Soft-Computing Analysis and Prediction of the Mechanical Properties of High-Volume Fly-Ash Concrete Containing Plastic Waste and Graphene Nanoplatelets

Abstract

The rising population and demand for plastic materials lead to increasing plastic waste (PW) annually, much of which is sent to landfills without adequate recycling, posing serious environmental risks globally. PWs are grinded to smaller sizes and used as aggregates in concrete, where they improve environmental and materials sustainability. On the other hand, PW causes a significant reduction in the mechanical properties and durability of concrete. To mitigate the negative effects of PW, highly reactive pozzolanic materials are normally added as additives to the concrete. In this study, PW was used as a partial substitute for coarse aggregate, and graphene nanoplatelets (GNPs) were used as additives to high-volume fly-ash concrete (HVFAC). Utilizing PW as aggregates and GNPs as additives has been found to enhance the mechanical properties of HVFAC. Hence, this study employed two machine-learning (ML) models, namely Gaussian Process Regression (GPR) and Elman Neural Network (ELNN), to forecast the mechanical properties of HVFAC. The study input variables were PW, FA, GNP, W/C, CP, density, and slump, where the target variables are compressive strength (CS), modulus of elasticity (ME), splitting tensile strength (STS), and flexural strength (FS). A total of 240 datasets were employed in this study and divided into calibration (70%) and validation (30%) sets. During the prediction of the CS, it was found that GPR-M3 outperforms all other models with an R-value equal to 0.9930 and PCC value of 0.9929 in the calibration phase, and R-value = 0.9505 and PCC = 0.9339 in the verification phase. Additionally, during the modeling of FS, it was also noticed that GPR-M3 surpasses all other combinations with R = 0.9973 and PCC = 0.9973 in calibration and R = 0.9684 and PCC = 0.9428 in the verification phase. Moreover, in ME modeling, GPR-M3 is the best modeling combination and shows high accuracy with R = 0.9945 and PCC = 0.9945 in calibration and R = 0.9665 and PCC = 0.9584 in the verification phase. On the other hand, GPR-M3 outperforms all other models during the modeling of STS with R = 0.9856 and PCC = 0.9855 in calibration, and R = 0.9482 and PCC = 0.9353 in the verification phase. Further quantitative analysis shows that, in the prediction of CS, the GPR improves the prediction accuracy of ELNN by 0.49%, while during the prediction of the splitting tensile strength, it was also found that the GPR improved the accuracy of ELNN by 1.54%. In FS prediction, it was also improved by 7.66%, while in ME, it was improved by 4.9%. In conclusion, this AI-based model proves how accurate and effective it was to employ an ML-based model in forecasting the mechanical properties of HVFAC.

1. Introduction

Plastic waste (PW) is a major source of solid waste, with thousands to millions of tons produced daily worldwide due to high plastic use in all areas of life. Modern urban lifestyles across developed and developing countries further drive this global increase in PW [1,2]. As per the reports from the United Nations Environment Assembly in 2021, worldwide, more than 7 billion tons of PW is generated annually, where only less than 10% of the produced waste is recycled and the remaining ends up discarded into the environment. Out of the amount disposed into the environment, about 75 to 199 million tons end up discarded into oceans, seas, and rivers [3,4]. Most of the generated PWs end up in landfills and open areas, posing risks to the environment through land pollution and shelter for harmful rodents and insects such as snakes, rats, mosquitoes, etc. Additionally, landfill disposal of PWs leads to substantial expenditures and requires massive land usage [1]. PW is non-biodegradable; hence, when it ends up in landfills, it occupies the land space for a very long period. With time, it can pollute the soil or even ground water through leaching by releasing toxic elements and gases. Most nations adopt the burning method to discard their PWs. However, this method causes significant threats to global warming potential by releasing toxic and poisonous greenhouse gases and fly and bottom ashes into the atmosphere. In the process of burning PW in landfills, soil is significantly weakened due to the heat, and some of the poisonous greenhouse gases are absorbed into the soil and groundwater through leachate, causing soil and water pollution. Burning plastic waste also affects inhabitants like animals, rodents and insects by killing them or disrupting their livelihood [5,6,7,8]. The most prevalent methods for end-of-life PW adopted globally include energy recovery, mechanical recycling, chemical recycling, decomposition of compostable plastics and landfilling. However, the low recycling rates worldwide is among the challenges associated with recycling mixed plastics, as well as compatibility issues and costs [9]. Due to the escalation in single-use PW and the challenges of its proper waste management, researchers are driven to discover safer, sustainable, and cost-effective ways of managing PW properly. PW possesses some desired properties that make it suitable for use as an alternative to natural aggregates in cementitious composites like concrete and mortar. Some of its superior properties over natural aggregates include higher elasticity, corrosion, and impact resistance, lower water absorption, and lower electrical and thermal conductivity [7,10]. Thus, recycling PW into concrete promotes a circular economy [9] and reduces human toxicity [11] and global warming potential [10].

Concrete ranks among the most widely consumed materials created by humans, and it is the most utilized material for construction and building [12,13]. Aggregate constituents make up the highest proportion of concrete’s basic materials, constituting about 60% to 80% of the total concrete volume. Therefore, aggregates have significant effects on the properties, performance, cost, and type of concrete. The natural aggregates used for making concrete, i.e., river sand and crushed stones, are non-renewable; hence, continuous use of these materials will lead to their depletion, which will consequently affect the materials’ sustainability. Thus, there is an utmost need to adopt sustainable and recyclable materials, including PW as an alternative to natural aggregates in concrete, to satisfy the increase in the construction industries’ demand for concrete and, at the same time, to improve sustainability concerning natural materials for future generations [1,14,15]. Extensive research has been conducted and has produced useful results concerning the use of PW as a partial substitute for fine or coarse aggregates or both in concrete. Due to its lower density, PW is a good alternative to fine and coarse aggregates when making lightweight concrete, as it significantly reduces the density of concrete [6,16,17,18]. PW has been shown to enhance the consistency of concrete, as reported by previous studies. The increase in workability is mainly caused by the lower water absorption of PW, which produces more free water during mixing. The hydrophobic nature of PW helps in entrapping air during mixing, thus reducing internal friction and enhancing workability [5,19,20,21]. Most studies have shown that the adoption of PW as a partial or a total substitute for natural aggregates causes significant deterioration concerning the mechanical properties, especially the compressive strength [5,18,19,20,22]. The reduction in mechanical properties is caused by the poor compatibility between the rubber particles and the cement matrix, creating a fragile interfacial transition zone (ITZ) between the cementitious matrix and rubber aggregates. This creates a weak path for premature failure under applied load. Additionally, the water-repellent properties of the PW caused an increase in pore volume in the concrete matrix, leading to a reduction in the mechanical properties of the concrete [7,23]. Previous studies have shown that PW, when used to partially replace aggregate in concrete, caused an increase in the porosity, water absorption, and permeability of the concrete, thus negatively affecting its durability performance [6,24,25,26]. Positive effects are evident when PW is partially used to replace natural aggregates (fine and coarse) in concrete. PW has been reported to reduce the thermal conductivity of concrete, thus enhancing its thermal insulation properties. The enhancement in the thermal insulation was ascribed to the higher thermal insulation and lower density of the PW in comparison to the natural aggregates it replaced [1,26,27,28]. PW enhances concrete’s impact resistance and energy absorption, owing to its greater flexibility and lower modulus of elasticity compared to the natural aggregates it replaced [7,29,30]. Several methods have been devised to mitigate the adverse effects of PW on the mechanical properties and durability performance of concrete. Some of the methods include the use of highly reactive pozzolanic materials as partial substitute to cement or as an additive to cementitious materials in the concrete containing PW. Some of the pozzolanic materials include metakaolin [31], waste glass powder [32], silica fume [19], and nano-silica [33,34].

