Analytical Solutions for Deep Tunnels in Viscoelastic-Plastic Rock Considering Rheological Damage Effects and the Lining Influence

Creep deformation of tunnel surrounding rock is a common phenomenon, posing a significant threat to the safe excavation and stable operation of the tunnel. In response to this issue, a set of theoretical models that can predict the deformation of tunnel surrounding rock is established based on the fractional order theory as well as the unified strength theory, and considering the influence of the supporting structure. The results show that: ① the fractional-order damage model takes into account the relaxation effect of the surrounding rock and has a good fitting effect on the rock creep. ② Tunnel deformation increases with the decrease of surrounding rock parameters, and the nonlinear effect of cohesion is especially significant. ③ The effect of damage parameters on surrounding rock deformation is greater than other parameters, indicating that the surrounding rock deformation can be effectively controlled by adjusting construction methods. ④ The influence of support structure type and support timing on the time-dependent deformation of surrounding rock is analyzed, especially the support timing of the second lining has a significant influence on the deformation of surrounding rock during the operation period of the tunnel. Finally, the comparison of the theoretical calculation results with the experimental data and field monitoring data verified the reliability of the theoretical model and analysis method. It provides a scientific basis for the control of tunnel deformation and the design of support measures.