An efficient multi-time-step method for train-track-bridge interaction

Zhihui Zhu, Wei Gong, Lidong Wang, Qi Li, Yu Bai, Zhiwu Yu, Issam E. Harik

Research output: Contribution to journalArticleResearchpeer-review

37 Citations (Scopus)


In this paper, the multi-time-step method (MTS) of time integration is proposed to reduce the computational cost of solving the dynamic interaction of a train-track-bridge coupled system (TTBS). Considering the different domain frequency characteristics of the dynamic responses of the train, track, and bridge, the MTS method decomposes the TTBS into two smaller subdomains: the train-track coupled subsystem with a high domain frequency, and the bridge subsystem with a low domain frequency. A fine time-step and a coarse time-step are respectively adopted for the train-track subsystem and the bridge subsystem to improve the computational efficiency. The two subsystems are coupled by the interaction forces between the track and bridge. Two partition types of the TTBS are introduced and the effect of different decomposition types on the accuracy and efficiency of the MTS method are discussed. The proposed method is validated by comparing the numerical results with field measurement data of a simply supported bridge. A numerical simulation of a train traversing a long-span cable-stayed bridge is used to demonstrate the computational efficiency and accuracy of the proposed method. It is shown that the proposed method is accurate and computationally more efficient than using a uniform time-step for the entire TTBS.

Original languageEnglish
Pages (from-to)36-48
Number of pages13
JournalComputers and Structures
Publication statusPublished - 1 Feb 2018


  • Computational efficiency
  • Dynamic model
  • Multi-time-step
  • Railway bridges
  • Train-track-bridge coupled system

Cite this