Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-19T22:10:23.368Z Has data issue: false hasContentIssue false
  • English
  • Français

A geometrical approach to percolation through random fractured rocks

Published online by Cambridge University Press:  01 May 2009

N. Rivier ,
E. Guyon  and
E. Charlaix
N. Rivier
Affiliation:
Institute for Theoretical Physics, University of California, Santa Barbara, California, 93106, USA Center for Nonlinear Studies, MS B 258, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
E. Guyon
Affiliation:
Institute for Theoretical Physics, University of California, Santa Barbara, California, 93106, USA Laboratoire d'Hydrodynamique et de Mécanique Physique, ERA 071000 du CNRS, Ecole Supérieure de Physique et Chimie Industrielles, 10, rue Vauquelin, 75231 Paris, Cedex 05, France
E. Charlaix
Affiliation:
Laboratoire d'Hydrodynamique et de Mécanique Physique, ERA 071000 du CNRS, Ecole Supérieure de Physique et Chimie Industrielles, 10, rue Vauquelin, 75231 Paris, Cedex 05, France
Get access Rights & Permissions [Opens in a new window]

Abstract

The permeability of rocks fractured by random, planar cracks, is expressed as a classical bond percolation problem on a random lattice, by Voronoi partition of space. The percolation threshold is determined as a function of the statistical characteristics of the cracks, or of their traces on an arbitrary face of the rock, by using an empirical quasi-invariant of percolation theory.

Type
Articles
Information
Geological Magazine , Volume 122 , Issue 2 , March 1985 , pp. 157 - 162
Copyright
Copyright © Cambridge University Press 1985

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Balberg, I., Binenbaum, N. & Wagner, N. 1984. Percolation thresholds in three dimensional stick systems. Physical Review Letters 52, 1465–8.CrossRefGoogle Scholar
Charlaix, E., Guyon, E. & Rivier, N. 1984. A criterion for percolation threshold in a random array of plates. Solid State Communications 50, 999–1002.CrossRefGoogle Scholar
Chelidze, T. L. 1982. Percolation and fracture. Physics of the Earth and Planetary Interiors 28, 93–101.CrossRefGoogle Scholar
Clerc, J. P., Giraud, G., Roussenq, J., Blanc, R., Carton, J.-P., Guyon, E., Ottavi, H. & Stauffer, D. 1983. La percolation, modéles, simulations analogiques et numériques. Annales de Physique 8, 1–106.CrossRefGoogle Scholar
Crain, I. K.. 1976. Statistical analysis of geotectonics. In Random Processes in Geology(ed. Merriam, D. F.), pp. 3–15.Springer.CrossRefGoogle Scholar
Dienes, J. K. 1979. On the inference of crack statistics from observations on an outcropping. 20th U.S. Symposium on Rock Mechanics, Austin, Texas, pp. 259–63.Google Scholar
Dienes, J. K. 1982. Permeability, percolation and statistical crack mechanics. 23rd U.S. Symposium on Rock Mechanics, Berkeley, CA.Google Scholar
Domb, C. & Dalton, N. W. 1966. Crystal statistics with long-range forces. I-Equivalent neighbour model. Proceedings of the Physical Society 89, 859–71.CrossRefGoogle Scholar
Englman, R., Gur, Y. & Jaeger, Z. 1983. Fluid flow through a crack network in rocks. Journal of Applied Mechanics 50, 707–11.CrossRefGoogle Scholar
Essam, J. W. 1980. Percolation theory. Reports on Progress in Physics 43, 853–912.CrossRefGoogle Scholar
De Gennes, P. G. 1976. The Physics of Liquid Crystals. Oxford University Press.Google Scholar
Gilbert, E. N. 1972. Random subdivision of space into crystals. Annals of Mathematical Statistics 33, 958–72.CrossRefGoogle Scholar
Hammersley, J. M. & Welsh, D. J. A. 1980. Percolation theory and its ramification. Contemporary Physics 21, 593–605.CrossRefGoogle Scholar
Jerauld, G. R., Hatfield, J. C., Scriven, L. E. & Davis, H. T. 1984. Percolation and conduction on Voronoi and triangular networks: a case study in topological disorder. Journal of Physics C 17, 1519–29.CrossRefGoogle Scholar
Van Kampen, N. G. 1981. Stochastic Processes in Physics and Chemistry. North-Holland Publishing Co.Google Scholar
Kendall, M. G. & Moran, P. A. P. 1963. Geometrical Probability. C. Griffin.Google Scholar
Long, J. C. S., Remer, J. S., Wilson, C. R. & Witherspoon, P. A. 1982. Porous media equivalents for networks of discontinuous fractures. Water Resources Research 18, 645–58.CrossRefGoogle Scholar
Meijering, J. L. 1953. Interface area, edge length, and number of vertices in crystal aggregates with random nucleation. Philips Research Reports 8, 270–90.Google Scholar
Pike, G. E. & Seager, C. H. 1974. Percolation and conductivity: A computer study. I. Physical Review B 10, 1421–34.CrossRefGoogle Scholar
Rivier, N. 1982. Recent results on the ideal structure of glasses. Journal de Physique (Colloques) 43, C9–91–5.Google Scholar
Robinson, P. C. 1983. Connectivity of fracture systems – a percolation theory approach. Journal of Physics A 16, 605–14.CrossRefGoogle Scholar
Smalley, I. J. 1966. Contraction crack networks in basalt flows. Geological Magazine 103, 110–4.CrossRefGoogle Scholar
Stevens, P. S. 1974. Patterns in Nature. Little, Brown and Co.Google Scholar
Underwood, E. E. 1970. Quantitative Stereology. Addison-Wesley.Google Scholar
Vyssotsky, V. A., Gordon, S. B., Frisch, H. L. & Hammersley, J. M. 1961. Critical percolation probabilities (Bond problem). Physical Review 123, 1506–7.CrossRefGoogle Scholar
Weaire, D. & Rivier, N. 1984. Soap, cells and statistics – random patterns in two dimensions. Contemporary Physics 25, 59–99.CrossRefGoogle Scholar
Wilke, S., Guyon, E. & De Marsily, G. 1984. Water penetration through fractured rocks: Test of a 3-dimensional percolation description. Journal of the International Association for Mathematical Geology.Google Scholar
Ziman, J. M. 1979. Models of Disorder. Cambridge University Press.Google Scholar