Machine Learning Framework for Predicting Critical Mix-Design and Strength Properties of Eco-Efficient Recycled Aggregate Concrete

Machine Learning Framework for Predicting Critical Mix-Design and Strength Properties of Eco-Efficient Recycled Aggregate Concrete | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Machine Learning Framework for Predicting Critical Mix-Design and Strength Properties of Eco-Efficient Recycled Aggregate Concrete Mohamed Elbleihy, Dorota Wolak, Amir Khan, Aneel Manan, Kennedy C. Onyelowe, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7168474/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Efforts to reduce concrete’s embodied carbon and the environmental impacts of construction-and-demolition (C&D) waste have increasingly shifted toward using recycled-aggregate concrete (RAC) to replace natural aggregate, either partially or entirely. Over the past two decades, dozens of studies have been conducted on the properties of RAC mixes. These studies provide a solid foundation for prediction models that eliminate the reliance on actual tests, which can be time-consuming. Machine learning (ML) models predict concrete properties from interacting variables, such as water-to-cement ratio, cement content, RAC replacement level, aggregate density, etc. These data-driven predictions are more reliable than traditional empirical formulas. ML model can capture nonlinear relationships among diverse input features, providing a framework for optimizing mix design and evaluating mechanical performance. In this study, a database of 358 mix designs from the literature was used to predict three key mechanical properties (compressive strength, split-tensile strength, and modulus of elasticity) of RAC-based concrete. The decision tree was used as the principal predictive model, and its robustness was verified through K-fold cross-validation. Model performance was high in training (R² = 0.93, 0.92, and 0.94, respectively) and remained acceptable in testing (R² = 0.75, 0.78, and 0.76). SHAP (SHapley Additive exPlanations) Analysis shows cement content and aggregate density are the most influential features across all three properties, followed by water-to-cement ratio and RAC replacement level. This interpretable ML framework streamlines mix-design optimization, reduces laboratory work, and guides production of low-carbon RAC with dependable mechanical performance. Physical sciences/Engineering Physical sciences/Materials science Recycled Aggregate Concrete Multi-prediction model sustainable concrete machine learning cross-validation Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 1. Introduction Each year, a total of 25 billion tons of concrete is consumed, making it the most used man-made material[ 1 ]. Global cement production now amounts to about 4 billion tons per year, consuming an equivalent volume of limestone extracted at rates that outstrip natural geological replenishment[ 2 ]. Concrete manufacturing alone withdraws between 190 and 642 L of freshwater per m³, roughly 9% of global industrial water withdrawals, placing severe stress on finite water resources[ 3 ]. Quarrying aggregate causes widespread land disturbance, depletes fossil resources at rates up to 1.48 × 10⁻⁶ Petajoules equivalent (PJ) per kg and emits about 1.6 billion tons of CO₂ each year[ 4 – 6 ], Fig. 1 shows the resource depletion over a 20-year period taken by satellite image. The demand for concrete globally has been growing due to the development of infrastructure and high rates of urbanization. Projected estimates show that by 2030, nearly 1 billion more people will live in urban areas[ 7 ]. This will lead to increased consumption of natural aggregate, which constitutes more than 60% of the volume of concrete. The current global aggregate consumption is approximately 50 billion tons per year[ 8 – 10 ]. Over the past 2 decades, Aggregate usage in China has increased approximately 430% [ 11 ]. Between 2009 and 2023, U.S. aggregate production climbed from 1.96 to 2.52 billion metric tons (a 29% increase), equal to an average annual growth of 1.72% per year [ 12 , 13 ] as shown in Fig. 2. To alleviate the demand on non-renewable raw materials, studies have investigated the incorporation of waste glass, scrap tires, and ceramic powders into concrete mixtures to mitigate concrete environmental impacts[ 14 – 17 ]. Each year, rapid industrialization and construction produce over 3 billion tons of demolition and construction waste, resulting in overflowing landfills, depleted resources, and serious environmental damage[ 18 , 19 ]. In the EU, Construction and Demolition (C&D) waste makes up 38.4% (≈ 850 million tons) of all waste, with a 70% recycling target set for 2030[ 20 – 22 ]. China generates the most C&D waste at 2,600 Mt, but recovers only 10% (260 Mt). Japan and Australia generate 78 Mt and 29.2 Mt, respectively, yet recover 88.2% and 81%. The EU produces 857 Mt with only ≈ 343 Mt recovered (40%), while the U.S. achieves 76% recovery from 600 Mt, and Canada 16% recovery from just 4 Mt, as shown in Table 1 . Disposal of concrete waste via landfilling consumes substantial embedded energy and occupies large volumes of landfill space, increasing greenhouse-gas emissions and land-use pressure[ 24 ]. Buried concrete waste can release harmful substances, such as heavy metals, into the soil and groundwater[ 24 , 25 ]. The widespread adoption of RAC could help mitigate these issues by recycling waste materials and reducing the need for virgin aggregate [ 26 ]. Recycling C&D waste into RAC can recover nearly 600 million tons per year, offset up to 25 percent of virgin aggregate demand in mature markets, and reduce embodied carbon dioxide emissions by 90 percent compared to quarried stone[ 27 , 28 ]. Life-cycle assessments indicate that replacing natural aggregate with 50% Recycled Aggregate Concrete can reduce cradle-to-gate CO₂ emissions by 22–65% and lower embodied carbon by 23–28% compared to conventional concrete, while cutting virgin aggregate consumption in half [ 20 , 29 ]. RAC concrete has been successfully applied in a range of infrastructure elements, including rigid concrete pavements[ 30 ], asphalt overlays[ 31 ], and reinforced concrete structural and nonstructural members[ 32 , 33 ]. The application of RAC in structural elements remains limited because its chemical and physical characteristics differ markedly from those of virgin aggregate. RAC contains residual adhered mortar with elevated alkali and sulfate concentrations, exhibits higher water absorption (typically 4–8% vs. 0.5–2%), lower specific gravity (2.2–2.4 vs. 2.6–2.7), increased porosity, and greater crushed-particle angularity that reduce compressive strength and mechanical performance[ 34 , 35 ]. Although using 100% RAC can reduce cradle-to-gate global warming potential by up to 25% [ 36 , 37 ], it typically decreases compressive strength by approximately 25% [ 38 ]. This strength loss is attributed to residual mortar on the RAC surface, which increases aggregate porosity and weakens the interfacial transition zone with the cementitious matrix, thereby reducing the concrete’s load-bearing capacity[ 38 ]. Table 1 C&D Waste Generation and Recovery Performance Across Leading Economies Countries C&D waste generation (Mt) C&D waste recovery (Mt) C&D waste recovery (%) References Australia 29.2 23.6 81% [ 39 ] China 2600 260 10 [ 40 – 43 ] Japan 78 69 88.2 [ 44 ] EU 857 ≈ 343 40 [ 45 , 46 ] Canada 4 0.64 16 [ 47 ] United States 600 456.6 76 [ 48 ] Although RAC typically shows a 15–25% reduction in compressive strength compared to conventional mixes, it still achieves acceptable mechanical properties, adequate for structural uses[ 49 ]. Suitable applications include leveling screeds, subbase layers for pavements, sidewalks, curb-and‐gutter, and trench backfill[ 50 ]. By diverting waste and lowering embodied carbon, RAC concrete delivers significant environmental benefits in contexts where ultra–high strength is not required[ 51 ]. In recent years, Extreme Gradient Boosting (XGBoost) has emerged as a premier machine-learning technique for modeling concrete properties, offering a combination of high predictive accuracy, efficient computation, and clear interpretability that outperforms both traditional regression and other ensemble methods[ 52 – 54 ]. Most Artificial Intelligence (AI) based studies, including artificial neural network (ANN) [ 55 ], XGBoost [ 56 ], and Random Forest [ 57 ], tend to focus on predicting individual properties such as compressive strength [ 58 ], split tensile strength [ 59 ], shear strength [ 60 ], or elastic modulus [ 61 ]. However, a gap remains in the literature for studies that simultaneously predict multiple properties and evaluate the performance of different AI algorithms. To improve accuracy in predicting concrete properties, it is essential to consider multiple characteristics at once. This research addresses the existing gap by developing a novel multi-target predictive model capable of simultaneously estimating several key concrete properties, including compressive strength, modulus of elasticity, and splitting tensile strength. The proposed model aims to capture the effect of RAC on concrete performance by incorporating a wide range of input features such as physical, mechanical, and compositional parameters, unlike previous studies that focus on isolated property prediction. The model’s output can facilitate informed decision-making in the construction industry, enabling the use of RAC in broader applications while balancing sustainability goals and structural requirements. This research contributes to the development of intelligent tools for optimizing RAC usage and advancing data-driven strategies for sustainable concrete. 2. Research Significance Despite growing interest in RAC as a sustainable alternative, its practical benefits remain unclear due to inconsistent findings across studies and varying material conditions. In this regard, the current research examines the future of RAC in structural concrete using a Decision Tree model that employs a machine-learning method that can support a wide range of input variables. The model is used to forecast important mechanical properties, which are compressive strength, tensile strength, and modulus of elasticity. The incremental components of the study include: (a) a comparative overview of concrete containing conventional aggregates versus RAC, (b) compilation of a consistent group of 358 experimental datasets of RAC and concrete to support the predictions required for multi-property, (c) evaluation of the Decision Tree model performance to validate its integrity when predicting properties of RAC, and (d) performance and validation using K-fold cross validation and SHAP to assess the relative significance and identify strongest among the ten input variables. 3. Methodology In this study, it was assumed that traditional statistical methods, such as linear regression, may be insufficient for modelling the complex, nonlinear relationships between concrete mix composition and its mechanical properties. Therefore, machine learning was applied—an approach based on algorithms capable of autonomously detecting patterns and relationships in data. Specifically, the decision tree (DT) algorithm was used, which is a fundamental supervised learning technique that builds a model in the form of a hierarchical structure of logical conditions (rules). This model recursively splits the input data space into smaller segments to maximize the homogeneity of the target variable within each node. Theoretically, decision trees handle heterogeneous and nonlinear data well and are attractive in engineering contexts due to their interpretability. To assess the reliability and generalizability of the model, the study employed K-fold cross-validation, a statistical method that divides the dataset into K equal parts (folds). The model is trained on K − 1 parts and tested on the remaining one; this process is repeated K times to ensure that each data point is used for both training and testing. This technique minimizes the impact of random data splits and provides a robust estimate of the model’s ability to generalize to new data. To quantitatively evaluate the regression model's accuracy, four standard statistical metrics were applied: R² (coefficient of determination) – measures the proportion of variance in the target variable explained by the model; values close to 1 indicate strong predictive performance; RMSE (Root Mean Squared Error) – reflects the average magnitude of prediction error, being sensitive to large deviations; MAE (Mean Absolute Error) – captures the average absolute differences between predicted and actual values, less affected by outliers than RMSE; MAPE (Mean Absolute Percentage Error) – expresses error as a percentage, allowing interpretation regardless of measurement units. To further enhance the model’s transparency and interpretability, the study employed SHAP (SHapley Additive exPlanations) analysis, which is based on cooperative game theory. SHAP assigns a numerical value to each input variable reflecting its contribution to the final prediction, considering all possible combinations of features. This is particularly useful in interpreting “black-box” models, where complex feature interactions may otherwise be hard to explain. The entire methodology is grounded in the assumption that secondary data from previous experiments can serve as a reliable basis for predictive modelling—provided the data is properly curated, cleaned, and balanced. 