Impact of Nanocarbon-Coated Calcium Carbonate on Asphalt Rutting: Experimental and Numerical Analyses

Abstract

Rutting is a significant form of pavement distress that arises from irreversible strains accumulating along wheel paths, directly impacting pavement safety. This research investigates the effectiveness of nanocarbon-coated micronized calcium carbonate powder as a modified filler to mitigate rutting, utilizing numerical methods via finite element software. The study specifically examines the addition of 5% by weight of this modified filler to the asphalt mix. To validate the numerical results, laboratory wheel-tracking tests were conducted on samples incorporating both conventional and modified fillers. The findings reveal that the modified calcium carbonate filler enhances the asphalt’s resistance to rutting, with the 5% inclusion demonstrating a marked improvement in durability and performance. The study also underscores the necessity of characterizing the elastic and visco-plastic properties of materials through rigorous testing methods, such as elastic modulus and dynamic creep tests, to better understand their behavior under load. Numerical analysis based on linear elastic conditions was prioritized over viscous conditions to effectively compare the results of these specialized materials. The strong correlation between the numerical simulations and laboratory results reinforces the effectiveness of finite element methods in predicting pavement behavior and optimizing asphalt mixtures.

1. Introduction

In recent years, the use of fillers in various materials has garnered significant attention, particularly in the fields of polymer composites, paints, and coatings. Among these fillers, nanocarbon coating on micronized calcium carbonate (NCMCC) has emerged as a versatile and cost-effective option, recognized for its ability to enhance mechanical properties. One of the major failures that occur in asphalt pavements is rutting or permanent deformation [1]. Investigations into this specialized material not only aim to enhance the performance and longevity of asphalt mixtures but also align with the increasing demand for sustainable and efficient solutions in bitumen technology. The findings of this research underscore the potential of carbon-coated micronized calcium carbonate as an effective additive that meets both performance and economic requirements in the field. As elucidated in prior scholarly investigations, the novel bitumen modifier creates a synergistic effect by serving as a beneficial alternative to the incineration of rigid plastic, thus utilizing it as a secondary raw material. This comprehensive analysis demonstrated that the newly modified asphalt mixture is the solution exhibiting the least environmental burden across all impact categories, thereby underscoring its significant role in the implementation of innovative strategies aimed at enhancing the environmental sustainability of roadway surfaces [2]. Asphalt rutting is the deformation of the pavement’s wearing course layer, forming longitudinal ruts under vehicle wheel loads, which negatively impacts pavement performance. The rheological properties of conventional bitumen modified with multi-walled carbon nanotubes (MWCNTs), which were chemically treated with acid, were evaluated through tests such as softening point, rotational viscometer, and dynamic shear. The results indicated that the incorporation of MWCNTs as a modifier effectively enhanced bitumen properties. Overall, it was found that the softening point and rotational viscosity increased, while the temperature sensitivity improved. Thus, the use of this additive makes asphalt better suited for warmer climates and higher traffic loads, effectively increasing its resistance to rutting [3].

Nanocarbon materials, such as graphene and carbon nanotubes, have attracted considerable research interest due to their exceptional mechanical reinforcement properties. A study published in 2024 indicated that the integration of nanocarbon-coated micronized calcium carbonate led to significant enhancements in the viscosity and thermal stability of asphalt mixtures, which in turn mitigated rutting potential under cyclical loading conditions [4]. These nanomaterials, characterized by diverse structures and conformations, enable the development of modified coatings that offer innovative functions for the protection and restoration of concrete structures. This results in improvements such as waterproofing of surfaces, enhanced resistance to corrosion and carbonization, aging mitigation, and structural strengthening. Moreover, a review published in the International Journal pointed out that nanocarbon coatings enhance the bond between filler particles and asphalt, thereby improving the overall durability of the composite structure [5]. Additionally, research featured in the journal examined the synergistic effects of nano-coatings on conventional fillers, demonstrating that a well-dispersed nanocarbon layer not only enhances the efficiency of fillers but also supports sustainable practices by minimizing the demand for extensive asphalt materials. The ongoing advancements in nanotechnology and polymer science are paving the way for the development of various smart materials, poised to address challenges in oil and gas well cementing. This review highlights initiatives aimed at fabricating smart cements for diverse applications [6].

