In concrete, non-uniformities in the hydration process, due to the the “wall effect” produeed by the aggregate (inclusion) particles, lead to an interfacial transition zone (ITZ) that is characterized by an increase in porosity near the inclusions. This increase in porosity may in turn be expected to cause a local decrease in the elastic moduli. We have modeled the effect of the ITZ by assuming that the elastic moduli vary smoothly in the vicinity of the inclusions, according to a power law. The exponent in the power law is chosen based on the estimated thickness of the ITZ. For this model, a closed-form expression can be found for the overall effective bulk modulus. The predicted bulk modulus of the concrete depends on known properties such as the elastic moduli of the bulk cement paste and the inclusions, the volume fraction of the inclusions, as well as on the elastic moduli at the interface. By comparing the model predictions to measured data, we can obtain estimates of the elastic moduli at the interface. Application of this inverse procedure to a set of data from the literature on mortar containing sand inclusions leads to the conclusion that the modulus at the interface is about 15–50% lower than in bulk cement paste.
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Lutz, M.P., Monteiro, P.J.M. Effect of the Transition Zone on the Bulk Modulus of Concrete. MRS Online Proceedings Library 370, 413–418 (1994). https://doi.org/10.1557/PROC-370-413