Elastoplastic analytical solutions for a shallow-buried circular tunnel in a semi-infinite medium

In order to explore the distribution pattern of the plastic zone around a shallow tunnel, the elastoplastic analytical solutions for a shallow-buried circular tunnel in a semi-infinite medium were proposed in this study to calculate the plastic zone radius and stresses around a shallow-buried circular tunnel. Based on the Hoek-Brown yield criterion, the solutions were derived by using the bipolar coordinate system method under the influence of the geotechnical gravity. The rationality of the proposed calculation method was verified by comparing with the existing calculation methods and numerical simulation methods, and the proposed method was further used to analyze the influence of the mechanical parameters of the rock and soil mass and uniform ground load on the plastic zone radius and stresses around a shallow-buried circular tunnel. The results show that the theoretical calculation results obtained by the proposed method fit better with the numerical simulation results, and the maximum and average errors between the two are 1.63% and 1.35%, respectively, so the calculation accuracy of the proposed method is proven to be high. The quality and strength of the geotechnical medium and the uniform ground load are both the main influencing factors of the plastic zone radius and stresses around a shallow-buried circular tunnel, and the plastic zone radius is negatively correlated with the quality and strength of the geotechnical medium, and the stresses are also negatively correlated with the quality and strength of the geotechnical medium, but are positively correlated with the uniform ground load. Therefore, the mechanical parameters of the rock and soil mass and uniform ground load should be controlled strictly to ensure the safety of shallow tunnels under construction.