The mortar was modeled as a three-phase, multiscale interactive composite similar in nature to those previously considered by Bentz and Garboczi. 37-39 A schematic of the model at the millimeter level is shown in Fig. 2. The model is considered interactive and multiscale because the volume fraction of aggregate (millimeter scale) and the thickness of the ITZ (micrometer scale) determine the final water/cement ratio of the matrix paste (micrometer scale). The median grain diameter of the cement used to make the pastes and mortars, 12 µm, was used as the thickness of the ITZ. The microstructure and properties of both the ITZ and matrix pastes are determined by a micrometer-scale microstructural model, and are used in conjunction with random-walk algorithms and differential-effective-medium theory to predict overall mortar conductivity. 37 The sand particles used in the model conformed to the particle size distribution of the sand used in the experiments and were assumed to be spherical, non-conductive, and unreactive. Similar to the experimental results, the modeled results were normalized by the conductivity of a paste with the same water/cement ratio and degree of hydration. The results are shown in Fig. 7.
Figure 7:Model mortar conductivities normalized by conductivity of a model paste (water/cement ratio = 0.4) versus volume fraction of sand.