多尺度裂隙介质中的水流和溶质运移随机模拟研究
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摘要
本文结合具体工程研究了裂隙介质中的水流和溶质运移规律，主要从模型的建立、方法的创新和工程的应用等方面作了深入的探讨，每部分内容都紧扣单裂隙和网络裂隙尺度进行了分析，同时所建立的模型和使用的方法都考虑了地质、水文地质要素(物理量)的随机性，通过研究取得了一些有益的成果。
基于裂隙几何要素的统计特征，应用Monte-Carlo方法随机生成裂隙网络系统。以裂隙交叉处作为节点，节点与节点之间的裂隙当作线单元，根据单裂隙立方体定律和质量守恒原则，建立了裂隙网络中水流运动的数学模型，并推导了数学模型的数值解法。同时自行开发研制了岩体裂隙地下水流数值模拟程序，主要由前处理部分程序Disc．for，计算程序Netw．for和后处理程序Vector．for组成，可以单独使用，也可以结合起来使用。
根据研究的实际问题进行了裂隙介质非均质各向异性的全耦合，与传统的耦合方法相比，该方法充分考虑了裂隙面几何要素的随机性。主要有两种耦合方式：其一是介质各向异性耦合，即用离散裂隙网络模型描述主干裂隙中的水流运动，用等效连续介质模型描述次要裂隙和孔隙中的水流运动。其二是非均质耦合，将研究区域按裂隙发育的情况进行分区，不同的分区使用不同的数学模型—区域分解算法。
提出了一种裂隙岩体模型参数识别的混沌遗传混合优化方法，该方法结合了混沌优化和遗传算法的优点，增大了搜索的范围又具备跳出局部最优的能力，算例表明混合优化方法很快能搜索到目标函数的最优值。
分别应用了改进的随机步行法和仿真模拟技术来模拟裂隙网络中的溶质运移，前者中时间步长采用自动调整的方式，避免了时间步长选得不合理而导致模拟结果的不准确，主要应用于单裂隙和平面网络裂隙的模拟；后者基于概率统计的方法进行研究，主要应用于平面和三维裂隙网络中。
将所建立的水流模型和使用的方法应用到实际王程中，取得了满意的结果。
In the paper, based on concrete engineering, laws of flow and solute transport are researched in fractured media. Some aspects involved in model constitution, methods innovation and engineering application are discussed detailedly. Furthermore, these contents are analyzed in single fracture and network fracture scales. Simultaneously, in the course of constituting model and using methods, randomness of geological and hydro-geological features, physical parameters, is taken into account. As a result, some beneficial results are obtained.Based on the statistic characteristics of fractured geometrical elements, fracture network system is made by the Monte-Carlo method. Fracture intersection points are acted as nodes, and fractures between nodes are regarded as linear element. According to cubic law of single fracture and mass conservation principle in fracture network, the seepage mathematics model for discrete fractured network is developed in fractured rock mass. Furthermore, the calculation of the model is, also, put forward. The numerical simulation programs of groundwater movement in fractured rock mass are explored and developed by the author. The programs are involved in preprocess program Disc.for, calculation program Netw.for, and post-process program Vector.for, which can be used independently or together.According to research problems, complete couple of inhomogeneous anisotropy is made in fractured media. Compared it with traditional couple, the couple methods adequately takes randomness of fractured geometrical characteristics into account. There are two couples for different problems. One is couple of anisotropy media, that is to say, flow movement of artery fractures is described by discrete fractured network model. At the same time, it of ramification fractures and pore by equivalent continuous media model. The other is couple of inhomogeneity. It divides research region into many parts according to growth of fractures. And different mathematical models are used in different parts, which is domain decomposition algorithm.A chaos-genetic hybrid numerical algorithm of model parameters identification is putforward in fractured rock mass. It combines the advantages of chaos optimization and geneticalgorithm and expands range of search. Further, the method is of ability of jumping localoptimization. Cases show it can search the optimization values of objection function quickly.Modified stochastic walk method and emulation simulation technique are applied to
modeling solute transport in fractured network. Time step of the former is adjusted automatically, which can avoid artificial factors of defining time step, as rationality of time step has an important effect on simulation results. It is usually applied to simulation of single and planar network fracture. The latter makes full use of the laws of probability statistics, and mainly applied to simulation of planar and three dimension network fractures.At last, constituting model and using methods are applied to practical engineering, and satisfactory results are obtained.
基于裂隙几何要素的统计特征，应用Monte-Carlo方法随机生成裂隙网络系统。以裂隙交叉处作为节点，节点与节点之间的裂隙当作线单元，根据单裂隙立方体定律和质量守恒原则，建立了裂隙网络中水流运动的数学模型，并推导了数学模型的数值解法。同时自行开发研制了岩体裂隙地下水流数值模拟程序，主要由前处理部分程序Disc．for，计算程序Netw．for和后处理程序Vector．for组成，可以单独使用，也可以结合起来使用。
根据研究的实际问题进行了裂隙介质非均质各向异性的全耦合，与传统的耦合方法相比，该方法充分考虑了裂隙面几何要素的随机性。主要有两种耦合方式：其一是介质各向异性耦合，即用离散裂隙网络模型描述主干裂隙中的水流运动，用等效连续介质模型描述次要裂隙和孔隙中的水流运动。其二是非均质耦合，将研究区域按裂隙发育的情况进行分区，不同的分区使用不同的数学模型—区域分解算法。
提出了一种裂隙岩体模型参数识别的混沌遗传混合优化方法，该方法结合了混沌优化和遗传算法的优点，增大了搜索的范围又具备跳出局部最优的能力，算例表明混合优化方法很快能搜索到目标函数的最优值。
分别应用了改进的随机步行法和仿真模拟技术来模拟裂隙网络中的溶质运移，前者中时间步长采用自动调整的方式，避免了时间步长选得不合理而导致模拟结果的不准确，主要应用于单裂隙和平面网络裂隙的模拟；后者基于概率统计的方法进行研究，主要应用于平面和三维裂隙网络中。
将所建立的水流模型和使用的方法应用到实际王程中，取得了满意的结果。
In the paper, based on concrete engineering, laws of flow and solute transport are researched in fractured media. Some aspects involved in model constitution, methods innovation and engineering application are discussed detailedly. Furthermore, these contents are analyzed in single fracture and network fracture scales. Simultaneously, in the course of constituting model and using methods, randomness of geological and hydro-geological features, physical parameters, is taken into account. As a result, some beneficial results are obtained.Based on the statistic characteristics of fractured geometrical elements, fracture network system is made by the Monte-Carlo method. Fracture intersection points are acted as nodes, and fractures between nodes are regarded as linear element. According to cubic law of single fracture and mass conservation principle in fracture network, the seepage mathematics model for discrete fractured network is developed in fractured rock mass. Furthermore, the calculation of the model is, also, put forward. The numerical simulation programs of groundwater movement in fractured rock mass are explored and developed by the author. The programs are involved in preprocess program Disc.for, calculation program Netw.for, and post-process program Vector.for, which can be used independently or together.According to research problems, complete couple of inhomogeneous anisotropy is made in fractured media. Compared it with traditional couple, the couple methods adequately takes randomness of fractured geometrical characteristics into account. There are two couples for different problems. One is couple of anisotropy media, that is to say, flow movement of artery fractures is described by discrete fractured network model. At the same time, it of ramification fractures and pore by equivalent continuous media model. The other is couple of inhomogeneity. It divides research region into many parts according to growth of fractures. And different mathematical models are used in different parts, which is domain decomposition algorithm.A chaos-genetic hybrid numerical algorithm of model parameters identification is putforward in fractured rock mass. It combines the advantages of chaos optimization and geneticalgorithm and expands range of search. Further, the method is of ability of jumping localoptimization. Cases show it can search the optimization values of objection function quickly.Modified stochastic walk method and emulation simulation technique are applied to
modeling solute transport in fractured network. Time step of the former is adjusted automatically, which can avoid artificial factors of defining time step, as rationality of time step has an important effect on simulation results. It is usually applied to simulation of single and planar network fracture. The latter makes full use of the laws of probability statistics, and mainly applied to simulation of planar and three dimension network fractures.At last, constituting model and using methods are applied to practical engineering, and satisfactory results are obtained.
