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A simplified relationship between the zero-percolation threshold and fracture set properties.

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Title: A simplified relationship between the zero-percolation threshold and fracture set properties.
Authors: Dong, Shaoqun1,2,3 (AUTHOR), Zeng, Lianbo3,4 (AUTHOR) lbzeng@sina.com, Xu, Chaoshui2 (AUTHOR), Dowd, Peter2 (AUTHOR), Xiong, Guohao1,3 (AUTHOR), Wang, Tao5 (AUTHOR), Lyu, Wenya3,4 (AUTHOR)
Source: Solid Earth. 2025, Vol. 16 Issue 11, p1269-1287. 19p.
Subjects: Percolation, Fracture mechanics, Computer simulation, Statistical correlation, Analytical solutions
Abstract: Percolation analysis is an efficient way of evaluating the connectivity of discrete fracture networks. Except for very simple cases, it is not feasible to use analytical approaches to find the percolation threshold of a discrete fracture network. The most commonly used percolation threshold corresponds to the occurrence of percolation on average for the set of parameters (p50), which is not adequate for applications in which a high confidence in the percolation threshold is required. This study investigates the direct relationships between the percolation threshold at low probability (p0 , referred to as zero-percolation threshold) and the properties of fracture networks with one set of fractures (fractures with similar orientations) in two-dimensional domains. A generalized non-linear multivariate relationship between p0 and fracture network parameters is established based on connectivity assessments of a significant number of numerical simulations of fracture networks. A feature of this relationship is the invariant shape of marginal relationships. A comparison study with an analytical solution and applications in both synthetic and real fracture networks shows that the derived relationship performs well in fracture networks of different sizes and orientations. A significant benefit of this relationship is that, when an analytical solution is not available, it can provide fast and reliable connectivity statistics of fracture networks based only on fracture parameters. [ABSTRACT FROM AUTHOR]
Copyright of Solid Earth is the property of Copernicus Gesellschaft mbH and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: A simplified relationship between the zero-percolation threshold and fracture set properties.
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  Data: <searchLink fieldCode="JN" term="%22Solid+Earth%22">Solid Earth</searchLink>. 2025, Vol. 16 Issue 11, p1269-1287. 19p.
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  Data: <searchLink fieldCode="DE" term="%22Percolation%22">Percolation</searchLink><br /><searchLink fieldCode="DE" term="%22Fracture+mechanics%22">Fracture mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+correlation%22">Statistical correlation</searchLink><br /><searchLink fieldCode="DE" term="%22Analytical+solutions%22">Analytical solutions</searchLink>
– Name: Abstract
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  Data: Percolation analysis is an efficient way of evaluating the connectivity of discrete fracture networks. Except for very simple cases, it is not feasible to use analytical approaches to find the percolation threshold of a discrete fracture network. The most commonly used percolation threshold corresponds to the occurrence of percolation on average for the set of parameters (p50), which is not adequate for applications in which a high confidence in the percolation threshold is required. This study investigates the direct relationships between the percolation threshold at low probability (p0 , referred to as zero-percolation threshold) and the properties of fracture networks with one set of fractures (fractures with similar orientations) in two-dimensional domains. A generalized non-linear multivariate relationship between p0 and fracture network parameters is established based on connectivity assessments of a significant number of numerical simulations of fracture networks. A feature of this relationship is the invariant shape of marginal relationships. A comparison study with an analytical solution and applications in both synthetic and real fracture networks shows that the derived relationship performs well in fracture networks of different sizes and orientations. A significant benefit of this relationship is that, when an analytical solution is not available, it can provide fast and reliable connectivity statistics of fracture networks based only on fracture parameters. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Solid Earth is the property of Copernicus Gesellschaft mbH and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.5194/se-16-1269-2025
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        Text: English
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              Text: 2025
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