Using mathematical methods for designing optimal mixtures for building bricks prepared by solid industrial waste

This study evaluates the use of solid industrial waste generated by a water treatment plant (WTP) at a pulp mill in Brazil for manufacturing building bricks. The sludge from the WTP was mixed with three different wastes generated by the same factory (dregs, grits, and lime mud) and other wastes generated from crushing and grinding granite rock (granite fines). Mathematical and statistical methods are proposed for designing mixtures that satisfy the material properties for ceramic processing and the mechanical properties for the end product. A method for solving a linear system of equations using fewer equations than variables was required, as the number of materials exceeded the number of reference grain size distributions. This type of system is generally compatible and indeterminate. To obtain feasible solutions, a combination-of-variables method is proposed to optimize the mixture design. The formulation of the mixtures was based on the grain size distribution of the residues and the proportions of calcium, sodium, and potassium oxides in the mixtures. The nonparametric Kruskal–Wallis test and the median test were applied for all mixtures, followed by a multiple comparison test of classes. The mechanical properties of the specimens were evaluated after drying (linear shrinkage and flexural strength) and firing (ignition loss, linear shrinkage, and flexural strength) according to the Brazilian Association of Technical Standards and Brazilian Standards for red ceramics.