OPTIMISATION OF WATER TREATMENT SLUDGE CONCRETE USING SCHEFFÉ'S FOURTH-DEGREE SIMPLEX LATTICE MODEL

Abstract The reuse of water treatment sludge (WTS) in concrete provides a sustainable option for waste valorisation; however, the variability of waste-based materials requires a systematic mix optimisation approach to ensure consistent mechanical performance. This study applies statistical mixture optimisation to WTS-modified concrete using Scheffé’s fourth-degree simplex lattice model for a five-component system consisting of water, cement, fine aggregate, water treatment sludge, and coarse aggregate. An N (5,4) simplex lattice design generated seventy concrete mixtures, which were tested for 28-day compressive and flexural strength. Fourth-degree Scheffé’s polynomial models were developed for both responses and validated using analysis of variance (ANOVA). The compressive strength model showed excellent accuracy with an R² value of 99.89%, while the flexural strength model achieved an R² of 95.70%, indicating strong predictive reliability. Optimisation of the validated models produced mix proportions yielding compressive strengths between 31.9 and 37.3 MPa and flexural strengths ranging from 3.12 to 3.21 MPa, meeting structural concrete requirements. These findings demonstrate that, with rigorous statistical mix design, water treatment sludge can be successfully used as a partial fine aggregate replacement in concrete without loss of mechanical performance. The study confirms Scheffé’s simplex lattice method as a reliable framework for optimising WTS-based concrete and advancing sustainable construction materials through data-driven mix design. Keywords Water treatment sludge; Concrete; Simplex lattice design; Scheffé polynomial; Mixture optimisation; Compressive strength; Flexural strength.