Journal of Civil Structural Health Monitoring

, Volume 7, Issue 5, pp 637–643 | Cite as

Quantifying live bending moments in rail using train-mounted vertical track deflection measurements and track modulus estimations

  • Saeideh Fallah Nafari
  • Mustafa GülEmail author
  • J. J. Roger Cheng
Original Paper


This paper presents a new methodology to quantify the vertical bending moments that generate in rail under the passage of train wheels. In this method, the rail-bending moments are quantified from track modulus estimated using train-mounted vertical track deflection (VTD) measurements. This provides a practical approach for quantifying the rail-bending moments along large railway networks. The method requires the mathematical correlations between VTD, track modulus and rail-bending moments. Hence, a detailed finite element model was developed to investigate and quantify the mathematical correlations between these parameters. Various track modulus distributions were simulated and the resultant VTD and rail-bending moments were calculated. The mathematical correlation between inputted track modulus, and modelled VTD and rail-bending moments were then quantified using statistical approaches. From the results, track modulus average and standard deviation can be estimated over track windows using the VTD measurements. These estimations can be then employed to quantify the average and peak for the envelope of the maximum vertical bending moment in rail over the same track window. The accuracy of the method was verified using a numerical case study for which a random track modulus distribution was considered and artificial noise was added to the modelled VTD.


Railroad tracks Track modulus variation Rail-bending moment Deflection measurement Continuous measurement Computer simulation 



The present study addressed part of an ongoing research project on rail integrity. The authors would like to acknowledge the Canadian Rail Research Laboratory (CaRRL) ( at the University of Alberta for facilitating and funding this project. CaRRL is funded by the Natural Sciences and Engineering Research Council of Canada (NSERC), Canadian Pacific Railway, Canadian National Railway, the Association of American Railroads—Transportation Technology Centre Inc., the National Research Council of Canada, Transport Canada and Alberta Innovates—Technology Futures.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Saeideh Fallah Nafari
    • 1
  • Mustafa Gül
    • 2
    Email author
  • J. J. Roger Cheng
    • 3
  1. 1.Department of Civil and Environmental EngineeringUniversity of AlbertaEdmontonCanada
  2. 2.Department of Civil and Environmental EngineeringUniversity of AlbertaEdmontonCanada
  3. 3.Department of Civil and Environmental EngineeringUniversity of AlbertaEdmontonCanada

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