Scheffe's Polynomial Optimisation of Laterite Concrete Incorporating Periwinkle Shells and Coir

Abstract

Recent emphases on minimising the carbon footprint of concrete have focused on the use of non-conventional materials for the production of low-cost concrete. Such materials include laterite, periwinkle shells and coir which have been reported as suitable for use as fine and coarse aggregate replacements in specified proportions. However, the use of two or more unconventional materials in a concrete mix would require significant experimental effort that is time- and resource-consuming and usually performed by trial and error to determine the optimum mix design. A popular optimisation technique used for concrete mix design is Scheffe's second-degree polynomial modelling. However, the application of a more accurate Scheffe's third-degree polynomial optimisation technique in designing cementitious composites incorporating unconventional aggregates is rare. This study, therefore, presents the use of Scheffe's third-degree model to determine the optimum proportions of coir, laterite and periwinkle shell aggregates in a concrete mix in order to obtain the best mechanical properties of the hardened concrete. The constituents of the concrete were optimised for seven components of water, cement, fine-aggregate, laterite soil, coarse aggregate, periwinkle shell and coir on an N(7, 3) Sheffe's factor space. The optimal mix ratio for compressive and flexural strengths of 11.33 and 1.20 MPa, respectively, was 0.5149, 1.044, 3.009, 0.126, 3.934, 0.054, and 0.0046 for pseudo-components Xi: {∀i = 1, 2 3, 4, 4, 6, 7}. The coefficients of determination (R2) were 98.74% and 98.53% for the compressive and flexural response models, respectively, while the p-values obtained for the response coefficient fit parameters βi, βij, βijk for (i = 1, 2, 3, 4, 5, 6, 7) were 96.77% and 91.49% for the compressive and flexural strength models, respectively. The optimised Low-Performance Concrete (LPC) is about 4% cheaper than LPC made from conventional aggregates and is adequate for patio slabs, pedestrian footpaths, kerbs, and floorings in residential buildings. The use of Sheffe's third-degree model eliminates the significant experimental efforts needed in the design of concrete mixes incorporating unconventional aggregates.