Predicting the Influence of Pulverized Oil Palm Clinker as a Sustainable Modifier on Bituminous Concrete Fatigue Life: Advancing Sustainable Development Goals through Statistical and Predictive Analysis

Abstract

Currently, the viscoelastic properties of conventional asphalt cement need to be improved to meet the increasing demands caused by larger traffic loads, increased stress, and changing environmental conditions. Thus, using modifiers is suggested. Furthermore, the Sustainable Development Goals (SDGs) promote using waste materials and new technologies in asphalt pavement technology. The present study aims to fill this gap by investigating the use of pulverized oil palm industry clinker (POPIC) as an asphalt–cement modifier to improve the fatigue life of bituminous concrete using an innovative prediction approach. Thus, this study proposes an approach that integrates statistically based machine learning approaches and investigates the effects of applied stress and temperature on the fatigue life of POPIC-modified bituminous concrete. POPIC-modified bituminous concrete (POPIC-MBC) is produced from a standard Marshall mix. The interactions between POPIC concentration, stress, and temperature were optimized using response surface methodology (RSM), resulting in 7.5% POPIC, 11.7 °C, and 0.2 MPa as the optimum parameters for fatigue life. To improve the prediction accuracy and robustness of the results, RSM and ANN models were used and analyzed using MATLAB and JMP Pro, respectively. The performance of the developed model was assessed using the coefficient of determination (R2), root mean square error (RMSE), and mean relative error (MRE). The study found that using RSM, MATLAB, and JMP Pro resulted in a comprehensive analysis. MATLAB achieved an R² value of 0.9844, RMSE of 3.094, and MRE of 312.427, and JMP Pro achieved an R² value of 0.998, RMSE of 1.245, and MRE of 126.243, demonstrating higher prediction accuracy and superior performance than RSM, which had an R² value of 0.979, RMSE of 3.757, and MRE of 357.846. Further validation with parity, Taylor, and violin plots demonstrates that both models have good prediction accuracy, with the JMP Pro ANN model outperforming in terms of accuracy and alignment. This demonstrates the machine learning approach’s efficiency in analyzing the fatigue life of POPIC-MBC, revealing it to be a useful tool for future research and practical applications. Furthermore, the study reveals that the innovative approach adopted and POPIC modifier, obtained from biomass waste, meets zero-waste and circular bioeconomy goals, contributing to the UN’s SDGs 9, 11, 12, and 13.

1. Introduction

The importance of road infrastructure in economic development and connectivity is generally recognized. Bituminous concrete, which is commonly used in road pavements, is crucial to ensuring the longevity and performance of transportation networks [1]. However, fatigue distress in bituminous concrete induced by sustained stress can generate surface issues such as alligator cracking, block cracking, permanent depressions, and rutting, all of which reduce road performance and durability. Researchers and engineers are addressing this difficulty through a variety of approaches [2]. Thicker asphalt layers, high-quality materials, and good pavement design, combined with regular maintenance, can improve the pavement’s ability to take repeated loads and lengthen its lifespan, hence decreasing fatigue [3,4]. Furthermore, researchers are investigating the use of sustainable modifiers in bituminous concrete to improve its performance and decrease pavement distress by ensuring the long-term reliability of bituminous concrete pavements [5,6]. The fatigue life of bituminous concrete is defined as its ability to sustain many loading cycles before failing due to fatigue. Fatigue failure in bituminous concrete occurs when the material is subjected to repeated stress and strain cycles, resulting in the creation and propagation of cracks that impair the pavement’s structural integrity [7]. To improve the fatigue life of bituminous concrete, improved binders, additives, or increased mix designs are frequently used to increase the material’s resistance to repeated loads. The goal is to create asphalt mixtures that can endure traffic and environmental stresses, extending the pavement’s service life [7,8]. The use of modified asphalt binder is a frequent method for addressing this problem, which has been identified as a serious concern in bituminous concrete. Asphalt binder that has been treated with additives has been shown to improve its flexibility, elasticity, and durability [3,7], enhancing bituminous concrete’s resilience to fatigue, reducing the chance of cracking, and extending the pavement’s overall service life [8].

The increasing availability of agro-industrial waste has generated interest in using it to minimize waste and increase construction sustainability. This tendency is consistent with the use of waste as extra construction materials, which lowers costs while preserving pavement performance [9]. Agricultural and industrial by-products with pozzolanic properties, such as fly ash, rice husk ash, oil palm ash, and natural fibers, have attracted interest because of their low cost and potential to improve bitumen and pavement mechanical performance [10,11]. Oil palm biomass waste, particularly oil palm industry clinker (OPIC), has the potential to be used due to its abundance and properties [12,13]. Despite the benefits and environmental limits, its potential is largely underutilized [14]. This study investigates the viability of using pulverized oil palm industry clinker (POPIC) as a modifier. POPIC, a waste product from the oil palm sector, offers an environmentally responsible waste management option when used in the pavement industry [10,15]. Incorporating POPIC into bituminous concrete compositions not only represents an environmentally friendly strategy by reusing agricultural waste, but it also has the potential to improve fatigue life characteristics, which are crucial for road pavements’ ability to endure repeated loading. However, predicting bituminous concrete performance is difficult due to the material’s complicated behavior under a variety of situations. The complex interplay of variables such as temperature changes, traffic loads, ambient conditions, binder aging, aggregate properties, construction procedures, and moisture sensitivity makes predicting bituminous concrete performance difficult. This intricacy highlights the difficulties in anticipating exactly how bituminous concrete will react over time, emphasizing the significance of a complete understanding of its multifaceted response to varied environments.

Conventionally, the One-Factor-at-a-Time (OFAT) methodology is employed as a trial-and-error method for fine-tuning multifactor experiments. In OFAT, one element is altered at a time within an experimental design, while the other factors are held constant [16]. However, OFAT falls short of yielding accurate results since it neglects all interactions among parameters, making it incapable of determining the genuine optimal value. As a solution, response surface methodology (RSM) has been introduced for parameter optimization. RSM reduces the number of experiments required and the complexity of parameter interactions to generate more accurate results [17]. Additionally, predicting the fatigue life features of modified bituminous concrete traditionally relies on empirical models and extensive laboratory testing, which can be time-consuming and costly [18,19]. Thus, the application of the RSM statistical approach has proven to be highly effective, allowing for efficient and accurate performance evaluation with a limited number of tests performed in a short time. Despite its extensive application in trial design and optimization across industries, the paving industry has yet to fully embrace this paradigm. Furthermore, the RSM technique has been used to evaluate its effect on bitumen rheological features and bituminous concrete performance properties [20]. Nonetheless, RSM has limitations because it assumes linear and quadratic connections between factors and responses, which may not be true in all cases. Furthermore, RSM requires rigorous experimental design and may be insufficient for systems characterized by significant nonlinearity.

Machine learning (ML), a rapidly evolving artificial intelligence technology, is gaining popularity and being widely used in the construction sector to forecast material qualities and behaviors. In response to these challenges, soft computing techniques have grown in favor of effective tools for modeling intricate material behaviors [21]. These innovations include several artificial intelligence and machine learning strategies that can learn from data patterns and make predictions without explicit programming [22,23]. The use of Artificial Neural Networks (ANNs) and other soft computing techniques in bituminous concrete is a game-changing method for enhancing a material’s performance and enhancing its properties [23,24]. Various ML techniques have been successfully applied in the construction sector for optimization, modeling, and prediction. By analyzing data, ANNs effectively estimate critical qualities like fatigue life, rutting resistance, and cracking behavior, allowing engineers to build pavements with desired properties [23]. These approaches can also help with material optimization, performance prediction, and cost reduction. ANNs also stimulate the use of sustainable resources, which contributes to environmentally responsible and economically viable road construction processes [25]. Soft computing in bituminous concrete lays the path for data-driven, adaptable, and long-term infrastructure development. Predicting bituminous concrete performance is difficult due to the material’s complex behavior under various conditions [24]. RSM and ANNs are precision techniques that recognize statistical interactions between input and output data. They help us comprehend input–output interactions and material behaviors, making them important for prediction. The partnership of ANNs and RSM in detecting these correlations is effective [19].

