Supervised machine learning driven analysis of compressive strength in concrete incorporating sustainable sludge with SHAP and PDP analyses

ABSTRACT

Due to the increasing demand for ready-made clothing, wastewater treatment facilities are producing large amounts of textile effluent sludge (TES), which is often dumped as backfill and contributes to groundwater and land contamination. Compressive strength (CS), a vital property of concrete, is usually measured through experimental tests that are both costly and time-consuming. To promote eco-friendly construction, this study investigates the mechanical, microstructural, environmental, and machine learning (ML) characteristics of concrete containing various TES percentages. The significance of this research lies in integrating TES as a partial cement and aggregate replacement with ML-based compressive strength prediction, providing a rapid cost cost-effective alternative to traditional experimental testing. Random forest (RF), linear regression (LR), extreme gradient boosting (XGB), and support vector regression (SVR) models were developed using 253 datasets from previous studies, with the RF model achieving superior performance with R² values of 0.927 for training and 0.915 for testing. Analysis revealed that 15% TES replacement reduced compressive strength by 25.21% after 28 days while decreasing the environmental footprint by 13.90%, indicating an optimal balance between sustainability and performance. SEM observations confirmed increased porosity and ettringite formation in TES-modified concrete, correlating with the slight reduction in strength. Overall, this study presents an innovative, eco-friendly concrete solution that transforms hazardous TES into a valuable construction material while enabling reliable ML-based property prediction.

Keywords:
Textile effluent sludge; Machine learning; Microstructural analysis; Compressive strength; SHAP; PDP.

1. INTRODUCTION

The most widely used construction material worldwide is concrete, which boasts a variety of advantages over other substances, including economy, versatility, longevity, and integrity. It is crucial to investigate the mechanical characteristics of concrete to create design techniques that better comprehend the performance of structures constructed of concrete under external loads. Among the numerous metrics of concrete’s characteristics, compressive strength is principally critical, as it correlates directly with the stability of the frameworks and is essential for the reliability inspection of the structures throughout their entire lifespan, from novel construction planning to old framework assessment. Nevertheless, concrete is widely acknowledged as a composite material that is produced by the uniform distribution of a variety of components throughout the entire matrix. As a result of the complexity of the system, predicting the concrete’s compressive strength is quite complicated [¹].

Conducting physical tests is usually the quickest and most accurate approach to determining the compressive strength of concrete. Typically, the cylinder or cubic samples were prepared in line with a specifically designed mix proportion and subsequently cured throughout the specified duration. Subsequently, utilization of the compressive test instrument facilitates the acquisition of compressive strength [²]. Nevertheless, this method is extremely expensive in terms of time as well as expenditure, resulting in a significantly reduced level of productivity. To forecast the compressive strength of concrete employing the specified planned mixing ratio of various ingredients, several statistical predictive strategies vary from the conventional experimental approaches [³,⁴,⁵]. Designing an appropriate approach to investigate concrete qualities is necessary because of the intricate nature and variability of concrete behaviour, as well as the different aspects that impact compressive strength. Recent years have seen the successful use of artificial intelligence (AI) techniques in building construction findings, with a growing trend towards using machine learning (ML) strategies for assessing the compressive strength of concrete [⁶, ⁷]. The regression analysis based on ML has several applications, one of which is the prediction of concrete compressive strength. ML has distinct benefits over more conventional regression approaches, as it incorporates methods that may gain insight from the data being used and provide extremely precise details for the generated data [⁸].

To predict the compressive strength of SCC that contains bottom ash, SIDDIQUE et al. [⁹] leveraged artificial neural networks (ANN). The strength of concrete containing construction detritus or recycled aggregate concrete was predicted using ANN by DANTAS et al. [¹⁰] and DUAN et al. [¹¹]. MOHAMMED et al. [¹²] tested 455 distinct concrete mixes with varying amounts of fly ash (FA) and ground-granulated blast furnace slag (GGBS). When evaluating the strength of carbon nanotube cement substances, YANG et al. [¹³] applied the random forest (RF) approach, which produced a high degree of predictability (R² = 0.98). Several models were employed by KAKASOR ISMAEL JAF et al. [¹⁴] to anticipate the compressive strength (CS) of various particle sizes and morphologies after analysing 236 data points of FA-modified concrete via multiple sources. KASHEM et al. [¹⁵] implemented the XGBoost methodology to assess the efficacy of rice husk ash, which resulted in an R² value of 0.95. ANN was employed by AYAT et al. [¹⁶] to forecast the CS of limestone-filled concrete, achieving a correlation coefficient result of 0.97. After developing several ML techniques using 120 data points, KUMAR et al. [¹⁷] found that the support vector machine (SVM) model was the most effective in predicting the CS of concrete. According to MOTTAKIN et al. [¹⁸], the RF model outperformed the alternatives while testing CS using textile slag, yielding an R² value of 0.88.

