裂隙岩体破坏和水力耦合数值模型研究
|
摘要
水力耦合效应是岩石工程中的一个重要研究课题,例如在废弃物的地质填埋,高陡岩石边坡和地下厂房等工程中,水力耦合在工程安全性评价中扮演着至关重要的角色。由于不连续结构面的存在,岩体水力性质很难确定。原位试验存在着技术上的困难,且价格昂贵,使得数值模型成为刻画岩石水-力性质的一个必不可少的工具。基于离散裂隙网络模型和改进刚体弹簧法,本文提出了一种显式考虑岩体细观结构的水力耦合计算模型。本文的主要工作列举如下,
(1)提出了一种用于岩石细观破坏模拟的改进刚块弹簧方法,该方法可以显式考虑预存裂隙网络等岩体细观结构,同时可以模拟新裂隙的产生、扩展和贯通的全过程。在该模型中,岩石基质由随机均布的多边形块体集合表示,相邻块体由共同界面上的弹簧相互连接,岩体的宏观变形由块体的相对位移或裂隙变形来表现。
(2)基于离散裂隙网络模型,提出了一种新的双重介质渗流模型。岩石基质的渗透性由沿着块体界面的液体流动来模拟。结合改进刚体弹簧方法,分析了岩石破坏过程中渗透特性变化规律和突变机理。
(3)提出了一种基于变分不等式方法的计算模型,用于求解贯通裂隙网络的自由面渗流问题。该方法对具有复杂拓扑关系和边界条件(如排水系统)的裂隙网络均具有很强的适用性,并已推广到三维问题。
(4)提出了一种用于模拟密集裂隙岩体水力耦合效应的模型。该模型忽略了岩石基质的变形和渗透特性,渗流和变形都发生在裂隙中。为合理反映裂隙的非线性变形特性,引入了同时考虑非线性法向应力变形关系、剪切滑动和剪胀效应的裂隙本构模型。分析了不同应力条件下水力耦合效应的控制性机理。
Estimation of hydro-mechanical coupling effects is very essential in many rock engineering projects, such as geological repository of wastes, high and steep rock slopes and underground hydropower houses. However, due to the presence of discontinuities, both hydraulic and mechanical properties of rock masses are difficult to characterize. In situ experiments are either expensive or impossible, making numerical modeling an inevitable way for characterization of rock mass behaviors.
In this thesis, a unified hydro-mechanical coupling model based on the discrete fracture network mode (DFN) and the improved rigid body spring method (RBSM) is proposed for both intact rock and fracture network. Specifically, the main contributions are listed as follows.
(1) A meso-scopic model for simulation of rock failure is proposed based on the improved rigid body spring method. In this model, the micro structures of rock mass such as pre-existing fracture network are explicitly considered and the whole process of initiation, propagation and coalescence of new cracks is can be simulated as well. The intact rock is represented by large numbers of uniformly distributed rigid blocks connected with each other by springs. Macro deformation is reflected by the local deformation of common interfaces between blocks.
(2) A dual porosity model for seepage flow in rock mass is proposed based on the discrete fracture network model. Combined with the improved rigid body spring method, the permeability variation during rock failure is investigated.
(3) A VI formulation for seepage problem with free surface is extended to fracture networks both in2-D and3-D space. This formulation is adapt to solve free surface problems in fracture network even with very complex topology and boundaries such as drainage tunnels.
(4) For densely fractured rock mass, the deformability and conductivity of intact rock is neglected. A non-linear fracture constitutive model is introduced to take into account the non-linear normal stress and deformation relationship, tangential shear slip and dilation effects. The controlling mechanisms of hydro-mechanical coupling under different stress conditions are detected.
(1)提出了一种用于岩石细观破坏模拟的改进刚块弹簧方法,该方法可以显式考虑预存裂隙网络等岩体细观结构,同时可以模拟新裂隙的产生、扩展和贯通的全过程。在该模型中,岩石基质由随机均布的多边形块体集合表示,相邻块体由共同界面上的弹簧相互连接,岩体的宏观变形由块体的相对位移或裂隙变形来表现。
(2)基于离散裂隙网络模型,提出了一种新的双重介质渗流模型。岩石基质的渗透性由沿着块体界面的液体流动来模拟。结合改进刚体弹簧方法,分析了岩石破坏过程中渗透特性变化规律和突变机理。
(3)提出了一种基于变分不等式方法的计算模型,用于求解贯通裂隙网络的自由面渗流问题。该方法对具有复杂拓扑关系和边界条件(如排水系统)的裂隙网络均具有很强的适用性,并已推广到三维问题。
(4)提出了一种用于模拟密集裂隙岩体水力耦合效应的模型。该模型忽略了岩石基质的变形和渗透特性,渗流和变形都发生在裂隙中。为合理反映裂隙的非线性变形特性,引入了同时考虑非线性法向应力变形关系、剪切滑动和剪胀效应的裂隙本构模型。分析了不同应力条件下水力耦合效应的控制性机理。
Estimation of hydro-mechanical coupling effects is very essential in many rock engineering projects, such as geological repository of wastes, high and steep rock slopes and underground hydropower houses. However, due to the presence of discontinuities, both hydraulic and mechanical properties of rock masses are difficult to characterize. In situ experiments are either expensive or impossible, making numerical modeling an inevitable way for characterization of rock mass behaviors.
In this thesis, a unified hydro-mechanical coupling model based on the discrete fracture network mode (DFN) and the improved rigid body spring method (RBSM) is proposed for both intact rock and fracture network. Specifically, the main contributions are listed as follows.
(1) A meso-scopic model for simulation of rock failure is proposed based on the improved rigid body spring method. In this model, the micro structures of rock mass such as pre-existing fracture network are explicitly considered and the whole process of initiation, propagation and coalescence of new cracks is can be simulated as well. The intact rock is represented by large numbers of uniformly distributed rigid blocks connected with each other by springs. Macro deformation is reflected by the local deformation of common interfaces between blocks.
(2) A dual porosity model for seepage flow in rock mass is proposed based on the discrete fracture network model. Combined with the improved rigid body spring method, the permeability variation during rock failure is investigated.
(3) A VI formulation for seepage problem with free surface is extended to fracture networks both in2-D and3-D space. This formulation is adapt to solve free surface problems in fracture network even with very complex topology and boundaries such as drainage tunnels.
(4) For densely fractured rock mass, the deformability and conductivity of intact rock is neglected. A non-linear fracture constitutive model is introduced to take into account the non-linear normal stress and deformation relationship, tangential shear slip and dilation effects. The controlling mechanisms of hydro-mechanical coupling under different stress conditions are detected.
引文
[1]Harrison, John P., and John A. Hudson. Engineering rock mechanics-an introduction to the principles. Elsevier Science,2000.
[2]Z. T. Bieniawski, "Determining rock mass deformability:experience from case histories", International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, vol 15, no 5, pp 237-247,1978.
[3]Y.-C. Liu and C.-S. Chen, "A new approach for application of rock mass classification on rock slope stability assessment", Engineering Geology, vol 89, no 1-2, pp 129-143, 2007.
[4]E. Hoek and M. S. Diederichs, "Empirical estimation of rock mass modulus", International Journal of Rock Mechanics and Mining Sciences, vol 43, no 2, pp 203-215,2006.
[5]N. Barton, R. Lien, and J. Lunde, "Engineering classification of rock masses for the design of tunnel support", Rock Mechanics, vol 6, no 4, pp 189-236, Dec 1974.
[6]E. Hoek and E. T. Brown, "Practical estimates of rock mass strength", International Journal of Rock Mechanics and Mining Sciences, vol 34, no 8, pp 1165-1186,1997.
[7]L. Jing and O. Stephansson, Fundamentals of Discrete Element Methods for Rock Engineering:Theory and Applications:Theory and Applications. Elsevier,2007.
[8]J. Rutqvist and O. Stephansson, "The role of hydromechanical coupling in fractured rock engineering", Hydrogeology Journal, vol 11, no 1, pp 7-40, Feb 2003.
[9]T. Kawai, "New discrete models and their application to seismic response analysis of structures", Nuclear Engineering and Design, vol 48, no 1, pp 207-229,1978.
[10]T. Belytschko, M. Plesha, and C. H. Dowding, "A computer method for stability analysis of caverns in jointed rock", International Journal for Numerical and Analytical Methods in Geomechanics, vol 8, no 5, pp 473-492,1984.
[11]Wang, Baolin, and Vinod K. Garga. "A numerical method for modelling large displacements of jointed rocks. I. Fundamentals." Canadian Geotechnical Journal 30.1 (1993):96-108.
[12]Garga, Vinod K., and Baolin Wang. "A numerical method for modelling large displacements of jointed rocks. II. Modelling of rock bolts and groundwater and applications." Canadian Geotechnical Journal 30.1 (1993):109-123.
[13]J. E. Bolander Jr. and S. Saito, "Fracture analyses using spring networks with random geometry", Engineering Fracture Mechanics, vol 61, no 5-6, pp 569-591,1998.
[14]K. Nagai, Y. Sato, and T. Ueda, "Mesoscopic Simulation of Failure of Mortar and Concrete by 2D RBSM", Journal of Advanced Concrete Technology, vol 2, no 3, pp 359-374,2004.
