Probabilistic analysis of train running safety on bridges: a state-of-the-art review

Eduardo C. Granato, Gonçalo Ferreira, Pedro Montenegro, António Abel Henriques, Rui Calçada and Túlio N. Bittencourt

International Journal of Rail Transportation, 2025, vol. 13, issue 6, 1059-1097

Abstract: Train running safety when crossing bridges is an important issue due to the catastrophic consequences of possible derailments. Recent developments in railway technology have led to a great increase in operational speeds and axle loads, leading to significant dynamic amplifications and possibly structural and running safety issues. Assessment of derailment coefficients and running safety indexes is performed using train–track–bridge interaction models, which have advanced in recent decades and reached a mature state. However, most sources of excitation to which train–bridge coupled systems are subject are stochastic in nature, such as winds, earthquakes, track irregularities, and others. Structural and vehicle properties are also associated with uncertainties, which play a major role in the estimation of dynamic responses and evaluation of train running safety. Therefore, probabilistic methodologies are essential to accurately assess the bounds of dynamic responses and derailment coefficients and explicitly evaluate their reliability. Safety coefficients and dynamic amplification factors associated with both direct and indirect train running safety indexes are currently not calibrated with target reliability indexes, which results in possibly inefficient or unsafe design of bridges. This paper aims to present the state-of-the-art of stochastic analyses in train running safety assessment, discuss the main train–track–bridge dynamic interaction models and probabilistic methods used, and systematically evaluate recent applications regarding different stochastic sources of excitation. Gaps identified in the literature are also presented along with guidance for the development of further research.

Date: 2025
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DOI: 10.1080/23248378.2024.2447033

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