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The exercise in Section 4.2 should in no way be considered to be a validation of the computer model presented here. It will be necessary for a complete set of experimental measurements to be obtained, including measurement of the degree of hydration of the concrete at the age at which its chloride diffusivity is measured, before Eqn. 4 can be applied with confidence. However, the overall results are encouraging enough to suggest that the trends indicated by the regression equation are indeed likely to be observed experimentally. Certainly, the computer study has suggested that the three key variables necessary to predict diffusivity are w/c ratio, degree of hydration, and volume fraction of aggregates. In addition, the influence of interfacial transition zone thickness and air content may warrant further experimental study. Hopefully, the experimental counterpart of the computer experiment summarized in Table 2 will be constructed in the not-too-distant future. This will allow the adjustment of the coefficients in Eqn. 4 to values which best represent field concrete.
The assumption of spherical-shaped aggregates is probably not a critical parameter for the following reason. While computer simulations have shown that ellipsoidal-shaped aggregates can significantly increase the volume of ITZ cement paste in a concrete [36], the present study has shown that this effect is offset by the concurrent reduction in the w/c ratio of the bulk cement paste. Thus, while aggregate surface area and VITZ were strongly influenced by the coarse and fine aggregate particle size distributions, these variables had practically no influence on the final resultant diffusivities of the model concretes.
It should also be pointed out that all of the results generated in this study are for a portland cement concrete and do not consider the addition of pozzolans such as silica fume and fly ash. Previous computer simulation [37] and experimental studies [38,39] have clearly shown that these pozzolans can greatly modify the interfacial transition zone microstructure in concrete. In addition, most diffusivity studies indicate that these pozzolanic materials also have a marked influence on the diffusion properties of concretes, and thus, their presence would almost certainly warrant the addition of another term (perhaps the ratio of pozzolan addition to cement, s/c) to the developed diffusivity equation. The presence of these materials also complicates the measurement of degree of hydration by non-evaporable water content [40,41], so that heat release measurements or a combination of analytical techniques [42] may be needed to gauge the progress of the hydration and pozzolanic reactions.
Once validated, Eqn. 4 could be incorporated into a durability-based design specification to predict the expected service life of a reinforced concrete exposed to an external chloride environment [1]. Current mixture proportioning practices generally consider only slump and compressive strength as performance parameters, with the additional specification of air entrainment, when necessary. Using the models developed here should allow the extension of these practices to also consider a priori the durability of the concrete in a chloride environment, perhaps as a supplement to the recently proposed performance criteria for highway concretes [43].
In summary, a computer experiment has been conducted to investigate the effects of mix parameters and curing on the chloride ion diffusivity of concrete. A set of multi-scale microstructural models has been used to quantitatively predict chloride diffusivity given the complete mixture proportions and projected degree of hydration of a concrete. Via this analysis, w/c ratio, degree of hydration, and volume fraction of aggregates have been identified as the three major variables affecting diffusion coefficients. An equation has been developed to quantitatively predict diffusion coefficients based on these three variables. While few data sets currently exist in the literature where the three key variables have been quantified and diffusion coefficients measured, previously developed equations and data where age is available as opposed to degree of hydration both provide reasonable agreement with the newly developed equation. Further simulations have been conducted to provide some insights into the optimum sampling procedure for determining the degree of hydration of a concrete sample and the extent of the surface layer effect. It is strongly recommended that future experimental studies of chloride ion diffusivity also include measurements of degree of hydration and quantitative reporting of the employed mixture proportions so that the regression coefficients determined in this computer study may be modified to best represent field concrete.