Explainable machine learning for predicting the mechanical strength of eco-friendly geopolymer concrete

Abstract

This study presents a clear machine learning framework aimed at forecasting the mechanical properties of environmentally sustainable geopolymer concrete (GPC) made from Ground Granulated Blast Furnace Slag (GGBS) and Sugarcane Bagasse Ash (SCBA). Four ensemble machine learning models: Random Forest (RF), AdaBoost, Gradient Boosting (GB) and XGBoost (XGB) were employed to estimate the Compressive Strength (CS), Split Tensile Strength (STS) and Flexural Strength (FS). Particle Swarm Optimization (PSO) and Bat Optimization Algorithm (BAT) algorithms were employed to optimize the hyperparameter of the model. The best test predictive accuracy with R² values for CS, STS and FS are 0.983 (GB- BAT), 0.991 (RF-BAT) and 0.985 (XGB-PSO) respectively with lower error metrics. To improve the model’s interpretability, we used SHapley Additive exPlanations and sensitivity analysis. The findings indicated that the anticipated results were significantly influenced by the GGBS content, curing duration and molarity. The study emphasizes a synergistic effect between GGBS replacement and curing age in enhancing strength development. Integrating explainable Artificial Intelligence (AI) with predictive modeling enhances clarity and provides a reliable way to get results without having lot of laboratory work. This framework is a useful tool for designing mixes based on data and encourages eco-friendly methods of building with cement-free concrete.

Graphical abstract

Keywords

GPC / machine learning / strength prediction / GGBS / SCBA / explainable AI

1 Introduction

The rapid pace of industrialization and urban development has escalated the global demand for concrete, making it the most consumed construction material after water. Traditional concrete production is heavily reliant on Ordinary Portland Cement (OPC), which serves as the principal binder for binding aggregates. However, the environmental impact of OPC production is alarming; it accounts for approximately 8% of global anthropogenic carbon dioxide (CO₂) emissions, due to the energy-intensive calcination of limestone and the combustion of fossil fuels [1]. These emissions contribute directly to climate change, prompting the need for greener alternatives in the construction sector.

In this context, Geopolymer Concrete (GPC) has emerged as a sustainable and innovative binder system. First introduced by Chowdhury et al. [2] in the late 1970s, GPC is formed by activating aluminosilicate-rich precursors with alkaline solutions such as sodium hydroxide (NaOH) and sodium silicate (Na₂SiO₃). This process forms polymeric Si-O-Al bonds, eliminating the need for calcium-based OPC and thereby significantly reducing CO₂ emissions. It has been revealed that GPC can reduce greenhouse gas emissions by as much as 80% in comparison to concrete produced with OPC. This positions it as an excellent option for low-carbon construction initiatives [3–5].

A multitude of studies has shown the potential of industrial by-products like fly ash, Ground Granulated Blast Furnace Slag (GGBS), rice husk ash, and Sugarcane Bagasse Ash (SCBA) in the production of GPC. The high calcium content of GGBS contributes to improved early strength and long-term durability [6–8]. SCBA, a byproduct of agriculture, contains a high level of amorphous silica and demonstrates pozzolanic reactivity, which allows it to be effectively used as a partial substitute in Geopolymer systems [9–11]. Studies have shown that including SCBA up to 20% enhances mechanical properties; however, higher replacement levels may lead to a decrease in strength [12–14]. The curing regime plays a crucial role, as both heat and steam curing greatly enhance the geopolymerization process. The GPC subjected to fly ash treatment at 200 °C exhibited a 33% enhancement in compressive strength (CS) when compared to specimens cured at ambient conditions [15]. GPC demonstrates its ability to uphold structural integrity at temperatures reaching 600 °C [16]. The design parameters, such as NaOH molarity, alkaline-to-binder ratio, and Na₂SiO₃-to-NaOH ratio, have a considerable impact on the setting time and strength. The mix design recommendations provided by Aleem et al. [17] and Madheswaran et al. [18] present proportioning guidelines for strength grades ranging from M20 to M60.

Machine learning (ML) models are being utilized more and more to analyze intricate relationships in concrete behavior. The models including Artificial Neural Networks, Adaptive Neuro-Fuzzy Inference Systems, Random Forest (RF), AdaBoost (AdaB), Gradient Boosting (GB), and XGBoost (XGB) were effectively utilized to forecast concrete properties [19–24]. Nonetheless, these models frequently operate as opaque systems, constraining understanding. The Explainable Artificial Intelligence (XAI) approach, such as SHapley Additive exPlanations (SHAP), has been created to overcome this limitation, allowing for the visualization of feature importance and fostering more transparent decision-making in material design [25,26].

Furthermore, traditional ML models frequently operate as opaque systems, providing minimal insight into the elements that affect their predictions [27]. This has sparked considerable interest in XAI techniques, which seek to improve model transparency and offer insights into how input features affect predicted outputs. The incorporation of XAI into GPC modeling frameworks can enhance mix design optimization and material selection, providing increased confidence and accountability.

Recent research has introduced transformer-based and meta-ensemble architectures for materials and structural modeling [28–35]. These advanced frameworks demonstrate excellent performance on large-scale and highly heterogeneous data sets by enabling deep feature extraction and achieving superior predictive accuracy. However, in laboratory-scale investigations characterized by a limited experimental data set and a narrowly defined geopolymer mix-design space ensemble models integrated with metaheuristic optimizers (Particle Swarm Optimization (PSO) and Bat Optimization Algorithm (BAT)) offer a pragmatic balance between predictive accuracy, interpretability, and computational efficiency. These models require fewer hyperparameters, effectively mitigate overfitting, and integrate seamlessly with explainable-AI tools such as SHAP and sensitivity analysis, ensuring physical interpretability of model behavior. Building upon these advances, the present work employs optimized ensemble ML models to predict the key mechanical properties CS, Split Tensile Strength (STS), and Flexural Strength (FS) of GPC produced using GGBS and SCBA. The integration of explainable-AI techniques, particularly SHAP, enables the evaluation of input-parameter significance and provides actionable insights for sustainable and data-driven mix design.

2 Materials and methods

2.1 Materials used

The GPC mix was designed based on the guidelines provided in IS 17452:2020 for M30 grade concrete. The primary binder used was GGBS, which was partially replaced by SCBA at 0%, 10%, 20%, and 30% by weight. The alkaline activator solution consisted of a combination of NaOH and Na₂SiO₃ in a fixed ratio of 1:2.5. The NaOH solution was made in concentrations of 8, 10, and 12 mol/L. Fine aggregate (FA) and coarse aggregate (CA) were used as per the specifications for concrete mix design.

