Coupled rheological behavior of tunnel rock masses reinforced by rock bolts based on the non-hydrostatic stress field

The stress and deformation characteristics of the rock mass and the rock bolt reinforcement structure change over time, as a result, it is of significance to understand the coupled rheological behavior of these two systems. In this paper, we first develop viscoelastic solutions for the rock mass reinforced by rock bolts under non-hydrostatic stresses based on the distributed force model. Subsequently, the Maxwell-Maxwell (M-M) and the MaxwellBurgers (M-B) constitutive models are applied to the rock bolts and the rock mass, respectively, and the corresponding viscoelastic analytical solutions are then obtained. Finally, the numerical software FLAC3D is used to verify the fidelity of the mechanistic model. Our results show that the lateral pressure coefficient is positively correlated with the radial stress and the radial displacement. The radial stress in the rock mass reaches a stable value with time. Furthermore, the lateral pressure coefficient has a positive correlation with the axial force in the rock bolts in elastic analysis. However, as the creep in the rock mass develops, the axial forces under different lateral pressure coefficients gradually reach a stable value. Moreover, the lateral pressure coefficient mainly affects the distribution of axial force and the slope of the axial force in the rock bolts.