computation Article The Use of Fragility Curves in the Life-Cycle Assessment of Deteriorating Bridge Structures Elsa Garavaglia 1 , Raffaella Pavani 2 and Luca Sgambi 3, *   Citation: Garavaglia, E.; Pavani, R.; Sgambi, L. The Use of Fragility Curves in the Life-Cycle Assessment of Deteriorating Bridge Structures. Computation 2021, 9, 25. https:// doi.org/10.3390/computation9030025 Academic Editor: Ali Cemal Benim Received: 26 January 2021 Accepted: 21 February 2021 Published: 25 February 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Department of Civil and Environmental Engineering, Politecnico di Milano, 20133 Milan, Italy; elsa.garavaglia@polimi.it 2 Department of Mathematics, Politecnico di Milano, 20133 Milan, Italy; raffaella.pavani@polimi.it 3 Faculty of Architecture, Architectural Engineering and Urban Planning, Université Catholique de Louvain, 7500 Tournai, Belgium * Correspondence: luca.sgambi@uclouvain.be Abstract: Within the context of structure deterioration studies, we propose a new numerical method based on the use of fragility curves. In particular, the present work aims to theoretically study the degradation of concrete bridge structures subjected to aggressive environments. A simple probabilistic method based on fragility curves is presented which allows the forecasting of the lifetime of the considered structural system and the best monitoring time. The method was applied to investigate the degradation of a concrete bridge used as a case study. A Monte Carlo numerical procedure was used to simulate the variation over time of the residual resistant section and the ultimate bending moment of the deck of the case study. Within this context, fragility curves are used as reliable indicators of possible monitoring scenarios. In comparison with other methods, the main advantage of the proposed approach is the small amount of computing time required to obtain rapid assessment of reliability and deterioration level of the considered structure. Keywords: life-cycle assessment; reinforce concrete bridges; concrete deterioration; probabilistic modelling; fragility curves 1. Introduction During their life spans, structures that are subjected to an aggressive environment can suffer deterioration of their component materials. Such damage may reduce the mechanical characteristics of the system and, with them, even its reliability. Due to high randomness, associated with the occurrence of critical attacks in the environment, it is suggested that the deterioration of structures and of structural materials is studied from a probabilistic point of view. Each probabilistic approach requires a series of reliable experimental data and a coherent and significant definition of the physical aspects of the phenomenon. It is known that managing both these aspects is not simple. In the last decade, many scientific papers were published which aimed to better define uncertainties within the context of engineering problems and to select the most suitable approaches. As described by Ang [1], first of all it is necessary to understand if the uncertainty is random (associated with natural randomness) or epistemic (associated with imperfect knowledge) and then to take one of the most appropriate approaches ([1] provides a framework for modelling and treatment of uncertainties). In general, the treatment of uncertainties can be performed through a probabilistic modelling [2–4] or a fuzzy approach [5–7]. In probabilistic methods (more suitable for a type of random uncertainty), the forecast of future damage is often evaluated with static or dynamic structural analyses, linear or not, based on the application of Monte Carlo simulations of the behavior over time of structures and structural elements affected by a certain deterioration. The application of this technique aims to formulate a reliable forecast of the evolution of the damage thanks Computation 2021, 9, 25. https://doi.org/10.3390/computation9030025 https://www.mdpi.com/journal/computation