Abstract
The modeling of fracture networks is useful for fluid flow and rock mechanics studies. About 6600 fracture traces were recorded on drifts of a uranium mine in a granite massif. The traces have an extension of 0.20–20 m. The network was studied by fractal and by geostatistical methods but can be considered neither as a fractal with a constant dimension nor a set of purely randomly located fractures. Two kinds of generalization of conventional models can still provide more flexibility for the characterization of the network: (a) a nonscaling fractal model with variable similarity dimension (for a 2-D network of traces, the dimension varying from 2 for the 10-m scale to 1 for the centimeter scale, (b) a parent-daughter model with a regionalized density; the geostatistical study allows a 3-D model to be established where: fractures are assumed to be discs; fractures are grouped in clusters or swarms; and fracturation density is regionalized (with two ranges at about 30 and 300 m). The fractal model is easy to fit and to simulate along a line, but 2-D and 3-D simulations are more difficult. The geostatistical model is more complex, but easy to simulate, even in 3-D.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andersson, J., Shapiro, A. M., and Bear, J., 1984, A Stochastic Model of a Fractured Rock Conditioned by Measured Information: Water Resour. Res., v. 20, no. 1, p. 79–88.
Baecher, G. B. and Lanney, N. A., 1978, Trace Length Biases in Joint Surveys,in Proceedings of the 19th U.S. Symposium on Rock Mechanics: A.I.M.E., p. 56–65.
Baecher, G. B., Lanney, N. A., and Einstein, H. H., 1977, Statistical Description of Rock Properties and Sampling,in Proceedings of the 18th U.S. Symposium on Rock Mechanics: A.I.M.E., p. 5C1-1–5C1-8.
Barton, C. C. and Larsen, E., 1985, Fractal Geometry of Two-Dimensional Fracture Networks at Yucca Mountain, Southwestern Nevada,in Proceedings of the International Symposium on Fundamentals of Rock Joints, Bjorkliden, p. 77–84.
Bertrand, L.; Beucher, H.; Creutin, D.; Feuga, B.; Landry, J.; and Thiéry, D. 1982, Essai de Détermination de la Distribution Régionale du Tenseur de Perméabilité du “Milieu Poreux Équivalent,”in Les Milieux Discontinus en Hydrogéologie, Documents du BRGM, No. 45: Bureau de Recherches Géologiques et Minières, Orléans, p. 97–120.
Blanchin, R., 1984, Etude Statistique et Géostatistique de la Fracturation de la Mine de Fanay-Augères, Report CCE/CEA/BRGM, no. 84, RDM 074 IM.
Blès, J. L.; Dutartre, P.; Feybesse, J. L.; Gros, Y.; and Martin, P. 1983, Etude Structurale de la Fracturation du Granite de Saint-Sylvestre, Report CCE/CEA/BRGM, no. 83 SGN 426 GEO.
Chilès, J. P., 1988, Three-Dimensional Geometric Modelling of a Fracture Network,in Proceedings of DOE/AECL'87 Conference, San Francisco, California.
Conrad, F. and Jacquin, C., 1973, Représentation d'un Réseau Bidimensionnel de Fractures par un Modèle Probabiliste. Application au Calcul des Grandeurs Géométriques des Blocs Matriciels: Revue de l'I.F.P., v. XXVIII, no. 6, Nov.−Dec., p. 843–890.
Coster, M. and Chermant, J. L., 1983, Recent Developments in Quantitative Fractography: Int. Met. Rev., v. 28, 46 p.
Cruden, D. M., 1977, Describing the Size of Discontinuities: Int. J. Rock Mech. Min. Sci. Geomech. Abstr., v. 14, p. 133–137.
Curl, R. L., 1986, Fractal Dimensions and the Geometries of Caves: Math. Geol., v. 18, no. 8, p. 765–783.
Delaney, P. T.; Pollard, D. D.; Ziony, J. I.; and McKee, E. H., 1986, Field Relations Between Dykes and Joints: Emplacement Processes and Paleostress Analysis: J. Geophys. Res., v. 91, no. B5, p. 4920–4938.
Deverly, F., 1984, Echantillonnage et Géostatistique, Thesis: E.N.S. des Mines de Paris, 152 p.
Feuga, B., 1983, Caractérisation du Milieu Poreux Équivalent à un Milieu Fracturé par Essais à l'Eau in Situ,in Proceedings of the International Symposium Reconnaissance des Sols et des Roches par Essais en Place, Paris.
