Prediction model of safe distance for shield tunnel crossing karst strata

Shield tunneling through complex karst formations presents significant engineering challenges due to construction-induced disturbances, which markedly increase the risk of excessive ground settlement and localized collapses. These phenomena pose serious threats to the safety and stability of tunneling operations. For the shield tunnel section between Tangye Station and Chengjiazhuang Station of Jinan Metro Line 4, numerical simulation methods were employed to analyze the evolution of the surrounding rock displacement field and plastic zone when the tunnel crosses karst caves above and laterally. Regression analysis was conducted on the simulation results. Based on the principle of plastic zone penetration, orthogonal experimental schemes considering three factors (surrounding rock grade, tunnel burial depth, and karst cave diameter) were developed to establish predictive models for the safe distance between karst caves and tunnels for both overhead and lateral crossings. The results indicate that when the tunnel crosses a karst cave overhead, as the distance between the cave and tunnel increases, the uplift at the tunnel invert increases, the settlement at the tunnel crown decreases, the horizontal displacements at the left and right tunnel haunches diminish, and the trend of plastic zone penetration weakens. When the tunnel crosses a karst cave laterally, with increasing distance between the cave and tunnel, the settlement at the tunnel crown decreases, the horizontal displacement at the tunnel haunch on the side closer to the cave diminishes, and the trend of plastic zone penetration also weakens. The safe distance between karst caves and tunnels increases with each factor. The extent of influence of different factors is ranked as follows: karst cave diameter > surrounding rock grade > tunnel burial depth. Through theoretical analysis and predictive models, reinforcement measures should be implemented within a 5 m radius below and a 3 m radius laterally of the shield tunnel section between Tangye Station and Chengjiazhuang Station. This study provides a theoretical basis for reinforcing the surrounding rock of the shield tunnel section crossing karst formations on Jinan Metro Line 4, which is of great significance for guiding on-site construction.