As a discontinuous ring structure, segmental longitudinal joints are a weakness of shield tunnels and play an important role in the determination of tunnel deformation caused by ground pressure. A longitudinal joint bending test is first carried out by employing a detailed 3D numerical model for the Shanghai Metro tunnel. This reveals that the joint stiffness varies nonlinearly with the axial force and bending moment. Based on numerical results, an analytical model for determining the joint rotational stiffness is provided, which takes the influence of the mechanical behavior of the concrete and steel bolts, the geometrical dimensions of the joint cross section and the subjected loads into account. Then, a simplified fitting equation is proposed, which has been verified by the experimental test results. This reveals that the results obtained from the proposed fitting equation are in good agreement with the experimental results before the joint reaches the limit state. Therefore, this proposed equation can be preliminarily adopted for the simulation of joint bending behavior and the determination of tunnel deformation in the tunnel design stage.

中文翻译：

---

考虑轴力的隧道纵向节点抗弯刚度数值模拟及简化分析模型

节段纵向节理作为一种不连续的环状结构，是盾构隧道的一个弱点，对确定地压引起的隧道变形具有重要作用。首先使用上海地铁隧道的详细 3D 数值模型进行纵向接头弯曲试验。这表明关节刚度随轴向力和弯矩非线性变化。基于数值结果，提供了一个确定节点旋转刚度的分析模型，该模型考虑了混凝土和钢螺栓的力学行为、节点横截面的几何尺寸和承受载荷的影响。然后，提出了一个简化的拟合方程，并得到了实验测试结果的验证。这表明从所提出的拟合方程获得的结果与接头达到极限状态之前的实验结果非常吻合。因此，该方程可初步用于隧道设计阶段节点弯曲行为的模拟和隧道变形的确定。