Approaches for predicting the probability of failure of bridges subjected to high-speed trains

The scope of this paper is to evaluate different approaches for the prediction of the probability of failure of uncertain railway bridges subjected to high-speed trains. The peak acceleration of a bridge, which is commonly the governing response quantity for dynamic bridge design and failure, depends strongly on the type of train and the train speed. Since in many cases the critical speeds related to response maximums are below the design speed and failure, and during operation the speed varies up to the design speed, the assessment of the probability of failure is not straightforward. In this contribution, several more sophisticated measures of the probability of failure of the bridge-train interaction problem are proposed, considering the peak acceleration as a function of the speed in a certain interval and the distribution of the actual train speed. These measures are tested on two random test bridges, taking into account the main sources of uncertainty, i.e. damping, track irregularities, and the environmental impact. The mechanical model used for the prediction of the dynamic bridge response is composed of a beam bridge crossed by a planar mass-spring-damper model of the train. In this simplest approach that considers explicitly dynamic bridge-train interaction, random irregularity profiles capture the effect of track irregularities. It is shown that in certain speed intervals the predicted probability of failure strongly depends on the underlying measure of the probability of failure. In the first example bridge, whose response is governed by a pronounced resonance peak, exceedance of the serviceability limit state is predicted by all measures at virtually the same speed. The second example problem, where track irregularities lead to considerable response amplifications, only some of the measures predict failure. The results of this study may serve as an impulse for a more in-depth discussion on the appropriate prediction of the probability of failure of bridge-train interaction.