Analytical formulas for interfacial transition zone properties

Two analytical results are presented that are of use to concrete material technologists. Using a model of concrete in which the aggregates are spherical, but with an arbitrary size distribution, a result from statistical geometry can be used to accurately give the total interfacial transition zone (ITZ) volume for any width ITZ and any volume fraction of aggregates. In reality, the ITZ contains a gradient of porosity and therefore a gradient of properties. When only a small volume fraction of aggregates is present (called the dilute limit), it is possible to analytically solve for the effect of the ITZ on the overall concrete properties. This calculation can be carried out for the effective linear elastic moduli, linear electrical conductivity/ionic diffusivity, and linear thermal/moisture shrinkage/expansion. The details of the calculation are summarized and applications described.