In 2019, researchers explored the mechanical properties of stone mastic asphalt (SMA) by incorporating VIATOP C25 fibers into the asphalt mixture. The study utilized a wheel-tracking device to assess the potential for rutting, revealing that the binder drainage from the aggregates at the production temperature was 0.1% lower when the mixture contained fibers compared to the fiber-free blend. Furthermore, the incorporation of VIATOP C25 fibers resulted in a significant 17% reduction in rutting [7]. Similarly, researchers examined factors influencing asphalt pavement rutting in 2020, finding that increases in temperature and wheel load correspondingly raised the rutting of asphalt mixtures. Their findings also emphasized the crucial roles of air void percentage and fine aggregate content in determining asphalt deformation [8]. Additionally, researchers investigated the rutting performance of bitumen containing rejuvenating agents, conducting tests under both wet and dry conditions on conventional and rejuvenator-laden asphalt mixtures. Their results indicated that asphalt mixtures with rejuvenators exhibited the poorest performance in wet conditions while performing best in dry conditions [9]. In 2020, a study highlighted the significance of nanomaterials, particularly carbon nanotubes (CNTs), as modifiers for bitumen. Various tests, including penetration grade, softening point, ductility, and viscosity, were carried out to evaluate the mechanical performance of CNT-modified binders, demonstrating improvements in both binder stiffness and asphalt rutting resistance [10]. Finally, in 2021, a study assessed the rutting performance of rubberized asphalt using the Hamburg wheel-tracking device and image processing techniques, finding that rubberized asphalt exhibited superior rutting resistance compared to traditional asphalt mixtures due to better compaction, adequate mechanical strength, and reduced sensitivity to water [11].

Recent studies have investigated the role of nanocarbon materials, such as graphene oxide and carbon nanotubes, in enhancing the properties of composites. Research has demonstrated that incorporating graphene oxide-coated fillers within polymer matrices significantly improved mechanical strength and thermal stability. This finding holds considerable potential implications for the application of micronized calcium carbonate (MCC) in similar contexts [12]. Furthermore, micronized calcium carbonate has been extensively studied for its applications in construction and various other industries. A previous study outlined the performance of MCC as a filler in asphalt, illustrating its favorable effects on both workability and durability. Their research underscored the necessity for further exploration into innovative coating techniques aimed at enhancing the material’s properties. Additionally, the mechanical enhancement achieved through the application of nanocarbon coatings has been further elucidated in studies where experimental testing was conducted on various coated fillers, including MCC. The findings indicated that nanocarbon coatings could lead to improved interfacial adhesion, facilitating better stress transfer between the filler and matrix, thus enhancing the overall performance of the composite [13]. Recent comparative studies have also examined the distinct benefits and trade-offs associated with various filler coatings. One such study contrasted the performance of uncoated versus nanocarbon-coated MCC in polymer applications, revealing significant differences in thermal and mechanical responses that warrant further exploration in both experimental and simulation contexts [14].

The integration of numerical methods in analyzing material behavior has gained significant traction in recent years. Researchers have emphasized the importance of finite element analysis (FEA) in predicting the performance of nanocarbon-coated fillers under complex loading conditions [15]. Their work provides a robust framework for simulating material responses to various environmental and mechanical stresses, thereby highlighting the critical role of accurate modeling in material design. Furthermore, empirical data and statistical modeling have proven essential in forecasting the degradation of materials subjected to stress. In this context, one prominent study proposed a predictive model for asphalt rutting based on comprehensive experimental observations [16,17]. This methodology reinforces the necessity of developing predictive capabilities for maintaining roadway integrity, as it facilitates proactive measures in infrastructure management.

The existing literature provides a strong foundation of both experimental data and numerical insights that substantiate the advantages of using nanocarbon coatings. Further research that bridges empirical findings with numerical analyses will be essential in fully understanding these advanced materials’ capabilities. This study employs a comprehensive approach that combines experimental testing The motivation behind this research is rooted in the pressing need to address the pervasive issue of pavement rutting, which significantly impacts roadway safety and infrastructure sustainability. As urbanization and traffic volumes continue to rise, the durability of asphalt pavements has become increasingly critical. Rutting, characterized by permanent deformations in the pavement surface, not only diminishes the structural integrity of roadways but also poses serious safety hazards, including increased vehicle hydroplaning and reduced skid resistance. Consequently, there is an urgent demand for innovative materials and methodologies that can effectively mitigate these issues. This study investigates the potential of nanocarbon-coated micronized calcium carbonate (NCMCC) as a modified filler in asphalt mixtures, aiming to enhance their resistance to rutting. By leveraging advanced materials science, our research seeks to provide a dual benefit: improving the mechanical properties of asphalt while promoting sustainable practices in road construction. Through a combination of empirical testing and finite element modeling, we aim to elucidate the mechanisms by which NCMCC enhances asphalt performance, thereby contributing to the development of more resilient and safer transportation infrastructure.

2. Materials and Methods

This research addresses rutting in asphalt paving, emphasizing its impact on road safety amidst increasing traffic and temperatures. It explores the effects of nanocarbon-coated calcium carbonate as a filler in asphalt mixes, utilizing ABAQUS-22 for numerical simulations to model rutting. The study compares simulation and laboratory results, ensuring reliability and contributing to advancements in pavement design.

