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This study is based upon the fractal feature of ideal Particle Size Distributions (PSD) suggested by numerous concrete mix designs, i.e. ideal PSD can be shown to be equivalent to a power law distributions  E C  ( ϕ  i ) ∝  ϕ i    − DF  ,  E C  ( ϕ  i ) is the number of grains of size greater than  ϕ  i , and  DF  is a nonwhole number called fractal dimension. This fact allows us to analyze the solid skeleton of a concrete mix (all solid components of the mixture) as a fractal structure, thus to determine some of physical properties of the concrete mixture. For  DF  ranging from 2.5 to 3, and based upon many parameters of the concrete mix (as the granular range, the volumetric fraction of solids in the concrete mixture…), analytical formulas have been proposed relating  DF  and some properties of the concrete in the solid state. The required properties are the coarse-to-fine aggregate ratio, the fineness modulus of the sand fraction, the average grain size and volume of the fine fraction in the concrete mix. The focus of this research is to develop formulas by which concrete properties can be predicted knowing the concrete mix gradation, i.e. the mix design method used.

Fractal dimension of concrete mix gradation: a quantitative parameter for some concrete properties