PSI - Issue 62

Simone Celati et al. / Procedia Structural Integrity 62 (2024) 361–368 Author name / Structural Integrity Procedia 00 (2019) 000 – 000 The time chlorides need to reach the wires’ surface ( ) is evaluated according to the next equation: ( ) = ∙ 4 1 , ( ) 2 −1 (1− ) (1) In Eq. (1) represent the model uncertainty for the chlorides ’ diffusion model, is the concrete cover [mm] , is the critical chloride concentration [wt.-%/c], and is the chloride content at concrete surface [wt.-%/c]. The apparent chloride diffusion coefficient ሺ , ሻ and the method for its evaluation are defined in Schießl et al. (2006). The distributions of the input variables for the evaluation of Eq. (1) are reported in Table 1. 2.1.2. Carbonation model During the carbonation process, carbon dioxide (CO 2 ) reacts with the calcium hydroxide in the concrete, resulting in a decrease in the overall pH to levels around 9/10 (Melchers and Chaves (2018)). Typically, models based on the diffusion process of CO 2 are employed to evaluate the time it takes for the carbonation front to reach the steel surface. However, in this paper, the empirical model proposed by Silva et al. (2014) is adopted. This model involves a statistical regression to predict the time for carbonation to occur. The authors have developed a piecewise linear model that effectively captures the variability observed in the collected data (Alexander and Beushausen (2019)). The following equations are employed to evaluate the time to carbonation ( ): = 2 2 ≤ 70% ; = 2 2 > 70% (2) Eq. (3) depends on the concrete cover ( ) [mm] and the relative humidity ( ) [%]. and can be evaluated through: = 1 ∙ [ 2 ]− 2 ∙ − 3 ∙ + 4 ; = 5 ∙ [ 2 ]− 6 ∙ − 7 ∙ + 8 (3) The carbonation parameters depend on both by the environment and the concrete characteristics. In particular, [ 2 ] represents the CO 2 content [%] variable and account for the Exposure class; ≔ {1 for 1; 2 for 3; 3 for 4} . Concrete characteristics are considered through the clinker content, [kg/m 3 ] and concrete compressive strength [MPa]. The distribution of each variable is shown in Table 1. Regression parameters ( ) are provided with their mean value and standard deviation. Thus, they are modelled as hyperparameters, to account for the model uncertainties. Their values are reported by Silva et al. (2014). The time to active corrosion ( ) is logically modelled as a parallel system. Its components are the chlorides diffusion process and the carbonation process, each developing independently. Hence, is defined as the maximum between and . The over-time propagation of corrosion is then evaluated based on the computed . ( ) = { ( ); } (4) 2.2. Propagation phase modelling The transition from the inactive to the active corrosion phase is enabled by the accomplishment of the thermodynamic conditions: critical concentration of chlorides at the wires and low alkalinity surroundings. The corrosion process not only leads to a reduction in the steel's cross-sectional area but can also result in a decrease in ductility and rupture strength. However, this study specifically focuses on pitting corrosion and exclusively considers the reduction in cross-sectional area, as the failure mechanism considered is yielding (Darmawan and Stewart (2006)). To quantify the progression of pitting corrosion over time and the maximum depth of pits (a) over time, the probabilistic model proposed by Darmawan and Stewart (2007) is employed (Eq. 5). Within this model, the maximum pit depth follows a Gumbel distribution with parameters 1/ and . The parameter of the Eq. (5) represents the ratio of increase in the volume of corrosion products when actual exposition periods are considered. The three parameters 363 3