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To attempt to represent concrete properly as a composite material, one must consider at least three phases: matrix, aggregates, and the interfacial transition zone (ITZ), a thin shell of altered matrix material surrounding each aggregate grain. Assigning each of these phases a different transport parameter, diffusivity or conductivity, results in a complicated composite transport problem. Random walk simulations can be performed for this system, but are time-consuming, hence the anticipated usefulness of effective medium theory. But, previous applications of differential effective medium theory were plagued by the need to use an arbitrary parameter chosen to fit the simulation results. A new kind of differential effective medium theory presented in this paper removes this need for a fitting parameter. An aggregate particle with a surrounding ITZ is mapped onto an effective particle of uniform conductivity, which is then treated in usual differential effective medium theory. The results of this theory compare favorably to random walk simulations for multi-scale concrete models with varying aggregate size distributions.