Time-Dependent Solutions for Lined Circular Tunnels Considering Rockbolts Reinforcement and Face Advancement Effects

During deep excavation in weak rock masses, the time-dependent deformation of the rock and longitudinal advancement process have significant influences on the tunnel performance. Accordingly, a combined support system consisting of rockbolts and linings is commonly used in such tunnels to ensure their stability. However, there are no well-established solutions for quickly and accurately evaluating the safety of those support systems. To address this problem, mechanical model of a circular tunnel with a rockbolt–lining combined system is analytically built in this study. Then mathematical formulas for the stresses and displacements around the tunnel are derived, considering the time-dependent behaviors of the rocks and tunnel face advancement effect. Furthermore, the analytical formula proposed in this study is compared with existing solutions and numerical results obtained using the finite-element software Abaqus, and a good agreement is achieved. Finally, a parametric investigation is conducted regarding the influences on the tunnel's mechanical performance. The results show that the installation time (t0) and distribution density of rockbolts (SθSz) and the installation time of the lining (t1) have a significant influence on the deformation of the surrounding rock. Although the installation times of bolt and lining are positively related to the deformation suppression effect of the surrounding rock, they are negatively related to the stress of the bolt and lining. It is found that the closer the installation time of bolt and lining, the greater the stress of lining; otherwise, the greater the stress of bolts. Furthermore, the initial release coefficient (m) and the ratio of tunnel excavation rate to influence radius can influence the deformation rate of surrounding rock. Finally, the study proposes a new method for quickly evaluating the viscoelastic deformation of a tunnel.