[15]K. Nagai, Y. Sato, and T. Ueda, "Mesoscopic Simulation of Failure of Mortar and Concrete by 3D RBSM", Journal of Advanced Concrete Technology, vol 3, no 3, pp 385-402,2005.
[16]L. Wang and T. Ueda, "Mesoscale Modelling of the Chloride Diffusion in Cracks and Cracked Concrete", Journal of Advanced Concrete Technology, vol 9, no 3, pp 241-249,2011.
[17]T. Ueda, M. Hasan, K. Nagai, Y. Sato, and L. Wang, "Mesoscale Simulation of Influence of Frost Damage on Mechanical Properties of Concrete", Journal of Materials in Civil Engineering, vol 21, no 6, pp 244-252,2009.
[18]K. Matsumoto, Y. Sato, T. Ueda, and L. Wang, "Mesoscopic Analysis of Mortar under High-Stress Creep and Low-Cycle Fatigue Loading", Journal of Advanced Concrete Technology, vol 6, no 2, pp 337-352,2008.
[19]M. Pieri, L. Burlini, K. Kunze, I. Stretton, and D. L. Olgaard, "Rheological and micro-structural evolution of Carrara marble with high shear strain:results from high temperature torsion experiments", Journal of Structural Geology, vol 23, no 9, pp 1393-1413,2001.
[20]W. Herbert, "Modelling approaches for discrete fracture network flow analysis", in Developments in Geotechnical Engineering, vol Volume 79, L. J. and C.-F. T. Ove Stephansson, Ed Elsevier,1996, pp 213-229.
[21]B. Berkowitz, "Characterizing flow and transport in fractured geological media:A review", Advances in Water Resources, vol 25, no 8-12, pp 861-884,2002.
[22]Sahimi, Muhammad. Flow and transport in porous media and fractured rock. Wiley-VCH,2012.
[23]Dershowitz, William S., Paul R. La Pointe, and Thomas W. Doe. "Advances in dicrete fracture network modeling." Proceedings of the US EPA/NGWA Fractured Rock Conference, Portland.2004.
[24]B. Berkowitz, "Analysis of fracture network connectivity using percolation theory", Mathematical Geology, vol 27, no 4, pp 467-483,1995.
[25]Balberg, B. Berkowitz, and G. E. Drachsler, "Application of a percolation model to flow in fractured hard rocks", J. Geophys. Res., vol 96, no B6, pp 10015-10,021,1991.
[26]J. Erhel, J.-R. de Dreuzy, and B. Poirriez, "Flow Simulation in Three-Dimensional Discrete Fracture Networks", SIAM Journal on Scientific Computing, vol 31, no 4, pp 2688-2705, Jan 2009.
[27]M. Wang, P. H. S. W. Kulatilake, B. B. Panda, and M. L. Rucker, "Groundwater resources evaluation case study via discrete fracture flow modeling", Engineering Geology, vol 62, no 4, pp 267-291,2001.
[28]V. V. Mourzenko, J.-F. Thovert, and P. M. Adler, "Macroscopic permeability of three-dimensional fracture networks with power-law size distribution", Phys. Rev. E, vol 69, no 6, p 066307,2004
[29]V. V. Mourzenko, J.-F. Thovert, and P. M. Adler, "Percolation of three-dimensional fracture networks with power-law size distribution", Phys. Rev. E, vol 72, no 3, p 036103,2005.
[30]M. Khamforoush, K. Shams, J.-F. Thovert, and P. M. Adler, "Permeability and percolation of anisotropic three-dimensional fracture networks", Phys. Rev. E, vol 77, no 5, p 056307,2008.
[31]Pouya and O. Fouche, "Permeability of 3D discontinuity networks:New tensors from boundary-conditioned homogenisation", Advances in Water Resources, vol 32, no 3, pp 303-314,2009.
[32]N. Koudina, R. Gonzalez Garcia, J.-F. Thovert, and P. M. Adler, "Permeability of three-dimensional fracture networks", Phys. Rev. E, vol 57, no 4, pp 4466-4479,1998.
[33]V. V. Mourzenko, I. I. Bogdanov, J.-F. Thovert, and P. M. Adler, "Three-dimensional numerical simulation of single-phase transient compressible flows and well-tests in fractured formations", Mathematics and Computers in Simulation, vol 81, no 10, pp 2270-2281,2011.
[1]L. Jing. A review of techniques, advances and outstandingissues in numerical modelling for rock mechanics and rock engineering. International Journal of Rock Mechanics and Mining Sciences.40,3, April 2003, Pages 283-353.
[2]Donze, F.V., V. Richefeu & S.-A. Magnier, Advances in Discrete Element Method applied to Soil, Rock and Concrete Mechanics, in:State of the art of geotechnical engineering, Electronic Journal of Geotechnical Engineering, p.44,2009
[3]D.O. Potyondy, P.A. Cundall. A bonded-particle model for rock. International Journal of Rock Mechanics & Mining Sciences 41 (2004):1329-1364
[4]Yuannian Wang, Fulvio Tonon. Modeling Lac du Bonnet granite using a discrete element model. International Journal of Rock Mechanics & Mining Sciences 46 (2009) 1124-1135
[5]Sebastien Hentz, Laurent Daudeville, and Frederic V. Donze. Identification and Validation of a Discrete Element Model for Concrete. Journal of Engineering Mechanics.130(6):709-720
[6]Tadahiko Kawai. New element models in discrete structural analysis. Journal of the Society of Naval Architects of Japan,141,187-193.
[7]J. E. Bolander Jr.*, Stefano Berton. Simulation of shrinkage induced cracking in cement composite overlays. Cement & Concrete Composites 26 (2004) 861-871
[8]Kohei Nagai, Yasuhiko Sato and Tamon Ueda. Mesoscopic Simulation of Failure of Motar and Concrete by 2D RBSM. Journal of Advanced Concrete Technology. 2004,2(3):359-374
[9]Zhang Xiong, Qian Lingxi. Rigid finite element and limit analysis. Acta Mechanica Sinica.9,2 (1993):156-162
[10]Qian Lingxi, Zhang Xiong. Rigid finite element and its applications in engineering. Acta Mechanica Sinica.11,1 (1995):44-50
[11]J.S.ZHUO, Q.ZHANG, N.ZHAO. Interface Stress Element Methods For Deformable Body With Discontinuous Media Such As Rock Mass.8th ISRM Congress, September 25-29,1995, Tokyo, Japan.
[12]J.E. Bolander, Jr, S. Saito. Fracture analysis using spring networks with random geometry. Engineering Fracture Mechanics.61 (1998):569-591
[13]F. Camborde, C. Mariotti, F.V. Donze. Numerical study of rock and concrete behavior by discrete element modeling.Computers and Geotechnics 27 (2000):225-247
[14]Goodman, R.E. (1976) Methods of geological engineering in discontinuous rocks, West Publishing Company, San Francisco, CA.
[15]Shi, G H. Discontinuous deformation analysis:a new numerical model for the statics and dynamics of deformable block structures. Engng ComputV9, N2, April 1992, P157-168
[16]Baolin Wang, Vinod K. Garga. A numerical method for modelling large displacements of jointed rocks. I. Fundamentals. Canadian Geotechnical Journal,1993,30(1):96-108.
[17]Yip, M., Mohle, J. and Bolander, J. E. (2005), Automated Modeling of Three-Dimensional Structural Components Using Irregular Lattices. Computer-Aided Civil and Infrastructure Engineering,20:393-407. doi:10.1111/j.1467-8667.2005. 00407.x
[18]Greengard, L., Rokhlin, V. (1987). A fast algorithm for particle simulations. Journal of Computational Physics,73(2),325-49.
[19]Steven Fortune (1987). A sweepline algorithm for Voronoi diagrams. Algorithmica. 2(1-4):153-174
[1]F. A. Donath, "Experimental Study of Shear Failure in Anisotropic Rocks", Geological Society of America Bulletin, vol 72, no 6, pp 985-989, Jan 1961.
[2]P. B. Attewell and M. R. Sandford, "Intrinsic shear strength of a brittle, anisotropic rock-Ⅰ: Experimental and mechanical interpretation", International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, vol 11, no 11, pp 423-430,1974.
[3]R. McLamore and K. E. Gray, "The Mechanical Behavior of Anisotropic Sedimentary Rocks", J. Manuf. Sci. Eng., vol 89, no 1, pp 62-73,1967.
[4]E. Hoek, "Strength of jointed rock masses", Geotechnique, vol 33, no 3, pp 187-223, Jan 1983.
[5]H. Niandou, J. F. Shao, J. P. Henry, and D. Fourmaintraux, "Laboratory investigation of the mechanical behaviour of Tournemire shale", pp 3-16, Jan 1997.
[6]Y. M. Tien, M. C. Kuo, and C. H. Juang, "An experimental investigation of the failure mechanism of simulated transversely isotropic rocks", International Journal of Rock Mechanics and Mining Sciences, vol 43, no 8, pp 1163-1181,2006.
[7]J. C. Jaeger, "Shear failure of anisotropic rocks", Geological Magazine, vol 97, no 1, pp 65-72, Jan 1960.
