Eco-friendly waste plastic-based mortar incorporating industrial waste powders: Interpretable models for flexural strength

Huina Jia; Yali Li; Ali H. AlAteah; Ali Alsubeai; Sadiq Alinsaif; Haseeb Murtaza

doi:10.1515/rams-2025-0150

Article Open Access

Eco-friendly waste plastic-based mortar incorporating industrial waste powders: Interpretable models for flexural strength

Huina Jia , Yali Li , Ali H. AlAteah , Ali Alsubeai , Sadiq Alinsaif and Haseeb Murtaza

Published/Copyright: September 24, 2025

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From the journal REVIEWS ON ADVANCED MATERIALS SCIENCE Volume 64 Issue 1

Abstract

Glass powder, silica fume, and marble powder (MP) were investigated for their potential as sustainable additives to enhance mechanical properties, reduce environmental impact, and improve resource utilization in mortar formulations. This study utilized gene expression programming (GEP) and multi-expression programming (MEP) with experimental data to develop flexural strength models using these materials as eco-friendly mortar cement substitutes. The models were evaluated using R² values, statistical tests, sensitivity analysis, partial dependence plots (PDPs), Taylor’s diagram generation, and test and predicted results. The statistical measures demonstrated that MEP was the more accurate model compared to GEP. The sensitivity study revealed that plastic and sand had the most significant influence on flexural strength prediction, emphasizing the importance of their proportions in the mixture. PDPs further showed that cement, silica fume, and MP positively impact flexural strength, while sand and plastic exhibit optimal levels for enhanced performance. The study also highlighted the particle interaction sensitivity of glass powder, underlining the importance of mix design optimization to achieve improved mechanical behavior. The findings support the use of equation-based modeling and sustainable industrial byproducts to optimize mortar formulations, contributing to greener construction practices and reduced dependence on conventional cement.

Keywords: sustainable mortar; flexural strength; equation-based models

1 Introduction

The widespread accessibility and robust performance characteristics of ordinary Portland cement (OPC) have established it as the preeminent binder in the building sector for an extended period [1]. However, the environmental impact of OPC has become increasingly concerning [2,3]. The cement industry is responsible for emitting between 600 and 900 kg of CO₂ per metric ton of cement that is produced [4,5]. This significant carbon footprint, along with the depletion of natural resources used in cement production, underscores the urgent need for more sustainable alternatives [6]. These alternatives aim to reduce overall environmental impact while maintaining or enhancing performance, contributing to the transition toward a circular economy and environmentally responsible building approaches [7]. The use of waste materials as environmentally friendly alternatives in construction materials production has been the subject of recent research [8–11]. Glass powder (G-P), silica fume (S-F), and marble powder (MP) have shown promise as partial replacements for cement, offering environmental benefits and improved concrete properties [12,13].

G-P has emerged as an effective supplementary cementitious material (SCM) in cement-based construction, offering both environmental and performance benefits. Using 20–30% G-P instead of cement improves workability and compressive strength, according to previous studies [14,15]. S-F is a well-known byproduct of making silicon and ferrosilicon alloys because of its ability to enhance the properties of concrete [16]. The tiny particle size of this highly reactive pozzolanic substance makes it an ideal filler, enhancing the mechanical qualities and longevity of concrete [17]. The optimal replacement percentage of cement with S-F is generally found to be between 10 and 15% by weight, resulting in significant improvements in concrete strength [16]. Studies have shown that S-F can increase compressive, tensile, flexural, and impact strengths while decreasing permeability and bleeding [18]. S-F’s overall usage in concrete offers both engineering potential and economic advantages, making it a valuable admixture for producing high-quality, sustainable concrete [17]. A by-product of the quarrying process, MP is a metamorphic rock with a high calcium oxide content of about 50%. This increases the amount of MP recovered from the parent rock, which is utilized frequently in buildings [19]. Since the reactivity efficiency is enhanced by the presence of lime, marble dust could be a great alternative to cementitious binders [19]. The selection of combined G-P, S-F, and MP was guided by their proven or potential reactivity, environmental impact mitigation, and complementary roles in mortar enhancement. G-P, with its amorphous silica content, exhibits pozzolanic activity [20]. S-F offers a high surface area and reactivity, significantly refining the pore structure [21]. MP, though largely inert, contributes through filler effects and improves workability [22]. Importantly, integrating these diverse industrial byproducts aligns with circular economy principles by diverting waste streams and minimizing clinker use in cementitious systems. Therefore, there is a need for advanced modeling-based research to study the impact of S-F, MP, and G-P when used in various combinations.