Graphene-based nanomaterials, such as graphene nanoplatelet (GNP), have also been used as an additive to cementitious materials to mitigate the negative effects of PW on the properties of concrete. As reported by previous studies, when GNP was incorporated as an additive in a dosage of up to 0.3% by weight of cementitious materials, there was a total recovery in the loss of the mechanical properties and durability of concrete caused by the negative effect of replacing up to 15% natural aggregate with PW. [5,35]. These improvements are linked to the larger surface area of the GNP (finer sizes on the nanoscale), allowing it to fill the pores created by the PW to nano size. Additionally, the GNP’s ability to form intercalation compounds with the cement hydration products and its nucleation site effect also contributed significantly to these improvements [36]. However, the high cost of GNP can make concrete unprofitable. To counteract this cost, GNP can be blended with other less expensive cement replacement materials, such as fly ash. This can lower the cost and improve concrete’s environmental sustainability, as cement is the most expensive and least user-friendly constituent material.

Historically, the mechanical properties of concrete have been predicted using empirical or analytical models based on laboratory experiments. These models are often limited to specific material compositions and ambient conditions and require large amounts of experimental data. Furthermore, the complexity of concrete’s mechanical properties and their numerous influencing factors make it difficult to create prediction models that are both accurate and widely applicable. Recently, artificial intelligence (AI) approaches, especially machine learning (ML), have gained widespread recognition in civil engineering because they are proficient in detecting complex relationships and patterns within large datasets [37]. AI techniques have demonstrated remarkable success in forecasting the properties and behaviors of various construction materials, including conventional concrete. Numerous studies have been conducted to predict the mechanical properties of concrete. A summary of some of these investigations is provided below. Al-Shamiri, Kim [38] applied ELM to forecast the compressive strength (CS) of high-strength concrete (HSC); the technique’s fast learning capability, as well as its good generalization performance, were affirmed. In their recent study, Hameed and Al Omar [39] established a mathematical equation to represent the CS of HSC using HORSM, with polynomials of 2nd, 3rd, 4th, and 5th degrees used. Moreover, Song and Ahmad [40] collected several experimental data and employed ML to predict the CS and analyzed the physio-chemical properties of the concrete containing fly ash. In comparison with the physics-based Q-F equations, Wen and Wang [41] found that an electronegativity difference-based model exhibits an enhanced efficiency for SS strengthening in HEAs. Furthermore, the work of Huang and Zhang [42] focused on environmentally sustainable rubberized concrete, which used an artificial neural network (ANN) to simulate the design correlation between the concrete mix components and multiple mechanical properties simultaneously. Meanwhile, Ahmad, Ahmad [43] utilized bagging, AdaBoost, gene expression programming, and decision tree models to predict the CS of concrete containing different supplementary cementitious materials. Yu, Fang [44] adopted Bayesian model updating and metaheuristic ML techniques to accurately predict the mechanical properties and optimize the mix proportions of concrete for improved performance and sustainability. Zhao, Hong [45] employed XGBoost and NSGA-II ML algorithms ML to predict and optimize the strength, cost, and carbon emissions of self-compacting concrete incorporating recycled aggregates. Cao, Fang [46] focused on numerous ML techniques to determine the magnitude of CS in GC to minimize the experimental time and efforts required by researchers to carry out a study. Finally, Huang, Sabri [47] developed a new firefly algorithm (FA) and random forest (RF)-based ML model for predicting the CS of cement–fly-ash–slag ternary concrete and confirmed that the proposed method can predict the CS for up to a value of 100 MPa with a high level of accuracy. Combining all this research, this paper demonstrates various practical domains in which ML models can be applied to predict the mechanical properties of concrete and provide accurate results in less time than conventional approaches.

PW, if not properly disposed of or recycled, poses serious threats and environmental concerns due to its inability to decompose naturally. A proper way to recycle PW is by grinding it to smaller sizes and using it as an alternative to fine and coarse aggregates in concrete. This will help address the shortcomings related to PW disposal and sustainability of the natural aggregates. Although PW offers several benefits when used as a substitute for natural aggregates in concrete, the major concerns are the reduction in the mechanical and durability performance of concrete with the addition of PW. To mitigate these effects, highly pozzolanic materials are typically used either as additive or partial substitutes for cement. Limited studies have utilized nanomaterials from the graphene family as additives to mitigate the negative effects of PW in concrete. However, some studies are available that used GNP and fly ash to mitigate the negative effects of PW in concrete. Some studies have employed experimental methods and response surface methodology techniques [5,35]. However, there is a significant knowledge gap to fill by utilizing various complex ML approaches to optimize and predict the properties of PW concrete modified with GNP and fly ash. Hence, in this study, different advanced ML approaches were adopted to predict and optimize the mechanical properties of PW concrete modified with GNP and fly ash.

2. Materials and Methods

2.1. Materials

The materials, experiments, and results used in this study were obtained from earlier research conducted by Adamu, Trabanpruek [5] and Adamu, Trabanpruek [35], where Type I cement was adopted as the main binder materials, adhering to the requirements of ASTM C150M-15 [48]. For the SCM, Class C fly ash was adopted. The fly ash adhered to the standard requirements of ASTM C618 [49]. Graphene nanoplatelet (GNP) was used as an additive to binder materials in the concrete. The GNP was in powdered form with a grey/black appearance, as shown in Figure 1a. The GNP has a carbon content greater than 99%, an average diameter of 2–7 μm, a thickness of 2–10 nm, and a specific surface area of 16.48 m²/g [5,35]. The aggregates used were fine and coarse aggregates, both adhering to the standard specifications of ASTM C33 [50]. Well-graded river sand with a maximum size of 4.75 mm, a specific gravity of 2.64, and a bulk density of 1560 kg/m³ was utilized as the fine aggregate. For the coarse aggregate, a well-graded crushed gravel was utilized. The coarse aggregate had a maximum size of 19 mm, a specific gravity of 2.67 and a bulk density of 1465 kg/m³. The plastic waste (PW) was processed from waste polypropylene. Two sizes of the PW, 9.5 mm and 12 mm, as shown in Figure 1b, were combined in equal proportions (50% each) and used as partial substitutes for coarse aggregate. The PW had a bulk density of 920 kg/m³ and a specific gravity of 0.9.