引文
[1] 陈洪凯．裂隙岩体渗流研究现状(Ⅰ)[J]．重庆交通学院学报，1996，15(1)：55-60
[2] 周志芳．岩体地下水运动模拟的理论与应用研究[D]．南京大学博士论文，1998．12，21-23
[3] Long C S, Gilmour P, Witherspoon P. A model for steady fluid flow in random three-dimensional networks of disk-chaped fractures[J]. Water Resour Res, 1985, 21(8): 1105-1115
[4] Dershowitz W S, Gordon B M, Kaffitsas J C. A new three dimensional model for flow of fractured rock[J]. Men Int Assoc Hydrogeol. 1985, 17: 441-448
[5] 万力，李定方，李吉庆．三维裂隙网络的多边形单元渗流模型[J]．水利水运科学研究．1993(4)：347-353
[6] 王洪涛，李永祥．三维随机裂隙网络非稳定渗流模型[J]．水利水运科学研究．1997(2)：139-146
[7] Elsworth. Hybrid boundary element-finite element analysis procedure for fluid flow simulation in fractured rock masses[J]. Int. J. Numer. Awal. Meth. Geomech., 1986a (10): 569-584
[8] Johan andersson, Bjorn Dverstorp Conditional simulations of fluid flow in three-dimensional networks of discrete fracture[J]. Water Resour. Res., 1987, 23(10): 1876-1886
[9] C. Cacas, E. Ledoux, G de Marsily, and B. Tillie. Modeling fracture flow with a stochastic discrete fracture network: calibration and validation[J]. Water Resour. Res., 1990, 26(3): 479-489
[10] A. WILLE NORDQVIST, Y. W. TSANG, ETC. A variable aperture fracture network model for flow and transport in fractured rocks[J]. Water Resour. Res., 1992, 28(6): 1703-1713
[11] Bjorn Dverstorp, Johan Andersson and Wille Ndqvist. Discrete fracture network interpretation of field tracer migration in sparsely fractured rock[J]. Water Resour. Res., 1992, 28(9): 2327-2343
[12] Dershowitz W. S. and C. Fidelibus. Derivation of equivalent pipe network ananogues for three-dimensional discrete fracture networks by the boundary element method[J]. Water Resour. Res., 1999, 35(9): 2685-2691
[13] 王恩志．岩体裂隙的网络分析及渗流模型[J]．岩石力学与工程学报，1993，12(3)：214-221
[14] 王恩志，王洪涛，孙役．双重裂隙系统渗流模型研究[J]．岩石力学与工程学报．2002，17(4)：400-406
[15] 毛昶熙，段祥宝，李定方．网络模型程序化及其应用[J]．水利水运科学研究，1994，(3)：197-209
[16] 仵彦卿，张倬元．岩体水力学导论[M]．西南交通火学出版社，成都：1994．10，45-65
[17] 切尔内绍夫．盛志浩，田开铭译．水在裂隙网络中运动[M]．北京：1987
[18] 刘中，张有天．有自由面三维裂隙网络渗流分析[J]．水利学报，1996(6)：34-38
[19] 杨太华，孙钧．岩体裂隙非规则几何水力特性研究[J]．岩土工程学报，1997，19(4)：10-14
[20] 汪卫明，徐明毅，陈胜宏．复杂边界条件下的岩体网络渗流分析[J]．岩石力学与工程学报．2001，20(4)：473-476
[21] 王恩志，孙役，黄远智．三维离散裂隙网络渗流模型与实验模拟[J]．水利学报，2002(5)：37-40
[22] Taylor, G. R. Dispersion of souble matter in solvent flowing slowly through a tube[J]. Proc. R. Soc. London A. 1953, 219: 186-203
[23] Aris, R. On the dispersion of a solute in a fluid flow through a tube[J]. Proc. R. Soc. London A. 1956, 235: 67-77
[24] Gill. W. N. and R. Sankarasubramanian. Exact analysis of unsteady convective diffusion[J]. Proc. R. Soc. London A. 1970, 316: 341-350
[25] John, L. E. and A. E. De Gance. Dispersion approximation to the multicomponent convective diffusion equation for chemically active system[J]. Chem. Eng. Sci,. 1975, 30: 1065-1067
[26] Sankarasubramanian R. and W. N. Gill, Unsteadu convective diffusion with interphase mas transfer[J]. Proc. R. Soc. London A. 1973, 333: 115-132
[27] De Gance. A. E., and L. E. Johns. The theory of dispersion of chemically active solutes in a rectilinear flow field[J]. Appl. Sci. Res., 1978a, 34: 189-225
[28] De Gance. A. E., and L. E. Johns. On the dispersion coefficients for Poiseuille flow in a circular cylinder[J]. Appl. Sci. Res., 1978b, 34: 227-258
[29] Russell L D, Harihar Rajaram and Glass R J. Solute transport in a variable aperture fractures: An investigation of the relative importance of Taylor dispersion and macrodispresion[J]. Water Resour. Res., 2000, 36(7): 1611-1625
[30] Golay M. J. E. Theory of chromatography in open and coated tubular columns with roundand rectangular cross-section[J]. Gas Chromatography, 1958, 5: 36-58
[31] Start J. L., Y. Parlange, B. L. Sawhney, and C. R. Frink. Diffusivity of solute in absorbing porous media, in surface and subsurface hydrology[M]. Fort Collins: Water resource Publ., 1979, 512-521
[32] Home R. N. and F. Rodriguez. Dispersion in tracer flow in geothermal systems[J]. Geophs. Res. Lett., 1983, 10(4): 289-292
[33] Brown S. R. and C. H. Scholz. Closure of random elastic surfaces in contact[J]. Geophs. Res., 1985, 90: 5531-5545
[34] Pyrak L. R. and N. G. Cook. Determination of fracture void geometry and contact area at different effective stress[J]. Eos Trans. AGU, 1985, 66(46): 903-908
[35] Neretnieks I. Diffusion in rock matrix: An important factor in radionuclide retardation?[J]. Geophs. Res., 1980, 85: 4379-4397
[36] Neretnieks I., T. Eriksen and P. Tahtinen. Tracer movement in a single fissure in granitic rock: some experimental result and their interpretation[J]. Water Resour. Res., 1982, 18(4): 849-858
[37] 李春江，陈式，林漳基等．花岗岩单裂隙中核素迁移的研究：弥散系数的测定[J]．核化学与放射化学．1999，21(3)：165-170
[38] 李春江，郭志明，林漳基．花岗岩体单裂隙中核素~(125)Ⅰ~-、~(134)Cs~+的弥散渗透实验[J]．水文地质工程地质．1999，35(6)：45-47
[39] 苏锐，李春江，王驹等．花岗岩体单裂隙中核素迁移数学模型：扩散模型及其有限单元法解[J]．核化学与放射化学．2000，22(2)：80-86
[40] Edson W. and Thomas H. Transport simulation with stochastic aperture for a single fracture comparison with a laboratory experiment[J]. Water Resour. Res., 2002, 38(1): 19-32
[41] Vandergraaf T. T. D. M. Grondin and D. J. Drew. Laboratory radionuclide migration experiments at a scale of one meter[J]. Mater. Res. Soc. Symp. Proc., 1988, 112: 159-168
[42] Laurence C. Hull, John D. Miller, and Tom M. Clemo. Laboratory and simulation studies of solute transport in fracture networks [J]. Water Resour. Res., 1987, 23(8): 1505-1513
[43] Witherspoon P. A., J. S. Y. Wang and K. Iwai et al. Validity of cubic law for fracture flow in a deformable rock fracture. Water Resour. Res., 1980, 16(6): 1016-1024
[44] Rasmusion A. and I. Neretnieks. Radionuclide transport in fast channels in crystalline rock[J]. Water Resour. Res., 1986, 22(8): 1247-1256
[45] Heath M. J. Solute migration experiments in fractured granite, South West England[J]. Proceedings of a joint CEC-NEA Workshop. 1985, 5: 191-200
[46] Bourke P. J. Channeling of flow through fractures in rock[J]. Proceedings of GEOVAL-87 International Symposium, Swedish Nuclear Power Inspectorate. Stockholm, 1987.
