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The study’s framing of geopolymer optimization reflects a broader shift in construction materials research away from single-property maximization toward balanced, application-driven design. In practical construction, a paste that achieves the highest possible compressive strength is not necessarily the most useful one: it may be too stiff to place and compact properly, or its raw material bill may make it uncompetitive with ordinary Portland cement concrete at scale. By treating compressive strength, flowability, and material cost as simultaneous objectives, the researchers acknowledged the inherent trade-offs that govern real-world mix design. The ternary precursor system they examined—combining fly ash, ground granulated blast furnace slag, and metakaolin—is itself a deliberate strategy to exploit complementary chemistries. Fly ash contributes reactive aluminosilicate glass that dissolves slowly under alkaline activation, slag supplies calcium that drives the formation of calcium-aluminosilicate-hydrate type gels with rapid setting characteristics, and metakaolin, a calcined clay, offers high surface reactivity and additional alumina that can refine the gel network. Balancing these three components allows formulators to tune setting time, strength development rate, and durability characteristics in ways that binary systems cannot easily achieve.

The choice of an L16 orthogonal array is central to the efficiency of the experimental program. Orthogonal designs, rooted in the work of Genichi Taguchi and classical factorial design theory, allow the independent estimation of main effects for multiple factors using a fraction of the full factorial run count. With five mix parameters under investigation—slag content, metakaolin content, sodium hydroxide molarity, the sodium silicate to sodium hydroxide ratio, and the alkali-to-binder ratio—a full factorial exploration at even modest resolution would require dozens to hundreds of paste batches. The L16 array compresses this into sixteen carefully balanced runs in which each factor level appears an equal number of times and factor levels are distributed orthogonally across columns. This balance means that, on average, the influence of one factor is not confounded with the linear influence of another, enabling analysis of variance to attribute portions of observed variance to individual parameters. The trade-off, as the authors themselves note, is that certain two-factor interactions cannot be fully disentangled from main effects within a resolution-limited array, a limitation that is well understood in design-of-experiments practice and typically addressed through follow-up experiments at the identified optimum.

The finding that the alkaline activator ratio exerted the greatest influence on compressive strength aligns with the fundamental chemistry of geopolymerisation. The sodium silicate to sodium hydroxide ratio controls the availability of dissolved silica in the activating solution, which in turn governs the Si/Al ratio of the forming gel network. Higher soluble silica content generally promotes denser, more cross-linked aluminosilicate gels and, in calcium-rich systems, modifies the composition of C-(A)-S-H phases toward higher chain length and greater mechanical integrity. Dissolved silica also moderates the highly caustic environment of sodium hydroxide, affecting the rate at which precursor particles dissolve and the degree to which dissolved species polycondense into stable networks. Meanwhile, the identification of the alkali-to-binder ratio as the dominant factor for flowability is consistent with rheological behavior in alkaline-activated pastes: the total volume of liquid relative to solid determines the spacing between particles and the viscosity of the suspending medium, and alkaline activator solutions are substantially more viscous than water, amplifying their effect on workability.

The economic dimension of the optimization deserves particular attention because it is frequently neglected in laboratory studies of alternative binders. Metakaolin, produced by calcining kaolinitic clay at moderate temperatures, carries an embodied energy cost and a market price considerably higher than that of fly ash or slag, which are industrial byproducts available at low cost near their points of generation. The study’s identification of metakaolin dosage as the dominant contributor to material cost therefore has direct practical consequences: even modest increases in metakaolin content can shift the economics of a mix substantially, which is why the optimal formulation converged on a low metakaolin fraction of ten percent. This cost sensitivity also highlights a general principle in sustainable materials engineering—the environmental and economic benefits of byproduct utilization depend heavily on local supply chains, transport distances, and competing demands for the same materials from other industries, factors that a laboratory cost model can only approximate.

The curing regime established in the preliminary single-factor experiments also merits scientific context. Geopolymerisation is a thermally activated dissolution-condensation process, and low-calcium fly ash systems in particular require elevated temperatures to achieve meaningful reaction within practical timeframes. Temperatures in the range of 60 to 80 degrees Celsius are commonly reported as favorable for fly ash activation, with the 60 degrees Celsius, 24-hour condition identified here as optimal balancing reaction extent against the risk of excessive water loss or gel coarsening at higher temperatures. The presence of slag in the ternary system partially relaxes this thermal requirement, since calcium-rich systems gain strength appreciably at ambient temperature, but heat curing remains beneficial for achieving early strength in blended systems. This thermal dependence has implications for field application, where ambient-temperature curing or modest heat treatment would be required, and it represents one of the practical hurdles that distinguishes geopolymer concretes from conventional Portland cement systems in cold-weather construction.

The microstructural observations reported through X-ray diffraction and scanning electron microscopy provide the mechanistic underpinning for the mechanical results. X-ray diffraction in geopolymer systems typically reveals the characteristic broad hump associated with short-range ordered aluminosilicate gel, superimposed on residual crystalline phases such as quartz and mullite inherited from the fly ash. Shifts in the position of this hump and changes in its relative intensity reflect alterations in gel composition and quantity. Scanning electron microscopy, in turn, allows direct visualization of gel morphology, unreacted particle remnants, and the pore network. The reported features of enhanced C-(A)-S-H and N-A-S-H gel formation, increased matrix densification, and reduced porosity in the optimized mixtures are exactly what reaction mechanism models would predict for a well-balanced ternary system: slag-derived calcium gel fills space and provides early binding, while fly ash and metakaolin-derived sodium aluminosilicate gel contributes to long-term framework development, and the coexistence of the two gel types in an intermixed morphology is widely associated with superior mechanical performance in hybrid systems.

