A Priori Determination of Track Modulus Based On Elastic Solutions

Tulika Bose, Eyal Levenberg

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The standard approach for modeling railway tracks idealizes the rails as two infinite beams, each supported by a continuous spring foundation. The foundation is characterized by a track modulus that embodies all components and materials underlying each rail as well as any cross-rail interaction. Track modulus is considered a basic parameter governing the field performance of tracks. Therefore, a priori determination of track modulus is needed in design of traditional railways, as well as in evaluating the performance-potential of non-traditional track solutions. In this study, a new method was suggested for a priori track modulus determination based on elastic solutions. Specifically sought were closed-form analytical formulations that could be representative and tractable. In this connection, a 3-D track model was developed, wherein: rail-pads were considered as linear springs, sleepers as finite beams, and all underlying soil-like materials as a homogenous half-space. Ultimately, track modulus was determined by linking calculations in the 3-D model and the standard model. This was done by requiring equal maximal displacement as well as identical load distribution along the rail under the weight of a single railcar axle. The method was illustrated considering a wide set of values for the different model parameters. The calculated results are comparable in magnitude and exhibit similar sensitivities to the input parameters as reported in field studies or as derived from elaborate numerical schemes.
Original languageEnglish
JournalK S C E Journal of Civil Engineering
Pages (from-to)2939–2948
Publication statusPublished - 2020


  • Track Modulus
  • Railway
  • Elasticity
  • Track stiffness
  • Rail track modeling


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