[8]G. Duveau and J. F. Shao, "A modified single plane of weakness theory for the failure of highly stratified rocks", International Journal of Rock Mechanics and Mining Sciences, vol 35, no 6, pp 807-813,1998.
[9]Hoek E, Brown ET. Underground excavation in rock. London:Institution of Mining and Metallurgy,1980. p.157-62.
[10]R. Hill, The Mathematical Theory of Plasticity. Oxford University Press,1998.
[11]Cazacu, N. D. Cristescu, and J. F. Shao, "A new failure criterion for transversely isotropic rocks", International Journal of Rock Mechanics and Mining Sciences, vol 35, no 4-5, p 421,1998.
[12]R. Nova, "The failure of transversely isotropic rocks in triaxial compression", International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, vol 17, no 6, pp 325-332,1980.
[13]Y. M. Tien and M. C. Kuo, "A failure criterion for transversely isotropic rocks", International Journal of Rock Mechanics and Mining Sciences, vol 38, no 3, pp 399-412,2001.
[14]Steven Fortune (1987). A sweepline algorithm for Voronoi diagrams. Algorithmica. 2(1-4):153-174
[1]M. Oda, T. Takemura, and T. Aoki, "Damage growth and permeability change in triaxial compression tests of Inada granite", Mechanics of Materials, vol 34, no 6, pp 313-331,2002.
[2]Schulze, T. Popp, and H. Kern, "Development of damage and permeability in deforming rock salt", Engineering Geology, vol 61, no 2-3, pp 163-180,2001.
[3]P. Bossart, P. M. Meier, A. Moeri, T. Trick, and J.-C. Mayor, "Geological and hydraulic characterisation of the excavation disturbed zone in the Opalinus Clay of the Mont Terri Rock Laboratory", Engineering Geology, vol 66, no 1-2, pp 19-38,2002.
[4]M. Souley, F. Homand, S. Pepa, and D. Hoxha, "Damage-induced permeability changes in granite:a case example at the URL in Canada", International Journal of Rock Mechanics and Mining Sciences, vol 38, no 2, pp 297-310,2001.
[5]F. Homand-Etienne, D. Hoxha, and J. F. Shao, "A continuum damage constitutive law for brittle rocks", Computers and Geotechnics, vol 22, no 2, pp 135-151,1998.
[6]J. F. Shao, H. Zhou, and K. T. Chau, "Coupling between anisotropic damage and permeability variation in brittle rocks", International Journal for Numerical and Analytical Methods in Geomechanics, vol 29, no 12, pp 1231-1247,2005.
[7]J. J. Zhou, J. F. Shao, and W. Y. Xu, "Coupled modeling of damage growth and permeability variation in brittle rocks", Mechanics Research Communications, vol 33, no 4, pp 450-459,2006.
[8]T. Jiang, J. F. Shao, W. Y. Xu, and C. B. Zhou, "Experimental investigation and micromechanical analysis of damage and permeability variation in brittle rocks", International Journal of Rock Mechanics and Mining Sciences, vol 47, no 5, pp 703-713,2010.
[9]J.-M. Pereira and C. Arson, "Retention and permeability properties of damaged porous rocks", Computers and Geotechnics, vol 48, pp 272-282,2013.
[10]M. S. Bruno, "Micromechanics of stress-induced permeability anisotropy and damage in sedimentary rock", Mechanics of Materials, vol 18, no 1, pp 31-48,1994.
[11]C. A. Tang, L..Tham, P. K.. Lee, T.. Yang, and L.. Li, "Coupled analysis of flow, stress and damage (FSD) in rock failure", International Journal of Rock Mechanics and Mining Sciences, vol 39, no 4, pp 477-489,2002.
[12]M. Mansouri, J.-Y. Delenne, A. Seridi, and M. S. El Youssoufi, "Numerical model for the computation of permeability of a cemented granular material", Powder Technology, vol 208, no 2, pp 532-536,2011.
[13]Yao C., Jiang QH, Shao JF, Zhou CB. A mesoscopic numerical model for simulation of rock fracturing. Chinese Journal of Rock Mechanics and Engineering.2013 (in press)
[14]Yao Chi, Jiang Qinghui, Ye Zuyang, Zhou Chuangbing. Initial flow method for unconfined seepage problems of fracture networks. Rock and Soil Mechanics, vol33, no 6, pp1896-1903,2012.
[15]Q. Jiang, C. Yao, Z. Ye, and C. Zhou, "Seepage flow with free surface in fracture networks", Water Resources Research, vol 49, no 1, pp 176-186,2013.
[16]M. F. Lough, S. H. Lee, and J. Kamath, "An Efficient Boundary Integral Formulation for Flow Through Fractured Porous Media", Journal of Computational Physics, vol 143, no 2, pp 462-483,1998.
[17]J. D. Byerlee, "Brittle-ductile transition in rocks", Journal of Geophysical Research, vol 73, no 14, pp 4741-4750,1968.
[18]Chen, G., J. M. Kemeny, and SatyaHarpalani. "Fracture propagation and coalescence in marble plates with pre-cut notches under compression." Fracture and Jointed Rock Mass 14 (1992):435-439.
[1]Alt, H. W. (1980), Numerical solution of steady-state porous flow free boundary problems, Numer. Math.,31,73-98.
[2]Andersson, J., and B. Dverstorp (1987), Conditional simulation of fluid flow in three-dimensional networks of discrete fractures, Water Resour. Res.,23(10), 1876-1886.
[3]Baghbanan, A., and L. Jing (2007), Hydraulic properties of fractured rock masses with correlated fracture length and aperture, Int. J. Rock Mech. Min. Sci.,44(5),704-719.
[4]Bathe, K. J., and M. R. Khoshgoftaar (1979), Finite element free surface seepage analysis without mesh iteration, Int. J. Nume.r Anal. Meth. Geomech.3,13-22.
[5]Berkowitz, B. (2002), Characterizing flow and transport in fractured geological media: A review, Adv. Water Resour.,25,861-884.
[6]Brezis, H., D. Kinderlehrer, and G. Stampacchia (1978), Sur une nouvelle formulation due probleme de l'ecoulement a travers une digue, Comptes Rendus de l'Academie des Sciences Paris Series A,287,711-714
[7]Cacas, M. C., E. Ledoux, G. de Marsily, B. Tillie, A. Barbreau, E. Durand, B. Feuga, and P. Peaudecerf (1990), Modeling fracture flow with a stochastic discrete fracture network:calibration and validation 1. The flow model, Water Resour. Res.26(3), 479-489.
[8]Desai, C. S., and G. C. Li (1983), A residual flow procedure and application for free surface flow in porous media, Adv. Water Resour.,6,27-35.
[9]Dershowitz, W. S., and H. H. Einstein (1987), Three dimensional flow modeling in jointed rock masses, In:Herget, Vongpaisal, editors. Proceedings of the sixth international congress on rock mechanics, vol.1., Rotterdam, Balkema, pp.87-92.
[10]Duiguid, J. O., and P. C. Y. Lee (1977), Flow in fractured porous media, Water Resour. Res.,13(3),25-28.
[11]Finn, W. D. L. (1967), Finite-element analysis of seepage through dams, J. Soil Mech. Foundat. Div., ASCE,93(SM6),41-48.
[12]Hsieh, P. A., and S. P. Neuman (1985), Field determination of the three dimensional hydraulic conductivity tensor of anisotropic media-1. Theory, Water Resour. Res., 21(11),1655-1665.
[13]Jackson, C. P., A. R. Hoch, and S. Todman (2000), Self-consistency of a heterogeneous continuum porous medium representation of a fractured medium, Water Resour. Res., 36(1),189-202.
[14]Jing, L., Y. Ma, and Z. Fang (2001), Modeling of fluid flow and solid deformation for fractured rocks with discontinuous deformation analysis (DDA) method, Int. J. Rock Mech. Min. Sci.,38(3),343-355.
[15]Kikuchi, N. (1977), An analysis of the variational inequalities of seepage flow by finite-element methods, Quart. Appl. Math.,35,149-63.
[16]Lacy, S. J., and J. H. Prevost (1987), Flow through porous media:a procedure for locating the free surface. Int. J. Numer. Anal. Meth. Geomech.,11,585-601.
[17]Long, J. C. S., P. Gilmour, and P. A. Witherspoon (1985), A method for steady fluid flow in random three-dimensional networks of disc-shaped fractures, Water Resour. Res.21(8),1105-1115.
[18]Long, J. C. S., J. S. Remer, C. R. Wilson, and P. A. Witherspoon (1982), Porous media equivalents for networks of discontinuous fractures, Water Resour. Res.,18(3), 645-658.
[19]Min, K. B., L. Jing, O. Stephansson (2004), Determining the equivalent permeability tensor for fractured rock masses using a stochastic REV approach:method and application to the field data from Sellafield UK, Hydrogeol. J.,12(5),497-510.
[20]Neuman, S. P., and P. A. Witherspoon (1970), Finite element method of analyzing steady seepage with a free surface, Water Resour. Res.,6(3),889-897.