2.1. Investigation of Rutting Tests on Asphalt Samples

Rutting is a significant distress that affects the performance and durability of asphalt pavements. This phenomenon arises due to the deformation of the pavement surface under repeated loading, primarily from traffic. The study of rutting is crucial, especially in regions experiencing heavy traffic loads. This research aims to evaluate the rutting behavior of asphalt samples prepared with ordinary calcium carbonate filler and modified calcium carbonate filler. The study utilizes the wheel-tracking test, consistent with ASTM-C29 standards, to facilitate this evaluation [18].

Despite high temperatures and constant stress, the deformation of asphalt mixtures continues at a slow rate, a phenomenon known as creep. Under fixed stress and temperature conditions, the creep rate remains relatively constant over an extended period. However, after this duration and a certain amount of deformation, the creep rate increases, ultimately leading to failure. A suitable model for determining time-dependent deformations of mixtures available in FE software is the power law creep model, specifically the time-hardening type utilized in this research. The model is expressed as follows Equation (1):

$${ϵ}^0=A{\sigma }^n{t}^m$$

(1)

where ${ϵ}^0$ is the uniaxial creep strain rate, $\sigma$ is the uniaxial stress, t is the loading duration, and A, n, and m are material creep parameters. This equation represents the power law, assuming that visco-plastic strain is the primary contributor to permanent deformation, thereby deeming instantaneous plastic strain as negligible [17]. In this study, dynamic creep testing was employed to determine the material parameters, while modulus of elasticity tests was conducted to characterize the elastic behavior of asphalt mixtures. Additionally, results from wheel-tracking tests on the mixtures were utilized to calibrate the developed finite element models.

Calcium carbonate, a naturally occurring substance, is represented by the chemical formula CaCO₃. It exists in various forms, including calcite, aragonite, and vaterite, and possesses a crystalline structure that contributes to its mechanical properties [18]. In the context of asphalt, calcium carbonate functions as a filler that enhances the mixture’s stability, a crucial parameter in resisting deformation. Bitumen, on the other hand, is a complex hydrocarbon mixture, primarily composed of aliphatic and aromatic hydrocarbons, represented by the general formula C_nH_m, where n and m can vary substantially based on the crude oil source and refining process. The molecular weight of bitumen can range from several hundred to thousands of atomic mass units. This complexity makes bitumen susceptible to various environmental and mechanical stresses, emphasizing the need for additives that can enhance its performance. Micronized calcium carbonate possesses a reduced particle size, typically in the range of micrometers, allowing for increased surface area and reactivity. The rigid structure of CaCO₃ contributes to the stiffness of the asphalt matrix, thus providing better resistance against deformation. The hydrophilic nature of calcium carbonate facilitates interactions with the polar components of bitumen, thereby promoting better adhesion and dispersion within the asphalt mixture. The presence of CaCO₃ modifies the microstructure of asphalt, effectively distributing stress more uniformly across the matrix and minimizing concentration points that lead to rutting. The polar nature of calcium carbonate’s (CaCO₃) bonds allows it to interact with water molecules, creating a degree of solubility in aqueous environments. In contrast, bitumen’s structure includes long-chain aliphatic and aromatic hydrocarbons, which repel water and are cohesive only among similar hydrophobic materials. The division between hydrophilic calcium carbonate and hydrophobic bitumen creates an inherent challenge for adhesion [19]. Research highlights that, even in the presence of calcium carbonate, the overall effectiveness of adhesion comes from the physical state of the binding materials (e.g., viscosity, temperature, and the presence of other additives) rather than purely chemical affinities [20]. Calcium carbonate’s role as a filler material extends beyond mere physical interaction or hydrophilic behavior. Various studies indicate that incorporating fillers assists in optimizing the viscoelastic properties of asphalt mixtures, thus improving their overall performance [21].

The advent of nanotechnology has led to the development of nanocarbon materials, which include carbon nanotubes, graphene, and other carbon-based structures that exhibit remarkable mechanical properties. The coating of micronized calcium carbonate with nanocarbon materials significantly alters its chemical and physical properties. Nanocarbon can be represented through its fundamental structures, such as graphene with a chemical formula of C₆H₆ (considering a simplified version) exhibiting high mechanical strength and flexibility. The surface modification through nanocarbon introduces functional groups that enhance chemical compatibility with the hydrocarbons in bitumen, promoting better bonding and reducing the risk of phase separation. The high tensile strength of nanocarbon structures aids in redistributing the loads applied to the pavement. This characteristic is vital in minimizing rut development under repeated traffic loads. Nanocarbon enhances thermal stability, allowing the asphalt to withstand higher temperatures without significant softening or flow, which is critical in preventing rut formation in high-temperature environments [22]. Recent studies have validated that the integration of nanocarbon materials results in improved tensile strength and load distribution in pavement applications, contributing to their enhanced durability and performance [23].

