1. Introduction

Carbonation is a phenomenon generated by the interaction between the concrete and the environment through the reaction of carbon dioxide (CO₂) from the air with calcium hydroxide (Ca(OH)₂), a cement hydration product. The reaction provides high alkalinity in the concrete interstitial solution, forming calcium carbonate (CaCO₃). The hydrated Portland cement of concrete has an alkaline pH (12-13), mainly due to Ca(OH)₂. However, the formation of CaCO₃ leads to a pH reduction that can reach 9.4 and the consequent CaCO₃ precipitation to the concrete surface. The cement matrix acidification causes steel reinforcement depassivation, making it susceptible to corrosion, the primary pathological manifestation in reinforced concrete structures (^{Peter et. al., 2008}; ^{Chen, 2019}).

The main factors that affect carbonation are temperature, relative humidity (RH), CO₂ concentration, surface coating, water/cement ratio, cement type, cement and water content, curing conditions, cement matrix degree of hydration, concrete permeability, and pore network (^{Ribeiro et. al., 2018}; ^{Li et. al., 2018}; ^{Song; Kwon, 2007}; Houst; Wittmann, 2002). The carbonation occurrence is low at early ages (up to 28 days, generally). However, with more prolonged CO₂-saturated environment exposure, the carbonation process becomes more evident in the concrete structure (^{RIBEIRO et. al., 2018}).

According to NBR 15575-1: Edificações habitacionais - Desempenho Parte 1 (translation: NBR 15575-1: Residential Buildings - Performance Part 1) (^{ABNT, 2013}), Service Life (SL) is the period in which a building and/or its systems provide the activities for which they were designed and built, meeting the performance levels established in this standard. Determining the service life of a carbonated concrete structure encompasses carbonation depth measurements and the use of mathematical models to determine the carbonation front speed affecting the structure (^{Possan, 2010}).

The models to estimate the carbonation depth assume that the concrete is homogeneous, which does not occur in real structures since concrete consistency depends on the compaction and curing time and the relative humidity (RH) conditions of the environment. However, this assumption ensures that the properties determining the carbonation rate are similar at all concrete depths, simplifying model assumptions (^{Köliö et. al., 2014}).

Due to the various factors discussed in the previous paragraphs, no model faithfully represents concrete carbonation. Therefore, choosing which model better represents a specific concrete structure depends on its characteristics and the variables considered in the model.

Thus, this paper analyzes the variability in SL predictions through four models that estimate the concrete carbonation depth based on a database of tests performed under natural aging and exposure conditions found in the literature. A sensibility analysis was performed to identify the parameters that most influence the variations found between the values estimated by the models and those obtained experimentally.

The primary purpose of this study is to contribute to the technical-scientific community on the subject of pathological manifestations, especially in the definition of models that can better estimate the carbonation front, helping in decision-making processes related to durability and SL of reinforced concrete structures in the design stage.

2. Method

The method comprehends i) Selecting mathematical models for predicting concrete carbonation depth; ii) Creating a concrete carbonation database; iii) Comparing the concrete carbonation models; iv) Sensitivity analysis to understand carbonation depth predictions, according to the variables considered by each concrete carbonation model.

3. Results and discussion

Figure 1 (a) shows a tendency for the models to generate different results from those observed in the experiments. These observations are more explicit for ^{Bob and Affana (1993}) model, which overestimated, and ^{Ho and Lewis (1987}) model, which underestimated the carbonation depths.

Data presented in Figure 1 (b) allows a comparison of the carbonation depths estimated by each model, relative to the real carbonation depths. The dashed red line represents equivalent results for the estimated and real values, obtained experimentally: points above the dashed line represent values that were overestimated by the model, while values under the dashed line represent underestimated estimates for carbonation depth. It can be observed that the ^{Ho and Lewis (1987}) model underestimates carbonation depths, while the ^{Bob and Affana (1993}) model overestimates them. The carbonation data estimated by ^{Possan (2010}) and ^{Ekolu (2018}) models, on the other hand, are closer to the dashed line, but still underestimate the carbonation depth.

Figure 1 Errors for carbonation depths as a function of time (a) and comparison between estimated and experimentally obtained carbonation depths (b). 

Figure 2 (a) shows the sensitivity analysis results for the models regarding the compressive strength, considering values between 20 and 40 MPa, in the natural carbonation process during 50 years. The figure shows carbonation depths and SL with the minimum concrete cover of 25 mm stipulated by NBR 6118 (2014) for reinforced concrete structures in urban environments (moderate aggressiveness, class II).

