The aim of this study is to develop coupled matrix formulations to characterize the dynamic interaction between the vehicle, track, and tunnel. The vehicle–track coupled system is established in light of vehicle–track coupled dynamics theory. The physical characteristics and mechanical behavior of tunnel segments and rings are modeled by the finite element method, while the soil layers of the vehicle–track–tunnel (VTT) system are modeled as an assemblage of 3-D mapping infinite elements by satisfying the boundary conditions at the infinite area. With novelty, the tunnel components, such as rings and segments, have been coupled to the vehicle–track systems using a matrix coupling method for finite elements. The responses of sub-systems included in the VTT interaction are obtained simultaneously to guarantee the solution accuracy. To relieve the computer storage and save the CPU time for the large-scale VTT dynamics system with high degrees of freedoms, a cyclic calculation method is introduced. Apart from model validations, the necessity of considering the tunnel substructures such as rings and segments is demonstrated. In addition, the maximum number of elements in the tunnel segment is confirmed by numerical simulations.

本研究的目的是开发耦合矩阵公式来表征车辆、轨道和隧道之间的动态相互作用。根据车辆-履带耦合动力学理论建立了车辆-履带耦合系统。隧道管段和隧道环的物理特性和力学行为通过有限元方法建模，而车辆-轨道-隧道 (VTT) 系统的土层通过满足边界来建模为 3-D 映射无限元素的组合无限区域的条件。新颖的是，隧道组件，例如环和管段，已使用有限元矩阵耦合方法耦合到车辆-轨道系统。同时获得包含在 VTT 交互中的子系统的响应，以保证求解的准确性。为减轻大型高自由度VTT动力学系统的计算机存储和CPU时间，引入循环计算方法。除了模型验证之外，还证明了考虑隧道子结构（例如环和管段）的必要性。此外，隧道段中的最大单元数通过数值模拟得到确认。