Topological Evolution and Prediction Method of Permeability in Fracture Networks

Aiming to predict the evolution of fracture structures under stress conditions and the Permeability process of the fracture network, a damage evolution model reflecting the coupling mechanism between topological characteristics and mechanical responses of fracture networks is established based on yield criteria and complex network theory, realizing a prediction for permeability processes. Firstly, key parameters such as degree centrality, betweenness centrality, and clustering coefficient of fracture nodes are extracted through complex network topological analysis. Combined with the finite element method to calculate the node shear stress transfer coefficient, a topology–mechanics coupling model of the fracture network is constructed. Secondly, the Coulomb–Mohr yield criterion is improved to establish a damage evolution equation considering normal stress and shear stiffness degradation. Based on the above theory, a fracture network permeability iterative algorithm was developed to simultaneously update the network topology and the stress distribution of the fracture network. The evolution process of the network was analyzed based on the adjacency matrix and the changes in the number of connected clusters. The results show that the average degree of the largest cluster directly reflects the connectivity of the fracture network; a higher average degree corresponds to greater damage to the fracture network under stress. The average clustering coefficient indicates the extent of local connectivity; a higher clustering coefficient signifies denser local connections, which enhances the fracture network connectivity. Compared with traditional static methods, the dynamic damage evolution model has a permeability prediction error within 7%, indicating the effectiveness of this method.