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.

1

J. Bencat, et al., "Microtremor due to Traffic", Research report A-4-92/b, UTC Zilina, SK, 1992. (in Slovak)

2

P. Broeck, G. Roeck, "The vertical receptance of track including soil-structure interaction", in "Eurodyn 99", Prague, CR, A.A. Balkema, 849-853, 1999.

3

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

4

K. Knothe, Y. Wu, "Receptance behaviour of railway track and subgrade", Archive of Applied Mechanics, 68, 457-470, 1998. doi:10.1007/s004190050179

5

C. Esveld, "Modern railway track", 2nd Ed., MRT Productions, Zaltbomel, 2001.

6

J. Turek, "The interaction model of the vehicle-track system", Research report 245/92 VUZ, Prague, CR, 1992. (in Czech)

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £65 +P&P)