In a design code, the factors that are considered to be the most essential are the mechanical strength of mortar, such as its flexural strength (F-S). F-S is a critical property of cement-based materials (CBMs), influencing their performance and durability. It is typically higher than tensile strength and depends on specimen geometry and stress distribution in the process zone [23]. It is possible to reduce the number of trial batches and tests needed to obtain usable design data by using dependable forecast models for the strength of concrete. Time and money saved are possible as a result of this [24]. Recent studies have investigated the prospect of predicting the mechanical properties of concrete mixes with various additives using state-of-the-art machine learning (ML) techniques like gene expression programming (GEP) and multi-expression programming (MEP) [25,26]. Predicting mechanical parameters, such as F-S, of CBMs using ML approaches has demonstrated encouraging outcomes. Several methods have been developed to forecast the F-S of various mortar mixes by using algorithms to model complicated relationships and predict the performance of the mixtures based on input parameters, such as the types and proportions of supplementary materials. These methods include GEP, MEP, random forest (RF), and boosting-based models [26,27].

A more precise representation of the technical properties of different materials is now possible owing to soft computing. The accuracy of predictions is significantly dependent on ML models that are supplied with data [28,29]. Due to their intricate intricacy and intrinsic unpredictability, construction materials are notoriously challenging to quantify precisely. Assessing the attributes of building materials is a major use of ML approaches. This study uses ML techniques to investigate the features of various concrete types, including both modern and classic variants. These varieties of concrete encompass recycled aggregate concrete, fiber-reinforced concrete, self-compacting concrete, lightweight concrete, and concrete incorporating phase change elements [30–34]. Numerous studies have demonstrated that ML models surpass predictive and empirical techniques in correctly evaluating particular technical characteristics. Resolving certain computational challenges is essential for making accurate predictions about the concrete’s properties. Problems arise due to the non-linear interaction between time, temperature, and the activity of the cement paste, as well as the complicated processes of cement hydration and microstructure development [35–37]. Training ML techniques with an input dataset on mix ratios and curing conditions facilitates accurate prediction of desired properties. The use of ML models has numerous advantages, including generalizability, precision, and consistency in predictions, minimal computational demands, and user-friendliness [38,39].

Using ML techniques like GEP and MEP was the goal of this study to forecast the F-S of plastic-based mortar, including additives S-F, MP, and G-P. The efficacy of ML algorithms was evaluated using a number of metrics, including the R ², arithmetical tests, and the scattering of expected results. The study aimed to assess the predictive capability of ML methods on material properties. ML methods can be employed to acquire the necessary dataset by conducting experiments or analyzing databases that already exist. ML algorithms might potentially improve their comprehension of material attributes through data analysis. ML algorithms predicting mortar F-S with input factors like cement, sand, plastic, S-F, MP, and G-P were evaluated by combining experimental data. Further inquiry was undertaken to investigate the significance of raw materials using sensitivity analysis (SA) and partial dependence plots (PDPs), which provided critical insights into the influence of individual variables and their interactions on the model’s predictions. Among the many potential uses for the newly collected attributes and ML models are improvements to the current database of sustainable materials and guidance in the creation of composite construction materials.

