Toward sustainability: Integrating experimental study and data-driven modeling for eco-friendly paver blocks containing plastic waste

2.1.1 Low-density polyethylene (LDPE)

In this study, the plastic type known as LDPE was utilized as a binding material in PSPB. The LDPE was obtained from the municipal authorities in Abbottabad, Pakistan. Following the collection process, the material was initially washed completely, cleaned, and dried to remove any pollutants that could hinder the melting process. In the end, the plastic material was transformed into small fragments using shredding. Table 1 shows the characteristics of LDPE utilized in this investigation.

2.1.2 Natural fine aggregates (sand)

The locally available sand was used as a fine material for the production of PSPB. Initially, two different types of sands were used to examine the impact of particle size on CS of PSPB. The properties of sand were assessed by conducting tests following the ASTM standards, as illustrated in Table 2. Specific gravity and sieve analysis tests were performed to ascertain the fineness modulus (FM) of both sands. A finer form of sand (Sand-1) was utilized for subsequent analysis.

2.1.3 Basalt fibers

Basalt fiber is labeled as a green industrial material. Basalt fiber is formally known as the “21st-century non-polluting green material” [39]. Quarried basalt rock, when heated to a temperature of 1,400°C, results in the formation of molten basalt rock. Extrusion of these molten rocks through small holes can be used to form basalt fibers. Due to its property to withstand high temperatures, basalt fiber is generally used in applications like heat-insulated materials, vehicle braking systems, and flame-retardant materials [40]. Basalt can be used as an aggregate, fiber, mesh, and rebar. Being a multi-performance fiber, basalt fiber has several advantages [41]: it has high thermal resistance to heat, it is a waste and renewable material, it is very light in weight, and it increases the flexural and CS of PBs. The present study employed basalt fibers of two different lengths, specifically 4 and 12 mm. Table 3 displays the chemical composition of the basalt fibers.

3.1.1 Database

A comprehensive data set for CS of PSPB was obtained by performing experimental testing in the laboratory. Raincloud plots with normal distribution curves were used to determine the potential outliers in the database, as shown in Figure 6. As can be seen, only a few points deviated from the normal trend, so those were deleted. The total database comprises 114 data records for CS. All the input variables were considered to ensure the universality and precision of the proposed model. Input variables include sand content, fiber content, plastic content, and size and length of the fiber used. Moreover, CS was considered as output for the development of the model. The performance and generalization capability of any model greatly depend on the distribution of input variables [51]. The frequency distribution histograms of input parameters are shown in Figure 7. It is obvious from contour plots that variables have higher frequencies, and the distribution of the input variables is not uniform. It is important to keep in mind that high variable frequencies are necessary for attaining a better model.

Figure 6

Raincloud plots for outlier detection.

Figure 7

Contour plots representing data distribution.

Additionally, Table 5 provides a summary of the statistics indicators and ranges of the various variables included in the development of the models for CS, making the data analysis simple. It is clear that sand and plastic contents lie in the range of 1,140–1,615 and 285–760 kg·m⁻³. Moreover, the values of CS lie in a range of 11–22.43 MPa. A smaller standard deviation indicates that the majority of the values cluster closely around the mean value. Conversely, a greater standard deviation indicates a wider dispersion of data. Skewness refers to the extent to which the probability distribution of a variable differs from being symmetrical around the mean. As stated by Sharma and Ojha [52], the optimal range for kurtosis values is between −10 and +10, which indicates the type of probability distribution. The statistical values of skewness and kurtosis indicate that the MEP-based models are viable for a wide range of input data, hence greatly increasing their potential applications. Furthermore, the entire database was divided into two distinct sections: the training area and the validation section. The predictive validity of the model was evaluated with the help of a validation database, and the overall development of the model was accomplished with the assistance of training data.

