Advanced explainable models for strength evaluation of self-compacting concrete modified with supplementary glass and marble powders

Nomenclature

BR

bagging regression

CS

compressive strength

CT

curing time

GB

gradient boosting

GP

glass powder

ICE

individual conditional expectation

MAE

mean absolute error

ML

machine learning

MSE

mean squared error

MP

marble powder

PDP

partial dependence plots

SCC

self-compacting concrete

SF

slump flow

SHAP

Shapley additive exPlanations

R ²

coefficient of determination

RF

random forest

RMSE

root mean squared error

RMSLE

root mean squared logarithmic error

1 Introduction

Concrete is the most widely used material in modern infrastructure due to its economic, structural, and environmental advantages. Among its many performance indicators, the 28-day compressive strength (CS) is critical for quality assessment [1]. Self-compacting concrete (SCC) emerged as a high-performance variant, capable of flowing under its weight without segregation or the need for mechanical vibration [2]. With growing concerns about construction waste and environmental sustainability, recycling materials such as demolition waste and glass powder (GP) have become essential [3,4,5]. Supplementary cementitious materials are used to improve packing, reduce water demand, and enhance strength [6,7]. Similarly, the incorporation of finely ground recycled materials has been shown to enhance mechanical performance and contribute to a denser microstructure [8]. Despite placement challenges, SCC offers excellent surface finish and high durability, aligning well with modern construction goals. The advantages of SCC are shown in Figure 1 [9].

Figure 1

Advantages of sustainable SCC. Adapted with modifications from [9].

GP is increasingly used in eco-friendly concrete due to its pozzolanic potential and moisture resistance [10]. However, concerns over alkali–silica reaction and its mitigation through proper curing and substitution limits have been noted [11,12]. Glass is a non-crystalline substance with high silica content, making it reactive under suitable conditions [13]. Some studies also explore adding rubber aggregates to SCC, though they often compromise mechanical strength [14,15,16,17]. The sustainability benefits of such materials must be balanced with mechanical performance. In SCC, the incorporation of waste-derived additives provides both environmental and durability benefits, yet requires precise proportioning to maintain self-compaction and stability [18,19].

Machine learning (ML) techniques have been widely employed for predictive modeling across various fields due to their ability to capture complex patterns within data [20]. In the field of concrete technology, ML has gained traction in predicting various properties, including CS [21,22]. Techniques such as support vector regression (SVR) [23,24], random forests (RF) [25], and gradient boosting (GB) [26] have been adopted to model the complex, nonlinear behavior of concrete, though many early models lacked scalability and interpretability [27,28]. Recent studies also highlight the lack of integration of explainable AI (XAI) tools to scientifically understand feature influence. The present research addresses this gap by employing ML algorithms to predict SCC strength using expanded datasets with waste marble powder (MP) and GP, further enhanced by interpretability tools. These algorithms are suited for capturing intricate interactions in concrete mixtures and are vital for optimizing performance and sustainability [29].

This study presents a hybrid ML framework using GB, RF, and bagging regression (BR), trained on experimentally derived data from SCC mixes with waste MP and GP. The models are validated using statistical error metrics, and interpretability is achieved through Shapley Additive exPlanations (SHAP) analysis, partial dependence plots (PDPs), and individual conditional expectation (ICE). These tools enable transparent understanding of input-feature influence, addressing the black-box nature of most ML predictions. The framework supports sustainable design by minimizing trial testing and providing reliable strength predictions based on material proportions. A summary of ML techniques applied previously is shown in Table 1. The integrated use of XAI in sustainable SCC modeling is a distinguishing feature of this study. Previous studies primarily focused on conventional supplementary cementitious materials (SCMs) like fly ash and slag, with limited exploration of waste materials such as MP and GP in SCC. Additionally, many ML-based predictions lacked interpretability, offering limited insights into feature influence. Few studies have integrated advanced XAI tools to support mix optimization. This study addresses these gaps by combining novel SCMs with interpretable ML models.

