Effect of the Cement-to-Water Ratio and Fractal Granular Model on the Prediction of Concretes Compressive Strength

The main objective of this work was to highlight the contribution of cement-to-water C/W ratio and the fractal dimension FD model to the prediction of the compressive strength of concrete. In particular, the fractal dimension FD concept relative to the size distribution of the granular mixtures provided an insight into the fineness and compactness of the granular mixtures. The unconventional fractal granular model FGM_g also effectively contributed to highlight the correlation between cement-to-water ratio and compressive strength R_C28 of concretes. Initially, 99 granular mixtures of concretes composition available in literature were investigated and for which the granular distributions by means of the fractal dimension FD model and the granular range D/d were we determined. Then, 36 concrete mixtures endowed with different granular mixtures were elaborated and analysed. These enabled to validate and evaluate the reliability of the basic granular fractal model FGM_g and the influence of cement–water C/W ratio of concretes mixtures when predicting the concretes compressive strength R_C28. The analytical model provided a close correlation with the experimental values of the compressive strength R_C28 of all the concretes. The correlation highlighted the relevance of including fractal granular model FGM_g that denoted the skeleton of the concretes and the cement–water C/W ratio that referred to the binders into concretes mixtures when predicting R_C28. The theoretical approach whose effectiveness was highlighted using a "limited" number of real case studies may pave the way for further studies, when selecting the two key-factors for the prediction of concretes compressive strength R_C28.