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# Discussion of Future Work

An important goal of future work, based on the techniques and results of this paper, will be to develop a general equation for the conductivity/diffusivity of concrete. The inputs to such an equation would be: 1) the chemistry, water:cement ratio, and degree of hydration of the cement, in order to determine the bulk matrix conductivity, 2) interfacial zone characteristics, 3) aggregate size distribution and volume fraction, and 4) computations like those in this paper. With such an equation, the conductivity/diffusivity of a concrete could be determined with good accuracy at the mix design stage, based on fundamental microstructural parameters.

There are two (at least) possible complications in determining the conductivity of mortar or concrete in such a general equation that is not directly addressed by the work covered in this paper. The first is the following. When a fixed water:cement ratio mortar is prepared, since the interfacial zone cement paste has less cement and therefore more porosity than would be expected for this water:cement ratio, that implies that the bulk cement paste will have slightly more cement and therefore a lower water:cement ratio than the nominal value. The results of Ref. [15] imply that a typical mortar or concrete has one quarter to one third of its cement paste volume in the interfacial region, where the interfacial region is taken to be about 20 micrometers, the region where most of the larger pores reside. This value implies that there could be a significant effect on the water:cement ratio of the bulk cement paste. This effect would have to be allowed for in a general equation (see Ref. [52,53]).

The second possible complication is that some kind of assumption about the uniformity of curing must be made, since the local electrical conductivity in a concrete will depend on the local degree of hydration. Water loss at surfaces and self-dessication, among other factors, will effect the uniformity of curing in a typical piece of concrete. A general equation for conductivity, as described above, must be able to be applied to concrete whose degree of hydration will probably not be uniform.

The same kind of model discussed in this paper can also be used to help understand the role of the interfacial zone on the elastic properties of mortar and concrete. The effect of interfacial zone cement paste on elastic moduli has already been experimentally studied [17]. Holding the aggregate in a mortar at fixed volume fraction, but varying the average aggregate size and thereby the surface area produced significantly lower elastic moduli [17]. Increasing the aggregate surface area at fixed aggregate volume fraction would certainly increase the volume fraction of interfacial zone cement paste at the expense of bulk cement paste, so that we may conclude that the elastic moduli of interfacial zone cement paste are smaller than that of bulk cement paste, in keeping with a higher interfacial zone porosity. Other recent analysis of elastic moduli led to this same conclusion [18]. It should be possible to carry out computations similar to those described in this paper for the elastic moduli of mortars, and quantitatively understand the effect of the interfacial zone phase on the composite elastic moduli. Work on 2-D digital-image-based models of mortars, which should give at least qualitative insight into real material behavior at arbitrary sand volume fractions, is currently being carried out on elastic moduli and elastic drying shrinkage [54]. The dilute limit for the elastic moduli of coated spheres has only very recently been derived [55,56], and will make possible analyses of dilute limit experimental measurements of the elastic moduli. These dilute limit moduli measurements will provide direct measurements of interfacial zone elastic properties.

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