管片衬砌梁–弹簧广义模型及接头转动非线性模拟

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

梁–弹簧模型法在盾构管片衬砌设计计算中逐渐得到广泛应用,但现有的梁–弹簧模型无法模拟盾构衬砌管片接头的不连续变形及接头转动刚度的非线性特性。基于此,开展了梁–弹簧模型在衬砌设计中的适用性及非线性接头转动刚度在梁–弹簧模型中的应用研究。研究表明:根据对相邻管片在接头位置结点位移处理的不同,可将梁–弹簧模型分为梁–弹簧连续模型和梁–弹簧不连续模型,后者又称为梁–接头模型,可准确分析盾构管片衬砌的内力及变形。采用梁–弹簧不连续模型求解衬砌内力及变形时:对于线性接头转动刚度模型,可基于卡氏第二定理求解;对于多段线性模型,可基于卡氏第一定理或克–恩定理求解;对于非线性模型,可采用增量–迭代法数值求解。

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.