A new statistical damage model for true triaxial pre-and post-peak behaviors of rock considering intermediate principal stress and initial compaction effects

Deep underground engineering excavation will induce complex change in the true three-dimensional stress state of the surrounding rock, causing rock damage and then leading to a change in mechanical properties. In this research, the true triaxial compression tests are conducted to study the influence of σ ₂ and σ ₃ on the mechanical properties of marble, such as the characteristic strength (crack initiation stress σ _ci , damage stress σ _cd , peak strength σ _p , and residual strength σ _r ), post-peak deformation, ductility and brittleness. The peak strength σ _p , crack initiation stress σ _ci and damage stress σ _cd of rock increase with the increase in σ ₂ , while the variation of residual strength σ _r with σ ₂ is different from that of peak strength. As σ ₂ increases or σ ₃ decreases, the pre-peak plasticity of the rock decreases, the post-peak curve shape of the rock changes significantly, and the overall shape of the post-peak curve transforms from Class I to Class II. The Mogi-Coulomb strength criterion with intermediate principal stress effect was used to characterize the rock microelement strength, and then the new statistical damage constitutive model considering the initial compaction effect and damage threshold was proposed, and the model validation was carried out based on the experimental results and the effects of the proposed model parameters m and F ₀ on the rock strength and post-peak curve morphology were further explored.