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This paper aims to express a mathematical model that predicts the effect of mineral additives on the physical–mechanical properties of high-performance sand concrete (HPSC), using SAS's JMP7 statistical analysis software.

A mixture design modeling approach is applied to sand concrete (SC) for optimizing mixtures without being obliged to do a lot of experiments, where the cement is partially replaced with two mineral additives silica fume (SF) and blast furnace slag (BFS) in proportions as high as 20% of the mass. A total of 15 mixtures of sand concrete is prepared in the laboratory using this analytical technique in combinations with binary and ternary systems to estimate the workability and the compressive strength (CS) of sand concrete at 7 and 28 days.

The results obtained showed that the use of derived models based on the experimental design approach greatly assisted in understanding the interactions between the various parameters of the studied mixtures; the mathematical models present excellent correlation coefficients (R² = 0.96 for CS7 days, R² = 0.93 for CS28 days and R² = 0.95 for slump) for all studied responses. Moreover, it was also found that the inclusion of additives (SF and BFS) in binary mixture SC12 and ternary mixtures SC8 leads to a significant improvement in mechanical strength compared to reference sand concrete SC15. These results give the possibility to obtain a formulation of HPSC.

This paper shows the possibility of manufacturing high-performance sand-concrete with good compressive strength; the developed mathematical model by using SAS's JMP7 statistical analysis software allowed us to reach a strength compression value of about 60 MPa, in 28 days, by replacing 10% of the cement weight with silica fume. Furthermore, with partial replacement of the cement weight (15%) with two additions such as silica fume (10%) and blast furnace slag (5%), a 58 MPa of compressive strength can be achieved, without overlooking the fact that this can be a key economic and environmental alternative.