A three-phase model of the elastic and shrinkage properties of mortar

Mortar and concrete are composite materials with overall properties that are influenced by the arrangement and characteristics of each constituent in the microstructure. Elastic shrinkage, like other properties of mortar and concrete, must be described by a three-phase model: aggregate, bulk cement paste, and interfacial transition zone (ITZ) cement paste. A simple two-dimensional digital-image-based model of a mortar is developed based on the hard core/soft shell percolation model. Specific attention is given to the properties of the ITZ between cement past and aggregate. The elastic shrinkage properties of this model are computed numerically, using a specialized finite-element technique. The effects of varying the elastic moduli and shrinkage properties of the ITZ and bulk cement paste are examined in parameter studies, both analytically, for low aggregate content, and numerically, for arbitrary aggregate content. Special attention is given to the effect that the topology of the ITZ has on overall shrinkage. A comparison is made between model predictions and the limited available experimental results (0.35 w/c, 65% hydration), assuming an ITZ width of 20 mu m. Based on this comparison, this paper introduces the prediction that the Young's modulus of the ITZ is one third to one half of the modulus for bulk cement paste and that the unrestrained shrinkage of the ITZ material is close to the shrinkage of bulk cement paste when both are averaged over a 20-mu m ITZ. This finding is supported by further analysis of a three-dimensional microstructural model of cement paste.