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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 99
Edited by: B.H.V. Topping
Paper 175

Numerical Analysis of Railway Track Vibrations

J. Bencat and J. Konar

Department of Structural Mechanics, Faculty of Civil Engineering, University of Zilina, Slovakia

Full Bibliographic Reference for this paper
J. Bencat, J. Konar, "Numerical Analysis of Railway Track Vibrations", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 175, 2012. doi:10.4203/ccp.99.175
Keywords: microtremor, railway traffic effects on structures, prediction, dynamic half space models, structure response models, in situ experimental tests, ground vibration, structure response spectra, spectral analysis.

A review of the literature [1,2,3,4] shows that present-day numerical models still use simplifications to predict the ground-borne vibrations arising from railway traffic. Most assumptions are introduced for the computation of the track-soil interaction forces. Some models consider these forces to be point loadings proportional to the deflection curve of a rail on an elastic foundation. Other models assume a frequency independent stress distribution beneath the sleeper for which the time history is derived from a train-track model with the sleeper support modelled as either rigid or as spring-damper systems. Soil models in the literature vary from approximate solutions, including only the surface wave contribution, to horizontally layered viscoelastic half-space models. Few models have developed a systematic procedure to account for the rail roughness.

The proposed numerical model which calculates the expected ground-borne vibration level arising from railway traffic can be divided in two steps. The first step determines the dynamic track-soil interaction forces using a detailed train model and the dynamic behaviour of the layered spring-damper system and the through-soil coupling of the sleepers are accounted for the soil model [1,5,6]. The calculation of the ground-borne vibration level at the distance in the second step is also based on the viscous-elastics soil model.

In this model the car-body, the bogie and the wheelset are modelled as rigid bodies connected by springs and dampers. The wheelset is connected to the rail with a linearised Hertzian spring. The rail is modelled as a hinged Rayleigh beam with rotational inertia. The rail is supported discretely by sleepers modelled as rigid bodies with spring-damper systems representing the railpads. The sleeper is modelled as a short Rayleigh beam resting on flexural mass layer supported by discretely Pasternak spring-damper systems representing the elastic and attenuation characteristics of the railway ballast and substrate soils. As a result, the model evaluates the track-soil interaction forces in terms of the spectral density function which is often used as the statistical description of the rail roughness. These calculations are followed by a second step in which the spectral density of the level of ground-borne vibrations is determined by the frequency response function between track and unbounded soil.

J. Bencat, et al., "Microtremor due to Traffic", Research report A-4-92/b, UTC Zilina, SK, 1992. (in Slovak)
P. Broeck, G. Roeck, "The vertical receptance of track including soil-structure interaction", in "Eurodyn 99", Prague, CR, A.A. Balkema, 849-853, 1999.
K. Knothe, S. Grassie, "Modelling of railway track and vehicle/track interaction at high frequencies", Vehicle Systems Dynamics, 22, 209-262, 1993. doi:10.1080/00423119308969027
K. Knothe, Y. Wu, "Receptance behaviour of railway track and subgrade", Archive of Applied Mechanics, 68, 457-470, 1998. doi:10.1007/s004190050179
C. Esveld, "Modern railway track", 2nd Ed., MRT Productions, Zaltbomel, 2001.
J. Turek, "The interaction model of the vehicle-track system", Research report 245/92 VUZ, Prague, CR, 1992. (in Czech)

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