Simplified Method for Predicting the Shield Tunnel Longitudinal Responses to Over-Crossing Tunneling Considering Circumferential Joint Effect

A simplified theoretical approach for predicting the longitudinal behaviors of the existing shield tunnel related to over-crossing tunneling is developed by considering the circumferential joint effect. A simplified beam-spring model (SBSM) is established to describe the shield tunnel longitudinal behaviors, in which the segmental linings are simplified into Euler-Bernoulli short beams, and the circumferential joints are represented using the linear rotation and shearing springs. The SBSM can reflect the opening and dislocation of shield tunnels simultaneously. The existing shield tunnel is then regarded as the SBSM lying on the Pasternak foundation, and the displacement and joint deformations of the existing tunnel are obtained by the finite-difference method (FDM). By virtue of the FDM, the complex tunnel-soil interaction and ring-to-ring interaction can be easily transformed into the numerical solutions. The feasibility of the present approach is examined by two published cases and comparison with previous solutions. Parametric analyses are also conducted to explore the impacts of several dominant variables. The findings showed that the predicted tunnel displacements from the present solution are almost the same as those from the Timoshenko beam model and the measurements, but the present method predicts a slightly higher joint opening and lower dislocation between rings than the Timoshenko beam model. In addition, the present method takes the stiffness reduction at circumferential joints into consideration, which leads to the obtained tunnel displacement curves being neither smooth nor continuous. The rigid motion primarily appears at the lining rings, whereas the rotation and dislocation appear at the circumferential joints. The existing solutions always give continuous tunnel heave curves, which fails to truly reflect the discontinuous deformations at circumferential joints.