Probabilistic models for the extent of damage in degrading reinforced concrete structures

Describing accurately damage in degrading reinforced concrete structures is of major interest in the context of durability analysis and maintenance. Due to numerous sources of uncertainty in the degradation models, a probabilistic approach is suitable. The probabilistic description of the extent of damage requires introducing random fields for modelling the spatial variability of the various parameters. In this paper, a general formulation for the spatial extent of damage is set up. This formulation allows to derive closed-form expressions for the mean value and standard deviation of the latter. Accordingly, practical computations can be carried out without discretizing the input fields. In order to check the accuracy of the proposed implementation, Monte Carlo simulation (MCS) of the extent of damage is also carried out, using an efficient random field discretization technique known as EOLE. Both approaches are compared to study the extent of rebars corrosion in a RC beam subjected to concrete carbonation. Furthermore, the Monte Carlo approach allows to compute the full probabilistic content on the extent of damage, e.g. histograms. It was shown that these histograms have a non-trivial shape, in the sense that probability spikes exist for the bound values (case of undamaged and fully damaged structures). The influence of the autocorrelation function of the various input random fields and that of their scale of fluctuation is finally studied.