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On the Density Variability of Poissonian Discrete Fracture Networks, with application to power-law fracture size distributions

Etienne Lavoine1,2, Philippe Davy1, Caroline Darcel2, & Romain Le Goc2

1Univ Rennes, CNRS, Géosciences Rennes, UMR 6118, 35000 Rennes, France
2Itasca Consultants S.A.S., Ecully, France

Lavoine, E., Davy, P., Darcel, C., & Le Goc, R. (2019). On the Density Variability of Poissonian Discrete Fracture Networks, with application to power-law fracture size distributions. Adv. Geosci., 49, 77-83. doi:10.5194/adgeo-49-77-2019

Abstract

This paper presents analytical solutions to estimate at any scale the fracture density variability associated to stochastic Discrete Fracture Networks. These analytical solutions are based upon the assumption that each fracture in the network is an independent event. Analytical solutions are developed for any kind of fracture density indicators. Those analytical solutions are verified by numerical computing of the fracture density variability in three-dimensional stochastic Discrete Fracture Network (DFN) models following various orientation and size distributions, including the heavytailed power-law fracture size distribution. We show that this variability is dependent on the fracture size distribution and the measurement scale, but not on the orientation distribution. We also show that for networks following power-law size distribution, the scaling of the three-dimensional fracture density variability clearly depends on the power-law exponent.

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