Feuga, B., 1986, Hydrogeologic Modeling of Fractured Rock: Jornadas Sobre Modelos Matematicos Aplicables al Almacenamiento de Residuos Radioactivos, Madrid, Escuela Superior de Engenieros de Minas de Madrid.
Gentier, S., 1986, Morphologie et Comportement Hydromécanique d'une Fracture Naturelle dans un Granite sous Contrainte Normale, Thesis: Université d'Orléans, 2 vol., 637 p.
Hestir, K.; Chilès, J. P.; Long, J.; and Billaux, D., 1986, Three Dimensional Modeling of Fractures in Rocks; from Data to a Regionalized Parent-Daughter Model. American Geophysical Union Meeting. San Francisco, California. (To appear in AGU Geophysical Monography volume on unsaturated fractured rock, 1987.)
Hudson, J. and Priest, S. D., 1979, Discontinuities and Rock Mass Geometry: Mt. J. Rock Mech. Min. Sci. Geomech. Abstr., v. 16, p. 339–362.
La Pointe, P. R., 1980, Analysis of the Spatial Variation in Rock Mass Properties Through Geostatistics,in Proceedings of the 21th U.S. Symposium on Rock Mechanics, Rolla, p. 570–580.
Laslett, G. M., 1982, Censoring and Edge Effect in Areal and Line Transect Sampling of Rock Joint Traces: Math. Geol., v. 14, no. 2, p. 125–140.
Loiseau, P., 1987, Etude Structurale et Géostatistique des gneiss de la Région du Cézallier: Modélisation Tridimensionnelle de Réseaux de Fractures; Application à l'Écoulement des Fluides, Thesis, Université d'Orléans, 200 p.
Long, J. C. S., 1986, Modeling of Fluid Flow and Transport in Fracture Networks, Jornadas Sobre Modelos Matematicos Aplicables al Almacenamiento de Residuos Radioactivos, Madrid, Escuela Superior de Engenieros de Minas de Madrid.
Mandelbrot, B. B., 1983, The Fractal Geometry of Nature, 2nd ed.: Freeman, New York, 468 p.
Mandelbrot, B. B., Passoja, D., and Paullay, A., 1984, Fractal Character of Fracture Surfaces of Metals: Nature, v. 308, p. 721–722.
Mantoglou, A., 1987, Digital Simulation of Multivariate Two- and Three-Dimensional Stochastic Processes with a Spectral Turning Bands Method: Math. Geol., v. 19, no. 2, p. 129–149.
Massoud, H., 1987, Modélisation de la Petite Fracturation par les Techniques de la Géostatistique, Thesis, E.N.S. des Mines de Paris, 173 p.
Matheron, G., 1973, The Intrinsic Random Functions and Their Applications, Adv. Appl. Prob., No. 5, p. 439–468.
Miller, S. M., 1979, Geostatistical Analysis for Evaluating Spatial Dependence of Fracture Set Characteristics,in Proceedings of 16th APCOM Symposium: SME-AIME, New York, p. 537–545.
Pahl, P. J., 1981, Estimating the Mean Length of Discontinuity Traces: Int. J. Rock Mech. Min. Sci. Geomech. Abstr., v. 18, p. 221–228.
Shaw, H. R. and Gartner, A. E., 1986, On the Graphical Interpretation of Paleoseismic Data: U.S. Geological Survey Open-file Report 86–394, 92 p.
Snow, D. T., 1970, The Frequency and Apertures of Fractures in Rock: Int. J. Rock Mech. Min. Sci., v. 7, p. 23–40.
Thomas, A., 1987, Structure Fractale de l'Architecture de Champs de Fractures en Milieu Rocheux: Compt. Rend. Acad. Sci. Paris, v. 304, Sér. II, no. 4, p. 181–186.
Turcotte, D. L., 1986, A Fractal Model for Crustal Deformation: Tectonophysics, v. 132, p. 261–269.
Warburton, P. M., 1980, A Stereological Interpretation of Joint Trace Data: Int. J. Rock Mech. Min. Sci. Geomech. Abstr., v. 17, p. 181–190.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chilès, J.P. Fractal and geostatistical methods for modeling of a fracture network. Math Geol 20, 631–654 (1988). https://doi.org/10.1007/BF00890581
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00890581