This research investigates statistical-based soft computing approaches for evaluating the fatigue life characteristics of bituminous concrete with pulverized oil palm industry clinker (POPIC). To do this, the dataset, which included POPIC content, stress levels, test temperatures, and fatigue life assessments, was statistically analyzed and optimized using RSM to create and train soft computing models, which were then tested using software tools such as MATLAB (Version R2023b) and JMP (pro Version 17.2). Furthermore, statistical techniques were used to assess the accuracy and generalizability of these models, demonstrating their dependability in real-world applications.

The significance of this research is that it addresses the persistent difficulty of stress and fatigue failure in bituminous concrete, which has a substantial impact on its performance throughout its service life. Incorporating POPIC as a sustainable modifier is a potential strategy; yet, correctly predicting the fatigue life of this modified concrete remains difficult. This work also introduces a novel strategy that uses statistically based machine learning approaches to explore the effect of applied stress and temperature on the fatigue life of POPIC-modified bituminous concrete. Furthermore, adopting other software tools for identical research has numerous benefits. The study also increases research credibility by being independent of a single program and gaining additional insight into the study topic by employing different software.

2. Methods

2.1. Materials

A local oil palm waste processing company provided the untreated oil palm industry clinker (OPIC) for this study. Following the removal of contaminants, the OPIC was dried at 100 °C for 24 h. The dry OPIC was then crushed into powder using a pulverizing machine. The pulverized OPIC, known as POPIC, was formed after passing through a No. 200 mm BS filter; its chemical composition is reported in

Table 1. Chemical composition of POPIC.

Chemical Composition	Oxide Content (%)
Fe2O3	4.82
SiO2	63.87
Al2O3	3.96
MgO	2.98
SO3	2.07
CaO	7.84
P2O5	2.94
K2O	6.78
TiO2	1.86

. Additionally, a 60/70 penetration bitumen from the PETRONAS Malaysian facility (Melaka, Malaysia) and crushed granite boulders sourced from a local quarry were used. These aggregates were chosen and tested using Malaysian road construction specifications JKR/SPJ/2008 [26]. Granitic dust was used as the mineral filler, which was then processed at a 0.075 mm standard size.

Table 2. Standard material properties.

Properties	Standards	Unit	Material	Range	Test Value
Absorption	ASTM C 127	%	Coarse aggregate	<2%	0.67
	ASTM C128	%	Fine aggregate	<2%	1.08
Abrasion loss	ASTM C131	%	Coarse aggregate	<30%	23.48
Specific gravity	ASTM C 127	g/m3	Coarse aggregate	-	2.73
	ASTM C 128	g/m3	Fine aggregate	-	2.68
	ASTM C188	g/m3	Filler	-	3.12
Penetration	ASTM D5	dmm	Bitumen	60–70	65
Softening point	ASTMD36	°C		49–56	50.26
Specific gravity	ASTM D70	-		1.01–1.05	1.029
Ductility	ASTMD113	cm		>100	125
Color	Dark grey	-	POPIC
Moisture content	ASTM D2216	%		-	0.94
Specific surface area	ASTM C1274	m2/g		-	1.0843
Loss of ignition	ASTM C311	%		-	6.97
Specific gravity	ASTM C188			-	2.59

shows the properties of the materials used in the study.

2.2. Sample Preparation and Marshall Properties

To prepare the bituminous mixtures, 1200 g of mixed aggregate, filler, and bitumen was heated to 160 °C for optimum blending. The temperature of 160 °C was determined based on the viscosity of the bitumen. The Marshall mix method was used following ASTM D6927 [27], with a nominal maximum aggregate size of 14 mm (AC14) as illustrated in Figure 1. Three duplicate samples were prepared at five bitumen percentages ranging from 4.0% to 6.0% by weight, with 0.5% increments for each mixture type, spanning from 0% to 8% POCF-MB with 2% increments. A gyratory compactor was used for the compaction process. Before performing performance testing, it was ensured that the bituminous concrete satisfied the volumetric and Marshall properties at the optimal bitumen content (OBC), all per JKR’s AC14 requirements [26].

2.3. Indirect Tensile Fatigue Test

The indirect tensile fatigue test (ITFT) was performed in a controlled stress mode following the BS EN 12697-24 standard [28]. Fatigue life is the number of load repetitions required for a sample to split according to stated criteria. The ITFT was carried out using a computer-controlled Universal Material Testing Apparatus (MATTA), IPC Global UTM-30 Servo−Hydraulic Universal Testing Machine (Model 79−PV70B12/I2), Control Group, Milan, Italy. The test included applying a compressive cyclic load to the specimen’s diametrical section using a haversine waveform with a 500 ms repetition period and a 100 ms pulse width. Stress values of 0.2 MPa, 0.3 MPa, and 0.4 MPa, which are widely used in pavement laboratories, were applied. Furthermore, temperatures of 5 °C, 20 °C, and 35 °C were tested to represent typical temperature ranges where fatigue damage occurs in pavements. To achieve the required laboratory temperature, all samples were preconditioned in a controlled temperature chamber for around 120 min before testing.

2.4. Statistical Modeling and Soft Computing Approaches

RSM allows for the systematic modeling and optimization of bituminous concrete fatigue life by thoroughly analyzing the correlations between the input factors. Furthermore, ANN validation enhances the model’s reliability and ability to provide accurate predictions with new data, demonstrating adaptability and generalizability.

2.4.1. Response Surface Methodology

RSM is a statistical approach used to optimize systems having several input parameters that influence the outcome [29]. Stat-Ease Inc.’s Design Expert application (Version 13.0.5.0) via RSM was used in this study for experimental design, statistical analysis, modeling, and optimization of the central composite design technique. Design and data analyses were carried out using a quadratic model created with RSM software (Version 13.0.5.0). The study looked at the impact of three independent numerical variables: POPIC modifier (A) ranging from 0 to 8%, stress levels (B) ranging from 0.2 MPa to 0.4 MPa, and temperatures ranging from 5 °C to 35 °C, all of which were tested at three levels. These variable selections and their respective ranges of interest were informed by the relevant literature and exploratory studies [30,31]. The experiment’s RSM design involved setting low and high levels, which resulted in the creation of twenty-eight random mixes, as shown in

Table 3. Designed RSM fatigue tests for POPIC-modified bituminous concrete.

Mix Design	Input Factors			Responses
	POPIC (%)	Temperature (°C)	Stress Level (MPa)	Logarithmic Fatigue Life
1	4	20	0.3	3.684
2	4	20	0.3	3.781
3	0	35	0.2	3.544
4	0	5	0.2	5.392
5	8	5	0.2	5.484
6	0	20	0.3	3.383
7	0	5	0.4	4.927
8	8	5	0.4	5.321
9	0	5	0.2	5.173
10	4	20	0.2	4.259
11	4	35	0.3	3.395
12	0	35	0.4	2.949
13	8	5	0.4	5.261
14	4	20	0.3	3.691
15	4	20	0.3	3.911
16	4	20	0.3	3.813
17	4	20	0.3	3.723
18	8	35	0.2	3.831
19	8	5	0.2	5.484
20	4	5	0.3	5.209
21	8	35	0.4	3.636
22	4	20	0.4	3.193
23	0	5	0.4	4.858
24	8	20	0.3	3.868
25	0	35	0.4	2.896
26	8	35	0.4	3.086
27	8	35	0.2	3.842
28	0	35	0.2	3.934

. The RSM program repeated the center point five times to improve experiment reliability, analysis, and error evaluation. The fatigue life was used to build the experimental model design. The dependent variables were calculated using a polynomial equation of the second degree. Furthermore, for accurately predicting the reactions, Equation (1), which represents the model’s generalized equation, was used.

$$Y=D+B_1\left(X_1\right)+B_2\left(X_2\right)+B_3\left(X_1^2\right)+B_4\left(X_2^2\right)+B_5\left(X_1{X}_2\right)$$

(1)

The equation is as follows: Y indicates the response (fatigue life), while $X_1$ and $X_2$ are the input factors (POPIC content, temperature, and stress level). The equation includes constants “$D$” and coefficients “$B_1$” through “$B_5$”.