The statistical methodology underlying the decision model also reflects current best practice in multi-criteria optimization. Entropy weighting is an objective technique that assigns greater weight to criteria exhibiting greater variability across the experimental alternatives, on the reasoning that a parameter that discriminates strongly between options carries more information for decision-making. Combining this with subjective weighting, which encodes engineering judgment about the relative importance of strength, workability, and cost, produces a synthetic weighting scheme that tempers purely data-driven assignment with domain expertise. This hybrid approach guards against the failure modes of either extreme: purely subjective weights can be arbitrary and difficult to defend, while purely entropy-based weights can overemphasize criteria whose variability is an artifact of the chosen experimental levels rather than of genuine practical importance. The convergence of the multi-objective analysis on a mixture with moderate values of most parameters—fifty percent slag, ten percent metakaolin, six molar sodium hydroxide, an activator ratio of one to one point five, and an alkali-to-binder ratio of zero point three five—is characteristic of Pareto-optimal solutions in multi-objective problems, where the best compromise rarely coincides with the extreme values that maximize any single objective.

The reported maximum compressive strength of 115.87 megapascals under one experimental condition is notable in the context of published geopolymer literature, where ambient-cured fly ash systems typically achieve strengths in the range of 30 to 70 megapascals and heat-cured or slag-rich systems can exceed 100 megapascals. The high value is consistent with the combination of substantial slag content, heat curing, and an activator chemistry favoring dense gel formation. However, the authors’ transparency about the replication structure of their testing is scientifically important. The three compressive strength specimens per mixture were subsamples drawn from a single batch rather than products of independent batch preparations, which means that the reported variability reflects within-batch homogeneity rather than between-batch reproducibility. Between-batch variation, arising from differences in mixing efficiency, temperature, activator preparation, and precursor sampling, is typically larger than within-batch variation, so the true uncertainty surrounding each mixture’s mean strength is likely wider than the within-batch statistics alone would suggest. The observation that repeat testing broadly preserved the relative ranking of selected mixtures is reassuring for the optimization conclusion, since ranking-based decisions are more robust to absolute strength uncertainty than threshold-based ones, but independent replication at the batch level remains a desirable confirmation step.

From a sustainability perspective, the study contributes to a growing body of evidence that industrial byproducts can substitute for Portland cement clinker at high replacement levels without sacrificing mechanical performance. Cement production is estimated to account for roughly seven to eight percent of global carbon dioxide emissions, driven both by the calcination of limestone and by the fossil fuel energy consumed in clinker kilns. Geopolymer binders eliminate the calcination step entirely, and while the alkaline activators—particularly sodium silicate—carry their own embodied emissions, life cycle assessments generally report substantial net reductions for geopolymer concretes relative to ordinary Portland cement equivalents, with the magnitude depending on activator dosage and transport distances. Ternary systems that incorporate slag, itself a finite byproduct facing increasing demand, raise questions about long-term resource availability, which strengthens the case for including calcined clays such as metakaolin in precursor blends, since clay reserves are abundant and calcination can be performed at temperatures far below those required for clinker production.

The workability findings also carry practical significance for construction practice. Flowability, typically assessed in paste systems through mini-slump or flow table tests, serves as a proxy for the fresh-state behavior of the corresponding concrete, where workability governs placement, compaction, and finishability. The strong influence of the alkali-to-binder ratio on flowability identified in the effect analysis suggests that contractors seeking to adjust workability in the field would have a more effective lever in the liquid content than in the activator composition, though such adjustments must be balanced against the strength consequences of diluting the alkaline environment. The interplay between workability and strength is a recurring theme in geopolymer technology, and the multi-objective framework applied here offers a structured way to navigate it rather than relying on iterative trial and error, which the authors correctly identify as laborious and inefficient for multi-parameter systems.

Finally, the methodological integration demonstrated in this study—combining screening-level single-factor experiments, an orthogonal array for efficient multi-factor assessment, analysis of variance for effect attribution, and a hybrid weighted decision model for multi-objective selection—constitutes a transferable template for other researchers working on complex binder systems. The approach is not limited to geopolymers; it applies equally to alkali-activated materials, limestone calcined clay cements, and other multi-component systems where formulation space is large and performance criteria are competing. The explicit acknowledgment of limitations, including the interaction confounding inherent in the chosen array and the subsample nature of the mechanical replicates, models the kind of methodological candor that allows subsequent studies to build incrementally on reported results, refining the optimum through targeted confirmation experiments and extending the framework to durability indicators, long-term strength development, and full-scale concrete applications where aggregate packing and interfacial transition zone effects introduce additional layers of complexity.

Subject of Research: …

Article Title: Optimization of a ternary geopolymer paste through orthogonal experimental design, ANOVA and entropy-based multi-objective decision analysis

Article References: Murugeswari, S., & Meena, T. (2026). Optimization of a ternary geopolymer paste through orthogonal experimental design, ANOVA and entropy-based multi-objective decision analysis. Frontiers in Built Environment, 12, Article 1934627. https://doi.org/10.3389/fbuil.2026.1934627

Image Credits: AI Generated

DOI: 10.3389/fbuil.2026.1934627

Keywords: geopolymer, fly ash, GGBS, metakaolin, orthogonal experimental design, ANOVA, entropy weighting, multi-objective optimization, compressive strength, sustainable construction, XRD, SEM