DOI QR코드

DOI QR Code

ANALYSIS OF THE PERMEABILITY CHARACTERISTICS ALONG ROUGH-WALLED FRACTURES USING A HOMOGENIZATION METHOD

  • Chae, Byung-Gon (Geologic Environment Division, Korea Institute of Geoscience and Mineral Resources) ;
  • Choi, Jung-Hae (Geologic Environment Division, Korea Institute of Geoscience and Mineral Resources) ;
  • Ichikawa, Yasuaki (Department of Environmental Design Engineering, Okayama University Okayama) ;
  • Seo, Yong-Seok (Department of Earth and Environmental Sciences, Chungbuk National University)
  • Received : 2011.06.17
  • Accepted : 2011.08.23
  • Published : 2012.02.25

Abstract

To compute a permeability coefficient along a rough fracture that takes into account the fracture geometry, this study performed detailed measurements of fracture roughness using a confocal laser scanning microscope, a quantitative analysis of roughness using a spectral analysis, and a homogenization analysis to calculate the permeability coefficient on the microand macro-scale. The homogenization analysis is a type of perturbation theory that characterizes the behavior of microscopically inhomogeneous material with a periodic boundary condition in the microstructure. Therefore, it is possible to analyze accurate permeability characteristics that are represented by the local effect of the facture geometry. The Cpermeability coefficients that are calculated using the homogenization analysis for each rough fracture model exhibit an irregular distribution and do not follow the relationship of the cubic law. This distribution suggests that the permeability characteristics strongly depend on the geometric conditions of the fractures, such as the roughness and the aperture variation. The homogenization analysis may allow us to produce more accurate results than are possible with the preexisting equations for calculating permeability.