3.1 Database A detailed dataset consisting of 358 experimental tests on concrete incorporating Recycled Aggregate Concrete (RAC) was gathered for analysis, following previous research [ 62 – 99 ]. The input parameters for modeling are the most common in a concrete design (as shown Table 2 ) is replacement rate of recycled aggregate to natural aggregate (RL), water cement ratio (w/c), aggregate cement ratio (A:C), sand cement ratio (S:C), density of RAC (RAC-D), density of NA (NA-D), aggregate size of recycled aggregate (RAC-S), aggregate size of natural aggregate (NA-S), and curing time (age). The output parameters will be the combined compressive strength (Fc), split tensile strength (STS), and modulus of elasticity (MOE). Fc, STS, and MOE are functions of the input parameters. Table 2 Definitions of Key Variables in RAC Machine Learning Dataset Symbol Parameter Name Typical Unit RL Recycled-to-Natural Aggregate Replacement Level % or decimal w/c Water-to-Cement Ratio — (unitless) A : C Aggregate-to-Cement Ratio — (unitless) S : C Sand-to-Cement Ratio — (unitless) RAC-D Density of Recycled Aggregate Concrete kg/m 3 NA-D Density of Natural Aggregate kg/m 3 RAC-S Maximum Size of Recycled Aggregate mm NA-S Maximum Size of Natural Aggregate mm Age Curing Time days Fc Compressive Strength MPa STS Split Tensile Strength MPa MOE Modulus of Elasticity MPa Table 3 Database descriptive statistics of Key Variables in RAC Machine Learning Dataset Input Mean Min Max Range SE Median Mode Kurtosis Skewness SD RL 54 0.00 100 100 1.86 50 100 -1.69 -0.07 42.13 w/c 0.44 0.19 0.61 0.42 0.00 0.45 0.36 -0.97 -0.07 0.09 A:C 2.84 1.20 5.75 4.55 0.03 2.60 2.30 2.91 1.59 0.75 C:S 0.62 0.00 1.50 1.50 0.01 0.57 1.00 -0.42 -0.02 0.29 Agg-S (mm) 13.59 0.00 38.00 38.00 0.41 16.00 0.00 -0.78 -0.22 9.25 NA-S (mm) 10.56 0.00 38.00 38.00 0.44 10.00 0.00 -1.23 0.20 10.00 CC (kg/m 3 ) 386 0.00 600 600 4.88 385 500 4.19 -1.69 110.69 RAC-D (kg/m 3 ) 1739 0.00 2661 2661 46.52 2320 0.00 -0.88 -1.04 1048.49 NA-D (kg/m 3 ) 1410 0.00 2870 2870 59.05 2540 0.00 -1.99 -0.10 1338.69 Age (days) 29.06 1.00 90 89 0.80 28 28 5.08 1.96 18.20 Output Fc 43.42 11.90 108.51 96.61 0.66 42.00 45.00 3.33 1.15 14.96 STS 3.35 1.00 10.10 9.10 0.04 3.30 3.20 9.66 1.69 1.01 MOE 30.32 11.30 50.41 39.11 0.32 30.20 30.10 0.92 0.32 6.06 A detailed analysis with ten input parameters and three output parameters enables an in-depth examination of the factors that impact the compressive, split tensile strength, and modulus of elasticity of RAC concrete. Table 3 provides the statistical properties for each parameter, complemented by the correlation matrix and frequency distribution histogram in Fig. 3 and Fig. 4 , respectively. Kurtosis is utilized to describe the shape of the probability distribution [ 100 ]. Figure 3 shows the strength of relationships between numerous variables in the data. The results show a negative correlation between the replacement level of RAC and the Fc, STS, and MOE levels. There were a couple of interesting relationships from the matrix; there are positive correlations between C and S, RAC-D and RAC-S, NA-D and NA-S. Negative correlations between the RL with both NA-D and NA-S, and between Fc and MOE, and many of these trends follow previous studies [ 101 ], RAC might have decreased the strength of concrete. Natural aggregate, unlike RAC, doesn't have the same level of porosity and absorption rate [ 102 – 104 ]. 3.2 Decision Tree (DT) Decision Tree (DT) is a machine learning algorithm used for both regression and classification [ 105 ]. The main advantage of DT is the working mechanism for a complex dataset, as it splits the dataset into different branches of values on the features. This breakdown of the dataset makes it easy to train the model. The intricate patterns can be easily for inputs and outputs. The flowchart of DT along with the natural tree is presented in Fig. 5 . Table 4 presents the tuning parameters for DT tree model optimization. The model complexity is determined by the size of depth (maximum depth of the tree), which results in the capture the patterns. However, deeper depth can make the model understand the complexity of the database, but it can lead to overfitting. In which the model is highly dependent on the training data and doesn’t perform well to new datasets. In such a situation, the depth of the model is set at a specific value, which leads to an accurate prediction. Table 4 Tuning parameters of the DT model Parameter Maxi depth of the tree Mini samples to split a node Mini samples at each leaf node Criterion for splitting Parameter Variation 5, 10, 20 2, 5, 10 1, 2, 5 'Gini', 'Entropy' Best Result Parameter None or determined by data 2 1 Gini or Entropy Another crucial factor that avoids splits with few datasets that could not generalize well is the minimal number of samples needed to split a node. The number of splits a node can be encouraged by set 2 parameters that enhance robustness and the available dataset. The minimum samples at each lead node also controls the number at each lead node for the decision. The splitting at each node is determined by the options which are “Entropy” and “Gini”, which determines the impurity in the dataset. Such a process is important to purify the dataset from non-homogeneity behavior and results in overfitting. Therefore, the selection of either parameter is crucial for model performance optimization. 3.3 Model accuracy Table 5 shows the evaluation of models' accuracy using a variety of major statistical metrics - coefficients of determination (R2), root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). R2 measures the coefficient of determination of values predicted against actual values, with values approaching 1 indicating a good relationship and predictive fit. RMSE indicates the average magnitude of errors, where larger errors will have a larger notation toward the average error. MAE defines the mean of absolute errors to actual value(s), as it offers a fair measurement to check predictive accuracy. MAPE, expressed as a percentage, provides the average deviation to the actual value(s), working as a consistent reference for overall accuracy. Therefore, lower ratings on RMSE, MAE and MAPE indicates higher degrees of predictability and reliability [ 106 ]. Table 5 Statistical metrics for model evaluation. Evaluation criteria Coefficient of determination (R 2 ) Root mean squared error (RMSE) Mean absolute error (MAE) Mean absolute percentage error (MAPE) Formula \(\:=1-\frac{{\sum\:}_{i=1}^{m}{({P}_{i}-{T}_{i})}^{2}}{{\sum\:}_{i=1}^{m}{({P}_{i}-{T}_{i})}^{2{\prime\:}}}\) \(\:=\frac{{\sum\:}_{i=1}^{m}\left|{P}_{i-}{T}_{i}\right|}{m}\) \(\:=\sqrt{\frac{{\int\:}_{i=1}^{m}{{(P}_{i-}{T}_{i})}^{2}}{{\int\:}_{i=1}^{m}{\left({T}_{i-}\stackrel{-}{T}\right)}^{2{\prime\:}}}}\) \(\:=\frac{1}{n}\sum\:_{i=,1}^{n}\left|\frac{{P}_{i}-{{T}_{i}}^{}}{m}\right|\times\:100\) Results Higher values indicate a better fit A lower value indicates better accuracy A lower value indicates better accuracy A lower value indicates better accuracy Range 0–1 0 - ∞ 0 - ∞ 0 - ∞ 4. Results and discussion The DT algorithm is a valid means of making concrete predictions of multi-outcome RAC outlined above in Table 6. For the Fc output, the DT model provided R2 values of 0.93 in training and 0.75 in testing, suggesting that it had excellent training predictive capacity, and respectable performance in testing. For STS output, the model provided an R2 of 0.92 in training and 0.78 in testing, while MOE had R2 values of 0.94 in training and 0.76 in testing. The RMSE and MAE values further confirmed the model accuracy with relatively low error in the training dataset across the three outputs; for example, the MAE for Fc was 0.54 in training and 2.01 in testing, STS had MAE of 0.13 in training and 2.58 in testing, while for MOE MAE was 0.28 in training and 2.68 in testing. To summarize, it could be concluded that the DT algorithm captured underlying structures of the dataset, with that conclusion being particularly valid for Fc and MOE values, while for STS, there is less clarity with regards to testing performance. Table 6 : Algorithm Performance Comparison Concrete Properties Training Testing R 2 RMSE MAE MAPE R 2 RMSE MAE MAPE Fc 0.93 1.45 0.54 0.06 0.85 6.43 2.01 0.65 STS 0.92 1.12 0.13 0.12 0.88 6.03 2.58 0.73 MOE 0.94 1.37 0.28 0.04 0.86 6.83 2.62 0.66 4.1. FC predicted results The results of the decision tree algorithm are shown in Figure 6, which highlights the training and testing dataset performance of 93% and 85% for Fc, respectively. These results indicate the high accuracy in the prediction performance in both training and testing. Additionally, it has been noted [107] that decision trees may struggle with stability due to sensitivity to small variations in data, which can affect predictive reliability. Prior studies [108] discuss that overfitting happens when a model is trained on noise in the training data, for which the model loses the ability to generalize to unseen data. The DT model tends to be less prone to overfitting than neural network models; however, such a model can still experience overfitting when attempting to model complex patterns. Nevertheless, reference [109] stated that a R2 value in the area of 60% or higher represents reasonable accuracy; hence, the 75% R2 value established in the testing was suitable for practical purposes in predicting concrete properties. Although the model’s testing performance is somewhat lower than in training, the DT remains an effective tool for forecasting compressive strength. Enhancements in feature selection and tuning may further improve its generalization and predictive accuracy. 4.2. STS predicted results The STS results between predicted and experimental values are demonstrated in Figure 7. The R2 values represent 92% for the training set and 88% for the testing set, indicating that the model is well suited to training data patterns and maintains reasonably good performance with testing data. However, the decline in R 2 from training to testing still suggests some degree of overfitting, where the model may be slightly over-adapted to the training data, limiting its generalization capability. Contributing factors to this overfitting could include the dataset's size, possible noise within the data, or model complexity. To improve the model’s generalizability, further adjustments may be considered, such as expanding the dataset or simplifying the model structure. Additional regularization techniques could also help reduce overfitting and enhance predictive accuracy for STS in new data. 4.3. MOE predicted results Figure 8 shows the corresponding predicted vs. experimental MOE values. The R2 values for the DT model were 94% and 86% for training and testing, respectively, a high level of predictive accuracy on the training dataset and a drop in testing accuracy, indicating potentially overfitting. As previous studies have shown [109], an R 2 greater than 60% can provide adequate predictive ability for concrete properties, and therefore, the testing R 2 of 76% gained here still represents reasonable predictive power. These results confirm the potential for the model to reliably predict the MOE value, even with the lower correlation in the testing dataset versus the training dataset. Having this level of performance demonstrates the applicability of the DT model for predicting concrete properties, but further adjustment of parameters and feature optimization may improve generalization. 4.4. K-fold cross-validation K-fold cross validation is a method for evaluating a machine learning model’s performance by splitting the dataset into K equally sized parts, or folds, as depicted in Figure 9 [110]. The algorithm uses an equally divided K-fold and runs the predictive model to determine the performance of the algorithm with an unseen new dataset. This rotation ensures every data point serves as both a training and testing sample, reducing variability and providing a more reliable performance assessment. By continuously testing the model on new data, K-fold cross-validation assesses its generalizability. After each round, performance metrics like R 2 scores are calculated on the test fold, and the results are averaged across all K iterations for an overall performance evaluation. 