3.1.2 MEP model development and assessment

As discussed earlier, to construct a reliable and widely applicable model, a number of MEP modeling parameters must be determined before the modeling process. Considering the prior recommendations, a hit-and-trial method was used in this study to select the best model-fitting parameters [53]. The size of the population determines how many programs will be included in the evolutionary process. If the population size of the model is large, the model will be complicated and precise and may take more time to converge. Overfitting of the model is a potential problem when a particular threshold has been reached. The procedure began with the assumption that there were ten distinct populations. For clarity, the function set considers just the four fundamental mathematical operators (+, −, ×, and /). The accuracy level of the model greatly relies on the number of generations. The statistical mistakes in the algorithm would be reduced by running the program for several generations. The frequency with which offspring experience these genetic changes is measured by the crossover rate and mutation. In general, the crossover rate is between 50 and 95%. Numerous combinations of these parametric settings were tried, and optimum parametric settings were selected based on the prediction performance of the models, as displayed in Table 6. Overfitting of the data is the major issue in ML-based models. To prevent this issue, it is suggested that the models should be trained on unseen data sets [54]. Following this, the whole data set has been separated into two parts, i.e., training and validation. Both of the data sets have been checked to make sure they have the same distribution. This work employed 70 and 30% of the dataset for training and validation, respectively. The proposed models performed well across both data sets. A commercially available software program, MEPX v1.0, was used to apply MEP models.

The first step in the model development is to produce an initial population of viable solutions. The iterative procedure is implemented, and each successive generation converges to the solution. Within the solution population, each generation’s fitness is continuously assessed. The MEP model will continue to develop until the predetermined fitness function, such as root mean squared error (RMSE) or R, no longer shows any indications of alteration. In order to address the problem of overfitting, the study additionally evaluates the objective function (OF). Suppose the findings of the model are not correct for both datasets (training and validation). In that case, the procedure is then rerun by progressively increasing both the number of subpopulations and their overall size. Following that, the model with the lowest OF is chosen as the best one. It is important to remember that the evolving time of the number of generations has an influence on the correctness of the model. Due to the introduction of additional variables in such methods, a model may keep evolving continuously. However, in this study, the model was terminated after 1,000 generations or when the variation in fitness value was smaller than 0.1%. The efficiency of the proposed models is determined by determining various statistical error indices. The metrics used in this analysis are the performance index (PI), the relative squared error (RSE), the relative root mean square error (RRMSE), the mean absolute error (MAE), and RMSE. Similarly, an alternative approach to mitigate overfitting is to select the optimal model by reducing the OF, as recommended by Iqbal et al. [55]. This methodology was chosen to address the problem in this study, and the term fitness function is used for OF. Eqs. (1)–(6) show the mathematical expressions for these statistical indices:

In the given expressions, exp _i and mod _i indicate the experimental and model anticipated outcomes, mod ¯ i and exp ¯ i signify the average model anticipated and experimental outcomes, respectively, and n represents total occurrences. A model is considered accurate when it has a high R-value and minimal statistical errors. Alabduljabbar et al. [56] and Alyami et al. [57] stated that an R-value of more than 0.8 indicates a strong connection between the anticipated and actual results. Since it is not affected by multiplying or dividing the outcome by a constant, it cannot be used as a solitary criterion for determining the overall effectiveness of the prediction models. RMSE and MAE are indicators that are used to measure the average errors. However, each of these indicators has its importance. RMSE gives greater importance to larger errors since they are squared before a mean is estimated. A high RMSE value shows that the number of estimates with high error is notably larger than anticipated and should be avoided. Meanwhile, MAE gives less importance to larger errors than RMSE. Both PI and OF values range between 0 and infinity. According to Liu et al. [58], the reliability of an ML model can be evaluated based on the values of PI and OF. A lesser value of OF indicates that the overall efficiency of a proposed model is better. As previously explained, several different trial runs were performed, and the model that produced the lowest OF is the one discussed in this study. In addition, external validation of the proposed model was done by using criteria given by various scholars [59].

4.1.1 CS

The laboratory-derived CS results of PSPB are depicted in Figure 8. As discussed earlier in the first stage, the effect of sand particle size on CS was determined, as shown in Figure 8(a). It can be seen that there is a reverse correlation between CS and sand particle size, indicating that as particle size increases, the CS decreases. This can be attributed to less cohesion between larger grain sizes due to increased contact area as compared to smaller grain sizes of sand [60]. The maximum CS was 15.93 MPa for the finest sand grain size of d < 0.420 mm at a fixed plastic-to-sand ratio of 25:75.