In all models of scenario A, the increase in concrete compressive strength results in lower carbonation depths. This behavior is consistent with that predicted in the literature since lower w/c ratios reduce the matrix porosity and carbonation depths, determining concrete strength (^{TUUTTI, 1982}; ^{HO and LEWIS, 1987}; ^{KULAKOWSKI, 2002}).

The reduction in carbonation depth caused by increasing the compressive strength of concrete from 20 to 40 MPa, considering results for the same period, is approximately 68.55%, 70.3%, 49.97%, and 50% for the models of ^{Possan (2010}), ^{Ekolu (2018}), ^{Ho and Lewis (1987}), ^{Bob and Affana (1993}), respectively. These values are obtained by fixing the formula variables of each method and varying the compressive strength. The compressive strength factor exerts more influence on the carbonation depths estimated by the models of Ho and Lewis (1987) and Bob and Affana (1993). In addition, the Possan (2010) and Bob and Affana (1993) models predict that 20 MPa concrete would not be able to meet an SL of 50 years with a concrete cover of 25 mm under the conditions stipulated for Scenario A. For the other models, 20 MPa concrete would already meet this requirement.

Figure 2 Service life and carbonation depth in relation to compressive strength - Scenario A - (a), carbon dioxide in the environment - Scenario B - (b), relative humidity of 50 and 70% - Scenario C - (c) and relative humidity of 30 and 90% - Scenario C - (d). 

Figure 2 (b) shows the sensitivity regarding the CO₂ concentration. The CO₂ concentrations were delimited based on the values obtained from the database and definitions presented in the publication of ^{Possan (2010}). Concentrations of 0.03% and 0.07% were then stipulated in the natural carbonation process during the 50 years. ^{Pires (2016}) presents CO₂ concentration as one of the intervening factors in the carbonation process of concrete, and ^{Cadore (2008}) suggests that the carbonation front speed is directly related to CO₂ concentration, i.e., the carbonation speed increases by increasing CO₂ concentration.

Note in Figure 2 (b) that although carbonation increases by increasing CO₂ levels, this growth is lower in the ^{Possan (2010}) and ^{Ho and Lewis (1987}) models. The carbonation depth increase caused by the CO₂ concentration growth is approximately 0.17%, 2.89%, 53.84%, and 100%, on average, for Possan (2010), ^{Ekolu (2018}), Ho and Lewis (1987), ^{Bob and Affana (1993}) models, respectively. This result indicates that the CO₂ factor of the Possan (2010) and Ekolu (2018) models exert less influence on the estimated carbonation depths for Scenario B compared to the other mentioned models. The Bob and Affana (1993) model suggests that in environments with 0.07% CO₂, concrete would not meet a 50-year SL with a 25 mm concrete cover under the conditions stipulated for Scenario B.

Figure 2 (c) illustrates the sensitivity to the ambient RH in the natural carbonation process for 50 years. The selected RH are extreme values found in the literature for the natural carbonation processes (^{Pauletti, 2009}; ^{Tasca, 2012}; ^{Rozière, 2009}; ^{Nardino, 2019}).

For scenario C, the increase of ambient RH reduces the carbonation depth for ^{Possan (2010}) and ^{Bob and Affana (1993}) models. However, while Possan (2010) model presents a 7.16% decrease on average, the Bob and Affana (1993) model results in a 30% decrease, which suggests that Bob and Affana (1993) model is more sensitive to this variable. For ^{Ekolu (2018}) model the carbonation depth increases by 8.44% on average. On the other hand, for Ho and Lewis (1987) model, the carbonation depths remain unchanged with the 20% increment in RH, which can be explained by the fact that the RH is not an input data, and therefore, the model is not sensitive to this factor.

Since RH is a relevant factor for the carbonation process, it should be accounted for, directly or indirectly, in SL prediction models by natural carbonation processes. The water present in the pores is responsible for dissolving the CO₂, forming carbonic acid (H₂CO₃) and Ca(OH)₂, resulting in CaCO₃ (^{Pauletti, 2009}). The volume and composition of pore water are influenced by factors such as the w/c ratio, curing time, temperature, and even the RH of the environment (^{Vieira et al., 2016}).

