Quantitatively ranking the importance of fractures in seepage processes of rock masses: A complex network perspective

Quantifying the contribution of each fracture within a fracture network to fluid flow is critical for understanding seepage in rock masses. However, systematic studies on the quantitative ranking of fracture importance in seepage processes of rock masses have been limited due to the complexity of fractures. This study tried to investigate this issue from the perspective of complex network, which originates from graph theory and has rapidly developed into an interdisciplinary research field in the 21st century. Initially, a fracture network is transformed into a complex network based on the intersection relationships between fractures. Subsequently, a fracture importance index is proposed using complex-network-based metrics, enabling the ranking of fracture importance. The removal of fractures with higher importance rankings results in more significant changes in the equivalent hydraulic conductivity (EHC) of the fracture network, as calculated by the FracMan software, thereby validating the accuracy of this ranking method. Furthermore, an analysis of radius distribution reveals two key findings: higher-ranked fracture subsets contain a larger proportion of large-scale fractures, and certain small-scale fractures also play a crucial role in seepage. Based on this quantitative ranking method, an empirical formula is derived for predicting the EHC of the fracture network. This prediction method not only enhances the computational efficiency of EHC calculations but also maintains a low error margin. The quantitative ranking method for fracture importance proposed in this paper offers valuable scientific guidance for enhancing or controlling fluid flow in rock engineering and holds significant practical potential for future research applications.