Numerical modelling of vibrations from a Thalys high speed train in the Groene Hart tunnel

This paper presents a numerical study of vibrations due to a Thalys high speed train in the Groene Hart tunnel, which is part of the high speed link South between Amsterdam and Antwerp and the world's largest bored tunnel.     

Local and global shape functions in a boundary element formulation for the calculation of traffic induced vibrations

This paper compares the use of local and global shape functions in a boundary element method that is used in a prediction model for traffic induced vibrations. The boundary element formulation describes the interaction problem between a linear elastic layered half-space and a longitudinally invariant structure representing a road or a railway track. The boundary element formulation in the frequency–wavenumber domain is obtained by means of a weighted residual method. Constant element shape functions, as well as Legendre and Chebyshev shape functions are considered. Their effect on both accuracy and computational effort is investigated. The presence of a singularity in the Chebyshev based shape functions allows to obtain a better approximation for the soil tractions. The theory is applied to road traffic induced vibrations where the response is calculated in a large number of output points.     

The influence of dynamic soil–structure interaction on traffic induced vibrations in buildings

This paper deals with the dynamic response of buildings due to traffic induced wave fields. The response of a two-storey single family dwelling due to the passage of a two-axle truck on a traffic plateau is computed with a model that fully accounts for the dynamic interaction between the soil and the structure. The results of three cases where the structure is founded on a slab foundation, a strip foundation and a box foundation are calculated and a comprehensive analysis of the dynamic structural response is performed. A methodology is also proposed to calculate the structural response, neglecting the effects of dynamic soil–structure interaction. A comparison with the results of calculations where dynamic soil–structure interaction is accounted for shows that a good approximation is obtained in the case of a rigid structure resting on a soft soil.     

Experimental validation of a numerical prediction model for free field traffic induced vibrations by in situ experiments

This paper deals with the validation of a numerical model for traffic induced vibrations. Road unevenness subjects the vehicle to vertical oscillations that cause dynamic axle loads, which generate waves propagating in the subsoil. A 2D vehicle model is used for the calculation of the axle loads from the longitudinal road profile. The free field soil response is calculated with the dynamic Betti–Rayleigh reciprocity theorem, using a transfer function between the road and the receiver that accounts for dynamic road–soil interaction. The validation relies on the measured response of the vehicle's axles and the soil during the passage of a truck on an artificial unevenness with speeds varying from 30 to 70 km/h. The agreement between the numerical and the experimental results is good: the influence of the vehicle speed and the distance from the road is well predicted, while the ratio of the predicted and the measured PPV is less than two.     

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

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, 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.     

Shinkansen high-speed train induced ground vibrations in view of viaduct–ground interaction

Train viaduct behavior and nearby ground motion under the high-speed train passage have been studied in this paper. First, the findings from the field measurement alongside the high-speed Shinkansen railway in Japan are interpreted. Then, the computer simulation is made based on the soil-foundation-viaduct interaction analysis under moving axle loads. The solution method is to apply the dynamic substructure method in the frequency domain. The viaduct girders including track structure and pier supports are modeled by the three-dimensional beam-column elements. The supporting pile foundation and nearby field are discretized by the axisymmetric three-dimensional finite elements and analyzed in a semi-analytical way, with a transmitting boundary replacing the far field based on the thin layer element method. Nearby ground motion during train passage on a viaduct have been calculated by superimposing the effects from neighboring pile foundations.The main parameters affecting viaduct vibrations are discussed by taking environmental vibration into consideration. The nearby ground motion along the viaduct is recomputed by applying the above determined forces to the foundation tops. The results from numerical studies are compared with the field test data, thus proving the present simulation to be effective and reliable.     

Prediction of free field vibrations due to pile driving using a dynamic soil–structure interaction formulation

This paper presents a numerical model for the prediction of free field vibrations due to vibratory and impact pile driving. As the focus is on the response in the far field where deformations are relatively small, a linear elastic constitutive behaviour is assumed for the soil. The free field vibrations are calculated by means of a coupled FE–BE model based on a subdomain formulation. First, the case of vibratory pile driving is considered, where the contributions of different types of waves are investigated for several penetration depths. In the near field, the soil response is dominated by a vertically polarized shear wave, whereas in the far field, body waves are importantly attenuated and Rayleigh waves dominate the ground vibration. Second, the case of impact pile driving is considered. A linear wave equation model is used to estimate the impact force during the driving process. Apart from the response of a homogeneous halfspace, it is also investigated how the soil stratification influences the ground vibration for the case of a soft layer on a stiffer halfspace. When the penetration depth is smaller than the layer thickness, the layered medium has no significant influence on ground vibrations. However, when the penetration depth is larger than the layer thickness, the influence of the layered medium becomes more significant. The computed ground vibrations are finally compared with field measurements reported in the literature.     