[47] Novakowski K. S., G. V. Evans D. A. Lever and K. G. Raven. A field example of measuring hydrodynamic dispersion in a single fracture[J]. Water Resour. Res., 1985, 21(8): 1165-1174
[48] Raven K. G. K. S. Novakowski and P. A. Lapcevic. Interpretation of field tracer tests of a single fracture using a transient solute storage model[J]. Water Resour. Res., 1988, 24(12): 2019-2032
[49] Shapiro A. M. and J. R. Nicholas. Assessing the validity of the channel model of fracture aperture under field conditions[J]. Water Resour. Res., 1989, 25(5): 817-828
[50] Moreno L. Y., W. Tsang, C. F. Tsang 等. Flow and tracer transport in a single fracture: A stochastic model and its relation to some field observations[J]. Water Resour. Res., 1988, 24(12): 2033-2048
[51] Dverstorp B., J. Andersson and W. Nordgvist. Discrete fracture network interpretation of field tracer migration in sparsely fractured rock[J]. Water Resour. Res., 1992, 28(9): 2327-2343
[52] Park and Lee. Effects of junction transfer characteristics on transport in fracture networks. Water Resour. Res., 2001, 37(4): 909-923
[53] Wilson C. R. and P. A. Witherspoon. Flow interference effects at fracture intersections[J]. Water Resour. Res.,1976,12(1): 102-104
[54] Schwartz F. W. L. Smith and A. S. Crowe. A stochastic analysis of macroscopic dispersion in fractured media[J]. Water Resour. Res., 1983, 19(5): 1253-1265
[55] Sahimi M. B., D. Hughes, and H. T. Davis. Dispersion in flow through porous media: one phase flow[J]. Chem. Eng.Sci., 1986,41(8): 2103-2122
[56] Schwartz F. W. and L. Smith. A continuum approach for modeling mass transport in fractured media[J]. Water Resour.Res., 1988, 24(8): 1360-1372
[57] Robinson J. W and J. E. Gale. A laboratory and numerical inverstigation of solute transport in discontinous fracture systems[J]. Ground water, 1990, 28(1): 25-36
[58] Brian Berkowitz. Mass transport at fractures intersections: an evaluation of mixing models[J]. Water Resour.Res., 1994, 30(6): 1765-1773
[59] Cacas M. C, E. Ledoux, G de Marsily et al. Modeling fracture flow with a stochastic discrete fracture network:Calibration and validation, 2, The transport model[J]. Water Resour. Res., 1990b, 26(6): 491-500
[60] Park Y. J., K. Lee and B.Berkowitz. Transport and intersection mixing in random fracture networks with power law length distribution[J]. Water Resour. Res.,2001, 37(10): 2493-2501
[61] Huseby. O.,J. F. Thovert and P. M. Adler. Dispersion in three dimensional fracture networks[J]. Phys. Fluid,2001,13(3): 594-615
[62] Olivier Bour and Philippe Davy. On the connectivity of three-dimension fault networks[J]. Water Resour. Res., 1998,34(11): 2611-2622
[63] Stockman H. W, J. Johnson and S. R. Brown. Mixing at fracture intersections: influence of channel geometry and the Reynolds and Peclet numbers, Gephys. Res. Lett., 2001, 28(22): 4299-4302
[64] Yong Jin Park and Kang kan Lee. Transport behavior in three-dimensional fracture intersection[J]. Water Resour. Res.,2003,39(8): 1215-1223
[65] Brown S. R. Fluid flow through rock joints: The effect of surface roughness[J]. J. Gephys. Res., 1987, 92: 1337-1347
[66] Y. W. Tsang and C. F. Tsang. Flow and tracer transport in fractured media: a variable aperture channel model and its properties[J]. Water Resour. Res., 1988, 24(12): 2049-2060
[67] Silliman S. E. An interpretation of the difference between aperture estimates derived from hydraulic and tracer tests in a single fracture[J]. Water Resour. Res., 1989, 25(10): 2275-2283
[68] Russell L. Detwiler, Harihar Rajaram. Solute transport in variable-aperture fractures: an investigation of the relative importance of Taylor dispersion and macrodispersion[J]. Water Resour. Res., 2000, 36(7): 1611-1625
[69] Hull, L. C, J. D. Miller, and T.M. Clemo. Laboratory and simulation studies of solute transport in fracture networks[J].Water Resour. Res., 1987, 23(8): 55-63
[70] Ippolito, I., G Daccord, E. J. Hinch and J. P. Hulin, Echo tracer dispersion in model fractures with a rectangular geometry[J]. J. Contam. Hydrol., 1994(16): 87-108
[71] Moreno, L., Y. W. Tsang, C. F. Tsang. Flow and tracer transport in a single fracture: Astochastic model and its relation to some field observations[J]. Water Resour. Res., 1988, 24(12): 2033-2048
[72] Thompson, M. E., Numerical simulation of solute transport in rough fractures[J]. J. Geophys. Res., 1991(96,B3):4157-4166
[73] Thompson, M. E., and S.R. Brown. The effect of anisotropic surface roughness on flow and transport in fractures[J].J. Geophys. Res., 1991(96,B13): 21923-21932
[74] Stockman, H. W., Alattice gas study of retardation and dispersion in fractures: Assessment of errors from desorption kinetics and buoyancy[J]. Water Resour. Res., 1997, 33(8): 1823-1831
[75] Roux, S., Plouraboue and J. P. Hulin. Tracer dispersion in rough open cracks[J]. Transp. Porous Media, 1998(32):97-116
[76] Gutfraind, R., I. Ippolito and A. Hansen. Study of tracer dispersion in self-affine fractures using lattices-gas automata[J]. Phys. Fluids, 1995,7(8): 1938-1948
[77] Koplic, J., I. Ippolito and J.P. Hulin. Tracer dispersion in rough channels: A two-dimensional numerical study[J]. Phys.Fluids A, 1993,5(6): 1333-1343
[78] Keller, A. A., P. V. Roberts and P.K. Kitankidis. Prediction of single phase transport parameters in a variable aperture fracture[J]. Geophys. Res. Lett., 1995(22), 1425-1428
[79] Keller, A. A., P. V. Roberts and M. J. Blunt. Effect of fracture aperture variations on the dispersion of contaminants[J].Water Resour. Res., 1999, 35(1): 55-63
[80] Dronfield, D. G, and S. E. Silliman. Velocity dependence of dispersion for transport through a single fracture of variable roughness[J]. Water Resour. Res., 1993, 29(10): 3477-3483
[81] Kennedy and Lennox. A control volume model of solute transport in a single fracture[J]. Water Resour. Res., 1995,31(2): 313-322
[82] Barkholder H. C. Methods and data for predicting nuclide migration in geologic media[J]. paper presented at International Symposium on Management of Watstes from the LWR Fuel Cycle, Denver, Colo., 1976