[21]Oda, M. (1985), Permeability tensor for discontinuous rock masses, Geotechnique, 35(4),483-495.
[22]Oda, M. (1986), An equivalent continuum model for coupled stress and fluid flow analysis in jointed rock masses, Water Resour. Res.,22 (13),1845-1856.
[23]Oden, J. T., and N. Kikuchi (1980), Recent advances:theory of variational inequalities with applications to problems of flow through porous media, Int. J. Eng. Sci.18, 1173-1284.
[24]Schwartz, F. W., W. L. Smith, and A. S. Crowe (1983), A stochastic analysis of microscopic dispersion in fractured media, Water Resour. Res.19(5),1253-1265.
[25]Snow, D. T. (1969), Anisotropic permeability of fractured media, Water Resour. Res., 5(6),1273-1289.
[26]Streltsova, T. D. (1981), Hydrodynamics of groundwater flow in a fractured formation, Water Resour. Res.17(4),21-22.
[27]Taylor, R. L., and C. B. Brown (1967), Darcy flow solutions with a free surface, J. Hydr. Div.,ASCE,93,25-33.
[28]Westbrook, D. R. (1985), Analysis of inequalities and residual flow procedures and an iterative scheme for free surface seepage, Int. J. Numer. Meth. Eng.21,1791-1802.
[29]Wilson, C. R., and P. A. Witherspoon (1974), Steady state flow in rigid networks of fractures, Water Resour. Res.,10(2),328-335.
[30]Zhang, Y. T., P. Chen, L. Wang (1988), Initial flow method for seepage analysis with free surface, Journal of Hydraulic Engineering,8(1),18-26.
[31]Zhang, Y. T. (1999), Water pressure of high rock slope and the permanent shiplock, in Deformation and stability of high rock slope, edited by Y. T. Zhang and W. Y. Zhou, pp. 76, China Water Power Press, Beijing.
[32]Zheng, T. S., L. Li, and Q. Y. Xu (1995), An iterative method for the discrete problems of class of elliptical variational inequalities, Applied Mathematics and Mechanics, 16(4),351-358.
[33]Zheng, H., D. F. Liu, C. F. Lee, L. G. Tham (2005), A new formulation of Signorini's type for seepage problems with free surfaces, Int. J. Numer. Meth. Eng.,64,1-16.
[34]Zhou, C. B., W. L. Xiong, and Y. G. Liang (1996), A new method for unconfined seepage field, J. Hydrodyn., Ser. A,11(5),528-534.
[1]Berkowitz B. Characterizing flow and transport in fractured geological media:a review[J]. Adv Water Resour,2002,25(8):3861-84.
[2]Neretnieks I, Eriksen T, Tahtinen P. Tracer movement in a singlefissure in granitic rock: some experimental results and theirinterpretation[J]. Water Resour Res 1982;18(4):849-58.
[3]Neretnieks I. Solute transport in fracture rock-Applications toradionuclide waste repositories. In:Bear J, Tsang CF, de MarsilyG, editors. Flow and contaminant transport in fractured rock.San Diego:Academic Press, Inc; 1993. p.39-127.
[4]Oda, M. (1985), Permeability tensor for discontinuous rock masses, Geotechnique, 35(4),483-495.
[5]Oda, M. (1986), An equivalent continuum model for coupled stress and fluid flow analysis in jointed rock masses, Water Resour. Res.,22 (13),1845-1856.
[6]Neuman, S. P. (1973), Saturated-unsaturated seepage by finite elements. Journal of the Hydraulics Division,99(12),2233-2250.
[7]Sahimi M. Flow and transport in porous media and fracturedrock:from classical methods to modern approaches. Weinheim,Germany:VCH; 1995.
[8]Adler PM, Thovert JF. Fractures and fracture networks. Netherlands:Kluwer Academic Publishers; 1999.
[9]M. C. Cacas, E. Ledoux, G. de Marsily, A. Barbreau, P. Calmels, B. Gaillard, and R. Margritta, "Modeling fracture flow with a stochastic discrete fracture network: Calibration and validation:2. The transport model", Water Resources Research, vol 26, no 3, pp 491-500,1990.
[10]W. Nordqvist, Y. W. Tsang, C. F. Tsang, B. Dverstorp, and J. Andersson, "A variable aperture fracture network model for flow and transport in fractured rocks", Water Resources Research, vol 28, no 6, pp 1703-1713,1992.
[11]Rouleau and J. E. Gale, "Stochastic discrete fracture simulation of groundwater flow into an underground excavation in granite", International Journal of Rock Mechanics and Mining Sciences &Geomechanics Abstracts, vol 24, no 2, pp 99-112,1987.
[12]J. Andersson and B. Dverstorp, "Conditional simulations of fluid flow in three-dimensional networks of discrete fractures", Water Resources Research, vol 23, no 10, pp 1876-1886,1987.
[13]N. Koudina, R. Gonzalez Garcia, J.-F. Thovert, and P. M. Adler, "Permeability of three-dimensional fracture networks", Phys. Rev. E, vol 57, no 4, pp 4466-4479,1998.
[14]M. Khamforoush, K. Shams, J.-F. Thovert, and P. M. Adler, "Permeability and percolation of anisotropic three-dimensional fracture networks", Phys. Rev. E, vol 77, no 5, p 056307,2008.
[15]V. V. Mourzenko, J.-F. Thovert, and P. M. Adler, "Permeability of isotropic and anisotropic fracture networks, from the percolation threshold to very large densities", Phys. Rev. E, vol 84, no 3, p 036307,2011.
[16]ZHANG Youtian,CHEN Ping,WANG Lei. Initial flow method for seepage analysis with free surface [J]. Journal of Hydraulic Engineering,1988,8 (1):18-26. (in Chinese)
[17]H. Zheng et al. A new formulation of Signorini's type for seepage problems with free surfaces. International journal for numerical methods in engineering 64, no.1 (2005): 1-16.
[18]Y. Chen, C. Zhou, and H. Zheng. A numerical solution to seepage problems with complex drainage systems. Computers and Geotechnics 35, no.3 (2008):383-393.
[19]WANG Enzhi. Seepage calculation method in fissure networks on vertical section. Hydrogeology & Engineering Geology,20, no.4 (1993):27-29. (in Chinese)
[20]CHAI Junrui, WUYanqing. The method for determination of the position of free surface in fractured rock masses.Geotechnical Investigation & Surveying, no.1 (2000): 23-24. (in Chinese)
[21]Yao Chi, Jiang Qinghui, Ye Zuyangetc..Thevariationalinequality based initial flow method for unconfined seepage problems of fracture networks[J]. Rock and Soil Mechanics,2012,33(6):1896-1903.(in Chinese)
[22]Jiang, Q., C. Yao, Z. Ye, and C. Zhou. Seepage flow with free surface in fracture networks. Water Resour. Res., (in press, accepted 12 November 2012)
[23]Q. Jiang, Z. Ye, C. Yao, and C. Zhou, A new variational inequality formulation for unconfined seepage flow through fracture networks, Sci. China Technol. Sci., vol 55, no 11, pp 3090-3101, Nov 2012.
[24]Liu Zhong, Zhang Youtian.Analysis of free surface seepage problems inthree dimensional network of fracture[J]. ShuiliXuebao.1996,6:34-38.(in Chinese)
[25]Zhang Qihua, Wu Aiqing. Three-dimensional arbitrary fracture network seepage model and its solution[J]. Chinese Journal Rock Mechanics and Engineering,2010,29(4): 720-730 (in Chinese)
[26]Zhang Qihua, Wu Aiqing. General methodology of spatial block topological identification with stochastic discontinuities cutting[J]. Chinese Journal Rock Mechanics and Engineering,2007,26(10):2044-2048 (in Chinese)
[27]MAO Changxi. Seepage Computation Analysis & Control. Beijing:China WaterPowerPress,2003. (in Chinese)
[1]Neretnieks. Diffusion in the rock matrix:an important factor in radionuclide retardation?[J]. J Geophys Res,1980,85 (B8):4379-4397.
[2]Witherspoon PA. Introduction to second world wide review of geological problems in radioactive waste isolation, Geological Problems in Radioactive Waste Isolation[R]. 1996, LBNL-38915, UC-814:1-4
[3]L. Jing, Y. Ma, and Z. Fang, Modeling of fluid flow and solid deformation for fractured rocks with discontinuous deformation analysis (DDA) method[J]. International Journal of Rock Mechanics and Mining Sciences,2001,38(3):343-355.
[4]X Zhang, DJ Sanderson. Effects of stress on the 2-D permeability tensor of natural fracture networks[J]. Geophys J Int,1996,125:912-924
[5]K.-B. Min, J. Rutqvist, C.-F. Tsang, et al. Stress-dependent permeability of fractured rock masses:a numerical study[J]. International Journal of Rock Mechanics and Mining Sciences,2004,41(7):1191-1210.
[6]Baghbanan and L. Jing. Stress effects on permeability in a fractured rock mass with correlated fracture length and aperture[J]. International Journal of Rock Mechanics and Mining Sciences,2008,45(8):1320-1334.
[7]Z. Zhao, L. Jing, I. Neretnieks, and L. Moreno. Numerical modeling of stress effects on solute transport in fractured rocks[J]. Computers and Geotechnics,2011,38(2):113-126.
