An Optimization of the Flexural Strength of Fibre Cement Mixtures Using Scheffe's Simplex Lattice
Abstract
Thirty two Flexural strength tests were conducted on Fibre Cement (FC) prism samples composed of cement, sand, fibre (coir) and water combined in specified proportions after curing for 28 days. A scientific approach is introduced to optimize flexural strengths of the FC composites by generating a mathematical model that can predict the mix proportions given specified strengths; in doing this, Scheffe's simplex lattice was adopted. The mix proportions were generated from matrix transformations after prescribing typical mix proportions at each of the four points of the tetrahedron lattice (i.e. Scheffe's factor space). The results of the tests were used to develop a mathematical model of the form; y = f(X1, X2, X3, x4); where f (X1, X2, X3, X4) is a real - valued polynomial function of volumetric proportions of water x1, cement x2 sand x3 and coir x4 respectively. Statistical adequacy tests carried out on the model using student 1 and Chi square confirmed the adequacy of the model. A computer programme was developed based on the model to generate mix proportions for any specified strength and to predict optimum strengths. The optimum flexural strength (measured as modulus of rupture) is 7.102079N/mm² after 28 days of curing with six mix combinations. The FC elements producer can use the model to generate combinations of mix proportions from which a final and economic FC product could be produced.
