Semi-analytical Study for Cylindrical Tunnels Reinforced by Bolt-Grouting in Elastic–Brittle–Plastic Surrounding Rock Considering Nonlinear Seepage

The bolt-grouting reinforcement method can reduce water inflow and reinforce the surrounding rock in a tunnel. However, analytical theories on bolt-grouting reinforcements that consider nonlinear seepage in water-rich tunnels are few. This study proposes an elastic–brittle–plastic semi-analytical solution that considers nonlinear seepage for surrounding rockbolt grouting reinforcement under axisymmetric conditions based on Izbash’s law, Terzaghi’s effective stress principle, the Mohr–Coulomb criterion, and a plastic constitutive model in terms of incremental plastic strain. The results of the proposed semi-analytical solutions were consistent with those of the finite element model, and the effects of bolt grouting and other design parameters on the maximum displacement of the tunnel wall and radius of the plastic region are discussed. As the grouting circle thickness increases, the deformation and plastic region radius decrease. The rockbolt length should be more than 0.3 times the diameter of the tunnel to ensure its effectiveness in the absence of support pressure. The data calculated using the proposed model also suggest that blindly increasing the length of the rockbolt and grouting circle thickness is not beneficial. The increase in the tunnel diameter and impermeability pressure hinder the stress state control and deformation of the host rock. The empirical coefficient of Izbash’s law increases the plastic region radius of the surrounding rock; however, an increase in the empirical coefficient could reduce the effective stress values.