The array of polar and non-polar functional groups on the nanocarbon surface promotes effective entanglement with the long hydrocarbon chains present in bitumen [24]. This entanglement can be expressed in terms of a modified equation for viscosity, wherein the presence of enhanced filler particles (nanocarbon-coated CaCO₃) leads to an increase in the effective viscosity of the bitumen matrix, thereby augmenting rut resistance. This relationship can be approximated in a generalized form (Equation (2)):

$${\eta }_{total}={\eta }_{Bitumen}+{\eta }_{filler}$$

(2)

where ${\eta }_{total}$ is the total viscosity of the modified bitumen, ${\eta }_{Bitumen}$ is the viscosity of the bitumen matrix, and ${\eta }_{filler}$, represents the enhancing contribution of the nanocarbon-coated filler. In the conducted research, asphalt samples were prepared using two different fillers: standard calcium carbonate and a modified version. The objective was to establish a comparative analysis of the rutting performance of each sample. The wheel-tracking test, a widely accepted method for assessing rutting potential, was employed.

2.2. Simulation Using Finite Element Method

The finite element method (FEM) represents a sophisticated numerical technique for addressing partial differential equations pertinent to one or two spatial variables. In this study, all numerical simulations were conducted using Abaqus-2020, a renowned finite element analysis software, providing robust capabilities for modeling complex engineering problems. The three-dimensional finite element method is gaining prominence as a superior alternative to traditional layered elastic and two-dimensional finite element approaches in modeling flexible pavements. This method is recognized as optimal for understanding pavement performance, effectively utilizing internal elements and springs to transfer shear between layers while accurately managing boundary conditions—both critical for analyzing the overall behavior of pavement systems. Despite yielding more realistic results than two-dimensional models, this three-dimensional approach necessitates complex preprocessing steps, leading to a significant increase in the number of elements and amount of computation time and memory requirements.

In the context of creep modeling, research has demonstrated that the response of asphalt mixtures is heavily influenced by temperature and loading duration. Perl’s investigations have illustrated that asphalt mixtures exhibit all three behaviors: viscous, linear elastic, and nonlinear elastic, collectively described as visco-elasto-plastic behavior. Depending on the temperature and loading rate, the contribution of each behavior to the mixture’s overall performance varies. At lower temperatures, the behavior can be approximated as linear elastic, while increasing temperatures lead to a reduction in linear elastic characteristics and an enhancement of nonlinear elastic properties. Further temperature increases transition the behavior toward viscosity. The creep model implemented within the finite element software utilized in this study provides an effective framework for determining time-dependent deformations of the mixtures. This model, though simplistic, is entirely suitable for addressing issues related to rutting. The time-dependent hardening behavior of the creep model is captured in the governing equation to achieve the objectives of this research, where parameters such as strain rate, uniaxial stress, and other material-dependent variables play crucial roles. Previous studies indicate that for rational materials (as illustrated in Equation (3)), the parameters A and n are positive, while m typically ranges between 0 and −1 [17].

$${\epsilon }_{vp}=A{\sigma }^n{t}^m$$

(3)

The three-dimensional modeling is conducted using 3D drawings with volume elements referred to as Solid3D within the software environment. Subsequently, the elastic and plastic characteristics along with the behavioral model (if required) for the pavement structure are introduced (as illustrated in Figure 1). The elastic parameters encompass the modulus of elasticity and Poisson’s ratio, while the plastic parameters largely include the stress–strain characteristics obtained for the asphalt mix through laboratory tests focused on resistance and durability. These parameters are derived and validated based on engineering judgment to establish the most accurate graph for modeling purposes. This graph shows the behavior of the material under loading as realistically as possible.

Following this, the loading methodology and its specific details are elucidated, alongside the type of analysis to be performed. The analysis can be defined as nonlinear static (considering large deformations and their effects); however, since the nature of traffic loads is fundamentally dynamic, the analysis is set as explicit dynamic. Accordingly, it becomes imperative to define the loading function as well. This loading function is represented as a triangular function, whereby its initial value is zero, reaching its maximum at the midpoint of the time interval of loading, and then reverting to zero by the conclusion of the loading period. Subsequently, the amount of applied load is input, and the software calculates the load variations based on the defined function, applying these changes to the model. The mesh refinement process was systematically applied, ensuring that both finer and coarser meshes were analyzed to establish optimal results for dynamic loading conditions.

