Optimization of Concrete Based on Scheffe’s Model Using Crushed Glass as Partial Replacement for Fine Aggregate

This study developed a mathematical model for optimizing the 28-day compressive strength of concrete containing crushed glass and Bida Natural Gravel, based on Scheffe's simplex theory. Using a total of 30 mix ratios, 90 concrete cubes were cast to validate the model. Fifteen mix ratios derived from simplex lattice points were used to calculate model coefficients, while the remaining 15 pseudo-random mixes served as control points. The model’s predictions were statistically validated using the Fischer test, demonstrating adequacy with a 95 percent confidence level. Optimization via MATLAB revealed an ideal 28-day compressive strength of 36.83 MPa, corresponding to an optimal mix ratio—0.4739:1:0.6854:0.1952:1.7612 for water, cement, sand, crushed glass, and BNG. This model enables prediction of mix ratios for desired strengths of concrete containing 0 percent to 25 percent crushed glass.