4.5. Compressive strength The DT predictive model for compressive strength for different K-fold subsets demonstrates that the maximum R 2 of 0.96 indicates a highly accurate predictive model for a certain dataset, as shown in Figure 10(a). The average and minimum values of 0.84 and 0.72, respectively, show a substantial portion of data variability. This conclusion is further supported by the analysis based on MAE values, as seen in Figure 10(b). The maximum MAE of 0.97 denotes cases with higher error, and the minimum MAE of 0.52 highlights the model accuracy in specific folds. Overall, the Fc predictive model of DT shows a robust foundation, with potential for further enhancement and optimization. 4.6. STS K-fold analysis The DT model for split tensile strength k-fold analysis shows that performance varies depending on the database. The model performs significantly well, as seen by the maximum R 2 value of 0.96, however, a minimum R 2 value of 0.19 indicates poorer performance on other folds. Although additional adjustments would be required, the model’s overall ability to capture some diversity in the data is indicated by the average R 2 value of 0.71. A variation in the value of 10-fold in terms of MAE is also noticed. The minimum value of 0.48 indicated a well performance on a certain fold, and the maximum value of 0.71 indicates high error but acceptable for the prediction. The model’s prediction accuracy is generally indicated by its average MAE of 0.58. This performance and consistency could be improved with additional tuning. 4.7. MOE k-fold analysis In the MOE, the maximum k-fold R2 of 0.99 demonstrates predictive performance accuracy on certain subsets, while the minimum k-fold R2 of 0.62 indicates some optimism for maximizing performance. The average k-fold R2 of 0.86 is a reasonable indication overall of the model's ability to predict the data's variability, as seen in Figure 12(a). Considering MAE, the maximum value of 1.59 indicates scenarios where the model's predictions are considerably deviated from the actual values. The minimum MAE value of 0.2 demonstrates situations where the model performance could enhance, as seen in Figure 12(b), The average MAE value of 0.84 provides an overall indication of the model's prediction accuracy for all folds that suggests, while the model can predict data variability satisfactorily, there is room for improvement in certain instances. 5. Sensitivity analysis The sensitivity analysis is executed by SHAP (SHapley Additive exPlanations), a well-established method for interpreting machine learning models, which is based on the idea of Shapley additive explanations[111]. Research [112] shows that Shapley values assess the relative importance of each input variable based on its contribution to the overall output. By looking at SHAP values, we can uncover the most significant features of a model and be able to look for any systematic behaviors across models. The so-called red dot means that a higher feature value had a larger SHAP score. This is similar to conducting a parametric analysis, where all but one variable is held constant and the other variable is allowed to vary in order to determine its effect on a target variable. In this instance, this section is used to understand the extent of each variable's influence on the RAC values and note the extent to which the input variables affect the output variables. 5.1. Sensitivity analysis for Fc The SHAP analysis of the compressive strength predictive model using DT offers valuable insights into the importance and interactions of various input features. The SHAP plots elements that are located furthest from the center (Figure 13). For example, a higher “C”, shown in red, has a positive impact. In contrast, higher values of the “w/c” tend to result in negative SHAP values, indicating a reduction in predicted compressive strength. Distinct clusters in the SHAP values of features like “C” and “w/c” suggest interactions between these variables, showing that different combinations of high and low values affect predictions in varying ways. Cement content has the strongest influence on the model’s predictions, with higher values aligning with increased concrete strength, as expected. Meanwhile, the w/c ratio typically impacts predictions negatively, as a higher ratio generally weakens concrete strength. Other features, such as replacement level (RL) and aggregate-to-cement ratio, also affect predictions, but to a lesser extent compared to cement content and the water-cement ratio. 5.2. Sensitivity analysis of STS Figure 14 provides an interpretation of the feature importance and interactions in the STS predictive model developed using a DT algorithm. Cement content (C) shows a strong positive impact on STS predictions when its values are high (in red), which is consistent with the understanding that higher cement content often enhances concrete’s tensile strength. The (w/c) displays a pattern where higher values generally result in negative SHAP values, indicating a decrease in predicted STS, as a higher w/c ratio typically weakens the tensile strength of concrete. The figure also suggests feature interactions, for example, certain clusters around the sand-cement ratio indicate that varying combinations of these values affect the model’s output differently. Other features like aggregate-cement ratio, natural aggregate density also play a role in shaping the predictions. Although their impact is comparatively less pronounced than cement content and w/c ratio. These insights help to validate the model and indicate which variables could be targeted for further refinement in enhancing the model’s accuracy. 5.3. Sensitivity analysis for MOE The SHAP analysis for MOE illustrates the influence of various features on the model’s predictions, as shown in Figure 15. In this analysis, the replacement level (RL) appears to have the most significant impact, with high values (red) generally pushing the MOE prediction higher, a trend that was not as pronounced in the previous SHAP analysis for Fc and STS. This suggests that RL may be a more crucial factor for MOE than for Fc and STS in this model. The w/c, similar to Fc and STS models, shows a strong negative impact when its values are high, as a high w/c ratio typically weakens both tensile and compressive strength in concrete. This consistency between the two models reinforces the inverse relationship between the w/c ratio and concrete strength properties. RAC-D and RAC size also play notable roles, primarily contributing positive SHAP values at higher feature values, implying that these recycled aggregate properties can improve tensile strength predictions. This influence aligns with the compressive strength model’s findings, though their impact here appears more substantial. In comparison with the previous SHAP analysis for Fc and STS, this figure emphasizes different key features, with RL taking a more prominent role in MOE, while “C” and aggregate size have relatively less impact on the MOE model prediction. 6. Conclusions This study examines the three concrete properties by applying a machine learning model to simultaneously predict Fc, STS, and MOE. The model was trained on a data set consisting of 358 data points, then validated by K-fold, and sensitivity analysis was completed by SHAP analysis to find which input parameter has a sensitivity that affects the concrete properties. The following are the main conclusions from the study: The decision tree model showed excellent predictive accuracy for compressive strength with a training R2 value of 0.93 and a testing R2 value of 0.85. Its accuracy was also reinforced with a training RMSE of 1.45 and MAE of 0.54 and a testing RMSE of 6.43 and MAE of 2.01, which shows the model was able to accurately predict compressive strength across multiple samples. The model achieved a training R 2 value of 0.92 and a testing R 2 value of 0.88 for STS, with training metrics RMSE of 1.12 and MAE of 0.13, and testing metrics RMSE of 6.03 and MAE of 2.58. These results highlight the decision tree utility in estimating tensile properties with reasonable consistency, as further validated by k-fold cross-validation. For predicting MOE, the decision tree model had a training R2 of 0.94 and a testing R2 of 0.86, with a training RMSE of 1.37 and MAE of 0.28, and testing RMSE of 6.83 and 2.62. The values signify the model's ability to accurately predict the elastic behavior of concrete. With SHAP analysis, we identified influential parameters that impact model accuracy for predicting concrete strength properties, with cement content and water-cement (w/c) ratio being the most significant factors. These results provide useful information for optimizing concrete mix design. This study emphasizes the potential of using decision tree models as interpretable and reliable predictive tools for estimating the three main mechanical properties of concrete with RAC. By predicting these performance outcomes based on the composition of the mix and the properties of the concrete materials, the presented model provides a practical solution to optimize a design without the need to conduct numerous laboratory trials and tests. By incorporating machine learning into the sustainable construction framework, engineers, contractors, and stakeholders are empowered to make decisions that positively impact material waste reduction, natural resource preservation, and the lowered environmental footprint of construction work. Additionally, using SHAP analysis provides transparency to the model by revealing the most impactful parameters, such as cement content and density of the aggregate, and facilitating improvements to the design. Declarations Data and code availability Author can provide data upon request: Aneel Manan, [email protected] Conflict of interest There is no conflict of interest. Funding statement declaration Funding: No funding. Author Contribution M.E. and D.W. conceived and designed the overall study.M.E. collected and curated the recycled‐aggregate concrete dataset, performed data preprocessing, and implemented the core machine‐learning models.D.W. and A.K. developed the feature‐engineering pipeline and optimized model hyperparameters.A.M. conducted exploratory data analyses, generated visualizations, and assisted with model validation.K.P.A. advised on algorithm selection and contributed to the interpretation of model outputs.K.C.O. supervised the project, coordinated collaboration among authors, and served as the corresponding author.M.E. drafted the main manuscript text; D.W., A.K., A.M., and K.P.A. critically revised it for important intellectual content.All authors reviewed and approved the final version of the manuscript. References Hasan, K., Islam, M. T., Ferdaus, R. & Yahaya, F. M. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7168474","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":492574899,"identity":"ccfcfd19-81bf-4538-a32b-550b64efecd2","order_by":0,"name":"Mohamed Elbleihy","email":"","orcid":"","institution":"Zhengzhou University","correspondingAuthor":false,"prefix":"","firstName":"Mohamed","middleName":"","lastName":"Elbleihy","suffix":""},{"id":492574901,"identity":"089bba28-e571-4ef0-a9f6-18f80a959dac","order_by":1,"name":"Dorota Wolak","email":"","orcid":"","institution":"University of Lodz","correspondingAuthor":false,"prefix":"","firstName":"Dorota","middleName":"","lastName":"Wolak","suffix":""},{"id":492574903,"identity":"c71a0505-bb93-4f93-8505-3570abd5302a","order_by":2,"name":"Amir Khan","email":"","orcid":"","institution":"Shenzhen University","correspondingAuthor":false,"prefix":"","firstName":"Amir","middleName":"","lastName":"Khan","suffix":""},{"id":492574905,"identity":"c5dc9ca4-8894-4dfc-a7c1-6fd9500d35c4","order_by":3,"name":"Aneel Manan","email":"","orcid":"","institution":"Zhengzhou University","correspondingAuthor":false,"prefix":"","firstName":"Aneel","middleName":"","lastName":"Manan","suffix":""},{"id":492574906,"identity":"de8f06cf-a8f7-4369-94c3-db50ea80ea28","order_by":4,"name":"Kennedy C. Onyelowe","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABCUlEQVRIiWNgGAWjYBACCTDJxsBgwMwDZspJMJOqxZgELQwQLYkzCDlMsr332IMPZYflzdl5j0n+qLiXPrOdx4DhRw1D4nwH7Fqkec6lG844d9hwZzNfmoTEmeLc2cw8Bow9xxgSNx7ArkVOIsdMmrftcILBYR4zCcO2hNx5QC0MvA1ALQ04tMi/MZP+C9OS2JaQLgey5S8eLdISPGbSjDAtB9sSEqSBWphBtszH5f2eHDPJHqB/NhzmS7ZsOJNgOLOZreCwzDEJ4w04tEgcP2Mm8aPMWt7g/NmDN39UJMhLnD+88eGbGhvZ+TgcBgXNqNwDoAgzOIBXSx0WMXn8toyCUTAKRsHIAQCqCVOfBlYrQQAAAABJRU5ErkJggg==","orcid":"","institution":"Kampala International University","correspondingAuthor":true,"prefix":"","firstName":"Kennedy","middleName":"C.","lastName":"Onyelowe","suffix":""},{"id":492574907,"identity":"ab998320-7768-4e4b-ad70-35d847a11937","order_by":5,"name":"Krishna Prakash Arunachalam","email":"","orcid":"","institution":"Metropolitan Technological University","correspondingAuthor":false,"prefix":"","firstName":"Krishna","middleName":"Prakash","lastName":"Arunachalam","suffix":""}],"badges":[],"createdAt":"2025-07-20 