[8]Berkowitz B. Characterizing flow and transport in fractured geological media:a review[J]. Adv Water Resour,2002,25(8):3861-84.
[9]Neuman SP. Trends, prospects and challenges in quantifying flow and transport through fractured rocks[J]. Hydrogeol J,2005,13(1):124-47.
[10]Neretnieks I. Fast method for simulation of radionuclide chain migration in dual porosity fracture rocks[J]. Journal of Contaminant Hydrology,2006,88:269-288.
[11]Kawai. A new element in discrete analysis of plane strain problems[J]. Seisan Kenkyu, 1977,29 (4):204-207
[12]Zhuo JiaShou, Zhao Ning. Piecewise Rigid Body Interface Spring Method for Problems of Discontinuous Medium[J]. Journal of Hohai University,1993, 21(5):34-43(in Chinese)
[13]Chen Shenghong. A general formulation of elastic-viscoplastic block theory of rock masses[J]. Journal of Hydraulic Engineering,1996,1:78-84 (in Chinese)
[14]Qian Lingxi, Zhang Xiong. Rigid Body Finite Element Method in Structural Analysis[J]. Computational Structural Mechanics and Applications,1991,8(1):1-14 (in Chinese)
[15]L. Moreno and I. Neretnieks. Fluid flow and solute transport in a network of channels[J]. Journal of Contaminant Hydrology,1993,14(3-4):163-192,.
[16]M. C. Cacas, 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 Resources Research,1990,26(3):491-500.
[17]R. YAMASHITA and H. KIMURA. Particle-tracking technique for nuclide decay chain transport in fractured porous media[J]. Journal of Nuclear Science and Technology, 1990,27(11):1041-1049.
[18]L. Jing, C.-F. Tsang, and O. Stephansson. DECOVALEX- An international co-operative research project on mathematical models of coupled THM processes for safety analysis of radioactive waste repositories[J].International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts,1995,32(5):389-398.
[19]Baolin Wang, Vinod K. Garga. A numerical method for modelling large displacements of jointed rocks. I. Fundamentals[J]. Canadian Geotechnical Journal,1993,30(1): 96-108.
[20]Yao Chi, Jiang Qinghui, Ye Zuyang etc.Initial flow method for unconfined seepage problems of fracture networks[J]. Rock and Soil Mechanics,2012,33(6):1896-1903.(in Chinese)
[21]Yao Chi, Jiang Qinghui, Chen Yifeng, Zhou Chuangbing. Numerical Simulation of Nuclide Transport in Complex Fracture Network[J]. Disaster Advances.2012, 5(4):197-201
[22]Iwai K. Fluid flow in simulated fractures[J]. Am Inst Chem Eng J 1976,2:259-263.
[23]Iwai K. Fundamental studies of fluid flow through a single fracture. [Ph.D. thesis] [D]. USA:Univ. of California, Berkeley,1976.
[24]T. Belytschko, M. Plesha, C. H Dowding, A computer method for stability analysis of caverns in jointed rock[J]. International journal for numerical and analytical methods in geomechanics,1984,8(5):473-492.
[25]Nirex. Data summary sheets in support of gross geotechnical predictions[R]. Nirex report SA/97/052, Harwell, UK; 1997a.
[26]Zhu Bofang. The finite element theory and applications. Beijing:China Water & Power Press,1998
[2]Z. T. Bieniawski, "Determining rock mass deformability:experience from case histories", International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, vol 15, no 5, pp 237-247,1978.
[3]Y.-C. Liu and C.-S. Chen, "A new approach for application of rock mass classification on rock slope stability assessment", Engineering Geology, vol 89, no 1-2, pp 129-143, 2007.
[4]E. Hoek and M. S. Diederichs, "Empirical estimation of rock mass modulus", International Journal of Rock Mechanics and Mining Sciences, vol 43, no 2, pp 203-215,2006.
[5]N. Barton, R. Lien, and J. Lunde, "Engineering classification of rock masses for the design of tunnel support", Rock Mechanics, vol 6, no 4, pp 189-236, Dec 1974.
[6]E. Hoek and E. T. Brown, "Practical estimates of rock mass strength", International Journal of Rock Mechanics and Mining Sciences, vol 34, no 8, pp 1165-1186,1997.
[7]L. Jing and O. Stephansson, Fundamentals of Discrete Element Methods for Rock Engineering:Theory and Applications:Theory and Applications. Elsevier,2007.
[8]J. Rutqvist and O. Stephansson, "The role of hydromechanical coupling in fractured rock engineering", Hydrogeology Journal, vol 11, no 1, pp 7-40, Feb 2003.
[9]T. Kawai, "New discrete models and their application to seismic response analysis of structures", Nuclear Engineering and Design, vol 48, no 1, pp 207-229,1978.
[10]T. Belytschko, M. Plesha, and C. H. Dowding, "A computer method for stability analysis of caverns in jointed rock", International Journal for Numerical and Analytical Methods in Geomechanics, vol 8, no 5, pp 473-492,1984.
[11]Wang, Baolin, and Vinod K. Garga. "A numerical method for modelling large displacements of jointed rocks. I. Fundamentals." Canadian Geotechnical Journal 30.1 (1993):96-108.
[12]Garga, Vinod K., and Baolin Wang. "A numerical method for modelling large displacements of jointed rocks. II. Modelling of rock bolts and groundwater and applications." Canadian Geotechnical Journal 30.1 (1993):109-123.
[13]J. E. Bolander Jr. and S. Saito, "Fracture analyses using spring networks with random geometry", Engineering Fracture Mechanics, vol 61, no 5-6, pp 569-591,1998.
[14]K. Nagai, Y. Sato, and T. Ueda, "Mesoscopic Simulation of Failure of Mortar and Concrete by 2D RBSM", Journal of Advanced Concrete Technology, vol 2, no 3, pp 359-374,2004.
[15]K. Nagai, Y. Sato, and T. Ueda, "Mesoscopic Simulation of Failure of Mortar and Concrete by 3D RBSM", Journal of Advanced Concrete Technology, vol 3, no 3, pp 385-402,2005.
[16]L. Wang and T. Ueda, "Mesoscale Modelling of the Chloride Diffusion in Cracks and Cracked Concrete", Journal of Advanced Concrete Technology, vol 9, no 3, pp 241-249,2011.
[17]T. Ueda, M. Hasan, K. Nagai, Y. Sato, and L. Wang, "Mesoscale Simulation of Influence of Frost Damage on Mechanical Properties of Concrete", Journal of Materials in Civil Engineering, vol 21, no 6, pp 244-252,2009.
[18]K. Matsumoto, Y. Sato, T. Ueda, and L. Wang, "Mesoscopic Analysis of Mortar under High-Stress Creep and Low-Cycle Fatigue Loading", Journal of Advanced Concrete Technology, vol 6, no 2, pp 337-352,2008.
[19]M. Pieri, L. Burlini, K. Kunze, I. Stretton, and D. L. Olgaard, "Rheological and micro-structural evolution of Carrara marble with high shear strain:results from high temperature torsion experiments", Journal of Structural Geology, vol 23, no 9, pp 1393-1413,2001.
[20]W. Herbert, "Modelling approaches for discrete fracture network flow analysis", in Developments in Geotechnical Engineering, vol Volume 79, L. J. and C.-F. T. Ove Stephansson, Ed Elsevier,1996, pp 213-229.
[21]B. Berkowitz, "Characterizing flow and transport in fractured geological media:A review", Advances in Water Resources, vol 25, no 8-12, pp 861-884,2002.
[22]Sahimi, Muhammad. Flow and transport in porous media and fractured rock. Wiley-VCH,2012.
[23]Dershowitz, William S., Paul R. La Pointe, and Thomas W. Doe. "Advances in dicrete fracture network modeling." Proceedings of the US EPA/NGWA Fractured Rock Conference, Portland.2004.
[24]B. Berkowitz, "Analysis of fracture network connectivity using percolation theory", Mathematical Geology, vol 27, no 4, pp 467-483,1995.
[25]Balberg, B. Berkowitz, and G. E. Drachsler, "Application of a percolation model to flow in fractured hard rocks", J. Geophys. Res., vol 96, no B6, pp 10015-10,021,1991.
[26]J. Erhel, J.-R. de Dreuzy, and B. Poirriez, "Flow Simulation in Three-Dimensional Discrete Fracture Networks", SIAM Journal on Scientific Computing, vol 31, no 4, pp 2688-2705, Jan 2009.
[27]M. Wang, P. H. S. W. Kulatilake, B. B. Panda, and M. L. Rucker, "Groundwater resources evaluation case study via discrete fracture flow modeling", Engineering Geology, vol 62, no 4, pp 267-291,2001.
[28]V. V. Mourzenko, J.-F. Thovert, and P. M. Adler, "Macroscopic permeability of three-dimensional fracture networks with power-law size distribution", Phys. Rev. E, vol 69, no 6, p 066307,2004
[29]V. V. Mourzenko, J.-F. Thovert, and P. M. Adler, "Percolation of three-dimensional fracture networks with power-law size distribution", Phys. Rev. E, vol 72, no 3, p 036103,2005.
