PSI - Issue 84

Mirko Calò et al. / Procedia Structural Integrity 84 (2026) 392–400

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The trained ML algorithm can be used to predict the outcome for a sample of N generated bridges within the input parameter space. The probability of failure, P[failure|α] , is given by Equation 2:   ( ) | fails N P failure N   = (2) where N fails (α) is the number of fails for a given α among N bridges. A closed-form fragility function (referred to as fragility curves hereinafter) for a given taxonomy branch can be derived by fitting a cumulative distribution function to the obtained dataset of P[failure|α] . 3. Results of the application The framework was applied to simply supported muti-girder prestressed reinforced concrete (PC) bridges as the most common superstructure system along the Italian transportation network (Salvatore et al., 2024). The corresponding ranges of associated parameters (i.e., L MAX and ξ ) were defined as reported in Table 2. The ranges of L MAX do not match the ones of the IG as each superstructure system is characterized by different ranges (Salvatore et al., 2024). For example, prestressed reinforced concrete girders are typically longer than reinforced concrete ones. Independent, Table 3, and dependent variables, Table 4, were identified as well considering proper statistical distributions based on existing literature studies (Jacinto et al., 2012; Miluccio et al., 2021; Nettis Al. et al., 2024). Through LHS an adequate number of bridge samples were generated for the push-down displacement control analysis. The sample size was assumed to be dependent on the number of taxonomy branches (Abarca et al., 2022) and on the extent of the database required to train and test the XGBoost algorithm which is mainly dependent on the number of input features. It is worth specifying that only independent variables and associated parameters were included as input parameters in the database, as dependent variables were derived from those ones (e.g., H b was derived from L MAX ). As for FE models, the midspan fiber section, characterized by a linear distribution of prestressing tendons near to the lower edge of the beam (i.e., not parabolic as for the entire beam), was considered for the entire longitudinal development of girder elements. This modelling approach, although simplified, was justified as the flexural collapse mechanism usually occurs at midspan sections where such distribution of prestressing tendons can be found. In the case of shear failure mechanism, this assumption does not account for the counter-shear at beam end sections induced by the eccentricity of the prestressing resultant with respect to the centroid of the cross-section. As result, the shear demand obtained from the push-down displacement-control analysis is higher (i.e., is conservative for the assessment) than the one computed considering the effective prestressing system layout. Modified stress-strain relationship of prestressing steel fibers was computed for each SDL classification. 300 realizations were generated for each taxonomy branch for a total of 4500 models by 15 combinations of taxonomy branches. The same sample of bridges was analyzed considering flexural and shear failure mechanism up to an α value of 4.5, with a 0.5 increment step due to the a-priori unknown im level corresponding to collapse LS of most of the models. The database was split into 70/30 for training and test of the XGBoost algorithm. Statistical metrics values of Accuracy, Precision, Recall and F1-Score were satisfying (above 0.9) for both collapse mechanisms (Fig. 2). Results about the eXplainability approach SHAP are reported in Fig.2. Input features are reported on the vertical axis, ranked based on their influence on the classification output, SHAP value, i.e. the impact of each feature on the model prediction, is shown in the horizontal axis. Yellow points correspond to contributions that increase the predicted probability of class “1” (failure), whereas violet points indicate contributions that decrease it and therefore increase the probability of class “0” (no failure). As expected, the most influent parameters are α , ξ , and L MAX . For flexural failure mechanism, f p,01 had a strong impact on the predictions as expected due to construction material of girders. Conversely, for shear failure mechanism f cm,b was found as influent as L MAX , which can be explained by the shear resistance formulation in absence of shear cracks at the supports provided by the Italian building code as implemented by Nettis Al. et al. (2024). In both cases, the number of beams, n b , is the less influent input parameter as the load redistribution of LM1 on girders is slightly different between the two cases (i.e., the one with three beams and the one with four beams).