Prediction of compressive strength and optimization of mixture proportioning in ternary cementitious systems

This paper discussed the application of the method of the simplex-lattice design for predicting the properties of cement-based composites. On the basis of the compressive strength, its use was demonstrated on ternary paste systems composed of cement, silica fume and fly ash with constant water to binder ratio and a mass fraction of mineral admixtures not exceeding 30%. The regression model between compressive strength of paste and binder proportion was built up. The F-test method was utilized for validation of the regression model. The nonlinear programming system with upper and lower bound was solved. This allowed assessment of optimum mixture proportions and corresponding maximum compressive strength. It was shown that: (1) the 3rd-order regression model constructed by using the simplex-lattice design method could accurately predict the compressive strength in ternary paste system made of cement, silica fume and fly ash (the total mass fraction of all mineral admixtures was up to 30%); (2) to solve the nonlinear programming with the constraints of upper and lower bound played an important role in getting the optimum compressive strength and its corresponding mixture proportion at different ages; (3) the combination of the simplex-lattice design method and the optimization theory could be valuable tool for optimization of cement-based composites' properties.