Modified analytical solution of shield tunnel lining considering nonlinear bending stiffness of longitudinal joint

Abstract

As discontinued segmental joint plays a great important role in the mechanical behavior of shield tunnel lining, design for the joint suffers much from the difficulty in selecting proper parameters i.e., reduction factor η, spring stiffness. The mechanical behavior of longitudinal joint is highly nonlinear and can be classified into four stages. A four stage analytical model for determining the joint bending stiffness is proposed considering the influence of bending moment and axial force. The proposed analytical model is verified by 3D FE model and experimental results of Shanghai Yangtze River Tunnel. An analytical full ring solution based on Lee’s model is proposed incorporating the nonlinear joint stiffness model. The modified analytical solution is compared with the Lee’s model and 3D FE model with a case study of metro tunnels. Compared to Lee’s model, the modified solution has a better prediction of bending moment distribution especially at tunnel invert while has a close prediction of axial force distribution. The proposed solution has a good agreement with FEM results in tunnel deformation including horizontal convergence and joint opening. The maximum prediction errors are 1.5 mm for horizontal convergence and 0.36 mm for joint opening compared to 3D FE model analysis.