Four-phase sphere modeling of effective bulk modulus of concrete

摘要

A four-phase sphere model, extended fromChristensen and Lo's three-phase sphere model for two-phasecomposite materials, was proposed to estimate the effective bulkmodulus of three-phase concrete. The formulations weredeveloped by reducing the four-phase sphere model to anequivalent three-phase sphere model and an equivalent two-phasesphere model. A distinctive characteristic of the proposed modelis that, in addition to considering other physical-mechanicalparameters, it is able to evaluate the effect of the maximumaggregate size and aggregate gradation on the effective bulkmodulus of concrete. Reasonable agreement was found betweenthe calculated effective Young's modulus and the experimentalresults from the literature. This suggests that the proposed four-phase sphere model is suitable for estimating the effective elasticmodulus of concrete. It is found that the maximum aggregate size,aggregate gradation, and the interfacial transition zone have asignificant effect of the effective modulus of concrete.