Using mathematical modeling for design of self compacting high strength concrete with metakaolin admixture

Metakaolin forms a part of a complex admixture to self-compacting high-strength concrete. The admixture contains superplasticizer addition of naphthalene formaldehyde or polycarboxylate type, yielding significant improvement in workability and uniformity of fresh concrete mix as well as mechanical properties and durability of hardened concrete. Mathematical modeling of self compacting high strength concrete at the design stage is aimed at determining optimal content of concrete components (in particular, chemical and mineral admixtures) to obtain the desired concrete properties. Three-parameter polynomial models are used for determining the superplasticizer content, required to obtain the same fresh concrete mix workability, hardened concrete compressive strength and correspondingly metakaolin efficiency factor from the strength increase viewpoint. It is demonstrated that the efficiency of metakaolin as an admixture to self compacting high strength concrete depends on the dosage of the first as well as on concrete binder content, water-binder ratio and by the type of superplasticizer used for concrete production. A concrete design method using traditional deterministic and stochastic dependencies is developed. Regression equations, describing the influence of water-binder ratio, binder content and metakaolin portion in binder on superplasticizer content, compressive strength and efficiency factor of metakaolin, are obtained. The concrete design objective function, proposed in this study, allows obtaining the required concrete strength by minimizing the cost of the most unsustainable concrete components, like cement, metakaolin and superplastisizer.