The literature also indicates that excessive or low RH environments are not conducive to the natural carbonation process. In the first situation, the concrete pores would be filled with water, hindering the penetration of CO₂ for H₂CO₃ formation. On the other hand, in low RH conditions, the water in the concrete pores would be insufficient to generate more accelerated natural carbonation rates since water is required to generate H₂CO₃ (^{Félix et al., 2017}; ^{POSSAN et al., 2017}; ^{Elsalamawy et al., 2019}; ^{Dierfeld et al., 2020}).

Considering Scenario C, results of ^{Possan (2010}) and ^{Bob and Affana (1993}) show a reduction in carbonation depths due to the RH increase from 50 to 70%, which suggests that the pore saturation is predicted in these ranges of ambient RH. In contrast, the ^{Ekolu (2018}) model results suggest that these RH contents are conducive to the carbonation process. In this regard, ^{Chen et al. (2018}) observed an increase in carbonation depth with an increase in ambient RH, with a peak of about 70%. Data obtained through the Ekolu (2018) model in Scenario C follows the one suggested by these authors.

For a better understanding, ^{Possan (2010}), ^{Ekolu (2018}), and ^{Bob and Affana (1993}) models were then tested in Scenario C, considering 30% and 90% RH. The results are shown in Figure 2 (d). For the Possan (2010) method, lower carbonation depths are obtained in 30% - 90% RH range compared to 50% - 70%. While the 50-year average carbonation depths for 50% and 70% RH are 8.01 mm and 7.43 mm, respectively, for 30% and 90% RH these values change for 4.10 and 3.28 mm, respectively. This indicates that the model is sensitive to both excess and low RH conditions.

Also, in ^{Ekolu (2018}) model, the 30% RH generates negative values, while 90% predicts significantly lower results than 50% and 70%. Thus, the model recognizes the 50% -70% RH range as the more favorable for the carbonation process. For ^{Bob and Affana (1993}) model, on the other hand, 30% RH results in carbonation depths equivalent to those estimated for 50% RH, since the model considers RH ranges instead of individual values. As the same coefficient (1.0) is used for RH equal to or below 60%, the model is not sensitive to RH below 60%. The same happens for RH values equal to or greater than 90%, where the coefficient 0.3 is adopted. However, the model considers that for RH equal to or below 60% the carbonation depth is higher than for RH equal to or greater than 90%. For 30% an average carbonation of 28.68 mm depth was obtained for 50 years, while for 90% the value was 8.6 mm. Figure 2 (c) also indicates that according to Bob and Affana model (1993), concrete in environments with 50 and 70% RH would not meet a 50-year SL with a 25 mm concrete cover in the conditions stipulated for Scenario C. Furthermore, according to Bob and Affana (1993) model, concrete in environment with 30% RH, and conditions as in Scenario C, Figure 2 (d), would not meet the 50-year SL for a 25 mm concrete cover.

4. Conclusion

The main considerations that can be made based on the results discussed in this paper are:

The ^{Possan (2010}) and ^{Ekolu (2018}) models result in carbonation depths closer to those found experimentally;

The ^{Ho and Lewis (1987}) model tends to underestimate the carbonation depth;

The ^{Bob and Affana (1993}) model tends to overestimate the carbonation depth;

The ^{Ho and Lewis (1987}) and ^{Bob and Affana (1993}) models showed a more significant influence of the compressive strength on the carbonation depths;

The CO₂ concentration factor of the ^{Possan (2010}) and ^{Ekolu (2018}) models exert the slightest influence on the estimated carbonation depths for Scenario B compared to the other models;

The ^{Bob and Affana (1993}) model has the highest sensitivity to the RH variable, while the ^{Ho and Lewis (1987}) model has no data input for this variable.

The ^{Possan (2010}) and ^{Bob and Affana (1993}) models with 20 MPa concrete in Scenario A, Bob and Affana (1993) model with concrete exposed to 0.07% CO₂ in the environment in Scenario B, and Bob and Affana (1993) model with concrete exposed in 30%, 50% and 70% RH environment in Scenario C, would not be able to meet a SL of 50 years with a concrete cover of 25 mm under the stipulated conditions.

Thus, it can be seen that there is variability in the results of carbonation front estimated by the selected models compared to the real results of natural carbonation. This variability occurs to a greater or lesser extent depending on the parameters considered in the model equations. The sensitivity analysis performed with compressive strength, CO₂ concentration, and relative humidity shows that these variables significantly influence the results issued by the models and, therefore, should be considered in the equations.