PSI - Issue 84

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

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Table 2. Ranges of associated parameters to each category.

Category Associate parameter Distribution Ranges/Value L_MAX L MAX Uniform

L : [25, 35); M :[35,45), H : [45, 50] L : 0; ML : 5; M : 10; MH : 15; H : 20 % [m]

Discrete

SDL

ξ

Table 3. Statistical distribution of independent and dependent ( d sp is the prestressing steel reinforcement height from the beam section top fiber) variables for fragility assessment under traffic loads ( ɳ , mean, and CoV, coefficient of variation). Variable Distribution/re Parameters Mean compressive strength of concrete ( f cm,b ) Lognormal ɳ = 38.5 CoV = 11.4% [MPa] Mean tensile strength of steel ( f sy,b ) Lognormal ɳ = 451 CoV = 7.2% [MPa] Conventional yielding strength of prestressing steel ( f p,01 ) Lognormal ɳ = 1665 CoV = 7.5% [MPa] Ultimate strain of prestressing steel ( ε pu ) Normal ɳ = 5 CoV = 8.0% % Elastic modulus of uncorroded prestressing steel ( E p ) Normal ɳ = 195 CoV = 2.5% [GPa] Slab thickness ( s ) Uniform [0.2; 0.3] [m] Road pavement thickness ( h bit ) Uniform [0.08; 0.2] [m] Residual stress level of prestressing steel ( σ sp ) Uniform [720; 840] [MPa] Number of beams ( n b ) Uniform (Discrete) [3; 4] -

Table 4. Statistical distributions and regression models for dependent variables. Variable

Predictors Distribution/Regression model

Bounds

Beam height ( H b ) Beam spacing ( i b )

Uniform

[ L MAX /20; L MAX /15] [m]

L b

L b , H b

H b = 0.28 i b + 0.03 L b

- -

[m]

Prestressing steel ratio ( ρ sp ) L b

ρ sp d sp = 8.16E-05 L b + 1.85E-05 L b 2

-

Fig. 2. XGBoost statistical metrics and SHAP values for: (a) bending failure mechanism; (b) shear failure mechanism.

Fragility curves derived through XGBoost algorithm predictions were validated with those obtained from numerical analysis with FE models (Fig. 3a and Fig. 3b) assuming a fixed classification for ξ (L) and considering the variability of L_MAX classification (L, M and H). For flexural failure, the median value of fragility curves ( μ ) was overestimated by 1% - 3%, while for all the other taxonomy branches the difference did not exceed 5%. Similar differences were found considering shear failure mechanism. In this case, μ values were underestimated using