PSI - Issue 78

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

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3. Case study The proposed framework was applied to one of the most diffused existing bridge typologies within the Italian transportation network that is simply supported RC girders (Salvatore et al., 2024) with single cylindrical RC pier (Abarca et al., 2022). T e ran es t e s alled “ass ated ara eters” were defined along with the independent variables before employing Latin Hypercube Sampling (Iman and Conover, 1982) as a statistical sampling technique for the random generation of a sample of bridge model realizations . tart n r t e “ass ated ara eters” in Table 2, the values adopted for the ranges of ρ L , ρ T and L AVG were derived from literature studies (Abarca et al., 2022; Nettis et al., 2024 and Salvatore et al., 2024) considering a uniform distribution, while Q S values were assumed deterministic and modeled via a degenerate distribution (i.e., a distribution that always returns the fixed value). Regarding independent variables, Table 3, the mean concrete compressive strength, f c , and mean steel tensile strength, f y , were assumed according to a uniform distribution and the values reported by Nettis et al., 2024. Instead, H pier and the pier diameter, D pier , were fixed in a range of possible values (in real case studies can be modified according to the information collected within the bridge portfolio). The sample size of bridge model realizations depends on several factors including the number of taxonomy branches (Abarca et al., 2022) and the extent of the database required for the training of the XGBoost classification algorithm. Approximately 300 realizations were considered for each tax n bran d e t t e ar ab l ty b t “ass ated ara eters” and nde endent ar ables , and en 90 taxonomic branches, a total of 30000 samples was generated. A torsionally flexible behavior of the deck was assumed, consistent with typical configurations of simply supported girders leaning on elastomeric bearings. In the end, the collapse LS was considered, and the pushover analysis was performed in the transverse direction, considered as the most critical direction with respect to the seismic response of the bridge piers. A suite of 100 natural ground motions was selected from the SIMBAD database (Smerzini et al. 2014) consistently with the characteristics of soil type, magnitude and distance of expected earthquakes in the bridge portfolio location, assumed in Basilicata region (Italy). The IM associated to each of the selected natural ground motion was the geometric average of spectral accelerations O’Re lly, 2021 , AvgSa , in the range of periods 0.5T min – 1.5T max .

Table 2. Ranges of associated parameters to each category. Category Associated parameter Distribution Ranges CP ρ L Uniform

45-80 : [0.2; 0.55); 80-03 : [0.55; 0.9); 03: [0.9; 1.2]

% %

SD

NS : [0.03; 0.08); S : [0.08; 0.16]

Uniform Uniform

ρ T

L_AVG

SS : [25; 35); MS : [35; 45); LS : [45; 50] L : 0; ML : 5; M : 10; MH : 15; H : 20

[m]

L AVG

SDL

Q S

Degenerate

%

Table 3. Statistical distributions for independent variables. Parameter Distribution

Ranges

Mean concrete compressive strength ( f c )

Uniform (Discrete) [25; 30; 35] MPa

Mean steel tensile strength ( f y )

Uniform (Discrete) [375; 440]

MPa

Pier diameter ( D pier ) Pier height ( H pier )

Uniform Uniform

[2; 3]

m m

[6; 20]

The database was split into 75/25 to train the XGBoost algorithm, and hyperparameter were optimized by maximizing the recall value. In the context of a binary classification problem, the decision to prioritize maximizing recall over the f1-score can be considered a conservative approach. Indeed, it is regarded as more beneficial to accurately predict collapses, even if this results in a higher number of false positives. Furthermore, the class prediction of the XGBoost is based on an internal threshold that was calibrated according to the value that maximizes the F1-score on the validation dataset, rather than relying on the default one (i.e., 0.5), Fig. 2(a). The optimal threshold of 0.87 ensured 87% precision and 91% accuracy. Fig. 2(b) reports the summary plot graph obtained through the eXplainability approach. The input features are ranked on the ordinate according to their influence on the results, and on the abscissa the value (SHAP value) of the impact of each feature on the predictive ability of the model are reported. As expected,