A novel hybrid method for predicting vertical levelling loss of railway track geometry under dynamic cyclic loadings

Andre Oliveira De Melo, Sakdirat Kaewunruen, Mayorkinos Papaelias, Ting Li

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With an emphasis on the integrated deterioration of railway track geometry and components, a new hybrid numerical-analytical method is proposed for the predictive analysis of track geometrical vertical levelling loss (VLL). In contrast to previous studies showing a dependency on the number of cycles, this research unprecedentedly incorporates the influence of operational, vehicle and track conditions. The numerical models are carried out using an explicit finite element (FE) package under cyclic loadings, and then, their outcomes are iteratively regressed by an analytical logarithmic function that accumulates permanent deformations in order to quantify VLL over a long term. The results are first compared with other previous studies, indicating a very good agreement with them. Then, field measurements have been used to further verify the results. In this study, parametric simulations are performed varying three key parameters: axle load, train velocity and ballast tangent stiffness. The parametric studies exhibit that the rate of VLL raises about 50% if the axle load increases only from 30 to 40 tonnes for a freight train running at 70 km/h on a stiffer ballast track. In contrast, for a 25-tonnes-axle-load train running from 60 km/h to 100 km/h on a similar track, the vertical levelling degradation reduces by approximately 20%. The main findings suggest that higher axle loads contribute significantly to the VLL due higher contact forces and, on the other hand, a lower train speed does not necessarily imply a low rate of VLL since the influence of train velocities on track geometry (VLL) is associated with the natural frequencies (or wavelengths) of the ballasted railway track. The insight demonstrates that the load frequencies play a key role on the deterioration of VLL.
Original languageEnglish
Article number2250162
JournalInternational Journal of Structural Stability and Dynamics
Issue number14
Early online date4 May 2022
Publication statusE-pub ahead of print - 4 May 2022


  • Track degradation
  • cyclic loading
  • finite element method (FEM)
  • track geometry
  • vertical levelling loss, ballast elastic-plastic behavior

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Building and Construction
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics


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