Moreover, according to KARIM et al. [¹⁹], the investigation used SHapley additive explanations (SHAP) and partial dependence plot (PDP) assessments to determine the optimum range for every parameter’s strength enhancement contribution. The PDP evaluation revealed the amount of each input parameter substance to be estimated effectively for the intended compressive strength, as stated by KASHEM et al. [²⁰]. Employing SHAP association plots, WANG et al. [²¹] demonstrated how different parameters impact the model’s prediction and shed light on the most suitable interval of metrics for basalt fiber properties. WANG et al. [²²] employed the SHAP technique to investigate the connections and implications between input factors and compressive strength. According to the findings reported by [²³] in their PDP analysis, the amount of every component can be simply calculated for the specified compressive strength. Additionally, DATTA et al. [²⁴] observed that using rice husk ash in concrete reduces embodied CO₂, significantly lowering its global warming potential. According to SOBUZ et al. [²⁵], substituting ordinary Portland cement with 0–20% marble powder resulted in a reduction of embodied CO₂ ranging from 10.67% to 30.70% relative to the control mix. In the economic analysis conducted by ISLAM et al. [²⁶], the inclusion of greater amounts of waste brick powder resulted in a 4.95% cost reduction, signifying appreciable economic advantages in concrete manufacturing.

Concerning the use of TES in concrete production, there is a dearth of thorough research. Although previous research [¹⁸] has demonstrated the potential for partial cement or aggregate replacement under the influence of TES, an extensive look into ML-based assessment is required. The purpose of this study was to fill a need in the literature by developing a model to estimate TES compressive strength utilizing ML techniques, such as random forest, support vector mac hine, linear regression, and extreme gradient boosting. In addition to this, the research examined 253 data points from prior literature and applied six critical input factors, which greatly improved compressive strength forecasting. Furthermore, the predictive algorithms were evaluated for accuracy by comparing expected outcomes with actual data sets and by using several statistical metrics to assess efficiency during both the testing and training stages. The study also implemented SHAP and PDP to evaluate the influence of features on the forecast of compressive strength. Notably, by striking the right balance between predictability and sustainability, the meticulously constructed predictive ML framework marks a critical milestone on the road to TES’s implementation in real-world research.

2. MATERIALS AND METHODS

To conduct the investigation, concrete mixtures with different TES substitution rates were prepared. Furthermore, specimens were cast, cured, and tested to determine mechanical and microstructural qualities using defined procedures. Furthermore, predictive algorithms were created to forecast concrete effectiveness, and multiple kinds of performance measures were used to evaluate the model’s reliability. Figure 1 displays a graphic representation of the entire research that was carried out for this study.

Figure 1
Schematic representation of the entire study methodology.

2.1. Mix description

OPC of type I, which was locally accessible, was implemented in this experiment in compliance with BDS EN 197-1 [²⁷]. This investigation used coarse aggregates with a maximum size of 19 mm. River sand was passed via a 4.75 mm sieve and used as a fine particle aggregate [²⁸]. In addition, a supplementary binding agent was incorporated by utilizing TES powder, which was obtained from a local producer. To increase the specific surface area of TES, it was sun-dried for four days, oven-dried at 105 ± 5 °C for 24 hours, and subsequently micronized at 50 rpm for 40 minutes using a Los Angeles machine. At last, the material was sieved through a 75 μm mesh and was prepared for use as a partial substitute for cement.

Concrete mix proportions were established in this investigation by evaluating the distinctive characteristics of the key components and the resulting concrete-specific desired qualities. In this investigation, TES was used at doses ranging from 5% to 20% to partially replace cement. In a volumetric ratio of 1:1.66:2.10, the basic mix composition consisted of binder, fine, and coarse aggregate. All of the mixtures maintained a water-to-binder (W/B) ratio of 0.32. The materials’ precise mix proportions are provided in Table 1.

Table 1
Detailing the mix proportions for 1 cubic meter of all mixtures.

MIX ID	OPC(Kg/m3)	FINE AGGREGATE (KG/M3)	COARSE AGGREGATE (KG/M3)	SLUDGE(Kg/m3)	WATER(Kg/m3)
TES 0	488.10	808.65	1026.25	0	157
TES 5	463.71	808.65	1026.25	24.40	157
TES 10	439.30	808.65	1026.25	48.80	157
TES 15	414.90	808.65	1026.25	73.20	157
TES 20	390.51	808.65	1026.25	97.60	157

2.2. Machine learning models

2.2.1. Linear regression

Predictive analysis often makes use of LR, a fundamental ML model. It uses linear equations to link a dependent variable with a set of independent variables [²⁹]. The linear relationship that the model assumes is represented by the following equation:

(1) $$y={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+\cdots +{\beta }_n{x}_n+\in$$

The predicted value is denoted by y, the input characteristics by x_i, the coefficients by β_i, and the error value by ∈. The objective is to find the optimal coefficients β that reduce the error. LR is widely used for baseline modelling and preliminary data analysis because it is simple, easy to learn and effective [³⁰]. The model was trained on the training set using ordinary least squares estimation. It assumes that data is linear, observations are independent of each other, and residuals are normally distributed.