Prediction of railway ground vibrations: Accuracy of a coupled lumped mass model for representing the track/soil interaction

Recent advances in railway-induced ground vibrations showed that the track/soil interaction plays an important role in the low frequency range. This paper contributes to the numerical analysis of train/track/foundation dynamics by presenting the accuracy of a coupled lumped mass (CLM) model devoted to the railway foundations and to the track/soil coupling. Following a summary of the background and the advantages of the CLM model, the coupling strategy is quantified through two application cases. Firstly, the dynamic track deflection is calculated for different railway lines considering various degrees of complexities of foundations. Then, the foundation responses are compared depending on whether detailed coupling is introduced or not. The benefit of the proposed model is emphasized by presenting free-field ground vibration responses generated by a tram and a high-speed train, obtained by a revisited two-step prediction model developed by the authors.     

Dynamic response of high-speed ballasted railway tracks: 3D periodic model and in situ measurements

A three-dimensional (3D) model for the soil–railway track system is proposed. It is based on a geometrical periodic hypothesis. The dynamic soil–structure interaction is taken into account. This representation is used for the case of a ballasted railway track subjected to high-speed moving loads and a new formulation of dynamic responses of the system is proposed. Moreover, recent in situ measurements performed in a high-speed line of the North of France are presented. Lateral and vertical accelerations in several locations of the railway track have been measured and the periodic model is confronted with these records.     

A note on benchmarking of numerical models for density dependent flow in porous media

Verification of numerical models for density dependent flow in porous media (DDFPM) by the means of appropriate benchmark problems is a very important step in developing and using these models. Recently, Infinite Horizontal Box (IHB) problem was suggested as a possible benchmark problem for verification of DDFPM codes. IHB is based on Horton–Rogers–Lapwood (HRL) problem. Suitability of this problem for the benchmarking purpose has been investigated in this paper. It is shown that the wavelength of instabilities fails to be a proper criterion to be considered for this problem. However, the threshold of instability formation has been found to be appropriate for benchmarking purpose.     

A coupling model of FE–BE–IE–IBE for non-linear layered soil–structure interactions

A coupling model of Finite Elements (FEs), Boundary Elements (BEs), Infinite Elements (IEs) and Infinite Boundary Elements (IBEs) is presented for analysis of soil–structure interaction (SSI). The radiation effects of the infinite layered soil are taken into account by FE–IE coupling, while the underlying bed rock half-space is discretized into BE–IBE coupling whereby the non-horizontal bed rock surface can be accounted for. Displacement compatabilities are satisfied for all types of aforementioned elements. The equivalent linear approach is employed for approximation of nonlinearity of the near field soil. This model has some advantages over the current SSI program in considering the bed rock half-space and non-vertical wave incidence from the far field. Examples of verification demonstrate the applicability and accuracy of the method when compared with the FLUSH program. Finally, the effects of the relative modulus ratio E_r/E_s of rock and soil and the incident angles of non-vertical waves on the responses of the structure and the soil are examined. Copyright © 1999 John Wiley & Sons, Ltd.     

On the performance of lumped parameter models with gyro‐mass elements for the impedance function of a pile‐group supporting a single‐degree‐of‐freedom system

Lumped parameter models with a so called “gyro‐mass” element (GLPMs) have been proposed recently in response to a strong demand for efficiently and accurately representing frequency‐dependent impedance functions of soil–foundation systems. Although GLPMs are considered to be powerful tools for practical applications in earthquake engineering, some problems remain. For instance, although GLPMs show fairly close agreement with the target impedance functions, the accuracy of the transfer functions and the time‐histories of dynamic responses in structural systems comprising GLPMs have never been verified. Furthermore, no assessment has been performed on how much difference appears in the accuracy of dynamic responses obtained from GLPMs and those from conventional Kelvin–Voigt models comprising a spring and a dashpot arranged in parallel with various frequency‐independent constants. Therefore, in this paper, these problems are examined using an example of 2×4 pile groups embedded in a layered soil medium, supporting a single‐degree‐of‐freedom system subjected to ground motions. The results suggest that GLPMs are a new option for highly accurate computations in evaluating the dynamic response of structural systems comprising typical pile groups, rather than conventional Kelvin–Voigt models. Copyright © 2011 John Wiley & Sons, Ltd.