Advances in simulation parameters and methods for three-dimensional mesoscopic model of asphalt mixture

Abstract

Asphalt mixtures are complex and heterogeneous materials whose performance is governed by their intricate mesostructure and multiphase interactions. Three-dimensional (3D) numerical simulation has emerged as a powerful tool for evaluating the structure and mechanical response of asphalt mixtures. This paper synthesizes recent advances in 3D mesoscopic simulation of asphalt mixtures, distinguishing the distinctions and benefits of image-based and user-defined 3D model generation techniques. This paper identifies the important parameters that affect the reliability of 3D models, encompassing aggregate parameters, asphalt mortar parameters and air void parameters. Furthermore, it outlines the advantages and disadvantages of mainstream 3D simulation methods for asphalt mixtures, along with recent developments in multi-method coupled 3D simulation. Finally, the process and challenges of model validation are discussed. Future research should focus on the precise characterization of aggregate size, morphology, and aggregate–aggregate contact models. The development of reusable digital aggregate libraries is essential to enhance the realism and efficiency of 3D model generation. Improvements in coupled simulation techniques are also needed to ensure interface data consistency and force–displacement synchronization. Moreover, researchers should provide more comprehensive documentation of parameter calibration and iterative optimization processes.

Graphical abstract

Keywords

asphalt mixture / numerical simulation / three-dimensional mesoscopic model / model generation

1 Introduction

Asphalt mixtures exhibited varied mechanical behaviors under different conditions due to their complex internal structures and multi-phase compositions [1,2]. Numerical simulation plays a pivotal role in understanding and predicting the performance of asphalt mixtures [3,4]. Numerical simulations also offer significant cost and time savings compared to traditional experimental methods, enabling the efficient exploration of innovative materials and construction techniques [5,6].

The history of numerical simulation in asphalt mixture research began in the mid-20th century, early studies mainly focused on simple models developed using the Finite Element Method (FEM) [7,8]. These foundational efforts paved the way for the development of two-dimensional (2D) mesoscopic modeling techniques in the late 1990s and early 2000s [9–11]. Researchers have achieved significant progress in studying the internal structure and mechanical properties of asphalt mixtures using 2D simulation techniques [12–14]. However, compared to actual three-dimensional (3D) structures, 2D simulation models often depict aggregate structures as larger than they are in reality [15,16]. By capturing only cross-sectional views, 2D simulations often lead to inaccuracies in the depiction of particle distribution and void structures [17,18]. This is due to the inherent difference between 2D area gradations and 3D volumetric gradations [19]. The stereology and inverse stereology techniques are employed to convert between these distributions, ensuring that the modeled aggregate structure reflects the actual mixture gradation more accurately [19,20]. But Filonzi et al. [21] point out that inverse stereology approach is not able to accurately represent the distribution of aspect ratios of aggregates. In addition, some researchers have observed that the straightforward superposition of 2D constitutive models often underestimates the interlocking effects within particle assemblies [22,23]. It was found that these models under-predicted mixture modulus and creep stiffness at all temperatures and loading frequencies, because of the limitation of aggregate–aggregate contact and interlock effects and the reduced microstructure in the 2D models [13,24,25]. The evolution of asphalt mixture modeling has transitioned from 2D to 3D in the recent year [26–28].

Researchers have employed 3D simulation techniques to analyze the micromechanical interactions between aggregates [29–31]. Early 3D modeling studies demonstrated the feasibility of simulating asphalt mesostructures and mechanical responses, while revealing challenges in realism and calibration. With the development of 3D FEM and Discrete Element Method (DEM), researchers have successfully simulated the intricate behavior of asphalt mortar within asphalt mixtures [32,33]. These studies have examined the distribution of contact forces within the asphalt mortar under specific conditions and its impact on the overall performance of the mixtures. Additionally, 3D FEM has been utilized to analyze the influence of aggregate particles on the mastic and air-voids in Asphalt Concrete (AC) [34]. The findings highlight 3D simulation as a promising and effective method for modeling aggregates, asphalt mortar, and voids in asphalt mixtures [35]. However, existing 3D mesoscopic models often lack interoperability, and the effects of parameter settings on model outcomes are not always thoroughly investigated.