2 Methodology

2.1 ML models

A controlled setting was used to examine the F-S of mortar that contained S-F, MP, and G-P. The results (F-S) were obtained by making use of six inputs. We used state-of-the-art ML techniques like GEP and MEP to forecast the F-S. It is possible to assess outcomes after applying ML algorithms to input data. The ML models were trained using 70% of the dataset, with 30% kept aside for testing. This conformed to the standard procedure for academics [40]. The anticipated R ² value indicated the model’s efficacy. In ML, a higher R ² score signifies superior model efficacy, with values approaching 1 denoting enhanced prediction capability. However, R ² scores can be affected by factors such as prevalence and experiment noise, which may limit the maximum attainable performance [41]. Figure 1 depicts the overall ML-based study approach, and Tables 1 and 2 represent the hyperparameters for GEP and MEP selected based on the trial-and-error method.

Figure 1

Flowchart of ML-based modeling methods.

Table 1

Predefined model factor for GEP

GEP
Hyperparameters	Settings	Hyperparameters	Settings
Genes	4	Stumbling mutation	0.00141
Gene recombination rate	0.00277	Number of genes	10
General	F-S	Inversion rate	0.00546
Mutation rate	0.00138	Head size	10
RIS transposition rate	0.00546	Data type	Floating number
Chromosomes	50	Two-point recombination rate	0.00277
Function set	Addition, division, subtraction, power, square root, multiplication, natural algorithm, and exponential	One-point recombination rate	0.00277
Leaf mutation	0.00546	Linking function	Addition
Gene transposition rate	0.00277	Lower bound	-10
Random chromosomes	0.0026	Upper bound	10
IS transposition rate	0.00546

Table 2

Predefined model factor for MEP

MEP
Hyperparameters	Settings	Hyperparameters	Settings
Operators/variables	0.5	Error	MSE, MAE
Code length	50	Crossover probability	0.9
Number of generations	300	Number of sub-populations	500
Replication number	15	Mutation probability	0.01
Sub-population size	200	Number of runs	10
Number of treads	2	Function set	Addition, division, subtraction, power, square root, multiplication, natural algorithm, and exponential
Terminal set	Problem input	Problem type	Regression

2.1.1 MEP technique

Computer programs can be generated to solve problems through simulated evolution using Genetic Programming (GP), an evolutionary computation method [42]. Evolving populations of programs according to fitness criteria, it works on the notion of natural selection [43,44]. The procedure entails establishing an initial population, assessing fitness, selecting viable individuals, and employing genetic operators such as crossover and mutation to produce subsequent generations, as shown in Figure 2(a) [42,44]. It is common practice to classify GP as either tree-based, graph-based, or linear-based [46]. One variation of GP that makes use of a linear model of chromosomes is MEP [46]. The technique has shown promising results in predicting mechanical properties of materials, with high accuracy and correlation coefficients exceeding 0.9 in some cases [47]. An MEP is a sequence of genes that encodes a sophisticated piece of software (MEPX).

Figure 2

Process flow diagrams: (a) MEP and (b) GEP [45].

2.1.2 GEP technique

The evolutionary algorithm known as Candida Ferreira’s GEP combines aspects of GP and genetic algorithms (GAs), as shown in Figure 2(b), to generate models and computer programs. GEP is a hybrid of GA and GP, the two mainstays of GAs [48]. GEP is an ML method that generates readable models through symbolic regression, allowing for both prediction and interpretation [49]. GA and its programmatic Darwinian counterpart, G-P, are both utilized to their full potential in order to take advantage of the optimization and search method that is based on natural selection and genetics [48]. In order to optimize functions, GEP employs a symbolic regression approach, which results in the generation of predictive equations. The availability of equations that can be utilized as predictive models is one of the most significant advantages of this technology [50]. It has shown promise in identifying prescribed functions and uncovering new model structures, with prediction capabilities comparable to other ML methods [49].

The typical procedure or function of GEP is briefly explained in the following steps:

Expression Trees (ETs) and Chromosomes: GEP makes use of fixed-length chromosomes composed of genes that are subsequently expressed as ETs. A complete model is formed by combining the sub-expressions or solutions that each gene encodes.
Genetic Operations: To evolve the chromosomes, GEP uses genetic operators like transposition, crossover, and mutation. By ensuring population variety, these operations enhance the sustainability of solutions throughout generations.
Techniques for Creating Constants: Since constants are not usually present in the original genetic composition, this article addresses how they might be created within GEP. Methods such as embedding constants directly into the chromosomes, fixed-point mutation, and random constant production are assessed.
Fitness Evaluation: An ET’s performance is gauged using a fitness function after its chromosomes have been decoded. This makes it possible for the GEP algorithm.

