A scalar elastic damage model for heterogeneous rocks

Geotectonic activities and rock engineering disasters are intrinsically linked to the mechanical response of rocks under external loading. Consequently, gaining a deeper understanding of rock deformation and failure mechanisms is of paramount importance. Statistical damage models are effective tools for this purpose, yet existing models often exhibit limitations in handling combined tensile-shear stress states or lack a built-in representation of material heterogeneity. To address these issues, this study develops a novel statistical damage constitutive model. The model is founded on the fundamental assumption that the mesoscopic mechanical parameters of rock materials conform to a Weibull distribution. Within this framework, a unified scalar damage variable, driven by an equivalent strain measure, is formulated through a weighted combination of distinct tensile and shear damage components—a key improvement that allows the model to handle complex multi-axial loading paths where both damage modes coexist. A comprehensive parameter sensitivity analysis reveals that the homogeneity index is the most influential factor, with the normalized uniaxial compressive strength and elastic modulus varying by up to 247% and 17%, respectively, as the homogeneity Index (m) changes from 1.5 to 200. In contrast, variations in other parameters (e.g., residual strength coefficient, damage evolution rate) have a comparatively minor impact on the pre-peak mechanical properties. The validity of the model is rigorously demonstrated through direct quantitative comparison with independent experimental data. The numerical simulations accurately replicate the stress-strain responses and failure patterns of sandstone under both uniaxial and confined compression (confining pressures up to 35 MPa), with errors in peak strength and elastic modulus all below 3%. The results confirm the model's robustness and its significant potential for application in rock mechanics analysis, providing a more general and numerically stable framework for simulating progressive failure in heterogeneous rocks.