This paper studies the efficiency of subgrade stiffening next to the track as a mitigation measure for railway induced vibrations by means of a two-and-a-half-dimensional coupled finite element -boundary element methodology. An analysis in the frequency-wavenumber domain for a homogeneous halfspace reveals that the block of stiffened soil next to the track can act as a wave impeding barrier. It is demonstrated that the wave impeding effect depends on the relation between the Rayleigh wavelength in the soil and the free bending wavelength in the block of stiffened soil, as the transmission of plane waves in the soil with a longitudinal wavelength smaller than the bending wavelength is hindered. This leads to a critical frequency from which this mitigation measure starts to be effective, depending on the stiffness contrast between the soil and the block of stiffened soil. The existence of a critical angle delimiting an area where vibration levels are reduced in case of harmonic excitation on the rail is also demonstrated. Two applications involving a layered halfspace are finally discussed to demonstrate that the performance of this mitigation measure critically depends on the soil characteristics.
Ground vibrations induced by railway traffic at grade and in tunnels are often studied by means of two-and-half dimensional (2.5D) models that are based on a Fourier transform of the coordinate in the longitudinal direction of the track. In this paper, the need for 2.5D coupled finite element-boundary element models is demonstrated in two cases where the prediction of railway induced vibrations is considered.A recently proposed novel 2.5D methodology is used where the finite element method is combined with a boundary element method, based on a regularized boundary integral equation. In the formulation of the boundary integral equation, the Green's functions of a layered elastic halfspace are used, so that no discretization of the free surface or the layer interfaces is required. In the first case, two alternative models for a ballasted track on an embankment are compared. In the first model, the ballast and the embankment are modelled as a continuum using 2.5D solid elements, whereas a simplified beam representation is adopted in the second model. The free field vibrations predicted by both models are compared to those measured during a passage of the TGVA at a site in Reugny (France). A very large difference is found for the free field response of both models that is due to the fact that the deformation of the cross section of the embankment is disregarded in the simplified representation. In the second case, the track and free field response due to a harmonic load in a tunnel embedded in a layered halfspace are considered. A simplified methodology based on the use of the full space Green's function in the tunnel-soil interaction problem is investigated. It is shown that the rigorous finite element-boundary element method is required when the distance between the tunnel and the free surface and the layer interfaces of the halfspace is small compared to the wavelength in the soil.
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