2.2 Collecting and analyzing data

In this study, the F-S of plastic-based mortars incorporating discarded S-F, MP, and G-P was modeled using advanced computational techniques, specifically GEP and MEP. Data were obtained from a previous experimental study comprising 408 data points with six input variables and one output [51]. Data preparation made it easier to gather and organize the data. Knowledge discovery from data is a popular procedure; however, there is a common strategy that helps overcome this obstacle: preprocessing data for data mining. The goal of cleaning up data is to get rid of any unnecessary information or noise. Methods for regression and error distribution were employed in the model analysis. Figure 3(a)–(g) shows histograms that display the frequencies of different values. When the distributions of the dataset’s different components are combined, the total frequency distribution of the dataset may be given. One can ascertain the frequency of specific values within a dataset by examining its relative frequency distribution. Additionally, to evaluate the probable effect of input features on outcome, the Pearson correlation (R) matrix was generated. A graphical depiction of R is shown in Figure 4. Correlations with R values near 0 are reflected to be weak, but R values falling among or close to +1 and −1 are reflected to be strongly positive or negatively related. The inputs have a strong association with F–S, as seen by the greatest positive R-value of 0.0.97, which is clear evidence of this link. Even while a weak link exists when R is near or equal to zero, it does not necessarily imply that the two variables are totally unrelated. One should remember this because it is crucial. To fully understand the connection between inputs and outputs, it is advised to examine models that are grounded in another study, like SHAP and SA.

Figure 3

Frequency distribution for the F-S dataset: (a) Cement, (b) sand, (c) plastic, (d) S-F, (e) G-P, (f) MP, and (g) F-S.

Figure 4

Pearson’s correlation plot for the input and output variables.

2.3 Validating the models

For the developed GEP- and MEP-based models, a separate test dataset was utilized to conduct numerical validation. The performance assessment relied on several statistical indicators, including root mean square error (RMSE), normalized root mean square error (NRMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), mean bias error (MBE), Nash–Sutcliffe efficiency (NSE), and Pearson’s correlation coefficient (R) [52–56]. Eqs. (1) –(7) present the formulas for various statistical indicators:

(1) R = ∑ i = 1 n ( O i − O ̅ ) ( P i − P ̅ ) ∑ i = 1 n ( O i − O ̅ ) 2 ∑ i = 1 n ( P i − P ̅ ) 2 ,

(2) MAE = 1 n ∑ i = 1 n | O i − Pi | ,

(3) RMSE = ∑ i = 1 n ( O i − P i ) 2 n ,

(4) NRMSE = RMSE O ̅ ,

(5) MAPE = 100 n ∑ i = 1 n | O i − P i | O i ,

(6) MBE = 1 n ∑ i = 1 n ( P i − O i ) ,

(7) NSE = 1 − ∑ i = 1 n ( O i − P i ) 2 ∑ i = 1 n ( O i − O ¯ ) 2 .

The following equations explain the relationship between the variables: O i stands for the observation value, P i for the prediction value, O ̅ for the average of the observed values, P ̅ for the average of the forecast values, and n for the total number of data points. When evaluating a model’s predictive power, R is a crucial metric to consider. When the R-value is high, it means that the actual output and predictions are strongly related [57]. R remains the same value regardless of division or multiplication. However, by considering both the actual and expected results, R ² generates a more accurate approximation of the actual value. When R ² values are closer to 1, it indicates that the model-building process is progressing more effectively [58,59]. The proposed model, like MAE and RMSE, shows that increasing the accuracy of predictions as the amount of errors lowers leads to higher performance with fewer outliers. On the flip side, when the margin of error grows wider, the results from both approaches inch closer to zero [60,61]. Nevertheless, a more comprehensive examination revealed that MAE genuinely thrives in uninterrupted and seamless databases [62]. Reducing the values of the previously computed mistakes usually improves the model’s performance.