Natural river sand conforming to IS: 383-2016 was utilized as FA. The CAs were crushed angular stones of 10 mm and 20 mm sizes. The results of testing both aggregates for specific gravity, water absorption, and other relevant parameters are detailed in Table 1.

2.2 Mix proportions

Twelve distinct concrete mixtures were created, with varied molarities (8, 10, and 12 mol/L) of NaOH and the replacement level of GGBS with SCBA (0, 10%, 20%, and 30%). All mixtures had a consistent binder content of 400 kg/m³ and an identical activator solution content. The FAs and CAs were adjusted slightly to maintain workability and desired strength.

2.3 Mixing and casting procedure

All mix components were batched by weight in tune with the mix design. Initially, dry materials like CA, FA, GGBS, and SCBA were mixed thoroughly in a mechanical mixer to ensure uniform distribution (Figs. 1(a) and 1(b)). A solution of alkaline activator was prepared one day prior to mixing by dissolving NaOH pellets in distilled water and then blending it with Na₂SiO₃ solution. This solution was stirred adequately to ensure a homogeneous mixture.

Following the dry mixing process, the alkaline solution was incrementally introduced to the mixture and thoroughly blended until a consistent fresh GPC mix was achieved. After that, the new concrete was poured into conventional molds in three layers. Each layer compacted manually using a tamping rod to remove entrapped air and ensure uniformity. Standard specimens were cast: 150 mm cubes (ASTM C39) for CS, 150 mm × 300 mm cylinders (ASTM C496) for STS, and 100 mm × 100 mm × 500 mm beams (ASTM C78) for FS tests.

In this study, for each mix and testing age, three specimens were prepared and tested for CS, STS and FS in accordance with ASTM standards. The reported values in the manuscript represent the average of these replicate measurements to ensure reliability and minimize experimental variability. This averaging procedure was consistently followed across all test conditions.

2.4 Curing regime

Curing of the specimens was done under ambient conditions. The molded specimens were kept at room temperature for 24 h. After demolding, they were exposed to direct sunlight for curing (Fig. 1(c)). This method was chosen to simulate field conditions for heat-assisted geopolymerization.

2.5 X-Ray Fluorescence (XRF) analysis

The chemical composition of GGBS and SCBA were determined using XRF from Jindal Bellary and the results as mentioned in Table 2.

2.6 X-Ray Diffraction (XRD) analysis

The analysis of XRD was adopted to detect the crystalline phases in GGBS and SCBA. The patterns were recorded in the 2θ range of 10° to 80° using Cu-Kα radiation. The XRD spectrum of GGBS, shown in Fig. 2(a) exhibited a broad hump around 30° to 35°, demonstrating its primary amorphous nature which enhances early-stage reactivity in geopolymer systems. The SCBA spectrum in Fig. 2(b) displayed sharp and distinct crystalline peaks associated with SiO₂, Al₂O₃, Fe₂O₃ and MgSiO₃. These phases confirm the existence of reactive silica and alumina, essential for pozzolanic activity and geopolymerization.

2.7 Scanning Electron Microscopy (SEM) analysis

The surface morphology of GGBS and SCBA were examined using a VEGA3 TESCAN Scanning Electron Microscope operated at 10.0 kV investigate the microstructural characteristics influencing their reactivity in GPC. Figure 3(a) displays the SEM images of GGBS, particles exhibited angular and denser particles with sharp edges and varying sizes, ranging approximately from 6 to 10 µm. These dense structures suggest high calcium content, responsible for improved early-stage strength and better particle packing in the binder matrix. On the other hand, Fig. 3(b) shows that SCBA exhibited irregular, porous, and flaky particles, which contribute to the high surface area and reactive nature of SCBA. These features are indicative of incomplete combustion of organic matter and a high content of amorphous silica, which enhances the pozzolanic activity of SCBA. The porous morphology contributes to increased surface area and reactivity.

2.8 Data exploration

This study employed a data set comprising 81 experimental data points, collected from an extensive laboratory investigation. As Zhao et al. [36] pointed out, earlier studies used data sets with 67 to 226 samples and more than 10 input variables to figure out how strong concrete is when it is compressed. From a ML perspective, it is advisable to uphold a minimum ratio of 1:10 between the quantity of input features and the overall number of data points [37,38].

For this study, five critical input parameters were selected: GGBS content, NaOH molarity, curing days, slump cone value, and compaction factor. The input-to-sample ratio stands at 1:16, exceeding the standard threshold. The availability of sufficient data for training ML models is indicated by this. Prior studies [39,40] served as a basis for the parameter selection process that yielded the CS, STS, and FS values for GPC. This well-chosen data set is great for insightful interpretability research and strong predictive modeling. The data set has been split into a training set and a test set in line with the suggestions made in the prior research [41]. Eighty percent of the data will be used to train the ML algorithms. Using the testing set, which makes up 20% of the data, we can evaluate how well the trained ML models performed. To prevent algorithms from becoming over fit to the training set, this data partition guarantees that they work well with both sets of data [42]. A fixed random seed (42) was applied to the train-test split to ensure reproducibility, and stratified sampling was adopted with respect to the strength outcomes (CS, STS, FS) so that both subsets preserved similar response distributions.

An in-depth analysis of the data’s distribution, a description of the input and output variables, and the exploration of potential correlations should all precede model training. Developing strong and generally applicable prediction models requires a variety of data types, according to studies [43]. A scatter matrix (Fig. 4) is used to show how variables are spread out and how they relate to each other in pairs. This statistical tool gives us useful information about regression patterns and how variables interact with each other, which helps us understand the structure of the data before we build a model [44]. A thorough data exploration was done in order to comprehend how the input and output variables behaved and interacted. As seen in Figs. 4 and 5, respectively, this included pairwise distribution analysis and correlation heatmap evaluation.