08:38:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7168474/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7168474/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":87915322,"identity":"b7291e6c-84c7-4a81-be91-9afa0086bf75","added_by":"auto","created_at":"2025-07-30 10:46:57","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":212868,"visible":true,"origin":"","legend":"\u003cp\u003eSatellite images of Calica Quarry in 2006 \u0026nbsp;\u0026nbsp;and 2025 illustrating the pit’s growth into a layered, multi-bench \u0026nbsp;\u0026nbsp;excavation. [23]\u003c/p\u003e","description":"","filename":"Picture1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7168474/v1/6a4233de684375390022affe.jpg"},{"id":87915336,"identity":"d1c40725-0c9f-40cf-81e1-e4729a56157f","added_by":"auto","created_at":"2025-07-30 10:46:57","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":139161,"visible":true,"origin":"","legend":"\u003cp\u003eBreakdown of Global Aggregate Production (Total = 50 Billion Tons)[9,10]\u003c/p\u003e","description":"","filename":"Picture2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7168474/v1/e703cbc5516e8a36968e4f99.jpg"},{"id":87915330,"identity":"8e5a5b54-f912-4a03-acfb-a9251387d61c","added_by":"auto","created_at":"2025-07-30 10:46:57","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":2621879,"visible":true,"origin":"","legend":"\u003cp\u003eCorrelation matrix of the dataset\u003c/p\u003e","description":"","filename":"Picture3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7168474/v1/ecf397e1bbf68c7b9d8d4d9b.jpg"},{"id":87915323,"identity":"71e4397e-e314-4896-a616-4b1070704307","added_by":"auto","created_at":"2025-07-30 10:46:57","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":394169,"visible":true,"origin":"","legend":"\u003cp\u003eFrequency distribution of input and output parameters\u003c/p\u003e","description":"","filename":"Picture4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7168474/v1/2d6ec72f7a94f00ec05fcf52.jpg"},{"id":87916170,"identity":"a60f2d17-473a-4938-88b3-82bccc9f0199","added_by":"auto","created_at":"2025-07-30 10:54:57","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":39906,"visible":true,"origin":"","legend":"\u003cp\u003eNature and Artificial Intelligence DT\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7168474/v1/dcc720d7db39501fc0a60e6b.jpg"},{"id":87915326,"identity":"63f5f5aa-3db4-4d1c-ab87-863e83379f4a","added_by":"auto","created_at":"2025-07-30 10:46:57","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":94915,"visible":true,"origin":"","legend":"\u003cp\u003eCompressive strength (a) Regression and (b) Predicted vs Experimental results\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7168474/v1/405fcc29db13230120b12dcb.jpg"},{"id":87915328,"identity":"265e6b51-8315-4210-a670-91a9db12c924","added_by":"auto","created_at":"2025-07-30 10:46:57","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":84917,"visible":true,"origin":"","legend":"\u003cp\u003eSplit Tensile strength (a) Regression and (b) Predicted vs Experimental results\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7168474/v1/dcff2b950c938b5223c38497.jpg"},{"id":87915335,"identity":"9ff82ca1-686d-44f5-b48e-f37fba64e44a","added_by":"auto","created_at":"2025-07-30 10:46:57","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":98854,"visible":true,"origin":"","legend":"\u003cp\u003eModulus of Elasticity (a) Regression and (b) Predicted vs Experimental results\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7168474/v1/1d0f1af306bab4187fd430b2.jpg"},{"id":87915338,"identity":"45f9c783-d5da-4e01-b436-091b2ced04b6","added_by":"auto","created_at":"2025-07-30 10:46:57","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":50381,"visible":true,"origin":"","legend":"\u003cp\u003eK fold validation working methodology\u003c/p\u003e","description":"","filename":"9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7168474/v1/e3b8d63b360728bd6540777c.jpg"},{"id":87915340,"identity":"f5deee2f-3615-492f-881f-e844e43c9785","added_by":"auto","created_at":"2025-07-30 10:46:57","extension":"jpg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":128365,"visible":true,"origin":"","legend":"\u003cp\u003eFc K fold validation (a) R\u003csup\u003e2\u003c/sup\u003e, (b) MAE\u003c/p\u003e","description":"","filename":"10.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7168474/v1/29ba784aa7484f9f53bb45c4.jpg"},{"id":87916172,"identity":"b85132de-2d2d-4526-a091-7f152e62298d","added_by":"auto","created_at":"2025-07-30 10:54:57","extension":"jpg","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":121357,"visible":true,"origin":"","legend":"\u003cp\u003eSTS K fold validation (a) R\u003csup\u003e2\u003c/sup\u003e, (b) MAE\u003c/p\u003e","description":"","filename":"11.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7168474/v1/ce56c9b1902a00a94f4f62ab.jpg"},{"id":87916173,"identity":"e32220a9-49cf-47d9-9d28-321df56c12c2","added_by":"auto","created_at":"2025-07-30 10:54:57","extension":"jpg","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":113814,"visible":true,"origin":"","legend":"\u003cp\u003eMOE K fold validation (a) R\u003csup\u003e2\u003c/sup\u003e, (b) MAE\u003c/p\u003e","description":"","filename":"12.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7168474/v1/62218178387637b563109293.jpg"},{"id":87915367,"identity":"451bc86b-e6bd-4320-8471-c5c77d59c47f","added_by":"auto","created_at":"2025-07-30 10:46:58","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":57716,"visible":true,"origin":"","legend":"\u003cp\u003eFc sensitivity analysis\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-7168474/v1/a17bee28c18e962d7930f3e3.png"},{"id":87915379,"identity":"d96c5cb4-753e-4738-ba32-ba06dd489406","added_by":"auto","created_at":"2025-07-30 10:46:59","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":50226,"visible":true,"origin":"","legend":"\u003cp\u003eSTS sensitivity analysis\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-7168474/v1/2183b9680bd9f1a2e47e7d9a.png"},{"id":87916188,"identity":"b1c9985e-6191-4a7f-b84f-0663818067c3","added_by":"auto","created_at":"2025-07-30 10:54:59","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":54725,"visible":true,"origin":"","legend":"\u003cp\u003eMOE sensitivity analysis\u003c/p\u003e","description":"","filename":"15.png","url":"https://assets-eu.researchsquare.com/files/rs-7168474/v1/807e3b68cb7c5e019fe85ce8.png"},{"id":90286145,"identity":"ae04441d-1b0f-43ec-be03-bc238deeed3a","added_by":"auto","created_at":"2025-09-01 06:17:37","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5531493,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7168474/v1/fc9cc627-8f08-4af0-b4b4-75abc4e75311.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Machine Learning Framework for Predicting Critical Mix-Design and Strength Properties of Eco-Efficient Recycled Aggregate Concrete","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eEach year, a total of 25\u0026nbsp;billion tons of concrete is consumed, making it the most used man-made material[\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e]. Global cement production now amounts to about 4\u0026nbsp;billion tons per year, consuming an equivalent volume of limestone extracted at rates that outstrip natural geological replenishment[\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e]. Concrete manufacturing alone withdraws between 190 and 642 L of freshwater per m\u0026sup3;, roughly 9% of global industrial water withdrawals, placing severe stress on finite water resources[\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e]. Quarrying aggregate causes widespread land disturbance, depletes fossil resources at rates up to 1.48 \u0026times; 10⁻⁶ Petajoules equivalent (PJ) per kg and emits about 1.6\u0026nbsp;billion tons of CO₂ each year[\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e], Fig.\u0026nbsp;1 shows the resource depletion over a 20-year period taken by satellite image. The demand for concrete globally has been growing due to the development of infrastructure and high rates of urbanization. Projected estimates show that by 2030, nearly 1\u0026nbsp;billion more people will live in urban areas[\u003cspan class=\"CitationRef\"\u003e7\u003c/span\u003e]. This will lead to increased consumption of natural aggregate, which constitutes more than 60% of the volume of concrete. The current global aggregate consumption is approximately 50\u0026nbsp;billion tons per year[\u003cspan class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e]. Over the past 2 decades, Aggregate usage in China has increased approximately 430% [\u003cspan class=\"CitationRef\"\u003e11\u003c/span\u003e]. Between 2009 and 2023, U.S. aggregate production climbed from 1.96 to 2.52\u0026nbsp;billion metric tons (a 29% increase), equal to an average annual growth of 1.72% per year [\u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e13\u003c/span\u003e] as shown in Fig.\u0026nbsp;2. To alleviate the demand on non-renewable raw materials, studies have investigated the incorporation of waste glass, scrap tires, and ceramic powders into concrete mixtures to mitigate concrete environmental impacts[\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eEach year, rapid industrialization and construction produce over 3\u0026nbsp;billion tons of demolition and construction waste, resulting in overflowing landfills, depleted resources, and serious environmental damage[\u003cspan class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e]. In the EU, Construction and Demolition (C\u0026amp;D) waste makes up 38.4% (\u0026asymp;\u0026thinsp;850\u0026nbsp;million tons) of all waste, with a 70% recycling target set for 2030[\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e]. China generates the most C\u0026amp;D waste at 2,600 Mt, but recovers only 10% (260 Mt). Japan and Australia generate 78 Mt and 29.2 Mt, respectively, yet recover 88.2% and 81%. The EU produces 857 Mt with only\u0026thinsp;\u0026asymp;\u0026thinsp;343 Mt recovered (40%), while the U.S. achieves 76% recovery from 600 Mt, and Canada 16% recovery from just 4 Mt, as shown in Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eDisposal of concrete waste via landfilling consumes substantial embedded energy and occupies large volumes of landfill space, increasing greenhouse-gas emissions and land-use pressure[\u003cspan class=\"CitationRef\"\u003e24\u003c/span\u003e]. Buried concrete waste can release harmful substances, such as heavy metals, into the soil and groundwater[\u003cspan class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e]. The widespread adoption of RAC could help mitigate these issues by recycling waste materials and reducing the need for virgin aggregate [\u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e]. Recycling C\u0026amp;D waste into RAC can recover nearly 600\u0026nbsp;million tons per year, offset up to 25 percent of virgin aggregate demand in mature markets, and reduce embodied carbon dioxide emissions by 90 percent compared to quarried stone[\u003cspan class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e28\u003c/span\u003e]. Life-cycle assessments indicate that replacing natural aggregate with 50% Recycled Aggregate Concrete can reduce cradle-to-gate CO₂ emissions by 22\u0026ndash;65% and lower embodied carbon by 23\u0026ndash;28% compared to conventional concrete, while cutting virgin aggregate consumption in half [\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e29\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003eRAC concrete has been successfully applied in a range of infrastructure elements, including rigid concrete pavements[\u003cspan class=\"CitationRef\"\u003e30\u003c/span\u003e], asphalt overlays[\u003cspan class=\"CitationRef\"\u003e31\u003c/span\u003e], and reinforced concrete structural and nonstructural members[\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e33\u003c/span\u003e]. The application of RAC in structural elements remains limited because its chemical and physical characteristics differ markedly from those of virgin aggregate. RAC contains residual adhered mortar with elevated alkali and sulfate concentrations, exhibits higher water absorption (typically 4\u0026ndash;8% vs. 0.5\u0026ndash;2%), lower specific gravity (2.2\u0026ndash;2.4 vs. 2.6\u0026ndash;2.7), increased porosity, and greater crushed-particle angularity that reduce compressive strength and mechanical performance[\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e35\u003c/span\u003e]. Although using 100% RAC can reduce cradle-to-gate global warming potential by up to 25% [\u003cspan class=\"CitationRef\"\u003e36\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e37\u003c/span\u003e], it typically decreases compressive strength by approximately 25% [\u003cspan class=\"CitationRef\"\u003e38\u003c/span\u003e]. This strength loss is attributed to residual mortar on the RAC surface, which increases aggregate porosity and weakens the interfacial transition zone with the cementitious matrix, thereby reducing the concrete\u0026rsquo;s load-bearing capacity[\u003cspan class=\"CitationRef\"\u003e38\u003c/span\u003e].