Analytical evaluation of cable corrosion effects on the residual prestressing coactive state in post-tensioned concrete elements

The paper provides an original analytical evaluation of the effects of cable corrosion on the prestressing coactive state in post-tensioned concrete elements (namely, beams and stays in prestressed bridges), in which steel cables are made adherent through subsequent cast-in-situ grouting. The corrosion is assumed to be homogeneously distributed over a finite portion of the sheathing duct characterized by lack of mortar injection, and modeled as a uniform cross-section loss. The study analytically demonstrates that the reduction of the cross-sectional area of the prestressing steel cables due to corrosion generates both (I) a loss of the prestressing force and (II) a stress redistribution within the residual cross-sectional area of the cables, which are limited to the zone lacking grouting. Ready-to-use closed-form mathematical expressions for these two effects are derived allowing direct quantification of the corrosion-induced variation of the prestressing state, for the two cases of concentric and eccentric tendons, and validated against experimental results available in the scientific literature. A numerical application to three typical existing bridge elements is also provided. The fundamental result is that the loss of the prestressing force is approximately equal to the cross-section loss, while the stress redistribution is comparatively small, providing a cable stress increase below 5% for bridge decks and below 25% for stays, even for highly corroded cables.