Towards greener roads: Evaluating the performance of sustainable grouts with reduced cement using hybrid machine learning models

2.1 Description of the dataset

The current study is based on the dataset collected from previous literature. 75 data points were extracted from the study done by Khan et al. (Muhammad Imran Khan et al., 2023) 156 data points were extracted from a study done by Khan, (K. Khan et al., 2022). Previous studies suggest that an adequate sample-to-variable ratio is important to ensure model stability and avoid overfitting. While no universal threshold exists, datasets containing 5 or more observations per predictor are generally considered more reliable, with higher ratios contributing to improved generalization capability (Frank and Todeschini, 1994; Gandomi et al., 2015). The compiled dataset of 231 data points consisted of 8 variables including water-cement-ratio (W/C), superplasticizer (SP) %, percentage of PET, percentage of SCMs like silica fume and fly ash, flow values of grout (sec), 1-day compressive strength (CS_1d), 7 days compressive strength (CS_7d), and CS_28d. The current study was performed with a database having seven variables and 231 data points, yielding a variable-to-data point ratio higher than 30. The descriptive statistics of the final dataset have been presented in Table 2. Based on the kurtosis of the data presented in the table, it can be observed that the majority of the features exhibited a near-normal distribution, except the flow value. Regarding flow values, kurtosis indicates the existence of sharper peaks than a normal distribution owing to the presence of higher flow values for control samples. In the same way, analyzing the skewness of the data reveals that all other variables exhibited mesokurtic distribution, except for flow values having leptokurtic distribution because of the presence of data points with significantly higher flow values than the majority of the data points. However, it is worth mentioning that no normalization or scaling was applied before model training, as the input variables were within comparable numerical ranges and did not exhibit significant scale imbalance.

2.2 Materials, grout preparation, and experimental testing

Materials used in the preparation of cement grouts are ordinary Portland cement, powdered waste PET, SCM (fly ash and silica fume), and SP. Based on literature research and experimental analysis, the SP (0–2%) and w/c ratio (0.25–0.45) were chosen. Powder waste PET (particles < 150 μm) and SCM were chosen in the range of 0-10% by weight of cement for producing cement grouts. The ranges of PET and SCM replacement levels were selected based on the authors’ previous experimental investigations and performance requirements of semi-flexible pavement grouts. Since grout materials must exhibit high flowability (flow time of 11–16 s) to ensure effective penetration into porous asphalt mixtures, replacement levels exceeding 10% resulted in increased flow time and reduced workability. Consequently, PET and SCM contents were limited to a maximum of 10% to maintain adequate flowability while ensuring sufficient compressive strength.

The grouts were made in accordance with ASTM C305 specification. The fresh cement grouts were tested for flowability by using the Malaysian flow cone in accordance with the requirements of City Hall Kuala Lumpur (CHKL) and REAM guidelines (REAM, 2007). Cubes of dimensions 50 mm× 50 mm× 50 mm were prepared for each of the grout types, and the 1-day, 7-day, and CS_28d of samples was measured. The compressive strength was tested by applying a pacing rate of 0.90 kN/second on an ELE Universal testing machine (UTM capacity of 3000 kN in accordance with ASTM C109 standard. Comprehensive information on the materials and grout preparation can be found in the author’s previously published articles (K. Khan et al., 2022; Muhammad Imran Khan et al., 2023).

2.3 Preprocessing

Upon compilation of the final dataset, a check for the presence of missing/nan values was applied using Python programming. However, no missing values were present in the dataset. Moreover, it is worth mentioning that the development of a machine learning model with high accuracy needs variables having sufficient correlation with the target variable. The current study focused on predicting the CS_28d of cementitious grouts prepared for semi-flexible pavement based on 7 input variables. Fig. 4. presents the Pearson correlation of every variable with the target and other input variables. From the figure, it can be observed that all the variables have a significant correlation with the CS_28d, where CS_1d and CS_7d showed the highest correlation with CS_28d. Including CS_1d and CS_7d as input variables is helpful as their early age strength has been found as reliable predictor of CS_28d (Hasan et al., 2013). In practical pavement construction, waiting the full 28 days to confirm design strength may delay quality approval, mixture optimization, and project scheduling decisions. Reliable estimation of 28-day strength based on 1-day and 7-day results enables earlier performance assessment, supports accelerated construction timelines, and may facilitate the timely opening of pavement facilities to traffic.