Figure 8

CS test laboratory results. (a) effect of sand particle size, (b) effect of plastic-sand proportions, (c) effect of basalt fiber (4 mm), and (d) effect of basalt fiber (12 mm).

The influence of varying plastic-to-sand proportions on the CS of PSPB is illustrated in Figure 8(b). An increase in the percentage of plastic content up to 30% results in an increase in CS. This can be explained by the fact that the optimal mixture was achieved with a plastic-to-sand ratio of 30:70. However, a further increase in plastic content results in a decline in CS. This decline in CS can be associated with an increase in the brittleness of the mixture due to the heating of PW. The highest CS was observed as 17.26 MP at a plastic-to-sand ratio of 30:70.

In addition, varying proportions of basalt fiber (0.1, 0.3, 0.5, and 1%) with lengths of 4 and 12 mm were used to further enhance the CS of PSPB, as depicted in Figure 8(c) and (d). The optimum proportions of the plastic-to-sand ratio of 30:70 with a particle size of sand less than 0.42 mm, as achieved in the initial stages, were used to determine the influence of fiber content in PSPB. The findings indicate that the addition of basalt fiber increases CS up to a certain proportion and then decreases. The optimum results of CS with the basalt fiber of 4 mm in length were noted as 19.61 MPa, whereas in the case of 12 mm, the highest CS value was measured as 21.65 MPa at 0.5% fiber content. It can be noted that the use of 4 mm basalt fiber leads to a significant improvement in CS, with an increase of 25.4% as compared to 12 mm, which results in only 13% enhancement in CS. It is due to the fact that there is a restriction on the number of fibers that can be mixed because fibers with a higher aspect ratio and greater lengths reduce workability noticeably, making the mixing process more difficult, which in turn affects their CS [61]. It is worth mentioning that the typical CS of concrete PBs was determined to be 19.8 MPa at 28 days’ curing time [62]. The ASTM standard (ASTM C902-00) specifies that for light vehicular traffic, the CS of pavement bricks must be a minimum of 20.7 MPa (the mean of 5) and 17 MPa (individual). Therefore, plastic, sand, and basalt fibers proposed in this study can be efficiently utilized in low-traffic regions. The addition of basalt fibers with a length of 4 mm at around 0.5% in PSPB yields optimum outcomes.

4.2.1 MEP model’s predictive performance

Figure 9 illustrates the comparison of the experimental and anticipated CS values of PSPB obtained from the optimum MEP-based model. The MEP model exhibited exceptional performance, with R ² values of 0.88 and 0.87 during the training and evaluation stages, respectively. Ideally, the slope of the regression line should approach a value of 1. The slope values of 0.87 and 0.79 for the training and evaluation (testing) phases indicate a significant connection between the predicted and actual values in the established model. Moreover, the values demonstrate a high degree of similarity and closely align with the desired fit throughout both the training and evaluation phases. This suggests that the proposed model received adequate training and possesses a strong predictive capability, performing equally well on unfamiliar data. This also illustrates that the issue of overfitting the model has been much mitigated.

Figure 9

Experimental vs MEP-anticipated outcomes.

Additionally, in order to comprehend the statistical analysis for the proposed models, absolute error analysis was performed, as shown in Figure 10. It can be noted that the average error in the anticipated values for CS is 4.5 MPa, with a higher error value that does not exceed 11 MPa. Overall, less than 5% of the total data points have an error value greater than 5 MPa. It is essential to emphasize the fact that the frequency of occurring maximum errors is substantially lower. Based on the above analysis, it can be stated that the developed MEP model for predicting the CS of PSPB can be used in the design process.

Figure 10

Error distribution in MEP-anticipated CS results.