This research is significant as it leverages ML not only for prediction but also for the interpretation of feature contributions in sustainable SCC mixes. It introduces a novel combination of GP and MP within SCC, explored through advanced ML algorithms that are optimized for accuracy and explainability. The study advances current knowledge by using an expanded dataset size, integrating explainable ML techniques (SHAP, PDP, and ICE) for enhanced model interpretability, and incorporating unique waste-based mix components. While past models often neglected feature transparency and focused narrowly on conventional SCMs, this study integrates SHAP, PDP, and ICE to ensure the interpretability of model outputs. The novelty lies in the application of explainable ML to quantify and visualize the influence of waste-based additives in SCC. It promotes more sustainable and intelligent mix design, reduces the reliance on extensive lab testing, and supports eco-conscious construction practices.

2 Data collection and analysis

The foundation for developing an ML model lies in gathering a dependable dataset. The purpose of this research was to forecast the CS of SCC. Various input variables are essential to generate the necessary output through ML methods. Thus, a credible database comprising 51 data points has been assembled from the literature to build strong models [32]. The dataset was expanded from its original 51 data points to 510 data points using a Python algorithm that followed a predetermined plan. The user is presented with the option to select a database file using a Tkinter-based file dialog, initiating the code execution. A Pandas DataFrame was utilized to import the file, after which the code verified the existing point count post-importation. A newly generated file including both synthetic and actual data was utilized to store the enhanced dataset post-creation. The script offers astute observations while augmenting the facts. The declarations encompass several details, such as the exact location of the stored file, the quantity of synthetic data items incorporated, and the overall count of data elements contributed. Moreover, the script addresses situations when resampling is required if no file is chosen. This strategy was employed in previous studies to augment the quantity of data points incorporated into a database [33,34]. As input features, eight characteristics were taken into consideration to forecast the CS of concrete, as shown in Table 2. The data should be divided into two or three sets to create a strong ML model [35,36]. Aggregate physical properties, including maximum size and fineness modulus, exhibited a high level of consistency or a small amount of fluctuation. Therefore, the investigation’s participants were not included in the current research. Every piece of data collected for this study complies with ASTM regulations. Therefore, it was assumed that the production of concrete was the same in every instance.

Similarly, the frequency distribution of the dataset was performed, as shown in Figure 2(a)–(i), through a histogram, which provides a visual representation of data distribution. It illustrates how frequently different values occur, making it easier to identify trends and patterns. The histogram helps in understanding the central tendencies and variations within the dataset. It also highlights any skewness or irregularities present in the data. This graphical approach enhances clarity and simplifies data interpretation. By analyzing the histogram, meaningful insights can be drawn for further evaluation. Such representation is essential for effective data analysis and decision-making.

Figure 2

Distribution diagrams: (a) Curing time, (b) water, (c) density, (d) GP, (e) slump flow, (f) cement, (g) MP, (h) water to binder (kg), and (i) CS.

According to researchers, the proposed model’s ability to function effectively depends on the ratio of data to inputs [37,38]. A ratio larger than 5 is necessary for an optimized model to analyze data points and determine the correlation between the necessary variables [38]. In the current study, the CS of SCC concrete is predicted using eight inputs, resulting in a 63.75 ratio that meets the study’s specifications. The relative frequency histograms associated with each characteristic employed in creating models are shown graphically in Figure 2(a)–(i).

Consequently, training and validation data are separated from the accumulated dataset. About 70% of the training data is used to train the model, while 30% of the validation data is used to determine its correctness. This section guarantees that the model adequately fits the training data and predicts the validation data with similar reliability [39]. The statistical data about inputs and outputs are briefly presented in Table 2. The upper and lower bounds for quantities are given by the statistical readings. The analysis includes statistical assessments of mean, skewness, mode, kurtosis, median, standard error, and standard deviation. Since values that are either equal to or nearly equal to zero occur more frequently than other values, the SCC dataset’s median and mode values were found to be zero. The dataset’s SCC score, which is almost zero, can be attributed to the small amounts of these ingredients that were added to the mixture. A statistical metric called skewness measures the imbalance in a given variable’s probability distribution, with fundamental values correlated with the variable’s mean. Within this context, negative values often indicate that the distribution curve shows a left-sided, protracted tail. Kurtosis measures how heavy or light the tail is in any given dataset and whether it fits within a normal distribution. It provides information on the vertical plane probability distribution. Table 2 displays a summary of each independent attribute’s statistical summary.

