Improving the Dynamic Design Philosophy of High-Speed Railway Bridges Using Reliability-Based Methods

Abstract: Modern railway infrastructures, especially bridges, are exposed to significant vibrations with potential safety implications. In this context, previous studies have shown the inconsistency and inadequacy of some conventional design methods necessitaing them to be improved. The assessment of safety inherently deals with uncertainties. Therefore, the current study is dedicated to this objective using reliability-based methods. Of the various possible failure modes, the investigations presented here are limited to running safety and passenger comfort. The investigation of these limit-states requires constructing complex computational models with train-track-bridge interaction capabilities. However, the application of these computationally intensive models in the context of structural reliability does not appear to be feasible. Simplifying the system, the vertical acceleration and the deflection of the bridge serve as implicit limit-state measures. Initially, using First Order Reliability Method (FORM) revealed limitations in the application of the current safety factor, resulting in inconsistent reliability indices. Therefore, probabilistic design curves are proposed, defining minimum required bridge mass and stiffness based on cross-section types, span configurations and train speeds. These results are obtained by formulating a FORM-based optimization. Subsequently, the results are used to investigate the sensitivity of the estimated failure probabilities with respect to the contributing basic random variables. Acknowledging the limitations of FORM, surrogate-assisted simulation-based reliability assessments were used for further investigations. A comparison of the performance of widely used regression-based surrogate models under an identical active learning scheme showed the superior performance of the Kriging method over the others. Within areliability-based design optimization framework, this Kriging model facilitates the generation of new probabilistic design curves. This is achieved by reformulating the conventional method to account for the dependency between design variables using the copula concept. In addition, the surrogate model aided in calibrating the safety factor associated with the vertical acceleration threshold, leading to a proposal of 1.38 as a new safety factor. Subsequently, the influence of soil-structure interaction on the estimated reliability indices is evaluated using an ensemble of classification-based surrogate models. Results highlighted its beneficial contribution in terms of increased damping for shorter spans, countered by adverse effects due to frequency shortening in longer bridges. Finally, the epistemic uncertainties arising from the limited knowledge of the vertical acceleration threshold are investigated. It is found that neglecting these uncertainties can lead to an overestimation of allowable train speeds by about 13%.