The distribution and correlations between all of the input variables (molarity, GGBS replacement (%), slump cone value, compaction factor value, and curing days) and output variables (FS, CS, and STS) are depicted in the pairplot (scatterplot matrix) in Fig. 4. Whereas the off-diagonal plots use regression lines and confidence intervals to show pairwise scatter relationships, the diagonal plots show the distributions of individual variables. FS, CS, and STS all demonstrate robust positive linear correlations with one another. slump cone and compaction factor values are positively connected with strength parameters, while GGBS replacement has a negative correlation with them. molarity and curing time exhibit moderately positive trends with strength properties, suggesting that they influence the evolution of the microstructure and the GPC.

The Pearson correlation coefficients between the output responses and all input features are displayed in the Fig. 5. Strong negative correlation is represented by a color scale of −1, while strong positive correlation is represented by a scale of +1 [45]. The correlation matrix is symmetric along its diagonal, which means the values in the upper and lower triangles are the same. A correlation coefficient (R) exceeding 0.8 typically indicates a strong relationship between two variables, values higher than 0.9 mean that the relationship is very strong [46].

The correlation between CS and FS is very high (R = 0.98), and STS is closely behind (R = 0.90 with CS and R = 0.88 with FS). Higher GGBS levels appear to decrease workability, as evidenced by the strong negative correlation between GGBS replacement and slump cone (R = −0.86) and compaction factor (R = −0.95). In line with the behavior of GPC, that is influenced by alkalinity and curing time, molarity, days and compaction factor show moderately positive correlations with mechanical properties. To find multicollinearity, comprehend variable distributions and direct feature selection and model training, this exploratory analysis was crucial. It attests to the applicability of each chosen input feature and their noteworthy impact on forecasting the mechanical performance of GPC.

2.9 Machine Learning

In this study, four ensemble-based ML models like RF, AdaB, GB and XGB were implemented using Python programming. These algorithms are well-regarded for their capacity to model and forecast intricate relationships between feature inputs and target outputs. These approaches have been useful in examining material qualities, including the impacts of temperature, mechanical strength, and long-term durability [47,48]. The modeling framework involved five independent variables and three dependent variables. The performance of each model was primarily assessed using the coefficient of determination (R²), which measures how well the predictions match the actual results. A high R² value (1) means that the model’s predictions and the actual data are closely related, whereas a low R² value (0) means that they are not [49].

To improve the predictive accuracy, optimization techniques; PSO and BAT Algorithms were integrated with the ML models. These nature-inspired optimization methods were utilized to fine-tune model parameters for improved performance. Moreover, k-fold cross-validation and standardization were adopted to guarantee the generalizability of the models. The evaluation of the model included various error metrics, specifically Mean Absolute Error (MAE), Mean Squared Error (MSE) and Root Mean Square Error (RMSE). Furthermore, techniques for enhancing interpretability in AI, particularly SHAP, were utilized to elucidate and visualize the influence of each input feature within the optimized models. This facilitated a deeper comprehension of the fundamental connections between inputs and target outputs. The comprehensive workflow of ML is depicted in the flowchart presented in Fig. 6.

2.9.1 Random Forest

RF is a potent ensemble ML algorithm which constructs numerous decision trees through bootstrap sampling and the choice of arbitrary features. The ultimate result is attained by the combination of predictions from each individual tree, thereby improving predictive accuracy and minimising the likelihood of overfitting. In regression tasks, the final prediction is computed by averaging the outputs of all trees, as demonstrated in Eq. (1), where {\hat{y}}_a denotes the prediction from the ath tree and N represents the total number of trees [50,51]:

(1){\hat{y}}_{}=\frac{1}{N}\sum _{a=1}^x{\hat{y}}_a.

This ensemble approach enhances the model’s capacity to effectively generalize on previously unobserved data. The mechanical behavior of GPC may be accurately predicted by RF because it captures the complicated, nonlinear interactions between mix design parameters and target qualities like as CS, STS, and FS. RF is a reliable solution for modeling in material science applications due to its extraordinary versatility and precision.

2.9.2 AdaBoost

Using a sequential ensemble learning approach, AdaB builds a robust prediction model by merging numerous weak learners, usually shallow decision trees. The AdaB method builds trees sequentially, as opposed to RF’s independent tree construction. The goal of each succeeding model is to fix the mistakes of the one before it by giving more weight to the cases that were incorrectly forecasted or misclassified [52,53].

To tackle regression challenges, AdaB focuses on the data points that have significant effects on the loss function and employs that information to reduce prediction error. In the end, all the weak learners’ predictions are weighted together. Improved generalizability, reduced bias, and enhanced model robustness are all outcomes of this process. The prediction function can be mathematically represented in Eq. (2):

(2){\hat{y}}_{\text{final}}=\sum _{m=1}^M{\alpha }_m{h}_m\left(x\right),

where h_m\left(x\right) is the prediction from the mth weak learner, {\alpha }_m is its corresponding weight, and M is the total number of learners.

AdaB has proven effective in modeling complex strength-related behaviors, particularly when subtle patterns and nonlinear dependencies exist in the data set. Its ability to sequentially focus on difficult-to-predict instances makes it well-suited for accurately estimating CS, STS and FS based on many mix design parameters.

2.9.3 Gradient Boosting

GB is an effective ensemble ML algorithm that constructs predictive models in a stage-wise manner by sequentially adding weak learners typically decision trees. Every tree in the sequence is designed to report the residual errors produced by the preceding ensemble, thus reducing the total prediction loss. The algorithm relies on gradient descent to optimize a specified loss function, hence the name gradient boosting [54,55].

In regression tasks, GB enhances accuracy by analyzing the gradients of the loss function in relation to each data point. The ultimate prediction is derived by aggregating the inputs from all contributors:

(3){\hat{y}}_{\text{final}}=\sum _{m=1}^M{h}_m\left(x\right),

where h_m\left(x\right) represents the mth decision tree. In this study, GB was employed to model the CS, STS and FS of GPC. The method’s ability to iteratively minimize prediction error and identify intricate, nonlinear relationships among input variables makes it highly effective for this application.

2.9.4 Extreme Gradient Boosting

XGB is an advanced implementation of gradient boosting that introduces system-level and algorithmic optimizations to improve speed, accuracy, and scalability. It incorporates regularization to penalize complex models, thereby preventing overfitting, which is particularly crucial when addressing noisy conditions or high-dimensional data [56,57].

Similar to GB, XGB constructs trees in a sequential manner, with each tree addressing the prediction errors made by its predecessor. However, XGB improves efficiency by using second-order derivatives in its loss function and employing parallel processing during tree construction. The final output is computed as:

(4){\hat{y}}_{\text{final}}=\sum _{m=1}^M{f}_m\left(x\right),f_m\in F,

where f_m denotes the mth regression tree in the function space F.

