Hydraulic aperture tensor of rough-walled fractures: Impact of compression and shearing

Fractures frequently are the primary channels for fluid flow in fractured porous media and significantly influence permeability and anisotropy. Accurately modeling their impact is critical in predicting subsurface flow capacity and mitigating risks. While many previous studies have explored factors influencing fracture permeability, they primarily focused on scalar representations of the hydraulic (apparent) aperture. As a result, they overlooked its tensorial nature, which is essential for capturing anisotropic flow behavior. In earlier work, we proposed a tensorial representation of the hydraulic aperture. In the present study, we build on that framework and investigate how shear and compression impact single fracture apparent aperture/permeability. Due to limitations in experimental designs, we employ numerical simulations at a microscale to examine the effects of shearing on hydraulic aperture tensors. Through fractional Brownian motion (fBm), we generate synthetic fracture walls and conduct fluid flow simulations to upscale hydraulic aperture tensors under varying states of shearing and compression. Our results show that the aperture tensor replicates well-documented trends in fractures undergoing shear and compression: (1) principal components of aperture tensors increase with shear displacement but are damped by compression; (2) principal orientation of aperture tensors align with shear direction; (3) anisotropy is mostly controlled by compression and remains largely insensitive to shear. These findings further validate the physical relevance of the aperture tensorial representation for modeling anisotropic flow in fractured rocks.