The model’s performance in terms of fatigue life was evaluated using ANOVA (Analysis of Variance). The adequacy of the regression models was assessed using ANOVA metrics such as lack of fit, F-value, and p-value. Additionally, a Design Expert created 3D model graphs based on the model’s predictions to visually explain the impact of input parameters on responses.

2.4.2. Artificial Neural Network

When trained, Artificial Neural Networks (ANNs) mimic human brain data processing skills by capturing detailed nonlinear connections between input and output variables for trend prediction [20,24]. These networks connect input and output using various data structures, resulting in statistical models with multiple neurons capable of performing complex calculations. ANNs perform functions such as predictions, clustering, optimizations, and evaluations of parameter impact [23]. Backpropagation improves ANN precision, and networks typically have input, hidden, and output layers. For this experiment, we used MATLAB R2023b and John’s Macintosh Project (JMP) pro software, each with one hidden layer and backpropagation. To prevent overfitting, the dataset was divided into training, cross-validation, and testing sets using split ratios of 60:20:20 for MATLAB R2023b and 70:15:15 for JMP pro software. In the JMP program, a feed-forward neural network with one hidden layer and backpropagation learning was used. To prevent overtraining and overparameterization, the dataset was divided into subgroups for training, cross-validation, and testing. The Levenberg–Marquardt backpropagation learning approach was used in the MATLAB modeling processes, with the number of neurons purposefully varied to explore various arrangements and determine the optimal structure [32]. The outcomes were then examined to identify which network produced the most effective solution. The ANN study used the same 28 dataset runs created by RSM for model training, validation, and testing, and used performance functions including root mean square error (RMSE) and coefficient of determination ($R^2$) values to evaluate the effectiveness of the ANN models.

2.4.3. Model Efficiency Comparison Parameters

The effectiveness and significance of the generated RSM and ANN models were evaluated using three major statistical performance metrics: the coefficient of determination ($R^2$), which measures the amount of variation explained by the model; the average prediction error (RMSE), which is assessed in the same units as the study data; and the mean relative error (MRE), which is evaluated as a percentage of actual values obtained using Equations (2)–(4). Taylor’s diagram was employed to compare model performance to observable data, focusing on correlation, variance, and bias, while violin charts were utilized as data visualization techniques to understand the distribution of data across different categories or groups.

$$R^2=1-\left({\displaystyle \frac{ {\sum }_{i=1}^s{\left(A_i-M_i\right)}^2}{{\sum }_{i=1 }^s{\left(P_i\right)}^2}}\right)$$

(2)

$$MRE \left(\%\right)={\displaystyle \frac{1}{s}}{\sum }_{i=1}^s\left|100{\displaystyle \frac{A_i-M_i}{A_i}}\right|$$

(3)

$$RMSE=\sqrt{{\displaystyle \frac{1}{s}} {\sum }_{i=1}^s{\left(A_i-M_i\right)}^2 }$$

(4)

In this context, “A_i” denotes the actual laboratory data, “M_i” denotes the model-predicted data values, and “s” denotes the size of the sample.

3. Results and Discussion

3.1. Conventional Testing for POPIC-Modified Bitumen

Table 4. POPIC modified bitumen convention characteristics with different content.

Blend Type	Specific Gravity	Penetration (dmm)	Softening Point (°C)	Ductility (cm)	Storage Stability (°C)
Reference	1.029	65	50.26	123	0.18
2% POPIC	1.032	61	50.97	110	0.84
4% POPIC	1.039	58	51.09	96	1.45
6% POPIC	1.045	55	51.24	82	1.58
8% POPIC	1.054	53	51.33	75	1.76

shows the properties of POPIC-modified bitumen at different concentrations. The experiment indicated significant changes in bitumen properties with varied POPIC levels in the base bitumen, ranging from 0% to 8%. First, the penetration grade of the bitumen was reduced, while the softening point increased. The negative association between penetration and softening point indicated that POPIC addition had a direct impact on these parameters. Furthermore, the addition of POPIC led to an increase in the asphaltene content of the bitumen due to maltene phase adsorption by micro-silica. Another notable finding was the enhanced stiffness of the bitumen mixtures, with POPIC particles being stiffer than regular bituminous materials. As the POPIC level increased, the bitumen blend became stiffer. This study demonstrates the significant impact of POPIC on bitumen stiffness characteristics. Importantly, these differences in bitumen characteristics have implications for practice. Bitumen mixtures with lower penetration and higher softening points are more resistant to temperature changes, making them less prone to rutting, especially under high temperatures.

When POPIC was added to the mixtures, there was a considerable increase in bitumen ductility, which measures adhesion and cohesion properties. The ductility of bitumen decreased as the POPIC content increased. This decrease in ductility might be attributed to an increase in viscosity and stiffness within the maltene phase because of a decrease in bitumen’s oily components. Table 4 clearly shows that as modified bitumen stiffens, its ductility diminishes in comparison to reference bitumen. The storage stability of POPIC-modified bitumen (POPIC-MB) was also evaluated. This finding emphasizes bitumen’s compatibility with POPIC, as indicated by a temperature difference of 2.2 °C or less between the softening points at the top and bottom regions of the aluminum tube. Furthermore, the storage study demonstrated that POPIC-MB exhibits a low segregation rate, indicating its stability even at high temperatures.

3.2. Volumetric and Marshall Characteristics of Modified Bituminous Concrete Mixes

Table 5. Summary of POPIC-modified bituminous concrete mix design at OBC.

Type of Mix	BSD	AV (%)	VMA (%)	VFB (%)	Stability (kN)	Flow (mm)	OBC (%)
Reference	2.376	4.07	15.39	72.03	10.96	3.32	5.18
2% POPIC	2.382	3.88	15.08	73.01	11.35	3.14	5.07
4% POPIC	2.393	3.76	14.95	73.98	13.97	3.01	4.96
6% POPIC	2.398	3.48	14.87	74.87	15.08	2.84	4.91
8% POPIC	2.401	3.37	14.72	75.16	14.21	2.86	4.94
JKR Limits	-	3–5	>14	70–80	>8	2–5	4–6

shows the volumetric and Marshall properties of several POPIC-MB bituminous concretes with optimal bitumen content (OBC) values. Interestingly, the OBC values of the POPIC-MB bituminous concrete are consistently lower than those of the reference bituminous concrete, indicating that the POPIC-MB concrete does not require much more bitumen content to attain optimal stability. This behavior is explained by the modified bitumen’s excellent viscosity at mixing and compaction temperatures. These qualities make efficient aggregate coating during compaction possible, which is aided by the shearing action of the Marshall compactor. The 8% POPIC-MB sample had slightly higher OBC than the 6% POPIC-MB sample. This modest increase is required to guarantee that the mixture maintains appropriate fluidity during construction. The bulk specific density (BSD) of the modified concrete samples increases significantly as the POPIC content increases, as indicated in Table 5. This improvement is due to POPIC’s capacity to increase the viscosity of the modified bitumen, allowing it to fill spaces between aggregates more efficiently and resulting in better bonding and density. The improved bulk density seen in the POPIC-MB concrete samples can be attributed to the mixture’s good workability and the modified bitumen’s increased viscosity. Furthermore, the creation of a sufficient layer around the aggregate contributes to the increased density of the mixture.

