Complex variable solution for ground deformation responses considering the grouting pressure of shallow shield

Abstract

During shield tunneling in shallow strata, ground deformation is highly sensitive to grouting pressure response. Excessive grouting pressure can cause ground uplift, and an excessively low grouting pressure can cause excessive ground settlement, affecting the surrounding environment. Current studies seldom analyze the influence of shield excavation on ground deformation when the grouting pressure is considered. To ensure micro-disturbance of the surrounding environment during shield tunneling, this study presents a complex variable analysis method for analyzing the influence of grouting pressure on surface settlement. This solution maps the semi-infinite strata outside the segment into circular domains by introducing a complex function conformal mapping method. The nonuniform convergence deformation pattern BC-4 was introduced as the boundary condition for the displacement around the tunnel. The Laurent series expansion of the analytical function considering the grouting pressure in the circular domain was substituted into each boundary condition to solve the analytical function. Subsequently, the accuracy of the analytical method was verified by combining it with a finite element numerical method. Finally, the influence of grouting pressure on ground deformation under different working conditions was analyzed through parameterization. This analytical method can provide a theoretical basis for controlling grouting pressure parameters in shield tunnels.