\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eC\u0026amp;D Waste Generation and Recovery Performance Across Leading Economies\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCountries\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eC\u0026amp;D waste generation (Mt)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eC\u0026amp;D waste recovery (Mt)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eC\u0026amp;D waste recovery (%)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eReferences\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAustralia\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e29.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e23.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e81%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e39\u003c/span\u003e]\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eChina\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2600\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e260\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e40\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e43\u003c/span\u003e]\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eJapan\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e88.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e44\u003c/span\u003e]\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eEU\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e857\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026asymp;\u0026thinsp;343\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e45\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e46\u003c/span\u003e]\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCanada\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e47\u003c/span\u003e]\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eUnited States\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e600\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e456.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e76\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e[\u003cspan class=\"CitationRef\"\u003e48\u003c/span\u003e]\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eAlthough RAC typically shows a 15\u0026ndash;25% reduction in compressive strength compared to conventional mixes, it still achieves acceptable mechanical properties, adequate for structural uses[\u003cspan class=\"CitationRef\"\u003e49\u003c/span\u003e]. Suitable applications include leveling screeds, subbase layers for pavements, sidewalks, curb-and‐gutter, and trench backfill[\u003cspan class=\"CitationRef\"\u003e50\u003c/span\u003e]. By diverting waste and lowering embodied carbon, RAC concrete delivers significant environmental benefits in contexts where ultra\u0026ndash;high strength is not required[\u003cspan class=\"CitationRef\"\u003e51\u003c/span\u003e]. In recent years, Extreme Gradient Boosting (XGBoost) has emerged as a premier machine-learning technique for modeling concrete properties, offering a combination of high predictive accuracy, efficient computation, and clear interpretability that outperforms both traditional regression and other ensemble methods[\u003cspan class=\"CitationRef\"\u003e52\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e54\u003c/span\u003e]. Most Artificial Intelligence (AI) based studies, including artificial neural network (ANN) [\u003cspan class=\"CitationRef\"\u003e55\u003c/span\u003e], XGBoost [\u003cspan class=\"CitationRef\"\u003e56\u003c/span\u003e], and Random Forest [\u003cspan class=\"CitationRef\"\u003e57\u003c/span\u003e], tend to focus on predicting individual properties such as compressive strength [\u003cspan class=\"CitationRef\"\u003e58\u003c/span\u003e], split tensile strength [\u003cspan class=\"CitationRef\"\u003e59\u003c/span\u003e], shear strength [\u003cspan class=\"CitationRef\"\u003e60\u003c/span\u003e], or elastic modulus [\u003cspan class=\"CitationRef\"\u003e61\u003c/span\u003e]. However, a gap remains in the literature for studies that simultaneously predict multiple properties and evaluate the performance of different AI algorithms. To improve accuracy in predicting concrete properties, it is essential to consider multiple characteristics at once.\u003c/p\u003e\n\u003cp\u003eThis research addresses the existing gap by developing a novel multi-target predictive model capable of simultaneously estimating several key concrete properties, including compressive strength, modulus of elasticity, and splitting tensile strength. The proposed model aims to capture the effect of RAC on concrete performance by incorporating a wide range of input features such as physical, mechanical, and compositional parameters, unlike previous studies that focus on isolated property prediction. The model\u0026rsquo;s output can facilitate informed decision-making in the construction industry, enabling the use of RAC in broader applications while balancing sustainability goals and structural requirements. This research contributes to the development of intelligent tools for optimizing RAC usage and advancing data-driven strategies for sustainable concrete.\u003c/p\u003e"},{"header":"2. Research Significance","content":"\u003cp\u003eDespite growing interest in RAC as a sustainable alternative, its practical benefits remain unclear due to inconsistent findings across studies and varying material conditions. In this regard, the current research examines the future of RAC in structural concrete using a Decision Tree model that employs a machine-learning method that can support a wide range of input variables. The model is used to forecast important mechanical properties, which are compressive strength, tensile strength, and modulus of elasticity. The incremental components of the study include: (a) a comparative overview of concrete containing conventional aggregates versus RAC, (b) compilation of a consistent group of 358 experimental datasets of RAC and concrete to support the predictions required for multi-property, (c) evaluation of the Decision Tree model performance to validate its integrity when predicting properties of RAC, and (d) performance and validation using K-fold cross validation and SHAP to assess the relative significance and identify strongest among the ten input variables.\u003c/p\u003e"},{"header":"3. Methodology","content":"\u003cp\u003eIn this study, it was assumed that traditional statistical methods, such as linear regression, may be insufficient for modelling the complex, nonlinear relationships between concrete mix composition and its mechanical properties. Therefore, machine learning was applied\u0026mdash;an approach based on algorithms capable of autonomously detecting patterns and relationships in data. Specifically, the decision tree (DT) algorithm was used, which is a fundamental supervised learning technique that builds a model in the form of a hierarchical structure of logical conditions (rules). This model recursively splits the input data space into smaller segments to maximize the homogeneity of the target variable within each node. Theoretically, decision trees handle heterogeneous and nonlinear data well and are attractive in engineering contexts due to their interpretability. To assess the reliability and generalizability of the model, the study employed K-fold cross-validation, a statistical method that divides the dataset into K equal parts (folds). The model is trained on K\u0026thinsp;\u0026minus;\u0026thinsp;1 parts and tested on the remaining one; this process is repeated K times to ensure that each data point is used for both training and testing. This technique minimizes the impact of random data splits and provides a robust estimate of the model\u0026rsquo;s ability to generalize to new data.\u003c/p\u003e\n\u003cp\u003eTo quantitatively evaluate the regression model\u0026apos;s accuracy, four standard statistical metrics were applied:\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003e\n \u003cp\u003eR\u0026sup2; (coefficient of determination) \u0026ndash; measures the proportion of variance in the target variable explained by the model; values close to 1 indicate strong predictive performance;\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eRMSE (Root Mean Squared Error) \u0026ndash; reflects the average magnitude of prediction error, being sensitive to large deviations;\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eMAE (Mean Absolute Error) \u0026ndash; captures the average absolute differences between predicted and actual values, less affected by outliers than RMSE;\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eMAPE (Mean Absolute Percentage Error) \u0026ndash; expresses error as a percentage, allowing interpretation regardless of measurement units.\u003c/p\u003e\n \u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eTo further enhance the model\u0026rsquo;s transparency and interpretability, the study employed SHAP (SHapley Additive exPlanations) analysis, which is based on cooperative game theory. SHAP assigns a numerical value to each input variable reflecting its contribution to the final prediction, considering all possible combinations of features. This is particularly useful in interpreting \u0026ldquo;black-box\u0026rdquo; models, where complex feature interactions may otherwise be hard to explain. The entire methodology is grounded in the assumption that secondary data from previous experiments can serve as a reliable basis for predictive modelling\u0026mdash;provided the data is properly curated, cleaned, and balanced.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.1 Database\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eA detailed dataset consisting of 358 experimental tests on concrete incorporating Recycled Aggregate Concrete (RAC) was gathered for analysis, following previous research [\u003cspan class=\"CitationRef\"\u003e62\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e99\u003c/span\u003e]. The input parameters for modeling are the most common in a concrete design (as shown Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e) is replacement rate of recycled aggregate to natural aggregate (RL), water cement ratio (w/c), aggregate cement ratio (A:C), sand cement ratio (S:C), density of RAC (RAC-D), density of NA (NA-D), aggregate size of recycled aggregate (RAC-S), aggregate size of natural aggregate (NA-S), and curing time (age). The output parameters will be the combined compressive strength (Fc), split tensile strength (STS), and modulus of elasticity (MOE). Fc, STS, and MOE are functions of the input parameters.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eDefinitions of Key Variables in RAC Machine Learning Dataset\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSymbol\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eParameter Name\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eTypical Unit\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eRL\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRecycled-to-Natural Aggregate Replacement Level\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e% or decimal\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ew/c\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWater-to-Cement Ratio\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026mdash; (unitless)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eA : C\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAggregate-to-Cement Ratio\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026mdash; (unitless)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eS : C\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSand-to-Cement Ratio\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026mdash; (unitless)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eRAC-D\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDensity of Recycled Aggregate Concrete\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ekg/m\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eNA-D\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eDensity of Natural Aggregate\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ekg/m\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eRAC-S\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMaximum Size of Recycled Aggregate\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003emm\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eNA-S\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMaximum Size of Natural Aggregate\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003emm\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eAge\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCuring Time\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003edays\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eFc\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCompressive Strength\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMPa\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eSTS\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSplit Tensile Strength\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMPa\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eMOE\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eModulus of Elasticity\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMPa\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cdiv class=\"gridtable\"\u003e\n \u003cdiv align=\"char\" class=\"colspec\"\u003e\u003cbr\u003e\u003c/div\u003e\n \u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eDatabase descriptive statistics of Key Variables in RAC Machine Learning Dataset\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eInput\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMean\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMin\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMax\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRange\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSE\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMedian\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMode\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eKurtosis\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSkewness\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSD\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eRL\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e54\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-1.69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e42.13\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003ew/c\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.44\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.09\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eA:C\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.75\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eC:S\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.29\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eAgg-S (mm)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13.59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e38.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e38.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e16.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9.25\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eNA-S (mm)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.56\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e38.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e38.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.44\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-1.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eCC (kg/m\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e386\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e600\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e600\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e385\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e500\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-1.69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e110.69\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eRAC-D (kg/m\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1739\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2661\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2661\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e46.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2320\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-1.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1048.49\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eNA-D (kg/m\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1410\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2870\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2870\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e59.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2540\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-1.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1338.69\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eAge (days)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e29.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e89\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e18.20\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eOutput\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eFc\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e43.42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e11.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e108.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e42.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e45.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e14.96\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eSTS\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.01\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eMOE\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e11.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e50.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e39.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.92\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6.06\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eA detailed analysis with ten input parameters and three output parameters enables an in-depth examination of the factors that impact the compressive, split tensile strength, and modulus of elasticity of RAC concrete. Table \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e provides the statistical properties for each parameter, complemented by the correlation matrix and frequency distribution histogram in Fig. 3 and Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e, respectively. Kurtosis is utilized to describe the shape of the probability distribution [\u003cspan class=\"CitationRef\"\u003e100\u003c/span\u003e]. Figure\u0026nbsp;3 shows the strength of relationships between numerous variables in the data. The results show a negative correlation between the replacement level of RAC and the Fc, STS, and MOE levels. There were a couple of interesting relationships from the matrix; there are positive correlations between C and S, RAC-D and RAC-S, NA-D and NA-S. Negative correlations between the RL with both NA-D and NA-S, and between Fc and MOE, and many of these trends follow previous studies [\u003cspan class=\"CitationRef\"\u003e101\u003c/span\u003e], RAC might have decreased the strength of concrete. Natural aggregate, unlike RAC, doesn\u0026apos;t have the same level of porosity and absorption rate [\u003cspan class=\"CitationRef\"\u003e102\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e104\u003c/span\u003e].\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.2 Decision Tree (DT)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eDecision Tree (DT) is a machine learning algorithm used for both regression and classification [\u003cspan class=\"CitationRef\"\u003e105\u003c/span\u003e]. The main advantage of DT is the working mechanism for a complex dataset, as it splits the dataset into different branches of values on the features. This breakdown of the dataset makes it easy to train the model. The intricate patterns can be easily for inputs and outputs. The flowchart of DT along with the natural tree is presented in Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e\n\u003cp\u003eTable\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e presents the tuning parameters for DT tree model optimization. The model complexity is determined by the size of depth (maximum depth of the tree), which results in the capture the patterns. However, deeper depth can make the model understand the complexity of the database, but it can lead to overfitting. In which the model is highly dependent on the training data and doesn\u0026rsquo;t perform well to new datasets. In such a situation, the depth of the model is set at a specific value, which leads to an accurate prediction.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab4\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eTuning parameters of the DT model\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eParameter\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMaxi depth of the tree\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMini samples to split a node\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMini samples at each leaf node\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCriterion for splitting\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eParameter Variation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5, 10, 20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2, 5, 10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1, 2, 5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026apos;Gini\u0026apos;, \u0026apos;Entropy\u0026apos;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eBest Result Parameter\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNone or determined by data\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGini or Entropy\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eAnother crucial factor that avoids splits with few datasets that could not generalize well is the minimal number of samples needed to split a node. The number of splits a node can be encouraged by set 2 parameters that enhance robustness and the available dataset. The minimum samples at each lead node also controls the number at each lead node for the decision.\u003c/p\u003e\n\u003cp\u003eThe splitting at each node is determined by the options which are \u0026ldquo;Entropy\u0026rdquo; and \u0026ldquo;Gini\u0026rdquo;, which determines the impurity in the dataset. Such a process is important to purify the dataset from non-homogeneity behavior and results in overfitting. Therefore, the selection of either parameter is crucial for model performance optimization.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.3 Model accuracy\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTable \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e shows the evaluation of models\u0026apos; accuracy using a variety of major statistical metrics - coefficients of determination (R2), root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). R2 measures the coefficient of determination of values predicted against actual values, with values approaching 1 indicating a good relationship and predictive fit. RMSE indicates the average magnitude of errors, where larger errors will have a larger notation toward the average error. MAE defines the mean of absolute errors to actual value(s), as it offers a fair measurement to check predictive accuracy. MAPE, expressed as a percentage, provides the average deviation to the actual value(s), working as a consistent reference for overall accuracy. Therefore, lower ratings on RMSE, MAE and MAPE indicates higher degrees of predictability and reliability [\u003cspan class=\"CitationRef\"\u003e106\u003c/span\u003e].\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n \u003ctable id=\"Tab5\" border=\"1\" class=\"fr-table-selection-hover\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eStatistical metrics for model evaluation.