In terms of POPIC-MB VMAs (voids in mineral aggregates), the highest POPIC level in bitumen resulted in the smallest reduction in VMAs. This behavior is caused by POPIC agglomeration in the concrete blend, which becomes more prominent as the POPIC dose in the bitumen increases. At greater concentrations, POPIC clumps, making bitumen absorption by aggregates more difficult. It is worth noting, however, that all POPIC-MB bituminous concrete met the JKR VMA criterion, showing sufficient void space. This favorable VMA value promotes adequate aggregate covering and improves bituminous concrete pavement. Furthermore, for the bituminous concrete AVs, the enhanced bitumen viscosity resulting from POPIC led to improved interaction with other mixture components, resulting in greater bulk density, as observed in Table 5. Because of its great workability while mixing, the 8% POPIC-MB mixture had the lowest air void rate. Bituminous concrete with smaller air holes allows for less air and water penetration, thereby enhancing stiffness and resistance to rutting. The enhanced stiffness of bituminous concrete caused by POPIC modification is due to the surface area of POPIC particles and their interaction with bitumen, which improves bitumen absorption. This behavior is due to the improved viscosity and compatibility of the POPIC-MB concrete blend, which allows for a more effective aggregate coating.

Furthermore, the POPIC-MB bituminous concrete had greater VFBs (voids filled with bitumen) than the reference bituminous concrete. Despite having a lower viscosity than unmodified bitumen, POPIC-MB displayed remarkable penetration into aggregate pores, resulting in a higher proportion of VFBs in bituminous concrete. The higher VFB proportion in the POPIC-MB bituminous concrete samples suggests that the modified bituminous concrete contains fewer air gaps than the reference samples.

Marshall’s stability improved as POPIC levels increased by up to 6%. However, stability was compromised when the POPIC content surpassed 6%. This increase in Marshall stability can be due to POPIC, which improves bonding between aggregate components. As a result, this reinforcement increases the stiffness of the bitumen samples, allowing them to withstand higher loads. The use of POPIC-MB increases bitumen stiffness, reinforcing weaker spots in bituminous concrete samples. Furthermore, the flow values of POPIC-MB bituminous concrete samples are significantly lower than those of reference bituminous concrete samples. This shows that the modified bituminous concrete samples are more resistant to deformation than their reference equivalents. This behavior can be attributed to bituminous concrete’s high viscosity and stability ratings. It is important to note that all POPIC-MB bituminous concrete samples meet the JKR limitations for volumetric and Marshall strengths, assuring compliance with the prescribed requirements.

3.3. Fatigue Life Analysis of POPIC-MB Bituminous Concrete Samples Utilizing the S-Nf Relationship

The relationship between the initial strain (S) and the loads applied (Nf) until specimen fracture in the reference and POPIC-MB bituminous concrete samples was examined. Wohler’s prediction model equation served as the basis for the fatigue line prediction equation [33,34].

Table 6. Indirect tensile fatigue test data for the reference and POPIC-MB bituminous concrete.

Temp. (°C)	Mixture Type	Sample Diameter/ Height	Stiffness (MPa)	Stress Level (MPa)	Maximum Tensile Strain (×106)	Cycles to Failure (Nf)	Logarithmic Fatigue Life
5	Reference	101.1/50.73	3725.65	0.2	347.01	210,377	5.323
		100.95/51.81	3445.38	0.3	520.21	106,414	5.027
		101.2/51.42	3236.84	0.4	711.05	66,988	4.826
	4% POPIC	101.01/50.97	3161.57	0.2	405.41	293,089	5.467
		100.94/50.96	2371.01	0.3	760.32	174,984	5.243
		101.2/51.54	1394.43	0.4	1089.78	128,529	5.109
	8% POPIC	100.36/50.34	2242.03	0.2	570.05	320,627	5.506
		100.74/50.91	1768.12	0.3	1020.19	223,357	5.349
		101.4/51.01	1489.01	0.4	1560.11	191,866	5.283
20	Reference	101.3/51.89	2483.77	0.2	227.47	100,540	5.002
		101/52.01	2294.15	0.3	344.81	23,341	4.368
		100.8/51.92	2157.86	0.4	471.38	13,183	4.120
	4% POPIC	100.97/51.37	2106.35	0.2	268.25	121,152	5.083
		100.84/51.81	1579.34	0.3	500.87	28,957	4.462
		101.2/41.94	1394.43	0.4	729.37	20,654	4.315
	8% POPIC	100.59/51.37	1492.91	0.2	378.47	139,124	5.143
		100.98/51.25	1168.69	0.3	676.86	34,610	4.539
		101.1/50.93	981.93	0.4	1035.78	25,642	4.409
35	Reference	101.84/51.65	1656.72	0.2	148.95	5433	3.735
		101.27/51.42	1531.03	0.3	231.07	1840	3.265
		101.53/51.29	1431.78	0.4	320.01	771	2.887
	4% POPIC	101.04/50.72	1398.91	0.2	181.91	7362	3.867
		101.02/50.89	1048.89	0.3	329.97	2917	3.465
		100.9/51.01	933.03	0.4	497.13	1426	3.154
	8% POPIC	100.87/50.71	991.03	0.2	247.98	7780	3.891
		101.13/51.15	773.21	0.3	459.04	3598	3.556
		100.67/50.99	659.91	0.4	681.76	2051	3.312

shows the results of fatigue tests on specimens of both the reference and POPIC-MB bituminous concrete using the UTM-30. Three replicate samples were tested at each stress level and each temperature range of 5 °C, 20 °C, and 35 °C.

The S-Nf curve is an effective tool for determining the average fatigue life performance of bituminous concrete at a given strain level. Figure 2 exhibits the S-Nf curve, which shows the fatigue lines for reference and POPIC-MB bituminous concrete. The results show a considerable difference in fatigue life between the reference and POPIC-MB bituminous concrete, implying that the mixture type has a major impact on initial stiffness. Furthermore, bituminous concrete with POPIC demonstrates better flexibility than the reference material. This enhancement comes from the presence of POPIC, which improves the cohesiveness of the bitumen and boosts elastic recovery in the modified bituminous concrete, enhancing the interaction between aggregate and bitumen. POPIC-MB’s higher adhesion promotes effective interaction between the modified bitumen and aggregate particles, resulting in improved fatigue resistance and greater fatigue life in the modified bituminous samples [34,35]. Furthermore, compared to the reference and POPIC-modified bituminous concrete, the fatigue lines in bituminous concrete containing 4% and 8% POPIC were significantly higher. This implies that the inclusion of POPIC improves the intrinsic flexibility of bituminous concrete. This improvement is due to the properties of POPIC, which, when used as a modifier in bituminous concrete, improves fatigue cracking resistance by reducing air gaps and improving packing density. POPIC’s mineral components distribute loads more uniformly and reduce stress by increasing adhesion between aggregates and bitumen [36]. Furthermore, POPIC improves thermal stability, maintains bitumen characteristics, and reduces oxidation and aging, all of which lead to improved pavement fatigue life.

3.4. Influence of Stress Levels and POPIC Content on Bituminous Concrete Fatigue Life

Figure 3 shows how stress levels and POPIC content influence the fatigue life resistance of modified bituminous concrete at 20 °C. The study’s findings indicate that raising the POPIC concentration of bituminous concrete improves fatigue resistance. Furthermore, higher stress levels resulted in shorter fatigue life for both the reference and POPIC-MB bituminous concrete [37]. Notably, fatigue resistance improved for POPIC-MB bituminous concrete at a lower stress level of 0.2 MPa, indicating that this material’s number of cycles to failure increased. It was also shown that increasing POPIC content resulted in longer fatigue life across all stress levels, implying that POPIC improves the material’s resilience to fatigue-induced damage [34]. Furthermore, assessing the fatigue life of bituminous concrete at various stress levels showed a considerable decline in fatigue cracking resistance for POPIC-MB bituminous concrete as stress increases [35] and a similar trend was observed in various studies [8,35,38]. At all stress levels, the results show that the fatigue behavior of the reference and POPIC-MB bituminous concrete differs significantly. The POPIC-MB bituminous concrete outlasted the reference bituminous concrete at all stress levels tested. Furthermore, the fatigue life of the combinations increased as the POPIC concentration increased in response to the applied stress levels. This indicates that bituminous concrete modified with POPIC possesses increased resistance to fatigue cracking and improved load-bearing capability [34,39].

