The control of the determination of concrete depends on the basic properties of the desired concrete and thanks to the type of granular mixture of concrete. We arrive at the required concrete quality. And in this study, we can identify the granular distribution class of concrete using the fractal model. In particular, the granular distribution can be determined by the fractal dimension, either for each granular component separately, or for the dry granular mixture of the concrete. The fractional dimension is obtained by transforming the particle size curve to a fractal line. In this study, we used some experimental results obtained from projects already carried out in arid regions. Knowing that we have applied parameters such as granular extent and fractional dimension to the study of these existing projects, we can define a dry mix of concrete through the granular distribution. Therefore, we used the program that we proposed previously of transforming the grain size curves to a fractal line which was obtained for each grain mixture with a very acceptable correlation.
The main objective of this work was to highlight the contribution of cement-to-water $$\mathrm{C}/\mathrm{W}$$
C
/
W
ratio and the fractal dimension $$\mathrm{FD}$$
FD
model to the prediction of the compressive strength of concrete. In particular, the fractal dimension $$\mathrm{FD}$$
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 $${\mathrm{FGM}}_{\mathrm{g}}$$
FGM
g
also effectively contributed to highlight the correlation between cement-to-water ratio and compressive strength $${\mathrm{R}}_{\mathrm{C}28}$$
R
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 $$\mathrm{FD}$$
FD
model and the granular range $$\mathrm{D}/\mathrm{d}$$
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 $${\mathrm{FGM}}_{\mathrm{g}}$$
FGM
g
and the influence of cement–water $$\mathrm{C}/\mathrm{W}$$
C
/
W
ratio of concretes mixtures when predicting the concretes compressive strength $${\mathrm{R}}_{\mathrm{C}28}.$$
R
C
28
.
The analytical model provided a close correlation with the experimental values of the compressive strength $${\mathrm{R}}_{\mathrm{C}28}$$
R
C
28
of all the concretes. The correlation highlighted the relevance of including fractal granular model $${\mathrm{FGM}}_{\mathrm{g}}$$
FGM
g
that denoted the skeleton of the concretes and the cement–water $$\mathrm{C}/\mathrm{W}$$
C
/
W
ratio that referred to the binders into concretes mixtures when predicting $${\mathrm{R}}_{\mathrm{C}28}$$
R
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 $${\mathrm{R}}_{\mathrm{C}28}$$
R
C
28
.
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