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

Abstract

The main objective of this work was to highlight the contribution of cement-to-water mathrm{C}/mathrm{W} ratio and the fractal dimension mathrm{FD} model to the prediction of the compressive strength of concrete. In particular, the fractal dimension mathrm{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 {mathrm{FGM}}_{mathrm{g}} also effectively contributed to highlight the correlation between cement-to-water ratio and compressive strength {mathrm{R}}_{mathrm{C}28} 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 mathrm{FD} model and the granular range mathrm{D}/mathrm{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 {mathrm{FGM}}_{mathrm{g}} and the influence of cement–water mathrm{C}/mathrm{W} ratio of concretes mixtures when predicting the concretes compressive strength {mathrm{R}}_{mathrm{C}28}. The analytical model provided a close correlation with the experimental values of the compressive strength {mathrm{R}}_{mathrm{C}28} of all the concretes. The correlation highlighted the relevance of including fractal granular model {mathrm{FGM}}_{mathrm{g}} that denoted the skeleton of the concretes and the cement–water mathrm{C}/mathrm{W} ratio that referred to the binders into concretes mixtures when predicting {mathrm{R}}_{mathrm{C}28}. 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 {mathrm{R}}_{mathrm{C}28}.