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Fig. 4. Pearson correlation between the input and output.

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On the other hand, variables like W/C, SP%, and SCMs% had a negative correlation, while the remaining variables had a positive correlation with the target variable. Before developing the models, the dataset was split into training and testing data. All the models were developed using the training dataset only. The testing dataset remained completely unseen during training and was used solely for final performance evaluation to prevent data leakage.

2.4 Model development

2.4.1 Artificial neural network (BaseNet)

The dataset was divided into 80% training and 20% validation data. A total of four neural network models, including the basic model (base model with no external optimizer), were developed by adopting different optimizers. All the models were trained and tested using the same set of values to compare the performance of the models in the absence of the effect of variations in data point distribution in the dataset. The best-performing model after 50 epochs during training was deployed as the final model based on mean squared error during training for both base and optimized models. The training error for every epoch for all the models has been presented in Fig. 5.

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Fig. 5. Fitness function over various epochs. (a) 1 to 10 epochs, (b) 11 to 50 epochs.

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2.4.2 Particle swarm optimized neural network (SwarmNet)

In 1995, R.C. Eberhart and James Kennedy created a random optimization method called particle swarm optimization (PSO) (Ullah et al., 2025). This approach is inspired by the natural behavior of swarming groups (Juneja et al., 2016). Every particle represents a potential solution. The group of potential solutions exists together and collaborates at the same time. Every particle in the swarm traverses the search space, seeking the optimal solution to settle. Thus, the search space consists of potential solutions, while the cluster (swarm) of moving particles symbolizes the evolving solutions. Over the generations (iterations), every particle monitors its individual best solution (optimum) along with the global best solution (optimum in the swarm). Next, it adjusts two factors, the flying speed (velocity) and the location. In particular, each particle modifies its flying speed dynamically based on its own flying experiences and those of its neighbors. Similarly, it attempts to adjust its position by utilizing data from its present location, speed, the gap between its current spot and personal best, as well as the current location and global best (Wang et al., 2018). The general flowchart of the PSO has been presented in Fig. 6. A hybrid neural network model in combination with PSO was developed using 80% of the data for training the model after 25 iterations of the PSO (shown in Fig. 5.) and 50 epochs of the neural network model following the parameters shown in Table 3. The best optimization iteration was adopted to train the neural networks trained for 50 epochs. The fitness of the model was measured using mean squared error, and the best model was deployed as the final SwarmNet model.

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Fig. 6. Working flowchart of particle swarm optimizer.

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Table 3. Optimizer’s tuning parameters.

Parameter	PSO	GWO	ACO
Population size	30	30	30
Number of iterations	25	25	25
Inertia weight	0.5	-	-
Cognitive coefficient	1.5	-	-
Social coefficient	1.5	-	-
Convergence factor	-	0.5	-
Pheromone evaporation rate	-	-	0.5
Pheromone importance	-	-	1.5
Heuristic importance	-	-	3

2.4.3 Gray wolf optimized neural network (WolfNet)

The gray wolf optimizer (GWO) draws inspiration from the social behaviors and hunting habits seen in GWs (Canis lupus). It mimics its hierarchical organization and predatory strategies by integrating four separate roles to steer its optimization procedure (Mirjalili et al., 2014). The hunting model of the grey wolf consists of: (i) pursuing and getting closer to the target, (ii) encircling and exhausting the target until it becomes unable to move, and (iii) striking the immobilized target (Mittal et al., 2016). GWO is commonly utilized for different optimization problems as it provides significant advantages over other swarm intelligence approaches (SIA). It does not need derivative data and requires just a few basic parameters for initial searches. Moreover, GWO is straightforward, easy to use, and flexible, possessing a distinct capability to modify exploitation and exploration, leading to efficient convergence (Faris et al., 2018). The search method in GWO is steered by the three dominant wolves in every iteration, which improves convergence to these solutions. Fig. 7 illustrates the social structure of GWs along with their respective solutions, while Table 3 presents the details on parameter tuning.

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Fig. 7. Working flowchart of the gray wolf optimizer.

