PSI - Issue 84

Federica Di Criscio et al. / Procedia Structural Integrity 84 (2026) 1023–1030

1026

according to the model proposed by Imperatore et al. (2017), while the degradation of concrete strength is modelled through the model proposed by Coronelli & Gambarova (2004); moreover, possible loss of confinement due to stirrup corrosion is accounted for adopting the model proposed by Mander et al. (1988). For PSC elements, additional mechanisms are considered to account for the different behaviour and failure modes of prestressing steel. In particular, the chain effect, arising from the heterogeneous corrosion of individual wires within a strand, leads to gradual and uneven wire rupture and to a non-uniform redistribution of stresses within the tendon. This mechanism is captured by the model proposed by Franceschini et al. (2023), which assigns a deteriorated constitutive law to each wire and reproduces wire interaction through an equivalent spring model, providing a fully degraded stress-strain response. Moreover, the loss of bond between steel and concrete induced by corrosion-related cracking leads to an increase in the transfer length - modelled in accordance with Anaya et al. (2022) - and a reduction of the effective prestressing force evaluated following the formulation proposed by Wang & Liu (2008). By applying these degradation models, each corrosion level is associated with a fully defined set of reduced material constitutive laws. 2.3. Capacity of corroded structural components Once the degraded constitutive laws are defined for each corrosion level, the structural capacity is evaluated at the sectional scale through moment–curvature (M– ϕ ) analysis (Step 3). This step is repeated for each corrosion level, using the updated material properties. Depending on the geometry and reinforcement layout, M– ϕ curves are obtained either through simplified analytical formulations or through detailed fiber-based modelling. The presence of corrosion leads to a reduction in initial stiffness, peak moment capacity, and curvature ductility with respect to the as-built (i.e., intact) configuration. For bridge piers, the M– ϕ relationship is converted into a force–displacement (F– δ) curve through simple structural design principles to capture the global cantilever response under seismic loading. This step allows identifying the plastic hinge location, displacement capacity, and overall deformation mechanism. More specifically, localized corrosion is expected to shift hinge formation to the deteriorated section, modifying the effective cantilever length and, possibly, reducing the ductility capacity of the structure. For girders, the required capacity representation depends on the structural scheme. In simply supported configurations, the flexural capacity is evaluated directly at the section level. Differently, in continuous girders, potential hinge formation at supports and midspan must be assessed, since corrosion may alter the expected collapse mechanism; therefore, in this specific case, the flexural capacity is evaluated in terms of force–displacement response. Shear resistance is evaluated according to the Italian building code, accounting for strength deterioration due to corrosion-induced degradation of transverse reinforcement. Finally, the global seismic capacity of the structure depends on the bridge configuration. For simply supported spans, each pier behaves independently, and the global capacity is governed by the most critical (weakest) pier. In contrast, for continuous-span bridges, the global capacity can be obtained through simplified displacement-based approaches (e.g., Dwairi & Kowalsky, 2006). 2.4. Structural Analysis Seismic response analysis is then performed according to state-of-the-art methodologies in the literature (Step 4). Seismic safety is evaluated through a capacity vs. demand comparison performed in the Acceleration Displacement Response Spectrum (ADRS). To quantify seismic safety, a “safety index” (i.e., capacity vs. demand ratio at the Life Safety limit state) is considered, according to the Italian building code (NTC2018). Clearly, by carrying out the safety evaluation at different times of the bridge’s life, it is possible to estimate the decay of the safety index over time. Gravitational safety is evaluated using the loading scheme provided by the Italian building code, with load effects maximized for the beam under investigation. Vehicular loads are distributed transversely via the Courbon method and combined with the external effects of prestressing. Finally, the vertical safety factor is evaluated as the ratio between the bending strength capacity and the maximum moment demand. 2.5. Time-dependent safety evaluation The final stage of the procedure (Step 5) consists of deriving time-dependent safety curves, reflecting the gradual loss of structural efficiency. For each predefined level of corrosion, the corresponding safety index is calculated and