2.2. Mix Proportioning

The mixes developed in the studies by Adamu, Trabanpruek [35] and Adamu, Trabanpruek [5] were adopted as the experimental mixes for this work. The control mix was developed in adherence to the methods outlined in ACI 211.1-91, targeting a strength of 37 MPa at 28 days. To generate the other mixes, fly ash was used to partially substitute cement in varying proportions of 0%, 20%, 40%, 60%, and 80% by volume. PW was used as a partial substitute to coarse aggregate in proportions of 0%, 15%, 30%, 45%, and 60% by volume. GNP was introduced as an additive to the cementitious materials in proportions of 0%, 0.075%, 0.15%, 0.225%, and 0.3% by mass of cementitious materials. A total of nineteen (19) mixes were generated, as shown in

Table 1. Mix Proportioning as adopted from [5,35].

Mix No	Variables (%)			Constituent Materials (kg/m3)
	PW	Fly Ash	GNP	Cement	Fly Ash	Fine Agg.	Coarse Agg.	PW	GNP	Water	S.P.
Control	0	0	0	420.7	0	653.9	1176.9	0	0	159.4	4.21
1	30	40	0.15	252.4	122.9	653.9	823.9	43.7	0.56	159.4	3.75
2	0	40	0.15	252.4	122.9	653.9	1176.9	0.0	0.56	159.4	3.75
3	45	60	0.075	168.3	184.3	653.9	647.3	65.5	0.26	159.4	3.53
4	30	40	0.3	252.4	122.9	653.9	823.9	43.7	1.13	159.4	3.75
5	60	40	0.15	252.4	122.9	653.9	470.8	87.4	0.56	159.4	3.75
6	15	20	0.225	336.6	61.4	653.9	1000.4	21.8	0.90	159.4	3.98
7	30	40	0.15	252.4	122.9	653.9	823.9	43.7	0.56	159.4	3.75
8	30	40	0.15	252.4	122.9	653.9	823.9	43.7	0.56	159.4	3.75
9	45	20	0.225	336.6	61.4	653.9	647.3	65.5	0.90	159.4	3.98
10	30	0	0.15	420.7	0.0	653.9	823.9	43.7	0.63	159.4	4.21
11	45	20	0.075	336.6	61.4	653.9	647.3	65.5	0.30	159.4	3.98
12	15	60	0.225	168.3	184.3	653.9	1000.4	21.8	0.79	159.4	3.53
13	30	40	0.15	252.4	122.9	653.9	823.9	43.7	0.56	159.4	3.75
14	15	60	0.075	168.3	184.3	653.9	1000.4	21.8	0.26	159.4	3.53
15	45	60	0.225	168.3	184.3	653.9	647.3	65.5	0.79	159.4	3.53
16	15	20	0.075	336.6	61.4	653.9	1000.4	21.8	0.30	159.4	3.98
17	30	40	0.15	252.4	122.9	653.9	823.9	43.7	0.56	159.4	3.75
18	30	80	0.15	84.1	245.8	653.9	823.9	43.7	0.49	159.4	3.30
19	30	40	0	252.4	122.9	653.9	823.9	43.7	0.00	159.4	3.75

PW = Plastic waste, GNP = Graphene nanoplatelets, Agg = Aggregate, S.P. = Superplasticizer.

, based on the data obtained from previous studied [5,35]. The results of these mixes, after preparing and testing in the laboratory, were used for the modeling and analysis.

2.3. Samples Preparations and Experimental Testing

The sample preparation methods were obtained from studies by Adamu, Trabanpruek [5] and Adamu, Trabanpruek [35]. The batching, weighing, and mixing procedures were carried out using the methods outlined in ASTM C192M-15 [51]. Before mixing the concrete, the superplasticizer and the GNP were combined with half of the mixing water and manually stirred with a stirring rod. The GNP mixture was then sonicated using a 60 Hz capacity Ultrasonicator for about 1 h to ensure complete dispersion of the GNP particles and prevent their agglomeration, as shown in Figure 2 [5,35]. The workability of the fresh concrete was measured using a slump test based on ASTM C143M-20 [52] guidelines. The fresh density of the concrete was also tested according to the guidelines of ASTM C138M [53]. After the fresh tests, the concrete was cast into the designated molds and left in the laboratory for 24 h to harden. Once hardened, the concrete samples were demolded and submerged in water for up to 28 days prior to testing.

The hardened concrete samples were tested for compressive strength using the methods outlined in the BS EN 12390-3 [54] code. Cubic samples measuring 100 mm were prepared and cured for 28 days in water before testing. For determining the split tensile strength, the methods specified in BS EN 12390-6 [55] were followed. Cylindrical concrete samples with a diameter of 100 mm and a height of 200 mm were prepared and cured in water for 28 days before testing. The flexural strength test was performed following the procedures outlined in ASTM C293/C293M [56], using prismatic samples with dimensions of 100 mm × 100 mm × 500 mm. These samples were produced and cured in water for 28 days before testing. The water absorption test was conducted in accordance with the methods specified in ASTM C642 [57] using 10 cm cubes that were cured in water for 28 days before the test.

2.4. Proposed AI-Based Methodology

This methodology combines Gaussian Process Regression (GPR) and Elman Neural Network (ELNN) to leverage their complementary strengths in forecasting the mechanical properties of concrete (MPC). Initially, GPR was employed to model complex non-linear relationships and capture the inherent uncertainties present in concrete property datasets. After preprocessing the data, GPR assimilates intricate patterns within the information, laying a robust foundation for prediction. Subsequently, an ELNN was introduced to capture the temporal dependencies in concrete properties. By leveraging the sequential nature of the data, the ELNN enhances the model’s ability to identify patterns that evolve over time. The integration of GPR and ELNN is expected to yield a hybrid model that excels not only in capturing non-linear relationships and uncertainties but also in encompassing temporal dynamics, resulting in a more accurate and flexible predictor for concrete mechanical properties. The use of data-driven algorithms in the field of process engineering has seen significant progress in recent years, particularly in estimating MPC. The foundation of this AI-based approach relies on data acquisition from open-source data, fieldwork, and laboratory results. In this study, two models, ELNN and GPR, were employed to forecast the MPC, encompassing compressive strength (CS), splitting tensile strength (STS), flexural strength (FS), and modulus of elasticity (ME). Figure 3 illustrates the step-by-step methodology followed in this study. The proposed modeling technique employs traditional feature extraction methods to simulate concrete’s mechanical properties by utilizing the correlation coefficient between the parameters.

