Response Surface Modelling and Multi-Objective Optimisation of Waste PET and Crumb Rubber Modified Asphalt Concrete

Waste polyethylene terephthalate (PET) and crumb rubber tyre (CRT) are now well established as partial replacements in bituminous concrete, yet most laboratory programmes vary one ingredient at a time and stop at a table of results. That approach cannot describe how the two wastes behave between the tested points, and it cannot separate their combined effect from their interaction. This paper takes the Marshall dataset of 48 specimens (16 mixtures, three briquettes each) from a companion experimental study, in which PET (0, 2, 4 and 6% by mass of bitumen) was crossed with the mineral-filler-to-crumb-rubber ratio (100:0, 75:25, 65:35 and 55:45), and fits second-order response surface models to bulk density, air voids, Marshall stability, flow and stiffness as continuous functions of PET content and rubber substitution. All five models are significant (p < 0.001) with adjusted coefficients of determination between 0.78 and 0.96 and adequate precision above 10 in every case. The analysis of variance shows that PET content controls stability and stiffness, rubber substitution controls flow, and a significant PET by rubber interaction governs stability and density. A desirability analysis, constrained to the Federal Ministry of Works Highway Manual criteria for heavy traffic, places the optimum in the high-PET, low-to-moderate rubber corner of the design space and predicts a compliant mixture at 6% PET. The models reproduce flow, density and voids at the experimentally best mixture (6% PET, 75:25) to within a few percent, but they under-predict its measured stability, because a smooth quadratic cannot fully resolve the sharp synergy that appears at 25% rubber. The study serves as a working document that can enable a mix designer predict Marshall properties, and the specification-compliant region, without running the full factorial.