A bridge failure can result in significant social, economic, and environmental problems; therefore, its reliability and risk management are essential. Bridges’ system reliability and risks are governed mainly by their redundancy and robustness, which currently are not adequately included in most design code specifications. Thus, in this study, a comprehensive comparison between relevant importance, redundancy, and robustness indicators found in the literature with different levels of complexity is carried out. The indicators under analysis have been used separately in different studies but have never been addressed together. Therefore, this study presents a joint evaluation of deterministic, reliability- and risk-based indicators to evaluate the differences in interpretation and information provided by the indicators. The approach is exemplified by analyzing a prestressed concrete bridge subjected to continuous degradation due to chloride ingress. A procedure is implemented to couple a metamodel-based reliability approach with a Nonlinear Finite Element Analysis (NLFEA). Based on the analysis performed, the comparison between indicators showed how different interpretations can be obtained depending on the implemented approach. Thus, creating more uniform formulations and agreeing on target values is necessary to help with redundancy and robustness interpretation.

Reliability analysis is crucial for evaluating structural performance, and advancements in computational technologies have enhanced the application of Finite Element Modeling (FEM) in this field. However, existing reliability methods face challenges, particularly with approximation methods that struggle with implicit limit state functions and simulation methods with cost. Metamodel-based approaches have gained popularity for their balance of efficiency and accuracy, yet most algorithms focus on independent variables. This paper presents an improved metamodel-based algorithm designed to assess structural reliability while considering variable dependency and FEM. The algorithm provides a methodology that ensures a rapid convergence of the iterative process when building the metamodel in the region of interest, i.e. where the Most Probable Point (MPP) is located. It uses a modified Design of Experiments (DoE) and integrates copula theory to model the joint probability distribution function (PDF). The algorithm enriches the experimental points matrix by finding points close to the Limit State Function (LSF) at 0 with high prediction variance using learning functions and with high joint PDF values using copula theory. Validation through various examples and an application example of a reinforced concrete bridge indicates that the proposed methodology is more efficient than most recent algorithms without reducing accuracy.

This paper presents a time-dependent reliability assessment that integrates experimental data with Bayesian updates and is applied to a 66-year-old prestressed concrete box-girder bridge. Non-destructive and destructive tests were performed to evaluate its actual serviceability condition. The tests included on-site prestress measurements, material evaluations, a serviceability-proof load test, and refining structural response and boundary conditions using monitoring system data. These tests offered crucial updates to assumptions based on the as-built drawings. The bridge’s structural reliability for serviceability is studied by comparing two approaches: (1) a prior reliability analysis based on traditional Eurocode methods to estimate prestress losses; and (2) a posterior reliability analysis incorporating on-site measurement for residual prestress and material properties. A Bayesian update was performed to refine the estimates of concrete strength and prestress losses and improve the accuracy of the reliability assessment. The results showed that updating material properties doubled the reliability index relative to the initial analysis. Similarly, updating residual prestress measurements via strand cutting and saw cut methods increased the reliability index from 1.75 to 2.84 and 2.35, respectively. These findings highlight the need for on-site prestress measurements and time-dependent reliability analyses to accurately assess the serviceability performance of ageing bridges accounting for long-term degradation.

Reinforced concrete (RC) trough bridges form a crucial part of Europe's railway infrastructure. These structures consist of a U-shaped cross-section (two longitudinal beams and a slab) designed to accommodate the ballast. For the case of the Iron Ore Line, a critical corridor located in the north of the country, RC trough bridges represent about 40 % of the railway bridge population. Many of these bridges have surpassed 50 years of service, enduring over 10 million cycles of fatigue loading, with increases of axle loads since their construction due to demands associated with the iron ore extraction and transportation. As these structures approach critical maintenance or replacement decisions, understanding their long-term performance and remaining capacity is essential. This study experimentally investigates the degradation behavior of a full-scale RC trough bridge subjected to progressive cyclic loading, simulating fatigue effects over time. During the controlled laboratory tests, the overall performance of the bridge is assessed, focusing on the stiffness loss of slab and beams, cracking, and force redistribution. Fatigue verifications based on Eurocode EN1992–1–1 and fib Model Code 2020 are performed alongside the reliability analysis using the First-Order Reliability Method (FORM) to evaluate structural safety levels. While fatigue damage is evident in the slab's tensile zone, the overall structural response indicates that the bridge maintains its functional capacity after simulating 48 years of service. However, the code-based reliability analysis indicates lower-than-target reliability levels for reinforcement, suggesting a conservative estimation of reinforcement capacity to withstand cyclic loading.

This paper presents a multi-level reliability framework for assessing the fatigue life of reinforced concrete (RC) railway trough bridges subjected to cyclic loading. The framework incorporates increasing levels of analytical complexity and real-world data in four steps. First, an analytical model applies S–N curves and the Palmgren–Miner rule with constant stress assumptions. Second, monitored strain data refine stress estimates. Third, a calibrated finite element (FE) model is used to simulate degradation and structural response. Fourth, survival information conditions the reliability on observed performance. The framework is applied to a RC trough bridge tested under representative railway loading using traffic data from Sweden’s Iron Ore Line. Results demonstrate the value of combining monitoring, FE modelling, and probabilistic methods for evaluating remaining service life (RSL). From step 1 to step 3, the methodology extended the RSL estimates by 39 years, allowing an increase in mean axle load by approximately 20%.