2.4.1. GPR Model

The methodology commonly used for approximating functions is referred to as Gaussian Process Regression (GPR). By leveraging the function space, the Gaussian Process (GP) can effectively perform Bayesian inference and describe the distribution of the function [58,59]. GPR, along with the powerful Bayesian optimization technique frequently employed in machine learning, exemplifies nonparametric models capable of effectively evaluating black-box functions and ensuring an accurate fit [60] The precision of the estimations produced by the GPR model is significantly influenced by the nature of the kernel function, making it well-suited for handling non-linear data formats [61,62]. At its essence, GPR operates under the assumption of a Gaussian distribution across the input variables (X) and output variables (Y). GPR constructs a model that relates the target variable to the input variables, with each distinct point in the input space associated with both a mean and a variance. The mean function represents the predicted value of the target variable, while the variance function captures the uncertainty or error in the predictions.

2.4.2. Elman Neural Network (ELNN)

Elman introduced the Elman neural network (ELNN) in 1990. This neural network is a type of recurrent neural network (RNN) consisting of numerous interconnected neurons. It was derived from the fundamental structure of the backpropagation neural network (BPNN) and includes an additional hidden layer. This added layer functions as a one-step delay unit, enabling the network to retain memory. Common network configurations are established based on the connections among neurons in a network. These include feedforward, recurrent, and self-organizing neural networks. Among them, the feedback network is distinctive as it transmits information in both directions, forward and reverse. Feedback data can affect neurons across different network layers or remain confined to a single layer. BPNN is a widely recognized multi-layer feedforward neural network with excellent generalization capabilities and powerful non-linear mapping characteristics. During the training process, the network weights are adjusted through the forward propagation of data and the backward flow of error signals. The weights and thresholds are optimized to ensure that the predicted output of the BPNN gradually approaches the target output. The Elman network’s hierarchical architecture typically consists of four distinct layers. Signals are transmitted to the hidden layer from the input layer, which is composed of linear neurons. Within the hidden layer, the signal is processed using an activation function. The subsequent context layer serves as a one-step delay operator, storing the previous values of the hidden layer’s output. This layer also incorporates a feedback feature. Finally, the output layer generates the final results [63,64]. Further insights into ELNN can be found in Wang, Zhang [65], and Selvi and Chandrasekaran [66]. The architecture of the ELNN is illustrated in Figure 4.

2.4.3. SHAP (Shapley Additive Explanations)

SHAP, an Explainable AI technique, aims to explain the output of machine-learning (ML) models by attributing the model’s prediction to its constituent features. It describes how each feature influences the final prediction and is based on cooperative game theory. SHAP relies on Shapley values, a concept from cooperative game theory that quantifies each player’s contribution in a cooperative game. In this concept, features are treated as “players” in a cooperative game, where each feature’s “payment” or contribution to prediction-making is assessed. SHAP values are assigned to each feature to reflect its influence on the prediction for every data instance. By explaining a specific prediction rather than just the overall model behavior, SHAP offers a local interpretation. This technique is compatible with any machine-learning model, such as neural networks, SVMs, tree-based models, etc. SHAP functions by generating an interpretability model that approximates the behavior of the complex underlying model. To effectively compute Shapley values, it employs a sophisticated technique that considers each feature combination and its impact on the prediction. The influence of each feature is assessed by comparing the model’s output with and without each feature. By determining the Shapley value for each feature and analyzing its contribution to the final prediction, SHAP identifies the relevance of each feature for a specific prediction [67,68].

2.4.4. Performance Evaluation Criteria

A pre-established array of criteria and measurements are used to assess the effectiveness, efficiency, and quality of predictive outcomes. These criteria provide a foundation for assessing performance and aiding decision-makers in making well-informed choices regarding improvements, rewards, and upgrades. In this study, six statistical metrics were employed to determine the accuracy of the models: mean square error (MSE), mean absolute error (MAE), mean absolute percentage error (MAPE), Pearson correlation coefficient (PCC), correlation coefficient (R), and Root mean square Error (RMSE).

Table 2. Performance criteria of the models.

Name	Formula	Range
R	${\displaystyle \frac{N\left(\sum Q_O{Q}_P\right)-\left(\sum Q_O\right)\left(\sum Q_P\right)}{\sqrt{[N\sum {Qo}^2](\sum {Qo)}^2[N\sum {Qp}^2](\sum {Qp)}^2}}}$	(−∞ < R< 1)
PCC	${\displaystyle \frac{\sum (Q_{0 }-Q_{om})(Q_p-Q_{pm})}{\sqrt{{(Q_p-Q_{pm})}^2-{(Q_0-Q_{0m})}^2}}}$	(−∞ < PCC < 1)
MSE	${\displaystyle \frac{\sum _{i=1}^N{Q_{\left(p\right)}-Q_{\left(o\right)})}^2}{N}}$	(0 < MSE < ∞)
MAE	${\displaystyle \frac{\sum _{i=1}^N{|Q}_{\left(p\right)}-Q_{\left(o\right)}|}{N}}$	(0 < MAE < ∞)
MAPE	${\displaystyle \frac{100}{N}} {\sum }_{i=1}^N\left|{\displaystyle \frac{Q_{\left(O\right)}-Q_{\left(P\right)}}{Q_{\left(o\right)}}}\right|$	(0 < MAPE < 100)
RMSE	$\sqrt{{\displaystyle \frac{\sum _{i=1}^N{Q_{\left(p\right)}-Q_{\left(o\right)})}^2}{N}}}$	(0 < MSE < ∞)

where Q_(p) and $Q_p$ indicates the predicted mechanical property of concrete, $Q_{pm}$, Predicted mean mechanical property of concrete, Q_(o) observed mechanical property of concrete, $Q_{0m}$ indicates the observed mean mechanical property of concrete, and N signifies the total number in the data set.

illustrates the defined ranges of the performance benchmarks, which are widely used in research to evaluate the expected outcomes of the model.

3. Results and Discussion

3.1. Experimental Results

The experimental results of this study were explained in detail in previous research by Adamu and Trabanpruek [5]. From the summary of results in

Table 3. Experimental Results [5].

Mix	PW (%)	Fly Ash (%)	GNP (%)	Slump (mm)	FD (kg/m3)	CS (MPa)	STS. (MPa)	FS (MPa)	WA (%)	ME (GPa)
Control	0	0	0	140	2497	37.81	3.32	8.31	3.43	37.00
M1	30	40	0.15	155	2275	31.66	3.29	7.53	3.77	32.97
M2	0	40	0.15	145	2328	40.14	3.88	9.77	2.71	35.69
M3	45	60	0.075	185	2155	30.11	2.02	6.96	5.44	27.59
M4	30	40	0.3	130	2300	35.2	3.65	8.01	3.36	26.42
M5	60	40	0.15	170	2005	26.86	2.28	8.15	4.64	21.37
M6	15	20	0.225	125	2380	41.59	4.23	8.50	2.12	43.02
M7	30	40	0.15	160	2295	33.32	3.22	7.61	4.09	33.13
M8	30	40	0.15	148	2306	27.35	3.04	7.12	3.86	19.06
M9	45	20	0.225	145	2285	34.3	3.14	7.86	2.98	23.76
M10	30	0	0.15	158	2365	39.21	3.96	8.81	2.76	37.63
M11	45	20	0.075	160	2279	36.11	2.95	7.92	4.16	15.95
M12	15	60	0.225	145	2170	36.71	3.26	7.73	3.48	42.13
M13	30	40	0.15	150	2260	34.64	3.03	7.90	3.45	34.87
M14	15	60	0.075	155	2153	36.27	2.86	8.33	3.73	34.19
M15	45	60	0.225	150	2056	30.28	3.02	8.32	4.44	26.60
M16	15	20	0.075	150	2335	37.08	3.47	10.59	2.56	35.85
M17	30	40	0.15	165	2280	30.49	3.16	7.79	3.54	33.13
M18	30	80	0.15	200	2105	25.46	2.33	7.56	5.10	22.44
M19	30	40	0	190	2250	26.77	2.16	7.08	5.04	27.09