Keywords

References

  1. Kranz, R.L., Frankel, A. and Engelder, T., "The permeability of whole and jointed Barre Granite," Eos Trans AGU, vol. 58, pp. 1229 (1979).
  2. Louis, C.A., "A study of groundwater flow in jointed rock and its influence on the stability of rock masses," Rock Mechanics Research Report, vol. 10 (1969).
  3. Renshaw, C.E., "On the relationship between mechanical and hydraulic apertures in rough-walled fractures," Journal of Geophysical Research, vol. 100, pp. 24629-24636 (1986). https://doi.org/10.1029/95JB02159
  4. Snow, D.T., "A parallel plate model of fractured permeable media," PhD thesis, University of Califonia, Berkeley, USA (1965).
  5. Tsang, Y.W. and Tsang, C.F., "Channel model of flow through fractured media," Water Resources Research, vol. 23, pp. 467-479 (1987). https://doi.org/10.1029/WR023i003p00467
  6. Brown, S.R., "Fluid flow through rock joints. The effect of surface roughness," Journal of Geophysical Research, vol. 92, pp. 1337-1347 (1987). https://doi.org/10.1029/JB092iB02p01337
  7. Cook, A.M., Myer, L.R., Cook, N.G.W. and Doyle, F.M., "The effects of tortuosity on flow through a natural fracture," Proceedings of the 31st US Symposium on Rock Mechanics, Colorado, USA, June 18-20, pp. 371-378 (1990).
  8. Neuzil, C.E. and Tracy, J.V., "Flow through fractures," Water Resources Research, vol. 17, pp. 191-199 (1981). https://doi.org/10.1029/WR017i001p00191
  9. Piggott, A.R. and Elsworth, D., "Analytical models for flow through obstructed domains," Journal of Geophysical Research, vol. 97, pp. 2085-2093 (1992). https://doi.org/10.1029/91JB02641
  10. Pyrak-Nolte, L.J., Cook, N.G.W. and Nolte, D.D., "Fluid percolation through single fractures," Geophysical Research Letters, vol. 15, pp. 1247-1250 (1988). https://doi.org/10.1029/GL015i011p01247
  11. Thompson, M.E. and Brown, S.R., "The effect of anisotropic surface roughness on flow and transport in fractures," Journal of Geophysical Research, vol. 96, pp. 21923-21932 (1991). https://doi.org/10.1029/91JB02252
  12. Tsang, Y.W. and Witherspoon, P.A., "The dependence of fracture mechanical and fluid flow properties on fracture roughness and sample size," Journal of Geophysical Research, vol. 88, pp. 2359-2366 (1983). https://doi.org/10.1029/JB088iB03p02359
  13. Witherspoon, P.A., Wang, J.S.Y., Iwai, K. and Gale, J.E., "Validity of cubic law for fluid flow in a deformable rock fracture," Water Resources Research, vol. 16, pp. 1016- 1024 (1980). https://doi.org/10.1029/WR016i006p01016
  14. Zimmerman, R.W., Chen, D. and Cook, N.G.W., "The effect of contact area on the permeability of fractures," Journal of Hydrology, vol. 139, pp. 79-96 (1992). https://doi.org/10.1016/0022-1694(92)90196-3
  15. Brown, S.R., "Transport of fluid and electric current through a single fracture," Journal of Geophysical Research, vol. 94, pp. 9429-9438 (1989). https://doi.org/10.1029/JB094iB07p09429
  16. Paillet, F., Hess, A.E., Cheng, C.H. and Hardin, E., "Characterization of fracture permeability with high resolution vertical flow measurements during borehole pumping," Ground Water, vol. 25, pp. 28-40 (1987). https://doi.org/10.1111/j.1745-6584.1987.tb02113.x
  17. Walsh, J.B. and Brace, W.F., "The effect of pressure on porosity and the transport properties of rock," International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstract, vol. 18, pp. 429-435 (1984).
  18. Taylor, W.L., Pollard, D.D. and Aydin, A., "Fluid flow in discrete joint sets: Field observations and numerical simulations," Journal of Geophysical Research, vol. 104, pp. 28983-29006 (1999). https://doi.org/10.1029/1999JB900179
  19. Gale, J.E., "The effects of fracture type (induced versus natural) on the stress-fracture closure-fracture permeability relationships," Proceedings of the 23rd US Symposium on Rock Mechanics, Berkeley, California, USA, August 25-27, pp. 290-298 (1982a).
  20. Iwai, K., "Fundamental studies of fluid flow through a single fracture," PhD thesis, University of Califonia, Berkeley, USA (1976).
  21. Olsson, W.A., "The effect of slip on the flow of fluid through a fracture," Geophysical Research Letters, vol. 19, pp. 541-543 (1992). https://doi.org/10.1029/92GL00197
  22. Raven, K.G., and Gale, J.E., "Water flow in a natural rock fracture as a function of stress and sample size," International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstract, vol. 22, pp. 251-261 (1985). https://doi.org/10.1016/0148-9062(85)92952-3
  23. Trimmer, D., Bonner, B., Heard, H.C. and Duba, A., "Effect of pressure and stress on water transport in intact and fractured gabbro and granite," Journal of Geophysical Research, vol. 85, pp. 7059-7071 (1980). https://doi.org/10.1029/JB085iB12p07059
  24. Zimmerman, R.W. and Bodvarsson, G.S., "Hydraulic conductivity of rock fractures," Transport in Porous Media, vol. 23, pp. 1-30 (1996).
  25. Brown, S.R. and Scholz, S.H., "Broad bandwidth study of the topography of natural rock surfaces," Journal of Geophysical Research, vol. 90, pp. 12575-12582 (1985). https://doi.org/10.1029/JB090iB14p12575
