Scheffe’s Polynomial Optimisation of Split Tensile Strength of Palm Kernel Shells Aggregate Modified Concrete

Abstract

The environmental consequence of natural aggregate exploitation and Agro-base waste management especially open-air incineration is immense. In this research a mathematical model was developed to optimize the mixture design of concrete using Palm Kernel Shells PKS as partial (60%) replacement in composite coarse aggregate of palm kernel shell and crushed granite (PKSCG) to forester environmental sustainability. The research work is to optimize the split tensile strength of Palm Kernel Shell aggregate modified concrete based on improved Scheffe`s second degree polynomial, where the strength was obtained for various ratios using the Scheffe`s simplex lattice method. To test for the adequacy of the model, student`s t-test and Fishers (ANOVA) were used where the results of test indicates that the model strengths are generally in good conformity with the corresponding observed experimental results. The optimised tensile strength by the model at 28 days of curing within the factor space was 1.06481Mpa, while the experimental results yield a maximum and minimum strength of 1.0963 MPa and 0.5658N MPa at same curing period with corresponding to mix ratio of [0.625:1.0:1.925:1.09:1.635]and [0.675:1.0:2.15:1.22:1.83] respectively for water, cement, fine aggregate, granite and PKS respectively. The coefficients of determination (????2) was 99.99% for the split tensile response models, while the p-value obtained for the response coefficient fit parameters ????????, ????????????, ???????????????? for (????=1,2,3,4,5) was 99.98% for the modelled strength. Wolfram Mathematica application was used for data fitting and optimization computation. The Scheffe`s optimization theory can be used to analyse and optimise concrete strength and possible mix proportions of concrete ingredient as the comparison of the split tensile strengths obtained between the laboratory test results and the model results show a good pact, consequently indicating that the optimisation equations can sufficiently predict the mechanical properties of the concrete at 28 days of curing. The palm kernel shells modified concrete is appropriate for applications necessitating Low- strength Concrete (LSC), and non-structural light weight concrete.