Anisotropic damage model for strength prediction and constitutive behavior of layered quasi-brittle rocks

Weakness planes in cohesive quasi-brittle rocks have a significant impact on their mechanical behavior, with the inclination angle of these planes leading to pronounced anisotropy. To address this, we present an orientation-dependent damage model that quantitatively incorporates the effects of varying inclination angles within the solid matrix. The model is developed within the frameworks of irreversible thermodynamics and Mori–Tanaka homogenization theory. Analytical solutions and their applicability ranges are derived, and macroscopic strength criteria are established to describe anisotropic failure under different triaxial compression conditions. Model predictions are validated against experimental results for Longmaxi Formation shale and layered sandstone. This work enhances our understanding of the anisotropic constitutive behavior of layered quasi-brittle rocks and provides a solid theoretical foundation for predicting their strength and deformation.