Rock fracture roughness and tortuosity caused by contact asperities produce extra resistance for fluid flow in comparison with the channel consisting of two smooth parallel plates. To characterise the role of roughness and tortuosity in water flow through rock fractures, the existing studies of the effect of fracture roughness and contact area (tortuosity) on fluid flow through rock fractures were firstly reviewed. Then, an explicit flow model was derived using the friction factor predictor previously proposed according to the flow data of sandstone fractures. Regarding the introduced relative roughness of rock fracture as the correction variable, the developed flow model can be considered as a corrected form of classic cubic law, where the relative roughness is defined as the ratio of the averaged peak asperity height to equivalent hydraulic aperture. Sensitivity analysis shows that the cubic law can overestimate the flow rate by 10 % when the relative roughness increases to 70.7. With further increase in relative roughness up to 300, which usually represents tight rock fractures, the flow rate is only approximately 64 % of that predicted by cubic law. The verification of this friction factor to granite and limestone fractures shows that the used friction factor predictor is in good accordance with the experimental data.
Zhang, Z., Nemcik, J., Qiao, Q., & Geng, X. (2015). A model for water flow through rock fractures based on friction factor. Rock Mechanics and Rock Engineering, 48(2), 559–571. https://doi.org/10.1007/s00603-014-0562-4