Modeling the elastic properties of concrete composites: Experiment, differential effective medium theory, and numerical simulation

Zhihui Sun*, Edward J. Garboczi, Surendra P Shah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

99 Scopus citations


Concrete is a mixture of cement, water and aggregates. In terms of microstructure, besides the cement paste matrix and aggregate inclusions, there is a third phase, which is called the interfacial transition zone (ITZ), which forms due to the wall effect and can be thought of as a thin shell that randomly forms around each aggregate. Thus, concrete can be viewed as a bulk paste matrix containing composite inclusions. To compute the elastic properties of a concrete composite, a differential effective medium theory (D-EMT) is used in this study by assigning elastic moduli to corresponding bulk paste matrix, ITZ and aggregate. In this special D-EMT, each aggregate particle, surrounded by a shell of ITZ of uniform thickness and properties, is mapped onto an effective particle with uniform elastic moduli. The resulting simpler composite, with a bulk paste matrix, is then treated by the usual D-EMT. This study shows that to assure the accuracy of the D-EMT calculation, it is important to consider the increase in the water:cement mass ratio (w/c) of the ITZ and the corresponding decrease in w/c ratio of the bulk matrix. Because of this difference in w/c ratio, the contrast of elastic moduli between the ITZ and the bulk paste matrix needs to be considered as a function of hydration age. The Virtual Cement and Concrete Testing Laboratory (VCCTL) cement hydration module is used to simulate the microstructure of cement paste both inside and outside the ITZ. The redistribution of calcium hydroxide between ITZ and bulk paste regions can further affect the elastic contrast between ITZ and bulk paste. The elastic properties of these two regions are computed with a finite element technique and used as input into the D-EMT calculation. The D-EMT predictions of the elastic properties of concrete composites are compared with the results measured directly with a resonant frequency method on corresponding composites. This comparison shows that the D-EMT predictions agree well with experimental measurements of the elastic properties of a variety of concrete mixtures.

Original languageEnglish (US)
Pages (from-to)22-38
Number of pages17
JournalCement and Concrete Composites
Issue number1
StatePublished - Jan 1 2007


  • Differential effective medium theory
  • Dynamic elastic moduli
  • Interfacial transition zone
  • Microstructure
  • Numerical simulation

ASJC Scopus subject areas

  • Building and Construction
  • Materials Science(all)


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