PSI - Issue 84

Vittorio Palma et al. / Procedia Structural Integrity 84 (2026) 630–637 633 operational threshold (e.g. ( ) ≥3 ) is adopted to identify higher urgency at equal primary class. The construction period accounts for the evolution of design practices and action levels in historical standards, with older bridges generally considered more critical for comparable defectiveness conditions. The average span length ˉ provides a synthetic geometric indicator of potential failure severity, with a discriminating threshold of 30 m. The parameters / and represent, respectively, the overall state of conservation derived from ordinary inspections and the exposure level, defined as a function of traffic demand, availability of alternative routes, and strategic relevance of the asset. The comparison between two bridges and is defined through a lexicographic ordering, first by priority class and, in the case of equality, by sequential comparison of the components of : ≺ ⇔ { ( ) < ( ), or ( ) = ( ) and ≺ lex . (3) where ≺ lex denotes a comparison according to a predefined and monotonic order (e.g. higher , higher ( ) , greater age , larger ˉ , higher / , higher ). This formalisation highlights the non-compensative nature of the criterion, since the severity of governs the main priority class, and its monotonicity with respect to the guiding parameter, while preserving a refined within-class ranking through . 4. Methodology for the programming of safety assessments The Guidelines define safety assessments (Level 4) as an in-depth phase aimed at verifying the adequacy of existing bridges and at identifying possible management measures and interventions. At the network level, Planning Level 2 introduces a programming criterion that, based on inspection outcomes and on the determination of the Classes of Attention (CdA), assigns each asset a priority class for initiating detailed safety assessments and subsequently ranks assets within the same class as a function of hazard and exposure. The methodology assumes the presence of critical conditions as the primary discriminating factor and, in their absence, the level of structural–foundation defectiveness, consistently with the Guidelines and related Operational Instructions. For each bridge , a binary indicator of criticality is first defined: ∈ {0,1} (4) where =1 denotes the presence of critical conditions or elements indicating potential incipient failure or short term safety impairment, and =0 their absence. The level of structural–foundation defectiveness is expressed through five ordinal classes (Low, Medium–Low, Medium, Medium–High, High) and is defined as a function of severity, extent, and relevance of the affected elements, explicitly including defects involving critical components. To account for actions and contextual factors governing the evolution of risk, an overall hazard indicator is introduced, obtained through the combination of hazard levels associated with the structural–foundation and seismic domains by means of coupling matrices. The exposure indicator is retained and defined on the basis of traffic demand, availability of alternative routes, and strategic relevance of the asset. Based on these variables, the priority class for safety assessment is defined as a discrete function: = ( , , , ), ∈ {1,…,5}, (5) where =1 represents the highest priority. The function (⋅) is rule-based and non-compensative: the presence of critical conditions ( =1 ) and/or a High level of defectiveness ( = High) directly leads to assignment to the highest priority classes, reflecting situations in which safety may be compromised. For assets without critical conditions, the primary priority class is governed by and refined through the combined effect of hazard and exposure , implemented through classification matrices that ensure explicit and reproducible decision rules. Similarly to the procedure adopted for special inspections, once the class has been assigned, the ranking within each class is refined through a non-compensative indicator: Π =( , ), =( , , ). (6)