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.

This study applied Scheffé’s fourth-degree simplex lattice methodology to optimise concrete incorporating Water Treatment Sludge (WTS within a constrained five-component mixture system. Based on the experimental results, statistical modelling, and optimisation analyses conducted, the following conclusions are drawn: 1. The N(5,4) Scheffé simplex lattice design provided a comprehensive and statistically rigorous framework for exploring the interaction effects among water, cement, fine aggregate, WTS, and coarse aggregate in WTS-modified concrete. 2. Fourth-degree Scheffé polynomial models developed for compressive and flexural strength exhibited excellent predictive performance, with coefficients of determination of 99.89% and 95.70%, respectively. This confirms that higher-order interaction effects play a significant role in governing the mechanical performance of WTS concrete. 3. Analysis of variance (ANOVA) demonstrated that the developed models are statistically significant, with model mean squares substantially exceeding error mean squares and negligible lack-of-fit, validating their suitability for mixture optimisation within the experimental domain. 4. Experimental results showed that WTS-modified concrete can achieve compressive strengths ranging from approximately 11 MPa to 18.5 MPa prior to optimisation, indicating fundamental material compatibility when WTS is used as a fine aggregate substitute. 5. Optimised mixture proportions derived from the validated models achieved predicted compressive strengths between 31.9 MPa and 37.3 MPa and flexural strengths in the range of 3.12–3.21 MPa, satisfying and exceeding the minimum requirements for structural- grade concrete. 6. The consistency between optimised compressive and flexural strength responses confirms the internal coherence of the mixture models and demonstrates that statistical optimisation enables the effective and reliable incorporation of WTS in concrete without compromising mechanical performance. Overall, the results confirm that Scheffé’s fourth-degree simplex lattice model is a robust and effective tool for optimising WTS-modified concrete and provides a scientifically sound basis for sustainable concrete mix proportioning.

1. Babatunde, A. O., and Zhao, Y. Q. (2007). “Constructive approaches toward water treatment works sludge management: An international review of beneficial reuses.” Critical Reviews in Environmental Science and Technology, 37(2), 129–164. 2. Ahmad, T., Ahmad, K., and Alam, M. (2016). “Sustainable management of water treatment sludge through beneficial reuse in construction materials: A review.” Journal of Cleaner Production, 141, 230–243. 3. Sales, A., and Lima, S. A. (2010). “Use of water treatment plant sludge in concrete.” Materials and Structures, 43(7), 973–986. 4. Huang, C. H., Wang, S. Y., and Chen, C. H. (2014). “Pozzolanic properties of water treatment sludge ash and its use in cement-based materials.” Construction and Building Materials, 63, 196–202. 5. Zhai, J., Wang, Y., and Wang, J. (2019). “Mechanical properties and durability of concrete containing water treatment sludge.” Journal of Materials in Civil Engineering, 31(6), 04019102. 6. Mehta, P. K., and Monteiro, P. J. M. (2014). Concrete: Microstructure, Properties, and Materials (4th ed.). McGraw-Hill Education, New York. 7. Neville, A. M. (2011). Properties of Concrete (5th ed.). Pearson Education, Harlow, UK. 8. Taylor, H. F. W. (1997). Cement Chemistry (2nd ed.). Thomas Telford, London. 9. Siddique, R., and Klaus, J. (2009). “Influence of metakaolin on the properties of mortar and concrete: A review.” Applied Clay Science, 43(3–4), 392–400. 10. Gartner, E., and Hirao, H. (2015). “A review of alternative approaches to the reduction of CO₂ emissions associated with the manufacture of the binder phase in concrete.” Cement and Concrete Research, 78, 126–142. 11. Scheffé, H. (1958). “Experiments with mixtures.” Journal of the Royal Statistical Society: Series B (Methodological), 20(2), 344–360. 12. Cornell, J. A. (2002). Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data (3rd ed.). John Wiley & Sons, New York. 13. Montgomery, D. C. (2017). Design and Analysis of Experiments (9th ed.). John Wiley & Sons, New York. 14. Box, G. E. P., and Draper, N. R. (2007). Response Surfaces, Mixtures, and Ridge Analyses (2nd ed.). John Wiley & Sons, New York. 15. Myers, R. H., Montgomery, D. C., and Anderson-Cook, C. M. (2016). Response Surface Methodology: Process and Product Optimization Using Designed Experiments (4th ed.). John Wiley & Sons, New York. 16. BS EN 206:2013. Concrete – Specification, Performance, Production and Conformity. British Standards Institution, London. 17. BS EN 12390-3:2019. Testing Hardened Concrete – Part 3: Compressive Strength of Test Specimens. BSI, London. 18. BS EN 12390-5:2019. Testing Hardened Concrete – Part 5: Flexural Strength of Test Specimens. BSI, London. 19. BS EN 1992-1-1:2004. Eurocode 2: Design of Concrete Structures – Part 1-1: General Rules and Rules for Buildings. European Committee for Standardization, Brussels. 20. Council for the Regulation of Engineering in Nigeria (COREN). (2010). Guidelines for Concrete Mix Design. Abuja, Nigeria.

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