Estimating the permeability of fractal rough rock fractures with variable apertures under normal and shear stresses
Hai Pu, Kangsheng Xue, Yu Wu, Shaojie Zhang, Dejun Liu, Junce Xu
Abstract
A prediction model for estimating the permeability of fractal rough surface fractures is proposed, in which the mechanical aperture and contact ratio are incorporated into mathematical equations. Fracture surfaces of different roughness were generated via an improved successive random addition algorithm. A series of fracture model that considers normal stress, shear displacement and surface roughness were constructed to investigate the evolution behaviors of the geometry and permeability. The results indicate that the joint roughness coefficient of the fracture profile and the aperture distribution during shear follow Gaussian functions. The aperture–frequency curve changes from sharp to flat as the shear displacement increases, indicating that the more anisotropic aperture and mechanical aperture increase. Both the mechanical aperture and the standard deviation of the aperture distribution increase with increasing fracture surface roughness during shear. The fracture aperture decreases with increasing normal stress, whereas the standard deviation of the aperture distribution increases with increasing normal stress. The effects of normal stress, shear displacement, and roughness on the evolution of the mechanical aperture and were investigated to further clarify their effects on fracture permeability. We found that the mechanical aperture and contact can be correlated with permeability via a power law, and multiple regression algorithms were applied to construct a mathematical model for estimating the permeability of rough surface fractures. The reasonableness of the prediction model proposed in this study was verified by comparing its results with laboratory seepage tests.