Beam-spring generalized model for segmental lining and simulation of its nonlinear rotation

The beam-spring model method has been widely used in the design and calculation of shield tunnel lining, but the existing beam-spring models cannot simulate the discontinuous deformation of the segmental joints and the nonlinear characteristics of the joint rotational stiffness. Therefore, the applicability of the beam-spring models in the design of shield lining and the application of nonlinear joint rotational stiffness in the beam-spring models are studied. The results show that according to the different disposal of the nodal displacement at the joint positions between the adjacent segments, the beam-spring models can be divided into the beam-spring continuous model and the beam-spring discontinuous model, and the latter is also called the beam-joint model, in which the internal force and deformation of the shield lining can be accurately analyzed. When the beam-spring discontinuous model is employed to calculate the internal force and deformation of shield lining structures, the Second Castigliano's Theorem can be used for the segmental joints with linear rotational stiffness model, the First Castigliano's Theorem or Crotti-Engesser's Theorem can be used for the segmental joints with multi-linear stiffness model, and the numerical solution based on the increment iteration method can be used for the segmental joints with nonlinear stiffness model.