Critical Threshold for Fluid Flow Transition from Linear to Nonlinear in Self-Affine Rough-Surfaced Rock Fractures: Effects of Shear and Confinement

Understanding nonlinear fluid flow in fractured rocks is critical for various geoengineering and geosciences. This study investigates the evolution of seepage behavior under varying fracture surface roughness, confining pressures, and shear displacements. A total of four sandstone fracture specimens were prepared using controlled splitting techniques, with surface morphology quantified by Joint Roughness Coefficient (JRC) values ranging from 2.8 to 17.7. Triaxial seepage tests were conducted under four confining pressures (3–9 MPa) and four shear displacements (0–1.5 mm). Experimental results reveal that permeability remains stable under low hydraulic gradients but transitions to nonlinear regimes as the flow rate increases, accompanied by significant energy loss and deviation from the cubic law. The onset of nonlinearity occurs earlier with higher roughness, stress, and displacement. A critical hydraulic gradient Jc was introduced to define the threshold at which inertial effects dominate. Forchheimer’s equation was employed to model nonlinear flow, and empirical regression models were developed to predict coefficients A, B, and Jc using hydraulic aperture and JRC as input variables. These models demonstrated high accuracy (R2 > 0.92). This work provides theoretical insights and predictive approaches for assessing nonlinear fluid transport in rock fracture. Future research will address mechanical–hydraulic coupling and incorporate additional factors such as scale effects and flow anisotropy.