Trace analysis for fracture networks with anisotropic orientations and heterogeneous distributions

V. V. Mourzenko, J.-F. Thovert, and P. M. Adler
Phys. Rev. E 83, 031104 – Published 7 March 2011

Abstract

Since only intersections with lines or planes are usually available to quantify the properties of real fracture networks, a stereological analysis of these intersections is a crucial issue. This article—the second of a series—is devoted to the derivation of the direct relations between the properties and the observable quantities. First, this derivation is achieved for anisotropic networks whose orientations obey a Fisher probability distribution function; second, it is extended to networks which are heterogeneous in space, i.e., whose density decays according to an exponential law. Five major quantities are determined: the excluded volume, the average number of intersections with a line and with a plane, the average trace length and the surface density of trace intersections. Some of these relations are valid for any convex fracture shape and some only for circular disks; however, numerical simulations show that excellent approximations are obtained by considering disks with the same area as the noncircular fractures. All the results are summarized in Table I.

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  • Received 3 October 2010

DOI:https://doi.org/10.1103/PhysRevE.83.031104

©2011 American Physical Society

Authors & Affiliations

V. V. Mourzenko* and J.-F. Thovert

  • Institut PPRIME, SP2MI, BP 30179, F-86962 Futuroscope Cedex, France

P. M. Adler

  • UPMC Sisyphe. Boîte 105, 4 place Jussieu, F-75252 Paris Cedex 05, France

  • *mourzenko@ensma.fr
  • thovert@ensma.fr
  • pierre.adler@upmc.fr

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Vol. 83, Iss. 3 — March 2011

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