[83] Freeze R. A. and J. A. Cherry. Groundwater, 604pp., Prentice-Hall, Englewood Cliffs N. J., 1979
[84] B. Berkowitz and J. Zhou. Reactive solute transport in a single fracture[J]. Water Resour. Res., 1996, 32(4): 901-913
[85] Christoph wells and Leslie Smith. Retardation of sorbing solutes in fractured media[J]. Water Resour. Res., 1994, 30(9):2547-2563
[86] Vandergraaf T. T., D. M. Grandin and D. J. Drew. Laboratory radionuclide migration experiments at a scale of one meter[J]. Mater. Res. Soc. Symp. Proc. 1988(112): 159-168
[87] Neretnieks. I., T. Eriksen and P.Tahtinen. Tracer movement in a single fissure in granitic rock: some experimental results and their interpretation[J]. Water Resour. Res., 1982, 18(2): 849-858
[88] Vandergraaf T. T.and D. J. Drew. Laboratory studies of radionuclide transport in fractural crystalline rock. Paper presented at 3rd international symposium on advanced nuclear energy research, Jpn. At. Energy Res. Inst. Mito Sity.1991
[89] Cvetkovic V. D and A. M. Shapiro. Mass arrival of sorptive solute in heterogenous porous media[J]. Water Resour.Res., 1990, 26(9): 2057-2067
[90] Valocchi A. J. Spatial moment analysis of transport of kinetically adsorbing solute through stratified aquifers[J]. Water Resour. Res., 1989, 25(1): 273-279
[91] De Josselin de Jong. Dispersion of a point injection in a anisotropic porous medium[J]. Published report 60. pp., N. M.Inst. Of Nim and Technol. Socorro, 1972
[92] Way and Mckee. Restoration of insitu coal gasification sites from naturally occering flow and dispersion[J], In situ ,1981, 5(2): 77-101
[93] A.Wille nordqvist, Y.W. Tsang, C.F. Tsang. A variable aperture fracture network model for flow and transport in fractured rocks[J]. Water Resour. Res.,1992, 28(6): 1703-1713
[94] Tsang Y. W. and C. F. Tsang. Channel model of flow through fractured media[J]. Water Resour. Res.,1987, 23(1):467-479
[95] Jane C. S. Long, Peggy Gilmour, and Paul A. Witherpoon. A model for steady fluid flow in random three dimensional networks of disc-shaped fractures[J]. Water Resour. Res., 1985,21(8): 1105-1115
[96] Englman, R., Y. Gur, and Z. Jaeger, Fluid flow through a crack network in rocks[J]. J. Appl.Mech., 1983, 50, 707-711
[97] Robinson, P. C, Numerical calculations of critical densities for lines and planes[J], J. Phys. A Math Gen., 1984(17):2823-2830
[98] Hestir , K., and J. C. S. Long. Analytical expressions for the permeability of random two-dimensional Possion fracture networks based on regular lattice percolation and equivalent media theories[J]. J. Geophys. Res., 1990(95):21565-21581
[99] Balberg, I., B. Berkowitz, and G E. Drachsler, Application of a percolation model to flow in fractured hard rocks[J], J. Geophys. Res., 1991(96): 10015-10021
[1
[100] Brekowitz, B., and I. Balberg. Percolation theory and its application to groundwater hydrology[J]. Water Resour. Res., 1993, 29(2): 775-794
[101] Brekowitz, B. Analysis of fracture network connectivity using percolation theory[J]. Math. Geol., 1995(27): 467-483
[102] Gennady M. B. Berkowitz and H. Scher. Structure, flow and generalized conductivity scaling in fracture networks. Water Resour. Res., 1998, 34(9): 2103-2121
[103] Young-Jin Pack and Kang-Kun Lee. Analytical solutions for solute transfer characteristics at continuous fracture junctions[J]. Water Resour. Res., 1999: 35(5), 1531-1537
[104] Gelhar L. W. Applications of stochastic models to solute transport in fractured rocks, Report Swed. Nucl. Fuel and Waste Manage. Co., Stockholm, 1987
[105] Gelhar L. W. Stochastic Subsurface Hydrology[M]. Prentice-Hall, Englewood Cliffs, N. J., 1993
[106] Andrew R. and D. Elsworth. Physical and numerical studies of a fracture system model[J]. Water Resour. Res., 1989, 25(3): 457-462
[107] 胡云进，速宝玉等．裂隙岩体非饱和渗流综述[J]．河海大学学报．2000，28(1)：40～45．
[108] 周志芳，腾建仁．三峡工程大坝坝基渗控分析[J]．岩石力学与工程学报．2001(9)：700-704
[109] 张倬元，王士天，王兰生．工程地质分析原理[M]．北京：地质出版社，1994，41-41
[110] Lomize G. M. Flow in fractured rocks[M]. Mosoow: Gesenergoizdat, 1951
[111] Louis C. A study of groundwater flow in jointed rock and its influence on the stability of rock masses[J]. In: Muler, eds. Rock Mech Res Rep 10, London: Imp. Coll., 1969
[112] Neuzil C. E., Tracy J V. Flow through fractures[J]. Water Resour Res., 1981, 17(1): 191-194
[113] Elsworth D. and Goodman R E. Characterization of rock fissure hydraulic conductivity using idealized wall roughness profiles[J]. Int. J Rock Mech Min Sci & Geomech Abstr, 1986, 23(3): 233-243
[114] Barton N. Bandis S., and Bakhta K. Strength deformation and conductivity coupling of rock joints[J]. Int. J Rock Mech Min Sci & Geomech Abstr, 1985, 22(3): 121-140
[115] Walsh J. B. Effect of porepressure and confining pressure on fracture permeability[J]. Int. J Rock Mech Min Sci & Geomech Abstr, 1981, 18: 429-435
[116] 王媛，速宝玉，徐志英．粗糙裂隙渗流及其受应力作用的计算机模拟[J]．河海大学学报，1997，25(6)：80-85
[117] 周志芳，王锦国．裂隙介质水动力学[M]．北京：中国水利水电出版社，2004，88-114
[118] 仵彦卿．岩体水力学基础(五)[J]．水文地质工程地质，1997，(5)：41-45
[119] 陈和群，彭宣茂．有限元法微机程序与图形处理[M]．南京：河海大学出版社．1992，219-221
[120] 黄勇，周志芳．岩体渗流模拟的二维随机裂隙网络模型[J]．河海大学学报．2004(1)：91-94
[121] C. Cacas, E. Ledoux, G de marsily, B. illie. Modeling fracture flow with a stochastic discrete fracture network: calibration and validation 1. the flow model[J]. Water Resour. Res., 1990, 26(3): 479-489
[122] Shemin G. E. A governing equation for fluid flow in rough fractures[J]. Water Resour. Res., 1997, 33(1): 53-61
[123] Y. W. Tsang. The effect of tortuosity on fluid flow through a single fracture[J]. Water Resour. Res., 1984, 20(9): 1209-1215
[124] 杨米加，陈明雄，贺永年．单裂隙曲折率对流体渗流过程的影响[J]．岩土力学．2001，22(1)：78-82
[125] Olivier bour, Philippe davy. Connectivity of random fault networks following a power law fault length distribution[J]. Water Resour. Res., 1997, 33(7): 1567-1583
[126] Carl E. Renshaw. Influence of subcritical fracture growth on the connectivity of fracture networks[J]. Water Resour. Res., 1996, 32(6): 1539-1530
[127] 黄国明，黄润秋．用窗口法估计不连续面的连通率[J]．水文地质工程地质．1998(6)：27-30
[128] 杜景灿，汪小刚，陈祖煜．结构面倾角对节理岩体的连通特性和综合抗剪强度的影响[J]．水利学报．2002(5)：41-46
[129] 王媛，速宝玉，徐志英．裂隙岩体渗流模型综述[J]．水科学进展．1996，7(3)：276-281