2.2.2. Support vector regression (SVR)

SVR is a machine learning method based on the principles of Support Vector Machines (SVMs). It is frequently used for regression tasks and seeks to minimize error within a predetermined margin while identifying a function that roughly represents the relationship between input data and the end variable [³¹]. In order to create a high-dimensional feature space from the original input space, SVR implicitly maps it using training data. SVR utilizes the training data to implicitly transform the original input variables into a higher-dimensional feature space. In this inquiry, the RBF function of the kernel was utilized to construct the SVR model. The equation can be expressed as:

(2) $$f(x)={\displaystyle {\sum }_{i=1}^n(a_i-{\overline{a}}_i)}k(x_i,x)+b$$

Where f_(x) is the predicted value, n is the number of support vectors, (a_i, a–_i) are LaGrange multipliers used to define the weights assigned to the support vectors, k(x_i, x) are the Kernel function that computes the similarity between the input x and support vector x_i and b is the bias term learned during training.

2.2.3. Random forest (RF)

The ensemble learning algorithm RF creates a prediction model by utilizing an ensemble of decision trees [³²]. It operates as a supervised method that can manage applications for both classification and regression. MAIMON and ROKACH [³³] state that RF techniques employ a mathematical model for data storage based on decision-making trees (DT), which serve as the foundation for information theory-based decision-making. DT can be used to predict both continuous and categorical data. The accuracy approach of the DT algorithm differs depending on whether tasks are being done for classification or regression [³⁴]. The bootstrap aggregation technique, also called bagging, reduces the variance of the trees by randomly selecting data subsets to build each tree. Prediction accuracy rises because the models are less likely to overfit the data, since they don’t rely only on one decision tree. In an RF model with M decision trees, each tree T_i makes a prediction f_i(x) for an input x. The final prediction Fˆ(x) is the average (regression) or majority vote (classification) of all trees’ predictions, as shown in Equation 3:

(3) $$\widehat{F}(x)=\frac{1}{M}{\displaystyle \sum _{i=1}^M{f}_i(x)}$$

Where Fˆ(x) is the output prediction for the input parameter x, f_i(x) is the forecast from the i-th decision tree, and M is the total number of trees in the RF model. Choosing the sample size is the initial stage in the functioning of this method. A decision tree is then constructed for every sample. The final forecast is decided by a voting mechanism after each tree has produced a prediction based on the input parameters.

2.2.4. Extreme gradient boosting (XGB)

CHEN and GUESTRIN [³⁵] developed XGB, an advanced machine learning technique, for supervised learning problems that integrate classification and regression. Because it combines the predictions of several weak models to produce a strong and dependable model, this enhanced distributed gradient boosting library is ideal for effective and scalable machine learning training. With the help of this effective technique, reliable, accurate models that function effectively with invisible data can be produced. In supervised learning, XGB is used to solve problems with regression, classification, and ranking. It has been frequently employed in industry due to its low feature engineering needs and outstanding problem-solving capabilities [³⁶]. With the help of this powerful approach, reliable and accurate models that perform well when applied to unobserved data can be produced. Large datasets with a lot of properties are ideal for this approach. This method sequentially generates decision trees. The XGB model used in this investigation was built with 150 trees and a learning rate of 0.05. When modeling a continuous target variable, XGB aggregates the outputs of multiple trees to generate the final prediction of CS. This process relies on an objective function f, which is defined as the combination of a loss component and a regularization term, as outlined in Equation 4.

(4) $$F={\displaystyle {\sum }_{i=1}^{n}l(y_i,{\overline{y}}_i)}+{\displaystyle {\sum }_{k=1}^k\cap (f_k)}$$

Where, l(y, y–_i) is the loss function for the prediction y–_i and true target y_i. ∩ (f_k) is the regularization term for each tree f_k, which helps prevent overfitting. For every prediction y–_i, Equation 5 is applied, where k corresponds to the total number of trees in the model.

(5) $${\overline{y}}_i={\displaystyle {\sum }_{k=1}^k{f}_k(x_i)}$$

2.3. SHapley additive exPlanations (SHAP)

SHAP is a machine learning technique that explicates each prediction a model generates [³⁷]. The method evaluates the contribution of each feature to the final prediction by applying game theory principles, specifically through the use of Shapley values [³⁸]. SHAP quantifies how much each input variable contributes to the model’s output relative to the baseline prediction. In the SHAP summary plot, the input features are arranged according to their influence on the output of the MLP model. For individual data samples, colored markers, ranging from red for higher values to blue for lower values, represent the magnitude of each feature. In the SHAP summary plot, the horizontal position of a sample corresponds to whether the feature increases or decreases its contribution to the model’s prediction. When the value of each input feature is incorporated into the set of positively weighted features within the model, the overall predictive accuracy is enhanced.

2.4. Partial dependence plots (PDP)

A PDP depicts how the output responds to variations in a given set of input parameters. It demonstrates the degree to which the predicted results are influenced by the values of the specific input variables under examination [³⁹]. The PDP also illustrates the impact of each parameter on the machine learning algorithm’s anticipated outcomes. It is considered a global method since it takes into account each case and illustrates the general relationship between a feature and the anticipated outcome. The plots offer comprehensive illustrations of the contributions made by each input variable concerning the expected outcome [²³]. This is particularly useful for complex models that include hard-to-understand feature interactions.