The mechanical properties of GPC were predicted using XGB due of its robust error measures (R² and RMSE) and its capacity to handle diverse data and model nonlinearity.

All models were developed in Python using open-source libraries. The ensemble algorithms (RF, AdaB, GB, and XGB) were implemented with Scikit-learn, while Optuna and custom Python scripts were employed to integrate the PSO and BAT optimization routines. SHAP analyses and visualizations were performed using the SHAP library within the Google Colab environment to ensure transparency and reproducibility. Separate models were trained independently for each target output (CS, STS, and FS) allowing each model to capture the distinct mechanical behavior and governing factors associated with its respective response.

2.10 Optimization techniques

To improve the ML models’ prediction abilities, hyperparameter were fine-tuned using two optimization methods that draw inspiration from nature: PSO and BAT. By utilizing these methods, one can find the best parameter combinations for minimizing prediction error and maximizing generalizability.

2.10.1 Particle Swarm Optimization

PSO is a method for stochastic optimization that takes a page out of the collective behaviors seen in fish schools and flocks of birds [58]. This method finds the best possible solution by navigating sets of possible ones through the search space. By combining its own optimal experience with the collective’s, it starts to take a different stance [59]. Using the following, we can update the position and speed of each particle:

(5)v_i^{t+1}=w{v}_i^t+c_1{r}_1\left(p_i^{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}-x_i^t\right)+c_2{r}_2\left(g^{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}-x_i^t\right),

(6)x_i^{t+1}=x_i^t+v_i^{t+1},

where v_i and x_i are the velocity and position of particle i, p_i^{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}} is its personal best position, g^{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}} is the global best, and w, c_1, c_2 are inertia and learning coefficients.

PSO was applied to fine-tune critical hyperparameters (e.g., number of estimators, learning rate and tree depth) of ensemble models such as RF, AdaB, GB, and XGB.

2.10.2 Bat Optimization Algorithm

BAT is a metaheuristic algorithm inspired by the echolocation behavior of microbats [60]. It uses frequency-tuned search strategies and loudness-adjusted exploration to balance global and local search. Each bat is characterized by its velocity, position, frequency, loudness, and pulse rate, which evolve dynamically during the optimization process [61].

The algorithm updates positions and velocities as follows:

(7)f_i=f_{min}+\left(f_{max}-f_{min}\right)\beta ,

(8)v_i^{t+1}=v_i^t+\left(x_i^t-x^{\ast }\right)f_i,

(9)x_i^{t+1}=x_i^t+v_i^{t+1},

where \beta is a random number in [0,1], and x^{\ast } is the current global best solution.

This study employed BAT to modify parameters by thoroughly exploring the search space, thereby ensuring strong model configurations for predicting the properties of GPC.

The convergence behavior of both optimization methods (PSO and BAT) was thoroughly evaluated by observing the goal fitness function, which is defined as the minimization of RMSE, over iterations. Convergence was proven when fitness values plateaued and showed no further meaningful improvement. To ensure robustness and prevent premature convergence, each method was tested on several independent runs. Because of its simple velocity-position update mechanism, the PSO approach converged faster, stabilizing after 20–30 iterations and requiring less computer power. In comparison, the BAT algorithm needed more iterations (about 50–70) but allowed a more extensive investigation of the search space via adaptive frequency, loudness, and pulse-rate control, occasionally identifying superior global optima. This comparison analysis revealed that the chosen hyperparameters were robust and not the result of early convergence, while also proving the complementing nature of PSO (efficient and rapid) and BAT (thorough and globally explorative) in model optimization.

2.11 Model evaluation

Upon completing the data preparation, the ML models were trained using 80% of the available data set, while the remaining 20% was set aside for testing the models. A 10-fold cross-validation approach was adopted to ensure reliable and unbiased performance assessment. The data set is divided into ten equal segments; during each iteration, one segment is used for validation while the other nine are employed for training [62]. The process is conducted ten times, and the mean outcome is utilized to assess the model’s ability to generalize. Four statistical metrics were employed to assess the prediction accuracy: R², MAE, MSE, and RMSE. The application of these metrics across all target variables, such as CS, STS, and FS, allowed for a thorough evaluation of the accuracy and stability of each model [63].

(10)R^2=1-\left(\frac{{\displaystyle \sum _{i=1}^n{\left(y_i-{\hat{y}}_i\right)}^2}}{{\displaystyle \sum _{i=1}^n{\left(y_i-\overline{y}\right)}^2}}\right),

(11)MAE=\frac{1}{n}\sum _{i=1}^n\left|y_i-{\hat{y}}_i\right|,

(12)MSE=\frac{1}{n}\sum _{i=1}^n{\left(y_i-{\hat{y}}_i\right)}^2,

(13)RMSE=\sqrt{\frac{1}{n}\sum _{i=1}^n{\left(y_i-{\hat{y}}_i\right)}^2},

where y_i is the observed value, {\hat{y}}_i is the predicted value, \overline{y} is the mean of observed values, n is the number of observations.

The selection of these metrics was intentional to capture complementary aspects of model performance. The R² measures the proportion of variance explained by the model, reflecting its overall predictive power. MAE quantifies the average magnitude of errors, providing an intuitive sense of typical deviation between observed and predicted values. MSE penalizes larger errors more strongly, making it sensitive to outliers and useful for identifying substantial deviations. RMSE being the square root of MSE, expresses prediction errors in the same unit as the response variables, which enhances interpretability. Using these metrics together allows for a robust evaluation of both accuracy and stability, ensuring that models are not judged solely on a single performance criterion.

A model exhibiting a higher R² value alongside lower MAE, MSE, and RMSE is considered to demonstrate superior performance. After finalizing the calculations for the evaluation metrics linked to each model, a comparative ranking was performed to identify the algorithm that achieved the highest accuracy in predicting the CS, STS, and FS of GPC.

2.12 Explainable Artificial Intelligence

The final stage of this study concentrated on evaluating how input features influenced the predicted outcomes produced by the most successful model. To achieve this, techniques from XAI are employed, providing insight into how each input variable influences the model’s output, thus enhancing interpretability and building trust in the prediction results.

