PSI - Issue 84

Matteo Vozzi et al. / Procedia Structural Integrity 84 (2026) 425–432 427 where represents the total economic damage caused by the exceedance of the j -th limit state, is the probability of exceeding the limit state in the considered time period (one year) calculated for the structure in its current condition, and 0 denotes the same probability calculated for the structure already repaired or strengthened. The cost is used as a metric to establish the priority of repair or strengthening interventions among a set of managed structures: the intervention associated with the highest postponement cost is considered the most urgent. In the estimation of the postponement cost the probability of collapse is calculated with reference to the current condition of the structure, neglecting the effect of material aging and degradation over the short reference period of one year. The estimation of the reliability index , corresponding to the annual probability of exceeding a given limit state, can be obtained through the following relationship proposed in document [15] and reported in Equation (2): = 0 + ( ⁄ ) √ 2 + 2 ⁄ (2) The meaning of the symbols is as follows: 0 is a constant expressing the minimum reliability index of a structure designed in compliance with the requirements of the current technical standards; is the ultimate resistance of the structure with respect to the considered limit state according to the current standards; is the maximum effect of the design loads determined according to the current standards at the same location; is a parameter expressing the statistical variability of ln( ) , and expresses the statistical variability of ln( ) . It is noted that the method is independent on the type of analysis performed to determine loads and resistances (accurate or simplified) and can, in principle, also be applied to limit states not related to traffic or seismic loads, for example those caused by hydrogeological issues. Moreover, the resistance value must be determined by considering not the original design conditions, but the current condition of the structure. According to the classification proposed in fib Bulletin No. 80, the damage caused by the structural collapse of a bridge can be evaluated as the sum of the following components: • cost of reconstructing the collapsed portion of the structure; • cost associated with the interruption of the infrastructure functionality, including lost revenues for the concessionaire company (in the case of toll roads) and costs to the regional economy due to road closure; • social consequences (loss of human lives); • adverse environmental effects and damage to the affected areas; • psychological effects (loss of reputation). Reference [13] provides an economic quantification for each of these components, using both formulations available in the literature, and the experience gained from past collapse events. The objective is to capture the order of magnitude of damage rather than provide its exact quantification. For small bridges and for secondary limit states, the most significant cost component is the damage associated with service interruption and the resulting delays for users. As the bridge length and height (and the associated consequences in case of collapse) increase, damages related to the probability of casualties become progressively more dominant in the prioritization. 3. Autonomous Province of Trento BMS approach: prioritization based on risk reduction The APT BMS methodology is based on the Priority Index , conceived as a cost-effectiveness indicator for infrastructure interventions. Assuming that infrastructure management aims at allocating limited resources so as to maximize risk reduction Δ while minimizing intervention costs , the Priority Index, according to [15], is defined as the ratio between the risk reduction achieved through the intervention and the associated cost, as expressed in Equation (3). = ∆ = / − / (3) where / represents the risk evaluated for the bridge in its current condition (defects present), and / the risk evaluated for the structure already repaired or strengthened (defects repaired) Even though, the overall risk associated with an infrastructure should account for multiple hazard components – including structural, seismic, landslide, and hydraulic hazards, this paper focuses specifically on the assessment of structural risk and does not explicitly address the other contributions to the overall risk framework. For the components related to natural hazards, consolidated methodologies are already available in the literature. For instance, such risks