A novel meso-damage constitutive model of rock under true triaxial stress with three-dimensional cracking strength, threshold and closure effect

Deep underground engineering is in a true three-dimensional stress state, and the adjustment of the three-dimensional stress state caused by engineering excavation will induce the fracture or even instability of the surrounding rock. However, three-dimensional mechanical model research suitable for the stability analysis of deep surrounding rock is very scarce. Therefore, a series of tests under different true triaxial stresses on two rocks (rhyodacite and marble) were conducted, and the characteristic strength (crack stable propagation initiation stress, crack unstable propagation initiation stress and peak strength) and deformation characteristics were further analyzed. After that, using the Lemaitre strain equivalence hypothesis and rock statistical damage theory, a new statistical damage constitutive model at true triaxial stress states was proposed, which introduced the three-dimensional strength criterion Modified Wiebols Cook to characterize the three-dimensional strength of the rock microelement. Therefore, the intermediate principal stress can be reasonably considered. The damage threshold, initial compaction effect and residual strength of the rock microelement at different true triaxial stress conditions were also considered. Then the relationships between the proposed model parameters and σ ₂ and σ ₃ were analyzed. Furthermore, sensitivity analysis of the influence of parameters m and F ₀ in proposed model on the shape of rock stress–strain curve and peak strength was also investigated. The comparison between the results predicted by proposed model and the experimental data shows that the new model established in this study can well simulate the prepeak and postpeak deformation characteristics of rock and the intermediate principal stress effect under true triaxial stress conditions.