Analytical algorithm of longitudinal bending stiffness of shield tunnel considering longitudinal residual jacking force

Abstract

Longitudinal bending stiffness is a fundamental parameter of shield tunnels, and its value directly affects the analysis of their longitudinal response. Existing studies have not considered the tensile stiffness of segment ring joints and longitudinal residual jacking force when determining the value of the longitudinal bending stiffness of an existing shield tunnel. Therefore, through theoretical analysis, this study considered the longitudinal bending deformation under an external load action as two parts, namely the longitudinal bending deformation of the homogeneous pipe and the longitudinal bending deformation induced by the opening of the segment ring joints. An analytical algorithm of the longitudinal bending stiffness of the shield tunnel was obtained, considering that this longitudinal bending stiffness was related to various factors such as the elastic modulus of the material of the segment ring, outer diameter of the shield tunnel, width of the segment ring, number of the segment ring joints and tensile stiffness of the connecting bolt. A scaled shield tunnel model that considered tensile stiffness of the segment ring joints and longitudinal residual jacking force was designed, and longitudinal bending stiffness tests of the model were conducted accordingly. The tests were designed to measure the longitudinal bending deformation and opening of the segment ring joints. The validation of the theoretical analysis result based on the test data demonstrates that the longitudinal residual jacking force could only reduce the longitudinal bending deformation and the opening of the segment ring joints at small loads, it had almost no effect under larger loads. The measured longitudinal bending stiffness of the shield tunnel model was generally consistent with that obtained using the theoretical algorithm. Thus, in the longitudinal response analysis of the shield tunnel, the effect of the longitudinal residual jacking force on the enhancement of the longitudinal bending stiffness need not be considered.