Simplified calculation method for the structure deformation response of the existing shield tunnel under surcharge

Abstract Surcharge loading compromises the original stress state of soil strata, generating detrimental additional stresses on the tunnel that critically threaten operational safety. Given this, the tunnel is equated to the Timoshenko beam resting on the three-parameter Kerr foundation model for this study. The theoretical models of the existing shield tunnel structural response under surcharge, considering and ignoring the impact of lateral soil, are proposed and solved using finite difference method. On this basis, the parameter sensitivity analysis is conducted. Finally, the prediction formula for the vertical deformation of the existing tunnel under surcharge is developed. The results show that the calculation results obtained by proposed theoretical models match well with the observation results from the finite-element method, existing analytical method, and field-measured data. In particular, the theoretical model considering the impact of lateral soil has higher calculation accuracy. Meanwhile, the parameter analysis shows that an increase in the area and amount of the surcharge causes increasing the tunnel longitudinal displacement. Conversely, increasing the elastic modulus of soil, the tunnel buried depth and the distance between the tunnel axis and the loading center decreases the tunnel longitudinal displacement. The proposed prediction formula has sufficient engineering accuracy and can serve as a valuable tool for quickly calculating the existing tunnel longitudinal deformation under surcharge.