Influence of deviatoric stress invariants on the surrounding rock of deep mining roadways and its engineering applications

The mechanical behavior of surrounding rock in deep roadways becomes highly complex under different horizontal stresses. Traditional two-dimensional stress analysis methods cannot accurately capture the true mechanical response. Elastoplastic mechanics theory and previous research on three-dimensional stress analysis are built upon. It also incorporates the Poisson effect to further derive analytical solutions for the second (J₂) and third (J₃) deviatoric stress invariants. The distribution and evolution of J₂ and J₃ under different horizontal stresses are then examined. Numerical simulations reveal how changes in the horizontal stress ratio significantly affect the distribution of deviatoric stress and the shape of the plastic zone. These effects are especially pronounced at higher horizontal stress ratios, where the stability of surrounding rock faces greater challenges. A numerical model is established to simulate the distribution of J₂ and J₃ and the expansion of the plastic zone around the roadway. Based on these findings, a combined support technology using advanced supports and rock bolts (cables) is proposed for asymmetric deviatoric stress conditions. Monitoring results confirm that this support strategy effectively controls rock deformation and failure, thereby enhancing overall roadway stability and safety.