[30]M. Khamforoush, K. Shams, J.-F. Thovert, and P. M. Adler, "Permeability and percolation of anisotropic three-dimensional fracture networks", Phys. Rev. E, vol 77, no 5, p 056307,2008.
[31]Pouya and O. Fouche, "Permeability of 3D discontinuity networks:New tensors from boundary-conditioned homogenisation", Advances in Water Resources, vol 32, no 3, pp 303-314,2009.
[32]N. Koudina, R. Gonzalez Garcia, J.-F. Thovert, and P. M. Adler, "Permeability of three-dimensional fracture networks", Phys. Rev. E, vol 57, no 4, pp 4466-4479,1998.
[33]V. V. Mourzenko, I. I. Bogdanov, J.-F. Thovert, and P. M. Adler, "Three-dimensional numerical simulation of single-phase transient compressible flows and well-tests in fractured formations", Mathematics and Computers in Simulation, vol 81, no 10, pp 2270-2281,2011.
[1]L. Jing. A review of techniques, advances and outstandingissues in numerical modelling for rock mechanics and rock engineering. International Journal of Rock Mechanics and Mining Sciences.40,3, April 2003, Pages 283-353.
[2]Donze, F.V., V. Richefeu & S.-A. Magnier, Advances in Discrete Element Method applied to Soil, Rock and Concrete Mechanics, in:State of the art of geotechnical engineering, Electronic Journal of Geotechnical Engineering, p.44,2009
[3]D.O. Potyondy, P.A. Cundall. A bonded-particle model for rock. International Journal of Rock Mechanics & Mining Sciences 41 (2004):1329-1364
[4]Yuannian Wang, Fulvio Tonon. Modeling Lac du Bonnet granite using a discrete element model. International Journal of Rock Mechanics & Mining Sciences 46 (2009) 1124-1135
[5]Sebastien Hentz, Laurent Daudeville, and Frederic V. Donze. Identification and Validation of a Discrete Element Model for Concrete. Journal of Engineering Mechanics.130(6):709-720
[6]Tadahiko Kawai. New element models in discrete structural analysis. Journal of the Society of Naval Architects of Japan,141,187-193.
[7]J. E. Bolander Jr.*, Stefano Berton. Simulation of shrinkage induced cracking in cement composite overlays. Cement & Concrete Composites 26 (2004) 861-871
[8]Kohei Nagai, Yasuhiko Sato and Tamon Ueda. Mesoscopic Simulation of Failure of Motar and Concrete by 2D RBSM. Journal of Advanced Concrete Technology. 2004,2(3):359-374
[9]Zhang Xiong, Qian Lingxi. Rigid finite element and limit analysis. Acta Mechanica Sinica.9,2 (1993):156-162
[10]Qian Lingxi, Zhang Xiong. Rigid finite element and its applications in engineering. Acta Mechanica Sinica.11,1 (1995):44-50
[11]J.S.ZHUO, Q.ZHANG, N.ZHAO. Interface Stress Element Methods For Deformable Body With Discontinuous Media Such As Rock Mass.8th ISRM Congress, September 25-29,1995, Tokyo, Japan.
[12]J.E. Bolander, Jr, S. Saito. Fracture analysis using spring networks with random geometry. Engineering Fracture Mechanics.61 (1998):569-591
[13]F. Camborde, C. Mariotti, F.V. Donze. Numerical study of rock and concrete behavior by discrete element modeling.Computers and Geotechnics 27 (2000):225-247
[14]Goodman, R.E. (1976) Methods of geological engineering in discontinuous rocks, West Publishing Company, San Francisco, CA.
[15]Shi, G H. Discontinuous deformation analysis:a new numerical model for the statics and dynamics of deformable block structures. Engng ComputV9, N2, April 1992, P157-168
[16]Baolin Wang, Vinod K. Garga. A numerical method for modelling large displacements of jointed rocks. I. Fundamentals. Canadian Geotechnical Journal,1993,30(1):96-108.
[17]Yip, M., Mohle, J. and Bolander, J. E. (2005), Automated Modeling of Three-Dimensional Structural Components Using Irregular Lattices. Computer-Aided Civil and Infrastructure Engineering,20:393-407. doi:10.1111/j.1467-8667.2005. 00407.x
[18]Greengard, L., Rokhlin, V. (1987). A fast algorithm for particle simulations. Journal of Computational Physics,73(2),325-49.
[19]Steven Fortune (1987). A sweepline algorithm for Voronoi diagrams. Algorithmica. 2(1-4):153-174
[1]F. A. Donath, "Experimental Study of Shear Failure in Anisotropic Rocks", Geological Society of America Bulletin, vol 72, no 6, pp 985-989, Jan 1961.
[2]P. B. Attewell and M. R. Sandford, "Intrinsic shear strength of a brittle, anisotropic rock-Ⅰ: Experimental and mechanical interpretation", International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, vol 11, no 11, pp 423-430,1974.
[3]R. McLamore and K. E. Gray, "The Mechanical Behavior of Anisotropic Sedimentary Rocks", J. Manuf. Sci. Eng., vol 89, no 1, pp 62-73,1967.
[4]E. Hoek, "Strength of jointed rock masses", Geotechnique, vol 33, no 3, pp 187-223, Jan 1983.
[5]H. Niandou, J. F. Shao, J. P. Henry, and D. Fourmaintraux, "Laboratory investigation of the mechanical behaviour of Tournemire shale", pp 3-16, Jan 1997.
[6]Y. M. Tien, M. C. Kuo, and C. H. Juang, "An experimental investigation of the failure mechanism of simulated transversely isotropic rocks", International Journal of Rock Mechanics and Mining Sciences, vol 43, no 8, pp 1163-1181,2006.
[7]J. C. Jaeger, "Shear failure of anisotropic rocks", Geological Magazine, vol 97, no 1, pp 65-72, Jan 1960.
[8]G. Duveau and J. F. Shao, "A modified single plane of weakness theory for the failure of highly stratified rocks", International Journal of Rock Mechanics and Mining Sciences, vol 35, no 6, pp 807-813,1998.
[9]Hoek E, Brown ET. Underground excavation in rock. London:Institution of Mining and Metallurgy,1980. p.157-62.
[10]R. Hill, The Mathematical Theory of Plasticity. Oxford University Press,1998.
[11]Cazacu, N. D. Cristescu, and J. F. Shao, "A new failure criterion for transversely isotropic rocks", International Journal of Rock Mechanics and Mining Sciences, vol 35, no 4-5, p 421,1998.
[12]R. Nova, "The failure of transversely isotropic rocks in triaxial compression", International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, vol 17, no 6, pp 325-332,1980.
[13]Y. M. Tien and M. C. Kuo, "A failure criterion for transversely isotropic rocks", International Journal of Rock Mechanics and Mining Sciences, vol 38, no 3, pp 399-412,2001.
[14]Steven Fortune (1987). A sweepline algorithm for Voronoi diagrams. Algorithmica. 2(1-4):153-174
[1]M. Oda, T. Takemura, and T. Aoki, "Damage growth and permeability change in triaxial compression tests of Inada granite", Mechanics of Materials, vol 34, no 6, pp 313-331,2002.
[2]Schulze, T. Popp, and H. Kern, "Development of damage and permeability in deforming rock salt", Engineering Geology, vol 61, no 2-3, pp 163-180,2001.
[3]P. Bossart, P. M. Meier, A. Moeri, T. Trick, and J.-C. Mayor, "Geological and hydraulic characterisation of the excavation disturbed zone in the Opalinus Clay of the Mont Terri Rock Laboratory", Engineering Geology, vol 66, no 1-2, pp 19-38,2002.
[4]M. Souley, F. Homand, S. Pepa, and D. Hoxha, "Damage-induced permeability changes in granite:a case example at the URL in Canada", International Journal of Rock Mechanics and Mining Sciences, vol 38, no 2, pp 297-310,2001.
[5]F. Homand-Etienne, D. Hoxha, and J. F. Shao, "A continuum damage constitutive law for brittle rocks", Computers and Geotechnics, vol 22, no 2, pp 135-151,1998.
[6]J. F. Shao, H. Zhou, and K. T. Chau, "Coupling between anisotropic damage and permeability variation in brittle rocks", International Journal for Numerical and Analytical Methods in Geomechanics, vol 29, no 12, pp 1231-1247,2005.
[7]J. J. Zhou, J. F. Shao, and W. Y. Xu, "Coupled modeling of damage growth and permeability variation in brittle rocks", Mechanics Research Communications, vol 33, no 4, pp 450-459,2006.
[8]T. Jiang, J. F. Shao, W. Y. Xu, and C. B. Zhou, "Experimental investigation and micromechanical analysis of damage and permeability variation in brittle rocks", International Journal of Rock Mechanics and Mining Sciences, vol 47, no 5, pp 703-713,2010.
[9]J.-M. Pereira and C. Arson, "Retention and permeability properties of damaged porous rocks", Computers and Geotechnics, vol 48, pp 272-282,2013.
[10]M. S. Bruno, "Micromechanics of stress-induced permeability anisotropy and damage in sedimentary rock", Mechanics of Materials, vol 18, no 1, pp 31-48,1994.
