This study uses the mathematical method of two-factors rotatable central compositional planning to predict and simulate the effect of the ratio of water-cement (N/X) and sand - binder (C/CKD) as the input parameters on the objective functions of the spreading flow of concrete mixtures and the compressive strength of fine-grained high-performence concrete (FGHPC) at 28 days. Results of the study showed that, from the material source in Vietnam, it is possible to FGHPC with a flow of 18.5 cm in the mini cone, its compressive and flexural strengths at the age of 28 days are 68.5 MPa and 6.13 MPa, respectively. Furthermore, from the obtained objective functions, it has been shown that the both two-input parameters have a significant influence on the values of the experimental models. Particularly, using Matlab software is showed the expression surface, the contour line of the experimental models, and determined the maximum value of compressive strength of FGHPC at this age of 69.84 MPa at N/X=0.326 and C/CKD=1.315. The contribution of this study is to obtain regression functions to predict the mechanical-physical properties of FGHPC that will be used in the next in-depth studies.
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