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eEvaluation criteria\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eCoefficient of determination\u003c/p\u003e\n \u003cp\u003e(R\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRoot mean squared error (RMSE)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMean absolute error (MAE)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMean absolute percentage error (MAPE)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFormula\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:=1-\\frac{{\\sum\\:}_{i=1}^{m}{({P}_{i}-{T}_{i})}^{2}}{{\\sum\\:}_{i=1}^{m}{({P}_{i}-{T}_{i})}^{2{\\prime\\:}}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:=\\frac{{\\sum\\:}_{i=1}^{m}\\left|{P}_{i-}{T}_{i}\\right|}{m}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:=\\sqrt{\\frac{{\\int\\:}_{i=1}^{m}{{(P}_{i-}{T}_{i})}^{2}}{{\\int\\:}_{i=1}^{m}{\\left({T}_{i-}\\stackrel{-}{T}\\right)}^{2{\\prime\\:}}}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:=\\frac{1}{n}\\sum\\:_{i=,1}^{n}\\left|\\frac{{P}_{i}-{{T}_{i}}^{}}{m}\\right|\\times\\:100\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eResults\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHigher values indicate a better fit\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA lower value indicates better accuracy\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA lower value indicates better accuracy\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eA lower value indicates better accuracy\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRange\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u0026ndash;1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0 - \u0026infin;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0 - \u0026infin;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0 - \u0026infin;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e"},{"header":"4. Results and discussion","content":"\u003cp\u003eThe DT algorithm is a valid means of making concrete predictions of multi-outcome RAC outlined above in\u0026nbsp;Table 6. For the Fc output, the DT model provided R2 values of 0.93 in training and 0.75 in testing, suggesting that it had excellent training predictive capacity, and respectable performance in testing. For STS output, the model provided an R2 of 0.92 in training and 0.78 in testing, while MOE had R2 values of 0.94 in training and 0.76 in testing. The RMSE and MAE values further confirmed the model accuracy with relatively low error in the training dataset across the three outputs; for example, the MAE for Fc was 0.54 in training and 2.01 in testing, STS had MAE of 0.13 in training and 2.58 in testing, while for MOE MAE was 0.28 in training and 2.68 in testing. To summarize, it could be concluded that the DT algorithm captured underlying structures of the dataset, with that conclusion being particularly valid for Fc and MOE values, while for STS, there is less clarity with regards to testing performance.\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"100%\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"9\" style=\"width: 100px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eTable\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e6\u003c/strong\u003e: Algorithm Performance Comparison\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" style=\"width: 15px;\"\u003e\n \u003cp\u003eConcrete\u0026nbsp;\u003c/p\u003e\n \u003cp\u003eProperties\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"4\" style=\"width: 42px;\"\u003e\n \u003cp\u003eTraining\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"4\" style=\"width: 42px;\"\u003e\n \u003cp\u003eTesting\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 8px;\"\u003e\n \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11px;\"\u003e\n \u003cp\u003eRMSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 10px;\"\u003e\n \u003cp\u003eMAE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11px;\"\u003e\n \u003cp\u003eMAPE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 8px;\"\u003e\n \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11px;\"\u003e\n \u003cp\u003eRMSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 10px;\"\u003e\n \u003cp\u003eMAE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11px;\"\u003e\n \u003cp\u003eMAPE\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 15px;\"\u003e\n \u003cp\u003eFc\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 8px;\"\u003e\n \u003cp\u003e0.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11px;\"\u003e\n \u003cp\u003e1.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 10px;\"\u003e\n \u003cp\u003e0.54\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11px;\"\u003e\n \u003cp\u003e0.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 8px;\"\u003e\n \u003cp\u003e0.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11px;\"\u003e\n \u003cp\u003e6.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 10px;\"\u003e\n \u003cp\u003e2.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11px;\"\u003e\n \u003cp\u003e0.65\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 15px;\"\u003e\n \u003cp\u003eSTS\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 8px;\"\u003e\n \u003cp\u003e0.92\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11px;\"\u003e\n \u003cp\u003e1.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 10px;\"\u003e\n \u003cp\u003e0.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11px;\"\u003e\n \u003cp\u003e0.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 8px;\"\u003e\n \u003cp\u003e0.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11px;\"\u003e\n \u003cp\u003e6.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 10px;\"\u003e\n \u003cp\u003e2.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11px;\"\u003e\n \u003cp\u003e0.73\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 15px;\"\u003e\n \u003cp\u003eMOE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 8px;\"\u003e\n \u003cp\u003e0.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11px;\"\u003e\n \u003cp\u003e1.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 10px;\"\u003e\n \u003cp\u003e0.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11px;\"\u003e\n \u003cp\u003e0.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 8px;\"\u003e\n \u003cp\u003e0.86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11px;\"\u003e\n \u003cp\u003e6.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 10px;\"\u003e\n \u003cp\u003e2.62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 11px;\"\u003e\n \u003cp\u003e0.66\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003ch2\u003e4.1. \u0026nbsp; \u0026nbsp; \u0026nbsp; FC predicted results\u003c/h2\u003e\n\u003cp\u003eThe results of the decision tree algorithm are shown in Figure 6, which highlights the training and testing dataset performance of 93% and 85% for Fc, respectively. These results indicate the high accuracy in the prediction performance in both training and testing. Additionally, it has been noted [107] that decision trees may struggle with stability due to sensitivity to small variations in data, which can affect predictive reliability. Prior studies [108] discuss that overfitting happens when a model is trained on noise in the training data, for which the model loses the ability to generalize to unseen data. The DT model tends to be less prone to overfitting than neural network models; however, such a model can still experience overfitting when attempting to model complex patterns. Nevertheless, reference [109] stated that a R2 value in the area of 60% or higher represents reasonable accuracy; hence, the 75% R2 value established in the testing was suitable for practical purposes in predicting concrete properties. Although the model\u0026rsquo;s testing performance is somewhat lower than in training, the DT remains an effective tool for forecasting compressive strength. Enhancements in feature selection and tuning may further improve its generalization and predictive accuracy.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e4.2.\u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp; STS predicted results\u003c/h2\u003e\n\u003cp\u003eThe STS results between predicted and experimental values are demonstrated in Figure 7. The R2 values represent 92% for the training set and 88% for the testing set, indicating that the model is well suited to training data patterns and maintains reasonably good performance with testing data. However, the decline in R\u003csup\u003e2\u003c/sup\u003e from training to testing still suggests some degree of overfitting, where the model may be slightly over-adapted to the training data, limiting its generalization capability. Contributing factors to this overfitting could include the dataset\u0026apos;s size, possible noise within the data, or model complexity. To improve the model\u0026rsquo;s generalizability, further adjustments may be considered, such as expanding the dataset or simplifying the model structure. Additional regularization techniques could also help reduce overfitting and enhance predictive accuracy for STS in new data.\u0026nbsp;\u003c/p\u003e\n\u003cdiv align=\"center\"\u003e\u003cbr\u003e\u003c/div\u003e\n\u003ch2\u003e4.3.\u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp; MOE predicted results\u003c/h2\u003e\n\u003cp\u003eFigure 8 shows the corresponding predicted vs. experimental MOE values. The R2 values for the DT model were 94% and 86% for training and testing, respectively, a high level of predictive accuracy on the training dataset and a drop in testing accuracy, indicating potentially overfitting. As previous studies have shown\u0026nbsp;[109], an R\u003csup\u003e2\u003c/sup\u003e greater than 60% can provide adequate predictive ability for concrete properties, and therefore, the testing R\u003csup\u003e2\u003c/sup\u003e of 76% gained here still represents reasonable predictive power. These results confirm the potential for the model to reliably predict the MOE value, even with the lower correlation in the testing dataset versus the training dataset. Having this level of performance demonstrates the applicability of the DT model for predicting concrete properties, but further adjustment of parameters and feature optimization may improve generalization.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e4.4. \u0026nbsp; \u0026nbsp; \u0026nbsp;K-fold cross-validation\u003c/h2\u003e\n\u003cp\u003eK-fold cross validation is a method for evaluating a machine learning model\u0026rsquo;s performance by splitting the dataset into K equally sized parts, or folds, as depicted in Figure 9 [110]. The algorithm uses an equally divided K-fold and runs the predictive model to determine the performance of the algorithm with an unseen new dataset. This rotation ensures every data point serves as both a training and testing sample, reducing variability and providing a more reliable performance assessment. By continuously testing the model on new data, K-fold cross-validation assesses its generalizability. After each round, performance metrics like R\u003csup\u003e2\u003c/sup\u003e scores are calculated on the test fold, and the results are averaged across all K iterations for an overall performance evaluation.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e4.5. \u0026nbsp; \u0026nbsp; \u0026nbsp;Compressive strength\u0026nbsp;\u003c/h2\u003e\n\u003cp\u003eThe DT predictive model for compressive strength for different K-fold subsets demonstrates that the maximum R\u003csup\u003e2\u003c/sup\u003e of 0.96 indicates a highly accurate predictive model for a certain dataset, as shown in Figure 10(a). The average and minimum values of 0.84 and 0.72, respectively, show a substantial portion of data variability. This conclusion is further supported by the analysis based on MAE values, as seen in Figure 10(b). The maximum MAE of 0.97 denotes cases with higher error, and the minimum MAE of 0.52 highlights the model accuracy in specific folds. Overall, the Fc predictive model of DT shows a robust foundation, with potential for further enhancement and optimization.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e4.6. \u0026nbsp; \u0026nbsp; \u0026nbsp; STS K-fold analysis\u003c/h2\u003e\n\u003cp\u003eThe DT model for split tensile strength k-fold analysis shows that performance varies depending on the database. The model performs significantly well, as seen by the maximum R\u003csup\u003e2\u003c/sup\u003e value of 0.96, however, a minimum R\u003csup\u003e2\u003c/sup\u003e value of 0.19 indicates poorer performance on other folds. Although additional adjustments would be required, the model\u0026rsquo;s overall ability to capture some diversity in the data is indicated by the average R\u003csup\u003e2\u0026nbsp;\u003c/sup\u003evalue of 0.71. A variation in the value of 10-fold in terms of MAE is also noticed. The minimum value of 0.48 indicated a well performance on a certain fold, and the maximum value of 0.71 indicates high error but acceptable for the prediction. The model\u0026rsquo;s prediction accuracy is generally indicated by its average MAE of 0.58. This performance and consistency could be improved with additional tuning.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e4.7. \u0026nbsp; \u0026nbsp; \u0026nbsp;MOE k-fold analysis\u003c/h2\u003e\n\u003cp\u003eIn the MOE, the maximum k-fold R2 of 0.99 demonstrates predictive performance accuracy on certain subsets, while the minimum k-fold R2 of 0.62 indicates some optimism for maximizing performance. The average k-fold R2 of 0.86 is a reasonable indication overall of the model\u0026apos;s ability to predict the data\u0026apos;s variability, as seen in Figure 12(a). Considering MAE, the maximum value of 1.59 indicates scenarios where the model\u0026apos;s predictions are considerably deviated from the actual values. The minimum MAE value of 0.2 demonstrates situations where the model performance could enhance, as seen in Figure 12(b), The average MAE value of 0.84 provides an overall indication of the model\u0026apos;s prediction accuracy for all folds that suggests, while the model can predict data variability satisfactorily, there is room for improvement in certain instances.