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2.4.4 Ant colony optimized neural network (AntNet)

The Ant colony optimization (ACO) algorithm is a nature-inspired metaheuristic technique used to solve combinatorial optimization problems by mimicking the foraging behavior of ants. Initially proposed by Dorigo et al. (1996) in the 1990s, ACO was based on how ants deposit pheromones to mark paths to food sources, influencing the movement of other ants toward optimal routes. The algorithm utilizes artificial ants that construct solutions iteratively, updating pheromone trails based on the quality of the solutions found. Over time, paths with stronger pheromone concentrations are reinforced, leading to the convergence of an optimal or near-optimal solution. The adaptability and robustness of ACO make it a powerful tool in artificial intelligence and optimization research (Dorigo et al., 2007). The essence of this behavior lies in the ants’ indirect communication through chemical pheromone trails, allowing them to locate shorter routes from their nest to food sources. This trait of actual ant colonies is utilized in ACO algorithms to address, for instance, discrete optimization issues (Blum, 2005). The overall flowchart of the ant colony optimizer can be seen in Fig. 8, and the tuning parameters have been mentioned in Table 3. ANN training epochs were set to 50 by convergence behavior monitored in initial experimentation. Fig. 5 shows that the performance of validation became stable with about 30-35 episodes, with a slight decrease beyond that point. Thus, 50 epochs were picked to balance sufficient learning and to be computationally efficient. In the same way, the metaheuristic optimizers were applied to 25 iterations. Fitness gains diminished past about 20-25 iterations, and additional gains brought no significant accuracy improvement but added to the computational expense.

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Fig. 8. Working flowchart of the ant colony optimizer.

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2.5 Model’s evaluation

The correlation coefficient (R) is the most commonly adopted technique to measure the performance of the model. However, because of its insensitivity to division and multiplication of the output by a constant, it is recommended not to rely solely on the values of R (Babanajad et al., 2017; Gandomi Amir et al., 2012). This is why the current study added relative root mean square error (RRMSE), root mean square error (RMSE), mean squared error (MSE), adjusted R-square (Adj-R²), and R-square (R²) as model performance evaluators. Performance index (PI) as adopted by Gandomi et al. (2015) and the a20-index was also adopted to measure the generalization power of the models. PI is calculated to estimate the predictive ability of the model as a function of R and RRMSE. According to Jamieson et al. (2012) and Heinemann et al. (1991) the performance of the model will be considered excellent if RRMSE is <10%, good if between 10% and <20%, fair if between 20% and <30%, and poor if ≥ 30%. On the other hand, a20-index is a new model performance evaluation technique adopted by several researchers to evaluate the performance of the model by calculating the total number of data points within a 20% standard deviation from the actual value (Apostolopoulou et al., 2019; Apostolopoulou et al., 2020; Armaghani et al., 2019; Asteris et al., 2020). The value of the a20-index varies between 0 and 1, where models having an a20-index close to 1 mean better performance and vice versa. The model’s performance was evaluated for both training and testing. Based on these performance evaluation criteria, the best-performing model was selected as the final model for further analysis. Mathematical equations for these criteria can be seen from Eqs. (1-8).

Whereas:

p, n = total inputs and observations,

$\widehat{Y_i}, y_i$ = predicted & actual output and,

$\overline{Y},\overline{y}$= predicted and actual mean outputs, respectively.

Machine learning models often face the issue of overfitting and sticking to the training data. In such cases, the training error may decrease with runs, but the testing errors keep on increasing (Gandomi Amir et al., 2012). Therefore, it was necessary to evaluate the model’s performance based on the fitness function (FF) as shown in Eq. (9) (Gandomi et al., 2015). FF considers the effect of R and RRMSE explicitly for both testing and training of the model.

Where PI is the performance index, t, and v stands for training and testing/validation, while n represents the number of data points. The model having FF close to zero indicates the best performance.

2.6 SHAP

SHAP is a highly effective, straightforward, and comprehensible way to grasp how various features influence the model’s predictions (Lundberg, 2017). SHAP employs cooperative game theory to analyze the predictions generated by a model (Molnar, 2020). In this approach, Shapley values (Shapley, 2016) are computed, where the independent variables are viewed as collaborators striving for a reward, which here is the model’s particular prediction minus the mean value of all predictions. The players “distribute” the payment according to their input, and this allocation is determined using the Shapley values. The mathematical foundation of SHAP establishes it as a robust interpretability theory. Moreover, in contrast to other methods, SHAP provides both local and global interpretations of the model’s outcomes, meaning it elucidates the impact of each variable on the model’s predictions and the significance of each variable in the total model results. Research indicates that these tools serve as feature selection methods, enhancing model accuracy and lowering the computational expenses associated with model training (Antonini et al., 2024).

