The paradigm based on the fractal model of granular distribution for the study of the mechanical strength of concrete.

Abstract Studies revealed that all the grain size-grading curves specified by concretes mix designs were all typified by an almost perfect quasi-fractal distribution of the aggregate particle size. This enabled to identify the basic granular mixture (no cement, fine or mineral addition) and determine the porosity, based on the granular fractal-identification modulus\("\text{F}\text{D}.\text{l}\text{o}\text{g}(\text{d}/\text{D})"\), comprising the fractal dimension \(\left(\text{F}\text{D}\right)\) of the aggregate involved and the granular range (\(\text{d}/\text{D}\)). The aim of this research work was to shed new light on the prediction of concrete mechanical compressive strength - as a major topic addressed by many researchers who investigated concretes - and introduce a new approach to expand the use of the \("\text{F}\text{D}.\text{l}\text{o}\text{g}(\text{d}/\text{D})"\) modulus, which explicitly addressed the aggregate granularity and implicitly determined the related compactness. The approach adopted a two-phase concrete model, where the first phase being the aggregate and the second phase referring to the paste (cement, water, mineral addition and possibly fines). The implemented granular fractal-identification modulus (GFIM) included new parameters of concretes mix designs as dosage and nature of the concrete components, comprising identical aggregates and hence similar (GFIM) and compactness values. Applying a reading array to experimental compiled results of more than 300 concretes selected from literature provided a clear correlation between the development of concrete compressive strength \({\text{R}}_{\text{C}28}\)and a combination of the classical parameters used. The approach thus established a new and more instructive as well as pedagogical paradigm for adequately assessing and controlling concretes performance on fractal basis.