Anisotropic energy-based progressive damage model for laminated geomaterials

Abstract

Laminated geomaterial widely exists in rock engineering construction. Inherent anisotropy of laminated geomaterial make its mechanical properties and mathematical constitutive model complicated. This study is devoted to developing an energy-based damage model for characterizing both the inherent anisotropy and the stress-induced anisotropy of laminated geomaterials. The fabric tensor is adopted to describe the inherent anisotropy. Then, the free energy potential is defined in combination with the fabric tensor. The general stress-strain relationship and anisotropic stiffness matrix are derived based on the irreversible thermodynamics theory. To reflect the anisotropy of damage during the application of force, a fourth-order damage tensor is defined. This damage tensor is dependent on two scalar damage factors, which depict the degeneration of stiffness along the normal direction of the bedding plane and in the isotropic plane, respectively. Equivalent energy release rates corresponding to these two damage factors are constructed in consideration of the effects of anisotropy. Taking a statistical approach, anisotropic damage evolution rules that distinguish the different mechanical responses of laminated geomaterials under compression and tension are proposed. Moreover, the calibration procedure for the unknown parameters in the model is described in detail, and the predictions from the proposed theoretical model are compared with those from existing models to verify the rationality of the present model. Triaxial compression and tensile tests are also adopted to facilitate a comparison with the results of numerical simulations, illustrating that the new constitutive model can capture the anisotropic mechanical deformation and the anisotropic damage evolution of a laminated geomaterial.