[11]C. A. Tang, L..Tham, P. K.. Lee, T.. Yang, and L.. Li, "Coupled analysis of flow, stress and damage (FSD) in rock failure", International Journal of Rock Mechanics and Mining Sciences, vol 39, no 4, pp 477-489,2002.
[12]M. Mansouri, J.-Y. Delenne, A. Seridi, and M. S. El Youssoufi, "Numerical model for the computation of permeability of a cemented granular material", Powder Technology, vol 208, no 2, pp 532-536,2011.
[13]Yao C., Jiang QH, Shao JF, Zhou CB. A mesoscopic numerical model for simulation of rock fracturing. Chinese Journal of Rock Mechanics and Engineering.2013 (in press)
[14]Yao Chi, Jiang Qinghui, Ye Zuyang, Zhou Chuangbing. Initial flow method for unconfined seepage problems of fracture networks. Rock and Soil Mechanics, vol33, no 6, pp1896-1903,2012.
[15]Q. Jiang, C. Yao, Z. Ye, and C. Zhou, "Seepage flow with free surface in fracture networks", Water Resources Research, vol 49, no 1, pp 176-186,2013.
[16]M. F. Lough, S. H. Lee, and J. Kamath, "An Efficient Boundary Integral Formulation for Flow Through Fractured Porous Media", Journal of Computational Physics, vol 143, no 2, pp 462-483,1998.
[17]J. D. Byerlee, "Brittle-ductile transition in rocks", Journal of Geophysical Research, vol 73, no 14, pp 4741-4750,1968.
[18]Chen, G., J. M. Kemeny, and SatyaHarpalani. "Fracture propagation and coalescence in marble plates with pre-cut notches under compression." Fracture and Jointed Rock Mass 14 (1992):435-439.
[1]Alt, H. W. (1980), Numerical solution of steady-state porous flow free boundary problems, Numer. Math.,31,73-98.
[2]Andersson, J., and B. Dverstorp (1987), Conditional simulation of fluid flow in three-dimensional networks of discrete fractures, Water Resour. Res.,23(10), 1876-1886.
[3]Baghbanan, A., and L. Jing (2007), Hydraulic properties of fractured rock masses with correlated fracture length and aperture, Int. J. Rock Mech. Min. Sci.,44(5),704-719.
[4]Bathe, K. J., and M. R. Khoshgoftaar (1979), Finite element free surface seepage analysis without mesh iteration, Int. J. Nume.r Anal. Meth. Geomech.3,13-22.
[5]Berkowitz, B. (2002), Characterizing flow and transport in fractured geological media: A review, Adv. Water Resour.,25,861-884.
[6]Brezis, H., D. Kinderlehrer, and G. Stampacchia (1978), Sur une nouvelle formulation due probleme de l'ecoulement a travers une digue, Comptes Rendus de l'Academie des Sciences Paris Series A,287,711-714
[7]Cacas, M. C., E. Ledoux, G. de Marsily, B. Tillie, A. Barbreau, E. Durand, B. Feuga, and P. Peaudecerf (1990), Modeling fracture flow with a stochastic discrete fracture network:calibration and validation 1. The flow model, Water Resour. Res.26(3), 479-489.
[8]Desai, C. S., and G. C. Li (1983), A residual flow procedure and application for free surface flow in porous media, Adv. Water Resour.,6,27-35.
[9]Dershowitz, W. S., and H. H. Einstein (1987), Three dimensional flow modeling in jointed rock masses, In:Herget, Vongpaisal, editors. Proceedings of the sixth international congress on rock mechanics, vol.1., Rotterdam, Balkema, pp.87-92.
[10]Duiguid, J. O., and P. C. Y. Lee (1977), Flow in fractured porous media, Water Resour. Res.,13(3),25-28.
[11]Finn, W. D. L. (1967), Finite-element analysis of seepage through dams, J. Soil Mech. Foundat. Div., ASCE,93(SM6),41-48.
[12]Hsieh, P. A., and S. P. Neuman (1985), Field determination of the three dimensional hydraulic conductivity tensor of anisotropic media-1. Theory, Water Resour. Res., 21(11),1655-1665.
[13]Jackson, C. P., A. R. Hoch, and S. Todman (2000), Self-consistency of a heterogeneous continuum porous medium representation of a fractured medium, Water Resour. Res., 36(1),189-202.
[14]Jing, L., Y. Ma, and Z. Fang (2001), Modeling of fluid flow and solid deformation for fractured rocks with discontinuous deformation analysis (DDA) method, Int. J. Rock Mech. Min. Sci.,38(3),343-355.
[15]Kikuchi, N. (1977), An analysis of the variational inequalities of seepage flow by finite-element methods, Quart. Appl. Math.,35,149-63.
[16]Lacy, S. J., and J. H. Prevost (1987), Flow through porous media:a procedure for locating the free surface. Int. J. Numer. Anal. Meth. Geomech.,11,585-601.
[17]Long, J. C. S., P. Gilmour, and P. A. Witherspoon (1985), A method for steady fluid flow in random three-dimensional networks of disc-shaped fractures, Water Resour. Res.21(8),1105-1115.
[18]Long, J. C. S., J. S. Remer, C. R. Wilson, and P. A. Witherspoon (1982), Porous media equivalents for networks of discontinuous fractures, Water Resour. Res.,18(3), 645-658.
[19]Min, K. B., L. Jing, O. Stephansson (2004), Determining the equivalent permeability tensor for fractured rock masses using a stochastic REV approach:method and application to the field data from Sellafield UK, Hydrogeol. J.,12(5),497-510.
[20]Neuman, S. P., and P. A. Witherspoon (1970), Finite element method of analyzing steady seepage with a free surface, Water Resour. Res.,6(3),889-897.
[21]Oda, M. (1985), Permeability tensor for discontinuous rock masses, Geotechnique, 35(4),483-495.
[22]Oda, M. (1986), An equivalent continuum model for coupled stress and fluid flow analysis in jointed rock masses, Water Resour. Res.,22 (13),1845-1856.
[23]Oden, J. T., and N. Kikuchi (1980), Recent advances:theory of variational inequalities with applications to problems of flow through porous media, Int. J. Eng. Sci.18, 1173-1284.
[24]Schwartz, F. W., W. L. Smith, and A. S. Crowe (1983), A stochastic analysis of microscopic dispersion in fractured media, Water Resour. Res.19(5),1253-1265.
[25]Snow, D. T. (1969), Anisotropic permeability of fractured media, Water Resour. Res., 5(6),1273-1289.
[26]Streltsova, T. D. (1981), Hydrodynamics of groundwater flow in a fractured formation, Water Resour. Res.17(4),21-22.
[27]Taylor, R. L., and C. B. Brown (1967), Darcy flow solutions with a free surface, J. Hydr. Div.,ASCE,93,25-33.
[28]Westbrook, D. R. (1985), Analysis of inequalities and residual flow procedures and an iterative scheme for free surface seepage, Int. J. Numer. Meth. Eng.21,1791-1802.
[29]Wilson, C. R., and P. A. Witherspoon (1974), Steady state flow in rigid networks of fractures, Water Resour. Res.,10(2),328-335.
[30]Zhang, Y. T., P. Chen, L. Wang (1988), Initial flow method for seepage analysis with free surface, Journal of Hydraulic Engineering,8(1),18-26.
[31]Zhang, Y. T. (1999), Water pressure of high rock slope and the permanent shiplock, in Deformation and stability of high rock slope, edited by Y. T. Zhang and W. Y. Zhou, pp. 76, China Water Power Press, Beijing.
[32]Zheng, T. S., L. Li, and Q. Y. Xu (1995), An iterative method for the discrete problems of class of elliptical variational inequalities, Applied Mathematics and Mechanics, 16(4),351-358.
[33]Zheng, H., D. F. Liu, C. F. Lee, L. G. Tham (2005), A new formulation of Signorini's type for seepage problems with free surfaces, Int. J. Numer. Meth. Eng.,64,1-16.
[34]Zhou, C. B., W. L. Xiong, and Y. G. Liang (1996), A new method for unconfined seepage field, J. Hydrodyn., Ser. A,11(5),528-534.
[1]Berkowitz B. Characterizing flow and transport in fractured geological media:a review[J]. Adv Water Resour,2002,25(8):3861-84.
[2]Neretnieks I, Eriksen T, Tahtinen P. Tracer movement in a singlefissure in granitic rock: some experimental results and theirinterpretation[J]. Water Resour Res 1982;18(4):849-58.
[3]Neretnieks I. Solute transport in fracture rock-Applications toradionuclide waste repositories. In:Bear J, Tsang CF, de MarsilyG, editors. Flow and contaminant transport in fractured rock.San Diego:Academic Press, Inc; 1993. p.39-127.
[4]Oda, M. (1985), Permeability tensor for discontinuous rock masses, Geotechnique, 35(4),483-495.
[5]Oda, M. (1986), An equivalent continuum model for coupled stress and fluid flow analysis in jointed rock masses, Water Resour. Res.,22 (13),1845-1856.
