An analytical method for prediction of the elastic modulus of concrete

Experimental and theoretical research has shown that in predicting its elastic modulus, concrete should be modelled as a three-phase material at a mesoscopic level and the proportions, mechanical properties and interaction of these three-phase constituents should all be considered in the prediction. The current paper attempts to develop an analytical method for prediction of the elastic modulus of concrete. A three-phase composite circle model for the concrete matrix is proposed to represent the heterogeneous nature of concrete. Based on the classic theory of elasticity, a closed-form solution to the plane strain bulk modulus of concrete is derived. After verifying the developed method with both experimental and numerical results, the effects of the aggregate area fraction, the elastic modulus of aggregate, the elastic modulus of interfacial transition zone (ITZ), the maximum aggregate diameter, the maximum cement diameter and the aggregate gradation on the elastic modulus of concrete are examined in a quantitative manner. It is found that the elastic modulus of concrete increases with the increase of the aggregate area fraction, the elastic modulus of aggregate, the elastic modulus of ITZ and the maximum aggregate diameter, but decreases with the increase of the maximum cement diameter. It is also found that the aggregate gradation affects the elastic modulus of concrete to a certain extent. The paper concludes that the analytical solution derived herein can predict the elastic modulus of concrete with reasonable accuracy.