Keywords: train track-ground dynamics, moving load, FEM, FEM-BEM, ground vibration, computer simulation, mitigation.

Computer simulation is performed to investigate the extraordinary response of a track due to high-speed trains as experienced by Swedish railways (BANVERKET [1,2]) at soft ground on West coast line. The points are focused first on the dynamic behavior of the track with the ground beneath it and the wave field along it. Detailed modelling is implemented to the previous work [3]. Special interest is placed in the critical situation where the train speed approaches that of the surface wave at site. Then, with the knowledge obtained, proposed is the vibration mitigation concept in reference to the soil improvement under the track that the BANVERKET took. The validation is made from the field measurement.

The FEM and FEM-BEM methods have been applied in this paper for the dynamic analysis of train track comprising rail-sleepers-ballast mat, with the ground beneath it. The formulation is based on the 2.5-dimensional analysis in the frequency domain that takes discretization in the plane normal to the track axis while wavenumber expansion along it. Different models, FEM and FEM-BEM, are taken for the purpose of cross check of the solutions. The solution strategy in the FEM is to adopt the band matrix procedure for reducing the memory storage capacity and in the FEM-BEM is to apply the FEM for the irregular zone while BEM for the layered soils. Once the FEM modelling is assured with respect to the ground depth from the FEM-BEM model, the former is extensively used for investigating the wave motions in the ground.

For illustrative example, the case of X-2000 high-speed train at the West Coast in Sweden is demonstrated. The solution accuracy is proved in comparison with the field test conducted by Swedish Railway.

Since the track and ground system undergoes an interaction behavior under the train running, its speed is one of the key factors that govern the vibration generation and transmission in ground. The computation results include the response time histories at the track and the nearby ground. Displacement field of the track and ground is depicted for the surface motion, and for the vertical sections along the track and perpendicular to it. The presence of the soft soil layer at shallow depth below the track gives rise to a very localized large response for high train-speed while no such intense response localization for slow train-speed. Such a drastic change of wave field is interpreted by referring to the wavenumber-frequency spectrum. Further, this spectrum is utilized for developing the vibration mitigation measure. The vibration contribution from the discretely arranged sleepers appears significantly in the acceleration response for slow train speed.

Stiffening of the soft soil under the track leads the spectrum ridge toward the higher frequency range for the same wavenumber range so that no crossing results in with the train speed line. Since the soil improvement work is a practice for it, the design of WIB is proposed in view of the wave mitigation theory. Herein, the case of rows of limestone columns that the Vanberket actually took beneath the track is interpreted by comparing the computation results with the field measurements before and after it.

The present modelling of the track-ground system by either FEM or FEM-BEM lead excellent response predictions in comparison with the field measurements. The sleepers' effect on vibration is clarified in the frequency domain: namely, at the low train-speed of 70 km/h they generated the frequencies that are determined by the integer multiplied quotient of train speed against sleepers spacing, however, for 200 km/h the dynamic wave generation more dominates the response so that the sleepers' effect appears almost negligibly small. The velocity component, on the other hand, is greatly affected by the presence of sleepers for the train speed of 70 km/h but not for the 200 km/h. There are different situations we concern for response levels either by displacement, velocity or acceleration. The appropriate engineering judgment should be made on the basis of most involved physical quantities.

For controlling of the track vibration installing WIB proved effective. The case of lime-cement columns beneath the track worked as the wave impeding barrier and proved to be very effective to reduce the large response displacements for 200 km/h to the very small level for 70 km/h. The visual presentation is demonstrated for easy understanding of the behaviour of track and the soil beneath it.

1

BANVERKET, Evaluation and analyses of measurements from the West Coast line, 1997, .Joint Nordic Railway Vibration Research Project, WP4, Field Measurement and Validations, 2002.

2

Takemiya, Controlling of track-ground vibration due high-speed train by WIB, Eurodyn2002, European Association for Structural Dynamics, Munich, 2002.9., 497-502.

3

H. Takemiya, "Simulation of track-ground vibrations due to high-speed train: The case of x-2000 at Lesdsgard", Journal of Sound and Vibration, Academic Press, 261(3), 503-526, 2003.3. doi:10.1016/S0022-460X(02)01007-6

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