2.7 Partial dependence plots (PDPs)

PDPs are simply a representation of the average of ceteris paribus (CP) profiles. CP profiles illustrate how a feature influences model output by demonstrating the changes that occur when the feature’s value is altered while keeping the values of other features constant. In PDP, CPs are generated for numerous observations and then averaged (Białek et al., 2022). This graphical representation can uncover trends, such as a rise in the feature results in increased or decreased predictions, and can assist in pinpointing significant features and interactions within the model (Goldstein et al., 2015). PDPs are adaptable approaches that can work with various machine-learning models. PDPs provide visual explanations of how features affect the model’s behavior and emphasize the significance of each feature, helping in grasping the model’s predictions. (Shi et al., 2023). These plots could be one-way (considering one feature at a time) or of higher dimensions (considering multiple features at a time) (Wright, 2018). This study adopted one-way PDPs to assess the impact of input features on the CS_28d based on the best-performing model. In this study, fly ash and silica fume were collectively categorized as SCMs to develop a generalized prediction model using literature-derived experimental data. While these SCMs exhibit different pozzolanic characteristics, both function primarily as cement replacement materials in semi-flexible pavement grouts. Aggregating them into a single variable improved dataset uniformity and prevented data sparsity associated with SCM-specific modeling. Therefore, SHAP and partial dependence plot (PDP) analyses presented in this study describe the global influence of SCM replacement level on compressive strength rather than material-specific effects.

3.1 Model development

The dataset was divided into 80% training data and 20% testing/validation data in a random fashion using Python programming. Once the splitting was completed, both these datasets were saved to ensure that all the models were developed with the same set of data points. A total of five different approaches were adopted, including BaseNet, SwarmNet, WolfNet, AntNet, and DT. For the hybrid models (neural networks combined with optimizers), a total of 25 iterations were trained using the respective optimizer, followed by 50 epochs of the neural network model. MSE was adopted as a fitness function during the training for both BaseNet and hybrid models. The performance of the models was observed through a coherence plot by comparing the magnitude of error in actual and predicted CS_28d for both the training and testing phases. Fig. 9 shows the overall trend of the model’s predictions and actual values for the developed models.

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Fig. 9. Coherence plots between actual and predicted CS_28d (a) BaseNet, (b) SwarmNet, (c) WolfNet, (d) AntNet, (e) DT.

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Figs. 9 (a-e) illustrate the coherence between actual and predicted CS_28d using respective models. All the models showed significant alignment between the actual values and predicted values, indicating that the models are capable of capturing the overall trend. However, the error plots depict the presence of higher peaks in the case of the DT model. BaseNet and hybrid neural network models showed promising results in both the training and testing phases. It was very hard to choose one among all the models based on error or coherence between the actual and predicted CS_28d. Therefore, the study compared the performance of the models using statistical performance evaluation techniques.

3.2 Statistical assessment

The effectiveness of the models in predicting the CS_28d was evaluated using several statistical approaches given in Eqs. (1-9). Table 4 presents the performance of the models in the form of statistical parameters for both the training and testing phases. From the table, it can be observed that all the models predicted the CS_28d with high accuracy, except the DT model. All the optimization techniques improved the performance of the BaseNet and showed tight competition while predicting the CS_28d. However, based on the listed parameters, WolfNet depicted the best performance among all the base models and hybrid models. Based on RRMSE, the performance of all the models was rated as excellent. However, the DT model showed RRMSE higher than 10% in the testing phase, which makes the DT model a good model rather than excellent. From the overall performance presented in Table 3, it can be observed that the a20-index for SwarmNet, WolfNet, and AntNet is the same. The a20-index has a limitation: it treats all ratios between the actual and predicted CS_28d values within the range of 0.8 to 1.2 as equal. This means that if multiple models have the same number of data points falling within this range, the a20-index will rank them equally, regardless of how close those ratios are to 1. This consideration makes it difficult to choose one among many models that have the same number of data points in the mentioned range, irrespective of the closeness to 1. This is why a20-index should be coupled with other statistical measures. Based on the FF score and other parameters, WolfNet showed better results than the rest of the hybrid and base models.