By comparing the results of indirect tensile tests conducted on 2D and 3D asphalt mixture simulations, researchers have concluded that the force–displacement results obtained from 3D simulations are more stable and reliable than those derived from 2D simulations [36]. 2D models fail to fully capture stress concentrations and strain processes in certain directions during crack propagation. 3D simulations provided a more accurate and comprehensive depiction of these critical mechanical behaviors [37,38]. Researchers have developed large-scale 3D asphalt pavement models to investigate mechanical responses under various loading conditions, offering valuable insights for optimizing pavement design through advanced numerical simulation techniques [39,40]. However, earlier 3D simulation studies were limited by computational constraints, often necessitating parameter simplifications that compromised result accuracy [41]. Moreover, these models frequently lacked precise boundary conditions, such as non-uniform loads and temperature gradients [42]. Recent advances in computational technology and enhanced understanding of asphalt mixture simulation have driven significant progress in the field [43,44]. Researchers conduct parameter sensitivity analyses for aggregates, asphalt mortar, and voids and have developed multi-method, multi-scale coupled 3D models to improve the reliability and realism of numerical simulations [45,46]. Despite these technological advancements and their broad applications, challenges remain in systematically synthesizing recent progress, identifying current limitations, and clarifying future research opportunities. A review of the current state of 3D simulation in asphalt mixtures is necessary.

The primary objective of this paper is to review and sum up the latest research findings and developments in 3D mesoscopic simulation for asphalt mixtures in recent years. This paper focuses on four key topics: 1) 3D modeling generation methods for asphalt mixtures; 2) important parameters of models; 3) 3D numerical simulation methods for asphalt mixtures; and 4) validation of 3D simulation. In addition, this paper also identifies future research opportunities in digital aggregate libraries, coupling algorithms, and standardized calibration protocols, aiming to provide a forward-looking perspective for advancing mesoscopic modeling of asphalt mixtures.

2 Different three-dimensional modeling generation methods for asphalt mixture

In early studies, asphalt mixtures were modeled as homogeneous materials for computational simplicity [47]. Over the past two decades, advances in mesoscale modeling techniques have enabled heterogeneous models, assigning distinct properties to aggregates and binder matrices, providing more realistic and reliable simulation outcomes compared to homogeneous approaches [48,49]. Currently, methods for 3D mesoscale heterogeneous model generation fall into two main categories, as shown in Figs. 1(a) and 1(b).

2.1 Image-based generation of three-dimensional models

Significant progress was achieved in depicting the intricacies of aggregate–asphalt interfaces and air void distribution within asphalt mixtures using X-ray Computed Tomography (CT) or optical imaging techniques [4,52]. The internal images of asphalt mixtures obtained through CT scanning require preprocessing steps [53–55]. Preprocessing of CT images includes denoising, normalization for consistent contrast, and binarization for simplification [56,57]. Morphological operations such as boundary detection and pore filling are crucial for accurate phase delineation [58]. The selection of image processing algorithms, particularly edge detection and morphological techniques, critically impacts feature extraction effectiveness and model precision [59,60]. The gathered data encompass various components of the asphalt mixture, including air voids, aggregates, asphalt mortar, and additional components like rubber, capsules, and fibers [60,61].

Meng et al. [59] and Xu et al. [62] generated 3D models of voids in asphalt mixtures based on images and conducted quantitative analysis of void characteristics and shape parameters. Similarly, Liu et al. [53] generated 3D models of coarse aggregates and quantitatively analyzed the characteristics and distribution of coarse aggregates. Jin et al. [45] and Sun et al. [50] generated 3D models of asphalt mortar within mixtures, focusing on the quantitative analysis of asphalt mastic distribution. Additionally, some researchers utilized image-based generation models to analysis the distribution and movement processes of additives in asphalt mixtures [57,63].

Over the past five years, approximately 75% of researchers using CT imaging for generated asphalt mixture models have focused on void structures. The advantage of image-based models lies in their ability to replicate the meso-structure of asphalt mixtures, resulting in generated models that closely align with actual conditions while eliminating the need for manually filling various elements within the asphalt mixture. The voids characteristics (especially equivalent diameter of voids) derived from image-based models is a key microparameter that plays an essential role in estimating the permeability of porous asphalt mixtures and Open Graded Friction Courses (OGFC) [64,65]. However, such models have notable drawbacks, including high generation costs and challenges in reproducibility. With the integration of CT into DEM and FEM models, the issue of reproducibility is being addressed [17,66].

