Permeability, deformation characteristics, and damage constitutive model of shale under triaxial hydromechanical coupling

Shale is one of the most widely distributed and common types of surrounding rock in underground structures such as tunnels. However, the mechanical strength of shale decreases significantly under the combined action of stress and osmotic pressure. In this study, we conducted triaxial compression tests under variable osmotic and confining pressures to evaluate the mechanical behavior of shale under a combination of stress and seepage. The peak mechanical strength of shale decreased as the osmotic pressure increased, which resulted in five different macro failure modes corresponding to different levels of osmotic pressures. Furthermore, high confining pressures induced failure of the compression band which considerably inhibited permeability, with stages of shale fracture developing in correspondence with changes in the permeability. The minimum permeability of shale occurred before the expansion point. While the confining pressure played an important role in the growth of cracks, the osmotic pressure had a relatively weak effect. The quantitative relationship between permeability, axial strain, and volumetric strain found in this study sufficiently reflects the evolution law of shale permeability during the deformation and failure processes. Based on these results, we developed a new damage constitutive model for rock under osmotic pressure by introducing statistical damage theory. The model can reflect the stress–strain relationship better under different confining and osmotic pressures, can accurately capture the key points of the mechanical response, and depends on parameters that are simple to calculate, which is important for engineering applications.