Keywords: dynamic analysis, railway bridges, key input data, key results, statistical analysis, design of experiments.

Dynamic analyses of railway bridges are still a subject of research given some uncertainties both of material characterization and of the numerical procedures associated with the model selected to represent the system. For instance, rules and strategies for execution of the numerical analyses are not yet well-defined and levels of possible simplifications and computational guidelines are not uniformly established.

Design engineers often completely rely on the output originated from the finite element calculations and seldom check or verify the accuracy of the results obtained. Railway bridges, in turn, are complex structures that require simplifications and implied uncertainties are always present in the numerical analysis of their dynamic behaviour. The potential of statistical methods of analysis to mitigate some of those limitations is often overlooked and seldom used among structural engineers.

By statistical analysis of numerical results obtained it is possible to establish a set of key input data and key results. Key input data in this context are defined as the ones whose change causes the largest changes in key results. Traditionally only one input parameter influence was analysed at each stage. Recently, the importance of studying the joint effect of several modelling parameters has been proven.

Satisfactory statistical analyses have to be supported using numerical models computationally accessible that provide results with sufficient accuracy. When statistical analysis is concluded, then the key results determined represent the characteristics to be measured using in-situ experiments. The key input data serve a twofold objective: (i) they are used for model calibration, (ii) they dictate additional tests to be performed in laboratory environment, in order to provide better estimates of the value to be implemented in the numerical model.

The work presented is performed within the SMARTRACK project. The dynamic behaviour of a railways viaduct modelled after an actual structure located in Santana do Cartaxo, Portugal, is analysed using a parametric statistical analysis. In this study the key parameters selected are the train speed and some of the parameters known to contribute to ballast behaviour. Natural frequencies, maxima in displacements and accelerations at mid-point of bridge spans were chosen as key response measures. The load applied corresponds to the locomotive used in the Intercidades train. In the preliminary stages, either one axle load is applied, or two axle loads moving in opposite directions are introduced. Factorial experimentation was selected for the statistical analysis. The viaduct model was developed using the ANSYS/LS-DYNA module. The database from REFER EP, the industrial partner of the project, was used for definition of the relevant data. The parametric analyses with automatic extraction of key results are coded using APDL (ANSYS parametric design language). The results are shown and interpreted in the paper.

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