PW = Plastic Waste, GNP = Graphene Nanoplatelet, FD = Fresh Density, CS = Compressive Strength, STS = Split tensile strength, FS = Flexural Strength, WA = Water Absorption.

, it can be observed that PW enhanced the workability of the concrete by increasing its slump values, with the mixes containing higher PW contents exhibiting greater slump values. Similarly, partial substitution of cement with fly ash also improved the workability of the concrete. In contrast, the addition of GNP reduced the workability e, which was ascribed to its larger surface area, causing it to absorb more water during mixing and reduce the concrete’s slump. The increase in slump with PW incorporation was due to the lower water absorption of the PW in comparison to the natural aggregate it replaced. The inclusion of PW and fly ash in the concrete reduced its fresh density, which was ascribed to the lower densities of the PW and fly ash compared to the coarse aggregate and cement, respectively, which they partially replaced. The summary of the results also indicates that the compressive strength, split tensile strength, flexural strength, and modulus of elasticity of the concrete decreased, while its water absorption increased with the partial substitution of coarse aggregate with PW and cement with fly ash. The reduction in the mechanical properties and increase in water absorption due to PW were ascribed to the weak bonding between the cement paste and the rubber particles caused by the smooth texture of the rubber. This created some weak interfacial transition zones in the cement matrix, leading to premature failure. Additionally, PW increased the pore volume in the cement matrix due to its hydrophobic nature, therefore reducing strength and increasing water absorption. The slower and weaker pozzolanic reaction of the fly ash at early ages was responsible for the reduction in the mechanical properties and increase in water absorption. From the results in Table 3, the addition of GNP to concrete containing PW and fly ash enhanced the mechanical strengths and modulus of elasticity (ME) of the concrete. Moreover, the GNP reduced the water absorption of the concrete. These improvements in concrete properties with the addition of GNP were attributed to the following reasons: the larger surface area of GNP makes it act as a filler material, filling the pores created by PW, densifying the concrete microstructure, and therefore enhancing its strength and reduced its water absorption. Additionally, the high reactivity of GNP enables it to react with SiO₂ and Al₂O₃ from fly ash and cement, consuming Portlandites (Ca(OH)₂) to produce additional calcium-silicate-hydrates (C-S-H) and calcium-aluminate-hydrates (C-A-H), which are the primary compounds for strength development and densification of the concrete’s microstructure.

3.2. Preliminary Analysis

This section explores preprocessing, model construction, and numerical findings derived from the data source. Utilizing ELNN and GPR models, the research examined the mechanical properties of concrete (MPC) in relation to other components. The development of the machine-learning models (ELNN and GPR) was carried out using the MATLAB R2023a toolkit, while E-Views 13.0 was employed for data preprocessing and post-processing. The training and validation of the ELNN and GPR models were conducted using MATLAB code. Achieving effective generalization required the appropriate selection of the model’s structure. Accordingly, such as setting the maximum number of iterations (1000), adjusting the learning rate (0.01), and configuring the mean square error (MSE) threshold (0.0001) were applied to the ELNN to handle hypersensitivity. The ELNN layer structure was identified using the formula (2n1/2 + m) to (2n + 1), where n represents the input neurons and m denotes the output nodes. A critical aspect of constructing an ELNN lies in establishing an appropriate number of hidden nodes.

Some studies propose using the expression (n + 1) to (n + 2) to mitigate the excessive reliance on trial-and-error methods, while others argue that hidden nodes could follow an elliptical structure. In this study, a range of 3–8 hidden nodes, 20–80 calibration epochs, and activation functions were used to determine the optimal ELNN configuration. To address overfitting, the dataset was partitioned into folds, with the performance of each fold assessed. GPR was implemented with a 10 k-fold cross-validation prediction speed of 120 obs/sec. Given the volatile nature induced by multiple variables and the characteristics of the raw water requiring treatment, the interconnections among the MPC constraints within a complex system may not exhibit linearity. The correlation between the independent and dependent variables is illustrated in Figure 5a–d (Correlation matrix). To succinctly convey the fundamental characteristics of the dataset, make comparisons between variables or groups, identify anomalies, maintain data accuracy, and help in decision-making processes,

Table 4. Statistical summaries of the datasets and essential data needed for model development.

Parameters	Mean	Median	Mode	Standard Deviation	Sample Variance	Kurtosis	Skewness	Minimum	Maximum
PW	28.5	30	30	15.0	223.7	−0.2	−0.1	0	60.0
FA	38	40	40	19.9	397.7	−0.2	−0.1	0	80.0
GNP	0.13625	0.15	0.15	0.1	0.0	0.0	0.1	0	0.3
W/C	0.4985	0.5	0.5	0.0	0.0	0.0	0.3	0.45	0.6
CP	9.5	5	0	11.0	120.8	−0.8	1.0	0	28.0
Density	631.521	0	0	1097.2	1,203,847.6	−0.6	1.2	0	2770.0
Slump	39.1167	0	0	68.6	4704.4	−0.4	1.2	0	210.0
CS	20.2353	24.065	0	13.1	171.6	−1.0	−0.5	0	46.0
STS	1.91187	2.20748	0	1.3	1.6	−1.1	−0.4	0	4.6
FS	3.76457	2.135	0	3.9	14.9	−1.8	0.1	0	11.0
ME	14.0927	6.93628	0	14.9	221.2	−1.6	0.3	0	44.1

provides statistical summaries of the datasets and essential data required for the model development. These summaries facilitate data exploration and help analysts and researchers to formulate intuitive interpretations from the data.

Furthermore, following an exhaustive analysis of the data, the dataset underwent normalization to mitigate data redundancy and enhance data integrity, utilizing Equation (1) as illustrated below.

$$X_i={\displaystyle \frac{x_{initial-} x_{minnum}}{x_{\mathrm{maxnum}-}{x}_{minnum}}}$$

(1)

where X_initial signifies the data that will be normalized, X_minnum and X_maximum denote the minimum and maximum data, respectively, in the variable range, and X_i presents the normalized data.

