Keywords: wave propagation, railway track, moving loads (train), Fourier transform, soft soils, in situ measurements.

In the North West of Europe, more particularly in the region of the Somme Bay in France where grounds are constituted mainly by water saturated peat, observations and measurements have revealed the presence of great displacements on the soil surface near railway tracks and in the track itself. In very soft soil conditions composing of a low Young modulus and important water content, these displacements can cause not only harmful effects for the neighbourhood of the track and the surrounding house but also damage or break in the track. These pollution also depend on the weight and the speed of the train mainly when this speed is near a critical speed corresponding to the Rayleigh wave speed [4].

This paper describes a 3D-model used in the prediction of vibrations near track [3]. It consist of a railway track model lying on a layered ground and submitted to a moving train. It includes all elements of the track (rails, pads, sleepers and ballast) [5] and allows a parametric analysis of its different elements and evaluation of vertical displacements according to the speed, the weight and the composition of the trains. The resolution method uses the formalism of Fourier transform for a semi-analytical resolution in the wave number domain [1]. The handwriting of a stiffness matrix for a layered ground with the help of a fitted phase angle of Helmoltz functions provides a fast numerical approach of the problem. The whole excitation It is a frequency dependant function supposing to occur in a range 0-80Hz [7]. It includes a quasi- static component produced by the weight of all axle loads and a harmonic component generated by irregularity between rail and wheel. Effect of all the track and soil parameters on the vibration attenuation are also studied.

Then in situ measurements are introduced with a view to the validation of the model. A parameter study of the ground undertaken by seismic measurements shows a critical speed near 100 m/s while the studied trains are moving with sub-Rayleigh speeds (20 to 50 m/s). Consequently, all the parameters needed for the numerical model are defined. Many measurements were done with a fast numerical camera which allows to notice the sheer size of the stress subjected to the track. Synchronised measurements of soil surface acceleration and track elements velocity were recorded. They give us a lot of information about lateral and vertical displacements of track elements and on the soil surface. For highest speeds and fright trains, measured displacements reach more than about 10 millimetres.

Finally, results are validated for different configurations. Measurements et simulation are compared in the time domain and in the term of spectral density [2]. A comparison against distance of the track is also done and show that contribution of the harmonic regime due to irregularities becomes more important farther from the track. The great accord find in the validation confirmed the good quality of the determination of mechanical parameters, particularly the parameters dependant on compression and shear waves speed.

On the whole study, comparison between 3D-model and in situ measurements leads to good results taking into account measurements difficulties, important number of unknown parameters and hypothesis of linearity of track element and homogeneity of soil layers. Particular velocities and maximum displacements at 2 and 5 meters from the track were compared to simulation. Spectral densities performed with the multi-frequential model had to be compared to in situ measurement and good results were obtained in the range 5 - 40 Hz. These studies [6] allow the construction of an available data basis for future development of models. Besides, the set of these researches will permit to apprehend with a believable and suitable approach phenomena of wave propagation from vehicles (especially trains) moving at constant speed.

1

Jones, D.V., Le Houédec, D., Peplow, A.T. and Petyt, M. 1998. Ground vibration in the vicinity of a moving harmonic rectangular load on a half space. European Journal of Mechanics A/Solids 17(1). pp. 153-166. doi:10.1016/S0997-7538(98)80069-7

2

Krylov, V.V. 1997. Spectra of low frequency ground vibrations generated by high speed trains on layered ground. Journal of Low Frequency Noise Vibration and Active Control 16(4). pp 257-270.

3

Lefeuve-Mesgouez, G. 1999. Ground propagation due to load moving at constant speed. Ph D thesis (in French), Ecole Centrale of Nantes. pp. 1-147.

4

Madshus, C. and Kaynia, A.M. 2000. High speed railway lines on soft ground: dynamic behaviour at critical train speed. Journal of Sound and Vibration 231(3) : 689-701. doi:10.1006/jsvi.1999.2647

5

Metrikine, A.V. and Popp, K. 1999. Vibration of a periodically supported beam on an elastic half space. European Journal of Mechanics A/Solids 18. pp. 679-701. doi:10.1016/S0997-7538(99)00141-2

6

Picoux, B. 2002. Theoretical and experimental works on wave propagation in soil emit by a railway traffic. Ph D thesis (in French), Ecole Centrale of Nantes. pp. 1-155.

7

Sheng, X., Jones, C.J.C. and Petyt, M. 1999. Ground vibration generated by a load moving along a railway track. Journal of Sound and Vibration 228(1). pp. 129-156. doi:10.1006/jsvi.1999.2406

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