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

Abstract

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.

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References

  1. 1.

    Transportation Safety Board of Canada (2015) Statistical summary railway occurrences 2014. Tech Rep TU1-2E-PDF

  2. 2.

    Saat MR, Barkan CPL, Liu X (2012) Analysis of causes of major train derailment and their effect on accident rates. Transp Res Rec 2289:154–163

    Article  Google Scholar 

  3. 3.

    Dick CT, Barkan CPL, Chapman ER, Stehly MP (2003) Multivariate statistical model for predicting the occurrence and location of broken rails. Transp Res Rec 1825:48–55

    Article  Google Scholar 

  4. 4.

    Cannon D, EDEL K, Grassie S, Sawley K (2003) Rail defects: an overview. Fatigue Fract Eng Mater Struct 26:865–886

    Article  Google Scholar 

  5. 5.

    Jeong DY, Tang YH, Orringer O (1998) Estimation of rail wear limits based on rail strength investigations. Tech Rep Federal Railroad Administration DOT/FRA/ORD-98/07, DOT-VNTSC-FRA-98-13

  6. 6.

    Zerbst U, Lundén R, Edel K, Smith RA (2009) Introduction to the damage tolerance behaviour of railway rails–a review. Eng Fract Mech 76:2563–2601

    Article  Google Scholar 

  7. 7.

    Orringer O, Tang YH, Gordon JE, Jeong DY, Morris JM, Perlman AB (1988) Crack propagation life of detail fractures in rails. Tech Rep Federal Railroad Administration, DOT/FRA/ORD-88/13, DOT-TSC-FRA-88-1

  8. 8.

    Jeong DY, Perlman AB (2011) Estimating track capacity based on rail stresses and metal fatigue. In: Proceedings of the 2011 ASME rail transportation division fall technical conference (RTDF2011), Minneapolis, Minnesota, USA, RTDF2011-67001, doi:10.1115/RTDF2011-67001

  9. 9.

    Enckell M, Glisic B, Myrvoll F, Bergstrand B (2011) Evaluation of a large-scale bridge strain, temperature and crack monitoring with distributed fibre optic sensors. J Civ Struct Health Monit 1(1–2):37–46

    Article  Google Scholar 

  10. 10.

    Gue C, Wilcock M, Alhaddad M, Elshafie M, Soga K, Mair R (2015) The monitoring of an existing cast iron tunnel with distributed fibre optic sensing (DFOS). J Civ Struct Health Monit 5(5):573–586

    Article  Google Scholar 

  11. 11.

    Porco F, Fiore A, Porco G, Uva G (2013) Monitoring and safety for prestressed bridge girders by SOFO sensors. J Civ Struct Health Monit 3(1):3–18

    Article  Google Scholar 

  12. 12.

    Sussman T, Ebersöhn W, Selig E (2001) Fundamental nonlinear track load-deflection behavior for condition evaluation. Transp Res Rec 1742:61–67

    Article  Google Scholar 

  13. 13.

    Dahlberg T (2010) Railway track stiffness variations-consequences and countermeasures. Int J Civ Eng 8(1):1–12

  14. 14.

    Selig ET, Li D (1994) Track modulus: its meaning and factors influencing it. Transp Res Rec 1470:47–54

    Google Scholar 

  15. 15.

    Berggren EG, Nissen A, Paulsson BS (2014) Track deflection and stiffness measurements from a track recording car. Proc IMechE Part F: J Rail Rapid Transit 228(6):570–580

    Google Scholar 

  16. 16.

    Li D, Thompson R, Marquez P, Kalay S (2004) Development and implementation of a continuous vertical track-support testing technique. Transp Res Rec 1863:68–73

    Article  Google Scholar 

  17. 17.

    Thompson R, Li D (2002) Automated vertical track strength testing using TTCI’s track loading vehicle. Technol Dig 1489:17–25

    Google Scholar 

  18. 18.

    Farritor S, Fateh M (2013) Measurement of vertical track deflection from a moving rail car. Tech Rep Federal Railroad Administration, DOT/FRA/ORD-13/08

  19. 19.

    Feng H (2011) 3D-models of railway track for dynamic analysis. Dissertation, Royal Institute of Technology

  20. 20.

    Kouroussis G, Caucheteur C, Kinet D, Alexandrou G, Verlinden O, Moeyaert V (2015) Review of trackside monitoring solutions: from strain gages to optical fibre sensors. Sensors 15(8):20115–20139. doi:10.3390/s150820115

    Article  Google Scholar 

  21. 21.

    Esveld C (2001) Modern railway track. MRT-productions, The Netherlands

    Google Scholar 

  22. 22.

    Hay WW (1982) Railroad engineering. Wiley, New Jersy

    Google Scholar 

  23. 23.

    Norman CD (2004) Measurement of track modulus from a moving railcar. Dissertation, University of Nebraska-Lincoln

  24. 24.

    Lu S (2008) Real-time vertical track deflection measurement system. Dissertation, University of Nebraska-Lincoln

  25. 25.

    Greisen CJ (2010) Measurement, simulation, and analysis of the mechanical response of railroad track. Dissertation, University of Nebraska-Lincoln

  26. 26.

    Greisen CJ, Lu S, Duan H, Farritor S, Arnold R, GeMeiner B, Clark D, Toth T, Hicks K, Sussmann T (2009) Estimation of rail bending stress from real-time vertical track deflection measurement. 2009 Joint Rail Conference, doi: 10.1115/JRC2009-63050

  27. 27.

    Roghani A, Hendry MT (2016) Continuous vertical track deflection measurements to map subgrade condition along a railway line: methodology and case studies. J Transp Eng. doi:10.1061/(ASCE)TE.1943-5436.0000892

    Google Scholar 

  28. 28.

    Roghani A, Macciotta R, Hendry MT (2015) Combining track quality and performance measures to assess track maintenance requirements. 2015 Joint Rail Conference, San Jose

    Google Scholar 

  29. 29.

    Computer and Structure Inc., CSiBridge 2014; Advanced W/Rating 16.1.0

  30. 30.

    Fallah Nafari S, Gül M, Roghani A, Hendry MT, Cheng RJJ (2015) Evaluating the potential of a rolling deflection measurement system to estimate track modulus. J Rail and Rapid Transit, Proc IMechE Part F. doi:10.1177/0954409716646404

    Google Scholar 

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Acknowledgements

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) (http://www.carrl.ca) 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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Correspondence to Mustafa Gül.

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Fallah Nafari, S., Gül, M. & Cheng, J.J.R. Quantifying live bending moments in rail using train-mounted vertical track deflection measurements and track modulus estimations. J Civil Struct Health Monit 7, 637–643 (2017). https://doi.org/10.1007/s13349-017-0248-1

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Keywords

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