2.5. Database

A comprehensive dataset encompassing diverse input factors that influence the compressive strength of TES concrete was compiled from existing literature. In total, 253 experimental data points were collected for this study. These values were derived from concrete tests where different proportions of cement and aggregates were substituted with TES powder. The selected input variables included water content, TES powder, coarse aggregate, sand, cement, and curing age, which were used to predict the compressive strength as the output. While numerous parameters can affect compressive strength, this research focused only on the most significant factors for which adequate experimental data on TES-based concrete were available.

2.6. Statistical dataset with heatmap association analysis

This database’s variables, unit, variance, mean, least, highest, 25th, and 75th percentile values are all included in Table 2 along with their respective statistical metrics. Each variable contains data sets with a large amount of variance to improve the precision and validity of the projected strength. During this phase, it is important to recognize that it is feasible that certain factors are interdependent.

Table 2
Statistical assessment of database features.

VARIABLES	UNIT	MEAN	STANDARD DEVIATION	MINIMUM	25% PERCENTILE	75% PERCENTILE	MAXIMUM
Cement	Kg/m3	416.72	51.32	329.88	373.50	450.50	530.00
Fine Aggregate	Kg/m3	687.81	129.20	461.83	636.00	798.00	894.00
Coarse Aggregate	Kg/m3	1183.10	276.14	821.39	1005.84	1380.00	1752.00
TES powder	Kg/m3	42.38	32.59	0.00	20.00	70.00	106.00
Water	Kg/m3	180.57	23.60		161.60	190.80	229.00
Age	Days	31.03	25.63		14.00	28.00	90.00
CS	MPa	27.89	4.93	17.01	24.11	31.89	39.22

Figure 2 displays the findings of evaluating the association coefficients for every prospective parameter. The Python script commences by modifying the font and graphic sizes to ensure a spacious plot area and simple perusal. The heatmap is generated by utilizing the sns.heatmap() function to visualize the interaction matrix cor. The function’s well-calibrated parameters include vmax = 0.8, which limits the maximum amount on the hue measure to 0.8, thereby preventing larger values from affecting the hue gradient. Inefficient and difficult interpretation of input variables’ behaviour under response conditions may result from a high beneficial or detrimental correlation factor. A correlation value close to 1 on an index from –1 to 1 depicts a substantial positive correlation, implying that a spike in one factor is likely to be followed by an expansion in another. In the absence of a strong linear correlation, a result close to 0 indicates that the two variables are not significantly related. Based on the data, the most significant relationships were noticed between coarse aggregate and water (+0.83), fine and coarse aggregate (+0.73), and OPC and fine aggregate (+0.32). Statistically significant correlations were not detected. It is crucial to consider that multicollinearity arises when variables demonstrate significant associations with each other. As a result, the ML model’s output might be misinterpreted [³⁶]. In their research, Kumar, Biswas [⁴⁰] employed a heatmap graphic to demonstrate a promising statistical assessment, which is substantially comparable to this analysis.

Figure 2
Coefficients of association between variables.

2.7. Machine learning modeling and performance evaluation

To determine the most suitable ML model for predicting the CS of TES concrete, the four algorithms were evaluated: LR, SVR, RF and XGB. The dataset was randomly divided into three portions: 60% for training, 20% for testing, and 20% for validation, ensuring uniformity across all models. The performance of the models was assessed using two primary approaches. First, prediction accuracy was evaluated using metrics such as mean MAE, RMSE and MSE to quantify the error in predictions. Second, the coefficient of determination (R²) was utilized to measure the models’ ability to capture the variability in the output. This dual evaluation framework ensures a comprehensive comparison, highlighting each model’s precision, robustness, and reliability in forecasting the compressive strength of TES concrete [⁴¹]. The following are the equations:

(6) $$\mathrm{MSE}=\frac{1}{n}{\displaystyle {\sum }_{i=1}^n{(Y-Y_i)}^2}$$

(7) $$R^2=1-\frac{{\displaystyle {\sum }_{i=1}^n{(Y-Y_i)}^2}}{{\displaystyle {\sum }_{i=1}^n{Y}_i^2}}$$

(8) $$\mathrm{RMSE}=\sqrt{\frac{1}{n}{\displaystyle {\sum }_{i=1}^n{(Y-Y_i)}^2}}$$

(9) $$\mathrm{MAE}=\frac{1}{n}{{\displaystyle {\sum }_{i=1}^n\left|Y-Y_i\right|}}^2$$

Here, Y represents the observed values, Yi indicates the mean of the predicted values, and n refers to the total number of samples. When assessing the efficacy and dependability of machine learning models in forecasting the CS of TES concrete, metrics for performance are essential. MAE provides an intuitive grasp of the distance between predicted and actual values, independent of direction, by measuring the average magnitude of prediction errors. By squaring the errors prior to averaging, MSE highlights greater errors, which makes it helpful for locating models that reduce notable variances. RMSE facilitates interpretability by offering statistics in the same units as the predicted variable. Finally, the coefficient of determination, or R², measures the percentage of variance in the real data that the model can account for; higher performance is indicated by values closer to 1 [⁴²]. The overall flowchart of the ML process is denoted in Figure 3.

