Semi-flexible pavements occupy an interesting middle ground in road engineering. They combine a porous, open-graded asphalt skeleton with a cement-based grout that is poured into the voids, producing a surface that behaves partly like a flexible asphalt layer and partly like a rigid concrete one. The result is a pavement that resists rutting under heavy loads and resists fuel spills and heat better than conventional asphalt, which is why it is popular for bus lanes, intersections, airports and heavy-duty industrial yards. The catch is the grout: a high-strength cement slurry demands a substantial cement content, and cement production is responsible for a significant share of global carbon dioxide emissions. Replacing even a fraction of that cement with an industrial by-product is therefore an attractive sustainability lever.

The research team, led by Muhammad Imran Khan of Imam Mohammad Ibn Saud Islamic University in Riyadh together with collaborators at Universiti Teknologi PETRONAS, the University of Tabuk and Kabul University, set out to quantify exactly how much cement could be swapped for waste marble dust without destroying the mechanical performance the grout needs. Rather than relying purely on trial-and-error laboratory work, they built a dataset of 72 experimental mixtures spanning water-to-cement ratios from 0.35 to 0.50, marble dust contents from 0 to 25 percent, measurements of grout flow, and compressive strengths recorded at both 7 and 28 days of curing. That structured dataset became the training ground for five different machine learning algorithms.

The five contenders represent a broad cross-section of supervised learning. Artificial neural networks, loosely inspired by the wiring of biological neurons, are famously flexible function approximators. Decision trees split the data through a cascade of simple yes-or-no questions, random forests average the votes of many such trees, support vector machines carve the input space with carefully placed boundaries, and k-nearest neighbor models simply look up the most similar past cases. Each model was asked to predict the 28-day compressive strength of the grout from the mixture variables, and their performance was scored using the mean absolute error, the coefficient of determination known as R-squared, and the adjusted R-squared, which penalizes needless complexity.

The surprise winner was not the flashiest algorithm. The humble decision tree, a model that essentially learns a flowchart of rules, achieved the highest predictive accuracy, with an R-squared of 0.994 and a mean absolute error of just 0.266 megapascals. In practical terms, the model could anticipate the strength of an unseen grout mixture to within roughly a quarter of a megapascal on average, a margin tight enough to be genuinely useful for mixture design. The result is a reminder that in materials informatics, the best model is not always the most elaborate one; when the underlying relationships in a well-controlled dataset are relatively clean, an interpretable model can match or beat its more sophisticated rivals.

Accuracy alone, however, was only half the goal. Modern machine learning in engineering increasingly demands explainability, and the researchers turned to two well-established tools to open the black box. SHapley Additive exPlanations, or SHAP, borrows ideas from cooperative game theory to assign each input variable a fair share of credit for every individual prediction, revealing which factors push the expected strength up or down. Partial dependence plots complement this by tracing how predictions shift as one variable changes while the others are held in place. Together, these methods let the team read the model’s reasoning the way one might read a lab notebook.

The explainability analysis produced a striking conclusion: the single most influential parameter governing the predicted 28-day strength was the 7-day compressive strength itself. That may sound circular, but it is not. The 7-day measurement is an experimentally observed snapshot of how the grout’s hydration and hardening are progressing at an early age, so it carries rich information about the mix’s intrinsic quality and its response to curing. A grout that is already strong at one week is very likely to be strong at four weeks, and the model captures that correlation with high confidence. For engineers, this suggests that early-age testing could serve as a powerful early-warning indicator, allowing underperforming mixtures to be flagged and discarded long before the standard 28-day verification is complete.

The second lesson from the model was more sobering for anyone hoping that marble dust is a free lunch. Increasing the water-to-cement ratio and increasing the marble dust content both reduced the 28-day compressive strength. Marble dust is largely inert or only weakly reactive compared with cement clinker, so as its share rises, there is simply less clinker available to form the binding phases that give the grout its strength, while additional water dilutes and weakens the matrix further. The physics and chemistry are straightforward, but the machine learning models quantified the trade-offs precisely and revealed where the sweet spot lies.

Using the trained models as an optimization engine, the team identified mixture proportions that push cement replacement surprisingly far. At a water-to-cement ratio of 0.40 and with a modest 0.5 percent superplasticizer dose, the optimization allowed up to 32 percent cement replacement with waste marble dust while still meeting the performance targets for the grout. The superplasticizer is the quiet hero here: by dispersing cement particles and improving workability without extra water, it creates headroom for the powder-rich substitution. The analysis also showed that the replacement strategy loses efficiency at higher water-to-cement ratios, meaning there is a genuine window of mixture design within which marble dust substitution is both technically viable and environmentally rewarding, and outside of which it is not.

The broader implications extend well beyond one pavement technology. The study demonstrates a data-driven template for sustainable mixture design: run a disciplined experimental campaign, train a family of models, validate them rigorously, explain them with SHAP and partial dependence analysis, and then use them to search a design space that would be prohibitively expensive to explore with physical trials alone. Applied to semi-flexible pavements, the workflow shows that a stone-industry waste product can displace nearly a third of the cement in the grout under the right conditions, cutting material costs, diverting landfill waste and lowering the embodied carbon of the road surface. As infrastructure owners worldwide face pressure to decarbonize, studies like this one suggest that the roads of the future may be paved, quite literally, with industrial by-products, guided by algorithms that know exactly how far the substitution can go before the pavement pays the price.

Subject of Research: Machine learning optimization of waste marble dust cementitious grouts for semi-flexible pavements

Article Title: Predictive modeling and optimization of eco-friendly cementitious grouts containing waste marble dust for semi-flexible pavements

Article References: Khan, M. I., Khan, N., Almutairi, O. E., Rafiq, W., & Paktin, H. (2026). Predictive modeling and optimization of eco-friendly cementitious grouts containing waste marble dust for semi-flexible pavements. Scientific Reports. https://doi.org/10.1038/s41598-026-75077-z

Image Credits: AI Generated

DOI: 10.1038/s41598-026-75077-z

Keywords: semi-flexible pavement, waste marble dust, cement replacement, machine learning, decision tree, SHAP, partial dependence plots, compressive strength, water-cement ratio, sustainable construction, grout optimization, circular economy