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We have developed a model for interfacial transport in a class of three phase composite materials that provides a reasonable starting point for the description of mortar and concrete. Assuming that the interfacial zone has a well-defined thickness and conductivity, we have shown how its presence influences the overall conductivity of the composite material. Although the aggregate size distribution used in our numerical calculations was typical of a mortar the same general behavior is expected of in concrete. Since the interfacial zone cement paste occupies a significant fraction of the total cement paste phase (up to one quarter or one third) and often forms a percolating channel, the higher conductivity of this phase will cause the overall conductivity of the mortar to be significantly higher than the value that would be obtained from a simple two-phase (bulk cement paste plus aggregate) composite model. The essential parameters of our model are the ratio σs / σp , the thickness h of the interfacial zone, and the aggregate concentration, c. For small values of c we have shown that the overall conductivity can be predicted analytically, for any given sand size distribution. For larger values of c, numerical calculations on three dimensional models are required and we have shown that random walk techniques can perform this task accurately.