3.5. RSM Statistical Approach

Table 7. RSM ANOVA analysis for the quadratic model for fatigue life.

Source	Sum of Squares	df	Mean Square	F-Value	p-Value	Remark
Model	18.57	9	2.06	74.10	<0.0001	Significant
A—POPIC	0.4223	1	0.4223	15.17	0.0011
B—Temperature	14.22	1	14.22	510.58	<0.0001
C—Stress level	1.29	1	1.29	46.28	<0.0001
AB	0.0010	1	0.0010	0.0368	0.8501
AC	0.0724	1	0.0724	2.60	0.1243
BC	0.1257	1	0.1257	4.51	0.0477
A2	0.0085	1	0.0085	0.3054	0.5873
B2	1.09	1	1.09	39.07	<0.0001
C2	0.0058	1	0.0058	0.2098	0.6524
Residual	0.5011	18	0.0278
Lack of Fit	0.2066	5	0.0413	1.82	0.1774	Insignificant
Pure Error	0.2946	13	0.0227
Cor Total	19.07	27

shows the RSM ANOVA model for the investigation. The model F-value of 74.10 indicates the model’s relevance, with only a 0.01% probability of such a high F-value being due to random variation. p-values < 0.0500 indicate that the model terms are significant [40]. In this context, the terms A, B, C, BC, and B2 are all relevant. Values above 0.1000 imply that the model terms are unimportant. The lack of fit F-value is 1.82, which means that it is not statistically significant when compared to pure error. Random variations have a 17.74% chance of producing a lack of fit F-value with this size. A non-significant lack of fit is preferred because it indicates that the model is well fitting. Furthermore, the lack of fit results revealed a link between residual errors and pure errors in the repeated design point, as confirmed by p-values of 0.1774. In addition, the research revealed that both test temperatures (B), with an F-value of 510.58, had the most significant influence on fatigue life in this study. Equation (5) depicts the statistical model developed to measure the rutting response of POPIC-MB bituminous concrete.

$$Fatigue life=3.732+0.153A-0.889B-0.268C-0.008AB+0.067AC-0.089BC-0.055A^2+0.622B^2+0.046C^2$$

(5)

where $A$, $B$, and $C$ denote the POPIC content dosage, temperature, and stress level, respectively.

3.5.1. Model Fit Analysis and Validation Parameter

Table 8. RSM fatigue life model fit analysis.

Model Parameter	Values
Standard deviation	0.167
Mean	4.130
Coefficient of variance	4.040
Adequate precision	26.262
$R^2$	0.974
Adjusted $R^2$	0.961
Predicted $R^2$	0.924

displays the model fit analysis, which shows that the predicted $R^2$ of 0.924 nearly matches the Adjusted $R^2$ of 0.961, with a difference of less than 0.2. Because the difference is less than 0.2, suggesting good prediction, this investigation establishes strong agreement between these values, hence proving the models’ validity. These $R^2$ values are approaching unity, indicating that the quadratic models are well fitted to the real data. Adequate precision evaluates the signal-to-noise ratio, with a ratio better than 4 regarded as acceptable [41]. The model ratio of 26.262 suggests an excellent ability to explore the design space. Furthermore, the model’s standard deviation was significantly lower than the mean values, demonstrating reliability and appropriate variance analysis [42]. This means less uncertainty in forecasting experimental data, confirming the model’s usefulness for the modeling, optimization, and prediction of the POPIC-MB bituminous concrete pavement fatigue life property.

3.5.2. RSM Diagnostic Plot Analysis

Diagnostic charts for model fitting were used to check that the findings were appropriate and distributed normally, as shown in Figure 4. Figure 4a shows the probability plot of the fatigue life model, which reveals a normally distributed residual pattern. Furthermore, the residual points are closely aligned with the straight line, confirming the utility and correctness of the regression models. To evaluate the model’s performance further, predicted and real values were compared, as shown in Figure 4b. Points were consistently distributed towards the equality line on all diagnostic plots for the fatigue life response. This shows that the produced models have a high level of fitting precision. Furthermore, the plots’ alignment of all points along the straight line indicates a positive correlation between predicted and actual values.

3.5.3. Synergistic Variables’ Effects on Fatigue Life Response

The combined effect of POPIC and test temperature on the fatigue life of POPIC-MB bituminous concrete is shown in Figure 5a,b. The contour plots show the combined effect of two input elements on the rutting response: POPIC content and temperature. Test temperatures ranging from 5 to 20 °C have a significant influence on fatigue life. The fatigue life of modified bituminous concrete improves noticeably with increasing POPIC content. This is because the modified bitumen has increased viscoelasticity and stiffness, which improves aggregate coverage and creates a well-connected aggregate–bitumen matrix, and as predicted, increasing the temperature also decreases the fatigue life of the modified bituminous concrete. POPIC, on the other hand, improves bituminous concrete by increasing its fatigue life. Furthermore, Figure 5c,d show an intriguing trend: as temperature and stress levels rise, fatigue life decreases. Temperature changes have a higher impact on fatigue life at all stress levels. To put it simply, higher temperatures produce decreased stiffness in the bitumen, potentially reducing fatigue resistance and, as a result, limiting the pavement’s fatigue life. Variations in stress levels, on the other hand, have a bigger effect on fatigue life at lower temperatures, where the cycles are more obvious. This study shows that stress levels have a substantial influence on the fatigue life of bituminous concrete on asphalt pavements, with higher stress levels causing faster fatigue damage and a shorter fatigue life than lower stress levels.

Figure 5e,f also reveal a synergistic relationship between POPIC content and stress levels in POPIC-modified bituminous concrete samples. Lower stress levels are associated with longer fatigue life, highlighting the importance of stress management in pavement performance. Furthermore, POPIC content has a considerable effect on bituminous concrete. Lowering the POPIC content reduces fatigue life at all stress levels, showing that the presence of POPIC improves the material’s resistance to fatigue-induced damage. POPIC-MB’s improved adhesion allows for effective interactions between modified bitumen and aggregate particles, resulting in improved fatigue resistance in modified bituminous samples and a longer fatigue life. Regardless of POPIC concentration, an increase in stress levels reduces the fatigue life of bituminous concrete, implying that stress levels are the most important factor in determining the material’s durability during fatigue loading.

3.5.4. Multi-Objective Optimization and Validation of RSM Models

The model’s input factor was determined using a multi-objective optimization technique. Based on the fatigue life response and the set bounds shown in

Table 9. Fatigue life optimization parameters.

Factor	POPIC (%)	Temperature (°C)	Stress Level (Mpa)	Logarithmic Fatigue Life
Range	0–8	5–25	0.2–0.4	2.896–5.484
Goal	Maximize	In range	In range	Maximize

, a desirability score (di) ranging from 0 (poor) to 1 (optimized) was calculated. The optimal input factors were tested three times, and the average result was chosen. The model’s accuracy was determined by comparing projected values to real data and calculating the absolute relative percentage error (ARPE) using Equation 6. Figure 6 shows the stochastic ramps used to optimize fatigue life. According to the RSM model for POPIC-MB bituminous concrete fatigue life, the ideal combination for achieving a fatigue life of 4.7149 is a 7.5% POPIC content at 11.706 °C and 0.2 MPa of stress.

$$ARPE=\left|1-{\displaystyle \frac{Model values}{Actual values }}\right|$$

(6)

Additional experiments were carried out within these parameters to test the reliability of the optimized parameters given by the RSM model. The average value of three samples was computed and shown. ARPE was utilized to contrast experimental rutting depth responses with anticipated rutting depth responses. The experimental fatigue life was 4.932 mm, with an ARPE of 4.61%, which is much less than the allowed limit of 5%, showing the RSM model’s accuracy.

