Modeling Compressive and Flexural Strength of Cement Grouts with Fly Ash, Silica Fume, and Polyethylene Terephthalate: A Correlated Multivariate Regression Approach in Compositional Data Analysis

An integrated statistical–graphical framework is introduced for designing sustainable cement grout mixes that incorporate polyethylene terephthalate (PET) waste and supplementary cementitious materials (SCMs) for semi-flexible pavement applications. A correlated multivariate linear mixed-effects model employs additive log-ratio transformations of PET and SCM proportions (fly ash or silica fume relative to cement) to predict 1-day, 7-day, and 28-day compressive strengths and 28-day flexural strength within a single unified framework. This approach quantifies both the systematic strength penalty of PET substitution and the benefits of SCM additions. The model results demonstrate high random-intercept correlations, substantial reductions in the Akaike information criterion (AIC) and root mean squared error (RMSE) compared to a null model, and marginal and conditional coefficient of determination (R2) values of 0.96 and 0.99, respectively, confirming major capture of the variance in the mechanical response. Complementary ternary plots visualize predicted 28-day performance across the cement–PET–SCM compositional space. These plots reveal that zero-PET formulations along the cement–binder edge achieve maximum strengths, with both fly ash and silica fume maximizing compressive and flexural strengths and any PET addition uniformly degrading performance. By combining rigorous compositional modeling with intuitive visualization, the proposed framework offers quantitative rigor, practical mix design guidelines, and a scalable protocol for optimizing sustainable grout formulations and informing future exploration of alternative fillers, flow regimes, and durability assessments.