Scheffé–Covariate Modeling of Rheology and Printability in 3D-Printed Concrete

Three-dimensional concrete printing (3DCP) requires precise control of fresh-state rheology to ensure continuous extrusion, geometric stability, and reliable layer bonding. However, most studies focus on individual factors such as water-to-binder ratio (W/B), supplementary cementitious materials (SCMs), fibers, or aggregate characteristics, which limits transferability across mixtures and processes. This work introduces a unified, statistically rigorous, and physically interpretable framework that integrates mixture geometry, process chemistry, and fiber morphology to predict key rheological responses for 3DCP.
A comprehensive literature-based database was harmonized to a common reference frame and modeled using a quadratic Scheffé simplex for seven volumetric components (cement, fly ash, silica fume, GGBS, fine aggregate, coarse aggregate, water). Additional process covariates—W/B, SP/B, VMA/B, and orthogonal Agg/B—capture effects not explained by mixture fractions, while fiber type, volume fraction, and aspect ratio describe morphological influences. Model reduction follows strong heredity principles, and final ordinary least squares fits are evaluated using grouped K-fold cross-validation and leave-one-out PRESS on the original SI scales.
Results show that the Scheffé block defines the baseline rheology, with physically consistent curvature driven by cement–water–fine aggregate interactions. Process terms act as targeted modifiers, notably SP×W/B and VMA/B, while fiber effects are secondary at typical print dosages but increase with aspect ratio, especially for steel. Calibration plots exhibit tight alignment to the identity line and stable residual structure, confirming strong internal generalization. Finally, compact design surfaces translate the model into practical dashboards that balance extrusion, buildability, and shape retention through coordinated adjustments of solids, W/B, and admixture contents. This transferable, non-commercial framework supports data-driven mixture design and process optimization for 3DCP.