Evaluation of Forchheimer equation coefficients for nonlinear flow through rough-walled fractures during shearing

The presence of complex geometric morphology of single rough-walled rock fractures and the occurrence of nonlinear flow complicate the fracture flow process. Even though the nonlinear flow behaviour in single rock fractures has been studied for decades, existing models are still limited in adequately evaluating nonlinear flow behaviour during shearing. In this study, a series of coupled shear-flow tests are conducted on single rock fractures with different surface characteristics under constant normal loads. Regression analyses of the experimental data demonstrate that the Forchheimer equation provides a robust description of nonlinear flow through rough fractures, and its nonlinear coefficients can be determined by quantifying the fracture geometries. The surface and interior geometric characteristics of the fracture are quantitatively represented. The evolutions of these geometric parameters, specifically the peak asperity height and hydraulic aperture, induced by shearing and their effects on nonlinear flow behaviours in rock fractures are also considered and incorporated. An empirical equation is then proposed for the parametric expression of the Forchheimer nonlinear coefficient, which is further used for the prediction of the flow rate during the shear-flow process and the representation of the critical Reynolds number with the fracture geometric characteristics. The proposed equations are validated against experimental results and proven to be effective in predicting and characterising the nonlinear flow behaviour in rock fractures during shearing. The experimental results and the proposed models are expected to advance the understanding and numerical modelling of the nonlinear flow behaviours in fractured rock masses for more practical applications.