4.2.2 MEP-based formulations

After performing the statistical examination of various MEP trials, the optimum trial was chosen for additional analysis. The selected MEP model for CS was decoded to develop the empirical equations based on five input parameters. The development of equations used four arithmetic operators, namely subtraction (−), addition (+), multiplication (×), and division (÷), as previously mentioned. The explicit formulations are represented as in Eq. (7). These mathematical formulas can be used to estimate the CS of PSPB:

4.2.3 External validation of the MEP model

The outcomes of statistical criteria employed for the external validation of the proposed models are shown in Table 7. Khan et al. [63] reported that for the proposed models to have a better level of precision, the slope of one of the regression lines (k or k′) that passes through the center should be relatively near to one. For proposed models, these values can be noted as 0.947, which is in the acceptable range. Furthermore, if the values of the evaluation metrics (i.e., m and n) are less than 0.1, then they are regarded as adequate. A number of researchers have suggested that the squared coefficient ( R o 2 ) of experimental and estimated values should also be near 1 [64]. It can be seen that all of the evaluated models lie in the recommended range of outcomes, making it obvious that the recommended models can satisfy the conditions for external verification. This demonstrates the MEP models’ exceptional validity, predictive capability, and independent correlations between the input and output.

4.2.4 SA and PA

While working with ML-based modeling, it is essential to carry out a wide range of assessments to validate that the indicated models are reliable and work efficiently when applied to a diverse set of data. In this study, SA and PA were done to ensure the validity of the proposed MEP models. First, SA is studied to determine the relative effect of input variables (ingredients) on the outcome (i.e., CS) of the proposed MEP model. The SA is evaluated by using Eqs. (9) and (10) for a given input parameter y _i:

where f max ( y i ) and f min ( y i ) indicate the largest and minimum of the forecasted outcome, accordingly on the basis of the ith input variable, while the other input variables are kept constant at their mean values. When SA is performed on the entire dataset, it shows how sensitive a constructed model is to a particular change in the defined parameters. The outcomes of the SA are shown in Figure 11. Among the five inputs being analyzed, the size of sand particles (S_S) and fiber content (F) have the greatest impact, contributing 33.02 and 21.56%, respectively, to the anticipated CS of PSPB. Conversely, the sand content (S) and fiber length (F_L) are identified as the least influential factors, contributing just 15.57 and 12.44%, respectively, to the predicted CS. These findings are highly comparable with experimental outcomes, indicating the validity of the models.

Figure 11

SA CS-MEP.

To further evaluate the validity of the recommended models, PA, also known as monotonicity analysis, has been recommended by various research studies, and thus, it is also implemented in the presented study. In the parametric study, one input variable varied while the values for other input variables were fixed at their mean values. When these input features are combined with the MEP models that have been developed, it is possible to determine the corresponding change in the output parameters, such as CS. The pattern of CS with a corresponding input parameter is presented by fixing all other variables at their average scores across the full range of defined input variables. Figure 12 provides the findings of the PA for the created CS-MEP model. The CS of PSPB is considerably influenced by increasing the plastic concentration up to a certain limit and then decreasing. At first, the CS experiences a rapid increase as a result of the initial mixing of the preheated plastic and sand. Nevertheless, after the addition of 500 kg·m⁻³ of plastic, this graph approaches a state of near-constancy. The results align with the findings of Iftikhar et al. [60,65], which indicates that an increase in the amount of plastic enhances the bonding between particles, increasing CS. The optimum amount of plastic content was noted as 28%, which is very near to the experimental findings, which was 30%. The inverse relationship between the particle size of sand and the CS of PSPB was observed. It is clear that an increase in sand size results in a decline in CS due to greater contact area and lesser cohesion between particles. The same trend was also found in experimental investigations. Likewise, the fiber content significantly impacts the CS of PSPB. By maintaining all other input components at a similar level, the increase in fiber content up to 0.48% (3 kg·m⁻³) results in an increase in CS; further addition of fiber leads to a decline in CS. These findings are well aligned with laboratory-derived outcomes. The prior research has already highlighted the identical impact of the fiber content on the CS of PSPB [66]. The sand content and fiber length have a relatively lower influence on the CS of PSPB. It can be noted that a fiber length of 4 mm has shown higher strength than 12 mm. In the case of sand content, the graph remains consistent with little increment in CS by decreasing sand initially and by increasing sand later.

