Tunnel and Underground Space (터널과지하공간)

Korean Society for Rock Mechanics and Rock Engineering (한국암반공학회)
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Characteristics of Block Hydraulic Conductivity of 2-D DFN System According to Block Size and Fracture Geometry

블록크기 및 균열의 기하학적 속성에 따른 2-D DFN 시스템의 블록수리전도도 특성

  • Received : 2015.10.05
  • Accepted : 2015.10.22
  • Published : 2015.10.31
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Abstract

Extensive numerical experiments have been carried out to investigate effect of block size and fracture geometry on hydraulic characteristics of fractured rock masses based on connected pipe flow in DFN systems. Using two fracture sets, a total of 72 2-D fracture configurations were generated with different combinations of fracture size distribution and deterministic fracture density. The directional block conductivity including the theoretical block conductivity, principal conductivity tensor and average block conductivity for each generated fracture network system were calculated using the 2-D equivalent pipe network method. There exist significant effects of block size, orientation, density and size of fractures in a fractured rock mass on its hydraulic behavior. We have been further verified that it is more difficult to reach the REV size for the fluid flow network with decreasing intersection angle of two fracture sets, fracture plane density and fracture size distribution.

본 연구는 블록크기 및 균열의 기하학적 속성이 균열암반의 수리적 특성에 미치는 효과를 파악하기 위해 이차원 등가파이프 연결구조에 기반을 둔 DFN 유체유동 해석기법을 적용하여 수치실험을 수행하였다. 두 개의 균열군을 사용하여 균열의 기하학적 속성 변화를 반영할 수 있도록 방향, 면적빈도, 길이분포를 달리하며 이차원 영역에 추계론적으로 생성한 총 72개의 DFN 블록에 대하여 방향에 따른 블록수리전도도가 산정되었다. 또한, 각각의 DFN 블록에서 이론적 블록수리전도도, 주 수리전도도텐서 및 평균블록수리전도도를 추정하여 비교분석한 결과, 블록크기 및 균열의 기하학적 속성은 균열성 암반의 수리적 특성에 큰 영향을 미치는 것으로 평가되었다. 균열군의 교차각이 작을수록, 면적빈도가 낮고 길이분포가 짧을수록 DFN 시스템은 유체유동에 대한 REV를 정의하기 어려우며 방향에 따른 블록수리전도도의 변동성이 강하게 나타났다. 일반적으로 블록크기가 커질수록 DFN 시스템에 대한 등가연속체 취급 가능성은 높아진다.

