水运动与资源评价．中国建筑工业出版社，1986．
[43] 钱孝星．水文地质计算．水利水电出版社，1995．
[44] 黄勇．南京玄武湖隧道工程水文地质参数的遗传反演．勘察科学技术，2002，(2)
[45] 徐仲．矩阵论简明教程．科学技术出版社，2001．
[46] 周志芳．岩体地下水运动模拟的理论与应用研究．南京大学博士学位论文，1998．12
[47] 谭浩强，田淑清．FORTRAN语言．清华大学出版社，1981．
[48] 中科院武汉岩土所．武汉大学出版社，2000．
[49] 赵汝嘉．SURFER应用教程．西安交通大学出版社，1998．
[50] 吕涛．区域分解算法：偏微分方程数值解新技术．北京：科学出版社，1992．5
[51] 王浩然．基于区域分解法的地下水耦和模型与并行模拟技术．南京大学博士学位论文，2002．6
[52] 中国地质科学院岩溶地质研究所．重庆大宁河中梁水库岩溶水示踪试验，2002．10
[2] 邹成杰．水利水电工程岩溶地质．水利水电出版社，1994．
[3] 任美锷等．岩溶学概论．商务印书馆，1983．
[4] Howard. A.D. and C. G. Groves. Early development of karst systems: 2. Turblent flow. Water Resourse Research. Vol. 31,No.4,1995
[5] 中国科学院地质研究所岩溶研究组．中国岩溶研究．科学出版社，1979
[6] 丁士群，傅瑞金．琅琊山抽水蓄能电站上水库副坝地段岩溶发育特征及渗漏分析[J]．中国岩溶，1997，16(1)：75-81
[7] 赖苗，赵坚．岩溶地下水渗流计算方法综述．水电能源科学[J]，2002，Vol．20，(4)，44-47
[8] Lomize G M.Groundwater in fractured[M].Gosenergoizdat, Moscow.1951
[9] Breaker R J.Liquid flow in fractured rocks[A].Proc.1 Vth Intern.Petrol.Congr. Well drilling and petroleum and gas production[M].Gostoptekhizdat, Moscow.1956
[10] Bocker T.Karstic water research in Hungary[A].Bull.OF the Inter.Assoc.of Sci.Hydrology[C], 1969, XIV4-12, 7～20
[11] Huitt J L.Fluid flow in simulated fractures[J].A.I.CH.E.Jour.1956, 2(2), 259～264
[12] Babushkin V D, Boker T, Borevsky B V, Kovalevsky V S.Regime of subterranean water flows in karst region.in Hydrogeology of karstic terrains[M].Paris:Inter.Union of Geol.Sci.B, 1975
[13] Borelli M, Pavlinz B.Approach to the problem of underground water leakage from the storages in karst regions[A].Hydrologie des Roches Fissures, Proc.Of the Dubrovnik Symposium[M], AIME, 1965, 32～62
[14] Pankow J F, Johoson R L, Hewetson J P, Cherry J A.An evaluation of contaminant migration patterns at two waste disposal on fractured porous media in terms of the porous medium(EMP) model[J].Journal of Contaminant Hydrology. 1986, 1(1), 65～86
[15] 夏日元，郭纯青．岩溶地下水系统单元网络数学模拟方法研究[J]．中国岩溶，1992，11(4)：267-276
[16] 陈崇希．岩溶管道-裂隙-孔隙三重介质地下水流模型及模拟方法研究[J]．地球科学，1995，20(4)：361-366
[17] 陈建梅，陈崇希．广西北山岩溶管道-裂隙-孔隙地下水流数值模拟初探[J]．水文地质工程地质，1998(4)：50-54
[18] M.M.斯维婷．喀斯特水和喀斯特水文学．地貌译丛，1978，第3号．
[19] 卢耀如．中国喀斯特地貌的演化模式．地理研究，1986．
[20] 铁道部第二勘测设计院．岩溶工程地质．中国铁道出版社，1984．
[21] 袁道先．岩溶环境学．重庆出版社，1988．
[22] 张英骏等．应用岩溶学与洞穴学．贵州人民出版社，1985．
[23] 邹成杰．岩溶管道水汇流理论研究．中国岩溶，1992(2)
[24] 郭东屏．地下水动力学．陕西科学技术出版社，1994．
[25] 代群力．地下水非线性流动模拟．水文地质工程地质，2000，(2)：50-51
[26] 重庆大宁河中梁水利水电工程地质报告．国电公司中南水利水电勘测设计研究院，2001
[27] Bear J.Hydraulics of Groundwater. New York:McGraw-Hill, 1979.
[28] 金光炎，汪家权．地下水计算参数的测定与估计．水科学进展，1997，8(1)：16-24
[29] 李炜，徐孝平．水力学[M]．武汉水利电力大学出版社．2000
[30] 柴军瑞．地下水非达西渗流分析．勘察科学技术．2002，(1)：25-27
[31] 梁昆淼．数学物理方法．高等教育出版社，北京，1996
[32] B.Li, V. K. Garga, M. H. Davies.Relationship for no-darcy flow in rockfill. Journal of Hydraulic Engineering. 1998, 124 (2): 206-212
[33] B.Li, V. K. Garga. Theorectical solution for seepage flow in overtopped rockfill. Journal of Hydraulic Engineering. 1998, 124(2):213-217
[34] Bear J. Dynamics of Fluids in Porous Media. New York: Elsevier, 1979
[35] 芮孝芳．产汇流理论．水利水电出版设，1995．
[36] 雒文生．河流水文学．水利水电出版设，1992．
[37] 范文生，王大齐．水资源水文学．水利水电出版社，1996．
[38] 任树梅，朱仲元．工程水文学．中国农业大学出版设，2001．
[39] 中国水文年鉴．1996，vol(5)
[40] 张顺联．地下水资源评价与计算．水利水电出版社，1992．
[41] 陆地水文学．成都水利水电学校主编．水利水电出版社，1979．
[42] 陈雨孙．地下水运动与资源评价．中国建筑工业出版社，1986．
[43] 钱孝星．水文地质计算．水利水电出版社，1995．
[44] 黄勇．南京玄武湖隧道工程水文地质参数的遗传反演．勘察科学技术，2002，(2)
[45] 徐仲．矩阵论简明教程．科学技术出版社，2001．
[46] 周志芳．岩体地下水运动模拟的理论与应用研究．南京大学博士学位论文，1998．12
[47] 谭浩强，田淑清．FORTRAN语言．清华大学出版社，1981．
[48] 中科院武汉岩土所．武汉大学出版社，2000．
[49] 赵汝嘉．SURFER应用教程．西安交通大学出版社，1998．
[50] 吕涛．区域分解算法：偏微分方程数值解新技术．北京：科学出版社，1992．5
[51] 王浩然．基于区域分解法的地下水耦和模型与并行模拟技术．南京大学博士学位论文，2002．6
[52] 中国地质科学院岩溶地质研究所．重庆大宁河中梁水库岩溶水示踪试验，2002．10