[6]Neuman, S. P. (1973), Saturated-unsaturated seepage by finite elements. Journal of the Hydraulics Division,99(12),2233-2250.
[7]Sahimi M. Flow and transport in porous media and fracturedrock:from classical methods to modern approaches. Weinheim,Germany:VCH; 1995.
[8]Adler PM, Thovert JF. Fractures and fracture networks. Netherlands:Kluwer Academic Publishers; 1999.
[9]M. C. Cacas, E. Ledoux, G. de Marsily, A. Barbreau, P. Calmels, B. Gaillard, and R. Margritta, "Modeling fracture flow with a stochastic discrete fracture network: Calibration and validation:2. The transport model", Water Resources Research, vol 26, no 3, pp 491-500,1990.
[10]W. Nordqvist, Y. W. Tsang, C. F. Tsang, B. Dverstorp, and J. Andersson, "A variable aperture fracture network model for flow and transport in fractured rocks", Water Resources Research, vol 28, no 6, pp 1703-1713,1992.
[11]Rouleau and J. E. Gale, "Stochastic discrete fracture simulation of groundwater flow into an underground excavation in granite", International Journal of Rock Mechanics and Mining Sciences &Geomechanics Abstracts, vol 24, no 2, pp 99-112,1987.
[12]J. Andersson and B. Dverstorp, "Conditional simulations of fluid flow in three-dimensional networks of discrete fractures", Water Resources Research, vol 23, no 10, pp 1876-1886,1987.
[13]N. Koudina, R. Gonzalez Garcia, J.-F. Thovert, and P. M. Adler, "Permeability of three-dimensional fracture networks", Phys. Rev. E, vol 57, no 4, pp 4466-4479,1998.
[14]M. Khamforoush, K. Shams, J.-F. Thovert, and P. M. Adler, "Permeability and percolation of anisotropic three-dimensional fracture networks", Phys. Rev. E, vol 77, no 5, p 056307,2008.
[15]V. V. Mourzenko, J.-F. Thovert, and P. M. Adler, "Permeability of isotropic and anisotropic fracture networks, from the percolation threshold to very large densities", Phys. Rev. E, vol 84, no 3, p 036307,2011.
[16]ZHANG Youtian,CHEN Ping,WANG Lei. Initial flow method for seepage analysis with free surface [J]. Journal of Hydraulic Engineering,1988,8 (1):18-26. (in Chinese)
[17]H. Zheng et al. A new formulation of Signorini's type for seepage problems with free surfaces. International journal for numerical methods in engineering 64, no.1 (2005): 1-16.
[18]Y. Chen, C. Zhou, and H. Zheng. A numerical solution to seepage problems with complex drainage systems. Computers and Geotechnics 35, no.3 (2008):383-393.
[19]WANG Enzhi. Seepage calculation method in fissure networks on vertical section. Hydrogeology & Engineering Geology,20, no.4 (1993):27-29. (in Chinese)
[20]CHAI Junrui, WUYanqing. The method for determination of the position of free surface in fractured rock masses.Geotechnical Investigation & Surveying, no.1 (2000): 23-24. (in Chinese)
[21]Yao Chi, Jiang Qinghui, Ye Zuyangetc..Thevariationalinequality based initial flow method for unconfined seepage problems of fracture networks[J]. Rock and Soil Mechanics,2012,33(6):1896-1903.(in Chinese)
[22]Jiang, Q., C. Yao, Z. Ye, and C. Zhou. Seepage flow with free surface in fracture networks. Water Resour. Res., (in press, accepted 12 November 2012)
[23]Q. Jiang, Z. Ye, C. Yao, and C. Zhou, A new variational inequality formulation for unconfined seepage flow through fracture networks, Sci. China Technol. Sci., vol 55, no 11, pp 3090-3101, Nov 2012.
[24]Liu Zhong, Zhang Youtian.Analysis of free surface seepage problems inthree dimensional network of fracture[J]. ShuiliXuebao.1996,6:34-38.(in Chinese)
[25]Zhang Qihua, Wu Aiqing. Three-dimensional arbitrary fracture network seepage model and its solution[J]. Chinese Journal Rock Mechanics and Engineering,2010,29(4): 720-730 (in Chinese)
[26]Zhang Qihua, Wu Aiqing. General methodology of spatial block topological identification with stochastic discontinuities cutting[J]. Chinese Journal Rock Mechanics and Engineering,2007,26(10):2044-2048 (in Chinese)
[27]MAO Changxi. Seepage Computation Analysis & Control. Beijing:China WaterPowerPress,2003. (in Chinese)
[1]Neretnieks. Diffusion in the rock matrix:an important factor in radionuclide retardation?[J]. J Geophys Res,1980,85 (B8):4379-4397.
[2]Witherspoon PA. Introduction to second world wide review of geological problems in radioactive waste isolation, Geological Problems in Radioactive Waste Isolation[R]. 1996, LBNL-38915, UC-814:1-4
[3]L. Jing, Y. Ma, and Z. Fang, Modeling of fluid flow and solid deformation for fractured rocks with discontinuous deformation analysis (DDA) method[J]. International Journal of Rock Mechanics and Mining Sciences,2001,38(3):343-355.
[4]X Zhang, DJ Sanderson. Effects of stress on the 2-D permeability tensor of natural fracture networks[J]. Geophys J Int,1996,125:912-924
[5]K.-B. Min, J. Rutqvist, C.-F. Tsang, et al. Stress-dependent permeability of fractured rock masses:a numerical study[J]. International Journal of Rock Mechanics and Mining Sciences,2004,41(7):1191-1210.
[6]Baghbanan and L. Jing. Stress effects on permeability in a fractured rock mass with correlated fracture length and aperture[J]. International Journal of Rock Mechanics and Mining Sciences,2008,45(8):1320-1334.
[7]Z. Zhao, L. Jing, I. Neretnieks, and L. Moreno. Numerical modeling of stress effects on solute transport in fractured rocks[J]. Computers and Geotechnics,2011,38(2):113-126.
[8]Berkowitz B. Characterizing flow and transport in fractured geological media:a review[J]. Adv Water Resour,2002,25(8):3861-84.
[9]Neuman SP. Trends, prospects and challenges in quantifying flow and transport through fractured rocks[J]. Hydrogeol J,2005,13(1):124-47.
[10]Neretnieks I. Fast method for simulation of radionuclide chain migration in dual porosity fracture rocks[J]. Journal of Contaminant Hydrology,2006,88:269-288.
[11]Kawai. A new element in discrete analysis of plane strain problems[J]. Seisan Kenkyu, 1977,29 (4):204-207
[12]Zhuo JiaShou, Zhao Ning. Piecewise Rigid Body Interface Spring Method for Problems of Discontinuous Medium[J]. Journal of Hohai University,1993, 21(5):34-43(in Chinese)
[13]Chen Shenghong. A general formulation of elastic-viscoplastic block theory of rock masses[J]. Journal of Hydraulic Engineering,1996,1:78-84 (in Chinese)
[14]Qian Lingxi, Zhang Xiong. Rigid Body Finite Element Method in Structural Analysis[J]. Computational Structural Mechanics and Applications,1991,8(1):1-14 (in Chinese)
[15]L. Moreno and I. Neretnieks. Fluid flow and solute transport in a network of channels[J]. Journal of Contaminant Hydrology,1993,14(3-4):163-192,.
[16]M. C. Cacas, 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 Resources Research,1990,26(3):491-500.
[17]R. YAMASHITA and H. KIMURA. Particle-tracking technique for nuclide decay chain transport in fractured porous media[J]. Journal of Nuclear Science and Technology, 1990,27(11):1041-1049.
[18]L. Jing, C.-F. Tsang, and O. Stephansson. DECOVALEX- An international co-operative research project on mathematical models of coupled THM processes for safety analysis of radioactive waste repositories[J].International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts,1995,32(5):389-398.
[19]Baolin Wang, Vinod K. Garga. A numerical method for modelling large displacements of jointed rocks. I. Fundamentals[J]. Canadian Geotechnical Journal,1993,30(1): 96-108.
[20]Yao Chi, Jiang Qinghui, Ye Zuyang etc.Initial flow method for unconfined seepage problems of fracture networks[J]. Rock and Soil Mechanics,2012,33(6):1896-1903.(in Chinese)
[21]Yao Chi, Jiang Qinghui, Chen Yifeng, Zhou Chuangbing. Numerical Simulation of Nuclide Transport in Complex Fracture Network[J]. Disaster Advances.2012, 5(4):197-201
[22]Iwai K. Fluid flow in simulated fractures[J]. Am Inst Chem Eng J 1976,2:259-263.
[23]Iwai K. Fundamental studies of fluid flow through a single fracture. [Ph.D. thesis] [D]. USA:Univ. of California, Berkeley,1976.
[24]T. Belytschko, M. Plesha, C. H Dowding, A computer method for stability analysis of caverns in jointed rock[J]. International journal for numerical and analytical methods in geomechanics,1984,8(5):473-492.
[25]Nirex. Data summary sheets in support of gross geotechnical predictions[R]. Nirex report SA/97/052, Harwell, UK; 1997a.
[26]Zhu Bofang. The finite element theory and applications. Beijing:China Water & Power Press,1998