PSI - Issue 84

Matteo Vozzi et al. / Procedia Structural Integrity 84 (2026) 425–432

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can be evaluated using established frameworks such as HAZUS, which is widely adopted for the assessment of seismic and flood vulnerability and loss estimation [16], while specifically for hydrogeological risks these can also be addressed through dedicated approaches such as those described in the British standard BD 97/12 and related design and assessment methods [17]. The approaches discussed herein consider the structural component of the overall infrastructure risk. According to reference [18], this is quantified as the product of the Probability of Failure , accounting for both Hazard and Vulnerability, and the Exposure as per Equation (4): = ⋅ (4) The Probability of Failure is derived from the Reliability Index as = (− ) , where the Reliability Index computed assuming the expression proposed by [18], according to Equation (5). = [ 0 + ( ∙ ) ,0 ] ∙ ,0 (5) where 0 is the Reliability Index of the structure in undamaged state, gauged over a 1-year Reference Period through Poisson processes [18]; the Damage Index; the Capacity Index; and and ,0 the Coefficients of Variation of the limit state under current and reference conditions, respectively, accounting for both model uncertainty and the intrinsic uncertainty associated with the damaged state of the structure. The parameters and capture the reduction of structural reliability due to damage evolution and the increased overload risk associated with outdated design codes. Reference values for for highway bridges designed under Italian standards are provided by [19], while the values of are derived by the characteristics of defects identified during inspections according to Defect Matrixes associating each defect’s intensity–extension pair with a discrete Damage Level as in [18]. The latter work also reports corresponding values of the Coefficients of Variation, accounting for both model uncertainty and the intrinsic uncertainty related to the damaged structural condition. It is worth noting that the referenced study also illustrates how the parameter D , and consequently the Probability of Failure, can be evaluated over different time horizons by accounting for the temporal evolution of existing defects as well as for the potential occurrence of new damage mechanisms. Accordingly, in Equation (3), the risk values / and / are computed by considering, respectively, , / , defined as the Probability of Failure evaluated using the values of and associated with the considered defect, and , / , representing the Probability of Failure in an undamaged condition, i.e., after defect removal. Having defined the Probability of Failure , the risk is computed multiplying by the Exposure that account for the consequences of collapse as per Equation (4). Following [15], these consequences are assumed to be dominated by casualties, whose associated costs largely outweigh any other direct or indirect losses according to APT’s assumptions. Accordingly, the Exposure is expressed in monetary terms as the sum of , accounting for potential casualties of users traveling on the bridge, and , accounting for potential casualties occurring in occupied areas beneath the bridge, as per Equation (6): = + = ( ⋅ ∙ / ℎ ∙ )+( ⋅ ∙ ) (6) where is the Average Daily traffic; the average speed of the vehicles on the bridge; is the length of the longest span; / ℎ the average number of occupants per vehicle; and the lethality factors for people on and under the bridge, respectively; and and the occupancy density and spatial extent of the area crossed by the bridge. Overall, the APT BMS methodology enables a consistent, quantitative comparison among alternative interventions by directly linking structural reliability, expected consequences, and economic efficiency within a

unified risk-based decision framework. 4. Comparison between the methods

The theoretical framework is based on risk for both approaches but the prioritization is performed based on different metrics: the one-year deferral cost for the SINA approach and the cost-effectiveness of the interventions for the APT. The expressions used to compute the reliability index, reported in equations 2 and 5, are very similar. The substantial difference arises from the knowledge required to compute the parameters in the two expressions.