From Figure 5, among all the dependent variables used to develop the model (PW, FA, GNP, W/C, CP, density, and slump), it was found that the highest correlation coefficients were depicted on slump and density, which show a good relationship with the targeted variables, when modeling compressive strength (CS) and curing period (CP), with values of −0.8847 and −0.8929, respectively. These coefficients indicate an inverse relationship. CP also demonstrated a significant correlation, although in the opposing direction, suggesting that the dependent variable is stationary. For modeling the flexural strength (FS), the correlation coefficient (CC) of CP and density were found to be 0.7832 and −0.56385, respectively, followed by a slump. For the modulus of elasticity (ME), CP and density showed the highest CC values of 0.7822 and −0.5476, respectively, followed by a slump. Similarly, for the splitting tensile strength, the highest CC values were observed in slump and density, with CC of −0.8560 and −0.8639, respectively, followed by CP. Evaluating Equations (2) and (3) identify the input feature combination to be used as inputs in the modeling ELNN and GPR models based on sensitivity analysis and CC.

$$\text{CS}, \text{FS}, \text{and} \text{STS}=\left\{\begin{array}{c}M1=CP+GNP \\ M2=Density+Slump+PW+{\displaystyle \frac{W}{C}}+FA \\ M3=Density+Slump+CP+PW+{\displaystyle \frac{W}{C}}+FA+GNP \\ \end{array} \right.$$

(2)

$$\mathrm{ME}=\left\{\begin{array}{c}M1=CP \\ M2=Density+Slump+PW+{\displaystyle \frac{W}{C}}+FA+GNP \\ M3=Density+Slump+CP+PW+{\displaystyle \frac{W}{C}}+FA+GNP \\ \end{array} \right.$$

(3)

The designations M1, M2, and M3 represent the various dependent configurations utilized for modeling training. The terms density, slump, CP, PW, W/C, FA, and GNP denote the input parameters, while CS, FS, ME, and STS refer to the output parameters. Through the application of an external validation procedure, a total of 240 datasets were employed in this study, divided into calibration (70%) and validation (30%) sets. Furthermore, it is imperative for any combination of models to incorporate a positive CC as an input to assess its impact on prediction accuracy. Similarly, the investigation of negative CC is also necessary. In conclusion, there is a need for a comprehensive integration of both positive and negative CC values to evaluate potential enhancements in prediction accuracy and to identify any adverse effects of negative CC on predictive performance.

3.3. Results of the Data-Driven Model

In this research, GPR and ELNN are used together because they have complementary strengths in predicting the mechanical properties of HVFAC. GPR is among the best models for dealing with uncertainties, generating accurate predictive intervals and making reliable predictions even with the significant levels of data nonlinearity. Moreover, GPR is an effective statistical approach for making predictions primarily based on informational factors. It is a type of machine-learning algorithm that falls into the broader category of Bayesian strategies. GPR leverages the concept of Gaussian methods to model the relationship between inputs and outputs, making it particularly useful in numerous prediction tasks. On the other hand, ELNN is a type of recurrent neural network suited for estimating complex patterns and dependencies between variables, making it ideal for modeling complex and sequential data sets. By integrating ELNN’s capability to recognize complex with GPR’s strength in quantifying uncertainties, the combined models achieve improved prediction efficiency and reliability, especially for outputs such as the compressive strength and the modulus of elasticity. This combination ultimately enhances the generalizability and effectiveness of the model in addressing the variability and complex nature of HVFAC’s mechanical behavior.

Table 5. (a) Results of standalone models for CS modeling in calibration and verification. (b) Results of standalone models for FS modeling in calibration and verification. (c) Results of standalone models for ME modeling in calibration and verification. (d) Results of standalone models for ME modeling in calibration and verification.

(a)
Calibration Phase CS
Model	GPR-M1	GPR-M2	GPR-M3	ELNN-M1	ELNN-M2	ELNN-M3
R	0.9559	0.9703	0.9930	0.9502	0.9713	0.9930
PCC	0.9554	0.9700	0.9929	0.9497	0.9710	0.9930
MSE	0.0063	0.0071	0.0010	0.0071	0.0083	0.0010
MAE	0.0519	0.0606	0.0225	0.0575	0.0633	0.0216
MAPE	10.1639	12.1774	4.0198	11.4610	13.2311	4.0734
RMSE	0.0797	0.0844	0.0320	0.0844	0.0914	0.0319
Verification phase CS
Model	GPR-M1	GPR-M2	GPR-M3	ELNN-M1	ELNN-M2	ELNN-M3
R	0.7046	0.8579	0.9505	0.6070	0.8658	0.9459
PCC	0.5786	0.8071	0.9339	0.4151	0.8172	0.9283
MSE	0.0129	0.0181	0.0025	0.0164	0.0154	0.0028
MAE	0.0951	0.1139	0.0396	0.1080	0.1062	0.0410
MAPE	15.0112	15.8288	5.9636	17.2098	15.0184	6.1183
RMSE	0.1137	0.1345	0.0499	0.1279	0.1242	0.0527
(b)
Calibration Phase FS
Model	GPR-M1	GPR-M2	GPR-M3	ELNN-M1	ELNN-M2	ELNN-M3
R	0.9853	0.4787	0.9973	0.9817	0.4768	0.9909
PCC	0.9853	0.4769	0.9973	0.9817	0.4750	0.9909
MSE	0.0026	0.0855	0.0005	0.0032	0.0961	0.0016
MAE	0.0220	0.2240	0.0094	0.0270	0.2194	0.0164
MAPE	3.5068	7.8800	1.3529	3.8288	6.6083	1.9067
RMSE	0.0506	0.2923	0.0217	0.0566	0.3100	0.0405
Verification phase FS
Model	GPR-M1	GPR-M2	GPR-M3	ELNN-M1	ELNN-M2	ELNN-M3
R	0.8428	0.7869	0.9684	0.7783	0.6351	0.8995
PCC	0.6930	0.5644	0.9428	0.5499	0.4253	0.8151
MSE	0.0046	0.0771	0.0010	0.0062	0.0622	0.0031
MAE	0.0483	0.2658	0.0260	0.0561	0.2303	0.0409
MAPE	6.7463	36.4975	3.6733	7.7968	31.7615	5.5832
RMSE	0.0675	0.2777	0.0314	0.0788	0.2493	0.0554
(c)
Calibration Phase ME
Model	GPR-M1	GPR-M2	GPR-M3	ELNN-M1	ELNN-M2	ELNN-M3
R	0.9726	0.4846	0.9945	0.9726	0.2998	0.9891
PCC	0.9726	0.4829	0.9945	0.9726	0.2968	0.9890
MSE	0.0044	0.0752	0.0009	0.0043	0.0894	0.0017
MAE	0.0287	0.2098	0.0144	0.0280	0.2739	0.0183
MAPE	4.9311	7.6619	2.1563	4.9164	11.1765	2.7859
RMSE	0.0660	0.2743	0.0294	0.0654	0.2990	0.0416
Verification phase ME
Model	GPR-M1	GPR-M2	GPR-M3	ELNN-M1	ELNN-M2	ELNN-M3
R	0.6101	0.8289	0.9665	0.6067	0.1047	0.9211
PCC	0.5115	0.8044	0.9584	0.5115	−0.1370	0.9015
MSE	0.0204	0.0782	0.0021	0.0206	0.1229	0.0049
MAE	0.1199	0.2531	0.0366	0.1203	0.3078	0.0573
MAPE	20.4107	35.7624	5.7617	20.5905	43.4695	9.0269
RMSE	0.1428	0.2797	0.0457	0.1436	0.3506	0.0697
(d)
Calibration Phase STS
Model	GPR-M1	GPR-M2	GPR-M3	ELNN-M1	ELNN-M2	ELNN-M3
R	0.9311	0.9627	0.9856	0.9214	0.9596	0.9850
PCC	0.9305	0.9623	0.9855	0.9207	0.9593	0.9849
MSE	0.0094	0.0076	0.0020	0.0106	0.0079	0.0021
MAE	0.0653	0.0589	0.0286	0.0682	0.0571	0.0292
MAPE	14.1846	13.7567	5.6602	15.7122	13.9598	5.8760
RMSE	0.0972	0.0869	0.0449	0.1029	0.0891	0.0459
Verification phase STS
Model	GPR-M1	GPR-M2	GPR-M3	ELNN-M1	ELNN-M2	ELNN-M3
R	0.7241	0.7975	0.9482	0.6684	0.7564	0.9338
PCC	0.6489	0.7401	0.9353	0.5640	0.6843	0.9173
MSE	0.0140	0.0208	0.0029	0.0163	0.0217	0.0037
MAE	0.0904	0.1227	0.0439	0.1001	0.1243	0.0476
MAPE	16.1952	18.6285	7.5270	17.9350	19.0498	8.2496
RMSE	0.1183	0.1442	0.0540	0.1278	0.1472	0.0609

