Modelling ground vibration from railways using wavenumber finite- and boundary-element methods

A trench can act as a barrier to ground vibration and is a potential mitigation measure for low frequency vibration induced by surface railways. However, to be effective at very low frequencies the depth required becomes impractical. Nevertheless, for soil with a layered structure in the top few metres, if a trench can be arranged to cut through the upper, soft layer of soil, it can be effective in reducing the most important components of vibration from the trains. This study considers the possibility of using such a realistically feasible solution.Barriers containing a soft fill material are also considered. The study uses coupled finite element / boundary element models expressed in terms of the axial wavenumber. It is found to be important to include the track in the model as this determines how the load is distributed at the soil's surface which significantly affects the insertion loss of the barrier. Calculations are presented for a range of typical layered grounds in which the depth of the upper soil layer is varied. Variations in the width and depth of the trench or barrier are also considered. The results show that, in all ground conditions considered, the notional rectangular open trench performs best. The depth is the most important parameter whereas the width has only a small influence on its performance. More practical arrangements are also considered in which the 2 sides of the trench are angled. Barriers consisting of a soft fill material are shown to be much less effective than an open trench but still have some potential benefit. It is found that the stiffness of the barrier material and not its impedance is the most important material parameter.

Section: 5d Finite Element / Boundary Element Modelmentioning

confidence: 99%

“…A three-dimensional analysis is carried out using the wavenumber (i.e. 2.5D) finite element-boundary element method [45][46][47]. As the layered ground properties can be important in determining the dominant frequency range of vibration, and potentially in the mechanism of attenuation due to a trench, various different layered grounds are considered.…”

mentioning

confidence: 99%

Reducing railway-induced ground-borne vibration by using open trenches and soft-filled barriers

Thompson

Jiang

Toward

et al. 2016

“…The corresponding two-dimensional problem is solved for each wavenumber and an inverse Fourier transform is used to recover the three-dimensional response. This so-called 2.5D method is computationally more efficient than a full threedimensional approach and has been widely used for railway vibration [22,23,26,27].…”

Section: 5d Finite Element / Boundary Element Approachmentioning

confidence: 99%

“…Therefore the ground surface and any layer interfaces need to be carefully meshed to a sufficient distance. A special edge element is used to avoid the reflections at the end of the ground or layer mesh [26]. In the situations considered here, the track is represented using finite elements while the ground and stiffened soil are modelled using boundary elements.…”

Section: 5d Finite Element / Boundary Element Approachmentioning

confidence: 99%

Mitigation of railway-induced vibration by using subgrade stiffening

Thompson

Jiang

Toward

et al. 2015

Railway-induced ground vibration is often associated with sites with soft ground. Stiffening of the subgrade beneath the railway track is one particular measure that has potential to reduce the vibration level at such sites. However, the mechanisms behind this reduction are not well understood. Here, the effects are examined in the context of two alternative approaches: (i) subgrade stiffening, where the soil directly under the track is stiffened, and (ii) stiff inclusions introduced at some depth beneath the track, sometimes known as 'wave impeding blocks'. The efficacy of the measures is considered for different ground types in a parametric study carried out using a 2.5D coupled finite-element / boundary-element methodology. The soil is considered to consist of a soft upper layer over a stiffer substratum; corresponding homogeneous grounds are also considered. With a 6 m wide, 1 m thick, concrete block directly under the track, the vibration between 16 and 50 Hz was found to be reduced by between 4 and 10 dB for ground with a 3 m deep soft upper layer. For a deeper soft layer the reductions were greater whereas, for a stiffer ground without the soft upper layer, the reductions in vibration from this block were negligible. Slightly smaller reductions in a similar frequency region were observed when the block was positioned 1 m below the 2 surface, suggesting that, as with stiffening directly under the track, the reduction in vibration was primarily due to the increase of the effective stiffness of the soil beneath the track rather than the effective creation of a new, thinner soil layer. Jet grouting is considered as an alternative to concrete and, although it is found to be less effective due to its comparatively low stiffness, it may still be considered as a practical measure for existing tracks on soft soil sites. The reduction in vibration from this form of soil improvement with a depth of 3 m is similar to that for a 1 m thick concrete block. Finally, results are presented for three example sites with different soil properties which show similar trends.

“…The tractionst s (N b2 )(k y , ω) are found by a 2.5D boundary element method, based on the integral equation that relates the displacements in the soil domain to the displacements and tractions on the soilstructure interface. The 2.5D boundary integral equation has been derived by Sheng et al [29] from the 5 2.5D reciprocal theorem. In this paper, a regularized version [22] of the 2.5D boundary integral equation is applied, leading to the following boundary element system of equations:…”

Section: The 25d Coupled Fe-be Modelmentioning

confidence: 99%

A 2.5D coupled FE-BE model for the prediction of railway induced vibrations

Galvín

François

Schevenels

et al. 2010

164

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.