The fractal geometry of flow paths in natural fractures in rock and the approach to percolation

Aharony, A. (1984),Percolation, Fractals, and Anomalous Diffusion, J. Stat. Phys.34, 931?939.

Balberg, I., Binenbaum, N., andAnderson, C. H. (1983),Critical Behavior of the Two-dimensional Sticks System, Phys. Rev. Lett.51, 1605?1608.

Bandis, S., Lumsden, A. C., andBarton, N. R., (1983),Fundamentals of Rock Joint Deformation, Int. J. Rock Mech. Min. Sci. and Geomech. Abstr.20, 249?268.

Böttger, H., andBryskin, V. V.,Hopping Conduction in Solids (VCH, Altenburg 1985).

Brown, S. R., andScholz, C. H. (1985),Closure of Random Elastic Surfaces in Contact, J. Geophys. Res.90(B7), 5531?5545.

Brown, S. R., Kranz, R. L., andBonner, B. P. (1986),Correlation between the Surfaces of Natural Rock Joints, Geophys. Res. Lett.13, 1430.

Brown, S. R. (1987),Fluid Flow through Rock Joints: The Effect of Surface Roughness, J. Geophys. Res.92(B2), 1337?1347.

Domb, C., andGreen, M. S. ed.,Phase Transitions and Critical Phenomena (Academic, London 1976).

Duncan, N., andHancock, K. E. (1966),The Concept of Contact Stress in Assessment of the Behavior of Rock Masses as Structural Foundations, Proc. First Cong. Int. Soc. Rock Mech., Lisbon,2, 487?492.

Elam, W. T., Kerstein, A. R., andRehr, J. J. (1984),Critical Properties of the Void Percolation Problems for Spheres, Phys. Rev. Lett.17, 1516?1519.

Engelder, T., andScholz, C. H. (1981),Fluid Flow Along Very Smooth Faults at Effective Pressures up to 200 Megapascals, Am. Geophys. Union Monogr.24, 147?152.

Essam, J. W. (1980),Percolation Theory, Rep. Prog. Phys.43, 833?912.

Gale, J. E., andRaven, K. G. (1980),Effects of Sample Size on the Stress-permeability Relationship for Natural Fractures, Lawrence Berkeley Laboratory Report, LBL-11865 (SAC-48), Berkeley, California.

Gawlinski, E. T., andStanley, H. E. 1981,Continuum Percolation in Two Dimensions: Monte Carlo Tests of Scaling and Universality for Noninteracting Discs, J. Phys.A4, L291-L299.

Halperin, B. I., Feng, S., andSen, P. N. (1985),Differences between Lattice and Continuum Percolation Transport Exponents, Phys. Rev. Lett.54, 2391?2394.

Klein, W. (1982),Potts-model Formulation of Continuum Percolation, Phys. Rev.B26, 2677?2678.

Iwai, K. (1976),Fundamentals of Fluid Flow through a Single Fracture, Ph. D. Thesis Univ. of California, Berkeley.

Kirkpatrick, S. (1973),Percolation and Conduction, Rev. Mod. Phys.45, 574?588.

Ma, S-K. (1973),Introduction to the Renormalization Group, Rev. Mod. Phys.45, 589?615.

Mandelbrot, B B.,The Fractal Geometry of Nature (W. H. Freeman, San Francisco 1983).

Mandelbrot, B. B. (1984),Fractals in Physics: Squig Clusters, Diffusions, Fractal Measures and the Universality of Fractal Dimension, J. Stat. Phys.34, 895?930.

Olkiewicz, A., Gale, J. E., Thorpe, R., andPaulsson, B. (1979),Geology and Fracture System at Stripa, Lawrence Berkeley Laboratory Report, LBL-8907 (SAC-21), Berkeley, California.

Phani, M. K., andDhar, D. J. (1984),Continuum Percolation with Discs having a Distribution of Radii, Phys.A17, L645-L649.

Pike, G. E., andSeager, C. H. (1974),Percolation and Conductivity: A Computer Study, Phys. Rev.B10, 1421?1434.

Pyrak-Nolte, L. J., Meyer, L. R., Cook, N. G. W., andWitherspoon, P. A. (1987),Hydraulic and mechanical properties of natural fractures in low permeable rock, Proc. 6th International Congress on Rock Mechanics (eds. Herget, G., and Vongpaisal, S.) Montreal, Canada (A. A. Balkema, Rotterdam 1987) pp. 225?231.

Pyrak-Nolte, L. J., Cook, N. G. W., andNolte, D. D. (1988),Fluid Percolation through Single Fractures, Geophys. Res. Lett.15, 1247?1250.

Raven, K. G., andGale, J. E. (1985),Water Flow in a Natural Rock Fracture, Int. J. Rock Mech. Min. Sci. Geomech.22, 251?261.

Reynolds, P. J., Stanley, H. E., andKlein, W. (1980),Large-cell Monte Carlo Renormalization Group for Percolation, Phys. Rev.B21, 1223?1245.

Robinson, P. C. (1983),Connectivity of Fracture Systems: A Percolation Theory Approach, J. Phys.A16, 605?614.

Schlifer, G. J., Klein, W., Reynolds, P. J., andStanley, H. E. (1979),Large-cell Renormalization Group for the Backbone Problem in Percolation, Phys.A12, L169-L174.

Seager, C. H., andPike, G. E. (1974),Percolation and Conductivity: A Computer Study. II, Phys. Rev.B10, 1435?1446.

Stanley, H. E. (1977),Cluster Shapes at the Percolation Threshold: An Effective Cluster Dimensionality and its Connection with Critical Point Exponents, J. Phys.A10, L211-L220.

Stauffer, D. (1980),Scaling Theory of Percolation Clusters, Phys. Rep.54, 1?74.

Tsang, Y. W., andWitherspoon, P. A. (1981),Hydromechanical Behavior of a Deformable Rock Fracture Subject to Normal Stress, J. Geophys. Res.86, 9287?9298.

Tsang, Y. W. (1984),The Effect of Tortuosity on Fluid Flow through a Single Fracture, Wat. Resources Res.20, 1209?1215.

Tuthill, G. F., andKlein, W. (1986),Renormalization Group for Percolation Using Correlation Parameters, J. Phys.A16 3561?3570.

Vicsek, T., andKertesz, J. (1981),Monte Carlo Renormalization Group Approach to Percolation on a Continuum: Test of Universality, J. Phys.A14, L31-L37.

Voss, R. F. (1984),The Fractal Dimension of Percolation Cluster Hulls, J. Phys.A17, L373-L377.

Walsh, J. B. (1981),Effect of Pore Pressure and Confining Pressure on Fracture Permeability, Int. J. Rock Mech. Min. Sci. Geomech. Abstr.18, 429?435.

Witherspoon, P. A., Wang, Y. S., Iwai, K., andGale, J. E. (1980),Validity of Cubic Law for Fluid Flow in a Deformable Rock Fracture, Wat. Resources Res.16, 1016?1024.