Size effect on hydraulic properties of rough-walled fractures upscaled from meter-scale granite fractures

Abstract

To better bridge the gap between lab-scale data and larger-scale applications. In this study, an integrated method was developed to investigate the size dependence of fluid flow through rough-walled fractures. Granite fracture surfaces of up to 1 m in size were first scanned to acquire data on their morphology and corresponding surface distribution, the asperity height of which was found to follow a normal distribution. Digital fracture surfaces were then created on the basis of the scanned data and upscaled to 20 m by a statistical method, and individual rough-walled fractures were constructed by superimposing two statistically generated surfaces. Fluid flow through the fractures was subsequently simulated by solving the Reynolds’ equation. The simulated results showed evident links between the hydraulic properties and sample sizes. Specifically, both hydraulic aperture and transmissivity of the fracture varied as sample sizes increased until a threshold ranging from 2 to 5 m, beyond which an invariant transmissivity was attained. Thus, the sample size corresponding to invariant transmissivity could be defined as the representative size, the value of which was found to depend on the fracture aperture and roughness. In particular, whereas the augmentation of the fracture aperture appeared to suppress the size dependence on hydraulic properties, increased roughness tended to increase size dependence. The data and modelling presented herein provide insights into the scale dependence of fluid flow through a single fracture. It is concluded that even samples as large as 1 m may not be sufficient to characterize the hydraulic properties of fractures according to the representative sizes obtained, which usually exceeded 2 m under the conditions specified in the present study.