Keywords: railway bridges, dynamic analyses, finite elements, ballast.

Static analyses are often used to estimate the fatigue life of railways bridges. However, dynamic analyses may be necessary in order to obtain a more accurate estimation. In particular, in recent research at the Division of Structural Engineering and Bridges at KTH it has been shown that the free vibrations of bridges after a train passage may influence the fatigue life. One issue regarding the dynamic behaviour of railway bridges is that discrepancies between calculations and experiments are often observed. This problem especially applies to short or median span bridges for which important differences between calculated and measured natural frequencies can be obtained. Several studies have also shown that, for such bridges, the natural frequencies vary as function of the amplitude of the vibration.

One difficulty in modelling relatively short railway bridges is that the influence of the track superstructure composed by rails, sleepers and ballast is not well known. As an example, there is, so far, no clear recommendation in the design codes to take the ballast into account in dynamic analyses.

The purpose of the present paper is to propose a new and simple approach to consider the influence of the ballast on the natural frequencies of railway bridges. The idea is to develop a simple two-dimensional beam finite element in which the effect of the ballast is taken into account by introducing a non-linear longitudinal stiffness associated to the slip at the interface between the bridge and the ballast. This approach has already been presented by Fink and Mähr [1], but in a continuum context, using differential equations.

Two examples are used to validate the present approach. The first one is the experimental bridge developed by Fink and Mähr whereas the second one is the Skidträsk bridge, a Swedish single span, concrete-steel composite bridge. In both cases, experimental data have shown that the first natural frequency depends on the amplitude of vibrations. A bilinear law between the slip and the shear force at the steel-concrete interface has been taken. The parameters of the bilinear law have been calibrated in order to match experimental data.

Using this simple numerical model, very good agreement with experiments has been obtained. In particular, it has been shown that the model can catch the influence of the amplitudes of vibrations on the value of the lowest bending natural frequency. This model is currently used to get a better estimation of the dynamic response of the Skidträsk bridge due to the passage of trains, and consequently a better estimation of the fatigue life.

1

J. Fink, T. Mähr, "Influence of ballast superstructure on the dynamics of slender railway bridge", Nordic Steel Construction Conference, 2009. http://www.nordicsteel2009.se

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