A Spectral Microplane Model for the Anisotropic Damage Behavior of Shales

The development of constitutive models for shales has been a challenge for decades due to the difficulty of characterizing the strongly anisotropic macroscopic behavior related to the inherent mesostructure and damage mechanisms. In this paper, a spectral microplane damage model is developed for the anisotropic damage behavior of shales. The modeling challenge of the anisotropic elasticity in the microplane model is theoretically overcome by the spectral decomposition theory without limitation on the degree of the anisotropy compared with other microplane models. The stiffness tensor of anisotropic shales is effectively decomposed into four different eigenmodes with the activation of certain groups of microplanes corresponding to the specific orientation of the applied stresses. The inherent and the induced anisotropic behavior is thus characterized by proposing suitable microplane relations on certain eigenmodes directly reflecting the initial mesostructure and the failure mechanisms. For the challenge of the postpeak softening behavior, two-scalar damage variables are introduced to characterize the tensile and the shear damage related to the opening and the closure of microcracks under different stress conditions. Comparison between numerical simulation and experimental data shows that the proposed model provides satisfactory predictions for both weakly and highly anisotropic shales including prepeak nonlinear behavior, failure strengths, and postpeak softening under different confining pressures and different bedding plane orientations.