A new method for network connectivity determination based on fracture network connected clusters

The scientific quantification of fracture network topology connectivity is essential for advancing fundamental theories such as rock mechanics. Essentially, it involves establishing a mapping relationship between the geometric topology of fracture networks and rock mechanics variables. To develop a universal evaluation system for fracture connectivity and to quantitatively characterize the topological geometric properties of multi-fracture connectivity, we focus on two key variables: connectivity strength and spatial connectivity effect, approached from both narrow and broad perspectives. Firstly, by considering the differences in coordination numbers between X-type and Y-type topological nodes, we define a new connectivity strength index that incorporates topological parameters of the fracture network. This index serves as a universal measurement tool for comparing the connectivity strength of multi-scale fracture networks. Secondly, using the method for assessing the intersection triangles of fracture geometries, we establish a general geometric criterion for both central and non-central connectivity. We identify three core elements for evaluating planar fracture connectivity: trace length, center position, and direction. We construct a maximum fracture cluster identification method utilizing an intersection node heat map and derive the theoretical expression for the critical trace length. Finally, we establish a percolation model to quantitatively describe the spatial distribution characteristics of fracture-connected clusters.