Quantitative Estimates of Non-Darcy Groundwater Flow Properties and Normalized Hydraulic Aperture through Discrete Open Rough-Walled Joints

Abstract

This study aimed to understand the behavior of non-Darcy water fluid flow through a single joint in rock. Water flow tests through three splitting mated granite joints with natural characteristics were conducted beyond the range of previously tested conditions using the designed experimental apparatus. This study expands on previous work as follows: (1) A rough rock joint with natural characteristics was adopted rather than a smooth, parallel plate model; (2) the aperture and surface roughness could be precisely controlled; and (3) the maximum pressure gradient could reach 25. A single fracture was formed by two mated rough joint surfaces with variable apertures ranging from .5 to 2 mm (constant opening between upper and lower parallel surfaces). The three-dimensional (3D) surface morphology of the rock joints was obtained from a noncontact, 3D stereotopometric measurement instrument before the rock joints were tested. The roughness parameters of the rock joints were then calculated by self-programmed software. For each specimen, flow tests were conducted for four mechanical apertures and eight pressure gradients (maximum of 25). A nonlinear relationship between hydraulic gradient and water flow velocity was demonstrated and fitted well with Izbash’s law. The effect of joint roughness and aperture on the coefficient λ and power exponent n of Izbash’s law was further explored in this experiment (i.e., to maintain the same joint roughness coefficient or aperture). Finally, a new relationship between aperture ratio (hydraulic aperture to mechanical aperture) and Reynolds number is proposed based on the laboratory observations. These findings may be beneficial for the design of model experiments and computational studies on coupled shear-flow properties through real rock joints or highly jointed rocks.