A Priori Determination of Track Modulus Based on Elastic Solutions
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pISSN 1226-7988, eISSN 1976-3808 www.springer.com/12205
DOI 10.1007/s12205-020-5372-5
Railroad Engineering
A Priori Determination of Track Modulus Based on Elastic Solutions Tulika Bose
a
and Eyal Levenberg
a
a
Dept. of Civil Engineering, Technical University of Denmark, Nordvej, Kgs. Lyngby 2800, Denmark
ARTICLE HISTORY
ABSTRACT
Received 5 March 2019 Revised 11 February 2020 Accepted 28 May 2020 Published Online 17 August 2020
The standard approach for modeling railway tracks idealizes the rails as two infinite beams, each supported over a separate 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 magnitudes and exhibit similar sensitivities to the input parameters as reported in field studies or as derived from elaborate numerical schemes.
KEYWORDS Track modulus Railway Elasticity Track stiffness Rail track modeling
1. Introduction Winkler’s (1867) hypothesis of subgrade reaction is widely practiced for design and analysis of soil-coupled constructions such as: 1) pile and raft foundations (Hemsley, 2000), 2) concrete pavements (Westergaard, 1948; Ioannides, 2006), 3) buried pipes (Rajani et al., 1996; Klar et al., 2005), and 4) tunnel linings (Wood, 1975; Lee et al., 2001; Mair, 2008). Essentially, this hypothesis is a radical mathematical simplification of actual soil behavior; it does not directly represent any basic material property. Because of this, problem-specific methods or guidelines are needed to suitably determine subgrade reaction values for subsequent structural evaluation. In an early contribution, Biot (1937) offered such guidelines for the case of an infinite beam resting on an elastic half-space and loaded by a concentrated force. The development was founded on theoretical arguments, and was based on requiring equivalency of maximal beam moments. Vesić (1961) extended Biot’s work to includ
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