2.3. Material Properties and Test

In this research, the potential for rutting in asphalt mixtures is investigated using a combination of two AASHTO-2021 aggregate grading ranges, as illustrated in Figure 2 [25]. The optimal asphalt binder content for each mix design was determined using the Marshall method. Subsequently, samples were prepared for dynamic creep tests, resilient modulus tests, and wheel-tracking tests at the optimal asphalt content, ensuring that the air voids in these samples matched the corresponding values from the Marshall samples. Notably, rutting failures in asphalt pavements typically occur in warm climatic conditions, and it has been observed that the predominant binder used in such regions is of the type PG 64-22 (AC60/70), the specifications of which are in

Table 1. Bitumen characteristics.

Test	Standard No.	Amount
Specific weight (g/cm3)	ASTM-D7052	1.02
Penetration (0.1 mm), 100 g, 5 s	ASTM-D5	64
Softness point (°C)	ASTM-D36	53
Flash point (°C)	ASTM-D92	297
Ductility (25 °C; cm)	ASTM-D113	135

; therefore, this study utilized this specific binder for all experimental samples.

In this study, stone aggregates from the local factory were utilized. To investigate and determine the properties of the materials, the following tests were conducted and the results are presented in

Table 2. Results of quality tests on stone aggregates.

Characteristic/Test	Standard Method	Value/Degree	Specification Limits
AASHTO	ASTM	Minimum	Maximum
Coarse Stone Aggregates
Weight Loss due to Abrasion by Los Angeles Method (percentage)
	Type of Gradation	T96	C131
Abrasion Percentage	22	-	-
Weight Loss due to Sodium Sulfate	T104	C88	0.7
Flat and Elongated Particles, 5:1 ratio	D4791	2	-
Fine Stone Aggregates
Plasticity Index Range	PI	T89	T90
Liquid Limit		Not Determined
Weight Loss due to Sodium Sulfate	T104	C88	1.5
Sand Equivalent Value of Cold Silo Aggregates	T176	D2419	65
Corner Roundness of Fine Stone Aggregate Test Method	T304	C1252	45.1

:

As seen in

Table 3. Characteristics of the carbon nanotubes.

Properties	Unit	Specifications of Carbon Nanotubes as Carbon-Based Nano Filler
Density	g/cm3	0.8
		1.8 (theoretical)
Young’s module	TPa	~1
		~0.3–1
Stress at break	GPa	50–500
		10–60
Resistivity	μΩ cm	5–50
Thermal conductivity	W·m−1·K−1	3000
Thermal stability	°C	>700 (in the air);
		2800 (under vacuum)
Specific surface	m2/g	10–20

, carbon nanotubes (CNTs) with a density ranging from 0.8 g/cm³ to 1.8 g/cm³ (theoretical) demonstrate impressive mechanical strength characterized by a Young’s modulus of approximately 1 TPa, with some variations between 0.3 and 1 TPa. Additionally, CNTs possess a specific surface area of 10–20 m²/g, enhancing their utility in diverse technological fields [26].

After the addition of micronized calcium carbonate with carbon to the bitumen, tests were conducted, with corresponding charts presented below each experiment. In mixing micronized calcium carbonate with carbon and bitumen, a high shear mixer was employed. Initially, the bitumen was heated to 150 degrees Celsius, after which the micronized calcium carbonate with carbon was introduced into the bitumen. The mixing process utilized a high shear mixer running at 3000 RPM for 20 min at a constant temperature (Figure 3).

In addition to the Marshall tests based on the ASTM D-1559 standard, dynamic load tests, especially creep, which express the permanent deformation behavior of the asphalt mixture, were also conducted. During this test, vertical stress is applied uniaxially in repetitive pulses to the asphalt sample, with deformations measured radially using sensors integrated into the apparatus. The applied stress is controlled, allowing the user to select the loading waveform (either sinusoidal or square pulses), the duration of the pulse, rest periods before subsequent pulses, deviator stress during each loading pulse, and contact stress to ensure that the load-bearing rod does not lift off the sample during rest periods.

Initially, a static pre-stress of 10 kPa over 600 s is applied to prepare the sample, with cumulative strain measured accordingly. These default values can be adjusted by the operator if necessary. Following a planned 20 s delay during which the stress is reduced to zero, the sample is subjected to repeated loading pulses for 1800 cycles with a stress level of 100 kPa. The applied stress and number of loading cycles can be modified if needed. Each pulse lasts 2 s, consisting of 1 s of loading followed by 1 s of rest, with square wave loading applied. The operator can adjust parameters related to pulse duration and repetition. Strain is measured during both static stress application and loading cycles using two LVDTs aligned with the loading axis. The end test conditions can also be predetermined, either by selecting a maximum axial strain or by setting a maximum number of loading cycles, which in this study, was fixed at 180 cycles. After the test, the experimental data can be plotted on a graph with horizontal and vertical axes.

