For spherical aggregates, of any size distribution, an analytical formula has been presented, taken from the statistical geometry of composites literature, that very accurately gives the total volume that lies within a distance r of an aggregate surface. This can be used to predict the ITZ volume in concrete. For a spherical aggregate, surrounded by a radially symmetric gradient in properties, it has been shown how to exactly solve for the effective concrete property in the dilute limit, where there is only less than or equal to about 5% by volume of aggregate. The properties solved for are electrical conductivity and ionic diffusivity, linear elastic moduli, and linear thermal and moisture-driven expansion and shrinkage. Both of these results should be of use to experimentalists and modellers in the field of cement-based materials.
The authors wish to acknowledge support from the National Science Foundation Science and Technology Center for Advanced Cement-Based Materials, and from the NIST High-Performance Construction Materials and Systems Program.