Determining periodic representative volumes of concrete mixtures based on the fractal analysis

In materials evaluation, determining an appropriate Representative Volume Element (RVE) of the material is of paramount importance. This paper is an attempt to provide a quantitative determination of the RVE of concrete mixtures, using fractal analysis. The key point of this study is to consider concrete mixture as a fractal and periodic structure and the basic periodic unit cell in this material as the RVE. Based on a new analytical approach, obtained results suggest that the ratio between the RVE size and the maximum particle size of concrete is likely to be 2.4–3.7, for increasing DF values from 2.5 to 3; DF being the fractal dimension of the concrete size distribution. Additional results were proposed for laboratory concrete testing, which suggest that for ordinary concretes, standard sample sizes, whatever the shape, should be at least around 3.5 times the nominal maximum size of aggregates. Although the proposed approach is based on simple mathematical formulas, obtained results appear broadly consistent with those of other studies based on extensive laboratory testing and modeling. The scope of application of the proposed approach can be extended to numerous solid materials that consist of grains.

► A new analytical approach is developed to predict the RVE of concrete mixtures.
► Concrete mixture is assumed as fractal and periodic structure.
► The smallest periodic cell in the concrete is the RVE.
► RVE size must be at least 2.4–3.7 times the max. aggregate size.
► Laboratory sample size must be at least 3.5 times the nominal max. aggregate size.