Exploring spatial heterogeneity and topological properties of fracture Networks: A statistical characterization

Analyzing fracture patterns and estimating their topological and spatial properties are essential for the predictive stochastic modelling of fractured rocks. In this study, we examined 83 natural fracture patterns compiled from existing literatures, covering diverse geological settings. To investigate spatial clustering in two dimensions (2D), we employed a multiscale spatial statistical parameter ‘Lacunarity’ which quantifies textural heterogeneity. Unlike previous studies that focused solely on the clustering of two-dimensional fracture arrays, our analysis also considers the spatial clustering of topological nodes—specifically, intersection and end-tip points within fracture networks.

Our findings indicate that the spatial distribution of nodes within a fracture network follows a non-random pattern. As fracture arrays become more clustered, the clustering of nodes also intensifies. With an increase in clustering of fracture arrays, the mean branch length weakly reduces owing to the proliferation of smaller branches within the network. Moreover, we noted that the clustering of fracture array has little correlation with the topological connectivity of the fracture networks. This is because topological connectivity only considers the abundance of different types of nodes within a pattern, without considering their spatial distribution. Finally, leveraging the estimated topological and spatial properties of the analyzed fracture patterns, we have proposed a statistical model, which would be useful to modellers and engineers involved in research on the circulation of any sub-surface fluid.