Stiffness matrices for layered soils

This paper investigates the effectiveness of a sheet pile wall to reduce railway induced vibration transmission by means of field measurements and numerical simulations. At Furet, Sweden, a sheet pile wall has been installed in the soil near the track to reduce train induced vibrations in houses close to the track. The depth of the sheet piles is 12 m with every fourth pile extended to 18 m. The efficacy of the wall is determined from in situ measurements of free field vibrations during train passages before and after installation of the sheet pile wall. The field test shows that the sheet pile wall reduces vibrations from 4 Hz upwards. Up till 16 − 20 Hz, the performance generally increases with frequency and typically decreases with increasing distance behind the wall. The performance is further studied by means of two-and-a-half-dimensional coupled finite element -boundary element models. The sheet pile wall is modeled as an orthotropic plate using finite elements, while the soil is modeled as a layered halfspace using boundary elements. The sheet pile wall acts as a stiff wave barrier and the efficacy is determined by the depth and the stiffness contrast with soil. The reduction of vibration levels is entirely due to the relatively high axial stiffness and plate bending stiffness with respect to the horizontal axis of the sheet pile wall; the plate bending stiffness with respect to the vertical axis is too low to affect the transmission of vibrations. Therefore, it is important to take into account the orthotropic behaviour of the sheet pile wall. It is concluded that a sheet pile wall can effectively act as a wave barrier in soft soil conditions provided that the wall is sufficiently deep.

Section: Methodsologymentioning

confidence: 99%

Efficacy of a sheet pile wall as a wave barrier for railway induced ground vibration

Dijckmans

Ekblad

Smekal

et al. 2016

“…This implies that the dynamic stiffness matrix of the soil in equation (5) is computed by solving the boundary element system of equations (6) in terms of the full space Green's functions. Second, the displacements and tractions at the tunnel-soil interface are used to compute the free field response according to equation (9) using the Green's function of a layered halfspace [31,38]. In this subsection, it is investigated under which conditions a similar approach can be followed to reduce the computational cost in the 2.5D framework.…”

Section: Simplified Methodsologymentioning

confidence: 99%

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

Galvín

François

Schevenels

et al. 2010

172

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.

“…This mesh ensures that there are at least 10 elements per wave length up to 100 Hz. Green's functions for a halfspace are used as fundamental solutions in the BE formulation [33,34]. The boundary element mesh can therefore be limited to the interface between the mass and the soil.…”

Section: Benchmark Reference Casementioning

confidence: 99%

Mitigation of railway induced ground vibration by heavy masses next to the track

Dijckmans

Coulier

Jiang

et al. 2015

The effectiveness of heavy masses next to the track as a measure for the reduction of railway induced ground vibration is investigated by means of numerical simulations. It is assumed that the heavy masses are placed in a continuous row along the track forming a wall. Such a continuous wall could be built as a gabion wall and also used as a noise barrier. Since the performance of mitigation measures on the transmission path strongly depends on local ground conditions, a parametric study is performed for a range of possible designs in a set of different ground types. A two-and-a-half dimensional coupled finite element -boundary element methodology is used, assuming that the geometry of the problem is uniform in the direction along the track. It is found that the heavy masses start to be effective above the mass-spring resonance frequency which is determined by the dynamic stiffness of the soil and the mass of the wall. At frequencies above this resonance frequency, masses at the soil's surface hinder the propagation of surface waves. It is therefore beneficial to make the footprint of the masses as large and stiff as possible. For homogeneous soil conditions, the effectiveness is nearly independent of the distance behind the wall. In the case of a layered soil with a soft top layer, the vibration reduction strongly decreases with increasing distance from the wall.