Optimizing Performance-Engineered Concrete Mixtures Using Linear Programming

This paper uses linear programming to optimize concrete mixture proportions while meeting target performance criteria that serve as constraints. The objective function, which is a weighted function of the material and carbon costs, is used to find the optimal mixture design based on the criteria that are most important to the user. The parameters in the objective function (e.g., material cost, carbon cost, construction cost, etc.) are user-adjustable. The constraints are the required mechanical properties (e.g., compressive strength, elastic modulus, etc.) and durability performance indicators of concrete such as formation factor, calcium hydroxide content, time-to-critical saturation, electrical resistivity and pH of concrete pore solution. A thermodynamics-based modeling framework is used to predict the mechanical and durability performance of concrete. A feasible region of mixture proportions is obtained after predicting concrete performance across a range of volumes of water and supplementary cementitious material in concrete where the target performance is met. The optimal mixture proportions (i.e., least cost, minimum carbon emissions, or a weighted combination of the two) can be obtained using the concepts of linear programming used in this framework. This powerful approach can be used to efficiently utilize resources and optimally design concrete mixtures.