One useful technique for demonstrating the connections between several variables in a dataset is a scatter plot matrix. It provides convenience for researchers to rapidly evaluate possible correlations and highlight trends by showing paired scatter plots in a matrix format [40]. A scatterplot is a type of data visualization that demonstrates the relationship or correlation between two or three variables. The identical dimension values are represented by the locations of the data points. Additional dimensions can be mapped to the color, size, or shape of the plotting symbol, while two or three dimensions can be seen directly [41].

A scatter plot matrix showing the pairwise relationships between the main input variables influencing the cementitious composites’ CS is shown in Figure 3. These variables include the cement content, slump flow, density, water-to-binder ratio, slump flow, slump flow, MP, GP, and curing time. While cement content, density, and curing time show positive relationships with CS, highlighting their influence on strength growth, the water-to-binder ratio exhibits a negative correlation. Plotting slump flow against density reveals an inverse connection, suggesting that more workability could result in less compact material. The distribution of MP and glass demonstrates how differently they affect performance. While outliers in CS and curing time may point to experimental variances, clustering patterns reveal particular mix design trends. Identifying crucial characteristics for predictive modeling in ML-driven mix design optimization is made easier by this analysis.

Figure 3

Pearson’s correlation scatter plot matrix.

3 Research methodology

The ML pipeline is depicted in the model training (learning), algorithm selection (algorithm), and data pretreatment (training data), which serve as the cornerstones. Predictions are produced by evaluating the resultant trained model (Results). This process ensures a successful approach to developing and applying ML models. Predictive ML algorithms are used in many academic fields to forecast and understand material performance. The ML processing mechanism is explained in this study, which estimates the CS of sustainable SCC using the GEP, MEP, and BR algorithms. These techniques are employed due to their extensive use, reliable predictive power in relevant studies, and status as the most effective data mining algorithms. Through comparison with real values, the correlation coefficient (R ²), which ranges between 0 and 0.99, is frequently used to assess how well algorithms predict features. An increased R ² value indicates that the selected methodology has yielded positive outcomes. The Orange framework (version 3.35.0), which is based on the Python language, was used as the software platform to implement the models, illustrating the complete flowchart for the present study, which is organized chronologically below. Using published research, an accurate registry of cement compounds based on SF was first constructed, taking into account factors including MP, GP, cement, w/b ratio, curing time, fraction of SF, and ρ. The data points were divided into training and testing groups at 70:30 after removing exceptions. Thereafter, the data were entered into Orange, an intuitive ML and data visualization tool, to build models that would forecast the sustainable SCC CS. Tasks like regression, feature selection, grouping, and classification were made easier by Orange’s visual interface, which made model development and management simpler. Independent and dependent features were found and linked to the GB, RF, and BR ML models after the dataset was analyzed. To optimize these models, hyperparameters were changed, guaranteeing that L1 and L2 for the LR model were regularized to avoid overtraining, as depicted in Figure 4.

Figure 4

Mechanism of ML.

The models’ performance was evaluated using R² and statistical errors in the “test and score” page of Orange. Finally, SHAP, PDP, and ICE analyses were applied to interpret the models, revealing the impact, trends, and interactions of features to optimize sustainable SCC mix design, as depicted in Figure 5.

Figure 5

A step-by-step research methodology followed in the study.

4 Results and discussion

4.1 GB results

According to Natekin and Knoll [63] and Dorogush et al. [64], GBR builds an ensemble of weak learners, typically decision trees, sequentially. Each new tree corrects the mistakes of its predecessors by focusing on the residuals. The final forecast is calculated by multiplying the learning rate by the sum of all the predictions provided by each tree. It is necessary to note that Figure 6, which depicts the predictive performance of the GB technique) shows a strong connection between the predicted and experimental values across all ML models. Specifically, Figure 6(a) shows an R ² value of 0.872 for the GB model. It is necessary to interpret that the error distribution in Figure 6(b) indicates a mean error of 2.76 MPa, with maximum and minimum errors of 6.4 and 0.71 MPa, respectively. Furthermore, 20.91% of the errors are below 1.5 MPa, where 50.32% are between 1.5 and 4 MPa, and 28.75% exceed 4 MPa.

