Probabilistic approach to corrosion risk due to carbonation via an adaptive response surface method

A study about a probabilistic approach to corrosion risk of reinforcements embedded in concrete due to carbonation is presented. The carbonation model is based on a single non-linear diffusion equation of the carbon dioxide. A global balance relationship between the carbon dioxide partial pressure and the solid calcium content in the hydrates of concrete is used in order to express the sink term of the equation and to render the solving easily tractable in a classical finite element analysis. The performance function invoked in the probabilistic approach is the deviation between the carbonation depth, i.e. the output of the carbonation model, and the concrete cover. The Hasofer–Lind reliability index is determined by the Rackwitz–Fiessler algorithm in which the performance function is replaced by a quadratic response surface in order to reduce computational cost and gain accuracy. An adaptive building of the numerical experimental design is proposed: points efficiently positioned with respect to the design point are re-used in the new iteration of the experimental design. In the case of explicit performance functions frequently reported in the literature comparisons with surface response techniques previously developed reveal the interest of the proposed technique. A practical application to a concrete girder shows that the reliability index decreases significantly with time.