Though SwarmNet had somewhat better R and R² during the testing phase, WolfNet had the lowest error-based rates (MSE, RMSE, RRMSE, PI, and FF). Minimization of prediction error is essential in reliable engineering estimation, and hence, WolfNet was picked as the final model due to its high quality in generalization.

3.3 Actual vs predicted data trends

Better models should depict the correlation between the predicted values and the actual values in both the training and testing phases. Fig. 10 presents the relationship between actual and predicted CS_28d using BaseNet, hybrid models, and the DT model. Each figure presents the relation for both training and testing data, the regression line, and the ideal line. A model with 100% accuracy will have a slope equal to “1” and an intercept equal to “0”. However, models having slopes close to 1 and intercepts close to 0 portray their high prediction power. Considering the center point of the regression line as a pivot point, the regression lines with high deviated slope or intercept values portray poor performance for values far from the mean values of target variables. This means that the model results in higher error as the values of the target go away from the mean values on either side of the line. From Fig. 10 (c), it can be observed that WolfNet results had the best R² in comparison to the other models. On the contrary, AntNet showed the least variation from the ideal slope, but on the other hand, the deviation of the intercept from the ideal was much higher than that of WolfNet. Additionally, the RMSE observed for WolfNet in the training phase was the least among other models. Furthermore, the WolfNet model depicted better generalization than other models by performing better against unseen testing. The DT model showed the least accuracy by predicting a constant CS_28d against varying inputs. This is why the trendline deviates the most in terms of slope and intercept from the ideal line, as shown in Fig. 10 (e). The relatively low result of the Decision Tree model can be explained by its piecewise partitioning procedure that might not be able to reflect the complicated nonlinear interaction of mixture parameters. Conversely, ANN-based models offer continuous nonlinear approximation of functions, which are more suitable for the interpretation of complex relationships of compressive strength development.

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Fig. 10. Correlation between actual and predicted CS_28d. (a) BaseNet, (b) SwarmNet, (c) WolfNet, (d) AntNet, (e) DT.

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3.4 Model’s interpretation using Taylor’s diagram

The Taylor diagram was also plotted to evaluate the performance of the developed models based on R, standard deviation, and RMSE. Evaluating the performance of models via Taylor’s diagram offers an alternative method since it assesses how well models track reference datasets. Depending solely on statistical tools can lead to misleading conclusions, as a model with the smallest standard deviation doesn’t guarantee superior performance. A model with a standard deviation that aligns more closely with that of the real dataset indicates improved performance, as it demonstrates the model’s ability to track the actual values more accurately (Taylor, 2001). The arcs originating from the origin represent the standard deviation, where the dashed line represents the standard deviation of the actual CS_28 days, the radial line stands for R-values, while the semi-circular lines originating from the reference points represent the RMSE values. Fig. 11. presents Taylor’s diagram for BaseNet, SwarmNet, WolfNet, AntNet, and DT models concerning the actual standard deviation of experimental data points. The actual data points’ RMSE and standard deviation values were used as a benchmark. From Fig. 11., it can be seen that BaseNet and other hybrid models are plotted very close to each other. However, WolfNet was found to be closer to the reference standard deviation line, had a higher R-value, and had a lower RMSE. The overall comparison of the models in the training and testing phases can be seen in Figs. 11 and 12. respectively. After a detailed performance evaluation using various approaches, it was concluded that WolfNet offers better results as compared to other models deployed in the study. Therefore, WolfNet was adopted to further evaluate the hidden effects of input variables on CS_28d using SHAP Interpretation and partial dependence plots.

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Fig. 11. Taylor’s diagram for the training phase.

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Fig. 12. Taylor’s diagram for the testing phase.

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3.5 SHAP value interpretation