During the wheel-tracking test, asphalt samples are submerged in hot water to simulate operating conditions. A steel wheel traverses the surface of the asphalt sample, replicating the action of vehicle tires. The depth of rutting is recorded after a specified number of cycles—in this case, 2000 cycles—providing a clear indication of the asphalt mixture’s susceptibility to permanent deformation, as illustrated in Figure 4.

The wheel-tracking test involves several critical steps. The asphalt mixtures containing either ordinary or modified calcium carbonate fillers that were compacted to achieve uniform density and integrity. Each sample was immersed in hot water to attain a temperature that emulates in-service conditions, allowing for accurate simulation of material behavior under traffic loads. A steel wheel is then set to travel a predetermined path across the asphalt sample. The weight of the wheel mimics that of a vehicle, allowing for an effective assessment of the material’s response to load. After the completion of 2000 cycles, the depth of any ruts formed was meticulously measured. These data reflect the resistance of the asphalt mixture to deformation resulting from wheel loading. A total of six series of Marshall samples with varying bitumen content were prepared, each undergoing three repetitions, along with two samples for the creep test and two samples for the rutting test.

The results obtained from the wheel-tracking test were analyzed quantitatively and qualitatively to draw meaningful conclusions regarding the performance of the asphalt samples. The preliminary results indicate a variance in rutting performance between samples containing ordinary calcium carbonate and those containing modified calcium carbonate. The wheel-tracking test serves as a reliable and effective method for evaluating the rutting potential of asphalt mixtures.

3. Results and Discussion

3.1. Laboratory Data

Determining the optimal asphalt binder content is a critical aspect of asphalt mixture design, particularly when incorporating calcium carbonate. In this section, the optimal binder percentages are derived from the Marshall test results, as presented in the accompanying tables. The samples utilized in the Marshall test were prepared in a standard cylindrical mold with a diameter of 10 cm and a height of nearly 7 cm, with three replicates performed for each variable. Following the definitions outlined in the previous chapter, the optimal binder content is determined through a comprehensive analysis of the Marshall stability, specific gravity, and void content graphs. Based on the graphical data, an optimal binder content of 4.4% is established, as illustrated in Figure 5.

Furthermore, the creep tests conducted are essential for evaluating the long-term durability of asphalt materials under sustained loads and high temperatures. While creep tests are commonly performed at elevated temperatures, some materials exhibit creep at ambient conditions as well. Permanent deformation, a prevalent failure mode in asphalt pavements, can be controlled through various tests, including wheel-rutting and creep assessments. Key parameters such as temperature, rest periods between loading cycles, and the number of loading cycles are carefully considered. The simple creep test developed by Shell in the 1970s applies uniaxial pressure to cylindrical bitumen samples, offering ease of sample preparation and low testing costs. Nevertheless, it is important to note that the static loading mechanism does not accurately simulate the traffic conditions asphalt experiences, which has implications for predicting crack depths within pavement systems. Dynamic tests present a more complex approach, applying cyclic loads and varying frequencies, thus requiring precise load application and deformation measurement systems. A comparative study on conventional versus carbon fillers in creep performance highlights significant differences in deformation behaviors, with a statistical analysis affirming the impact of these materials on performance outcomes, as illustrated in

Table 4. The results of the creep test on asphalt mixtures.

Creep Test	1st	2nd	3rd	Average	Shapiro–Wilk	T	Sig
Base	0.65	0.59	0.61	0.616	0.637	39.5	0.001
Main	0.38	0.32	0.36	0.353	0.637

.

In the context of evaluating asphalt pavement performance, particularly under load conditions, incorporating trace orbit analysis can significantly enhance our understanding of through-the-thickness displacement or deformation, especially when considering the rigidity of nano fillers. The rutting test, a pivotal aspect of this investigation, served as a key indicator of asphalt degradation. To comprehensively assess the effects of conventional versus carbon fillers, the wheel-tracking test was executed over 2000 cycles. The findings, illustrated in Figure 6, reveal a marked improvement in the resistance to deformation when carbon filler is utilized, as evidenced by the reduced rut depth observed in the asphalt surface. This reduction highlights the superior performance of carbon filler in enhancing pavement durability, suggesting its potential for broader applications in road construction and maintenance strategies.

