## 1 Introduction  
After the Second World War (WW II), prestressed concrete technology developed rapidly in Europe and has since become the dominant choice for infrastructure worldwide due to its effectiveness in both design and construction [1]. By this technology, prestressing is deliberately introduced to induce compressive stresses in the concrete, counteracting tensile stresses that would otherwise develop under service loads, thereby preventing cracking and controlling deflections. However, in the post-WW II period, the available technologies, materials, and construction methods lacked extensive experience on post-tensioning systems, leading to a design approach primarily focused on the increase in strength, with less emphasis on durability. As a result, many prestressed concrete structures today, several decades old and often near the end of their service life, show significant signs of deterioration, compromising their safety and functionality. Recent events have underscored this issue, such as the collapses of the Fossano Viaduct in 2017 and of the Polcevera Viaduct in 2018 [2], within the Italian context, and other tragic events worldwide [3]. The fundamental components of the post-tensioning (PT) system are the cables or tendons, which consist of high-strength steel strands placed inside the concrete structure. The tendons are housed within steel or plastic ducts and anchored at both ends to the concrete element. After concrete has hardened, the tendons are stretched using hydraulic jacks, then locked in place. The resulting compression strengthens the concrete, allowing it to resist tension forces, reduce cracking, and support heavier loads over longer spans. To prevent corrosion of the steel tendons, the ducts are injected with a cementitious grout, which creates an alkaline environment and ensures their bond with the surrounding concrete. The primary issue in post-tensioned structures is the loss of tension in PT cables, which may arise from several causes, such as cable corrosion, anchorage degradation, and long-term effects related to the viscosity of steel and concrete. The corrosion of steel cables is an electrochemical process triggered by voids in the grout, which trap water and moisture. Over time, corrosion leads to section loss; decrease in the overall tension within the cable; and, ultimately, strand breakage. Anchorage degradation manifests through various mechanisms. Corrosion is a major concern, often initiated by moisture and contaminants penetrating the anchorage assembly and attacking the wedges and the steel strands within. High bearing stresses at the anchorages can induce cracking in the surrounding concrete, creating pathways for water and aggressive substances to reach the tendons and anchorages, further accelerating degradation. Finally, issues during the initial tensioning process can lead to slippage or improper seating of strands at the anchorage, resulting in an initial loss of prestress. Also long-term phenomena, such as shrinkage and creep in the concrete and relaxation in the steel, contribute significantly to the reduction in prestressing efficiency. Creep and shrinkage of the concrete depend on multiple factors, including ambient humidity, dimensions of the element, concrete composition, and curing conditions. Creep is further influenced by the maturity of the concrete at the time of first loading and the duration and magnitude of the applied load. Steel relaxation leads to a gradual loss of stress in the tendons over time after initial tensioning. While long-term losses are typically considered in the design, predictive models may sometimes prove inaccurate in practical applications due to the complexity of such effects, e.g., reference [4]. Moreover, estimating only long-term tension losses is not sufficient to assess the residual prestressing of an in-service bridge. Structural degradation over its service life can lead to additional, unforeseen tension losses.