本研究主要目的為評估破裂岩體水力及污染物傳輸行為，藉由當量化之數值破裂岩體模型，分析不同岩體幾何模型對破裂岩體之水力性質影響，以建立破裂岩體模式選擇方法，並融合離散及連續模式之優點，發展以破裂面為主及異質岩體為輔之複合物件/像素破裂岩體模式(hybrid object/pixel model)，有效整合於隧道滲流研究及破裂岩體污染物傳輸之分析。
本研究首先利用三種典型空間幾何模型，包含Enhanced Baecher Model(EBM)、Levy-Lee Fractal Model(LLFM)及Nearest Neighbourhood Model(NNM)等模式，應用台灣蘭嶼地區參數，探討破裂面密度對地下水流動之影響。其中，空間破裂面密度分佈(P32)將直接影響滲透係數空間分佈，其總水頭分佈將隨滲透係數之變動，而表現出程度不等的偏移。另外，由地下水流速與破裂面密度之相關係數結果顯示，僅研究破裂面密度並非是影響地下水流況之主要因子，而透過粒子追蹤方法可得知Levy-Lee Fractal Model(LLFM)將相對其他模式適用，將可提供於後續破裂岩體模式進階研究之參考。
在建構複合物件/像素破裂岩體模式之研究上，主要以發展破裂面密度及破裂面位態參數生成之模型，透過循序階層化技術、破裂面間距及破裂面生長規則等限制條件，產生破裂面空間分佈並計算等效滲透係數數值網格，以更有彈性及效率拓璞破裂岩體空間。其中，於處置隧道滲流研究中，可發現因介質滲透性差異導致滲流方向將往破裂面叢集處集中，致使總水頭場形成明顯變化的管道效應；當釋放一固定污染源，其污染團將於緩衝帶內呈現出橢圓形擴散，隨著其接觸周圍破裂岩體時，污染團將往滲流方向及破裂面優勢方向運移。而由於周遭破裂面交接重疊成一介面，將可有效阻隔污染擴展及傳輸，且污染團僅約比初始位置擴張約20至30米左右。
最後，本研究應用此四種模式(離散破裂面模式、當量破裂岩體模式、複合物件/像素破裂岩體模式及傳統連體模式)於台灣蘭嶼地區。而由粒子累積機率分佈曲線之比較，可發現模擬趨勢與日本H12計畫成果Doughty and Karasaki (1999)相符。其中，離散破裂面模式粒子傳輸時間最短；而傳統連體模式模式粒子傳輸時間最長，而本研究發展之破裂岩體模式，其粒子傳輸時間則介於離散及連續兩種模式之間，代表此方法皆可有效顯示出複合破裂岩體之傳輸特性，更凸顯本研究已具備多種不同破裂岩體概念的模擬能力，將會是相關問題探討中之重要研究貢獻。

This study aims to assess the rock mass hydraulic and contaminant transport behavior. Firstly, the equvalent model is employed to make analysis on hydraulic properties through different geometrical models and to build the initial chice of fracture generation. Secondly, the hybrid object/pixel model is also integrated by the merits of discrete and continuum method to follow case of a disposal tunnel seepage and contaminant transport.
Three conceptually classical models following a stochastic realization of polygonal fractures classified by a crack tensor approach such as the Enhanced Baecher’s model, the Levy-Lee Fractal’s model and the Nearest Neighborhood’s model are generated in this study.
Models are developed from a geological data set of fractured andesite in LanYu island (Taiwan). Three different cases of conceptual models are erected, such as an Enhanced Baecher's model (EBM), a Levy-Lee Fractal model (LLFM) and a Nearest Neighborhood model (NNM). Simulated flow field is disclosed that the EBM model is smoother than the others. And resulting flow vectors are very sensitive to spatial fracture intensity (P32). Flow velocity increases with higher fracture intensity (P32) but the R-squared values of regression analysis for the variable velocity (V/Vmax) and fracture intensity (P32) in whole fractured rock are less than 0.7, implicitly meaning that the fracture intensity will not be great enough to master the groundwater flow. From the particles’ transport, Levy-Lee Fractal model will be compared with others and provide a basis for advanced simulation.