Statistical validation and the use of a Taylor diagram are two useful ways to evaluate the performance of a prediction model. By comparing the models’ deviations from the actual or reference point, this Taylor diagram is useful for analyzing the models’ precision and reliability utilizing datasets [63,64]. Standard deviation is shown on the y- and x-axis, R is shown by the radial lines, and RMSE is indicated by the circular lines, which are marked at the actual value point. It is possible to use three separate metrics to get close to the ideal location of a gadget. Generally speaking, a model is considered more trustworthy if it consistently produces better results when tested for prediction accuracy [63].

2.4 SA

One of the most well-known ways to pick out the most important elements in a dataset is by using SA [65]. In other words, it is a way to find out what happens when the input parameters to a model are altered and see how the output changes. This may be useful to learn all about the different consequences of each tested variable. To diminish model complexity and training duration, this can offer guidance on the most critical input variables. The input matrix can be reduced by deleting the less significant elements. Two approaches exist for conducting SAs: the global approach and the local approach. This research made use of one of the two approaches, the global SA [66].

2.5 PDPs

To learn how certain features affect an ML model’s predictions, either singly or in combination, PDP analysis is a great tool to use [34]. Depending on the intricacy or simplicity of the relationship between the input factors and the output, partial dependence charts can be used to explain it [67]. Given a constant parameter value across all datasets, the PDP function will show the mean prediction for that variable. The computation of a PDP does not alter any other features, which permits a concentrated investigation of the average impact of a feature on predictions [68]. The process of estimating PDPs requires modifying the value of either one input (which results in a 1D-PDP) or two inputs (which results in a 2D-PDP) while maintaining the values of the other inputs at their original levels. This forms the basis for the findings and discussion presented.

3 Results and analysis of the models

3.1 Regression analysis of the F-S GEP model

Models based on ETs can anticipate mathematical linkages for estimating F-S; the GEP technique used information on chromosomal number and head size to construct these models. Most F-S sub-ETs in the plastic-based mortars are built with the six mathematical operations: addition, subtraction, multiplication, division, power, square root, natural algorithm, and exponential. After the sub-ETs produced by the GEP model undergo encryption, a mathematical equation is revealed, as shown in Eq. (8). The advanced model excels, outperforming a flawless model in ideal conditions, backed by adequate data. Lines of F-S in Figure 5 show the difference between the values that were observed and those that were predicted by the models for the training and testing sets. The GEP technique produces highly accurate predictions of the F-S of mortar, as evidenced by the remarkable correlation between the predicted and observed outcomes (R ³ value of 0.9497). The discrepancies between the experimental data and the GEP model, as well as the absolute error, are illustrated in Figure 6. Findings within the 0–0.370 MPa range proved that the GEP equation produced reliable predictions. The average error was 0.117 MPa. As shown in Figure 7, the errors followed a bell curve distribution. There were 6 readings higher than 0.3 MPa, 18 readings falling between 0.2 and 0.3 MPa, and 112 readings below 0.2 MPa. The high R ² value, combined with the consistent distribution of errors at lower ranges, strongly demonstrates the remarkable accuracy of the GEP approach.

(8) FS ( MPa ) = 2 PC + Sa − SF − MP Pt + PC − 9.83 + 0.79 + 3.85 + ( − 3.60 ⋅ GP ) − 3.85 + ( 7.96 ⋅ Sa ) + 8.46 ,

where FS is the predicted flexural strength, MP denotes marble powder, GP denotes glass powder, PC denotes plain cement, SF denotes silica fume, Sa denotes sand, and Pt denotes plastic.

Figure 5

Scatter plot between the GEP forecasted vs actual F-S.

Figure 6

GEP model error spreads of F-S mortar between the anticipated and test values.

Figure 7

Violin plot – GEP errors.