SHAP is a technique for interpreting models after they have been developed, based on principles from cooperative game theory. This method develops a framework for additive feature attribution, enabling the assessment of each input variable’s distinct impact on the predictions generated by the model. For each predicted sample, SHAP allocates a value to every feature, reflecting its positive or negative influence on the final output. The values provide important insights into the input features that greatly influence the prediction outcomes [64,65].

Mathematically, the SHAP value for a feature is computed as:

(14){\hat{y}}_i={\Phi }_0+\sum _{i=1}^n{\Phi }_j,

where {\hat{y}}_i is the predicted output for the ith sample, {\Phi }_0 is the model’s baseline value (typically the average prediction over the training set), {\Phi }_j is the SHAP value representing the contribution of the feature, n is the total number of input features.

Each prediction is the sum of a base value and the individual SHAP contributions from all features. SHAP provides consistency and local accuracy by considering all possible feature coalitions. This methodology was crucial in identifying which features (e.g., GGBS content, activator ratio and curing time) most significantly influenced the prediction of strength characteristics in GPC.

SHAP allocates the prediction across the input variables in an appropriate and precise manner, illustrating the extent to which each feature contributes to or deviates from the output compared to the average value. Thus the model makes more transparent and improves trust in its predictions.

3 Results and discussion

The prediction of CS, STS, and FS for GPC made with GGBS and SCBA was conducted utilizing four ensemble ML models: RF, AdaB, GB and XGB. To identify the most precise and reliable model, two optimization techniques, namely PSO and BAT algorithms, were utilized with each ML model. The evaluation of all models was conducted through four standard indicators: R², MAE, MSE and RMSE. The comprehensive analyses of each output are presented individually in the subsequent subsections.

3.1 Machine Learning

3.1.1 Compressive Strength

The prediction of CS was conducted using four ensemble models and optimized using PSO and BAT algorithms. The results are summarized in Table 3, indicate the both GB and XGB models achieved exceptionally high training and test accuracies (R² > 0.98), with low error values across all metrics.

Among all models, the GB model optimized with BAT showed superior performance in both training and testing phases, achieving the lowest MAE (0.2689) MSE (0.1769) and RMSE (0.4206), while maintaining a high testing R² = 0.983 during testing. These metrics demonstrate both excellent accuracy and generalization. In contrast, AdaB underperformed, especially during testing, showing higher error values and lower R². To visualize model performance, only the optimal model’s output is plotted. The experimental versus predicted CS values using the GB-BAT model are shown in Fig. 7, with a ±5% deviation band demonstrating a robust correlation between the anticipated outcomes and the observed results. Figure 8 illustrates a comparison of the experimental and anticipated results on a sample-wise basis, including the corresponding errors. The minimal and consistent deviation across test samples suggests the model’s stable and reliable prediction behavior. These findings confirm that the GB-BAT model not only captures the nonlinear relationships effectively but also avoids overfitting.

Although the ensemble models demonstrated very high R² values with low error metrics, we recognize the potential risk of overfitting. To mitigate this, only a limited number of input features were used relative to the data set size, a 10-fold cross-validation approach was adopted, and independent test sets were employed for evaluation. The close agreement between cross-validation scores and test set performance confirms that the models maintained stability and generalization rather than fitting spurious patterns.

Compared with previous studies, the proposed GB-BAT model demonstrates significantly improved predictive performance. Gogineni et al. [66] reported testing R² values of approximately 0.94 using RF and GB models, while Ahmad et al. [67] achieved an R² of 0.96 with a MAE of 1.69 MPa for GPC. Tanyildizi [68] applied a deep learning model (Long Short-Term Memory (LSTM)) and attained an accuracy of 99.23%. In contrast, the current study achieved a higher testing R² of 0.9967 and a substantially lower MAE of 0.2273 MPa using the GB-BAT model, indicating superior predictive capability and generalization.

To further evaluate model performance, Fig. 9 presents a radar chart comparing the testing-phase evaluation metrics for all four ensemble models optimized using the BAT algorithm. It is clearly evident that the GB and XGB models exhibit the most compact and minimal error profiles. The values presented here are significantly less than those associated with the RF and AdaB models, which cover more extensive regions in the radar chart. This suggests that the GB-BAT and XGB-BAT algorithms demonstrate greater accuracy and stability, rendering them more effective in capturing the nonlinear behavior of CS in GPC.

In support of this, Fig. 10 illustrates a parallel coordinates plot comparing the R² scores of the models under PSO and BAT optimization techniques. The results highlight a notable improvement in R² scores for GB and XGB models when optimized with BAT, demonstrating the efficiency of the BAT algorithm in enhancing model generalization. Conversely, RF demonstrates a moderate gain, while AdaB yields negligible improvement, suggesting its lesser sensitivity to the choice of optimization algorithm.

Collectively, these analyses validate that the GB model optimized with BAT not only achieves the highest accuracy but also maintains robustness and generalizability, outperforming other models and optimization combinations. The choice of optimization algorithm, especially BAT, proves to be a critical factor in maximizing predictive performance.

3.1.2 Split tensile strength

STS prediction results for GPC using the optimized ensemble models are summarized in Table 4. Among all models, the GB with BAT optimization achieved the highest training accuracy (R² ≈1.0) with near-zero error metrics. However, throughout testing, the RF model optimized with BAT performed best, achieving R² = 0.9912, with low MAE (0.04130), MSE (0.00295) and RMSE (0.05434), indicating strong generalization. The experimental vs. predicted STS values for the optimal model (RF-BAT) are shown in Fig. 5, which clearly shows the predicted values closely following the equality line, with the majority of data points situated within the ±5% deviation band.

The XGB-PSO model also provided competitive results, while AdaB showed the lowest accuracy across both phases. To visualize model performance, only the best model’s output is presented in Fig. 11, showing the actual versus predicted STS using the RF-BAT model. The performance of the RF-BAT model is further highlighted in Fig. 12, which compares the actual and predicted STS values for the test samples, along with the corresponding prediction errors. The actual and predicted curves nearly overlap across all samples, reflecting the model’s high prediction fidelity. Furthermore, the error values remain consistently low and stable, without noticeable spikes or outliers, confirming the model’s robustness and generalization capability. These results affirm that the RF-BAT model can reliably capture the complex relationships in GPC data, making it an appropriate instrument for applications that require accuracy STS estimation.

