A multiscale modeling of damage accumulation and permeability variation in shale rocks under mechanical loading

This paper presents a hierarchal multiscale model to simulate the damage behavior of transversely isotropic shales, where the damage mechanism is attributed to micmcrack growth under mechanical loading. An anisotropic damage model is presented in which the state of damage is described by a scalar crack density parameter. Furthermore, a simplified permeability model is incorporated to couple the evolution of damage to permeability variation through the damage density parameter. The Maximum Entropy principle is employed to account for uncertainty in the main parameters of the multiscale model representing the subscale structural and compositional features. This probabilistic multiscale damage model provides a framework to simulate the probabilistic descriptions of poromechanical and damage properties and the subsequent variation in microcrack-induced permeability. This framework is used to simulate nonlinear stress-strain behavior in uniaxial compression tests for varying loading directions with respect to the bedding plane of transversely isotropic shale rocks. The outcome of this study includes probabilistic characteristics of stiffness degradation, crack growth, and permeability variation under different loading conditions.