\u0026nbsp;\u003c/p\u003e"},{"header":"5. Sensitivity analysis","content":"\u003cp\u003eThe sensitivity analysis is executed by SHAP (SHapley Additive exPlanations), a well-established method for interpreting machine learning models, which is based on the idea of Shapley additive explanations[111]. Research [112] shows that Shapley values assess the relative importance of each input variable based on its contribution to the overall output. By looking at SHAP values, we can uncover the most significant features of a model and be able to look for any systematic behaviors across models. The so-called red dot means that a higher feature value had a larger SHAP score. This is similar to conducting a parametric analysis, where all but one variable is held constant and the other variable is allowed to vary in order to determine its effect on a target variable. In this instance, this section is used to understand the extent of each variable\u0026apos;s influence on the RAC values and note the extent to which the input variables affect the output variables.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e5.1. \u0026nbsp; \u0026nbsp; \u0026nbsp;Sensitivity analysis for Fc\u0026nbsp;\u003c/h2\u003e\n\u003cp\u003eThe SHAP analysis of the compressive strength predictive model using DT offers valuable insights into the importance and interactions of various input features. The SHAP plots elements that are located furthest from the center (Figure 13). For example, a higher \u0026ldquo;C\u0026rdquo;, shown in red, has a positive impact. In contrast, higher values of the \u0026ldquo;w/c\u0026rdquo; tend to result in negative SHAP values, indicating a reduction in predicted compressive strength. Distinct clusters in the SHAP values of features like \u0026ldquo;C\u0026rdquo; and \u0026ldquo;w/c\u0026rdquo; suggest interactions between these variables, showing that different combinations of high and low values affect predictions in varying ways.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eCement content has the strongest influence on the model\u0026rsquo;s predictions, with higher values aligning with increased concrete strength, as expected. Meanwhile, the w/c ratio typically impacts predictions negatively, as a higher ratio generally weakens concrete strength. Other features, such as replacement level (RL) and aggregate-to-cement ratio, also affect predictions, but to a lesser extent compared to cement content and the water-cement ratio.\u003c/p\u003e\n\u003ch2\u003e5.2. \u0026nbsp; \u0026nbsp; \u0026nbsp;Sensitivity analysis of STS\u003c/h2\u003e\n\u003cp\u003eFigure 14 provides an interpretation of the feature importance and interactions in the STS predictive model developed using a DT algorithm. Cement content (C) shows a strong positive impact on STS predictions when its values are high (in red), which is consistent with the understanding that higher cement content often enhances concrete\u0026rsquo;s tensile strength. The (w/c) displays a pattern where higher values generally result in negative SHAP values, indicating a decrease in predicted STS, as a higher w/c ratio typically weakens the tensile strength of concrete. The figure also suggests feature interactions, for example, certain clusters around the sand-cement ratio indicate that varying combinations of these values affect the model\u0026rsquo;s output differently. Other features like aggregate-cement ratio, natural aggregate density also play a role in shaping the predictions. Although their impact is comparatively less pronounced than cement content and w/c ratio. These insights help to validate the model and indicate which variables could be targeted for further refinement in enhancing the model\u0026rsquo;s accuracy. \u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e5.3. \u0026nbsp; \u0026nbsp; \u0026nbsp; Sensitivity analysis for MOE\u003c/h2\u003e\n\u003cp\u003eThe SHAP analysis for MOE illustrates the influence of various features on the model\u0026rsquo;s predictions, as shown in Figure 15. In this analysis, the replacement level (RL) appears to have the most significant impact, with high values (red) generally pushing the MOE prediction higher, a trend that was not as pronounced in the previous SHAP analysis for Fc and STS. This suggests that RL may be a more crucial factor for MOE than for Fc and STS in this model. The w/c, similar to Fc and STS models, shows a strong negative impact when its values are high, as a high w/c ratio typically weakens both tensile and compressive strength in concrete. This consistency between the two models reinforces the inverse relationship between the w/c ratio and concrete strength properties. RAC-D and RAC size also play notable roles, primarily contributing positive SHAP values at higher feature values, implying that these recycled aggregate properties can improve tensile strength predictions. This influence aligns with the compressive strength model\u0026rsquo;s findings, though their impact here appears more substantial. In comparison with the previous SHAP analysis for Fc and STS, this figure emphasizes different key features, with RL taking a more prominent role in MOE, while \u0026ldquo;C\u0026rdquo; and aggregate size have relatively less impact on the MOE model prediction.\u0026nbsp;\u003c/p\u003e"},{"header":"6. Conclusions","content":"\u003cp\u003eThis study examines the three concrete properties by applying a machine learning model to simultaneously predict Fc, STS, and MOE. The model was trained on a data set consisting of 358 data points, then validated by K-fold, and sensitivity analysis was completed by SHAP analysis to find which input parameter has a sensitivity that affects the concrete properties. The following are the main conclusions from the study:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eThe decision tree model showed excellent predictive accuracy for compressive strength with a training R2 value of 0.93 and a testing R2 value of 0.85. Its accuracy was also reinforced with a training RMSE of 1.45 and MAE of 0.54 and a testing RMSE of 6.43 and MAE of 2.01, which shows the model was able to accurately predict compressive strength across multiple samples. The model achieved a training R\u003csup\u003e2\u003c/sup\u003e value of 0.92 and a testing R\u003csup\u003e2\u003c/sup\u003e value of 0.88 for STS, with training metrics RMSE of 1.12 and MAE of 0.13, and testing metrics RMSE of 6.03 and MAE of 2.58. These results highlight the decision tree utility in estimating tensile properties with reasonable consistency, as further validated by k-fold cross-validation.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eFor predicting MOE, the decision tree model had a training R2 of 0.94 and a testing R2 of 0.86, with a training RMSE of 1.37 and MAE of 0.28, and testing RMSE of 6.83 and 2.62. The values signify the model's ability to accurately predict the elastic behavior of concrete.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eWith SHAP analysis, we identified influential parameters that impact model accuracy for predicting concrete strength properties, with cement content and water-cement (w/c) ratio being the most significant factors. These results provide useful information for optimizing concrete mix design.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eThis study emphasizes the potential of using decision tree models as interpretable and reliable predictive tools for estimating the three main mechanical properties of concrete with RAC. By predicting these performance outcomes based on the composition of the mix and the properties of the concrete materials, the presented model provides a practical solution to optimize a design without the need to conduct numerous laboratory trials and tests. By incorporating machine learning into the sustainable construction framework, engineers, contractors, and stakeholders are empowered to make decisions that positively impact material waste reduction, natural resource preservation, and the lowered environmental footprint of construction work. Additionally, using SHAP analysis provides transparency to the model by revealing the most impactful parameters, such as cement content and density of the aggregate, and facilitating improvements to the design.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData and code availability\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAuthor can provide data upon request:\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAneel Manan, [email protected] \u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of interest\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThere is no conflict of interest.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding statement declaration\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eFunding: No funding.\u003c/p\u003e\n\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eM.E. and D.W. conceived and designed the overall study.M.E. collected and curated the recycled‐aggregate concrete dataset, performed data preprocessing, and implemented the core machine‐learning models.D.W. and A.K. developed the feature‐engineering pipeline and optimized model hyperparameters.A.M. conducted exploratory data analyses, generated visualizations, and assisted with model validation.K.P.A. advised on algorithm selection and contributed to the interpretation of model outputs.K.C.O. supervised the project, coordinated collaboration among authors, and served as the corresponding author.M.E. drafted the main manuscript text; D.W., A.K., A.M., and K.P.A. critically revised it for important intellectual content.All authors reviewed and approved the final version of the manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eHasan, K., Islam, M. 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Mater.\u003c/em\u003e \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.conbuildmat.2022.128296\u003c/span\u003e\u003cspan address=\"10.1016/j.conbuildmat.2022.128296\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2022).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Recycled Aggregate Concrete, Multi-prediction model, sustainable concrete, machine learning, cross-validation","lastPublishedDoi":"10.21203/rs.3.rs-7168474/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7168474/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eEfforts to reduce concrete\u0026rsquo;s embodied carbon and the environmental impacts of construction-and-demolition (C\u0026amp;D) waste have increasingly shifted toward using recycled-aggregate concrete (RAC) to replace natural aggregate, either partially or entirely. Over the past two decades, dozens of studies have been conducted on the properties of RAC mixes. These studies provide a solid foundation for prediction models that eliminate the reliance on actual tests, which can be time-consuming. Machine learning (ML) models predict concrete properties from interacting variables, such as water-to-cement ratio, cement content, RAC replacement level, aggregate density, etc. These data-driven predictions are more reliable than traditional empirical formulas. ML model can capture nonlinear relationships among diverse input features, providing a framework for optimizing mix design and evaluating mechanical performance. In this study, a database of 358 mix designs from the literature was used to predict three key mechanical properties (compressive strength, split-tensile strength, and modulus of elasticity) of RAC-based concrete. The decision tree was used as the principal predictive model, and its robustness was verified through K-fold cross-validation. Model performance was high in training (R\u0026sup2; = 0.93, 0.92, and 0.94, respectively) and remained acceptable in testing (R\u0026sup2; = 0.75, 0.78, and 0.76). SHAP (SHapley Additive exPlanations) Analysis shows cement content and aggregate density are the most influential features across all three properties, followed by water-to-cement ratio and RAC replacement level. This interpretable ML framework streamlines mix-design optimization, reduces laboratory work, and guides production of low-carbon RAC with dependable mechanical performance.\u003c/p\u003e","manuscriptTitle":"Machine Learning Framework for Predicting Critical Mix-Design and Strength Properties of Eco-Efficient Recycled Aggregate Concrete","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-30 10:46:52","doi":"10.21203/rs.3.rs-7168474/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"6fe50c39-2cc7-4726-87ae-6d628792fe49","owner":[],"postedDate":"July 30th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":52302241,"name":"Physical sciences/Engineering"},{"id":52302242,"name":"Physical sciences/Materials science"}],"tags":[],"updatedAt":"2025-09-01T06:09:08+00:00","versionOfRecord":[],"versionCreatedAt":"2025-07-30 10:46:52","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7168474","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7168474","identity":"rs-7168474","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}