a presents the calibration and verification predictions made by ELNN and GPR for CS. The data in Table 5a indicates that the performance indicators used in this study, including MSE, MAPE, MAE, and RMSE, are unitless, while R and PCC are dimensionless due to the normalization step in the modeling process. The remarkable responses of the pragmatic AI-based and linear models to the various combination models CS (MPa) are highlighted in Table 5a. During the calibration phase, the prediction accuracy for CS (MPa) varied between 40 and 50%, 50 and 70%, 70 and 80%, and 80 and 100%, while PCC and MAE ranged from 0.02 to 0.115, respectively. Notably, during the modeling phase, ELNN-M3 demonstrated the highest predicted accuracy for both R and PCC (0.9930), along with the lowest MAE value of 0.0216 in the calibration phase. In the verification phase, GPR-M3 achieved the highest predicted accuracy, with R and PCC values of 0.9505 and 0.9339, respectively, and the lowest MAE value of 0.0396. From Table 5b, it can be observed that, during the modeling of FS, the prediction accuracy ranged between 40 and 50%, 50 and 70%, 70 and 80%, and 80 and 100%, with PCC and MAE values ranging from 0.009 to 0.24, respectively. During the modeling phase of FS, GPR-M3 exhibited the highest prediction accuracy for both R and PCC (0.9973) and the lowest MAE value of 0.0094 in the calibration phase. In the verification phase, GPR-M3 again displayed superior prediction accuracy, with R and PCC values of 0.9684 and 0.9428, respectively, and the lowest MAE value of 0.026. Similarly, as shown in Table 5c, during the modeling of ME, the prediction accuracy varied between 40 and 50%, 50 and 70%, 70 and 80%, and 80 and 100%, with PCC and MAE ranging from 0.0144 to 0.3 for PCC and MAE, respectively. During the ME modeling phase, GPR-M3 achieved the highest prediction accuracy of both R and PCC (0.9945), with the lowest MAE value of 0.0144 in the calibration phase. In the verification phase, GPR-M3 maintained the highest prediction accuracy, with R and PCC values of 0.9665 and 0.9584, respectively, with the lowest MAE value of 0.0366. Finally, as detailed in Table 5d, during the modeling of STS, the prediction accuracy ranged between 50 and 70%, 70 and 80%, and 80 and 100%, with PCC and MAE values ranging from 0.0286 to 0.122, respectively. In the STS modeling phase, GPR-M3 achieved the highest prediction accuracy for both R and PCC (0.9856 and 0.9855, respectively), along with the lowest MAE value of 0.0286 in the calibration phase. During the verification phase, GPR-M3 once again displayed the highest prediction accuracy, with R and PCC values of 0.9482 and 0.9353 and the lowest value of MAE of 0.0439.

In conclusion, using an equation modeling combination, the modeling of FS demonstrated the highest prediction accuracy in both the calibration and verification phases, with R and PCC values of 0.9973 (calibration) and 0.9684 and 0.9428 (in the verification phase), respectively. This was followed by CS modeling and, lastly, STS modeling. These results highlight the accuracy of machine-learning techniques in predicting the mechanical properties of concrete.

Scatter plots are a vital component of data analysis and graphical visualization, as they provide a clear visual representation of the correlation between two variables. They offer variable selection, model validation, and the identification of patterns, correlations, and outliers. Using scatter plots, it becomes easier to understand data, formulate hypotheses, and effectively communicate findings. The scatter plot of the mechanical properties of concrete models is displayed in Figure 6.

The radar plots in Figure 7 are useful for identifying patterns or trends among multiple variables during the modeling phase. The structure of the polygon reflects the overall characteristic or profile of the item based on the variables plotted. Examples of patterns include shapes that are symmetric, convex, concave, irregular, or indicative of linkages or interactions between multiple components. Additionally, a residual plot known as a diagnostic plot, is a graphical tool used to assess the quality of fit or accuracy of a statistical model. It enables the detection of trends, patterns, or irregularities in the residuals (the variances between the actual and predicted values), providing valuable insights into the model’s behavior and highlighting any issues or assumptions that may have been violated.

3.4. Second Scenario of Modeling STS and FS

When modeling concrete mechanical properties like STS and FS, including the CS as an input variable is crucial. CS serves as a fundamental indicator of concrete’s strength and durability. It influences the internal structure and coherence of the concrete, affecting its ability to withstand tensile and flexural stresses. Incorporating CS in the modeling of STS ensures consideration of the concrete’s overall structural integrity and its resistance to cracking under tensile forces. Similarly, using STS as an input variable in the modeling of FS accounts for the concrete’s ability to withstand bending and shear forces, which are closely related to its tensile performance. These interdependencies result in more accurate and comprehensive predictions of concrete performance in various applications. This section explores the modeling behavior of STS and FS, considering CS as an input variable in STS modeling and CS and STS as input variables in the modeling of FS.

From

Table 6. Calibration and verification results of the STS and FS.

