Experimental and analytical study on longitudinal bending behavior of shield tunnel subjected to longitudinal axial forces

Longitudinal bending stiffness efficiency (LBSE) is a key parameter for analyzing longitudinal behavior of shield tunnel. The LBSE is defined as the deformation ratio of a uniform beam to the corresponding segmented non-uniform beam when subjected to the same load. Traditionally, the LBSE is treated as a constant, which can be evaluated by various longitudinal equivalent continuous models (LECMs). However, the effect of longitudinal axial forces (N) on the LBSE is often excluded. In this study, model tests are designed to investigate the LBSE subjected to longitudinal axial forces. The tests reveal that the LBSE is not a constant and it increases with the increasement of longitudinal axial forces. A regressed equation is obtained to revise the traditional LBSE based on the model test results. A modified LECM is proposed to calculate the LBSE, and the analytical results fit with the model tests well. The highlight of the proposed model is that the effect of longitudinal axial force is included. According to the analytical analysis, the LBSE is related to lambda ( =N.r/2M), in which r is distance from segment rings' center to bolts, N is longitudinal axial force, and M is bending moment. When lambda = 0, the modified LECM reduces to the Shiba-LECM. When lambda increases from 0 to 1, the LBSE increases from Shiba-LECM result to 100%. When lambda >= 1, the LBSE remains 100%.