Application of the reliability theory to the assessment of the corrosion risk due to carbonation

Atmospheric carbonation is one of the most significant degradation factors in the durability of reinforced concrete structures, since its consequences on the corrosion of steel rebars are disastrous. Due to the random nature of physically- and chemically-based properties of concrete (concerning the carbonation phenomenon) and given the uncertainties involved with the cover thickness and environmental factors, it is necessary to match deterministic carbonation models with probabilistic approaches in order to make a relevant prediction. The reliability theory provides interesting features as a decision-making framework for the optimization (serviceability limit state design) of concrete structures. The Papadakis' and Bakker's carbonation models are studied in this paper through a reliability analysis. The first model predicts the formation of a sharp carbonation front which evolves as a square root of time law. The Bakker's model improves the Papadakis' approach by taking into account the influence of wetting and drying cycles. A performance function is introduced to express the margin between the carbonation depth and the concrete cover. The serviceability limit state is reached when this margin vanishes. The result of the durability assessment is a limit state-based failure probability which is assessed with the Hasofer-Lind reliability index determined using the Rackwitz-Fiessler algorithm. In a first stage, a sensitivity analysis is performed in order to identify and quantify the most sensitive variables to be considered as probabilistic while some others can be treated as deterministic. In a second stage, a reliability analysis is carried out, as an illustration, to assess the residual service life of a 16-year old reinforced concrete structure. Finally, this study focuses on the use of field data (e.g. a depth of carbonation at a given time) for updating the reliability analysis according to a Bayesian approach.