Besides, a hybrid object/pixel approach of fracture continuum model is formulated for the advanced study on small-scale flow analysis on seepage of disposal tunnel within much various material of permeability. On account of the uncertainty of fractures distributed in space and the sensitivity of up-scaling, it is proposed that in near field the fractures are topologically mapped in details however in the far field the fractures are equivalently up-scaling the grids of fractures. And the flow will be caused to channel effect because of converge on fractures. The contaminants’ transport is utilized in the center of the tunnel where plume will be following the domiant direction of flow and the spreading of the plume is apparently prohibited from the existing fractures. The expansion of the plume is only about 20 to 30 meters larger than the initial position.
Finally, four different models are compared with particles’ transport. Overall, the travelling time of discrete fracture network model is the fast among all models because only fractures are considered. On the contrary the travelling time of traditional porous model is the most time-comsuing. On account of the two models developed in this research, the average behavior of transport is among the discrete and the porous models showing that the two methods have the ability to uncover the characteristics of transport very important to issues related to research methods.

1. Ando, K., A. Kostner, and S. P. Neuman. (2003), “Stochastic continuum modeling of flow and transport in a crystalline rock mass: Fanay-Augres, France, revisited”, Hydrogeol. J., 11 521–535.
2. Baecher, G. B. (1983), “Statistical analysis of rock mass fracturing”, Math. Geo., 15, 329-347,.
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, 704–71.
4. Barenblatt, G.E., Zheltov, I.P., and Kochina, I.N. (1960), “Basic concepts in the theory of homogeneous liquids in fissured rocks”, J. Applied Math.Mech., 24(5), 1286-1303.
5. Barton, C.A., Zoback, M.D., and Moos, D. (1995), “Fluid flow along potentially active faults in crystalline rock”, Geology, 23(8), 683-686.
6. Bear, J. (1972), “Dynamics of fluids in porous media.”Elsevier, New York.
7. Bill, X. Hu., H. Huang., and D. Zhang. (2002), “Stochastic analysis of solute transport in heterogeneous, dual-permeability media”, Water Resour. Res., 38(9), 1175 doi:10.1029/2001WR00042,.
8. Botros, F. E., A. E. Hassan, D. M. Reeves, and G. Pohll. (2008), “On mapping fracture networks onto continuum”, Water Resour. Res., 44, W08435, doi:10.1029/2007WR006092.
9. Bourbiaux, B., et al. (1998), “A rapid and efficient methodology to convert fractured reservoir images into a dual‐porosity model”, Rev. Inst. Fr. Pet.,53(6), 785–799.
10. Brace W. F. (1980), “Permeability of argillaceous and crystalline rocks”, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 17, 241-251.
11. Brooks, B. A., R. W. Allmendinger, and G. I. de al Barra. (1996), “Fault spacing in the El Teniente Mine, central Chile: evidence of nonfractal fault geometry”, J. Geophy. Res., 101(B6), 13,633–653.
12. Cacas, M. C., E. Ledoux, G. de Marsily, A. Barbreau, P. Calmels, B. Gaillard, and R. Margritta. (1990b), “Modeling fracture flow with a stochastic discrete fracture network: calibration and validation 2. The Transport Model”, Water Resour. Res., 26(3), 491—500.
13. Cacas, M. C., E. Ledoux, G. de Marsily, B. Tillie, A. Barbreau, E. Durand, B. Feuga, and P. Peaudecerf. (1990a), “Modeling fracture flow with a stochastic discrete fracture network: calibration and validation 1. The Flow Model”, Water Resour. Res., 26(3), 479–489.
14. Cacas, M.C. J.M. Daniel, and J. Letouzey. (2001), “Nested geological modelling of naturally fractured reservoirs”, Petrol. Geosci., 7, S43–S52.
15. Call, R. D., Savely, J. P. and Nicholas, D. E. (1976), “Estimation of joint set characteristics from surface mapping”, U.S. Symp. On Rock Mech., 2B2-1-2B2.
16. Chen, R. H., Lee, C. H. and Chen, C. S. (2001), “Evaluation of transport of radioactive contaminant in fracture rock”, Environ. Geo., 41, 440-450.