[130] 王洪涛．裂隙网络渗流与离散元耦合分析充水岩质高边坡的稳定性[J]．水文地质工程地质．2000(2)：30-33
[131] 王媛，速宝玉，徐志英．三维裂隙岩体渗流耦合模型及其有限元模拟[J]．水文地质工程地质．1995(3)：1-5
[132] 王洪涛，聂永丰，李雨松．耦合岩体主干裂隙和网络状裂隙渗流分析及其应用[J]．清华大学学报．1998，38(12)：23-26
[133] 王恩志，王洪涛，孙役．双重裂隙系统渗流模型研究[J]．岩石力学与工程学报．2001，17(4)：400-406
[134] 杜广林，周维垣，赵吉东．裂隙介质中多重裂隙网络渗流模型[J]．岩石力学与工程学报．2000，19(增)：1014-1018
[135] 宋丽红，杨天行．边界元区域分解算法在地下水中的应用[J]．世界地质．2002，21(1)：50-52
[136] 吕涛，石济民，林振宝．区域分解算法—偏微分方程数值解新技术[M]．北京：科学出版社，1991
[137] 严仁军，龚朴，黄玉盈．基于区域分解算法的非均匀介质的反分析计算[J]．武汉交通科技大学学报．1998，22(3)：277-279
[138] 朱景辉．有限差分法中的区域分解算法[J]．厦门大学学报．1995，34(4)：517-524
[139] 卫加宁，章社生，郭庆平等．预处理性质及其在非重叠区域分解算法中应用[J]．武汉理工大学学报．2001，23(9)：74-76
[140] 王浩然．基于区域分解算法的地下水耦合模型与并行模拟技术[D]．博士学位论文．南京大学．2002
[141] 周志芳等．有限分析法在反求裂隙岩体渗透张量中的应用[J]．水利学报．1993(5)：68-75
[142] 周志芳，杨建，杨建宏．确定缓倾结构面渗透性参数的现场试验法[J]．工程地质学报．1999，7(4)：375-379
[143] 王登刚，刘迎曦，李守巨．非线性最优化问题的一种混合解法[J]．工程力学，2001，18(3)：61-66
[144] 刘盛松，侯志俭，蒋传文．基于混沌优化和BFGS方法的最优潮流算法[J]．电力系统自动化，2002，(10)：13-17
[145] 李英，胡云昌，曹宏铎．加速混沌优化方法及其应用[J]．系统工程学报，2002，17(1)：41-44
[146] 周激流，丁晶，金菊良．一种新型遗传算法及其在暴雨强度公式参数优化中的应用研究[J]．四川大学学报(自然科学版)，2000，37(4)：543-547
[147] 郭惠昕．混沌遗传优化算法及其程序研制[J]．常德师范学院学报(自然科学版)，2002，14(4)：40-42
[148] 金忠青，周志芳．工程水力学反问题[M]．南京：河海大学出版社．1997，59-75
[149] 黄勇，周志芳．裂隙网络介质地下水流运动参数反演分析[J]．水电能源科学．2004(2)：12-15
[150] 王军辉．小尺度裂隙岩体地下水溶质运移模拟研究[D]．河海大学硕士论文．2001，1-3
[151] 王锦国，周志芳．裂隙岩体地下水溶质运移的尺度问题[J]．水科学进展．2002，13(2)：239-245
[152] 成建梅，胡进武．饱和水流溶质运移问题数值解法综述[J]．水文地质工程地质．2003(2)：99-106
[153] 程诚，吴吉春，葛锐等．单裂隙介质中的溶质运移研究综述[J]．水科学进展．2003，14(4)：502-508
[154] Scott C. James, Constantinos V. Chrysikopoulos. An efficient particle tracking equation with specified spatial step for the solution of the diffusion equation[J]. Chemical Engineering Science, 2001, 56. 6535-6543
[155] Uffink, G. J. M. Modeling of solute transport with the random walk method [J]. InE. Custodio, A Gurgui, J. P. Lobo Ferreira, 1988: 247-265
[156] Thompson, A. F. B., and L. W. Gelhar. Numerical simulation of solute transport in three-dimensional, randomly heterogeneous porous media[J]. Water Resour. Res., 1990: 26(10), 2541-2562
[157] Franklin W. schwartz and Leslie Smith. A continuum approach for modeling mass transport in fractured media[J]. Water Resour. Res., 1988, 24(8): 1360-1372
[158] Gennady margolin, Brian Berkowitz and Harvey scher. Structure, flow and generalized conductivity scaling in fracture networks[J]. Water Resour. Res., 1998, 34(9): 2103-2121
[159] R. zhang, K. Huang, And M. T. Van Genuc. An efficient Eulerian-Lagrangian method for solving solute transport problems in steady and transient flow fields[J]. Water Resour. Res., 1993, 29(12): 4131-4138
[160] Tory, E. M. Stochastic sedimentation and hydrodynamic diffusion [J]. Chemical Engineering Journal, 2000, 80: 81-89
[161] Young-Jin Pack, Jean-Raynald de Dreuzy. Transport and intersection mixing in random fracture networks with power law length distributions[J]. Water Resour. Res., 2001 : 37(10), 2493-2501
[162] Young-Jin Pack and Kang-Kun Lee. Analytical solutions for solute transfer characteristics at continuous fracture junctions[J]. Water Resour. Res., 1999: 35(5), 1531-1537
[163] 冯允成，吕春莲．随机网络及其应用[M]．北京：北京航空学院出版社．1987：1-100
[2] 周志芳．岩体地下水运动模拟的理论与应用研究[D]．南京大学博士论文，1998．12，21-23
[3] Long C S, Gilmour P, Witherspoon P. A model for steady fluid flow in random three-dimensional networks of disk-chaped fractures[J]. Water Resour Res, 1985, 21(8): 1105-1115
[4] Dershowitz W S, Gordon B M, Kaffitsas J C. A new three dimensional model for flow of fractured rock[J]. Men Int Assoc Hydrogeol. 1985, 17: 441-448
[5] 万力，李定方，李吉庆．三维裂隙网络的多边形单元渗流模型[J]．水利水运科学研究．1993(4)：347-353
[6] 王洪涛，李永祥．三维随机裂隙网络非稳定渗流模型[J]．水利水运科学研究．1997(2)：139-146
[7] Elsworth. Hybrid boundary element-finite element analysis procedure for fluid flow simulation in fractured rock masses[J]. Int. J. Numer. Awal. Meth. Geomech., 1986a (10): 569-584
[8] Johan andersson, Bjorn Dverstorp Conditional simulations of fluid flow in three-dimensional networks of discrete fracture[J]. Water Resour. Res., 1987, 23(10): 1876-1886
[9] C. Cacas, E. Ledoux, G de Marsily, and B. Tillie. Modeling fracture flow with a stochastic discrete fracture network: calibration and validation[J]. Water Resour. Res., 1990, 26(3): 479-489
[10] A. WILLE NORDQVIST, Y. W. TSANG, ETC. A variable aperture fracture network model for flow and transport in fractured rocks[J]. Water Resour. Res., 1992, 28(6): 1703-1713
[11] Bjorn Dverstorp, Johan Andersson and Wille Ndqvist. Discrete fracture network interpretation of field tracer migration in sparsely fractured rock[J]. Water Resour. Res., 1992, 28(9): 2327-2343
[12] Dershowitz W. S. and C. Fidelibus. Derivation of equivalent pipe network ananogues for three-dimensional discrete fracture networks by the boundary element method[J]. Water Resour. Res., 1999, 35(9): 2685-2691
[13] 王恩志．岩体裂隙的网络分析及渗流模型[J]．岩石力学与工程学报，1993，12(3)：214-221
[14] 王恩志，王洪涛，孙役．双重裂隙系统渗流模型研究[J]．岩石力学与工程学报．2002，17(4)：400-406
[15] 毛昶熙，段祥宝，李定方．网络模型程序化及其应用[J]．水利水运科学研究，1994，(3)：197-209
[16] 仵彦卿，张倬元．岩体水力学导论[M]．西南交通火学出版社，成都：1994．10，45-65
[17] 切尔内绍夫．盛志浩，田开铭译．水在裂隙网络中运动[M]．北京：1987
[18] 刘中，张有天．有自由面三维裂隙网络渗流分析[J]．水利学报，1996(6)：34-38
[19] 杨太华，孙钧．岩体裂隙非规则几何水力特性研究[J]．岩土工程学报，1997，19(4)：10-14
[20] 汪卫明，徐明毅，陈胜宏．复杂边界条件下的岩体网络渗流分析[J]．岩石力学与工程学报．2001，20(4)：473-476
[21] 王恩志，孙役，黄远智．三维离散裂隙网络渗流模型与实验模拟[J]．水利学报，2002(5)：37-40
[22] Taylor, G. R. Dispersion of souble matter in solvent flowing slowly through a tube[J]. Proc. R. Soc. London A. 1953, 219: 186-203
[23] Aris, R. On the dispersion of a solute in a fluid flow through a tube[J]. Proc. R. Soc. London A. 1956, 235: 67-77
[24] Gill. W. N. and R. Sankarasubramanian. Exact analysis of unsteady convective diffusion[J]. Proc. R. Soc. London A. 1970, 316: 341-350
[25] John, L. E. and A. E. De Gance. Dispersion approximation to the multicomponent convective diffusion equation for chemically active system[J]. Chem. Eng. Sci,. 1975, 30: 1065-1067
[26] Sankarasubramanian R. and W. N. Gill, Unsteadu convective diffusion with interphase mas transfer[J]. Proc. R. Soc. London A. 1973, 333: 115-132
[27] De Gance. A. E., and L. E. Johns. The theory of dispersion of chemically active solutes in a rectilinear flow field[J]. Appl. Sci. Res., 1978a, 34: 189-225
