A Statistical Anisotropic Damage Constitutive Model for Shale Including the Effects of Confining Pressure and Strain Rate

Confining pressure, strain rate and anisotropy are three essential factors that affect the mechanical behaviors of shale. In this study, a damage constitutive model including the effects of all these three factors is developed to predict the deformation and strength of sedimentary shale. The inherent elastic tensor and the damage of shale are considered to be transversely isotropic. The statistical trans-scale theory is adopted to establish the formulation of the damage variable which connects the microscopic element damage to macroscopic rock failure. A generalized Lade criterion combined with the fabric tensor is proposed to take into account the anisotropic strength and tension-compression asymmetry of shale, which successfully predicts the different properties under tension and compression. The strain rate and confining pressure change shale's stiffness and strength by influencing anisotropic elastic moduli and damage evolution rates. The theoretical predictions of the established model are in good agreement with the experimental results in the literature for various cases, demonstrating that the model can predict the stress-strain relations of transversely isotropic shale under complicated loading conditions. A damage constitutive model is developed to predict deformation and strength of shale, considering confining pressure, strain rate, and anisotropy.The statistical trans-scale theory is used to establish the damage variable, connecting microscopic element damage to macroscopic rock failure.A generalized Lade criterion with the fabric tensor accounts for anisotropic strength and tension-compression asymmetry.The theoretical prediction agrees well with experimental results, showing its ability to describe stress-strain relations of shale.