Influence of Rail Track Foundation Parameters on the Nonlinear Dynamic Response of a Railway Track

Kozioł, Piotr; Pilecki, Zenon

doi:10.37705/TechTrans/e2025021

Abstract

The dynamic response of railway tracks is a key factor influencing the operational safety and reliability of rail transport. Classical analytical methods for modelling track dynamics become insufficient at higher operating speeds, as they typically assume linear behaviour and cannot account for nonlinearities present in the fastening system or in the rail track foundation response. This increases the risk of damage, leading to traffic interruptions, financial losses, and reduced safety. To support predictive maintenance, it is necessary to develop databases based on in-situ measurements, complemented with synthetic data obtained from validated analytical and semi-analytical models. This paper presents such a model, designed to analyse how the parameters of the track foundation – including stiffness and damping – affect the track’s dynamic response to loads generated by a moving railway vehicle. The model incorporates experimentally confirmed nonlinear stiffness of the fastening system, represented by a viscoelastic layer that provides continuous support for the rails.

References

Adomian, G. (1989). Nonlinear Stochastic Systems Theory and Application to Physics. Dordrecht: Kluwer Academic Publishers.
Search in Google Scholar Back to article
Adomian, G. (1994). Solving Frontier Problems of Physics: The Decomposition Method. Boston: Kluwer.
Search in Google Scholar Back to article
Monzón, L., Beylkin, G., Hereman, W. (1999). Compactly supported wavelets based on almost interpolating and nearly linear phase filters (coiflets). Applied and Computational Harmonic Analysis 7(2), 184–210. https://doi.org/10.1006/acha.1999.0266
Search in Google Scholar Back to article
Bogacz, R., Czyczula, W. (2008). Response of beam on viscoelastic foundation to moving distributed load. Journal of Theoretical and Applied Mechanics 46(4), 763–775.
Search in Google Scholar Back to article
Bogacz, R., Krzyzynski, T., Popp, K. (1998). Wave propagation in two dynamically coupled periodic systems. In: Proceedings of the International Symposium on Dynamics of Continua (pp. 55–64). Bad Honnef: Shaker Verlag.
Search in Google Scholar Back to article
Czyczuła, W., Chudyba, L., Kapturkiewicz, D., Lisowicz, T. (2023). Nieliniowa aproksymacja oporów systemów przytwierdzeń. Konferencja Naukowo-Techniczna: Drogi Kolejowe 2023, Kraków.
Search in Google Scholar Back to article
Czyczuła, W., Koziol, P., Kudla, D., Lisowski, S. (2017). Analytical evaluation of track response in the vertical direction due to a moving load. Journal of Vibration and Control 23(18), 2989–3006. https://doi.org/10.1177/1077546315612120
Search in Google Scholar Back to article
Fathi, S., Mehravar, M., Rahman, M. (2023). Development of FWD based hybrid back-analysis technique for railway track condition assessment, Transportation Geotechnics 38, 100894, ISSN 2214-3912. https://doi.org/10.1016/j.trgeo.2022.100894
Search in Google Scholar Back to article
Fryba, L. (1972). Vibration of Solids and Structures under Moving Loads. Groningen: Noordhoff International Publishing.
Search in Google Scholar Back to article
Koziol, P. (2010). Wavelet approach for the vibratory analysis of beam-soil structures: Vibrations of dynamically loaded systems. Saarbrucken: VDM Verlag Dr. Müller.
Search in Google Scholar Back to article
Koziol, P. (2014). Wavelet approximation of Adomian’s decomposition applied to the nonlinear problem of a double-beam response subject to a series of moving loads. Journal of Theoretical and Applied Mechanics 52(3), 687–697.
Search in Google Scholar Back to article
Koziol, P. (2016). Experimental validation of wavelet based solution for dynamic response of railway track subjected to a moving train. Mechanical Systems and Signal Processing 79, 174–181. https://doi.org/10.1016/j.ymssp.2015.03.011
Search in Google Scholar Back to article
Koziol, P. (2023). Nonlinear “Beam Inside Beam” Model Analysis by Using a Hybrid Semi-analytical Wavelet Based Method. In: Recent Trends in Wave Mechanics and Vibrations (pp. 615–621). Springer. https://doi.org/10.1007/978-3-031-23560-3_46
Search in Google Scholar Back to article
Koziol, P., Dimitrovova, Z., Pilecki, R. (2021). Dynamic properties of a nonlinear double-beam system subjected to a series of moving loads. In: Proceedings of the 14th World Congress on Computational Mechanics (WCCM XIV) and 8th European Congress on Computational Methods in Applied Science and Engineering (ECCOMAS 2020), 2661–2662.
Search in Google Scholar Back to article
Koziol, P., Kudla, D. (2018). Vertical vibrations of rail track generated by random irregularities of rail head rolling surface. Journal of Physics: Conference Series 1106, 012007. https://doi.org/10.1088/1742-6596/1106/1/012007
Search in Google Scholar Back to article
