The geometry of a single fracture

Pierre M. Adler, Jean-François Thovert and Valeri V. Mourzenko

in Fractured Porous Media

Published in print October 2012 | ISBN: 9780199666515
Published online January 2013 | e-ISBN: 9780191748639 | DOI:
The geometry of a single fracture

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This chapter addresses the geometry of a single fracture with a double objective which is to characterize it and to reproduce it. The geometrical quantities which characterize the structure of a fracture are the mean aperture, the probability density of the fluctuations of the fracture surfaces, the autocorrelation function of these fluctuations along each surface and the intercorrelation between the two surfaces. There are two major classes of autocorrelation functions, namely the Gaussian and the self-affine autocorrelation. A schematic presentation of the generation of random fractures which possess these characteristics, is provided. Then, the resulting geometrical properties are analysed. The concepts of percolation, fractals, universal exponents and self-similarity are briefly presented. Finally, the generation of correlated fields and the properties of self-affine fields are summarized.

Keywords: aperture; probability density; autocorrelation; intercorrelation; Gaussian; self-affine; fractals

Chapter.  8686 words.  Illustrated.

Subjects: Condensed Matter Physics

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