Four-phase sphere modeling of effective bulk modulus of concrete

A four-phase sphere model, extended from Christensen and Lo's three-phase sphere model for two-phase composite materials, was proposed to estimate the effective bulk modulus of three-phase concrete. The formulations were developed by reducing the four-phase sphere model to an equivalent three-phase sphere model and an equivalent two-phase sphere model. A distinctive characteristic of the proposed model is that, in addition to considering other physical-mechanical parameters, it is able to evaluate the effect of the maximum aggregate size and aggregate gradation on the effective bulk modulus of concrete. Reasonable agreement was found between the calculated effective Young's modulus and the experimental results from the literature. This suggests that the proposed four-phase sphere model is suitable for estimating the effective elastic modulus of concrete. It is found that the maximum aggregate size, aggregate gradation, and the interfacial transition zone have a significant effect on the effective modulus of concrete. (C) 1999 Elsevier Science Ltd. All rights reserved.