The SHAP values offer key insights into the effect of input parameters in the CS_28d based on the WolfNet model. SHAP value is calculated in reference to a base value (mean prediction) by evaluating the model’s predictions multiple times with a subset of data for each feature. The impact of the presence and absence of a feature on the target is measured for every data point. Finally, this impact is summarized in the form of a bee swarm scatter plot, where higher scatteredness of the points along the x-axis stands for higher impact. The summary plot presented in Fig. 13. reveals that CS_7d and CS_1d are the key features. Their scatteredness signifies their impactful contribution to the model’s predictions. Greater values of these attributes typically result in an enhancement of the predicted strength, easing ways to assess the CS _28d at early ages. PET (%) also has a key influence, indicating a significant effect on the model’s predictions, depicting that the presence of plastic waste has an impact on CS_28d. The effect of every input variable on the CS_28d for individual data points has been presented in Fig. 13. However, the mean of these values presents a better idea about the contribution of every variable in the study. The mean SHAP values based on the WolfNet model have been presented in Fig. 14 (a). The figure quantifies the contributions of input variables, showing that CS_7d and CS_1d possess the highest mean SHAP values, confirming their major impact. However, Fig. 14 (b) presents the relative contribution of every input variable in predicting the CS_28d. From the figure, it can be observed that CS_7d had the highest contribution of 47.38% among all the variables.

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Fig. 13. Individual SHAP value against CS_28d.

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Fig. 14. SHAP value interpretation. (a) mean SHAP value, (b) relative contribution of input.

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The mean SHAP values presented in Fig. 14(a) are calculated based on the contribution of each variable in terms of pushing the predicted CS_28d towards the mean value of predicted CS_28d. From the figure, it can be observed that the mean force applied by the CS_7d to make the predictions closer to the mean predicted CS_28d was 8.14. CS_7d was followed by CS_1d and the PET percentage. WC made the least contribution of 0.04 in the collective effort of all the variables to follow the CS_28d.

3.6 PDPs

The PDPs demonstrate how specific features affect the predicted CS_28d. The majority of features, such as WC, SP %, PET %, SCM %, CS_1d, and CS_7d, demonstrate a linear correlation with compressive strength, suggesting that an increase in these factors leads to a corresponding increase in strength. Nonetheless, Flow exhibits a nonlinear pattern, indicating the impact of flow on the CS_28d is higher for flow values ranging between 10 and 18 sec. However, this effect was reduced once the flow values went past 18 sec. Such nonlinear effects of flow time on compressive strength can be explained by the fact that it is dependent on the superplasticizer dosage and water-cement ratio. Reduced flow times are usually associated with increased water content that can increase capillary porosity and make them weaker.

The significant impact of CS_7d and CS_1d enhances their importance as primary predictors, whereas PET % and SCM % also offer positive contributions, illustrating the advantageous effects of SCMs. The minor positive correlation of WC indicates that regulated water content contributes to enhancing strength. Nevertheless, it is worth mentioning that the results of PDPs support the results of the mean SHAP values. From Fig. 15. it can be observed that the range of partial dependence values on the y-axis for CS_7d is the highest, followed by CS_1d, while the W/C ratio depicts the lowest variation in the PDP values among all. By comparing Figs. 14 (a) and 15., it can be observed that the W/C had the least impact on CS_28d. The values of CS_28d change only by 0.2 MPa as a result of increasing W/C from 0.25 to 0.45. However, these results were obtained for a one-way PDP where the impact of other variables is not considered while drawing the relation of a specific variable with the output.

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Fig. 15. Partial dependence of CS_28d on each input variable.

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3.7 Practical application

The WolfNet hybrid model adopted in the current study was deployed into a user-friendly GUI for future applications. Fig. 16. presents the interface of the developed GUI, which has the capability of predicting the CS_28d in standalone applications. As presented in the figure, the application asks the user to enter the input values to predict the CS_28d using the WolfNet model.

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Fig. 16. The graphical user interface for predicting CS_28d.

