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# Directional Pair-Correlation Analysis of Fracture Networks

Abstract : We analyze statistically fractures on surface exposures, which may be considered planar sections through three-dimensional fracture networks (FN). For this planar case, there exist established statistical methods which yield first-order or mean-value characteristics such as fracture density, fracture length distribution or rose of directions. We extend this situation by presenting a statistical second-order theory, which aims to characterize the inner variability of planar FN. For this purpose we use ideas from the theory of marked point processes or object models, where the points' are centers of fractures or fracture branches and the marks' are lengths and strike azimuths. The statistics are based on oriented distances between object centers. These distances are represented by so-called pair correlation and mark correlation functions, which we recommend as new variability characteristics for fracture networks. The form of he corresponding plots gives information on the degree of randomness, on most frequent inter-center distances, and on possible local order, all with respect to fracture directions. We demonstrate the application of these ideas by analysis of three FN. First, we study a synthetic structure, serving as a benchmark to test the methods under ideal conditions. Then, we analyze two field exposures already studied in the geological literature: a well developed and highly connected FN and a highly irregular FN with many small and isolated fractures. The different spatial arrangements of fractures are characterized by the correlation functions.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.univ-lorraine.fr/hal-03659512
Contributor : François Bonneau Connect in order to contact the contributor
Submitted on : Thursday, May 5, 2022 - 9:56:29 AM
Last modification on : Friday, May 6, 2022 - 3:38:41 AM

### File

FNSecOrderChara_agu_review.pdf
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### Identifiers

• HAL Id : hal-03659512, version 1

### Citation

François Bonneau, Dietrich Stoyan. Directional Pair-Correlation Analysis of Fracture Networks. 2022. ⟨hal-03659512⟩

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