17. Chiles, J. P. (1988), “Fractal and geo-statistical methods for modeling of a fracture network”, Math. Geo., 20(6), 631-654.
18. Cruden, D. M. (1977), “Describing the size of discontinuities”, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 14, 133-137.
19. Doughty, C. and K. Karasaki (1999), “Using an effective continuum model for flow and transport in fractured rock: The H-12 flow comparison”, Rep. LBNL-44966, Lawrence Berkeley National Laboratory,Berkeley, Calif., 1999.
20. Cvetkovic, V., S. Painter, N. Outters, and J. O. Selroos. (2004), “Stochastic simulation of radionuclide migration in discretely fractured rock near the Aspo Hard Rock Laboratory”, Water Resour. Res., 40, W02404,doi:10.1029/2003WR002655.
21. Deng, H., Z. Dai., A. Wolfsberg, Z. Lu, M. Ye, and P. Reimus. (2010), “Upscaling of reactive mass transport in fractured rocks with multimodal reactive mineral facies”, Water Resour. Res., 46, W06501, doi:10.1029/2009WR008363.
22. Dershowitz, W., Lee, G., Geler, J., Foxford, T., La, Pointe and Thomas, P. (1998), “A FracMan: interactive discrete feature data analysis, geometric modeling, and exploration simulation, version 2.6.User documentation” , Golder’s Associates, Seattle, Washington.
23. Dershowitz, W., and H.H. Herda. (1992), “Interpretation of fracture spacing and intensity”, Proceedings of the 33rd U.S. Symposium on Rock Mechanics, Santa Fe, NM, 757.
24. Dershowitz, W., G. Lee, and T. Foxford, (2004) “FracWorks XP discrete fracture modeling software, User Documentation”, WA, Golder.
25. Dershowitz, W., S., (1984) “Rock joint system”, Ph.D. Thesis Massachusetts Institute of Technology, Cambridge, Massachusetts.
26. Dershowitz, W.S. and Einstein, H.H. (1988), “Characterizing rock joint geometry with joint system models”, Rock Mechan. and Rock Eng., 21, 21–51.
27. Deutsch, C.V. and Journel, A.G. (1998), “GSLIB: Geostatistical Software Library and user’s guide, 2nd edition”, Oxford University Press, New York, 368 p.
28. Donald, M. R., D. A. Benson, and M. M. Meerschaert (2008a), “Transport of conservative solutes in simulated fracture networks: 1.Synthetic data generation”, Water Resour. Res. 44, W05404, doi:10.1029/2007WR006069.
29. Donald M. R., D. A. Benson, and M. M. Meerschaert (2008b), “Transport of conservative solutes in simulated fracture networks: 2. Ensemble solute transport and the correspondence to operator-stable limit distributions”, Water Resour. Res. 44, W05410, doi:10.1029/2007WR006858.
30. Dreuzy, J. R., Davy, P., and Bour, O. (2001), “Hydraulic properties of two dimensional random fracture networks following a power law distribution 1.Effective Connectivity”, Water Resour. Res., 37(8),2065-2078.
31. Frampton. A., and V. Cvetkovic (2008), “Significance of injection modes and heterogeneity on spatial and temporal dispersion of advecting particles in two-dimensional discrete fracture networks”, Adv. in Water Resour., doi:10.1016/j.advwatres.2008.07.010.
32. Goodman, R.E. (1976), “Methods of geological engineering in discontinuous rock”, West, St. Paul, MN, 58-90.
33. Granet, S., P. Fabrie, P. Lemonnier, and M. Quintard (2001), “A two-phase f low simulation of a fractured reservoir using a new fissure element method”, J. Petro. Sci. Eng., 32, 35–52.
34. Gringarten, E. J. (1998), “Fracnet: stochastic simulation of fractures in layered systems”, Com.& Geosci., 24(8), 729-736.
35. Haldorsen, H.H. and E. Damsleth (1990), “Stochastic modeling”, J. Petro. Tech., 42(4): 404-412.
36. Hsieh. P.A., Neuman, S.P., Stiles, G.K., Simpon, E.S. (1985), “Field determination of the three-dimensional hydraulic conductivity tensor of anisotropic media,2, methodology and application to fractured rocks”,Water Resour Res 21, 1667-1676.
