PSI - Issue 78

Mirko Calò et al. / Procedia Structural Integrity 78 (2026) 710–717

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2. Machine learning based framework to derive seismic fragility curves of reinforced concrete bridges The ML-based framework designed to derive seismic fragility curves described in this section is structured as reported in Fig. 1. The starting point is the identification of a bridge superstructure-substructure system within the class of reinforced concrete bridges to reduce the number of taxonomy branches, while ensuring the applicability to a wide range of structures within a bridge portfolio. As first step, the definition of a taxonomy is required to identify the archetype structures to be analyzed for the derivation of seismic fragility curves. The proposed taxonomy, Table 1, is based on the structural and geometric information available at the end of the risk classification level of the Italian guidelines. The known parameters at this stage are construction period (CP), adoption of seismic design criteria (SD), average span length (L_AVG), and seismic defectiveness level (SDL). This parameter influences the seismic capacity of the pier, leading to different results in the evaluation when considered (Choe et al.,2008; Dizaj et al., 2023). Each taxonomy branch is identified using a set of labels that represent different combinations of these categories (CP/SD/L_AVG/SDL). As example, 45-80/NS/LS indicates bridges designed between 1945 and 1980 without the adoption of seismic design criteria characterized by average span length above 45 meters. To differentiate the archetypes of each taxonomy branch, it is necessary to associate a structural or geometrical parameter with each category, under the assumption that the parameter is representative of the category itself (see the "associated parameter" column in Table 1). Specifically, the pier longitudinal reinforcement ratio, ρ L , is considered to be representative of CP, assuming that the evolution of design codes has led to more stringent requirements and an increase in traffic loads, and thus an increasing structural demand in terms of bending moment at the base of the pier. With the same consideration, this time regarding the prescriptions about seismic design action, the pier transverse reinforcement ratio is considered representative of SD. The parameter associated with L_AVG is the average span length itself, L AVG, and is considered representative of the deck mass on top of the pier. Finally, the parameter associated with SDL is the amount of corrosion of reinforcement in terms of weight loss, Q S (Du et al., 2005). The structural and geometrical parameters can be discretized in different ranges according to the classification of each category and characterized by statistical distributions. When data concerning these parameters is not available, a uniform distribution can be employed to represent the maximum uncertainty, as asserted by Celik and Ellingwood (2010). The second step regards the definition of the FE model and the implementation of the CSM. Given that the CSM method is based on the backbone curves of single degree of freedom systems (SDoF). Consequently, a nonlinear FE model of the pier-superstructure system is employed. The rationale behind this choice is that the computational effort required for the NLTHA of archetypes for each taxonomy branch is considerable and increases with the number of taxonomy branches. Moreover, the information at disposal at this stage of the analysis is such that a simplified model of the pier is preferable to a complete model of the bridge. Focusing on the non-linear behaviour of the pier, the FE model of the pier is composed of two parts: the one at the bottom, for a distance equal to 1/10 of its total height ( H pier ), is considered the dissipative one, while the one at the top for the remaining length of 9/10 of H pier is considered as elastic. The two components are characterized by a different number of integration points and are subdivided into fibers with proper materials.

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Fig. 1. Workflow of the proposed ML-based for seismic fragility assessment framework.