Analytical solution for shield tunnel structural behavior considering nonlinear shear stiffness of circumferential joint

When analyzing the deformation and internal forces of shield tunnels subjected to external disturbances such as surface surcharge and nearby deep excavation, the assumption of linear or constant shear stiffness of segmental joints, commonly adopted in current design practices, cannot adequately capture the nonlinear degradation of shear stiffness with increasing circumferential joint dislocation. To address this limitation, this paper focuses on circumferential joints with oblique bolt connections and analyzes the nonlinear relationship between shear stiffness and joint dislocation of oblique bolts at various positions. The study then aggregates the shear stiffness of all oblique bolts and concrete segments to obtain the circumferential joint shear stiffness and determine the key parameters in the nonlinear expression. Taking surface surcharge as a case study, the deformation and internal forces of the shield tunnel are derived using a numerical solution based on the finite difference method, with results verified by a refined 3D finite element model. The results indicate that the nonlinear relationship between shear stiffness and circumferential joint dislocation can be represented by a logistic function with three parameters: initial maximum stiffness K₀, critical dislocation δ₀, and degradation rate d'. The proposed model effectively characterizes the sharp variations in shear forces acting on segments and joints, providing significant advantages for identifying vulnerable locations under extreme loads or joint performance degradation scenarios. The parametric study reveals that decreasing initial maximum shear stiffness K₀ increases tunnel settlement and joint dislocation while reducing segment bending moments and shear forces. For critical dislocation δ₀, lower values reduce the failure threshold, with significant joint failures corresponding to circumferential joint dislocations of approximately 3.8 mm occurring at 0.2×δ₀, particularly near surcharge boundaries at -15 m and 15 m. Variations in degradation rate d' show minimal impact because the joint dislocations remain within the high-stiffness range under the studied scenarios.