Quantitative characterization of power-law fracture networks: A fully coupled perspective on water inrush in coal seams

Water inrush events during coal seam mining, especially in the presence of gas, pose a significant threat to operational efficiency and miner safety. Existing models are insufficient to fully capture the complex interactions between fracture networks, mining-induced stress changes, gas presence, and water seepage. To address this gap, we propose a novel fully coupled hydraulic model that integrates the power-law distribution characteristics of the fracture network within the framework of porous media theory. By uniquely combining three interdisciplinary models—a water migration permeability model, a hydro-mechanical coupling model, and a porosity evolution model—we quantitatively characterize the fracture structure and dynamic evolution for coal seam. This integrated approach allows for a more accurate representation of water migration pathways in gas-rich environments. Finite element analysis validates the model’s ability to accurately capture the role of the fracture network in water seepage phenomena. The quantitative analysis of key fracture parameters shows that the fracture density directly affects the water seepage intensity and coal seam stability under hydraulic coupling, with the maximum fracture length being the most important factor affecting the surrounding rock stability. By emphasizing the conditions under which gas is present, this study deepens the understanding of the water inrush mechanism and provides a comprehensive modeling approach that overcomes the limitations of previous models. This improves the accuracy of quantitative risk assessment and provides a reference for developing effective mitigation strategies for coal mining susceptible to gas.