3.2 Regression analysis of the F-S MEP model

In order to determine the F-S of mortar, an empirical formula was created using the MEP data. This formula accounts for the effects of the six separate components. The complete set of all the modelled mathematical equations is shown in Eq. (9). The findings from a comparison of the MEP model target and delivered values are displayed in Figure 8. The data indicate that the MEP forecast error margins ranged from 0.000 to 0.357 MPa, with an average of 0.099 MPa.The average error values were below 0.3 MPa, with 123 measurements below 0.2 MPa, 10 values between 0.2 and 0.3 MPa, and 3 readings beyond 0.3 MPa. When applied to fresh, untested data, the trained MEP model manages oversimplification admirably, yielding a respectable R ² value of 0.9646 (Figure 9). With a higher R ² value, the F-S-MEP model appears to be marginally more accurate than the F-S-GEP model. Even in the worst-case scenarios, the MEP model predicts less variation in results compared to the GEP model. The MEP and GEP models can provide accurate predictions. Both the correlation coefficients and the standard deviations of errors are reduced when the MEP equation is implemented. Because it is simple and flexible, the MEP equation sees extensive use. It would appear that the MEP model outperforms the GEP model, as shown in Figure 10, due to its greater correlation coefficient and lower error levels. One probable explanation for the MEP’s superior accuracy over the GEP could be its transparent and simple features. The mathematical representation of the collective influence of the material constituents on the outcome (F-S) is an equation that serves as the foundation for MEP prediction. The equation provided is advantageous for pragmatic implementations due to its relatively high level of interpretability and comprehensibility. Conversely, the GEP model is characterized by a sophisticated non-linear expression that is derived through the application of GA. The expression’s complexity may present difficulties in its interpretation, potentially impeding the capacity to identify clear insights regarding the interdependence between parameters [69,70]:

(9) FS ( MPa ) = Sa − ( MP + GP + SF + Sa − PC + Pt ) − 3 Pt + Sa Sa ,

where FS is the predicted flexural strength, MP denotes marble powder, SF denotes silica fume, GP denotes glass powder, Pt denotes plastic, PC denotes plain cement, and Sa denotes sand.

Figure 8

Scatter plot between the MEP forecasted vs actual F-S.

Figure 9

MEP model error spreads of F-S mortar between anticipated and test values.

Figure 10

Violin plot – MEP errors.

3.3 Validation and comparison of models

Table 3 displays the outcomes of the computations for efficiency and error (R, MAE, RMSE, NRMSE, MAPE, MBE, and NSE) performed using Eqs. (1)–(7). With lower error values and greater efficiency-metrics values, the produced models’ prediction accuracy is enhanced. According to Table 3, which compares the two models in depth using error and efficiency criteria, MEP performs better than GEP. Among the error metrics, MEP consistently exhibits greater accuracy, with lower MAE (0.099 vs 0.117 MPa), RMSE (0.123 vs 0.145 MPa), NRMSE (0.032 vs 0.038 MPa), MAPE (2.6% vs 3.0%), and MBE (0.017 vs 0.018 MPa), indicating its ability to minimize prediction deviations. In terms of efficiency metrics, MEP achieves a higher correlation coefficient (r = 0.982 vs 0.975) and Nash–Sutcliffe efficiency (NSE = 0.959 vs 0.948), reflecting its stronger agreement with the observed data and overall predictive reliability. In summary, the MEP method demonstrated superior performance over the GEP model, as validated by the statistical metrics analysis.

Table 3

Statistical assessment outcomes

Property	F-S
Property	GEP	MEP
R	0.975	0.982
MAE (MPa)	0.117	0.099
RMSE (MPa)	0.145	0.123
NRMSE (MPa)	0.038	0.032
MAPE (%)	3.000	2.600
MBE (MPa)	0.018	0.017
NSE	0.948	0.959

The performance of GEP and MEP models is compared to the real F-S values using the Taylor diagram in Figure 11. The diagram shows the standard deviation, R, and centered root-mean-square deviation. The MEP model shows a higher correlation coefficient, placing it closer to the reference point, indicating better association with the test values. Additionally, the MEP model demonstrates a standard deviation that is closer to that of the actual F-S, suggesting its capability to replicate the variability in the data more accurately than the GEP model. In contrast, the GEP model, while also performing well, is slightly further from the reference point, reflecting comparatively lower predictive accuracy. The compact clustering of the MEP marker near the ideal point validates its superior predictive consistency and reliability. In summary, the statistical analysis is supported by the Taylor diagram, which shows that the MEP model is better at simulating the actual F-S behavior than the GEP model.

