Analysis of an existing methodology for assessing vehicle-track interaction under reliability conditions
Abstract
This paper presents a focused analytical audit of two simplified vehicle-track interaction schemes reported in the State Standard for 1,520 mm Gauge Railways: (i) a wheel-on-rail stability scheme intended to characterize flange-climb resistance and (ii) a track lateral stability scheme intended to estimate sleeper-rail-grid shift under train loading. The aim is twofold: first, to identify the internal inconsistencies of these specific formulations; second, to derive general lessons for transparent and reproducible safety assessment in railway engineering. The audit is organized around three steps: reconstruction of the source free-body diagrams and symbol definitions, point-by-point consistency checks of the equilibrium relations, and formulation of corrected self-contained equations in a unified coordinate system. The revised presentation shows that the source schemes mix force and moment terms, use ambiguous coordinate conventions, and in several places produce self-referential or physically trivial coefficients. A compact worked example is provided to illustrate the numerical difference between a parameter-independent source-style ratio and the corrected parameter-dependent contact-equilibrium relation. The paper also clarifies the status of each figure as either adapted from the source schemes or reconstructed by the authors and condenses the normative background to the material strictly needed for interpretation. Overall, the revised workflow improves traceability, reproducibility, and engineering interpretability.
Copyright (c) 2026 Shuxrat Djabbarov, Bakhrom Abdullayev, Aziz Gayipov, Abdusaid Yuldashov, Nodir B. Adilov, Irina Soboleva

This work is licensed under a Creative Commons Attribution 4.0 International License.
References
[1]Ministry of Railways of the Russian Federation (MPS RF), 2000. CPT-52-14: Methodology for Assessing the Impact of Rolling Stock on Track under Reliability Conditions. (in Russian)
[2]Vinogradov VV, Nikonov AM, Yakovleva TG, et al. Calculations and Design of Railway Track: Study Guide for Railway University Students. Vinogradov VV, Nikonov AM (editors). Marshrut; 2003. (in Russian)
[3]Yablonskiy AA, Nikiforova VM. Course of Theoretical Mechanics. Lan; 1998. (in Russian)
[4]Turanov KT. Theoretical Mechanics in Freight Transportation Problems. Nauka Siberian Branch of the Russian Academy of Sciences; 2009. (in Russian)
[5]Turanov KT. Interaction of Open Rolling Stock and Solid Cargo. PiarPress; 2010. (in Russian)
[6]Konorev NS (editor). Great Encyclopedia of Transport, Vol. 4: Railway Transport. Great Russian Encyclopedia; 2003. (in Russian)
[7]Shakhunyants GM. Railway Track. Transport; 1987. (in Russian)
[8]Glushko MI. Wheelset-Rail Interaction. Transport of the Urals. 2008; (4): 41. (in Russian)
[9]Akkerman GL, Akkerman SL, Golubev OV, et al. Assessment of Railway Track Condition. Transport of the Urals. 2006; 6: 37–47. (in Russian)
[10]Iwnicki S (editor). Handbook of Railway Vehicle Dynamics. CRC Press; 2006.
[11]Knothe K, Stichel S. Rail Vehicle Dynamics. Springer; 2017. doi: 10.1007/978-3-319-45376-7
[12]Zhai W. Vehicle–Track Coupled Dynamics: Theory and Applications. Singapore: Springer; 2020. doi: 10.1007/978-981-32-9283-3
[13]EN 14363:2016+A2:2022. Railway Applications—Testing and Simulation for the Acceptance of Running Characteristics of Railway Vehicles—Running Behaviour and Stationary Tests. 2022.
[14]International Union of Railways (UIC). UIC Leaflet 518: Testing and Approval of Railway Vehicles from the Point of View of Their Dynamic Behaviour—Safety—Track Fatigue—Ride Quality, 4th ed. UIC; 2009.
[15]Zeng J, Wu P. Study on the wheel/rail interaction and derailment safety. Wear. 2008; 265(9–10): 1452–1459. doi: 10.1016/j.wear.2008.01.031
[16]Marquis BP, Greif R. Paper No. JRC2011-56064: Application of Nadal Limit in the Prediction of Wheel Climb Derailment. In Proceedings of the ASME/ASCE/IEEE 2011 Joint Rail Conference; 16–18 March 2011; Pueblo, CO, USA. pp. 273–280.
[17]Kuo CM, Lin CC. Analysis of derailment criteria. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit. 2016; 230(4): 1158–1163. doi: 10.1177/0954409715583692
[18]Kalker JJ. The computation of three-dimensional rolling contact with dry friction. International Journal for Numerical Methods in Engineering. 1979; 14(9): 1293–1307.
[19]Johnson KL. Contact Mechanics. Cambridge University Press; 1985.
[20]Selig ET, Waters JM. Track Geotechnology and Substructure Management. Thomas Telford Publications; 1994.
[21]Kish A. New Track Shift Safety Limits for High-Speed Rail Applications. U.S. Federal Railroad Administration; 2001.
[22]Samavedam G, Blader F, Thompson D. Safety of High Speed Ground Transportation Systems: Track Lateral Shift: Fundamentals and State-of-the-Art Review. U.S. Department of Transportation, Federal Railroad Administration; 1996. Available online: https://rosap.ntl.bts.gov/view/dot/62397
[23]Samavedam G, Blader F, Thompson D. Analyses of Track Shift under High-Speed Vehicle–Track Interaction. U.S. Federal Railroad Administration; 1997.
[24]Schmid R, Micić Batka V, Pospischil F. Prud’homme criterion: A review of its application in railway vehicle approval. International Journal of Rail Transportation. 2026; 14(1): 1–16. doi: 10.1080/23248378.2025.2496360
[25]Le Pen L, Bhandari AR, Powrie W. Sleeper end resistance of ballasted railway track. Journal of Geotechnical and Geoenvironmental Engineering. 2014; 140(5): 04014004. doi: 10.1061/(ASCE)GT.1943-5606.0001088
[26]Koike Y, Nakamura T, Hayano K, et al. Numerical method for evaluating the lateral resistance of sleepers in ballasted tracks. Soils and Foundations. 2014; 54(3): 502–514. doi: 10.1016/j.sandf.2014.04.014
[27]Koyama E, Ito K, Hayano K, et al. A new approach for evaluating lateral resistance of railway ballast associated with extended sleeper spacing. Soils and Foundations. 2021; 61(6): 1565–1580. doi: 10.1016/j.sandf.2021.09.004
[28]Kabo E. A numerical study of the lateral ballast resistance in railway tracks. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit. 2006; 220(4): 425–433. doi: 10.1243/0954409jrrt61
[29]Ngamkhanong K, Feng H, Tutumluer E, et al. Evaluation of lateral stability of railway tracks due to ballast degradation. Construction and Building Materials. 2021; 278: 122342. doi: 10.1016/j.conbuildmat.2021.122342
[30]Khatibi F, Esmaeili M, Mohammadzadeh S. DEM analysis of railway track lateral resistance. Soils and Foundations. 2017; 57(4): 587–602. doi: 10.1016/j.sandf.2017.04.001




