Closed-form solution for predicting elastic modulus of concrete

In predicting the mechanical properties of concrete, the concrete should be modeled as a three-phase material; and the morphological characteristics of these three phases, the mechanical properties of each phase’s constituent material, and the interaction of these three phases in the concrete matrix should all be taken into account. This paper attempts to develop an analytical method to achieve this, and a closed-form solution for predicting the elastic modulus of concrete is presented. After verifying the derived solution with both experimental and numerical results, the effects of key factors affecting the elastic modulus of concrete are examined in a quantitative manner. The research shows that the two most important factors affecting the elastic modulus of concrete are 1) the elastic modulus of aggregate; and 2) the water-cement ratio (w/c). It is also found that the elastic modulus of concrete increases with an increase in the aggregate volume fraction, the elastic modulus of aggregate, the elastic modulus of interfacial transition zone, and the maximum aggregate diameter; but it decreases with an increase in the maximum cement diameter and the w/c. The paper concludes that, when the properties and proportions of the constituent materials are known, the solution presented in the paper is very effective in predicting the elastic modulus of concrete