Figure 3
Flowchart of the proposed ML modeling process.

3. RESULTS AND DISCUSSION

3.1. Effects of TES on compressive strength

As shown in Figure 4, the compressive strength of the concrete specimens decreased with higher proportions of TES. Across all curing periods (7, 28, and 56 days), the TES 20 mix demonstrated the lowest strength, while the TES 0 mix achieved the highest performance. The compressive strengths of the TES 5 mix showed a little decline compared to the control mix at 7, 28, and 56 days, with reductions of 8.49%, 7.87%, and 7.48%, respectively. Comparatively, the TES 10 mix reduced 12.85% of its strength after 7 days, 13.21% after 28 days, and 12.36% after 56 days compared to the control mix. The TES 15 mix demonstrated a noticeable decline in compressive strength, with reductions of 24.72%, 25.21%, and 23.40% at 7, 28, and 56 days, respectively. In comparison, the TES 20 mix recorded the most substantial loss in strength, decreasing by 32.07%, 32.81%, and 31.37% at the same curing ages relative to the control mix. The decrease in compressive strength is caused by TES’s less reactive binding capability, as well as by dilution effects, higher water requirement, and variability in TES characteristics. Increasing the amount of replacement also weakens the concrete by reducing C–S–H formation and disrupting particle distribution caused by excess fines. According to SANDESH et al. [⁴³], the compressive strength of concrete decreased by 17.44%, 37.5%, and 42.64% with 5%, 7%, and 9% ETP sediment replacement, respectively, which aligns closely with the findings of this study.

Figure 4
Compressive strength of all TES-based concrete.

3.2. Data distribution

3.2.1. Histogram analysis

Histogram analyses of various distribution variables are illustrated in Figure 5. By employing the Seaborn and Matplotlib libraries, this code portion produces an array of histogram graphs that each depict the distribution of distinctive features within the broadened data. To generate each histogram, the histplot function is employed, with kernel density estimation (KDE) applied to ensure an ideal representation of its data distribution. The grid is set up to hold multiple plots, and for clarity’s sake, each one has been given a different colour from the listed options. Employing less TES powder resulted in a higher anticipated strength. For precise forecasting, it was necessary to have a water distribution that was in phase with the OPC ratio. Reducing the quantity of aggregate used was also crucial for a dependable strength projection. Similar to the present study, ALMAHAMEED and SOBUZ [⁴⁴] showed encouraging predictive results in their earlier work.

Figure 5
Parameter dispersion examined via histogram analysis.

3.2.2. Multivariate adaptive analysis

For the input data, the variables are compressive strength; Figure 6 shows the results of the multivariate analysis. By using Seaborn’s sns.pairplot() method, a pairplot is generated, with uniformly formatted off-diagonal scatter plots (plot_kws) and diagonal kernel density plots (diag_kws). Consequently, the dataset’s pairwise connections and distributions are cohesively visualized. The multivariate analysis approach is used to forecast all of the collected data in the machine learning process. The models displayed the dispersed data with various material mixing scenarios, and all of them were compared with one another. This method elucidates the interactions and interrelations between the materials based on their strength. Examination of the scattered graph indicates that the maximum values exceed 35 MPa. To comprehend its clarity, this investigation aligns with a multivariate approach that takes component data as inputs and utilizes strength projection as output values.

Figure 6
Evaluation of input factors using multivariate analysis.

3.3. Predictive machine learning analysis

3.3.1. Training outcomes analysis

The efficacy results of various regression analysis techniques, such as RF, LR, XGB, and SVR, are illustrated in Figure 7. By employing a variety of metrics, these methodologies are assessed for their forecasting abilities and precision. The RF model achieves an impressive R² value of 0.927 during training. The robustness of its capabilities to elucidate the discrepancy in the analysed data is indicated by the value. In comparison to RF models, the XGB approach demonstrates slightly inferior performance, as evidenced by an R² coefficient of 0.924, which suggests that the forecasts generated by XGB are less precise than RF models. The R² values for LR and SVR are considerably lower than RF’s, at 0.917 and 0.895, respectively, indicating even weaker performance. These results suggest that regression analysis employing the LR and SVR techniques results in reduced accuracy. Along with the graphical depiction, these regression visualizations offer quantitative details into the model’s fit to the data in terms of reflecting underlying trends and patterns. R² values reveal the extent to which variability in actual outcomes can be accounted for by anticipated outcomes, which is employed to evaluate the model’s accuracy. SHIULY et al. [⁴⁵] found that, while employing waste plastic aggregate-based concrete, the adaptive neuro-fuzzy inference system model effectively predicted the attributes of the material with an excellent result (R² = 0.98).

Figure 7
Regression evaluation of training data employing ML approaches for prediction.