3.6. Soft Computing Approach

Soft computing refers to a wide range of computer techniques aimed at mimicking human-like cognitive processes, with ANNs playing a significant role as they are inspired by the neural structure of the human brain [32]. Soft computing technologies have grown in popularity because of their wide range of applications in modeling complex, nonlinear interactions between input and output components. ANNs are used in soft computing for pattern detection, categorization, optimization, and prediction, making them versatile tools [21]. Researchers have recently shown an increased interest in soft computing techniques. To predict the fatigue life of bituminous concrete, this study combines two well-known software packages: JMP pro and MATLAB.

3.6.1. The Artificial Neural Network (ANN) Approach

An effective ANN must go through several critical steps, such as choosing input variables, setting up the network architecture, and dealing with model uncertainty [32]. In this study, RSM data were used to improve the ANN design matrix for the JMP pro and MATLAB software packages to find the best possible parameter combination. The RSM optimization data were used for training, testing, and validating the ANN prediction model on all software platforms. The input variables were POPIC content, temperature, and stress intensity, and the output variable was logarithmic fatigue life. A feed-forward backpropagation network with different numbers of neurons in the hidden layer was optimally designed [20,43].

3.6.2. JMP Pro

The RSM dataset was divided randomly into three sets: 70% for training, 15% for validation, and 15% for testing. It is important to note that the same dataset was used consistently throughout the experiment. The number of hidden layer neurons in the models was incrementally increased from 3 to 10, and the results were thoroughly analyzed to identify the network with the most accurate predictive capabilities. To facilitate comparison, the performance of each model was evaluated and documented. The model performance exhibited a nonlinear trend, with R-squared ($R^2$) values of 0.998 and 0.991, and Root Average Square Error (RASE) values of 0.041 and 0.068 during training and validation, respectively. As previously stated, the most optimal network design for the responses was identified as a three-layer structure with a logarithmic fatigue life configuration of 2-8-1. Figure 7 depicts the neural network design used in this study, which has three layers. The first layer contains three input neurons that represent the POPIC content, temperature, and stress level. The second layer contains eight hidden neurons, while the third layer contains one neuron that predicts the logarithmic fatigue life of bituminous concrete.

The scatter plots displaying the logarithmic fatigue life response, as shown in Figure 8a–c, demonstrate a significant correlation between predicted and actual values, with $R^2$ values of 0.998, 0.991, and 0.985 for the training, validation, and testing sets. These scatter plots show the ANN model’s high accuracy in modeling this variable. The data points are closely aligned with the 45° line, suggesting a significant agreement between the ANN’s predicted values and the actual test results. Furthermore, the strong $R^2$ values reported between the test values and ANN-predicted outputs demonstrate the ANN model’s efficacy in predicting the logarithmic fatigue life of POPIC-MB bituminous concrete when trained with test data.

3.6.3. MATLAB

To develop the ANN models, seven normalized input variables were combined with three target attributes to create ANN models. The dataset was separated into three sections training, validation, and testing with allocations of 60%, 20%, and 20%, respectively. To guarantee that the random selection technique was consistent between iterations, a random number generator was initialized before allocation. The modeling procedures used Levenberg–Marquardt’s backpropagation learning method. The number of neurons in the models gradually increased from one to ten, and the results were analyzed before selecting the network that provided the best solution. The ANN models were created using MATLAB’s Neural Network Fitting tool (2023b). Mean square error (MSE) and $R$ values were used to evaluate the effectiveness of the ANN models. The study used a feed-forward neural network with backpropagation, as shown in Figure 9. Achieving an optimal network architecture (ONA) within the defined range for modeling any given attribute necessitates careful balancing. A neural network’s efficacy is measured by its capacity to achieve a harmonious balance of $R$ values throughout the training, validation, and testing datasets. Figure 10 depicts the MATLAB ANN-optimized architecture for estimating logarithmic fatigue life.

The utilization of an ANN configured as 3-6-1 is optimal in predicting logarithmic fatigue life. This determination was made based on the network’s ability to reduce the MSE to a remarkably low value of 13.75, while also exhibiting minimal discrepancies between the $R$ values of the (a) training (0.993), (b) validation (0.985), (c) testing (0.989) and (d) all model datasets, as depicted in Figure 11. All $R$ values utilized for training, validation, and testing the model surpass the impressive threshold of 0.983, making them almost indistinguishable from the ideal match. The data points closely overlap with the equality line, showing a high level of agreement between the ANN predictions and the actual test results. A closer examination of the response values reveals a striking similarity between the observed and predicted responses. An $R$ value greater than 0.9 indicates that the model makes exceptionally accurate predictions. Furthermore, the $R$ values derived for the test results and the ANN-generated forecasts demonstrate the ANN model’s capacity to predict the logarithmic fatigue life of POPIC-MB bituminous concrete when trained with the test data.

3.7. Model Performance Evaluation Assessment

In our performance analysis, we use the APE technique to compare the anticipated logarithmic fatigue life of POPIC-MB bituminous concrete with laboratory testing data, as shown in

Table 10. Model comparison for POPIC-MB bituminous concrete logarithmic fatigue life.

Exp. Run	Logarithmic Fatigue Life
	Actual	RSM		ANN
				JMP pro		MATLAB
		Predicted	APE (%)	Predicted	APE (%)	Predicted	APE (%)
1	3.684	3.982	8.089	3.832	4.017	3.892	5.646
2	3.781	3.491	7.670	3.694	2.301	3.991	5.554
3	3.544	3.932	10.948	3.737	5.446	3.732	5.305
4	5.392	5.984	10.979	5.222	3.153	5.924	9.866
5	5.484	6.281	14.533	5.613	2.352	5.981	9.063
6	3.383	3.743	10.641	3.528	4.286	3.903	15.371
7	4.927	4.432	10.047	4.838	1.806	4.432	10.047
8	5.321	4.792	9.9421	5.082	4.492	4.974	6.521
9	5.173	5.924	14.518	5.324	2.919	5.524	6.785
10	4.259	3.751	11.928	4.056	4.766	3.911	8.171
11	3.395	3.972	16.996	3.473	2.297	3.972	16.996
12	2.949	2.491	15.531	2.692	8.715	2.491	15.531
13	5.261	5.982	13.705	5.487	4.296	5.782	9.903
14	3.691	3.141	14.901	3.938	6.692	3.141	14.901
15	3.911	3.339	14.625	3.819	2.352	3.539	9.512
16	3.813	3.144	17.545	3.937	3.252	3.144	17.545
17	3.723	3.135	15.794	3.935	5.694	3.135	15.794
18	3.831	3.192	16.680	3.993	4.229	3.392	11.459
19	5.484	6.283	14.570	5.714	4.194	5.013	8.589
20	5.209	4.641	10.904	5.447	4.569	4.671	10.328
21	3.636	3.217	11.524	3.313	8.883	3.217	11.524
22	3.193	3.516	10.116	3.512	9.991	3.506	9.803
23	4.858	4.304	11.404	4.963	2.161	4.434	8.728
24	3.868	3.456	10.651	3.635	6.024	3.356	13.237
25	2.896	2.553	11.844	2.994	3.384	2.553	11.844
26	3.086	3.812	23.526	3.319	7.550	4.012	30.006
27	3.842	3.389	11.791	3.992	3.904	3.489	9.188
28	3.934	3.287	16.446	3.835	2.517	3.729	5.211

. Furthermore, a comparison analysis of the various models used in our research is performed. To assess the accuracy of the equations, four critical measures based on $R^2$, MRE, and RMSE are used. This comprehensive review, highlighted by the substantial correlation discovered among many variables, decisively validates the models’ applicability in recreating real-world results. The study’s findings indicate that the ANN model’s predictions surpassed those of the RSM model, which is very remarkable. This study emphasizes the ANN model’s improved capacity to generalize and make effective predictions, differentiating it as a more resilient and versatile tool for data analysis and modeling.

