Experimental and numerical studies on non-Darcian flow in single rough-walled rock fracture

A series of rough-walled rock fracture specimens with specific surface roughnesses are made by using the three- dimensional carving. After that, the self-designed apparatus which can quantitatively change the aperture of single rock fracture is adopted to realize the purpose of aperture and surface roughness to be quantitatively controlled in the experiment. The seepage experiments on all rock fracture replicas at different flow rates are carried out to study the influences of the mean aperture and surface roughness on the non-Darcian flow in a single rough-walled rock fracture. The results show that the Forchheimer equation is suitable for characterizing the non-Darcian flow in rough-walled fractures. The fractal dimension is an effective parameter to reflect the surface roughness of rock fracture, and the increase of fractal dimension mainly leads to an enlargement in degree of tortuousness and results in the increased complexity of flow paths. An empirical quantification model is established to relate the inertial permeability to the mean aperture and fractal dimension. The numerical simulations by directly solving the Navier-Stokes equation are performed to investigate the non-Darcian flow in three-dimensional rough-walled fractures with different apertures and roughnesses. The inertial permeabilities of the simulated results agree well with those of the empirical quantification model and experiments, indicating that both the model and the experiments are reliable. The prediction accuracy of the empirical model increases with the decrease of the mean aperture and increase of surface roughness.