3.3.2. Testing outcomes analysis

Figure 8 presents the findings of a regression examination comparing the expected and actual outcomes of testing data in four distinct ML techniques, namely RF, XGB, LR, and SVR. To accurately assess the model’s efficacy, normalized data is employed, which eliminates variances caused by alterations to the magnitude or size of the inputs. The RF model stands out with an outstanding R² value of 0.915, showcasing its exceptional ability to capture and explain the variance in the analysed dataset. This high performance underscores the model’s robustness and precision in predictive tasks. In contrast, the XGB model, while delivering competitive results, achieves a slightly lower R² value of 0.914. This suggests that XGB, though effective, offers marginally reduced accuracy compared to RF in this specific analysis. The R² value for LR stands at 0.907, reflecting a moderate ability to explain data variability, whereas the SVR model trails further with an R² value of 0.874, indicating comparatively poor predictive accuracy. These results demonstrate that RF not only outperforms XGB but also significantly surpasses LR and SVR in predictive strength, reinforcing its suitability for regression tasks where high precision is required. According to ASADI SHAMSABADI et al. [⁴⁶], ML analysis findings showed that XGB could accurately forecast the compressive strength of marble powder concrete, with testing results showing a high level of precision (R² > 0.97). Regarding machine learning performance, the RF and XGB models achieved R² values of 0.915–0.927, comparable to the performance metrics reported in previous ML-based studies on sustainable concrete, such as YANG et al. [¹³] (R² = 0.98) and MOTTAKIN et al. [¹⁸] (R² = 0.88). This agreement confirms the consistency of the predictive behavior across studies.

Figure 8
Regression evaluation of testing data employing ML approaches for prediction.

3.3.3. Performance assessment matrices

Figure 9 clearly shows the generated model’s accuracy across numerous variables. The accuracy of every model is determined by determining critical performance statistics, such as MSE, RMSE, and MAE. This comprehensive evaluation aids in the identification of the approach that produces far more precise forecasts of compressive strength, thereby enabling the selection of the best-performing model for future scenarios. The RF model demonstrates superior performance in terms of MSE, achieving the lowest values among all models for both testing and training datasets, with 2.161 and 1.767, respectively. This indicates RF’s ability to minimize prediction errors effectively. Comparatively, the XGB model yields slightly higher MSE values, at 2.167 for testing and 1.842 for training, showcasing competitive but marginally inferior performance to RF. The LR model records even higher MSE values of 2.326 for testing and 1.990 for training, reflecting reduced predictive accuracy. Similarly, the SVR model results in an MSE for testing (3.076) and shows a higher training MSE of 2.471, suggesting a weaker generalization capability compared to RF. In terms of RMSE, the RF model again outperforms the others, with values of 1.470 for testing and 1.329 for training, further demonstrating its precision and reliability. The XGB model follows closely, with RMSE values of 1.472 and 1.357 for testing and training, respectively, indicating slightly higher errors than RF. The LR and SVR models exhibit higher RMSE values, with LR at 1.525 for testing and 1.411 for training, and SVR at 1.754 and 1.572, respectively. The same trend is observed in MAE, where the RF model shows the lowest variances, recording MAE values of 2.354 for testing and 1.882 for training, indicating its exceptional ability to reduce absolute deviations between actual and predicted values. The XGB model also performs well, though slightly behind RF, while LR and SVR models display significantly higher MAE values. Specifically, the LR model records MAE values of 2.554 for testing and 2.148 for training, whereas the SVR model exhibits the poorest performance, with MAE values of 3.485 for testing and 2.732 for training. KHAN et al. [⁴⁷] demonstrated that the Adaboost regressor reliably predicted the compressive strength of concrete glass powder using the metrics of MAE and RMSE.

Figure 9
Metrics for estimation of the model’s compressive strength precision analysis of (a) MSE (b) RMSE and (c) MAE.

3.3.4. Cross-validation of models

Figures 10 and 11 show the error metrics and regression plots of the validation sets. LR shows the highest RMSE and MSE, likely due to underfitting, though its R² value of 0.909 suggests it still explains a fair portion of the variance. RF shows stronger performance with lower error metrics and a high R² of 0.949, indicating good predictive power and generalization. SVR, despite its low RMSE and MAE, has a relatively lower R² of 0.845, which suggests that it struggles to capture the overall variance in the data, possibly hinting at overfitting or sensitivity to certain patterns. XGB had a very good R² value of 0.946 with low RMSE, MSE, and MAE values of 1.2479, 1.5573, and 1.0569, respectively. But RF once again stands out as the best performer with the lowest error metrics and the highest R² of 0.949, suggesting excellent generalization. Comparing the validation sets, RF had the best R² value, closely followed by XGB, but both RF and XGB performed better than the rest in having lower MAE, RMSE, and MSE.

Figure 10
Metrics for validation of ML models: (a) RMSE (b) MSE and (c) MAE.

Figure 11
Regression evaluation of testing data employing ML approaches for prediction.

