An Efficient User‐Defined Element Framework for Joint Behavior Simulation and Transverse Deformation Analysis in Shield Tunnels

ABSTRACT This study proposes an efficient modeling approach for shield tunnel joints based on user‐defined elements (UELs), which is applied to the analysis of transverse deformation in shield tunnels. The element stiffness matrix of longitudinal joints with irregular geometric configurations was derived under arbitrary loading conditions. The solution procedure of the stiffness matrix was then incorporated into the UEL algorithm framework. The developed element simultaneously accounts for the varying load state at longitudinal joints, geometric configurations of the joint, and material nonlinearity, as well as their coupling effect on the load‐bearing capacity of the joint. Subsequently, the feasibility and accuracy of the UEL‐based modeling approach were evaluated across multiple modeling scales. The results demonstrate that this element not only significantly simplifies the modeling process but also effectively captures the nonlinear characteristics of tunnel convergence deformation observed in practical engineering scenarios. In addition, the UEL‐based modeling approach was employed to investigate the transverse deformation of shield tunnels subjected to an extreme surcharge–unloading–grouting rehabilitation sequence. Lining displacement–subgrade reaction and in situ stress state were appropriately incorporated into the numerical model. The effects of initial soil stiffness and the coefficient of earth pressure at rest on tunnel transverse deformation were quantitatively examined, along with the relationship between tunnel convergence and joint rotation. The results reveal a flag‐shaped hysteresis in the moment‐rotation response of tunnel joints under unloading and grouting, underscoring the importance of precisely capturing the multi‐degree‐of‐freedom coupling in joint element for practical engineering applications.