A complex-network-based estimation of the representative elementary volume and equivalent permeability coefficient for fractured rock masses

The determination of the representative elementary volume (REV) and equivalent permeability coefficient (EPC) of fractured rock masses is crucial for studying the hydraulic behaviors of engineering rock masses. The complex network originated from graph theory and represents a rapidly developing interdisciplinary field in the 21st century. In this paper, we propose a novel method that utilizes complex-network-based metrics to estimate the REV and EPC of fractured rock masses. In this method, fractures and their intersections are treated as nodes and edges of a complex network, respectively. We propose a transformation procedure of a discrete fracture network (DFN) into a complex network, and the corresponding algorithms are conducted in MATLAB. Subsequently, we obtain a complex network, and several complex-network-based metrics, such as average degree, average clustering coefficient, and graph density, are calculated using Gephi software. We employ the average degree to estimate the REV size of DFN models, while the coefficient of variation is used to quantitatively assess changes in the average degree of multiple random models. Furthermore, we establish an empirical formula utilizing the average degree, average clustering coefficient, and graph density to estimate the EPC of a large-scale DFN model based on the EPC of a small-scale DFN model. To verify the developed method, we conduct numerical experiments using the MAFIC (Matrix/Fracture Interaction Code) solver within the FracMan software. This enabled us to calculate the EPC, which was then used to determine the REV. The results demonstrate that: (a) the REV size estimated by the average degree aligns with the REV size obtained through numerical simulations for both isotropic and anisotropic DFN models, and (b) the error rates between the average EPC calculated by the empirical formula and that obtained by numerical simulations are within 10%. Thus, the proposed seepage parameter estimation methods are deemed valid.