To evaluate the accuracy of the RSM and ANN models, a comparison was conducted between their predictions and actual data, as shown in Figure 12. Plots were created to show the link between each data point and the number of runs performed, indicating a good fit between the model’s predictions and the actual values. In terms of predicted accuracy, the ANN model outperformed the RSM model, demonstrating that it can generalize data better than the RSM model [44,45,46].

3.8. Statistical Measures for the Developed Models

The results from the statistical investigations were evaluated and interpreted using a variety of statistical measures, including distribution, dispersion, and correlation. These measures are critical for understanding and interpreting the study’s datasets.

Table 11. Statistical measures for the proposed models.

Statistical Metrics	Logarithmic Fatigue Life Models
	RSM	JMP pro	MATLAB
MRE	357.846	126.243	312.427
RMSE	3.757	1.245	3.094
R2	0.979	0.998	0.984
Standard deviation	1.112	0.857	0.958
Mean	4.041	4.178	4.030
Variance	1.236	0.734	0.918
Coefficient of variance	27.51	20.51	23.77

indicates the statistical significance and remarkable predictive capability of both the RSM and ANN models when compared to experimental data. Notably, the ANN model outperforms the RSM model in forecasting logarithmic fatigue life, with R2 values of 0.998 (JMP pro) and 0.984 (MATLAB), as opposed to the RSM’s $R^2$ value of 0.979. Furthermore, the ANN model has substantially lower RMSE values, with 1.245 (JMP pro) and 3.094 (MATLAB), while the RSM model has an MRE of 3.757. Furthermore, the MRE for the ANN model is significantly lower, with values of 126.243 (JMP pro) and 312.427 (MATLAB), whereas the MRE for the RSM model is 357.846. The ANN model’s greater prediction accuracy is ascribed to its capacity to simulate human intellect and detect complex patterns in data. Unlike RSM, which is based on proven mathematical formulae, ANNs excel at handling the complex, nonlinear interactions found in real-world data. They can adjust to changing input conditions and automatically discover important features, resulting in more accurate predictions. Furthermore, ANNs have better generalization capabilities, which allow them to correctly apply learned patterns to new data, minimizing the disparity between predicted and actual results [44,45].

Furthermore, the mean value of the generated models was calculated to analyze the data’s central tendency, with a larger mean indicating a better-predicted result. Based on the data, the JMP pro model appears to produce the most anticipated outcomes overall, with a mean of 4.178. Furthermore, the standard deviation was used to measure data variability, and it was discovered that the JMP pro model (0.857) had a lower standard deviation, indicating less variation in predicted values, followed by the MATLAB model (0.958) and the RSM model (1.112), which had the highest standard deviation. Furthermore, the variance, which represents the average squared difference between each data point and the mean, was calculated. The JMP pro model has the lowest variance (0.734), indicating less overall unpredictability in its predictions than the MATLAB (0.958) and RSM (1.236) models. The coefficient of variation was also calculated, and the JMP pro model (20.51%) produced the lowest value, indicating lower variability relative to the mean and more consistent predictions around the mean. The MATLAB model came in second with a coefficient of variation of 23.77%, while the RSM model had the highest variability relative to its mean, with a coefficient of variation of 27.51%. Considering these variables, the JMP pro model emerges as the best alternative because of its higher mean, smaller standard deviation, coefficient of variation, and lower variance than the RSM and MATLAB models. The JMP pro model produces more accurate and reliable predictions than the other two; hence, it is the preferred alternative. Additionally, ANNs benefit from parallel processing, extensive model change, and access to immense quantities of data, all of which contribute to their superior prediction accuracy when compared to the RSM model [44,46].

3.9. Predictive Model Data Variability, Validation, and Comparison

3.9.1. Violin Plots

Violin plots were used to analyze the variety in predictions provided by both models, as shown in Figure 13. When compared to experimental data for logarithmic fatigue life prediction, these visualizations show the variation in the interquartile range (IQR) for both the RSM and several ANN models from the JMP pro and MATLAB software. Each density curve has a small box plot in the center, with the rectangle designating the ends of the first and third quartiles and the central dot representing the median. The graphic clearly shows that the prediction models offered reasonable matches to the actual data. However, the RSM and MATLAB models have a more extended distribution than the JMP pro model, with no clear peaks indicating greater variability. The actual data and the JMP pro model both have a lower median and IQR than the RSM and MATLAB models, indicating variations in central tendency and spread. While the RSM and MATLAB models show a single mode, the real data and the JMP pro model show bimodality, indicating the presence of two separate subpopulations within the dataset. Interestingly, the IQR for the JMP pro models was somewhat smaller than that observed for the RSM and MATLAB models. Because a thinner IQR implies that the central data points are closely packed together, indicating a higher level of consistency, whereas a broader IQR indicates greater unpredictability in predictions. The JMP pro model has a thinner IQR than the MATLAB and RSM models. Furthermore, the nearly comparable general shape of the violin plots shows that the predictions will accurately mirror the actual data.

3.9.2. Taylors Model Comparison

Figure 14 shows how the Taylor diagram was used to compare models. It gives a graphical picture of a model’s prediction capability by visualizing its differences from a benchmark observational dataset [47]. The position of each model in this graphic represents the degree of accuracy it achieves while predicting experimental logarithmic fatigue life [47,48]. The ANN models were designated as the baseline models for logarithmic fatigue life prediction since they outperformed the RSM model in terms of performance. Among the ANN models, the one designed with JMP pro software demonstrated the highest correlation coefficient and lowest standard deviation, positioning it closer to the actual data compared to the other models. The high $R^2$ values of the software indicate the ANN model’s proficiency in elucidating the relationship between the input variables and the predicted outcome for bituminous concrete logarithmic fatigue life prediction.

3.9.3. Model External Validation

Prior studies have demonstrated a stronger agreement between the ANN model and experimental findings, as seen by the high $R^2$ and lower MRE, and RMSE. Another external validation test was carried out to demonstrate the accuracy of both models. A new series of laboratory tests was conducted methodically to properly evaluate the efficacy of both models. This involves running five different data runs that were not used during the initial model construction phase. Three samples of each of these one-of-a-kind combos were methodically constructed and evaluated. The resultant average values were carefully examined and documented for use in the logarithmic fatigue life model.

Table 12. Dataset for logarithmic fatigue life model validation.

Run	POPIC (%)	Temp. (°C)	Stress Level (MPa)	Logarithmic Fatigue Life
				Actual	Values for Predictive Models
					RSM	APE	JMP Pro	APE	MATLAB	APE
1	2	15	0.25	4.285	4.152	3.20	4.176	2.61	4.163	2.93
2	3.5	25	0.45	3.215	3.129	2.75	3.187	0.87	3.179	1.13
3	6.5	40	0.00	4.978	5.161	3.54	5.053	1.48	5.107	2.53
4	8	10	0.15	5.148	5.027	2.41	5.096	1.02	5.072	1.49
5	5.5	25	0.10	4.465	4.278	4.37	4.369	2.19	4.357	2.48

presents the actual logarithmic fatigue life values alongside their respective predicted model values. The logarithmic fatigue life $R^2$ values in the new dataset performed exceptionally well, with values of 0.991 for the RSM model, 0.995 for JMP pro, and 0.992 for the MATLAB ANNS model. Furthermore, the Absolute Percent Error (APE) between the actual and model-predicted logarithmic fatigue life values was well below the 5% limit. This serves as persuasive evidence of the models’ utility and precision in estimating the logarithmic fatigue life of POPIC-MB bituminous concrete. When comparing the ANN model to the RSM model, the ANN model demonstrates a more diverse and potent applicability. This improved potential is due to its ability to efficiently describe a diverse spectrum of nonlinear polynomials. In comparison, the RSM model has limited capabilities, excelling mostly in capturing quadratic approximations. This basic difference in modeling capabilities is responsible for the ANN model’s higher performance.

