TY - JOUR
T1 - Fractal and multifractal characterization of stochastic fracture networks and real outcrops
AU - Zhu, Weiwei
AU - Lei, Gang
AU - He, Xupeng
AU - Patzek, Tadeusz
AU - Wang, Moran
N1 - KAUST Repository Item: Exported on 2022-01-19
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.
PY - 2022/1
Y1 - 2022/1
N2 - The fractal dimension and multifractal spectrum are widely used to characterize the complexity of natural fractures. However, systematic investigations, considering impacts of different fracture geometrical properties (fracture lengths, orientations, center positions) and system sizes, on the fractal and multifractal characterization of complex fracture networks are insufficient. Here, we utilize an in-house developed DFN modeling software, hatchfrac, to construct stochastic fracture networks with prescribed distributions and systematically study the impact of three geometrical properties of fractures and system sizes on the fractal and multifractal characterization. We calculate the single fractal dimension and multifractal spectrum with the box-counting method. The single fractal dimension, D, and the difference of singularity exponent, Δα, are used to represent the fractal and multifractal patterns, respectively. We find that fracture lengths, orientations and system sizes positively correlate with D and Δα, while the system size has the most significant impact among the four parameters. D is uncorrelated with fracture positions (FD), which means that a single fractal dimension cannot capture the complexity caused by clustering effects. However, Δα has a strong negative correlation with FD, implying that clustering effects make fracture networks more complex, and Δα can capture the difference. We also digitize 80 outcrop maps with a novel fracture detection algorithm and calculate their fractal dimension and multifractal spectrum. We find wide variations of D and Δα on those outcrop maps, even for outcrops at similar scales, indicating that a universal indicator for characterizing fracture networks at different scales or the same scale is almost impossible. D and Δα have negligible correlations with scales, supporting the self-similarity patterns of natural fracture networks.
AB - The fractal dimension and multifractal spectrum are widely used to characterize the complexity of natural fractures. However, systematic investigations, considering impacts of different fracture geometrical properties (fracture lengths, orientations, center positions) and system sizes, on the fractal and multifractal characterization of complex fracture networks are insufficient. Here, we utilize an in-house developed DFN modeling software, hatchfrac, to construct stochastic fracture networks with prescribed distributions and systematically study the impact of three geometrical properties of fractures and system sizes on the fractal and multifractal characterization. We calculate the single fractal dimension and multifractal spectrum with the box-counting method. The single fractal dimension, D, and the difference of singularity exponent, Δα, are used to represent the fractal and multifractal patterns, respectively. We find that fracture lengths, orientations and system sizes positively correlate with D and Δα, while the system size has the most significant impact among the four parameters. D is uncorrelated with fracture positions (FD), which means that a single fractal dimension cannot capture the complexity caused by clustering effects. However, Δα has a strong negative correlation with FD, implying that clustering effects make fracture networks more complex, and Δα can capture the difference. We also digitize 80 outcrop maps with a novel fracture detection algorithm and calculate their fractal dimension and multifractal spectrum. We find wide variations of D and Δα on those outcrop maps, even for outcrops at similar scales, indicating that a universal indicator for characterizing fracture networks at different scales or the same scale is almost impossible. D and Δα have negligible correlations with scales, supporting the self-similarity patterns of natural fracture networks.
UR - http://hdl.handle.net/10754/675030
UR - https://linkinghub.elsevier.com/retrieve/pii/S0191814121002327
U2 - 10.1016/j.jsg.2021.104508
DO - 10.1016/j.jsg.2021.104508
M3 - Article
SN - 0191-8141
SP - 104508
JO - Journal of Structural Geology
JF - Journal of Structural Geology
ER -