ORIGINAL PAPER Using mathematical methods for designing optimal mixtures for building bricks prepared by solid industrial waste Eliane Wolff 1 • Wilfrid Keller Schwabe 2 • Samuel Vieira Conceic ¸a ˜o 4 • Jisela Aparecida Santanna-Greco 5 • Marcelo Greco 6 • Raiane Ribeiro Machado 3 Received: 26 November 2015 / Accepted: 25 May 2016 Ó Springer-Verlag Berlin Heidelberg 2016 Abstract 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. Keywords Water treatment plant sludge  Building bricks  Mixture design  Combination of variables  Pulp mill Introduction There are thousands of pulp and paper mills worldwide. The utilization of the waste they produce is a problem of particular importance (Vochozka et al. 2016). Inadequate disposal may create hazardous waste sites and impair the quality of life for present and future generations. In Brazil, this type of problem has triggered the development of public policies and legislation focused on environmental sustainability and the preservation of human health. The Brazilian Environment Council (CONAMA) and the State Environmental Agencies regulate, control, and enforce environmental preservation. The National and State 1 Policy of Solid Waste, Law 12.305 (Brasil 2010) and Law 18.031 (Minas Gerais 2009), the National and State Policy on Water Resources, Law 9.433 (Brasil 1997) and Law 13.199 & Samuel Vieira Conceic ¸a ˜o svieira@dep.ufmg.br 1 WW Environmental Consulting Company, Avenida Augusto de Lima 1646/1005, Belo Horizonte, Minas Gerais 30190-003, Brazil 2 Department of Sanitary and Environmental Engineering, School of Engineering, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais 31270-901, Brazil 3 Universidade Federal de Vic ¸osa – MG, Vic ¸osa, Brazil 4 Department of Industrial Engineering, School of Engineering, Universidade Federal de Minas Gerais , Belo Horizonte, Minas Gerais 31270-901, Brazil 5 Transport and Geotechnics Engineering Department, School of Engineering, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais 31270-901, Brazil 6 Graduate Program in Structural Engineering, Department of Structural Engineering, School of Engineering, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais 31270-901, Brazil 1 The state of Minas Gerais where this work was developed. 123 Clean Techn Environ Policy DOI 10.1007/s10098-016-1223-y