Figure 12

PA of input parameters.

4.2.5 MEP model evolution and comparison with multi-linear regression (MLR)

The size of the database utilized for developing a model substantially affects the credibility of the model. Previous studies recommended that the ratio of recorded data points to the number of input parameters that were used in both the training and evaluation (testing) stages should exceed 5. In this study, this ratio is 23, which is much higher than the recommended values. The efficacy of the suggested model is examined by using statistical measures, as discussed in Section 3.1.2, and the results are also compared with MLR, as shown in Table 8. It can be noted that MEP shows enhanced performance as compared to MLR, as is evidenced by a strong relationship between actual and anticipated values, exhibiting R values of 0.938 and 0.936 for the training and testing set of the CS-MEP as compared to MLR, which has R ²-value 0.861 and 0.825. The high efficiency and generalizability of the proposed MEP models are also indicated by substantially low values of MAE, RMSE, and RRSME across both sets. The RMSE for CS is close to 0.81 and 0.944 MPa, whereas the values for the MLR model are 1.2 and 0.97 MPa for the training and validation stages, respectively. The MAE values are 0.54 and 0.724 MPa for MEP, while the MLR model has values around 0.8 and 0.811 MPa. The values for PI are less than 0.20 for both the training and validation stages of MEP and MLR models. Therefore, the models have higher accuracy and prediction performance. Overall, based on comparison, it can be stated that MEP outperformed MLR with enhanced accuracy in terms of error analysis. The comparison among experimental, MEP, and MLR CS values is visually presented in Figure 13. It is clear that there is a minor difference between the outcomes, which indicates the better efficacy of the proposed models.

Figure 13

Comparison between MLR and MEP models for CS.

4.2.6 Comparison with the literature

This study employs a data set from experimental investigations performed in the laboratory to create models, as previously stated. Therefore, there are no existing models with similar datasets to compare the effectiveness of the proposed models. Nevertheless, the outcomes of the present investigation are compared with alternative machine learning models that are constructed employing other databases on PSPB, as depicted in Table 9. The outcomes that result from the proposed model demonstrate a significant similarity to the findings reported in the available research for different models. The findings of this study demonstrate that equations derived from the MEP are reliable and useful pre-design predictors for the eco-friendly. The probable use of this innovation can significantly decrease time, expenditure, and allocation of resources, which represents a notable advancement for the corresponding field.

4.2.7 Role of AI in sustainable built environments

AI is essential in developing a sustainable environment by providing efficient waste management methods, such as using plastic trash as a construction material in concrete products. Previously, various AI applications have been successfully used to address the problems associated with the environment, such as waste management [68,69]. AI-based models provide cost-effective and time-saving models with accurate estimations [70,71]. Considering the above fact, this study utilized MEP-based ML models to make fast predictions and create mathematical formulas for determining the optimum use of waste plastic in producing PBs. MEP models provide economical methods for tackling difficulties related to reducing PW, which enables their incorporation into practical applications. This novel method not only promotes ecologically sustainable environments but also demonstrates the adaptability of AI in enhancing resource efficiency in handling waste.

The present study utilizes extensive validation approaches such as statistical evaluations, comparison with MLR, and SA to assure the dependability of the MEP models. These approaches evaluate the precision and resilience of the prediction models, offering a thorough assessment of their performance. Utilizing these validation methodologies improves the credibility of the AI-based solutions used for eco-friendly environments. This study also provides a graphical user interface (GUI) based on the data gathered from the training database, which will be a useful tool for estimating the CS of plastic PBs and their desired elemental proportions. Users can utilize GUI to assess the CS of PBs by inputting certain parameters inside the defined data range of the research. The GUI enables easy access for users and encourages more usage of AI-driven waste management solutions for sustainable and effective resource utilization in building applications. The developed GUI is visually depicted in Figure 14.

Figure 14

GUI for estimating CS of PSPB.