Figure 11

Taylor’s diagram-based efficiency assessment of the models.

3.4 SA

The aim of this study is to evaluate the impact that various input factors have on the performance of F-S prediction for mortar. There is a high correlation between the input components and the outcome that is anticipated [71]. Figure 12 displays the effects of each variable on the F-S of mortar, providing insight into the potential future of this material as well as concrete and other construction materials. Sand (32%), plain cement (4.0%), S-F (3%), MP (2%), and G-P (1%), in that order, had the greatest influence on predicting the F-S of mortar (63%). A direct link appeared between the quantity of data points and model parameters included in SAs and the results. It was demonstrated that the analytical outcomes were greatly affected by several input parameters, including the amounts of concrete mix used in the ML technique. Eqs. (10) and (11) were utilized to find the relative importance of each input parameter to the model:

(10) N i = f max ( x i ) − f min ( x i ) ,

(11) S i = N i ∑ j − i n N j ,

where f max ( x i ) represents the maximum and f min ( x i ) represents the least projected value over all ith outputs.

Figure 12

SA using the Pie chart.

3.5 PDPs

PDPs are an essential visualization tool in ML, offering insights into the association between individual input parameters and the predicted output while averaging over the influence of other variables [72]. In the context of mortar and concrete strength prediction, PDPs help identify the contribution of key parameters, guiding mix design optimization and enhancing material performance [73]. The PDPs in Figure 13(a)–(f) illustrate the influence of various input variables on the F-S of mortar. Cement (P-C) exhibits a strong positive correlation with F-S, emphasizing its critical role in enhancing the mortar matrix’s load-bearing capacity. Sand (Sa) shows diminishing returns after an optimal level, indicating the importance of balanced proportions for effective bonding. Plastic (Pt) has a nonlinear effect, with F-S peaking at moderate levels but decreasing at higher contents due to potential matrix disruption or increased porosity. S-F consistently improves F-S by refining the microstructure and enhancing particle packing through pozzolanic reactions. MP initially increases F-S steeply before stabilizing, reflecting its filler effect and chemical compatibility up to a saturation point. G-P displays fluctuating behavior, highlighting the sensitivity of F-S to particle size distribution and matrix interactions. These trends underscore the significance of optimizing each variable for improved F-S, with PDPs offering valuable insights into the material behavior and performance.

Figure 13

PDPs for input variables: (a) P-C, (b) Sa, (c) Pt, (d) S-F, (e) MP, and (f) G-P.

4 Discussion

This research concentrates on employing GEP and MEP models to forecast the F-S of plastic-based mortar. Six input parameters are meticulously defined for this purpose. This intentional restriction is crucial to guarantee accuracy and reliability in the models’ predictions. The reliability of the F-S predictions is significantly improved by the application of uniform unit measurements and standardized testing methodologies throughout this study. Researchers can obtain substantial insights into the mix design and understand the influence of each parameter on the overall F-S by generating mathematical equations from these models. Although the structure of these models is strong, it is crucial to understand that increasing the input variables beyond the existing six can limit their ability to make predictions. Ensuring that the training data matches the modeling objectives is crucial; discrepancies in input parameter units or alignment could lead to significant deviations in predicted outcomes, potentially inflating or underestimating the F-S. Therefore, it is essential to maintain consistency in the measurement units for effective use of these models.