To compare performance across models, Fig. 13 displays a radar chart of MAE, MSE, and RMSE for each BAT-optimized model. The RF model shows the most compact error zone, reinforcing its status as the top-performing model in this context. In contrast, AdaB and GB models exhibit wider radar areas, signifying higher error levels and relatively weaker performance. Additional insights can be found in Fig. 14, which presents the parallel coordinates plot of R² scores for each model utilizing PSO and BAT optimization. Notably, the RF model shows a marked improvement in R² from PSO to BAT, confirming the effectiveness of BAT in tuning model hyperparameters. While AdaB also shows marginal improvement, GB and XGB experienced slight declines in R², suggesting sensitivity to overfitting or optimization strategy.

The findings align with existing literature. For instance, Diksha et al. [69], reported that RF and GB performed best for STS prediction in GPC. Wu et al. [70] similarly confirmed the superior accuracy of RF in forecasting STS of high-performance concrete. The findings from these studies reinforce our observation that the RF-BAT model successfully captures the nonlinear relationships in GPC and can function as a reliable tool for STS estimation in real-world applications.

3.1.3 Flexural Strength

FS prediction was conducted utilizing the same four ensemble models along with PSO and BAT optimization techniques. The results of the performance are encapsulated in Table 5. The XGB model optimized with PSO demonstrated superior testing performance, achieving R² = 0.98503, MAE = 0.02708, MSE = 0.0017, and RMSE = 0.04122, which reflects outstanding prediction accuracy and generalization capabilities.

Throughout the training phase, the GB-BAT model demonstrated exceptional accuracy (R² = 0.9999) with minimal errors (MAE = 0.00196, MSE = 0.000013), indicating an almost flawless fit. During the testing phase, XGB-PSO demonstrated superior performance compared to all other methods in achieving a balance between prediction accuracy and error minimization. The AdaB model exhibited the least effective performance overall, achieving R² values of 0.9232 (BAT) and 0.9836 (PSO) in the testing phase, accompanied by relatively elevated MAE and MSE values. Figure 15 illustrates the actual versus anticipated FS values for the XGB-PSO model, showing close alignment along the equality line, containing the majority of data points in the ±5% error band. Moreover, the prediction error trend is further analyzed in Fig. 16, which compares actual and predicted FS values across the test data set. The figure demonstrates that predicted values closely track the actual values across all test samples, indicating strong model reliability. The corresponding prediction errors remain consistently low and stable, with no significant deviation, reinforcing the model’s robustness and accuracy for FS prediction in GPC.

Figure 17 presents a radar chart of evaluation metrics (MAE, MSE, RMSE) for all models under PSO optimization for FS prediction. The XGB model forms the smallest polygon, indicating the lowest error among all models. In contrast, AdaB and GB models exhibit wider spreads, highlighting comparatively higher error rates and reduced accuracy in FS prediction. The influence of optimization techniques is further analyzed in Fig. 18, which shows the parallel coordinates plot comparing R² scores of each model under PSO and BAT. Interestingly, all models except XGB experienced a decline in R² when optimized with BAT, confirming that PSO is better suited for FS prediction tasks in this context. Notably, XGB maintained high R² values under both techniques, reinforcing its reliability and adaptability.

The results are consistent with earlier studies indicating that ensemble models such as XGB and RF demonstrate enhanced effectiveness in forecasting the FS of concrete. For example, Han et al. [71] found that the XGB model reached a R² of 0.93 during testing, surpassing other models such as Linear Regression and RF. In the same way, Abbas et al. [72] demonstrated that the RF model exhibited superior predictive and generalization abilities relative to other ML techniques in forecasting the FS of concrete incorporating metakaolin. The precedents highlight the robustness of ensemble models, particularly the XGB-PSO model developed in this study, as effective model for predicting FS in GPC with optimal accuracy.

3.1.4 Sensitivity analysis

A sensitivity analysis was carried out using feature significance scores obtained from the XGB model to better comprehend the impact of each input parameter on the ML models’ prediction capabilities. Each feature’s contribution to lowering prediction error is reflected in the gain-based feature importance [73]. Figure 19 show the results for CS (Fig. 19(a)), STS (Fig. 19(b)) and FS (Fig. 19(c)).

GGBS replacement was responsible for a gain of 0.674 for CS (Fig. 19(a)), which was followed by molarity (0.215) and curing days (0.109). slump cone and compaction factor value, two metrics related to workability, had very little impact. GGBS replacement once again had the highest ranking (0.441) for STS (Fig. 19(b)), followed by curing days (0.263) and molarity (0.152). Significantly, the compaction factor value (0.129) demonstrated a comparatively greater significance in this instance, indicating its connection to the influence of microstructural homogeneity on tensile resistance. A similar pattern was seen in the case of FS (Fig. 19(c)), where curing days had a moderate impact (0.112) and GGBS replacement (0.663) and molarity (0.220) were the main contributors. According to the chemistry of geopolymerization, where the binder content and its reactivity have a considerable influence on the final strength, these observations demonstrate that the GGBS content is crucial to strength development. curing days show how strength increases gradually, while molarity regulates the alkalinity and rate of dissolution of precursors.

It’s interesting to note that although data exploration (Subsection 3.8) revealed moderate linear correlations for parameters such as days and molarity, the sensitivity analysis validates their nonlinear, model-learned impact on strength predictions. The difference between statistical correlation and model-based feature importance was further highlighted by the fact that features such as slump cone and compaction factor, although exhibiting some correlation patterns, made minimal contributions to the predictive performance. The model’s learning behavior is generally validated by the sensitivity analysis, which also verifies the physical relevance of important features and offers guidance for setting variable priorities in upcoming mix design and optimization research.

Although the models achieved high accuracy, the data set size (81 samples) is limited. Overfitting risks were mitigated through 10-fold cross-validation, independent testing, and replicate averaging. External validation was not conducted due to material variability, and future studies will address this using larger data sets for broader validation. The predictive validity of the developed ML models is restricted to the specific material domain, the defined input variable ranges, and the geopolymer mix design space employed in this study. Therefore, extrapolation beyond these experimental boundaries should be interpreted with caution, as the models are optimized for the present data set characteristics.

3.2 Synergistic impact of Ground Granulated Blast Furnace Slag content and curing age on geopolymer strength performance

3D surface plots were created to visually represent the combined effects of curing days and GGBS replacement (%) on the mechanical strength performance of GPC. These plots (Fig. 20) show how variations in binder composition and curing time affect CS, STS and FS.