Calibration Phase of STS			Calibration Phase of FS
Model	GPR	ELNN	Model	GPR	ELNN
R	0.9861	0.9849	R	0.9985	0.997283
PCC	0.9860	0.9847	PCC	0.9985	0.997277
MSE	0.0019	0.0021	MSE	0.00026	0.00048
MAE	0.0281	0.0284	MAE	0.00873	0.010056
MAPE	5.6172	5.8442	MAPE	0.97414	1.377609
RMSE	0.0441	0.0461	RMSE	0.01623	0.021915
Verification Phase of STS			Verification phase of FS
Model	GPR	ELNN	Model	GPR	ELNN
R	0.9494	0.9438	R	0.98756	0.95889
PCC	0.9368	0.9302	PCC	0.97754	0.925991
MSE	0.0028	0.0032	MSE	0.00039	0.001325
MAE	0.0433	0.0457	MAE	0.01619	0.025256
MAPE	7.4168	7.7756	MAPE	2.33304	3.579094
RMSE	0.0534	0.0565	RMSE	0.0198	0.036394

, it can be observed that the prediction accuracy of STS, combined with CS as an input variable, ranged from 90% to 100%, with PCC and MAE values of 0.0286 and 0.0281, respectively. During the modeling phase of STS, the GPR model demonstrated the highest prediction accuracy, with R and PCC values of 0.9861 and 0.9860, respectively, and the lowest MAE value of 0.0281 in the calibration phase. In the verification phase, the GPR model also achieved the highest prediction accuracy, with R and PCC values of 0.9494 and 0.9368, respectively, and the lowest MAE value of 0.0433. On the other hand, during the modeling phase of FS, the prediction accuracy ranged from 90% to 100% for R and PCC, with MAE values ranging from 0.00873 to 0.01619. During the modeling phase of FS, the GPR model exhibited the highest prediction accuracy, with R and PCC of 0.9985 for both metrics and the lowest MAE value of 0.00873 in the calibration phase. In the verification phase, the GPR model again achieved the highest prediction accuracy, with R and PCC values of 0.98756 and 0.97754, respectively, and the lowest MAE value of 0.01619.

In comparison with the first-phase modeling of STS and FS, the second-phase modeling shows an increase in the prediction accuracy of STS by 0.04753% and 0.152% for R and PCC, respectively, while the MAE was reduced by 1.86% and 1.27% in calibration and verification phase, respectively. Similarly, the prediction accuracy of FS increased by 0.119% and 1.97% for R and PCC, respectively, and the MAE reduced by 7.29% and 37.7% in the calibration and verification phases, respectively. This highlights the significance of including CS as an input variable when modeling STS and incorporating both CS and STS in FS modeling.

Figure 8 illustrates a box plot, also known as a field-and-whisker plot, which provides a graphical representation of the distribution of a dataset. It provides a visual overview of the dataset’s central tendency, spread, and skewness. The box inside the plot represents the interquartile range (IQR), which encompasses the central 50% of the data. The line within the box marks the median or the central value of the dataset. The whiskers extend from the edges of the box to indicate the range of the data, excluding outliers. Outliers, if present, are shown as individual points beyond the whiskers. Box plots are invaluable for comparing distributions, identifying outliers, and gaining insights into the spread and variability of a dataset, making them a powerful tool for statistical analysis and data visualization.

3.5. Explainable AI Result (SHAP)

Insightful interpretations of the GPR model predictions have been provided using an Explainable AI model that employs SHAP analysis. The contributions that each feature made to the model’s output, or SHAP values, provide a precise image of the variables affecting the predictions. To assist users in identifying the most important feature across the model, Figure 9 presents the summary plot that can be used.

The feature importance plot depicted in Figure 9 summarizes the influence of different features on the model predictions, as ordered along the y-axis. Slump is identified as the most important feature, as indicated by the SHAP values, and varies significantly across all data points. This variability implies that the feature contributes to both the positive and negative directions of the model’s prediction, depending on a particular data point. Density, FA, and CP are also relevant features, but their effects are less significant and more compared to slump. Figure 9 contains a dot for every data point, where the x-axis represents the SHAP value (i.e., the feature’s contribution to the prediction), and the color represents the actual feature value. The red color indicates a higher value, and the blue color indicates a lower value. For instance, in the case of slump, a lower value is associated with a negative impact on the model’s output, while a higher value is associated with a positive impact. This color gradient provides insight t into the relationship between each feature and its importance in predictions, whether at high or low values. Overall, the plot not only highlights which features are important but also demonstrates how different values of these features influence the model’s output.

To further understand the feature importance of each variable, a feature importance bar plot, which shows the average impact of each feature on the model’s output, is presented in Figure 10.

The SHAP feature importance bar plot above represents the ordered mean absolute SHAP values, which indicates the average contribution of features to the model. Slump has the largest mean value, suggesting that it is the most influential feature for determining the model’s output. FA also has significant effects, while density takes the second position and exhibits an inconsistent dependence on its measure. It is observed that CP moderately affects the model, while GNP, W/C, and PW contribute relatively less to the model’s constraints. The height of each bar corresponds to the average SHAP value of the corresponding feature, enabling the bars to be sorted by their height. This plot is instrumental in identifying that the model relies on extensively to make predictions.

According to the findings of this research, GPR models demonstrate superior accuracy in estimating the mechanical properties of HVFAC in the intended applications, combining precision and sustainability. By incorporating more GNP and PW into the enhanced HVFAC, these models exhibit greater sensitivity, verifiable predictive reliability of compressive strength, modulus of elasticity, and other structural properties. This predictive capability makes the concrete mix easier to optimize, and the environmentally friendly use of PW positions it as a strong contender in the green building industry. These results establish a foundation for widespread industrial application and open prospects for further investigation into the properties and performance of HVFAC.

4. Conclusions

This study conducted an extensive analysis of the mechanical properties of high-volume fly-ash concrete (HVFAC) containing PW and GNP by employing various machine-learning (ML) techniques to predict the properties of the HVFAC. Models such as Gaussian Process Regression (GPR) and Elman Neural Network (ELNN) were utilized to predict key properties, including compressive strength (CS), flexural strength (FS), modulus of elasticity (ME), and splitting tensile strength (STS). The findings revealed that the GPR-M3 model (45% PW, 60%Fly ash, 0.075% GNP) exhibited superior prediction accuracy during both the testing and validation phases for all the modeled properties, proving to be the most effective approach.

Combination M3 (45% PW, 60% Fly ash, 0.075% GNP) demonstrated the best performance evaluation criteria. Based on general performance evaluations, the proposed models are a valuable tool for predicting the mechanical properties of concrete containing PW, GNP, and high-value fly ash.

The incorporation of PW as a partial substitute to aggregate, blended with GNP as an additive to cement, significantly enhanced the mechanical properties of HVFAC. The use of these advanced materials and soft-computing models addressed the complexities and nonlinearities inherent in concrete mixtures, offering a cost-effective and environmentally sustainable solution for modern construction.