Predictive analytics integration can improve maintenance scheduling and increase energy efficiency in different construction activities. Nevertheless, there are specific challenges that accompany these advantages, especially in terms of maintaining data integrity and accuracy caused by human errors in input that may weaken the credibility of the forecasts. To improve ML-driven solutions, future research may explore incorporating advanced technologies like IoT (Internet of Things) devices for real-time data collection and monitoring, enabling more precise predictions. Moreover, the creation of hybrid models blending different methodologies may enhance predictive accuracy, while explainable AI methods could enhance transparency for clearer interpretation by practitioners. Highlighting the importance of sustainability in model design is essential as it promotes actions that coincide with environmental concerns. Technological advancements could transform the construction field by augmenting efficiency, safety, and sustainability. By simplifying processes and providing better insights for decision-making, these advancements could result in major decreases in project duration and resource inefficiencies. The results of this research could encourage a shift toward sustainable construction methods, promoting the use of eco-friendly materials that meet performance standards and have a positive impact on the environment. As the construction sector adjusts to these technological changes, it is ready to welcome a future that values both financial feasibility and ecological accountability, ultimately promoting behaviors that support long-lasting sustainability objectives.

5 Conclusion

Using MEP and GEP, this work aims to construct prediction models for the F-S of plastic-based mortars, including MP, S-F, and G-P. Using a comprehensive dataset collected from F-S experiments, the models were trained, tested, and verified. The principal findings of the investigation are as follows:

The MEP approach demonstrated greater accuracy (R ² = 0.96) in forecasting F-S in mortar compared to the GEP method, which was reasonably accurate (R ² = 0.95) in this regard.
The mean discrepancy between the actual and calculated F-S (errors) in the MEP approach was 0.099 MPa, but in the GEP method, it was 0.117 MPa. The error rates demonstrated the accuracy of the GEP model and demonstrated the MEP method’s dominance in predicting the F-S of mortar.
Statistical validation has demonstrated the models’ usefulness. There has been an improvement in the R ² and error rates of the ML models. The MAPE of the GEP model was 3.0%, which was much higher than the MEP model (2.66%). In comparison to the MEP model, which had an MAE of 0.018 MPa, the GEP model attained a lower MAE of 0.117 MPa. The aforementioned decisions have enhanced other aspects of assessing the model’s performance.
SA revealed that the forecast for F-S of mortar was predominantly impacted by plastic at 60%, followed by sand at 30%, cement at 4%, S-F at 3%, MP at 2%, and G-P at 1%.
The PDPs revealed that cement, S-F, and MP positively influence F-S, while sand and plastic exhibit optimal levels, and G-P shows sensitivity to particle interactions, highlighting the importance of mix optimization.

The unique mathematical approaches of GEP and MEP make them crucial tools for predicting features in different datasets. These methods enable quick assessment, improvement, and enhancement of forecasting models, which are particularly beneficial in engineering and material science. In determining the proportion of mortar mixtures, GEP and MEP allow researchers and engineers to create precise and understandable mathematical models that can forecast how various mix compositions will perform. This ability helps streamline design processes, minimizes material wastage, and enhances the overall quality and longevity of construction materials.

Acknowledgments

The authors acknowledge their respective institutions for supporting this study.

Funding information: The authors state no funding involved.
Author contributions: H.J.: conceptualization, supervision, methodology, formal analysis, and writing-original draft. Y.L.: resources, data acquisition, project administration, visualization, investigation, writing, reviewing, and editing. A.H.A.: data acquisition, validation, visualization, methodology, writing, reviewing, and editing. A.A.: formal analysis, conceptualization, investigation, resources, writing, reviewing, and editing. S.A.: software, visualization, formal analysis, and validation. H.M.: software, supervision, resources, methodology, writing, reviewing, and editing. All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
Conflict of interest: The authors state no conflict of interest.
Data availability statement: The datasets generated and/or analysed during the current study are available from the corresponding author on reasonable request.

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Received: 2025-01-27

Revised: 2025-06-23

Accepted: 2025-08-18

Published Online: 2025-09-24

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/rams-2025-0150

Keywords for this article

sustainable mortar; flexural strength; equation-based models

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