37. 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, doi:10.1029/1999WR900249.
38. Johnson, J., and S. R. Brown (2001)., “Experimental mixing variability in intersecting natural fractures”, Geophy. Res. Let., 28(22), 4303-4306.
39. Karimi‐Fard, M., B. Gong, and L. J. Durlofsky (2006), “Generation of coarse‐scale continuum flow models from detailed fracture characterizations”,Water Resour. Res., 42(10), W10423, doi:10.1029/2006WR005015.
40. Khamforoush.M., and K. Shams. (2007), “Percolation thresholds of a group of anisotropic three-dimensional fracture networks”, Phy. A., 385: 407-420.
41. Kulatilakea, Pinnaduwa, H.S.W., Jeong-gi Uma., M. Wanga., F. E, Richard, and John, N. (2003), “Stochastic fracture geometry modeling in 3-D including validations for a part of Arrowhead East Tunnel, California, USA”, Eng. Geo., 70: 131-155.
42. Law, A. M. and Kelton, W. D. (1991), “Simulation modeling and analysis”, McGraw-Hill International Edistionsm New-York, U.S.A., 420-492.
43. Lee, C. C. , C. H. Lee H. F. Yeh and H.I. Lin (2011), “Modeling spatial fracture intensity as a control on flow in fractured Rock”, Environ. Earth Sci.,(accepted for publication).
44. Lee, C.C., T.F. Tseng, F.L. Chang, W.S Chuang, H.F. Yeh, C.H. Lee (2008), “Evaluation of the flow and transport of granite using a 3-D discrete fracture network model”, E.A.F.O.R.M., Tokyo.
45. Lee, C.H., C.C. Lee, and B.S. Lin (2007), “The estimation of dispersion behavior in discrete fractured networks of andesite in Lan-Yu Island, Taiwan”, Environ. Geo. 52(7), 1297-1306.
46. Lin, B. S., and C.H. Lee (1998), “Percolation and dispersion of mass transport in saturated fracture network”, Water Resou. Manage. 12, 409-432.
47. Lin, B. S., C.H. Lee, and J.L.Yu (2000), “Analysis of groundwater seepage of tunnels in fracture rock”, J. Chine.Institute Environ. Engin., 23(3), 155-160.
48. Long, J.C.S., Remer, C.R., Wilsion, C.R., and Witherspoon, P.A. (1982), “Porous media equivalents for networks of discontinuous fractures”, Water Resour. Res., 18(3), 645-648.
49. Loosveld, R.J.H. and R.C.M.W. Franssen (1992), “Extensional vs. shear fractures: Implications for reservoir characterization.” Proceed. Euro. Petro. Con., Cannes, France, 23-30.
50. Martin, G. and John, H. (2008), “A design methodology for rock slopes susceptible to wedge failure using fracture system modeling”, Eng. Geo., 96, 78–93.
51. Min, K.B, L. Jing, Ove. 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, 497-510.
52. Moench, A. F. (1984), “Double-Porosity models for a fissured groundwater reservoir with fracture skin”, Water Resour. Res., 20(7), 831-846.
53. Mourzenko, V. V., F. Yousefian, B. Kolbah, J.F. Thovert, and P. M. Adler (2001), “Solute transport at fracture intersections,” Water Resour. Res. 38(1), 1000, doi:10.1029/2000WR000211.
54. Moussa, K., Rachid, A., Benoit, N., and Michel, Q. (2004), “Matrix-fracture exchange in a fractured porous medium: stochastic upscaling”, C. R. Mecanique, 332, 679-686.
55. Nakaya, S. and K. Nakamura (2007), “Percolation conditions in fractured hard rocks: A numerical approach using the three‐dimensional binary fractal fracture network (3D‐BFFN) model”, J. Geophys. Res., 112, B12203, doi:10.1029/2006JB004670.
56. National Research Council (1996), “Rock fractures and fluid flow: contemporary understanding and applications”, Washington, D.C.: National Academy Press.
