Permeability Prediction Model of Fractal Rough Fractures Under Coupled Shear and Normal Stress

The hydro-mechanical coupling in fractures plays a significant role in fluid transport through fracture networks. However, current studies still exhibit certain limitations in the multi-parameter characterization of fracture permeability under stress conditions. To address this, a hydro-mechanical coupling model was developed to investigate the coupled hydro-mechanical behavior of fractures under different stress states and shear displacements. The results show that fluid flow patterns within fractures exhibit notable heterogeneity and anisotropy, influenced by aperture distribution and the connectivity of preferential flow paths. High normal stress significantly reduces the mechanical aperture while enhancing its anisotropy, as the normal stress increased from 2 MPa to 8 MPa, the average mechanical aperture of the fractures decreased by 61% to 65%. With increasing shear displacement, both the mechanical aperture and its standard deviation increase, and the aperture distribution shifts from a sharply peaked pattern to a more flattened one, the maximum aperture increased by 23–38%, reflecting enhanced variability in fracture structure. Increased surface roughness amplifies the effect of shear displacement on the evolution of fracture architecture. Under low normal stress conditions, the mechanical aperture increases gradually with higher roughness, the mechanical aperture decreased more significantly in high-roughness (JRC = 17.94) fractures (28–31% greater reduction) compared to low-roughness ones (JRC = 2.01). To assess fracture permeability, a predictive model was developed and validated against further data, confirming its effectiveness in evaluating permeability. This study highlights the mechanisms by which shear displacement and normal stress influence fracture permeability.