In the context of evaluating asphalt pavement performance, particularly under load conditions, incorporating rutting analysis can significantly enhance our understanding of through-the-thickness displacement or deformation, especially when considering the rigidity of nano fillers. The rutting test, a pivotal aspect of this investigation, served as a key indicator of asphalt degradation. The reduced creep exhibited by nanocarbon-coated calcium carbonate can be attributed to several factors, primarily concerning its interfacial bonding properties and mechanical constraints imposed by nanocarbon. The nanocarbon coating enhances the compatibility of the calcium carbonate particles with the asphalt binder. The high specific surface area of the nanocarbon allows for better anchoring and interlocking of the filler within the asphalt matrix. This positive interaction minimizes movement among particles when subjected to loading, thereby decreasing the likelihood of deformational creep. Nanocarbon materials often exhibit lower thermal expansion than conventional fillers. As asphalt pavements experience temperature fluctuations, materials expand and contract. The thermal stability provided by nanocarbon coatings contributes to reducing the softening of asphalt, which is often responsible for rutting. The stiffness of asphalt mixtures can be effectively enhanced by incorporating nanocarbon-coated fillers.

A stiffer mixture is inherently more resistant to permanent deformation under load, thus reducing the occurrences of both short-term and long-term deformation processes. A number of research articles have previously addressed the use of modified fillers in asphalt mixtures, illustrating similar findings of enhanced mechanical properties and reduced deformation. In the study, the authors demonstrated that the introduction of modified calcium carbonate resulted in a reduction in the rut depth of asphalt mixes when subjected to wheel-tracking tests [27]. This research effectively indicates that the modification of fillers leads to significant enhancements in resistance to rutting. Similarly, in another study, the authors explored the impact of incorporating multi-walled carbon nanotubes into asphalt mixtures [3]. Their findings suggested a notable increase in the stiffness modulus, which, in turn, contributed to improved performance regarding both creep and rutting resistance. The findings from both studies align with the hypothesis that the modification of fillers can lead to significant enhancements in the behavior of asphalt mixtures. A comprehensive analysis involving numerous tests and various conditions is essential for reaching definitive conclusions. This study specifically focuses on comparative research, exploring the causal relationships between variables.

3.2. Numerical Analysis Data

In this research, the planar strain model is initially analyzed, followed by a three-dimensional model assessment. The value of E for the asphalt mixture is assumed to be approximately 1800 mPa, with a Poisson’s ratio of 0.35, as indicated in prior studies. The modulus of elasticity (E) is crucial for understanding material stiffness and performance in asphalt mixtures, as established in existing research [28]. The distribution of stress, strain, deformation, and acceleration resulting from loading is presented in Figure 7 and Figure 8, based on both two-dimensional and three-dimensional analyses. Although the depth of the rutting and deformation parameters were derived from software simulations, it is important to note that the width of the wheel equipment was assessed experimentally. Unfortunately, a comprehensive three-dimensional analysis was not conducted in this study.

The curves derived from these analyses, utilizing both software and laboratory methods, are illustrated in Figure 9 and Figure 10, where the horizontal axis represents the number of loading cycles, while the vertical axis denotes the displacement corresponding to the number of loading cycles. The outcomes of the numerical analysis for displacement in the two-dimensional scenario indicated a maximum relative error of up to 12% compared to the experimental results, which can be minimized through mesh refinement and adjustments via trial and error. Generally, a finer mesh results in softer model behavior and increased deformations, while a coarser mesh yields a stiffer model. However, for dynamic loading, a mesh that is either finer or coarser than the average could yield opposite results; thus, an initial medium mesh was considered, followed by gradual refinement or coarsening. Furthermore, the results from the three-dimensional analysis show an average increase in the number of cycles (and consequently sample resistance) of up to 35% compared to the resistance of the two-dimensional model for samples with ordinary calcium carbonate and approximately 50% for samples with carbon-coated calcium carbonate. The investigation into the deformation and fracture profiles during wheel loading is crucial for understanding the mechanical behavior of materials under stress. Although the depth of the rutting and deformation parameters were derived from software simulations, it is important to note that the width of the wheel equipment was assessed experimentally.

The use of linear elastic parameters offers a notable advantage due to the model’s simplicity compared to plastic or viscoelastic methods, facilitating quicker computations and easier result interpretation, particularly in preliminary assessments or design phases. However, it is essential to recognize the limitations of this approach, as asphalt exhibits nonlinear behavior under repeated loading and varying temperatures [29]. Relying solely on linear elasticity may underestimate the stress–strain response, affecting predictions related to crack formation. This research conducted a comparative analysis of two Euler states and examined two-dimensional versus three-dimensional scenarios, focusing on the elastic properties of materials to elucidate the impact of dimensionality and model selection on performance outcomes. Numerous experimental and regression models were established to represent pavement behavior, complementing the numerical simulations employed in this study.