57. Novakowski, K.S., Evans, G.V., Lever, D,A., Raven, K,G. (1985), “A field example of measuring hydrodynamic dispersion in a single fracture”, Water Resour. Res. 21, 1165-1174.
58. 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.
59. Oda, M. (1985), “Permeability Tensor for Discontinuous Rock Masses”, Geotech., 35,483-495.
60. Outters, N., and D. Shuttle (2000), “Sensitivity analysis of a discrete fracture network model for performance assessment of Aberg”, Rep. 00-48, Swed.Nucl. Fuel Waste Manage. Co., Stockholm.
61. Pahl, P. J. (1981), “Estimation the mean length of discontinuity traces”, Int. J. Rock Mechan. Min. Sci. & Geomechan. Abstr., 18, 221-228.
62. Pan J. B., C. C. Lee, C. H. Lee, H. F. Yeh and H.I. Lin (2010), “Application of fracture network model with crack permeability tensor on flow and transport in fractured rock”, Eng. Geo., 116, pp.166-177.
63. Park, Y.J., K,K., Lee, G. Kosakowski, and B. Berkowitz (2003), “Transport behavior in three-dimensional fracture intersections”, Water Resour. Res.. 39(8), 1215, doi:10.1029/2002WR001801.
64. Park, Y.J., K.K. Lee, and B. Berkowitz (2001), “Effects of junction transfer characteristics on yransport in fracture networks”, Water Resource Research, 37(4), 909–923.
65. Piggott, A.R. (1997), “Fractal relations for the diameter and trace length of dis-shaped fractures”, J. Geophy. Res., 102(B8), 1800-1821.
66. Priest, S. D. and Hudson, J. A. (1976), “Discontinuity spacings in rock” Int. J. Rock Mechan. & Min. Sci., 113, 135-148.
67. Priest, S. D. and Samaniego, A. (1983), “A model for the analysis of discontinuity characteristic in two dimension”, Proc. 5th Cong. ISRM, Melbourn, F199-F207.
68. Priest, S. D. (1993), Discontinuity analysis for rock engineering, Chapman and Hall.
69. Priest, S.D. and Hudson J.A. (1976), “Discontinuity spacings in rock”, Int. J. Rock Mechan. & Min. Sci., 13(5), 135-148.
70. Reeves, D. M., D. A. Benson, and M. M. Meerschaert (2008),“Transport of conservative solutes in simulated fracture networks: 1. Synthetic data generation”, Water Resour. Res., 44(5), W05404, doi:10.1029/2007WR006069.
71. Rives, T., M. Razack, J.P. Petit, and K. D. Rawnsley (1992), “Joint spacing: analogue and numerical simulations”, J. Structur. Geo., 14, 925–937.
72. Rocha, M, and Franciss, F. (1977), “Determination of permeability in anistropic rock masses from integral samples”, Int. J. Rock Mech. 9 : 55-71.
73. Roubinet, D., J.‐R. de Dreuzy, and P. Davy (2010), “Connectivity‐consistent mapping method for 2‐D discrete fracture networks”, Water Resour. Res., 46, W07532, doi:10.1029/2009WR008302.
74. Rouleau, A., and Gale, J.E. (1987), “Stochastic discrete fracture simulation of groudwater flow into an underground excavation in granite”, Int. J. Rock Mechan. Min. Sci. & Geomechan. Abstr. 24(2), 99-112.
75. Samardzioska, T., and V. Popov (2005), “Numerical comparison of the equivalent continuum, non-homogeneous and dual porosity models for flow and transport in fractured porous media”, Advan. in Water Resour., 28, 235– 255.
76. Schwartz, F. W., L. Smith, and A. S. Crowe (1983), “A stochastic analysis of macroscopic dispersion in fractured media”, Water Resour. Res., 19(5), 1253–1265.
77. Smith, L., and F. W. Schwartz (1984), “An analysis on the influence of fracture geometry on mass transport in fractured media”, Water Resour. Res., 20(9), 1241–1252.
78. Snow, D,T. (1968), “Rock fracture spacings, openings and porosities.”J. Soil Mech. Found. Div. A.S.C.E .94(SM1), 73-91.
