Localizing gradient damage model of rock under compression based on stress decomposition

Simulating the failure process of quasi-brittle rock under compressive stress remains a formidable challenge, primarily due to the tension–compression asymmetry of rock materials and mesh dependency. To address this issue, this paper proposes a localizing gradient damage model based on stress spectral decomposition. The core theoretical contribution lies in extending the classical localizing gradient damage framework, which traditionally considers only tensile damage, to capture the complex evolution of compressive–shear damage. By decomposing the effective stress tensor, the model employs a modified Rankine criterion to characterize tensile damage, while compressive–shear damage is independently driven by an equivalent strain calculated based on the Mohr–Coulomb criterion. Numerical simulations of double-edge-notch (DEN) specimens, pre-existing fissure rock specimens, and Brazilian disks validate the effectiveness of the proposed model. The model can capture the evolution of wing cracks and secondary cracks without relying on a predefined path and exhibits low mesh dependency. The research results provide a reference for studying mixed-mode fracture mechanisms in geotechnical engineering.