A micro-macro fracture model for evaluating the brittle-ductile transition and rockburst of rock in true triaxial compression

In deep underground engineering, true triaxial compressive stress and internal microcrack characteristics significantly influence the brittle-ductile transition and anisotropic mechanical behavior of rock, thereby affecting the engineering life cycle. However, current research on the micro-macro mechanical model under true triaxial compressive stress, particularly regarding the rock's brittle-ductile transition and anisotropic damage, is extremely limited. This paper aims to propose a macro-micromechanical model to describe the aforementioned physical and mechanical properties of rocks. The model introduces a lateral stress function into the micro-macro damage formula and derives the axial stress-strain relationship during crack propagation by incorporating the stress-crack length relationship under true triaxial stress. By considering the stress effects on the effective elastic modulus and nominal Poisson's ratio, the lateral stress-strain relationship is derived, resulting in a complete stress-strain curve. Finally, based on the relationships between triaxial principal strains, elastic deformation and triaxial principal stresses, the relationships between rock volumetric strain, crack volumetric strain, and triaxial principal stress are separately established. The influence of lateral principal stress on characteristic stresses is analyzed. The resulting model is combined with the brittleness evaluation index and the residual elastic energy index, respectively, to analyze the effects of micro parameters and principal stresses on brittleness and rockburst proneness. A comparative analysis of the similarities and differences between brittleness and rockburst proneness is conducted, revealing a positive correlation between the ratio of residual elastic energy and the post-peak to pre-peak brittleness index, expressed as CEF∝Bi2/Bi1. The proposed model theoretically addresses the issues of brittle-ductile transition and anisotropic damage under true triaxial conditions. It can also be applied to explain and predict rockburst proneness.