3.4. SHAP analysis

Figure 12(a) presents the bar chart depicting the average SHAP values, highlighting how various features influence the compressive strength of TES concrete. The plot, which is a horizontal bar chart, displays the average SHAP values for the many characteristics that are used to estimate the CS of TES concrete. A bar is used to symbolize each feature, and the length of the bar indicates how much the feature contributes on average to the model’s predictions. Based on their mean SHAP scores, they are ranked in decreasing order of significance. Coarse aggregate (+0.3) has the lowest mean SHAP value, indicating a relatively small impact on CS, while curing age (+2.5) has the highest, indicating the greatest influence. TES powder (+1.5) and cement (+1.2) also have a moderate impact on the strength of the concrete.

Figure 12
(a) Bar chart for mean SHAP and (b) SHAP summary plots.

Figure 12(b) illustrates the SHAP summary plots for each feature. The contribution of each feature is quantified by the SHAP values (X-axis) in the SHAP summary plot, which shows how input features affect the prediction of compressive strength. Predicted compressive strength increases with positive SHAP values and decreases with negative values. With SHAP values rising to roughly +3.5 for increasing feature values (red dots), Age has the strongest positive effect among the features, indicating that the strength is improved with longer curing periods. Extended curing periods lead to increased compressive strength, as the ongoing hydration reaction fosters the development of additional C–S–H bonds [⁴⁸]. Likewise, cement exhibits a significant beneficial impact, with SHAP values reaching +2.0 for higher values, underscoring its crucial function in strength growth. The identical trend observed in SHAP plots can be explained by the fact that a larger cement concentration will result in a denser concrete matrix with augmented C–S–H bonds, enhancing strength [⁴⁹]. On the other hand, water has a primarily negative effect; for increased water content, SHAP values can drop as low as –4.5, which is consistent with the inverse connection between compressive strength and water content. A high water-to-cement ratio might cause pore formation and segregation, which weakens the cement paste [⁵⁰, ⁵¹]. The effects of features like TES powder and aggregates are rather moderate, with SHAP values falling between –1.0 and +1.5. TES is beneficial to the strength of concrete at lower replacement levels and reduces strength at higher replacement levels due to poor interfacial bonding [⁵², ⁵³]. This plot provides a clear and interpretable view of how material properties contribute to the model’s output.

3.5. PDP analysis

PDP analysis was used to visualize the relationship between the feature and the predicted outcome, as shown in Figure 13. The plots reveal that cement content and curing age are the most significant factors influencing concrete strength in MPa, with CS increasing from approximately 20 MPa to over 40 MPa as cement content rises from 300 to 500 Kg/m³ and curing age extends from 7 to 56 days. Water content shows a strong negative impact, with CS decreasing sharply from 35 MPa to below 20 MPa as water increases from 140 to 180 Kg/m³, emphasizing the importance of controlling the water-to-cement ratio. In contrast, fine aggregate (700–850 Kg/m³) and coarse aggregate (1000–1100 Kg/m³) have minimal influence, causing variations of less than 5 MPa. As TES powder increases from 0 to 100 Kg/m³, CS slightly declines, dropping by approximately 5 MPa, suggesting excessive TES powder may reduce structural integrity. TES powder showed a moderate effect, improving strength at lower replacement levels but reducing it at higher dosages; therefore, TES content should be carefully limited to around 10–15% to achieve sustainability benefits without compromising mechanical performance. Based on these findings, civil engineers can use TES sustainably by limiting TES replacement to low percentages, ensuring adequate cementitious content, tightly controlling water content, and extending curing duration. Aggregates exhibited minimal influence, allowing standard aggregate proportions to be maintained. The role of PDP analysis in interpreting machine-learning-based concrete predictions is consistent with practices observed in recent literature. The study by SOBUZ et al. [⁵⁴] on engineered graphene concrete (EGC) employed PDP to illustrate how variations in graphene content, cement dosage, fly ash replacement, and aggregate proportions influence compressive strength. These findings offer practical value for civil engineers working with sustainable concrete by enabling data-driven optimization of mix designs, reducing dependency on costly experimental methods, and providing strategies to ensure strength and durability when incorporating industrial by-products.

Figure 13
Partial dependence plots analysis.

3.6. Discussion on microstructural properties of TES-based concrete

SEM images of both the control mix and the TES05 mix provide valuable information regarding the concrete’s microstructural characteristics and overall behavior. The control mix (TES00) contained no sludge, while mixes TES05 to TES20 replaced cement with TES at 5%, 10%, 15%, and 20% by weight, respectively. The SEM micrographs of the control mix reveal a uniform distribution of cementitious materials, aggregates, and other constituents throughout the matrix. As illustrated in Figure 14(a), the matrix appears dense and well-structured, with only minor cracks, which contribute to improved structural integrity. In contrast, the TES05 mix displays greater porosity within the matrix, as shown in Figure 14(b). The incorporation of TES particles leads to the formation of voids and pores that allow easier moisture penetration, negatively affecting both the permeability and mechanical performance of the concrete. Furthermore, Figure 14 indicates that while the control mix predominantly produces C–S–H gel, the TES-modified mixes are characterized mainly by voids and the presence of ettringite.

Figure 14
SEM image of the (a) control mix and (b) TES05 mix.

