Abstract
The mechanical and hydrological behaviour of fractured media depends on the morphology of single fractures. Geostatistics enables modelling of the topography of both fracture surfaces and the aperture. The small-scale variations of a fracture surface depend on the angularity of individual grain facets and are modelled by means of a combined variography of the elevation and its first derivatives. The topography of the two fracture sides and the void height are studied simultaneously and consistently with specific tools, such as cross-covariance and the translatogram.
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References
Billaux, D. (1990). Hydrogéologie des milieux fracturés. Géométrie, connectivité, et comportement hydraulique. Doctoral thesis, E.N.S. des Mines de Paris, 277 p.
Billaux, D., and S. Gentier (1990). Numerical and laboratory studies for flow in a fracture. In Rock joints, N. Barton and O. Stephansson (Eds), Balkema, Rotterdam, Netherlands, pp. 369–373.
Brown, S.R., and C.H. Scholz (1985). Broad bandwidth of the topography of natural rock surfaces. Journal of geophysical research, Vol. 90, No. B14, pp. 12575–12582.
Chilès, J.P. (1977). Géostatistique des phénomènes non stationnaires. Thesis, Nancy-I University, France, 152 p.
Chilès, J.P. (1979). Le variogramme généralisé. Internal report, N-612, Centre de Géostatistique, Fontainebleau.
Chilès, J.P. (1989a). Three-dimensional geometric modelling of a fracture network. In Geostatistical, sensitivity, and uncertainty methods for ground-water flow and radionuclide transport modeling, B.E. Buxton, (Ed.), Batteile Press, Columbus, Ohio, pp. 361–385.
Chilès, J.P. (1989b). Modélisation géométrique de réseaux de fractures. In Geostatistics, M. Armstrong (Ed.), Kluwer Academic Publishers, Dordrecht, Netherlands, Vol. 1, pp. 57–76.
Chilès, J.P. (1992). Geostatistical modelling of the geometry of a single fracture. Internal report, BRGM, SGN/ISA, Orléans, France.
Durham, W.B., and B.P. Bonner (1992). Closure and fluid flow in discrete fractures. Proceedings of Fractured and jointed rock masses, Lake Tahoe, California, to be published.
Gentier, S. (1986). Morphologie et comportement hydromécanique d’une fracture naturelle dans un granite sous contrainte normale. Doctoral thesis, Université d’Orléans. Document du BRGM, No. 134, BRGM, Orléans, France, 597 p.
Gentier, S., and J. Riss (1990). Quantitative description and modelling of joints morphology. In Rock joints, N. Barton and O. Stephansson (Eds.), Balkema, Rotterdam, Netherlands, pp. 375–382.
Gentier, S., J.P. Chilès, and J. Riss (1991). Analyse et simulation d’une surface de fracture rocheuse. Cahiers de géostatistique, Fasc. 1, ENS des Mines de Paris, pp. 77–87.
Mandelbrot, B.B., D.E. Passoja, and A.J. Paullay (1984). Fractal character of fracture surfaces of metals. Nature, Vol. 308, pp. 721–722.
Matheron, G. (1965). Les variables régionalisées et leur estimation. Masson, Paris, 306 p.
Matheron, G. (1989). The internal consistency of models in geostatistics. In Geostatistics, M. Armstrong (Ed.), Kluwer Academic Publishers, Dordrecht, Netherlands, Vol. 1, pp. 21–38.
Sayles, R.S., and T.R. Thomas (1977). The spatial representation of surface roughness by means of the structure function: a practical alternative to correlation. Wear, Vol. 42, pp. 263–276.
Serra, J. (1982). Image analysis and mathematical morphology. Academic Press, London, 628 p.
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© 1993 Kluwer Academic Publishers
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Chilès, JP., Gentier, S. (1993). Geostatistical Modelling of a Single Fracture. In: Soares, A. (eds) Geostatistics Tróia ’92. Quantitative Geology and Geostatistics, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1739-5_9
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DOI: https://doi.org/10.1007/978-94-011-1739-5_9
Publisher Name: Springer, Dordrecht
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