Koziol, P., Hryniewicz, Z. (2012). Dynamic response of a beam resting on a nonlinear foundation to a moving load: coiflet-based solution. Shock and Vibration 19, 995–1007. https://doi.org/10.1155/2012/389476
Search in Google Scholar Back to article
Koziol, P., Mares, C. (2010). Wavelet approach for vibration analysis of fast moving load on a viscoelastic medium. Shock and Vibration 17(4–5), 461–472. https://doi.org/10.1155/2010/579310
Search in Google Scholar Back to article
Koziol, P., Pilecki, R. (2020). Semi-analytical modelling of multilayer continuous systems nonlinear dynamics. Archives of Civil Engineering 66(2), 165–178. https://doi.org/10.24425/ace.2020.131803
Search in Google Scholar Back to article
Koziol, P., Pilecki, R. (2021). Nonlinear double-beam system dynamics. Archives of Civil Engineering 67(2), 337–353. https://doi.org/10.24425/ace.2021.137172
Search in Google Scholar Back to article
Lasisi, A., Attoh-Okine, N. (2021). Hybrid rail track quality analysis using nonlinear dimension reduction technique with machine learning. Canadian Journal of Civil Engineering. https://doi.org/10.1139/cjce-2019-0832
Search in Google Scholar Back to article
Lombaert, G., Galvin, P., Francois, S., et al. (2014). Quantification of uncertainty in the prediction of railway induced ground vibration due to the use of statistical track unevenness data. Journal of Sound and Vibration 333, 4232–4253. https://doi.org/10.1016/j.jsv.2014.03.027
Search in Google Scholar Back to article
Mallat, S. (1998). A Wavelet Tour of Signal Processing. Academic Press, London.
Search in Google Scholar Back to article
Mathews, P.M. (1958). Vibration of beam on elastic foundation. Zeitschrift für Angewandte Mathematik und Mechanik 38, 105–115. https://doi.org/10.1002/zamm.19580380117
Search in Google Scholar Back to article
Qu, S., Yang, J., Zhu, S., Zhai, W., Kouroussis, G. (2021). A hybrid methodology for predicting train-induced vibration on sensitive equipment in far-field buildings, Transportation Geotechnics 31, 100682. https://doi.org/10.1016/j.trgeo.2021.100682
Search in Google Scholar Back to article
Ramos, A., Correia, A.G., Nasrollahi, K., Nielsen, J.C.O., Calçada, R. (2024). Machine Learning Models for Predicting Permanent Deformation in Railway Tracks, Transportation Geotechnics 47, 101289. https://doi.org/10.1016/j.trgeo.2024.101289
Search in Google Scholar Back to article
Sun, L., Luo, F. (2008). Steady-state dynamic response of a Bernoulli–Euler beam on viscoelastic foundation subjected to a platoon of moving dynamic loads. Journal of Vibration and Acoustics 130(051002-17), 1–19. https://doi.org/10.1115/1.2943570
Search in Google Scholar Back to article
Sun, L., Seyedkazemi, M., Nguyen, C.C., Zhang, J. (2025). Dynamics of Train– Track–Subway System Interaction—A Review, Machines 13(11), 1013. https://doi.org/10.3390/machines13111013
Search in Google Scholar Back to article
Timoshenko, S. (1926). Method of analysis of static and dynamic stresses in rail. In: Proceedings of the 2nd International Congress on Applied Mechanics (pp. 407–418). Zurich, Switzerland.
Search in Google Scholar Back to article
Wang, X., Bai, Y., Liu, X. (2023). Prediction of railroad track geometry change using a hybrid CNN-LSTM spatial-temporal model, Advanced Engineering Informatics 58, 102235. https://doi.org/10.1016/j.aei.2023.102235
Search in Google Scholar Back to article
Wazwaz, A.M. (1999). A reliable modification of Adomian decomposition method. Applied Mathematics and Computation 102, 77–86. https://doi.org/10.1016/S0096-3003(98)10191-6
Search in Google Scholar Back to article
Wojtaszczyk, P. (2000). Teoria falek. Podstawy matematyczne. Warszawa: PWN.
Search in Google Scholar Back to article
Xie, J., Huang, J., Zeng, C., Jiang, S.-H., Podlich, N. (2020). Systematic Literature Review on Data-Driven Models for Predictive Maintenance of Railway Track: Implications in Geotechnical Engineering, Geosciences 10(11), 425. https://doi.org/10.3390/geosciences10110425
Search in Google Scholar Back to article
Xin, T., Wang, S., Wang, P., Yang, Y., Dai, C. (2024). A Hybrid Method for Vehicle– Track Coupling Dynamics by Analytical and Finite Element Combination Technique, International Journal of Structural Stability and Dynamics 24(10), 2450105. https://doi.org/10.1142/S0219455424501050
Search in Google Scholar Back to article
Zadeh S.S.A., Edwards, J.R., de O. Lima, A., Dersch, M.S., Palma, P. (2024). A data-driven approach to quantify track buckling strength through the development and application of a Track Strength Index (TSI), Transportation Geotechnics 48, 101359. https://doi.org/10.1016/j.trgeo.2024.101359
Search in Google Scholar Back to article
Zhai, W., Stichel, S., Ling, L. (2025). Train–track coupled dynamics problems in heavy-haul rail transportation, Vehicle System Dynamics, International Journal of Vehicle Mechanics and Mobility 63(7), 1187–1240. https://doi.org/10.1080/00423114.2025.2494834
Search in Google Scholar Back to article

Influence of Rail Track Foundation Parameters on the Nonlinear Dynamic Response of a Railway Track

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