[28] De Gance. A. E., and L. E. Johns. On the dispersion coefficients for Poiseuille flow in a circular cylinder[J]. Appl. Sci. Res., 1978b, 34: 227-258
[29] Russell L D, Harihar Rajaram and Glass R J. Solute transport in a variable aperture fractures: An investigation of the relative importance of Taylor dispersion and macrodispresion[J]. Water Resour. Res., 2000, 36(7): 1611-1625
[30] Golay M. J. E. Theory of chromatography in open and coated tubular columns with roundand rectangular cross-section[J]. Gas Chromatography, 1958, 5: 36-58
[31] Start J. L., Y. Parlange, B. L. Sawhney, and C. R. Frink. Diffusivity of solute in absorbing porous media, in surface and subsurface hydrology[M]. Fort Collins: Water resource Publ., 1979, 512-521
[32] Home R. N. and F. Rodriguez. Dispersion in tracer flow in geothermal systems[J]. Geophs. Res. Lett., 1983, 10(4): 289-292
[33] Brown S. R. and C. H. Scholz. Closure of random elastic surfaces in contact[J]. Geophs. Res., 1985, 90: 5531-5545
[34] Pyrak L. R. and N. G. Cook. Determination of fracture void geometry and contact area at different effective stress[J]. Eos Trans. AGU, 1985, 66(46): 903-908
[35] Neretnieks I. Diffusion in rock matrix: An important factor in radionuclide retardation?[J]. Geophs. Res., 1980, 85: 4379-4397
[36] Neretnieks I., T. Eriksen and P. Tahtinen. Tracer movement in a single fissure in granitic rock: some experimental result and their interpretation[J]. Water Resour. Res., 1982, 18(4): 849-858
[37] 李春江，陈式，林漳基等．花岗岩单裂隙中核素迁移的研究：弥散系数的测定[J]．核化学与放射化学．1999，21(3)：165-170
[38] 李春江，郭志明，林漳基．花岗岩体单裂隙中核素~(125)Ⅰ~-、~(134)Cs~+的弥散渗透实验[J]．水文地质工程地质．1999，35(6)：45-47
[39] 苏锐，李春江，王驹等．花岗岩体单裂隙中核素迁移数学模型：扩散模型及其有限单元法解[J]．核化学与放射化学．2000，22(2)：80-86
[40] Edson W. and Thomas H. Transport simulation with stochastic aperture for a single fracture comparison with a laboratory experiment[J]. Water Resour. Res., 2002, 38(1): 19-32
[41] Vandergraaf T. T. D. M. Grondin and D. J. Drew. Laboratory radionuclide migration experiments at a scale of one meter[J]. Mater. Res. Soc. Symp. Proc., 1988, 112: 159-168
[42] Laurence C. Hull, John D. Miller, and Tom M. Clemo. Laboratory and simulation studies of solute transport in fracture networks [J]. Water Resour. Res., 1987, 23(8): 1505-1513
[43] Witherspoon P. A., J. S. Y. Wang and K. Iwai et al. Validity of cubic law for fracture flow in a deformable rock fracture. Water Resour. Res., 1980, 16(6): 1016-1024
[44] Rasmusion A. and I. Neretnieks. Radionuclide transport in fast channels in crystalline rock[J]. Water Resour. Res., 1986, 22(8): 1247-1256
[45] Heath M. J. Solute migration experiments in fractured granite, South West England[J]. Proceedings of a joint CEC-NEA Workshop. 1985, 5: 191-200
[46] Bourke P. J. Channeling of flow through fractures in rock[J]. Proceedings of GEOVAL-87 International Symposium, Swedish Nuclear Power Inspectorate. Stockholm, 1987.
[47] Novakowski K. S., G. V. Evans D. A. Lever and K. G. Raven. A field example of measuring hydrodynamic dispersion in a single fracture[J]. Water Resour. Res., 1985, 21(8): 1165-1174
[48] Raven K. G. K. S. Novakowski and P. A. Lapcevic. Interpretation of field tracer tests of a single fracture using a transient solute storage model[J]. Water Resour. Res., 1988, 24(12): 2019-2032
[49] Shapiro A. M. and J. R. Nicholas. Assessing the validity of the channel model of fracture aperture under field conditions[J]. Water Resour. Res., 1989, 25(5): 817-828
[50] Moreno L. Y., W. Tsang, C. F. Tsang 等. Flow and tracer transport in a single fracture: A stochastic model and its relation to some field observations[J]. Water Resour. Res., 1988, 24(12): 2033-2048
[51] Dverstorp B., J. Andersson and W. Nordgvist. Discrete fracture network interpretation of field tracer migration in sparsely fractured rock[J]. Water Resour. Res., 1992, 28(9): 2327-2343
[52] Park and Lee. Effects of junction transfer characteristics on transport in fracture networks. Water Resour. Res., 2001, 37(4): 909-923
[53] Wilson C. R. and P. A. Witherspoon. Flow interference effects at fracture intersections[J]. Water Resour. Res.,1976,12(1): 102-104
[54] Schwartz F. W. L. Smith and A. S. Crowe. A stochastic analysis of macroscopic dispersion in fractured media[J]. Water Resour. Res., 1983, 19(5): 1253-1265
[55] Sahimi M. B., D. Hughes, and H. T. Davis. Dispersion in flow through porous media: one phase flow[J]. Chem. Eng.Sci., 1986,41(8): 2103-2122
[56] Schwartz F. W. and L. Smith. A continuum approach for modeling mass transport in fractured media[J]. Water Resour.Res., 1988, 24(8): 1360-1372
[57] Robinson J. W and J. E. Gale. A laboratory and numerical inverstigation of solute transport in discontinous fracture systems[J]. Ground water, 1990, 28(1): 25-36
[58] Brian Berkowitz. Mass transport at fractures intersections: an evaluation of mixing models[J]. Water Resour.Res., 1994, 30(6): 1765-1773
[59] Cacas M. C, E. Ledoux, G de Marsily et al. Modeling fracture flow with a stochastic discrete fracture network:Calibration and validation, 2, The transport model[J]. Water Resour. Res., 1990b, 26(6): 491-500
[60] Park Y. J., K. Lee and B.Berkowitz. Transport and intersection mixing in random fracture networks with power law length distribution[J]. Water Resour. Res.,2001, 37(10): 2493-2501
[61] Huseby. O.,J. F. Thovert and P. M. Adler. Dispersion in three dimensional fracture networks[J]. Phys. Fluid,2001,13(3): 594-615
[62] Olivier Bour and Philippe Davy. On the connectivity of three-dimension fault networks[J]. Water Resour. Res., 1998,34(11): 2611-2622
[63] Stockman H. W, J. Johnson and S. R. Brown. Mixing at fracture intersections: influence of channel geometry and the Reynolds and Peclet numbers, Gephys. Res. Lett., 2001, 28(22): 4299-4302
[64] Yong Jin Park and Kang kan Lee. Transport behavior in three-dimensional fracture intersection[J]. Water Resour. Res.,2003,39(8): 1215-1223
[65] Brown S. R. Fluid flow through rock joints: The effect of surface roughness[J]. J. Gephys. Res., 1987, 92: 1337-1347