The outcomes of this study are consistent with earlier studies emphasizing the need to use computer-based technologies in traditional pavement design processes to improve performance and efficiency [49,50]. The key advantage of this approach is its ability to predict not only logarithmic fatigue life but also to pick the best input parameters required for optimal performance. This capacity utilizes the interaction effects provided by RSM modeling, thus reinventing the bituminous concrete design process. As a result, combining RSM and ANN techniques with different software platforms provides various advantages in terms of improving overall design consistency and increasing the logarithmic fatigue life of bituminous concrete mixtures. To obtain deeper insights and evaluate the performance of the proposed model in the current study, a comparison analysis was performed using comparable variables from relevant studies in the literature.

Table 13. Comparison of previous study models with the present study.

Reference	Approach	Input Factors	Responses	${\mathit{R}}^2$
[51]	RSM and various machine learning models using MATLAB	Waste denim fiber and nano-silica	Rutting parameter	RSM > 0.80 Decision tree regression > 0.99
[52]	ANN	Water–cement ratio and superplasticizer	Flow value and compressive strength	ANN > 0.984
[53]	RSM and ANN	Waste plastic dosage and temperature	Rutting and stiffness modulus of mixtures	ANN > 0.99 RSM > 0.97
[54]	RSM and ANN	Colloidal nano-silica content and surface area	Compressive strength at different aging period	RSM > 0.86 Gaussian process regression > 0.925
[55]	RSM and various machine learning algorithms	Nano-silica and denim fiber	Complex modulus, phase angle, and rutting parameter	RSM > 0.97 Gaussian process regression > 0.99
[46]	RSM and ANN	Marble powder and rice husk ash	Porosity, thermal conductivity, and compressive and flexural strength	RSM > 0.93 ANN > 0.96
[20]	RSM and ANN	Palm waste content and temperature	Rutting and stiffness performance of mixtures	RSM > 0.99 ANN > 0.99
[56]	RSM and various machine learning methods	Crude oil palm and pyrolyzed tire oil	Shear velocity blending and compacting temperature	RSM > 0.82 Forest regression > 0.93
[57]	RSM and ANN	Cement, water–binder ratio, aggregates, and silica fume	Compressive strength at 7 and 28 days	ANN > 0.912 RSM > 0.892
[45]	RSM and ANN	Aggregate gradation and compaction level	Air void and permeability	RSM > 0.83 ANN > 0.85
[44]	RSM and ANN	Washingtonia robusta palm waste and biochar	Water absorption, porosity, and compressive and flexural strength	ANN > 0.98 RSM > 0.91
Present study	RSM and ANN approach using different software	POPIC content, temperature, and stress level	Fatigue life	RSM > 0.97 ANN > 0.98

compares past research with the models utilized in this study.

The current work shows consistently high R² values for both ANN and RSM techniques, showing strong, efficient, and reliable fatigue life prediction models based on stress level, temperature, and POPIC concentration. The current study’s usage of innovative software tools such as MATLAB and JMP pro for ANNs and having a comparison helps to achieve improved accuracy and prediction performance when compared to earlier studies.

3.10. Developed Model Summary, Assumptions, and Limitations

Based on the study findings, RSM and ANNs have significant advantages and disadvantages in optimization, modeling, and prediction tasks. In bituminous concrete applications, the nature of the problem, accessible data, and specific objectives all influence method selection. RSM distinguishes itself through its simplicity, interpretability, successful exploration of design spaces, and statistical rigor. In contrast, ANNs excel at capturing nonlinear correlations, handling complexity, adjusting to new data, and delivering improved accuracy and predictive power, making them a viable tool for optimizing and forecasting asphalt pavement behavior. Therefore, it was essential to combine the strengths of both approaches, resulting in an integrated strategy that harnesses the robust statistical foundation of RSM along with the predictive capability and adaptability of ANNs.

The model’s basic assumption is that the dataset, which includes variables like POPIC concentration, stress levels, test temperatures, and fatigue life assessments, has a normal distribution. This assumption is important for different statistical studies and soft computing techniques. Furthermore, it is assumed that the model’s error variance is consistent across all levels of independent variables to enable an accurate estimate of model parameters and prediction intervals. Furthermore, for RSM modeling approaches, variables such as POPIC concentration, stress levels, test temperatures, and fatigue life evaluations are expected to have a linear and quadratic interaction. The studies’ scope is limited since the dataset utilized for model building and assessment may not include all possible scenarios or conditions experienced in practical applications. Furthermore, the sophistication of the soft computing models generated has limitations; highly complicated models may overfit the training data, failing to generalize to new data. Also, potential errors, inconsistencies, or missing values in the dataset could jeopardize the reliability and precision of the statistical analysis and modeling process. Furthermore, the lack of external validation using independent datasets makes it difficult to assess the model’s robustness and dependability in predicting fatigue life characteristics across various conditions or environments.

4. Conclusions

Statistical analysis was utilized in this study to investigate the impact of stress level and temperature on the fatigue life of POPIC-MB-modified bituminous concrete. Additionally, soft computing approaches, specifically RSM and ANNs implemented in MATLAB and JMP pro, were employed for predicting the logarithmic fatigue life of POPIC-MB-modified concrete. The performance of these models was evaluated using statistical metrics. The key findings of the research are outlined below:

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A high degree of agreement was observed between predicted and actual values, indicating the efficacy of statistical models in predicting fatigue life under specific conditions. Also, the study highlights the superiority of a statistically based machine learning approach, particularly the ANNs, over conventional methods like RSM.

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The results indicate that POPIC-MAB bituminous concrete exhibits a longer fatigue life at lower stress levels and temperatures, with temperature exerting a greater influence than stress and POPIC content. Additionally, the study identifies the optimal improvement in logarithmic fatigue life for POPIC-MB bituminous concrete at 7.5% POPIC, 11.706 °C, and a stress level of 0.2.

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The ANN model accurately predicts the POPIC-MB bituminous logarithmic fatigue life by capturing complicated nonlinear connections. This is demonstrated by its close alignment with the actual laboratory results, low error percentages, and high R2 values.

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Comparing parity, Taylor, and violin plots, JMP pro and MATLAB-based ANN models, as well as the RSM model, show unbiased prediction accuracy. In terms of accuracy and dataset alignment, the JMP pro-based ANN model performs better.

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Study limitations include a focus on specific stress, temperature, and POPIC content ranges, limiting generalization, and potential variations in real-world performance due to external factors influencing field conditions.

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Future research should evaluate the impact of environmental variables on POPIC-MBC performance, including long-term durability and performance under varying traffic and weather situations. Furthermore, additional studies with different binder modifiers may improve the model’s adaptability.

In conclusion, this study demonstrates the usefulness of combining statistically based machine learning methodologies for predicting and optimizing POPIC-MBC fatigue life. In terms of accuracy, ANN models, notably those in JMP pro, outperform classic RSM methods. Although there are limits, these findings point to future research directions, emphasizing the necessity of real-world validation and investigating larger aspects influencing POPIC-MBC effectiveness. The current study offers a novel application of POPIC in bituminous concrete, improving its theoretical contribution and providing a new viewpoint on the utilization of industrial wastes in sustainable construction. This study improves the understanding of using waste products to improve pavement performance by combining RSM and ANNs, developing theoretical frameworks for fatigue life prediction and material optimization, and encouraging sustainable building practices. The proposed method for predicting fatigue life in POPIC-modified bituminous concrete has the potential to benefit future research and applications, such as other construction materials, soft computing model optimization, experimental integration, environmental impact assessment, infrastructure design, real-world validation, and potential inclusion in industry standards. Future studies should explore varied environmental circumstances and additional modifiers to enable thorough understanding and broad applicability in construction.