79. Snow, D.T. (1969), “Anisotropic permeability of fractured media”, Water Resour. Res., 5, 1273-1289.
80. Snow, D.T. (1970), “The frequency and apertures of fractures in rock”, Int. J. Rock Mechan. Min. Sci. & Geomech. Abstr., 7, 23-40.
81. Stockman, H. W., J. Johnson. and S. R. Brown (2001), “Mixing at fracture intersections: Influences of channel geometry and the Reynolds and Peclet numbers”, Geophy. Res. Let. 28(22), 4299-4302.
82. Surrette, M., D. M. Allen, and M. Journeay (2008), “Regional evaluation of hydraulic properties in variably fractured rock using a hydro-structural domain approach”, Hydrogeol. J., 16,11–30.
83. Svensson, U. (2001), “A continuum representation of fracture networks.Part I: Method and basic test cases”, J. Hydrol., 250(1–4),170–186,doi:10.1016/S0022-1694(01)00435-8.
84. Villaescusa, E. and Brown, E. T. (1990), “Characterizing joint spatial correlation using geostastical methods”, Rock Joint, Barton and Stephansson, Balkema, 115-122.
85. Wallis, P.E. and King, M.S. (1980), “Discontinuity spacing in a crystalline rock”, Int. J. Rock Mechan. Min. Sci. & Geomechan. Abstr., 17, 63-66.
86. Warren, J.E., and Root, P.J. (1963), “The behavior of naturally fractured reservoirs”, Trans. Society Petro. Eng. A.I.M.E., 3(3), 245-255.
87. Wines, D. R., and P. A. Lilly (2002), “Measurement and analysis of rock mass discontinuity spacing and frequency in part of the Fimiston Open Pit operation in Kalgoorlie, West Australia: A case study”, Inte. J. Rock Mechan. Min. Sci., 39, 589–602.
88. Witherspoon, P.A., Wang, J.C.Y., Iwall, K., Gale, J.E. (1980),“Validity of cubic law for fluid flow in a deformable rock fracture”, Water Resour Res 16,1016-1024.
89. Xu, W. (1996), “Conditional curvilinear stochastic simulation using pixel-based algorithms”, Math. Geo., 28(7), 937-950.
90. Xu, C., P. A. Dowd, K. V. Mardia, and R. J. Fowell (2006), “A connectivity index for discrete fracture networks”, Math.l Geo., 38(5), 611-634.
91. Zimmerman, R. W., Chen, G., Hadgu, T. and Bodvarsson, G. S. (1993), “A numerical dual－porosity Model with Semianalytical treatment of fracture/matrix flow”, Water Resour.Res., 29(7), 2127-2137.
92. 原子能委員會核能廢料管理處，「我國用過核燃料長程處置計劃」，蘭嶼地質調查報告書，(1991)。
93. 吳育生，「破碎岩體中破裂面特性及透水係數張量之研究」，碩士論文，國立成功大學礦冶及材料科學研究所，(1994)。
94. 李振誥、余進利「節理與流動模型」，地工技術雜誌，33，68-82頁，(1991).
95. 李振誥、李森吉、張瑞麟、陳時祖，「估計岩體中不連續面組數，及各組之平均位態與頻率之探討」，地工技術雜誌，第39期，64-76頁，(1992).
96. 林碧山，「破裂岩體地下水滲流與溶質傳輸」，博士論文，國立成功大學資源工程學系，(2000).
97. 林宏奕，「破裂岩體優勢水流路徑之研究」，博士論文，國立成功大學資源工程學系，(2009).
98. 許廣宗，「地表補注對破裂岩體入滲行為之研究—應用蘭嶼地區安山岩體」，碩士論文，國立成功大學資源工程研究所，(1996).
99. 金門縣政府，http://www.kinmen.gov.tw/
100. 陳榮華，「破裂安山岩體放射性核種傳輸之研究」，博士論文，國立成功大學資源工程學系，(2001).
101. 蔡明謙，「岩體節理痕跡線長度及其空間結構變異性分析之研究-以蘭嶼虎頭坡地區安山岩節理面為例」，碩士論文，國立成功大學資源工程學系，(1995).