Probabilistic evaluation of time to corrosion initiation in RC elements exposed to chlorides: 2-D modelling

Corrosion of reinforcing steel is one of the main causes of deterioration of reinforced concrete (RC) bridges. The deterioration may propagate relatively fast and initially manifests itself in cracking of the concrete cover that affects bridge serviceability. Usually, the time between corrosion initiation and the serviceability failure caused by cracking is shorter than the time required for the corrosion initiation. Therefore, the time to corrosion initiation represents a major parameter controlling deterioration of RC bridges exposed to chlorides. The time to corrosion initiation depends on the ingress of chloride ions into concrete, which is a complex process involving such transport mechanisms as ionic diffusion and convection. The process is affected by a large number of factors including the properties of concrete (i.e., its composition and microstructure), the degree of concrete pore saturation, and the exposure conditions. Another important factor is chloride binding (i.e., the interaction of chloride ions with the cement past hydration products) since only free chloride ions can penetrate into concrete. Since chloride ions are charged particles their ingress into concrete will depend also on their achieved concentration and on the content of other ions presented in the concrete pore solution. A number of these factors are inter- and time- and temperature-dependent. Models of different level of sophistication have been proposed to describe the chloride ingress into concrete. The most sophisticated models consider it as a process involving ionic diffusion and convection, which are affected by heat transfer. More simple but still quite complex models take into account diffusion, convection, and heat transfer but neglect the ionic nature of diffusion (i.e., that chloride ions are charged particles) (e.g., Saetta et al. 1993, Martin-Perez et al. 2001, Meijers et al. 2005). However, in practice, chloride ingress is still usually modelled as a pure diffusion process described by Fick's second law (e.g., DuraCrete 2000). Modelling such a complex process as chloride ingress into concrete entails major uncertainty due to inevitable simplifications made to develop predictive models as well as due to inherent variability of concrete properties and environmental conditions. A number of studies accounting for various sources of uncertainty and considering the problem of chloride ingress and corrosion initiation in RC structures in probabilistic terms have been undertaken. In most of these studies chloride ingress was modelled as a one-dimensional (1-D) diffusion process (e.g., Engelund & Sørensen 1998, DuraCrete 2000, Vu & Stewart 2000, Kong et al. 2002). While for such elements like RC decks or walls 1-D modelling of chloride ingress is certainly justified, for RC beams and columns this may result in overestimation of the time to corrosion initiation, especially for reinforcing bars in corners of the elements. This was demonstrated by Frier & Sørensen (2005), who evaluated the probability distribution of time to corrosion initiation for a RC bridge pier in a marine environment modelling the chloride ingress as a 2-D pure diffusion process (i.e., chloride binding and convection were not considered). In the present paper a 2-D model for chloride ingress into concrete, which accounts for both diffusion and convection, is employed. Initially, a 1-D deterministic analysis is carried out to examine the influence of chloride binding isotherms (Langmuir and Freundlich) on the evaluation of chloride penetration into concrete. According to results of the analysis this influence is insignificant and further, in probabilistic analysis, the Langmuir isotherm is used since the use of the Freundlich isotherm creates numerical difficulties when values of chloride concentration are very low. The analysis has been carried out for two different boundary conditions - timevarying ambient relative humidity and constant relative humidity, whose value is equal to the average value of the time-varying one. The results show that replacing time-varying humidity by its average value leads to underestimation of chlorides inside the concrete. This indicates the importance of taking into account the effect of convection on chloride ingress. A probabilistic analysis is then performed to estimate the probability of corrosion initiation in RC wall (1-D analysis) and column (2-D analysis) with the same thickness of the concrete cover. Uncertainties in concrete properties, models describing moisture and chloride diffusion, the concrete cover thickness, and the threshold chloride concentration are taken into account. Spatial variability of a number of parameters (such as the humidity and chloride diffusion coefficients, the surface chloride concentration, the concrete cover thickness) is not considered in this study as well as possible correlation between some of them (e.g., between the humidity and chloride diffusion coefficients). According to results of the analysis the probability of corrosion initiation in the corner reinforcing bars of the RC column is much higher than in reinforcing bars in the middle part of the RC wall. This demonstrates the importance of 2-D modelling for correct prediction of corrosion initiation in such RC elements as beams and columns.