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Based on the developed hybrid model presented in Fig. 16. CS_28d was predicted for various percentages of SP, PET, and SCMs. While making these predictions, the rest of the variables were set to mean values as adopted by (Iqbal et al., 2021). Fig. 17 (a) illustrates the CS_28d of cementitious grouts for semiflexible pavements as influenced by varying amounts of SP and PET. By examining the trends, it is clear that when the PET content was increased from 0% to 10%, the compressive strength was reduced. Likewise, the influence of SP on compressive strength is evident, as higher SP content typically resulted in the reduction of CS_28d. This reduction could be potentially due to increased workability leading to excessive porosity or weaker cementitious bonds. The lowest strength, around 44 MPa, was observed at the 2% SP in the absence of PET. It can be concluded that excessive superplasticizer use is detrimental to the grout’s structural integrity. On the other hand, Fig. 17 (b) presents the combined effect of SP and SCMs on the CS_28d. From the figure, it can be observed that the addition of SP reduced the CS_28d, and the SCMs enhanced the CS_28d. Furthermore, it can also be observed that the highest CS_28d of 54.665 MPa was observed at 10% SCMs and 0% SP. This means that the combination of SP with both PET and SCM negatively affects the CS_28d. However, the rate of reduction in CS_28d as a result of the addition of SP slowed down for higher SCMs and PET in the mix. For instance, from Fig. 17 (b), it can be observed that the CS_28d dropped from 50.496 MPa to 46.44 MPa by increasing the SP content from 0% to 2%. The addition of the same quantity of SP in the presence of 10% SCM resulted in around 5.8% drop in comparison to an 8% drop in the previous case. From these observations, it can be concluded that the addition of both PET and SCMs results in the enhancement of CS_28d. The relation between PET and SCM can be observed in Fig. 17 (c). From the figure, it can be seen that the CS_28d increased from 46.75 MPa to 51.758 MPa by adding SCM in the presence of PET. However, it increased to 58.414 when no PET was added.

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Fig. 17. Effect of SP, PET, and SCM on CS_28d (a) PET vs. SP, (b) SCM vs. SP, (c) SCM vs. PET.

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To validate the findings of this study, there is no standard available to date to assist researchers in optimizing the mix design according to compressive strength for semi-flexible pavements. This study aimed to assess CS_28d by correlating the findings with previous literature. Afonso et al. (2016) discovered that semiflexible samples with a compressive strength of 14 MPa exhibited a Marshall stability of 53.9 KN. The findings were confirmed by Bharath et al. (2020), who reported that samples with a compressive strength of 2.2 MPa yielded 17.3 KN of Marshall stability. Two separate investigations conducted by Imran et al. (2021) and Khan et al. (2022) determined that semi-flexible pavement utilizing standard PET-modified grouts has a Marshall stability of 44.12 KN, while the same mixture exhibited a compressive strength of approximately 43 MPa. Additionally, according to the standards set by Jabatan Kerja Raya (JKR) Malaysia (Raya, 2008), the stability of hot mix asphalt must exceed 8KN, indicating that all combinations examined in this study could meet the minimum Marshall stability requirement based on the predicted values from the ANN model. Additionally, the CS_28d predicted with the developed model is higher than 44 MPa for all the combinations of SP, PET, and SCM. This strength is well aligned with the findings of various studies for grouting materials where the CS_28 ranges between 30 and 50 MPa (Hou et al., 2017; Huang et al., 2012; Zhang et al., 2019). Moreover, according to (Song et al., 2024), the CS_28d for cementitious grouts should be higher than 30 MPa. By observing the findings of the current study, it can be concluded that all the combinations of SP, PET, and SCMs possess enough compressive strength to sustain heavy loads. In order to maximize the incorporation of waste materials as a partial replacement for cement, a combination of 10% PET and 10% SCMs was identified as the optimum mix proportion for cement grout formulations. This composition was selected based on its balanced performance in terms of physical (flow value of 11 to 16 sec) and mechanical strength (28d compressive strength of 58.41 MPa), while also contributing to sustainable material utilization.

3.8 Experimental validation of modeled values

Validating the results derived from modeled predictions through actual experiments is a critical step in ensuring the accuracy and reliability of any modeling approach. In this study, after the development of the optimum model, an additional set of experimental trials was carried out to verify the predictions. For this purpose, a cement grout was prepared and tested with the optimal parameters: 10% PET, 10% SCM, 1% SP, and W/C of 0.40, as shown in Table 5. The optimized mixture achieved a 20% reduction in cement content through partial replacement with PET (10%) and SCM (10%). Given that cement production represents the primary contributor to embodied carbon in cementitious materials (Andrew, 2018), this reduction indicates meaningful sustainability potential. Comprehensive life cycle (LCA) and durability evaluations could further elucidate the long-term environmental performance of the proposed system.

The optimization aimed to maximize cement replacement content while maintaining flow within the acceptable range (11–16 s) and satisfying the required 28-day strength. The optimized mix was experimentally validated using three replicate specimens. The 2.59 % deviation between predicted and measured strength falls within typical experimental variability limits, supporting the reliability of the optimization approach. Both the flow value and the compressive strength showed deviations of less than 5%, indicating a strong correlation and supporting the use of the model for predicting concrete performance with PET and SCM additives.