Uncertainty Impact of the Effective Diffusion Coefficient on the Concrete Chemical Degradation

Article history Received: 25-01-2015 Revised: 31-03-2015 Accepted: 28-04-2015 Abstract: Reinforced concrete is the construction material widely used in civil engineering. However, knowledge of its long-term performance and the uncertain impact of the environment on his behaviour make it difficult to accurate assessment of the durability of structures with time. When a structure is put into service, it is likely to damage, which origin can be physical, mechanical or chemical. Chemical factors are frequently the most important, since the concrete can be degraded by reaction (dissolution, swelling) of the concrete constituents. In this paper, a probabilistic formulation is applied to carbonation phenomenon and statistics regarding carbonation time required for the carbonation depth reaches the reinforcement concrete are investigated by performing a parametric analysis which integrates the influence of variation of porosity and effective diffusion coefficient of carbonic gas.


Introduction
Carbon dioxide and chlorides are the most important buildings aggressive agents which may be exposed. They are responsible for one of the main mechanisms of degradation of existing structures.
These phenomena are respectively identified by the corrosion due to penetration of chlorides or corrosion by carbonation The speed of concrete carbonation depends mainly on the dioxide carbon penetration inside the cement matrix. Indeed, the diffusion of carbon dioxide through the porous structure of concrete is determined by the Water to cement ratio and porosity. Badaoui et al. (2012;Castellote et al., 2001) and are identified in italic type, within parentheses.

Concrete Carbonation Theory
Carbonation originates from the low amount of carbon dioxide in the air; it reflects the action of CO 2 diffusion within the pores of the concrete and reactions with hydrates. When the portlandite is consumed, the pH drops to a value below 9, thus initiating the corrosion of steels (Ang and Tang, 2005).
Carbonation has a beneficial aspect of cementitious materials; crystals of calcite CaCO 3 that form from of the hydrates can increase the resistance of concrete to the diffusion of aggressive agents.
The Ca(OH) 2 reacts with carbon dioxide to form calcite, according to the following reactions (Castellote et al., 2001) Portlandite carbonation is overall accompanied by water release of structure

Statistical Investigation of Concrete Carbonation
In this article, the statistics corresponding the time required for the carbonation depth reach the steel are studied, by performing a parametric study that incorporates the influence of the uncertainty of the effective diffusion coefficient of carbon dioxide and the porosity of the paste of the carbonated concrete on time carbonation, taking a log-normal distribution.
To evolve towards the probabilistic approach, we used the Duracrete deterministic model calculating the carbonation time T1 according to following equation (Duracrete. 2000) Equation 4: a is the quantity of material carbonated given by Equation 5 RH abs = 75%, RH lab = 65%, k e = 0.69. k C is a parameter taking account of the conditions of curing compound concrete, given by Equation 7: Where: t c = The duration of cure, t c = 1 day and k C = 3 D eff = The effective coefficient of diffusion of CO 2 Equation 8: ε c is the porosity of the paste of the carbonated concrete Cs is the CO 2 pressure on the surface of the concrete, Cs = 6.1 kg/m 3 T the expiry considers (year), t 0 is the reference period "28 days"

Study Materials
The characteristics of studied concrete and cement chemical composition are shown in For the composition of concrete proposed, the effective coefficient of diffusion can be estimated at D eff = 3.92 10 −12 m 2 /s, with a value of porosity ε c = 0.45, α h = 80%, β ch = 85% and a = 65.2 kg/m 3 (Badaoui et al., 2012).
It is considered that this concrete is located inside of a building where the humidity of the ambient air is medium or high. It is therefore subject to the exposure class XC3, the numerical values for the composition parameters are identical to those of the class XF1 (Norm NA 16002, 2004;Norm NA 442, 2006).

Numerical Implementation of the Simulations
One has to solve a conventional random problem for a large number of input parameters by using Monte Carlo simulations (Rubinstein and Kroese, 1981).
The mean value of the effective coefficient of diffusion is D eff = 3.92 10 −12 m 2 /s and the coefficient of variation Cv Deff varies between 0 and 0.1.
For the porosity ε c , the mean value is µ εc = 0.45 and its coefficient of variation Cv εc also varies between 0 and 0.1.
In order to determine the time carbonation, the Chi-Square goodness of fit test is used to evaluate the fit of the assumed carbonation parameters probability distribution and the shape of the corresponding histograms suggests a log-normal distribution, which is adopted in this study is shown in Fig. 1 The behavior of the coefficient of variation of carbonation time versus the number of realizations is also investigated and shown in Fig. 2.
The convergence of the final settlement coefficient of variation is observed for a number of realizations N samp around 300, this number is chosen equal to 10000.  We remark that when Cv Deff and Cv εc increase, the mean and the standard deviation augment significantly; indicating that the diffusion of CO 2 from the outside to the heart of the concrete requires a longer time.

Results and Discussion
The confidence intervals are important indicating that the variability of the D eff affects the carbonation time.
The SDT value of the carbonation time increases which indicates that the uncertainty on the εc causes a delay in the carbonation process.
Reacting the hydrate of concrete with carbon dioxide leads to the production of water.
Greater the quantity of carbon dioxide released into the pores is larger, the amount of water formed during carbonation is important, this formation will also affect the process and increase the time of carbonation.

Conclusion
Carbonation of the concrete has an impact on the effective diffusion coefficient; this coefficient is decreased after carbonation. The interaction between the ions of carbon dioxide and the Calcium Silicate Hydrate surface (C-S-H) negatively charged form an electric double layer on the pores surface of the and slows the CO 2 diffusion. Indeed, the time required for the carbonation depth reaches the reinforcement concrete depends on the effective diffusion coefficient of CO 2 , "D eff ", which is linearly related to water to cement ratio and relative humidity.