A damage rock model considering shear failure by modified logistic growth theory

Localized rock failures, like cracks or shear bands, demand specific attention in modeling for solids and structures. This is due to the uncertainty of conventional continuum-based mechanical models when localized inelastic deformation has emerged. In such scenarios, as macroscopic inelastic reactions are primarily influenced by deformation and microstructural alterations within the localized area, internal variables that signify these microstructural changes should be established within this zone. Thus, localized deformation characteristics of rocks are studied here by the preset angle shear experiment. A method based on shear displacement and shear stress differences is proposed to identify the compaction, yielding, and residual points for enhancing the model's effectiveness and minimizing subjective influences. Next, a mechanical model for the localized shear band is depicted as an elasto-plastic model outlining the stress-displacement relation across both sides of the shear band. Incorporating damage theory and an elasto-plastic model, a proposed damage model is introduced to replicate shear stress-displacement responses and localized damage evolution in intact rocks experiencing shear failure. Subsequently, a novel nonlinear mathematical model based on modified logistic growth theory is proposed for depicting the shear band's damage evolution pattern. Thereafter, an innovative damage model is proposed to effectively encompass diverse rock material behaviors, including elasticity, plasticity, and softening behaviors. Ultimately, the effects of the preset angles, temperature, normal stresses and the residual shear strength are carefully discussed. This discovery enhances rock research in the proposed damage model, particularly regarding shear failure mode.