PSI - Issue 78

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

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Table 1. Typological, geometrical and structural parameters considered for the proposed taxonomy along with associated parameters t e ate r es “ nstr t n ater al” and “ pier typology ” are n t nserted, be a se t e r ed re s re erred t a xed er ty l y characterized by an assigned construction material). Category Classification Associated parameter Construction period ( CP ) 1945-1980 ( 45-80 ) Pier longitudinal reinforcement ratio ( ρ L ) 1980-2003 ( 80-03 ) > 2003 ( 03 ) Seismic criteria for design ( SD ) Non seismic ( NS ) Pier transverse reinforcement ratio ( ρ T ) Seismic ( S ) Average span length ( L_AVG ) < 35 m ( SS ) Average span length 35 – 45 m ( MS ) > 45 m ( LS ) Seismic defectiveness level ( SDL ) Low ( L ) Amount of corrosion of reinforcement in terms of weight loss (Q S ) Medium-Low ( ML ) Medium ( M ) Medium-High ( MH ) High ( H ) In particular, the corrosion is considered as the main degradation process affecting the pier and it is accounted for in the definition of the SDL classification. Modified stress-strain relationships of both concrete and steel (Du et al., 2005; Lee and Cho, 2009; Manderer et al., 1998; Opabola, 2002) are employed for the fibers in the bottom part of the pier starting from Q S . A significant modelling assumption regards boundary conditions at the pier top related, for example, to the torsional stiffness of the deck and the bearing typologies. However, given the goal of the framework, a simplified modelling strategy is suggested implementing links and lumped masses. Additional information to those provided by the abovementioned parameters (i.e., associated parameters) are required for the model generation. For this reason, other independent variables are defined, such as material mechanical properties (e.g., concrete compressive strength) and geometric properties of the pier (e.g., H pier and a synthetic parameter for the section, depending on the shape of the pier cross-section). Regarding the application of the CSM, once a LS is fixed (e.g., collapse) together with an engineering demand parameter representing the capacity of the structure at the LS (e.g., ultimate displacement of the system in the case of collapse LS), the result of the CSM is recorded in a database according to a Boolean value: “Tr e” t e s ex eeded, “ alse” t e s n t ex eeded. The selected IM is stored in the database along with the characteristics of the structural model. This database is required for training and testing the ML algorithm. In the last step, the XGBoost algorithm is trained via supervised classification to predict whether a structure with given characteristics under a seismic demand at a generic intensity measure level (input variables), im , exceeds the LS or not (output variable). As with any ML algorithm, accurate tuning of hyperparameter is required. This process is based on the division of the database into training and test sets, the implementation of a grid search with cross validation strategy and a proper evaluation function. The performance of the XGBoost algorithm can be evaluated by considering the confusion matrix, and the values of Precision, Recall, and F1-score. Furthermore, an eXplainability approach, namely SHAP (Scott and Lee, 2017), is proposed to investigate the impact of each input feature on the prediction of the model (Calò et al., 2024). The trained XGBoost algorithm can be used to predict for a sample of N generated bridges for each taxonomy branch the exceedance of the LS for a set of im . The corresponding seismic fragility curve, that is the probability of failure, P[failure|IM=im], conditioned to an IM equal to im is given by Equation 1 where ɸ (.) is the standard normal cumulative distribution function, μ is the median of the fragility function and β is the standard deviation of the ln IM (Baker, 2014).

( ) ln / im 

 

  





| P failure IM im

 = = 

(1)

