Computational modeling for strength prediction of nano silica-metakaolin blended concrete: a hybrid response surface methodology-machine learning approach

Purpose Accurately predicting the compressive strength (CS) of nano-micro blended concrete (NMBC) is challenging due to the intricate interactions between nano- and micro-scale additives, beyond the scope of conventional methods. This study proposes an integrated approach for improving prediction accuracy and optimizing NMBC mix design by combining experimental testing, statistical modeling and machine learning (ML) techniques. Design/methodology/approach The study initiates with the optimization of the mix design utilizing Response Surface Methodology (RSM), followed by experimental validation of the modified mixture. To further enhance the prediction of CS, ML algorithms like CatBoost, Gradient Boosting, Ridge Regression and XGBoost were employed. Furthermore, the evaluation of model performance was conducted employing various metrics, which include performance metrices, the Regression Error Characteristic (REC) curve and Shapley Additive Explanations (SHAP) analysis. To deepen the understanding of the effects on strength, microstructural analysis was then conducted using X-ray diffraction (XRD) and Field Emission scanning electron microscopy (FE-SEM). Findings RSM effectively optimized the mix design, providing the highest predictive accuracy (R2), while CatBoost outperformed the other ML models in capturing nonlinear relationships, resulting in strong alignment with experimental data. The optimal mix, comprising 2% nano-silica (NS) and 12.5% metakaolin (MK), was experimentally and microstructurally validated. SHAP analysis further identified NS, MK, cement and superplasticizer as the most influential factors affecting CS. Originality/value This work uniquely integrates statistical, ML and microstructural techniques to provide a comprehensive framework for predicting and optimizing NMBC, advancing the development of high-performance concretes. Graphical abstract A workflow for N M B C showing R S M optimization, material mixing, compressive testing, machine learning, and more. In the upper row, on the left, a square box titled “Optimization of N M B C Using R S M” contains a three-dimensional cube plot. The plot is labeled at the corners and center with coordinates like “(positive 1, positive 1, 0),” “(negative 1, negative 1, positive 1),” and the origin “(0, 0, 0)” marked in red. Purple stars and green dots highlight specific parameter sets on the axes. In the central and largest rectangle, labeled “Development of Nano micro blended concrete (N M B C),” five images are aligned horizontally at the top, depicting various materials: white powder, brown powder, off-white powder, yellowish sand, and coarse gray aggregate. Below the material images, labeled brackets converge arrows into the next row, where a schematic diagram shows “Water” and “Superplasticizer” combining in a beaker with a black arrow pointing right. This flows into a color photograph of a blue concrete mixer with an open drum, and a black arrow leads further to the right toward a photo of a gray cubic specimen. On the right, a tall rectangle titled “Compressive strength testing of N M B C” displays a photo of a compression testing machine with a gray cube sample placed between metal platens. In the lower row, on the left side, there is a rectangular section labeled “Prediction and Feature importance using Machine learning.” Inside this section, there are three different visual plots. The far left plot is a vertical scatter plot showing “S H A P value impact on model output” for parameters labeled “N S,” “M K,” “Cement,” “S P,” “Water,” “C A,” and “F A.” In the middle, a polygonal radar chart maps several metrics (“R M S E,” “M A E,” “R 2,” “R S E,” “P I,” “A 20-index,” “S I”) for performance, and axis labels for “C S, 7 D” and “C S, 28 D” are visible. On the far right, a colored heatmap matrix is present showing comparative results with upper and lower color scales, and metric or correlation values inside each cell. Below these plots, the text reads: “Machine learning models: CatBoost, X G Boost, Ridge regression, Gradient Boost. Best Model: CatBoost” in bold red font. The right rectangle contains two plots: on the left, a contour plot labeled “COMPRESSIVE STRENGTH-28TH DAY (Mega Pascals)” with a color gradient and axis labeled “A: N S” and “B: M K.” On the right, a 3 D surface plot with axes “B: M K,” “A: N S,” and “COMPRESSIVE STRENGTH-28TH DAY (Mega Pascals)” is included. At the bottom, red text reads “Optimized mix 2 percent N S and 12.5 percent M K.” The diagram labeled “Optimization of N M B C Using R S M” leads rightward to the diagram labeled “Development of Nano micro blended concrete (N M B C).” The diagram labeled “Development of Nano micro blended concrete (N M B C)” leads rightward to a diagram labeled “Compressive strength testing of N M B C.” Further, the diagram labeled “Compressive strength testing of N M B C” leads downward to a diagram labeled “Validation using RSM.” The “Validation using RSM” leads leftward to a diagram labeled “Prediction and feature importance using machine learning.”