Moreover, the ITZ was modified by the inclusion of TES particles. These changes in the ITZ affected the bond between aggregates and the cement paste, which may reduce the overall strength and durability of the concrete. The combined effects of reduced uniformity, increased porosity, and an altered transition zone contribute to the weaker mechanical and structural properties of TES05 concrete when compared with the control mix. SEM analyses confirmed that TES particles compromise the microstructural stability of the concrete and lead to declines in key properties such as strength, permeability, and electrical resistivity. The microstructural characteristics, higher porosity, weaker ITZ, and ettringite formation are in accordance with the observations of ZHAN et al. [⁵²] and ZHAN and POON [⁵³], who noted that TES addition disrupts the microstructure and reduces hydration-product density.

3.7. Embodied CO₂ and cost assessment

The embodied CO₂ and cost analysis of concrete mixes incorporating varying proportions of textile effluent treatment sludge powder are illustrated in Figure 15. The control mix (TES00) contained no sludge, while mixes TES05 to TES20 replaced cement with TES at 5%, 10%, 15%, and 20% by weight, respectively. A consistent reduction in both embodied CO₂ and production cost was observed with increasing sludge content. Compared to the control mix (TES00) embodied CO₂ decreased by 4.63%, 9.27%, 13.90%, and 18.53% in TES05, TES10, TES15, and TES20, respectively. This indicates a significant environmental benefit from substituting cement with TES, owing to the high carbon footprint associated with cement production. Similarly, the cost of concrete showed a corresponding decline: a reduction of 3.46% in TES05, reaching up to 13.77% in TES20. The decrease in cost can be attributed to the replacement of a relatively expensive cement component with a low-cost industrial by-product. The dual benefits of reduced embodied CO₂ and cost suggest that TES is a promising supplementary cementitious material. The findings support the feasibility of sustainable, cost-effective concrete production by integrating waste-derived materials, thereby advancing circular economy goals in the construction industry.

Figure 15
Embodied CO₂ and cost assessment of TES concrete.

4. CONCLUSIONS

The goal of this study was to develop predictive models for assessing the strength of concrete that has been blended with textile effluent sludge. To achieve this, a methodical data analysis procedure was used to assess the experimental results. To assess their predictive performance, four models, such as LR, SVR, RF, and XGB were created. SHAP and PDP were also conducted to provide a thorough understanding of each component influencing strength. The following is a list of the research project’s primary findings:

• Concrete incorporating 15% TES achieved a 28-day compressive strength of 25.62 MPa, showing only a slight reduction compared with the control mix, while higher replacement levels led to more notable strength losses.

• The statistical evaluation confirmed meaningful interactions among mixed components, although no correlation met the threshold for statistical significance.

• The regression analysis highlights the RF model as the most effective, with an R² value of 0.927 (train), demonstrating its robust ability to explain variability in the data and produce precise predictions. The XGB model follows closely with a training R² value of 0.924, showcasing competitive but slightly reduced performance. All models show good performance overall.

• Among the machine learning models developed, Random Forest consistently demonstrated the strongest predictive capability, achieving R² values of 0.927 (training) and 0.915 (testing), supported by the lowest error indicators. XGB showed competitive performance, whereas LR and SVR performed comparatively weaker.

• SHAP results revealed curing age (+2.5), TES content (+1.5), and cement (+1.2) as the most influential positive contributors to strength, while water exhibited the strongest negative effect (–4.5).

• The PDP analysis further confirmed that curing age (7–56 days) and cement content (300–500 kg/m³) were the primary drivers of strength gain, while increased water content (140–180 kg/m³) led to a marked reduction in compressive strength. TES additions caused a modest decline of approximately 5 MPa at higher replacement levels.

• SEM analysis showed that TES increased porosity and altered the transition zone, weakening the concrete’s microstructure.

• The embodied CO₂ and cost analysis showed that TES replacement reduced both environmental impact and production costs, making it a sustainable and cost-effective concrete additive.

This study has several limitations. The machine learning models were trained on a relatively small dataset (n = 253), which may limit generalization across broader ranges of mix designs or regional sludge characteristics. TES replacement levels were restricted to a maximum of 20%, which constrains conclusions about higher substitution rates. Additionally, environmental and cost assessments were based on standard assumptions for cement and transportation emissions, and may vary across regions. Future research should expand the database, explore higher TES contents, and incorporate durability metrics such as chloride resistance, shrinkage, and long-term creep. In addition, practical recommendations were established, suggesting the use of higher cement content, extended curing durations, strict control of water-to-cement ratio, and limited TES replacement levels to ensure both strength and sustainability. The ML analysis results offer civil engineers valuable, data-driven strategies for designing sustainable concrete mixes with industrial by-products while minimizing reliance on extensive experimental trials.

5. ACKNOWLEDGMENTS

The authors are thankful to the Deanship of Graduate Studies and Scientific Research at Najran University for funding this work under the Student Research Funding Program grant code (NU/SRP/SERC/14/3349-2).

6. DATA AVAILABILITY

The data are available from the corresponding author upon request.

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Publication Dates

• Publication in this collection
  29 May 2026
• Date of issue
  2026

History

• Received
  12 Sept 2025
• Accepted
  17 Mar 2026