Transverse isotropic slate damage modeling under triaxial compression conditions

Studies of the mechanical response behavior of slate and the establishment of corresponding damage-ontological relationships are crucial for improving safety and avoiding disasters in construction projects. For the study reported in this paper, we first assumed that slate is a transverse isotropic body. Next, to characterize disparities in elastic characteristics between axial and radial orientations, we introduced five distinct elastic parameters for these two directions. Specifically, these parameters were Young’s modulus E₁, Poisson’s coefficient v₁ (associated with parallel bedding planes), Young’s modulus E₂, Poisson’s coefficient v₂, and shear modulus G₂ (associated with perpendicular bedding planes). We then established a statistical damage-evolution equation for transverse isotropic slate based on a lognormal distribution, and we constructed a statistical damage-constitutive model for laminated slate under three-way stress by considering the shear–slip deformation and closure deformation of the laminated surface. Finally, we demonstrated the effectiveness of our model by comparing its output data with results obtained in triaxial compression tests on slate. We found that the differential stress–strain curves obtained from the model and the tests were in good agreement in the peak front. Average relative errors of 15.62% and 16.19% were recorded for cases of 5 Mpa and 10 Mpa of enclosing pressure, respectively. The rationality of the established transverse isotropic slate damage-constitutive relationship was therefore proved.