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Air entrainment in self-compacting concrete (SCC) is governed by coupled interactions between chemical admixtures, empirical workability behaviour, aggregate-skeleton geometry and early air-bubble stability. In highly flowable mixtures, the hardened air-void system cannot be assessed reliably from total air content alone because bubble escape, redistribution and coalescence in the fresh state may change the final pore structure. This study evaluates the link between early fresh-air retention and hardened air-void characteristics in 25 SCC mixtures arranged according to a five-level Graeco-Latin square design. The analysed factors were air-entraining admixture (AEA) dosage (0.00–0.20% by mass of cement), binder type, water-to-binder ratio (0.29–0.41) and the volumetric paste-to-aggregate filling parameter φ (1.1–1.5). The aggregate skeleton was kept constant to separate paste-composition and volumetric-filling effects from aggregate grading. Fresh concrete was characterised by slump-flow diameter, T₅₀ flow time, density and air content after 5 and 15 min; these quantities were treated as empirical workability and early-retention indicators, not as direct rheological parameters. Hardened concrete was examined after 28 days according to EN 480-11 using total hardened air content A, spacing factor L, micropore content A₃₀₀ and specific surface α. The slump-flow diameter ranged from 50 to 79 cm, fresh air content after 5 min from 1.6% to 8.6%, air loss between 5 and 15 min from 0.41 to 1.12 percentage points, hardened air content from 1.20% to 8.59%, and spacing factor from 0.13 to 0.44 mm. Strong correlations were obtained between fresh and hardened air contents (A₅ vs. A: r = 0.920, R² = 0.846, p < 0.001, 95% CI for r: 0.824–0.964; A₁₅ vs. A: r = 0.922, R² = 0.849, p < 0.001, 95% CI for r: 0.828–0.965), while hardened air content was strongly and inversely related to spacing factor (A vs. L: r = −0.907, R² = 0.822, p < 0.001, 95% CI for r: −0.958 to −0.797). The recalculated ANOVA showed that statistical significance was response-dependent: w/b was significant for early air loss ΔA (F = 4.190, p = 0.040, partial η² = 0.677) and micropore content A₃₀₀ (F = 4.058, p = 0.044, partial η² = 0.670), whereas binder type showed near-threshold tendencies for fresh and hardened air contents. No single factor was statistically significant for all air-void descriptors. The SDI-based approach is therefore presented as a bounded explanatory framework, not as an externally validated prediction model. Direct durability claims, including freeze–thaw resistance, require separate experimental verification. Full article

Experimental designs are commonly used to produce valid, defensible, and supportable conclusions. Among commonly used block designs, the class of Latin square designs is used to study factors or treatment levels expressed as Latin letters and applying two blocking factors in rows and columns to simultaneously control two sources of nuisance variability. Another block design in which the error can be controlled by blocking three nuisance factors is obtained by simply using two superimposed Latin square designs, with one using the Latin letters and the other using the Greek letters. Such a design is termed as a Graeco-Latin square (GLS) design. While observing or measuring data in field or lab experiments, it is often noted to have vague, incomplete, and imprecise data for whatsoever reasons. In this regard, researchers have proposed various emerging approaches, which are based on fuzzy, intuitionistic fuzzy, and neutrosophic logic, and provide deeper understanding, analysis, and interpretations of the data. In this paper, we provide a brief review of the history of GLS designs and propose a neutrosophic Graeco-Latin square design, its model, and the analysis. To illustrate this, we have considered an experimental study which analyzes the effects of different formulations of a rocket propellant, which are used in aircrew escape systems, on the observed burning rate. Full article