Probabilistic Dynamic Design Curves Optimized for High-Speed Reinforced Concrete Railway Bridges Using First-Order Reliability Method

Increasing the operating speed of trains in modern railway networks can induce greater actions on the infrastructure than was previously the case. This is due, in particular, to the occurrence of the resonance phenomenon in railway bridges, which is the focus of this paper and was not traditionally considered as a concern. In this context, the vibrations experienced by bridges, both vertical accelerations and displacements, are limited by design regulations to ensure that the safety of train passages over bridges and the comfort of passengers are guaranteed. However, previous studies have shown that the conventional dynamic design methods do not always result in conservative designs, nor is the achieved safety always consistent. Therefore, a probabilistic approach is adopted in this study to optimize the cross-section properties of various railway bridges in a wide design range including section types, span lengths, and number of spans. For this purpose, an iterative line search-based optimization problem is formulated to minimize the thickness of the cross-sections under consideration and consequently the linear mass of the bridges. Meanwhile, the associated failure probabilities of the above dynamic limit states are constrained to be less than the desired level of safety by incorporating them into the optimization constraint. In this regard, First-Order Reliability Method (FORM) is adopted to perform reliability analyses. Thus, the obtained results are presented in the form of design curves that may assist designers to select minimum cross-section dimensions satisfying the desired level of safety in terms of dynamic limit states. This objective can be achieved using the proposed design curves without the need to construct associated complex computational models and perform computationally expensive dynamic analyses.