Figure 6

(a) Experimental vs predicted value for the GB model, and (b) error graph for the GB model.

4.2 BR results

The BR technique yields 20 sub-models, the same as the GB method, and the optimized sub-model is selected based on R ². Substitution sampling, which is used in the BR approach, may improve accuracy by repeating certain observations in each new testing dataset. The results of the predictions generated by the BR approach are shown in Figure 7. It has been suggested that every ML technique produces results that show a close relationship between the predicted values and the experimental outputs. Moreover, the BR model also has an R ² of 0.922, as shown in Figure 7(a). The error divergence between the experimental and predicted entities is shown in Figure 7(b). The mean error of the BR model is approximately 2.013 MPa, while the maximum error is nearly 5.617 MPa, and the minimum error is approximately 0.41613 MPa. Likewise, about 52.28% of the anticipated outcomes errors are below 1.5 MPa, 37.25% range between 1.5 and 4 MPa, and only 10.45% are above 4 MPa.

Figure 7

(a) Experimental vs predicted value for the BR model, and (b) error graph for the BR model.

4.3 RF results

Using the hyperparameters from the studies, five RF models were trained to predict slump, CS, static/dynamic yield stresses, and plastic viscosity. After that, a testing dataset was used to validate the models, making sure that neither overfitting nor underfitting occurred for practical use [65,66]. A difficulty with the former occurs when the model fits the training data set so well that it has learned to identify the noise and anomalies in the data and cannot accurately depict the underlying relationships in the testing set. A model is eventually considered to be undertraining if it is too simplistic and cannot capture the trend in both training and testing sets. With an R ² value of 0.95, the RF method shows a strong correlation with the expected target values, as shown in Figure 8(a). The higher accuracy of the RF model (R² = 0.95) compared to the BR and GB can be explained by its ability to reduce overfitting through random feature selection and ensemble averaging. Unlike bagging, which only relies on bootstrapped samples, RF also introduces feature randomness, leading to less correlation among trees and better generalization. It is also less sensitive to noise and outliers and performs well with non-linear relationships, which are often present in concrete strength prediction. Moreover, it requires less-intensive hyperparameter tuning compared to GB, contributing to its stable and reliable performance.

Figure 8

(a) Experimental vs predicted value for the RF model, and (b) error graph for the RF model.

Figure 8(b) illustrates the error distribution for the model, effectively highlighting the variation of errors with an average around 2.50 MPa. The data suggest that about 86.52% of the error distribution remains below 5 MPa. The error distribution indicates that approximately 10.64% of the errors are in the range of 5–10 MPa, while 2.84% exceed 10 MPa. Interestingly, the maximum error recorded is 16.93 MPa, whereas the minimum error stands at 0.04 MPa, as shown in Figure 8(b).

4.4 Comparison and validation of the model

The performance of the generated models was assessed using statistical metrics such as R ², RMSE, RMSLE, MAE, and MAPE. Significantly, the RF model outperformed others with an R ² of 0.95, an RMSE of 1.86 MPa, and an MAE of 1.42 MPa, indicating high predictive accuracy. Its RMSLE and MAPE values were also the lowest, at 0.061 MPa and 4.90%, respectively. The RF model achieved higher accuracy due to its robust ensemble of multiple decision trees, which effectively reduces overfitting and variance. Unlike GB and BR, RF combines bootstrapping with feature randomness, enabling it to capture complex, nonlinear interactions in the SCC dataset more efficiently and maintain stability across varying input conditions. In comparison, the GB model showed the least accuracy, with an R ² of 0.872, an RMSE of 3.1 MPa, an MAE of 2.76 MPa, an RMSLE of 0.101 MPa, and an MAPE of 9.50%. The BR model exhibited intermediate performance, with an MAPE of 7.20% and an RMSLE of 0.079 MPa. Moreover, the Taylor plot in Figure 9 prominently shows the RF model’s superior alignment with actual CS values, while the GB model shows the weakest link, strengthening the RF model’s reliability. The total inaccuracy of RF is indicated by the distance between its point and the reference point, where SD = 1 and R = 1, which reduces distances and signifies better performance. Nonetheless, RF performs well in terms of precision and consistency, as evidenced by its relative proximity to this reference point.

