Effect of the Cement-to-Water Ratio and Fractal Granular Model on the Prediction of Concretes Compressive Strength
Mhammed Abdeldjalil, Kaddour Chouicha
Abstract
Abstract The main objective of this work was to highlight the contribution of cement-to-water $$\mathrm{C}/\mathrm{W}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mo>/</mml:mo> <mml:mi>W</mml:mi> </mml:mrow> </mml:math> ratio and the fractal dimension $$\mathrm{FD}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>FD</mml:mi> </mml:math> model to the prediction of the compressive strength of concrete. In particular, the fractal dimension $$\mathrm{FD}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>FD</mml:mi> </mml:math> 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 $${\mathrm{FGM}}_{\mathrm{g}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>FGM</mml:mi> <mml:mi>g</mml:mi> </mml:msub> </mml:math> also effectively contributed to highlight the correlation between cement-to-water ratio and compressive strength $${\mathrm{R}}_{\mathrm{C}28}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>R</mml:mi> <mml:mrow> <mml:mi>C</mml:mi> <mml:mn>28</mml:mn> </mml:mrow> </mml:msub> </mml:math> 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 $$\mathrm{FD}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>FD</mml:mi> </mml:math> model and the granular range $$\mathrm{D}/\mathrm{d}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>/</mml:mo> <mml:mi>d</mml:mi> </mml:mrow> </mml:math> 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 $${\mathrm{FGM}}_{\mathrm{g}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>FGM</mml:mi> <mml:mi>g</mml:mi> </mml:msub> </mml:math> and the influence of cement–water $$\mathrm{C}/\mathrm{W}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mo>/</mml:mo> <mml:mi>W</mml:mi> </mml:mrow> </mml:math> ratio of concretes mixtures when predicting the concretes compressive strength $${\mathrm{R}}_{\mathrm{C}28}.$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>R</mml:mi> <mml:mrow> <mml:mi>C</mml:mi> <mml:mn>28</mml:mn> </mml:mrow> </mml:msub> <mml:mo>.</mml:mo> </mml:mrow> </mml:math> The analytical model provided a close correlation with the experimental values of the compressive strength $${\mathrm{R}}_{\mathrm{C}28}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>R</mml:mi> <mml:mrow> <mml:mi>C</mml:mi> <mml:mn>28</mml:mn> </mml:mrow> </mml:msub> </mml:math> of all the concretes. The correlation highlighted the relevance of including fractal granular model $${\mathrm{FGM}}_{\mathrm{g}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>FGM</mml:mi> <mml:mi>g</mml:mi> </mml:msub> </mml:math> that denoted the skeleton of the concretes and the cement–water $$\mathrm{C}/\mathrm{W}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mo>/</mml:mo> <mml:mi>W</mml:mi> </mml:mrow> </mml:math> ratio that referred to the binders into concretes mixtures when predicting $${\mathrm{R}}_{\mathrm{C}28}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>R</mml:mi> <mml:mrow> <mml:mi>C</mml:mi> <mml:mn>28</mml:mn> </mml:mrow> </mml:msub> </mml:math> . 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 $${\mathrm{R}}_{\mathrm{C}28}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>R</mml:mi> <mml:mrow> <mml:mi>C</mml:mi> <mml:mn>28</mml:mn> </mml:mrow> </mml:msub> </mml:math> .