Complexity analysis of three-dimensional stochastic discrete fracture networks with fractal and multifractal techniques

Weiwei Zhu, Xupeng He, Gang Lei, Moran Wang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Systematic analysis of the complexity of fracture systems, especially for three-dimensional (3D) fracture networks, is largely insufficient. In this work, we generate different fracture networks with various geometries with a stochastic discrete fracture network method. The fractal dimension (D) and the singularity variation in a multifractal spectrum (Δα) are utilized to quantify the complexity of fracture networks in different aspects (spatial filling and heterogeneity). Influential factors of complexity, including geometrical fracture properties and system size, are then systematically studied. We generalize the analysis by considering two critical (percolative and over-percolative) stages of fracture networks. At the first stage, κ (fracture orientation) is the most significant parameter for D, following a (fracture length) and L (system size). FD (fracture positions) has a weak correlation with D but a strong correlation with Δα. At the second stage, the sensitivity results of each geometrical parameter and the system size are the same as in stage one for D. For Δα, κ and FD become more significant. For both stages, there is a weak finite-size effect for D and no finite-size effect for Δα. Therefore, a large fracture system is more suitable for a stable fractal dimension estimation, but no requirement for the estimation of Δα. D and Δα are almost independent. Therefore, they can separately quantify different aspects of complexity.
Original languageEnglish (US)
Pages (from-to)104690
JournalJournal of Structural Geology
StatePublished - Aug 11 2022

Bibliographical note

KAUST Repository Item: Exported on 2022-09-14
Acknowledgements: This project was supported by the National Key Research and Development Program of China (No. 2019YFA0708704). The authors would like to thank all editors and anonymous reviewers for their comments and suggestions.

ASJC Scopus subject areas

  • Geology


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