Figure 9

Taylor plot for the developed model.

4.7 Explanatory analysis

To gain an understanding of the prediction process and to make black-box models more transparent, post-hoc analysis of the produced ML models is essential [69]. It is necessary to highlight that this study describes how the constructed ML models are subjected to three different kinds of explanatory analyses: PDP 3D analysis, SHAP analysis, and ICE analysis. GB and RF are considered black-box models due to their limited interpretability. BR is also categorized as a black-box model and falls under ensemble methods; therefore, it was selected for the explanatory analyses [70]. The most accurate algorithm for predicting the CS of sustainable SCC was found to be RF. Hence, it was decided to carry out these studies to provide precise insights into the relevance of different input variables to predict output.

4.7.1 SHAP analysis

SHAP analysis is an interpretability framework based on coalitional game theory, where each input feature is treated as a player in a coalition, and its contribution to the model’s prediction is quantified as an SHAP value [71,72]. This technique provides a unified measure for feature importance by evaluating how much each feature contributes to increasing or decreasing a specific prediction. SHAP values allow for both global and local interpretation, enhancing the transparency of complex, black-box ML models used in empirical research [73].

Figure 10 presents the SHAP summary plot for the SCC prediction model, offering insight into the global significance and directional effect of each feature. The x-axis shows SHAP values: positive values indicate that the feature increases the predicted CS, while negative values decrease it. The y-axis ranks features by their average impact across the dataset. The color gradient (red = high, blue = low) represents the actual feature values. Features such as CT, cement, and W/B ratio exhibit wide SHAP value distributions, highlighting strong and variable influence on predictions. In contrast, features like water and MP show limited spread around zero, reflecting lower importance. This plot effectively communicates both the relative importance of each input and whether its influence is positively or negatively associated with the model’s output.

Figure 10

SHAP global interpretation of the model.

4.7.2 ICE analysis

ICE plots highlight how an ML model’s output does not represent the average impact; rather, it varies for individual cases when a feature value changes [49]. ICE charts provide indications of prediction behavior by displaying the variation in model outputs for particular cases. However, generalization may be difficult due to their instance-specific character. This work addresses this by combining ICE charts and PDPs, which offer a thorough comprehension of the behavior of the ML model across feature values and individual cases. This integrated technique allows the analysis of the optimized model. The average value of a function F over N observations is determined using the ICE equation, as shown in Eq. (9):

(9) F ̅ s = 1 N ∑ i = 1 N F ̅ ( k s , k i . g ) ,

where k _g is the complement such that k _g ∪ k _s = s, dP(k _g) and k _s are the examined features of the input variables, and (k _g) stands for the k _g’s marginal effect.

The ICE plots for the models created in this study are displayed in Figure 11 and offer a useful and interactive way to show how the output of the model changes when the values of the four input variables change. To create the ICE plot, one variable was varied over its range, while the other variables were set to their average values. Plotting the resulting change in the given models’ predictions against the variable values revealed that the thick blue curve represented the average reaction, whereas each curve represented a sample of the data.

Figure 11

ICE analysis to show the relationship between inputs and output: (a) Cement (kg·m⁻³), (b) curing time, (c) density (kg·m⁻³), (d) GP (kg·m⁻³), (e) MP (kg·m⁻³), (f) slump flow (mm), (g) water (kg·m⁻³), and (h) water/binder ratio.

