Mesoscopic Deformation of a Hydraulic and Mechanical Aperture of a Single Fracture under Normal Stress

Studies have focused on describing the interactions between the fluid flow characteristics and structural deformation of fractures at the mesoscopic scale, which is a scale between the macroscale and the microscale. In this work, a three-dimensional numerical simulation based on the Navier-Stokes equation was carried out to investigate the effect of normal stress on the fracture morphology distribution, the fluid flow characteristics distribution, and the interdependence between the flow and stress in a single mesoscopic fracture. Two fracture surfaces of a mesoscopic rough-walled fracture model were created. Results suggest that the nonlinear relationship between the normal stress and deformation due to the area of the total closure increases unevenly. Distributions of the mechanical aperture are approximated well by a normal distribution. Change in the fluid flow is due to the increase in the fractional contact area. The low-velocity zones are surrounded by relatively smaller apertures, which gradually close and join the areas of total closure. Under the limitation of the total closure areas of the two fracture surfaces, the appearance of channel flow behavior. Compared with the flow in the X- and Y-directions, normal stress-induced flow anisotropy occurred. The mesoscopic quantitative relationship between the strains in terms of the mechanical/hydraulic aperture was determined and proven. A macroscopic relationship between the intrinsic permeability and the strain was deduced, which enhances the evaluation and design of various geological engineering applications in which fracture deformation is considered.