Keywords

References

  1. Andersson, J. and B. Dverstorp, 1987, Conditional simulations of fluid flow in three dimensional networks of discrete fractures, Water Resour. Res. 23.10, 1876-1886. https://doi.org/10.1029/WR023i010p01876
  2. Bang, S., S. Jeon and J. Choe, 2003, Determination of equivalent hydraulic conductivity of rock mass using three-dimensional discontinuity network, J. of Korean Society for Rock Mech., 13, 52-3.
  3. Bear, J., C.F. Tsang and G. de Marsily, 1993, Flow and Contaminant Transport in Fractured Rock, Academic Press, San Diego, 560p.
  4. 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. https://doi.org/10.1029/WR026i003p00479
  5. 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. https://doi.org/10.1029/WR026i003p00491
  6. Carrera J., J. Heredia, S. Vomvoris and P. Hufschmied, 1990, Modeling of flow on a small fractured monzonitic gneiss block, Selected paper in Hydrogeolgy of low permeability Environments, Int. Assoc. of hydrogeologists, Hydrogeology. 2, 115-167.
  7. Dershowitz, W.S. and H.H. Einstein, 1987, Three-dimensional flow modeling in jointed rock masses. In: Herget, O., Vongpaisal, O. (Eds.), Proceedings of the Sixth Congress on ISRM, Montreal, Canada, 87-92.
  8. Dershowitz, W.S. and C. Fidelibus, 1999, Derivation of equivalent pipe network analogues for three-dimensional discrete fracture networks by the boundary element method, Water Resour. Res. 35.9, 2685-2691. https://doi.org/10.1029/1999WR900118
  9. Diodato, D.M., 1994. A compendium of Fracture Flow Models, 1994, Argonne National Laboratory Report, 88p.
  10. Dverstorp, B. and J. Andersson, 1989, Application of the discrete fracture network concept with field data: possibilities of model calibration and validation, Water Resour. Res. 25.3, 540-550. https://doi.org/10.1029/WR025i003p00540
  11. Elsworth, D., 1986a, A hybrid boundary element-finite element analysis procedure for fluid flow simulation in fractured rock masses, Int. J. Numer. Anal. Meth. Geomech. 10.6, 569-584. https://doi.org/10.1002/nag.1610100603
  12. Elsworth, D., 1986b, A model to evaluate the transient hydraulic response of three-dimensional sparsely fractured rock masses, Water Resour. Res. 22.13, 1809-1819. https://doi.org/10.1029/WR022i013p01809
  13. Herbert, A.W., 1996, Modelling approaches for discrete fracture network flow analysis. In: Stephansson, O., Jing, L., Tang, C.F. (Eds.), Coupled Thermo-hydro-mechnical Processes of Fractured Media-mathematical and Experiment Studies, Elsevier, Amsterdam, 213-229.
  14. 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. https://doi.org/10.1029/WR021i011p01655
  15. Jing, L. and J. Hudson, 2002, Numerical methods in rock mechanics, Int. J. Rock Mech. Min. Sci. 39.4, 409-427. https://doi.org/10.1016/S1365-1609(02)00065-5
  16. Kantani, K., 1984, Distribution of directional data and fabric tensors, Int. J. Engng Sci. 22.2, 149-164. https://doi.org/10.1016/0020-7225(84)90090-9
  17. Kulatilake, P.H.S.W. and B.B. Panda, 2000, Effect of block size and joint geometry on jointed rock hydraulics and REV, J. Eng. Mech. 126, 850-858. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:8(850)
  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. https://doi.org/10.1029/WR018i003p00645
  19. Long, J.C.S., P. Gilmour and P.A. Witherspoon, 1985, A model for steady fluid flow in random three-dimensional networks of disc-shaped fractures, Water Resour. Res. 21.8, 1105-1115. https://doi.org/10.1029/WR021i008p01105
  20. Neuman, S.P. and J.S. Depner, 1988, Use of variable-scale pressure test data to estimate the log hydraulic conductivity covariance and dispersivity of fractured granites near Oracle, Arizona, J. Hydrol. 102, 475-501. https://doi.org/10.1016/0022-1694(88)90112-6
  21. Oda, M., 1985, Permeability tensor for discontinuous rock masses, Geotechnique. 35.4, 483-495. https://doi.org/10.1680/geot.1985.35.4.483
  22. Park, B.Y., K.S. Kim, C.S. Kim, D.S. Bae and H.K. Lee, 2001, Analysis of the pathways and travel times for groundwater in volcanic rock using 3D fracture network, J. of Korean Society for Rock Mech., 11, 42-58.
  23. Park, J.S., D.W. Ryu, C.H. Ryu and C.I. Lee, 2007, Groundwater flow analysis around hydraulic excavation damaged zone, J. of Korean Society for Rock Mech., 17, 109-118.
  24. Priest, S.D., 1993, Discontinuity Analysis for Rock Engineering, Chapman & Hall, London, 473p.
  25. Rouleau, A. and J.E. Gale, 1987, Stochastic discrete fracture simulation of ground water flow into an underground excavation in granite, Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 24.2, 99-112. https://doi.org/10.1016/0148-9062(87)91929-2
  26. 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. https://doi.org/10.1029/WR019i005p01253
  27. Shapiro, A.M. and J. Andersson, 1985, Simulation of steady state flow in three dimensional fracture networks using boundary element method, Advances in Water Resour. 8.3, 106-110. https://doi.org/10.1016/0309-1708(85)90049-1
  28. Song, M.K., K.S. Jue and H.K. Moon, 1994, A theoretical and numerical study on channel flow in rock joints and fracture networks, J. of Korean Society for Rock Mech., 4, 1-16.
  29. Sudicky, E.A. and R.G. McLaren, 1992, The Laplace Transform Galerkin technique for large-scale simulation of mass transport in discretely fractured porous formations, Water Resour. Res. 28.2, 499-514. https://doi.org/10.1029/91WR02560
  30. Wilcock, P., 1996, The NAPSAC fracture network code. In: Stephansson, O., Jing, L., Tang, C.F. (Eds.), Coupled Thermo-hydro-mechanical Processes of fractured Media, Elsevier, Rotterdam, 529-538.
  31. Zimmerman, R.W. and G.S. Bodvarsson, 1995, Effective Transmissivity of Two-dimensional Fracture Networks, LBL Report, 19p.