[66] Y. W. Tsang and C. F. Tsang. Flow and tracer transport in fractured media: a variable aperture channel model and its properties[J]. Water Resour. Res., 1988, 24(12): 2049-2060
[67] Silliman S. E. An interpretation of the difference between aperture estimates derived from hydraulic and tracer tests in a single fracture[J]. Water Resour. Res., 1989, 25(10): 2275-2283
[68] Russell L. Detwiler, Harihar Rajaram. Solute transport in variable-aperture fractures: an investigation of the relative importance of Taylor dispersion and macrodispersion[J]. Water Resour. Res., 2000, 36(7): 1611-1625
[69] Hull, L. C, J. D. Miller, and T.M. Clemo. Laboratory and simulation studies of solute transport in fracture networks[J].Water Resour. Res., 1987, 23(8): 55-63
[70] Ippolito, I., G Daccord, E. J. Hinch and J. P. Hulin, Echo tracer dispersion in model fractures with a rectangular geometry[J]. J. Contam. Hydrol., 1994(16): 87-108
[71] Moreno, L., Y. W. Tsang, C. F. Tsang. Flow and tracer transport in a single fracture: Astochastic model and its relation to some field observations[J]. Water Resour. Res., 1988, 24(12): 2033-2048
[72] Thompson, M. E., Numerical simulation of solute transport in rough fractures[J]. J. Geophys. Res., 1991(96,B3):4157-4166
[73] Thompson, M. E., and S.R. Brown. The effect of anisotropic surface roughness on flow and transport in fractures[J].J. Geophys. Res., 1991(96,B13): 21923-21932
[74] Stockman, H. W., Alattice gas study of retardation and dispersion in fractures: Assessment of errors from desorption kinetics and buoyancy[J]. Water Resour. Res., 1997, 33(8): 1823-1831
[75] Roux, S., Plouraboue and J. P. Hulin. Tracer dispersion in rough open cracks[J]. Transp. Porous Media, 1998(32):97-116
[76] Gutfraind, R., I. Ippolito and A. Hansen. Study of tracer dispersion in self-affine fractures using lattices-gas automata[J]. Phys. Fluids, 1995,7(8): 1938-1948
[77] Koplic, J., I. Ippolito and J.P. Hulin. Tracer dispersion in rough channels: A two-dimensional numerical study[J]. Phys.Fluids A, 1993,5(6): 1333-1343
[78] Keller, A. A., P. V. Roberts and P.K. Kitankidis. Prediction of single phase transport parameters in a variable aperture fracture[J]. Geophys. Res. Lett., 1995(22), 1425-1428
[79] Keller, A. A., P. V. Roberts and M. J. Blunt. Effect of fracture aperture variations on the dispersion of contaminants[J].Water Resour. Res., 1999, 35(1): 55-63
[80] Dronfield, D. G, and S. E. Silliman. Velocity dependence of dispersion for transport through a single fracture of variable roughness[J]. Water Resour. Res., 1993, 29(10): 3477-3483
[81] Kennedy and Lennox. A control volume model of solute transport in a single fracture[J]. Water Resour. Res., 1995,31(2): 313-322
[82] Barkholder H. C. Methods and data for predicting nuclide migration in geologic media[J]. paper presented at International Symposium on Management of Watstes from the LWR Fuel Cycle, Denver, Colo., 1976
[83] Freeze R. A. and J. A. Cherry. Groundwater, 604pp., Prentice-Hall, Englewood Cliffs N. J., 1979
[84] B. Berkowitz and J. Zhou. Reactive solute transport in a single fracture[J]. Water Resour. Res., 1996, 32(4): 901-913
[85] Christoph wells and Leslie Smith. Retardation of sorbing solutes in fractured media[J]. Water Resour. Res., 1994, 30(9):2547-2563
[86] Vandergraaf T. T., D. M. Grandin and D. J. Drew. Laboratory radionuclide migration experiments at a scale of one meter[J]. Mater. Res. Soc. Symp. Proc. 1988(112): 159-168
[87] Neretnieks. I., T. Eriksen and P.Tahtinen. Tracer movement in a single fissure in granitic rock: some experimental results and their interpretation[J]. Water Resour. Res., 1982, 18(2): 849-858
[88] Vandergraaf T. T.and D. J. Drew. Laboratory studies of radionuclide transport in fractural crystalline rock. Paper presented at 3rd international symposium on advanced nuclear energy research, Jpn. At. Energy Res. Inst. Mito Sity.1991
[89] Cvetkovic V. D and A. M. Shapiro. Mass arrival of sorptive solute in heterogenous porous media[J]. Water Resour.Res., 1990, 26(9): 2057-2067
[90] Valocchi A. J. Spatial moment analysis of transport of kinetically adsorbing solute through stratified aquifers[J]. Water Resour. Res., 1989, 25(1): 273-279
[91] De Josselin de Jong. Dispersion of a point injection in a anisotropic porous medium[J]. Published report 60. pp., N. M.Inst. Of Nim and Technol. Socorro, 1972
[92] Way and Mckee. Restoration of insitu coal gasification sites from naturally occering flow and dispersion[J], In situ ,1981, 5(2): 77-101
[93] A.Wille nordqvist, Y.W. Tsang, C.F. Tsang. A variable aperture fracture network model for flow and transport in fractured rocks[J]. Water Resour. Res.,1992, 28(6): 1703-1713
[94] Tsang Y. W. and C. F. Tsang. Channel model of flow through fractured media[J]. Water Resour. Res.,1987, 23(1):467-479
[95] Jane C. S. Long, Peggy Gilmour, and Paul A. Witherpoon. A model for steady fluid flow in random three dimensional networks of disc-shaped fractures[J]. Water Resour. Res., 1985,21(8): 1105-1115
[96] Englman, R., Y. Gur, and Z. Jaeger, Fluid flow through a crack network in rocks[J]. J. Appl.Mech., 1983, 50, 707-711
[97] Robinson, P. C, Numerical calculations of critical densities for lines and planes[J], J. Phys. A Math Gen., 1984(17):2823-2830
[98] Hestir , K., and J. C. S. Long. Analytical expressions for the permeability of random two-dimensional Possion fracture networks based on regular lattice percolation and equivalent media theories[J]. J. Geophys. Res., 1990(95):21565-21581
[99] Balberg, I., B. Berkowitz, and G E. Drachsler, Application of a percolation model to flow in fractured hard rocks[J], J. Geophys. Res., 1991(96): 10015-10021
[1
[100] Brekowitz, B., and I. Balberg. Percolation theory and its application to groundwater hydrology[J]. Water Resour. Res., 1993, 29(2): 775-794
[101] Brekowitz, B. Analysis of fracture network connectivity using percolation theory[J]. Math. Geol., 1995(27): 467-483
[102] Gennady M. B. Berkowitz and H. Scher. Structure, flow and generalized conductivity scaling in fracture networks. Water Resour. Res., 1998, 34(9): 2103-2121