Based on the findings of the sensitivity analysis using the XGB model, GGBS replacement and curing days were chosen as the primary variables for interaction analysis. In all three target properties (CS, STS, and FS), these two characteristics were consistently rated as the two most important inputs.

According to the gain-based importance scores, curing days had a significant impact on long-term strength development, while GGBS replacement made the biggest contribution to lowering prediction error. To comprehend their combined nonlinear interaction and impact on mechanical properties, a targeted 3D visualization was carried out. In line with best practices in interpretable ML and experimental concrete research, this method is data-driven and supported by science.

CS (Fig. 20(a)) shows a decreasing trend as GGBS replacement increases, particularly above 20%. On the other hand, strength at all replacement levels is greatly increased with increasing curing age. This result is consistent with research by Bandi and Kolhar [74], which found that longer curing increases the degree of geopolymerization and consequently strength, especially for mixes that are rich in GGBS. For STS, a comparable interaction is seen in Fig. 20(b). Higher GGBS content results in lower strength values, whereas longer curing times lead to increased strength. Zuaiter et al. [75], who emphasized the curing-time dependency of geopolymer tensile properties because of continuous aluminosilicate gel formation, support this behavior. The same pattern can be seen in Fig. 20(c) (FS), which steadily increases with curing time and decreases with GGBS content. Longer curing times and lower GGBS levels are indicative of more consistent flexural behavior on the smoother surface. The findings of Rattanasak and Chindaprasirt [76], who highlighted the significance of curing conditions in the flexural performance of slag-based geopolymer systems, are supported by this result.

SCBA, utilized as a partial binder in this study, demonstrated behavior similar to other supplementary cementitious materials while also showcasing unique characteristics. The elevated amorphous silica content facilitated early geopolymerization, leading to enhanced initial strength development. Nevertheless, past specific replacement thresholds, the increase in strength was less than what is typically seen with conventional supplementary cementitious materials like fly ash or slag, probably because of its inconsistent particle size distribution and remaining carbon content. The findings validate SCBA’s potential as a viable sustainable option, highlighting the importance of meticulously fine-tuning replacement ratios to attain performance levels akin to traditional materials.

The interaction between GGBS replacement and curing duration exhibited clear threshold behavior. The strength showed a significant increase up to approximately 20% GGBS replacement, after which the enhancement appeared to level off or experience a slight decline. Extended curing durations consistently improved strength progression across all mixtures, with the most notable advancements recorded between 28 and 90 d. The findings suggest that prolonged curing may help mitigate the decrease in strength associated with increased GGBS levels, although this benefit is constrained after reaching a specific limit. This emphasizes the complex interplay between binder composition and curing conditions in affecting the performance of GPC.

3.3 Explainable AI

To enhance the interpretability and trustworthiness of the optimized ensemble models, XAI techniques were applied to the best-performing models for each outputs namely CS, STS and FS. SHAP was utilized to reveal the significance of input features and their roles in the predictions made by each model [77]. The following discussion provides insights obtained from the SHAP visualizations and emphasizes the primary influencing factors for each output response.

This investigation involved conducting sensitivity analysis independently through gain-based feature importance scores obtained from the XGB model, while SHAP analysis was utilized separately to offer both global and local interpretability. The two approaches worked in harmony: sensitivity analysis provided a numerical ranking of variable impact, while SHAP delivered in-depth insights into input-output relationships at both the data set and individual instance levels.

1) CS Prediction

The application of XAI enhanced the transparency and interpretability of the optimized XGB-PSO model developed for predicting CS. Specifically, SHAP were employed to evaluate the global and local contributions of each input feature to the predictions made by the model. This enabled a deeper understanding of feature effects and interaction behaviors compared to what conventional importance rankings could provide. Figures 21(a) and 21(b) present the results of the global interpretation.

The model’s predictions were most significantly impacted by GGBS replacement (3.630), followed by curing days (2.903) and molarity (2.402), according to Fig. 21(a) (Mean Absolute SHAP Values). These rankings are consistent with previous sensitivity and feature importance analyses. The distribution of SHAP values across all data instances is shown in Fig. 21(b) (bee swarm plot). It demonstrates that while lower GGBS values (blue) cause predictions to shift upward, higher GGBS replacement values (red) cause predictions to decrease. Longer curing times also consistently improve strength predictions, demonstrating their crucial function in geopolymerization.

A localized prediction for a test instance with a CS of 30.56 MPa is shown in Fig. 22(a) (SHAP force plot). According to the model, curing days and molarity have a positive impact, while GGBS replacement and slump cone have a negative one. This illustrates how the predicted output is modified by the individual feature values in relation to the base value. Interaction effects between features are shown in Fig. 22(b) (SHAP Partial Dependence Plots (PDPs)). For example, the effect of molarity is dependent on the level of GGBS, and the effect of GGBS replacement varies with curing days. These intricate relationships draw attention to the shortcomings of linear correlation analysis and emphasize the necessity of tools for model interpretability such as SHAP.

For every input, Fig. 23 shows the PDPs and Individual Conditional Expectation (ICE): Fig. 23(a) (GGBS replacement): SHAP values show a sharp decline in strength contribution after 20%, suggesting a performance threshold. CS rises nonlinearly in Fig. 23(b) (curing days), showing noticeable increases after 28 d and peak contributions at about 90 d. Figure 23(c) (molarity): A chemical activation threshold is confirmed by the steep rise in SHAP values after a limited influence up to 10 M. Figures 23(d) and 23(e) (compaction factor and slump cone): These variables’ low global SHAP scores are consistent with their little effect throughout the data set.

The SHAP analysis confirms and elaborates on previous findings by providing instance-level attribution and highlighting threshold-based effects [78]. The main predictors of CS are molarity, curing days, and GGBS replacement. After 20%–25% GGBS replacement, performance drastically declines, and strength increases after 10 M molarity and longer curing (> 28 d). Their exclusion from optimization-focused studies is further supported by the fact that workability features (compaction factor, slump cone) have very little effect. In general, XAI improves the model’s transparency, validates its accuracy, and offers useful information for optimizing mix design and forecasting performance in GPC applications.

2) STS Prediction

To enhance the interpretability of the XGB-PSO model used for predicting STS, XAI techniques were employed using SHAP. SHAP enables the quantification and visualization of the contribution of each input feature to the model’s predictions. The global and local interpretations are discussed below.

