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 $${\mathrm{R}}_{\mathrm{C}28}$$.