[103] Young-Jin Pack and Kang-Kun Lee. Analytical solutions for solute transfer characteristics at continuous fracture junctions[J]. Water Resour. Res., 1999: 35(5), 1531-1537
[104] Gelhar L. W. Applications of stochastic models to solute transport in fractured rocks, Report Swed. Nucl. Fuel and Waste Manage. Co., Stockholm, 1987
[105] Gelhar L. W. Stochastic Subsurface Hydrology[M]. Prentice-Hall, Englewood Cliffs, N. J., 1993
[106] Andrew R. and D. Elsworth. Physical and numerical studies of a fracture system model[J]. Water Resour. Res., 1989, 25(3): 457-462
[107] 胡云进，速宝玉等．裂隙岩体非饱和渗流综述[J]．河海大学学报．2000，28(1)：40～45．
[108] 周志芳，腾建仁．三峡工程大坝坝基渗控分析[J]．岩石力学与工程学报．2001(9)：700-704
[109] 张倬元，王士天，王兰生．工程地质分析原理[M]．北京：地质出版社，1994，41-41
[110] Lomize G. M. Flow in fractured rocks[M]. Mosoow: Gesenergoizdat, 1951
[111] Louis C. A study of groundwater flow in jointed rock and its influence on the stability of rock masses[J]. In: Muler, eds. Rock Mech Res Rep 10, London: Imp. Coll., 1969
[112] Neuzil C. E., Tracy J V. Flow through fractures[J]. Water Resour Res., 1981, 17(1): 191-194
[113] Elsworth D. and Goodman R E. Characterization of rock fissure hydraulic conductivity using idealized wall roughness profiles[J]. Int. J Rock Mech Min Sci & Geomech Abstr, 1986, 23(3): 233-243
[114] Barton N. Bandis S., and Bakhta K. Strength deformation and conductivity coupling of rock joints[J]. Int. J Rock Mech Min Sci & Geomech Abstr, 1985, 22(3): 121-140
[115] Walsh J. B. Effect of porepressure and confining pressure on fracture permeability[J]. Int. J Rock Mech Min Sci & Geomech Abstr, 1981, 18: 429-435
[116] 王媛，速宝玉，徐志英．粗糙裂隙渗流及其受应力作用的计算机模拟[J]．河海大学学报，1997，25(6)：80-85
[117] 周志芳，王锦国．裂隙介质水动力学[M]．北京：中国水利水电出版社，2004，88-114
[118] 仵彦卿．岩体水力学基础(五)[J]．水文地质工程地质，1997，(5)：41-45
[119] 陈和群，彭宣茂．有限元法微机程序与图形处理[M]．南京：河海大学出版社．1992，219-221
[120] 黄勇，周志芳．岩体渗流模拟的二维随机裂隙网络模型[J]．河海大学学报．2004(1)：91-94
[121] C. Cacas, E. Ledoux, G de marsily, B. illie. Modeling fracture flow with a stochastic discrete fracture network: calibration and validation 1. the flow model[J]. Water Resour. Res., 1990, 26(3): 479-489
[122] Shemin G. E. A governing equation for fluid flow in rough fractures[J]. Water Resour. Res., 1997, 33(1): 53-61
[123] Y. W. Tsang. The effect of tortuosity on fluid flow through a single fracture[J]. Water Resour. Res., 1984, 20(9): 1209-1215
[124] 杨米加，陈明雄，贺永年．单裂隙曲折率对流体渗流过程的影响[J]．岩土力学．2001，22(1)：78-82
[125] Olivier bour, Philippe davy. Connectivity of random fault networks following a power law fault length distribution[J]. Water Resour. Res., 1997, 33(7): 1567-1583
[126] Carl E. Renshaw. Influence of subcritical fracture growth on the connectivity of fracture networks[J]. Water Resour. Res., 1996, 32(6): 1539-1530
[127] 黄国明，黄润秋．用窗口法估计不连续面的连通率[J]．水文地质工程地质．1998(6)：27-30
[128] 杜景灿，汪小刚，陈祖煜．结构面倾角对节理岩体的连通特性和综合抗剪强度的影响[J]．水利学报．2002(5)：41-46
[129] 王媛，速宝玉，徐志英．裂隙岩体渗流模型综述[J]．水科学进展．1996，7(3)：276-281
[130] 王洪涛．裂隙网络渗流与离散元耦合分析充水岩质高边坡的稳定性[J]．水文地质工程地质．2000(2)：30-33
[131] 王媛，速宝玉，徐志英．三维裂隙岩体渗流耦合模型及其有限元模拟[J]．水文地质工程地质．1995(3)：1-5
[132] 王洪涛，聂永丰，李雨松．耦合岩体主干裂隙和网络状裂隙渗流分析及其应用[J]．清华大学学报．1998，38(12)：23-26
[133] 王恩志，王洪涛，孙役．双重裂隙系统渗流模型研究[J]．岩石力学与工程学报．2001，17(4)：400-406
[134] 杜广林，周维垣，赵吉东．裂隙介质中多重裂隙网络渗流模型[J]．岩石力学与工程学报．2000，19(增)：1014-1018
[135] 宋丽红，杨天行．边界元区域分解算法在地下水中的应用[J]．世界地质．2002，21(1)：50-52
[136] 吕涛，石济民，林振宝．区域分解算法—偏微分方程数值解新技术[M]．北京：科学出版社，1991
[137] 严仁军，龚朴，黄玉盈．基于区域分解算法的非均匀介质的反分析计算[J]．武汉交通科技大学学报．1998，22(3)：277-279
[138] 朱景辉．有限差分法中的区域分解算法[J]．厦门大学学报．1995，34(4)：517-524
[139] 卫加宁，章社生，郭庆平等．预处理性质及其在非重叠区域分解算法中应用[J]．武汉理工大学学报．2001，23(9)：74-76
[140] 王浩然．基于区域分解算法的地下水耦合模型与并行模拟技术[D]．博士学位论文．南京大学．2002
[141] 周志芳等．有限分析法在反求裂隙岩体渗透张量中的应用[J]．水利学报．1993(5)：68-75
[142] 周志芳，杨建，杨建宏．确定缓倾结构面渗透性参数的现场试验法[J]．工程地质学报．1999，7(4)：375-379
[143] 王登刚，刘迎曦，李守巨．非线性最优化问题的一种混合解法[J]．工程力学，2001，18(3)：61-66
[144] 刘盛松，侯志俭，蒋传文．基于混沌优化和BFGS方法的最优潮流算法[J]．电力系统自动化，2002，(10)：13-17
[145] 李英，胡云昌，曹宏铎．加速混沌优化方法及其应用[J]．系统工程学报，2002，17(1)：41-44
[146] 周激流，丁晶，金菊良．一种新型遗传算法及其在暴雨强度公式参数优化中的应用研究[J]．四川大学学报(自然科学版)，2000，37(4)：543-547
[147] 郭惠昕．混沌遗传优化算法及其程序研制[J]．常德师范学院学报(自然科学版)，2002，14(4)：40-42
[148] 金忠青，周志芳．工程水力学反问题[M]．南京：河海大学出版社．1997，59-75
[149] 黄勇，周志芳．裂隙网络介质地下水流运动参数反演分析[J]．水电能源科学．2004(2)：12-15
[150] 王军辉．小尺度裂隙岩体地下水溶质运移模拟研究[D]．河海大学硕士论文．2001，1-3
[151] 王锦国，周志芳．裂隙岩体地下水溶质运移的尺度问题[J]．水科学进展．2002，13(2)：239-245
[152] 成建梅，胡进武．饱和水流溶质运移问题数值解法综述[J]．水文地质工程地质．2003(2)：99-106
[153] 程诚，吴吉春，葛锐等．单裂隙介质中的溶质运移研究综述[J]．水科学进展．2003，14(4)：502-508
[154] Scott C. James, Constantinos V. Chrysikopoulos. An efficient particle tracking equation with specified spatial step for the solution of the diffusion equation[J]. Chemical Engineering Science, 2001, 56. 6535-6543
[155] Uffink, G. J. M. Modeling of solute transport with the random walk method [J]. InE. Custodio, A Gurgui, J. P. Lobo Ferreira, 1988: 247-265
[156] Thompson, A. F. B., and L. W. Gelhar. Numerical simulation of solute transport in three-dimensional, randomly heterogeneous porous media[J]. Water Resour. Res., 1990: 26(10), 2541-2562
[157] Franklin W. schwartz and Leslie Smith. A continuum approach for modeling mass transport in fractured media[J]. Water Resour. Res., 1988, 24(8): 1360-1372
[158] Gennady margolin, Brian Berkowitz and Harvey scher. Structure, flow and generalized conductivity scaling in fracture networks[J]. Water Resour. Res., 1998, 34(9): 2103-2121
[159] R. zhang, K. Huang, And M. T. Van Genuc. An efficient Eulerian-Lagrangian method for solving solute transport problems in steady and transient flow fields[J]. Water Resour. Res., 1993, 29(12): 4131-4138
[160] Tory, E. M. Stochastic sedimentation and hydrodynamic diffusion [J]. Chemical Engineering Journal, 2000, 80: 81-89
[161] Young-Jin Pack, Jean-Raynald de Dreuzy. Transport and intersection mixing in random fracture networks with power law length distributions[J]. Water Resour. Res., 2001 : 37(10), 2493-2501
[162] Young-Jin Pack and Kang-Kun Lee. Analytical solutions for solute transfer characteristics at continuous fracture junctions[J]. Water Resour. Res., 1999: 35(5), 1531-1537
[163] 冯允成，吕春莲．随机网络及其应用[M]．北京：北京航空学院出版社．1987：1-100
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