An enhanced analytical model for predicting the nonlinear longitudinal equivalent bending stiffness of shield tunnels incorporating combined N-M actions

Abstract

The longitudinal equivalent bending stiffness (LEBS) is a key parameter of the longitudinal equivalent continuous model (LECM) of shield tunnels. When the incorporating combined actions of axial force and bending moment, i.e., N-M actions, is considered, the LEBS exhibits a significant nonlinearity. In this study, to reflect the actual action range of the circumferential joint and the coupling effect generated by the transverse and longitudinal performance of the shield tunnel, the impact factor of circumferential joint (λ) and the impact factor of transverse bending stiffness of the segmental lining (ψ) are introduced, and an enhanced analytical model for calculating the LBSE is proposed. Four types of longitudinal bending deformation modes of the shield tunnel are divided based on the contact state of circumferential joint and the corresponding neutral axis position. The LEBS of each mode is derived based on the strict elliptical integrals, and the load condition conditions to distinguish the different deformation modes are expressed. Then the performance of the proposed model is verified via the calibrated FEM model, available model tests, and other analytical models. Next, the influences of λ and ψ on the robustness of the proposed model are analyzed. Results show that there is a significant influence of ψ on the LBSE, especially the load combination is compression-bending, and λ also affects the LBSE significantly if λ ≤ 1.