Figure 24 presents the global contribution of each input feature. In Fig. 24(a), the most significant input was GGBS replacement (0.300), followed by curing days (0.281) and molarity (0.196). These features had the highest average impact on the prediction of STS. The Fig. 24(b) shows that higher GGBS replacement values cause SHAP values to shift to the negative side, indicating decreased strength. Higher molarity values and longer curing times, on the other hand, typically improve the anticipated STS [79,80].

A test sample with a predicted STS of 3.51 MPa is depicted in the SHAP Force Plot in Fig. 25(a). In this case, curing days (3 d) and molarity (12 M) had a positive impact on the result, whereas GGBS replacement (20%) had a negative impact on the prediction. The patterns observed in global SHAP summaries are supported by this case-level interpretation.

Important interactions are also shown in Fig. 25(b). For instance, the effect of GGBS replacement changes with curing age, and the effect of molarity increases when GGBS is less than 20%. These connections highlight how crucial it is to take feature combinations into account rather than just individual effects.

ICE and PDP are shown in Fig. 26. A strength-reducing threshold is confirmed by Fig. 26(a) (GGBS replacement), which clearly shows a drop in SHAP values above 20%. A positive trend in strength with curing age is shown in Fig. 26(b) (curing days), which is particularly apparent after 28 d and continues for up to 90 d. Figure 26(c) (molarity): Has a strong positive contribution above 10 M, but has little influence below that. Figures 26(d) and 26(e) (compaction factor value and slump cone): show very little variance and almost zero SHAP values, indicating little impact on the prediction of STS.

The SHAP-based analysis for STS validates the robustness of the XGB-PSO model and emphasizes the importance of GGBS replacement, curing age, and molarity as the primary influencing factors. A detrimental effect is observed when GGBS content exceeds 20%, while nonlinear strength gains occur with molarity levels above 10 M and extended curing durations. In agreement with earlier sensitivity and performance evaluations, slump cone and compaction factor have negligible influence. These insights significantly enhance model interpretability and support the development of more efficient geopolymer mix designs for improved tensile performance

3) FS Prediction

To interpret the predictive behavior of the XGB-PSO model for FS, XAI methods were applied using SHAP. This approach provides a detailed breakdown of how input variables contribute to model predictions both globally and locally.

The findings on the global feature relevance are displayed in Fig. 27. GGBS replacement (0.206) has the largest average contribution; followed by curing days (0.163) and molarity (0.149), according to Fig. 27(a). Figure 27(b) shows that the anticipated FS (indicated by negative SHAP values) decreases with increasing GGBS replacement values, while increases in curing time and molarity lead to a shift toward higher strength values.

The SHAP Force Plot (Fig. 28(a)) shows how each input contributes to a single prediction. Days (56 d) and molarity (8 M) had a positive contribution, while GGBS replacement decreased the FS prediction. The patterns found in global SHAP plots are consistent with this. Figure 28(b) SHAP PDPs provide additional evidence that: At higher levels, the effects of GGBS replacement are more pronounced and are influenced by additional characteristics. When combined with low-to-moderate GGBS levels, molarity becomes more advantageous. Compaction factor and slump cone show little to no interaction, which confirms their low significance.

While the global SHAP plots provided an overall ranking of feature importance across the data set, the local SHAP plots revealed context-specific interactions. For instance, molarity contributed positively to CS when GGBS replacement was low, but its influence diminished at higher GGBS levels. Similarly, for FS, local SHAP clarified that molarity effects became more pronounced when combined with extended curing. This comparison indicates that global SHAP is valuable for identifying general trends, whereas local SHAP enhances understanding of sample-specific feature interactions, improving the interpretability of the models

Figure 29 displays the ICE and the PDPs. Figure 29(a) shows that the predictive influence is stable up to around 20%, after which it drops significantly (GGBS replacement). Figure 29(b) (curing days) shows that FS improves steadily with curing time, especially after 28 and 56 d. There is no discernible upward movement after 10 M, but Fig. 29(c) (molarity) shows minimal influence up to that point. With nearly flat curves and zero SHAP values, Figs. 29(d) and 29(e) (compaction factor and slump cone) demonstrate that they have a negligible impact on FS.

For FS, the SHAP-based interpretability analysis validates the dominating roles of molarity, curing days, and GGBS replacement. Similar to the trend observed in CS and STS, GGBS replacement has a negative impact above 20%. Curing periods and molarity values above 10 M are associated with an increase in nonlinear strength. Consistent with previous sensitivity results, compaction factor and slump cone had little to no impact. With these findings, model decision-making is better understood and GPC mix compositions are optimized for improved FS.

4 Conclusions

The present study established a comprehensive ML framework for predicting the CS, TS, and FS of GPC incorporating GGBS and SCBA. PSO and BAT were used to improve four ensemble models: RF, AdaB, GB and XGB. The best test predictive accuracy with R² values for CS, TS and FS are 0.983(GB- BAT), 0.991 (RF-BAT) and 0.985 (XGB-PSO) respectively with lower error metrics.

Explainable AI methods such as SHAP and sensitivity analysis were employed to interpret the models’ predictions, revealing that GGBS content, curing time, and molarity were the most influential parameters governing GPC strength. The synergistic interaction between higher GGBS replacement and longer curing duration significantly enhanced mechanical performance. Although the ensemble models achieved very high predictive accuracy, the relatively small data set size may limit the generalizability of the results. Overfitting risks were mitigated through 10-fold cross-validation, averaging replicate tests, and independent test-set evaluation, which confirmed consistent model behavior. Future studies will focus on validating the framework using larger and more diverse data sets to ensure greater robustness and transferability.

The proposed data-driven and interpretable modeling approach offers a practical alternative to extensive laboratory experimentation, supporting faster and more sustainable concrete mix design. Future research will explore deep learning models (e.g., Convolutional Neural Networks, LSTM) and interactive prediction tools using platforms such as Streamlit or Dash, as well as long-term durability prediction through advanced explainability techniques like Local Interpretable Model-Agnostic Explanations. The developed framework can also serve as a practical decision-support tool for engineers allowing users to input key mix parameters (GGBS content, molarity, curing age) to predict strength outcomes, optimize mix proportions, and make data-driven decisions for sustainable and eco-friendly concrete development.

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