One should note that the aggregate sieve analyses given in Table 1 involve extremal values of recommended concrete mixtures [4,30], while the sieve analysis given in Table 3 is from the middle of the range recomended for the aggregate size distributions [16,30]. It is comforting to note that the D-EMT seems to work somewhat better for the usual concrete mixture designs (Table 3), rather than for unusual values (Table 1).
As was stated in the Introduction, concrete is actually even more complicated than the three-phase system discussed in this paper, for several reasons. First, aggregates are only approximately spherical. Second, the ITZ has a gradient of properties extending out to its width, and is not a uniform property shell . And third, concrete is an interactive composite, where the amount of aggregates affects the properties of the matrix [15,9]. For these reasons, a multi-scale approach has been taken to model concrete diffusivity/conductivity. In part of this model, the actual ITZ microstructure near an aggregate, as well as the global arrangement of ITZ regions, is used both to map the ITZ gradient into a uniform property region, and to derive an accurate value of the ratio of ITZ to bulk matrix properties. By doing this multi-scale procedure carefully, the best value of the ITZ thickness and conductivity are used. It is known that the ITZ thickness and conductivity, when mapping onto a uniform property shell, are not independent of each other .
In the multi-scale model, the conductivity of the resulting three-phase effective microstructure was computed using random walk simulations. The reason for developing an improved D-EMT was to replace these rather lengthy random walk simulations [15,4]. The random walk part is CPU time-intensive, and a fairly simple formula, or algorithm, which could reproduce simulation results with an uncertainty of 10 % to 20 % for the usual range of concrete mixtures studied, would be very useful. The new D-EMT derived in this paper seems to fit the requirements (uncertainly of usually 10 % or better), and should be able to serve as a routine replacement for the random walk simulations in the multi-scale microstructural model for predicting concrete diffusivity.
EMT is an uncontrolled approximation, in the following sense: There is no parameter in EMT that tells the user how much error to expect. Many times EMT works quite well; sometimes it fails miserably. This paper showed that the new form of D-EMT worked quite well for the class of problems considered. If a new form of concrete is considered, with a quite different kind of aggregate particles, then it is conceivable that the errors incurred using the D-EMT may be significantly larger. It will be necessary to use random walk simulations to periodically check the performance of the D-EMT equation for new and significantly different concrete formulations. However, the aggregates and their size distributions in most concretes resemble those considered here, so the D-EMT is expected to work well for most concrete materials encountered in current practice.