The curves obtained from both models based on computational and laboratory methods are depicted in Figure 9 and Figure 10, wherein the horizontal axis represents the number of loading cycles and the vertical axis indicates the corresponding displacement for those cycles. This study highlights that the calibration of the finite element model against experimental data ensures accurate representation of material behavior under load, confirming convergence criteria. Notably, mesh refinement and the use of both two-dimensional and three-dimensional analyses significantly enhance the accuracy of deformation predictions. Generally finer mesh results in a softer model behavior and increased deformations, whereas coarser mesh yields a stiffer model. 2D FEM simulations of flexible pavement under dynamic loading show model dimensions of 5 m × 3 m for accuracy and validity. [30]. However, for dynamic loading conditions, both excessively fine and overly coarse meshes can yield counterintuitive results, necessitating an initial moderate mesh, followed by gradual refinement or coarsening. Additionally, the three-dimensional analysis demonstrated an average increase in cycle count (and consequently, sample resistance) of up to 35% relative to the two-dimensional model for specimens using regular calcium carbonate and approximately 50% for those coated with carbon. The comparison of predicted rutting values with measured results indicates a discrepancy of 11.5% for the three-dimensional case and 13.5% for the two-dimensional case, thereby establishing a sound validation for the modeling approach embraced in this research based on prior studies. From a mechanics’ perspective, the principle of superposition is essential for analyzing deformations, particularly in 3D modeling, where the interplay of horizontal and vertical stresses can be effectively assessed. Rutting mechanics, influenced by shear and vertical stresses, are better understood within a 3D context. This modeling approach not only simulates plastic flow mechanisms but also reveals microstructural changes in asphalt mixtures due to cyclic loading. Moreover, 3D modeling addresses spatial variations in material properties within asphalt layers, with implications for performance amid factors like density and composition. By incorporating real-world variables, such as moisture and aggregate interlocking, these models enhance the accuracy of pavement behavior representation, aiding engineers in optimizing material designs and paving practices. Figure 9 and Figure 10 illustrate the comparison between the predicted and measured rut depths for the two-dimensional and three-dimensional models, respectively. As evidenced in these graphs, calibration efforts resulted in a reduction in discrepancies, with the fitting slope approaching unity. This study offers a significant advancement in understanding the behavior of modified asphalt mixtures through innovative filler materials. By correlating experimental results with numerical simulations, it provides a comprehensive framework for predicting rutting behavior.

4. Conclusions

The study investigates rutting in asphalt pavements, a significant failure influenced by traffic, climate, materials, and time. It begins by assessing the elastic and visco-plastic properties of materials through tests like the bending modulus and dynamic creep tests. A finite element model for wheel-tracking tests was developed and calibrated against experimental results. This research also explores the effect of carbon-coated micronized calcium carbonate as a modified filler, utilizing numerical methods in FE software to compare findings with laboratory results.

Rutting, a primary failure mechanism in asphalt pavements, arises from traffic, environmental conditions, material properties, and time, necessitating an in-depth investigation of these contributing factors to devise effective preventive strategies.

The study emphasizes the importance of characterizing both elastic and visco-plastic properties through rigorous testing methods, including the elastic modulus and dynamic creep tests, which are critical for understanding material behavior under load. Developing and calibrating a finite element model based on wheel-tracking tests allows for accurate predictions of rut depth in asphalt pavements, thereby enhancing the reliability of engineering assessments and design strategies.

The results obtained from the numerical analysis of displacements in a two-dimensional state show a relative error of up to 12% between the experimental results and numerical modeling. This error can be reduced based on mesh refinement and through trial and error by adjusting the mesh density. Generally, a finer mesh leads to softer model behavior and increased deformations, while a coarser mesh results in a stiffer model. However, for dynamic loading, a mesh that is either finer than average or coarser than average can yield opposite results. Therefore, an average mesh density is initially considered as the standard, which is then gradually refined or coarsened. This study underscores the critical importance of three-dimensional (3D) modeling in effectively simulating the intricate interactions present within asphalt mixtures. It highlights the model’s advanced capability to precisely represent the distributions of vertical and shear stresses, which are significant factors influencing rutting behavior. Furthermore, the research demonstrates that the modeling framework not only mirrors the underlying physical mechanisms at play but also aligns closely with performance conditions observed in real-world applications. By leveraging this sophisticated modeling approach, the findings provide valuable insights that can enhance our understanding of asphalt performance.

Additionally, the results of the three-dimensional analysis demonstrate, on average, an increase in deformations of up to 35% compared to the two-dimensional model. This not only emphasizes the necessity of using a three-dimensional model for simulating the problem (as the results are significantly higher) but also indicates that the three-dimensional model is more realistic compared to the two-dimensional one.

Incorporating a carbon-coated micronized calcium carbonate powder as a modified filler significantly reduces rut depth, demonstrating the potential of innovative materials in improving asphalt performance and longevity. The strong correlation between numerical simulations and laboratory results validates the use of finite element methods, highlighting the effectiveness of advanced modeling techniques in predicting pavement behavior and optimizing asphalt mixtures.