  26. Develi, K., Babadagli, T. and Comlekci, C., "A new computer-controlled surface-scanning device for measurement of fracture surface roughness," Computers and Geosciences, vol. 27, pp. 265-277 (2001). https://doi.org/10.1016/S0098-3004(00)00083-2
  27. Durham, W.B. and Bonner, B.P., "PEAK : A new kind of surface microscope," International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstract, vol. 30, pp. 699-702 (1993). https://doi.org/10.1016/0148-9062(93)90008-2
  28. International Society for Rock Mechanics Commission on Standardization of Laboratory and Field Tests, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstract, vol. 15, pp. 319-368 (1978). https://doi.org/10.1016/0148-9062(78)91472-9
  29. Keller, K. and Bonner, B.P., "Automatic, digital system for profiling rough surfaces," Rev Sci Instrument, vol. 56, pp. 330-331 (1985). https://doi.org/10.1063/1.1138299
  30. Kulatilake, P.H.S.W., Shou, G., Huang, T.H. and Morgan, R.M., "New peak shear strength criteria for anisotropic rock joints," International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstract, vol. 32, pp. 673-697 (1995). https://doi.org/10.1016/0148-9062(95)00022-9
  31. Lee, Y.H., Carr, J.R., Barr, D.J. and Haas, C.J., "The fractal dimension as a measure of the roughness of rock discontinuity profiles," International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstract, vol. 27, pp. 453-464 (1990). https://doi.org/10.1016/0148-9062(90)90998-H
  32. Lespinasse, M. and Sausse, J., "Quantification of fluid flow: hydro-mechanical behaviour of different natural rough fractures," Journal of Geochemical Exploration, vol. 69-70, pp. 483-486 (2000). https://doi.org/10.1016/S0375-6742(00)00111-4
  33. Plouraboue, F., Kurowski, P., Boffa, J.-M., Hulin, J.-P. and Roux S., "Experimental study of the transport properties of rough self-affine fractures," Journal of Contaminant Hydrology, vol. 46, pp. 295-318 (2000). https://doi.org/10.1016/S0169-7722(00)00134-0
  34. Power, W.L. and Durham, W.B., "Topography of natural and artificial fractures in granitic rocks: implications for studies of rock friction and fluid migration," International Journal of Rock Mechanics and Mining Sciences, vol. 34, pp. 979-989 (1997). https://doi.org/10.1016/S1365-1609(97)80007-X
  35. Jesselle, M.W., Cox, S.J.D., Schwarze, P. and Power, W., "The anisotropy of surface roughness measured using a digital photogrammetric technique," Special Pub Geol Soc London, vol. 92, pp. 27-37 (1995). https://doi.org/10.1144/GSL.SP.1995.092.01.03
  36. Krohn, C.E. and Thompson, A.H., "Fractal sandstone pores: automated measurements using scanning-electronmicroscope images," Physical Review, B 33, pp. 6366-6374 (1986). https://doi.org/10.1103/PhysRevB.33.6366
  37. Maerz, N.H., Franklin, J.A. and Bennett, C.P., "Joint roughness measurement using shadow profilometry," International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstract, vol. 27, pp. 329-343 (1990).
  38. Ichikawa, Y., Kawamura, K., Nakano, M., Kitayama, K. and Kawamura, H., "Unified molecular dynamics and homogenization analysis for bentonite behavior: current results and future possibilities," Engineering Geology, vol. 54, pp. 21-31 (1999). https://doi.org/10.1016/S0013-7952(99)00058-7
  39. Sanchez-Palencia, E., Non-homogeneous media and vibration theory, Springer-Verlag (1980).
  40. Chae, B.G., Ichikawa, Y., Jeong, G.C., Seo, Y.S. and Kim, B.C., "Roughness measurement of rock discontinuities using a confocal laser scanning microscope and the Fourier spectral analysis," Engineering Geology, vol. 72, pp. 181-199 (2004). https://doi.org/10.1016/j.enggeo.2003.08.002
  41. Ohsaki, Y., Introduction to spectral analysis of seismic motion, Kajima Publication (1981).
  42. Chae, B.G., "Application of the homogenization analysis to calculation of a permeability coefficient," The Journal of Korean Society of Soil and Groundwater Environment, vol. 9, pp. 79-86 (2004).
  43. Chae, B.G., Ichikawa, Y., Jeong, G.C. and Seo, Y.S., "Aperture of Granite Fracture and Effects for Fluid Flow," Materials Science Research International, vol. 9, pp. 270-277 (2003).
  44. Gale, J.E., "Assessing the permeability characteristics of fractured rock," GSA. Special Paper, vol. 189, pp. 163-181 (1982b).
  45. Tsang, Y.W. and Witherspoon, P.A., "Hydromechanical behavior of a deformable rock fracture subject to normal stress," Journal of Geophysical Research, vol. 86, pp. 9287-9298 (1981). https://doi.org/10.1029/JB086iB10p09287
  46. Tsang, Y.W., Tsang, C.F., Neretnieks, I. and Moreno, L., "Flow and tracer transport in fractured media: A variable aperture channel model and its properties," Water Resources Research, vol. 24, pp. 2049-2060 (1988). https://doi.org/10.1029/WR024i012p02049

Cited by

  1. Effects of degree of compaction and fines content of the subgrade bottom layer on moisture migration in the substructure of high-speed railways pp.2041-3017, 2017, https://doi.org/10.1177/0954409717710838