Predicting the Magnitude of Microsphere Parameters Obtained from Microscopical Examination of Hardened Concrete

Abstract

Abstract Geometric probability concepts are used to establish a quantitative basis for predicting the magnitude of microscopically determined parameters of polymeric microsphere systems in hardened concretes relative to the actual magnitude of the parameters. Both a hypothetical discrete size distribution and a representative continuous size distribution of the microspheres are considered in the analysis. It is predicted that for a random section through the concrete, the magnitudes of the measured microsphere volume fraction and specific surface relative to the respective actual values would depend on the proportion of the total number of microspheres counted on the section. The lower the proportion of microspheres counted, the lower the ratios of measured-to-actual volume fraction and measured-to-actual specific surface would be. For the test data presented, the proportion of microspheres counted was calculated to have an average value of 0.75. Ratios of predicted-to-actual volume fraction and predicted-to-actual specific surface are compared with the respective measured ratios and found to be quite accurate. When there is a significant spread in the microsphere size distribution and relatively few microspheres are missed during a microscopical examination of a single section of concrete, the measured volume fraction would be higher and the measured specific surface would be lower, relative to the respective actual values. This is because a random section through the concrete has a greater chance of intersecting large microspheres than small ones, with large microspheres having a relatively higher contribution to volume and a relatively lower contribution to specific surface than small microspheres. These findings are relevant for air-entrained concrete as well when measurements obtained by microscopical examination of hardened concrete are compared with air content measured by the pressure method or with air content and specific surface measured by an air void analyzer.