The ICE plots illustrate the effect of varying material properties on the predicted response. The cement content (kg·m⁻³) in Figure 11(a) shows that predictions remain constant at approximately 29.0 kg·m⁻³ between 225 and 275 kg·m⁻³, with a sharp increase to 31.0 kg·m⁻³ between 275 and 325 kg·m⁻³, followed by stabilization at 31.5 kg·m⁻³ beyond 325 kg·m⁻³, suggesting a diminishing return. Thereafter, for curing time (days), predictions are stable around 26 up to 40 days, then increase sharply to 30, peaking at 38 beyond 80 days, as shown in Figure 11(b). The density plot (kg·m⁻³) in Figure 11(c) shows a similar step function, with constant predicted values within specific density intervals of 2,350–2,650 kg·m⁻³. In Figure 11(d), the GP plot (kg·m⁻³) exhibits stepwise changes, with expected values remaining constant in intervals between 0 and 80 kg·m⁻³. Figure 11(e) and (f) depicts that MP and SF plots similarly show step functions, indicating distinct changes at specific intervals 0–80 kg·m⁻³ for MP and 650–825 mm for SF, essential for understanding and optimizing material properties. The water content plot in Figure 11(g) shows expected values increasing at distinct steps within the range of 160–200 kg·m⁻³, highlighting key thresholds in material behavior. Finally, the plot of w/b in Figure 11(h) shows a negative impact with increasing w/b beyond 0.45.

4.7.3 PDPs

The PDP is a popular technique for displaying strong connections between input data and model outputs. However, to the best of our knowledge, they have only been used in the study [74]. Instead of exhibiting the average effect, ICE plots, as opposed to PDPs, show how an ML model’s output differs for particular cases as a feature value changes [49]. ICE charts provide a comprehensive understanding of forecasting behavior by illustrating the variability in model outputs for various cases. However, generalization can be inherently challenging due to the instance-specific nature of the methodology. The average partial dependence function (F _s) is computed based on a selected subset of predictors (k _s), as defined in Eq. (10):

(10) F s ̅ ( z s ) = 1 N ∑ i = 1 N F ̅ ( k s , k i . g ) .

Here, k _i.g represents the actual value of the ith input variable in the dataset, and N denotes the total number of samples.

Figure 12 presents PDP-3D, illustrating the relationships between material properties and CS, providing essential information for optimizing construction materials. The plots show that water, cement content, GP, SF, ρ, and other additives all have a substantial impact on CS. For instance, Figure 12(a) depicts the interaction of GP (0–1,200 kg·m⁻³) and water (0–500 kg·m⁻³), with CS highest at 32.2 MPa. As shown in Figure 12(b), the Cem. content is between 240 and 400 kg·m⁻³, and the CT changes dramatically from 0 to 85 days, which affects the CS; the longer the curing time, the greater the strength. Similarly, higher Cem. content is about 400–600 kg·m⁻³, and the density ranges from 2,200 to 2,400 kg·m⁻³ (Figure 12(c)), which enhances CS, emphasizing material optimization. The interaction of cement is 300–500 kg·m⁻³, and GP is 0–80 kg·m⁻³, as shown in Figure 12(d); CS peaks at 33 MPa with optimal ranges of 500 kg·m⁻³ cement and 40–60 kg·m⁻³ GP. Cement and activatable powder are in between 0 and 60 kg·m⁻³ as shown in Figure 12(e), depicting a nonlinear increase in CS of 28–33 MPa, with significant gains observed at 400 kg·m⁻³ cement and 20–40 kg·m⁻³ powder. Furthermore, higher slump flow is about ≥500 mm, whereas for cement, it is ≥400 kg·m⁻³. As shown in Figure 12(f), CS reaches a maximum of 34 MPa, while lower ranges remain around 27 MPa. Figure 12(g) shows that increasing cement (300–500 kg·m⁻³) and reducing water (240–360 kg·m⁻³) enhance CS, peaking at 32 MPa. Figure 12(h) highlights that extended curing commences from 0 to 8 days, and higher SF ranges from 600 to 870 mm, contributing to improved CS. As shown in Figure 12(i), density varies from 2,000 to 2,400 kg·m⁻³, and curing duration ranges from 3 to 8 days, which significantly increases CS from 26 to 40 MPa. Figure 12(j) reveals that CS peaks at 36 MPa with GP beginning with 0–10 kg·m⁻³, and curing beyond 5 days. Figure 12(k) indicates that GP starts from 0 to 10 kg·m⁻³ and density varies from 2,250 to 2,400 kg·m⁻³, resulting in CS ranging from 29.5 to 32.5 MPa.

Figure 12

PDP- 3D: (a) GP with water, (b) cement with curing time, (c) cement with density, (d) cement with GP, (e) cement with MP, (f) cement (kg·m⁻³) with slump flow, (g) cement with water (kg·m⁻³), (h) slump flow (mm) with curing time, (i) density with curing time, (j) density with curing time, (k) GP (kg·m⁻³) with density (kg·m⁻³), (l) GP (kg·m⁻³) with water (kg·m⁻³), (m) MP with water (kg·m⁻³), (n) water/binder ratio with cement, and (o) water/binder ratio with density.

Figure 12(l) analysis reveals that varying GP and water content, ranging from 0 to 100 kg·m⁻³, significantly influences CS between 31.0 and 32.2 MPa, with increases in both stimulating strengths. Thereafter, MP spans from 0 to 1,000 kg·m⁻³ and water ranges from 0 to 500 kg·m⁻³, as shown in Figure 12(m), increasing the CS approach to 31.7 MPa, emphasizing the importance of optimized material proportions. These findings demonstrate the critical role of balancing material properties to achieve optimal CS in construction applications. Higher densities and GP content generally improve CS, with the peak values observed at maximum density and GP levels. Thereafter, the w/b ratio and Cem. content is around 380–460 kg·m⁻³, as shown in Figure 12(n), and how deviations in these factors influence CS, critical for concrete mix design optimization. Similarly, Figure 12(o) shows variations in the w/b ratio in the range 0.38–0.50 and density in the range 2,400–2,600 kg·m⁻³, and CS of 29.0–33.0 MPa. A 3D surface plot highlights the importance of optimizing these parameters to improve CS, which is crucial for construction and engineering applications. Finally, these illustrations provide important details for material design and optimization in construction engineering, helping in the development of stronger, more efficient building materials.

5 Conclusions

This study employed ML techniques, including GB, BR, and RF, to predict the CS of SCC, incorporating MP and GP. By utilizing experimental data, the developed models were trained and validated to assess their predictive accuracy and reliability. Various statistical and graphical analyses were conducted to evaluate model performance and identify key factors influencing SCC strength. The following are the primary findings of the study:

• The developed models showed strong agreement with experimental results, with the RF model demonstrating the highest accuracy for CS prediction of SCC. The R² values for BR and GB were found to be 0.922 and 0.872, while RF achieved the highest value of 0.95.

• Statistical validation further confirmed the model accuracy, with RF yielding the lowest errors: MAE of 1.42, MAPE of 4.90%, RMSE of 1.86, and RMSLE of 0.061. These assessments validated the superior predictive capability of RF over BR and GB.

• The Taylor plot analysis reinforced the robustness of the RF model, highlighting its reduced standard deviation and improved consistency in estimating SCC CS.

• SHAP analysis showed that CT was the most influential factor affecting SCC strength, followed by SF, while MP had the least impact. These findings align with experimental data and provide useful insights for optimizing the SCC mix design.

• PDP and ICE analyses of RF-based predictive models indicated that RF effectively captured dominant linear trends and feature-specific variations, confirming its superior predictive accuracy over BR and GB for modeling the CS of SCC.

The analytical results demonstrated that the developed models achieved high accuracy and reliability, highlighting their potential for predicting the CS of SCC in future applications. Importantly, the insights gained from SHAP, PDP, and ICE analyses provide practical guidance for engineers and material designers by identifying the most influential factors and their acceptable ranges for optimizing the SCC mix design. However, the study is limited by the relatively small and specific dataset used, which may affect the models’ generalizability to different SCC compositions and environmental conditions. To further enhance predictive performance, future studies should focus on constructing larger and more diverse datasets to develop robust and comprehensive models.