2.2 User-defined generation of three-dimensional models

The generation of 3D asphalt mixture models based on user-defined methods primarily involves two key steps: the numerical components modeling and components filling. The components in a 3D asphalt mixture model primarily include aggregates, asphalt mortar, and air voids [67,68]. The coarse aggregate model is the most critical component, as it often determines the distribution of asphalt mortar and air voids [69,70].

The first step is typically the creation of a numerical model for coarse aggregates, which can be categorized as idealized, irregular angle, and realistic coarse aggregate model, as shown in Figs. 2(a)–2(c). Idealized aggregate models use geometric shapes like circles, quadrilaterals, or hexagons to simulate coarse aggregates [72,73]. Irregular angle aggregate models generate aggregates with irregular shapes using random methods [74,75]. Realistic models are based on real coarse aggregate and CT scanning [55]. After constructing a large number of digital aggregate models, researchers have established digital aggregate library based on morphological characteristics of realistic aggregates [45,76–78], as shown in Fig. 2(d).

To classify the real aggregates in the database, it is necessary to quantify the morphological characteristics of the aggregate model [79,80]. For the quantification of these morphological indices, the aggregate surface was segmented into numerous small triangular facets, adhering to a predefined fitting accuracy [81], as shown in Fig. 3. The dihedral angles between any two such clusters were calculated as surface angles. This is to avoid concave areas on the surface of the model that may result in significant loss of shape [82]. To ensure the accuracy and representativeness of aggregate feature extraction, surface discretization and statistical quantification methods are employed, while digital aggregate libraries are validated against empirical data to ensure that the stored morphological characteristics reliably reflect real aggregate geometries.

In addition to common aggregates, digital models of reclaimed asphalt pavement aggregate have also been developed by researchers [65,83]. In contrast to numerical models derived from X-ray imaging of composite specimens, models based on realistic aggregate representations offer advantages in terms of time and resource efficiency.

The second step in user-defined generation of 3D models involves volume discretization. The method of discretizing the volume within the 3D model is a key factor affecting the authenticity of the simulation. Table 1 shows the main methods of volume discretization along with their advantages and disadvantages.

The choice of volume discretization method should depend on the specific research needs and computational complexity. Virtual compaction method excels in simulating the real compaction process, providing realistic aggregate distribution and movement states [87,88]. The main steps of the virtual compaction method are shown in Fig. 4. During the discretization process, virtual compaction employs three mainstream control methods: specimen height control, compaction frequency control, and compaction stress control [44,90].

2.3 Future directions in three-dimensional generation methods

Image-based generation methods provide highly accurate reconstructions of asphalt mesostructures but are hindered by high computational cost and limited reproducibility. Conversely, user-defined methods offer efficiency and flexibility but heavily rely on parameter assumptions, which may compromise realism. Thus, it is proposed to establish a digital library of realistic aggregates to store and reuse these models efficiently, in which aggregate particles are quantified and classified by size, surface and shape descriptors. Such a library will enable consistent reuse of validated particles, significantly reducing model construction time and ensuring morphological fidelity. Furthermore, user-defined virtual compaction methods, which replicate the densification process via stress-controlled or frequency-controlled packing. This method can better represent aggregate movement, contact evolution, and structural skeleton formation. Future developments should focus on coupling digital aggregate libraries with physically-informed compaction algorithms to achieve accurate 3D model representations of asphalt mixtures [91].

3 Important parameters of three-dimensional numerical models of asphalt mixtures

In the generation and simulation experiments of 3D asphalt mixture models, the parameters of the numerical model play a critical role. Among these parameters, those related to the aggregates, asphalt mortar and void are pivotal in determining the model’s predictive accuracy.

3.1 Aggregate simulation parameters

Typically, the characterization of aggregate is categorized into four types: size, shape, angularity, and texture [92,93]. The aggregates size parameters represent their macroscopic characteristics and are considered by some researchers to be the most critical aggregate parameters in numerical simulations [93–95]. Due to its primary association with the mixture’s gradation.

Li et al. [95] demonstrated the dependence of simulation results on aggregate size parameters, highlighting the significant influence of size on the magnitude and distribution of stresses between aggregates. Zhu et al. [43] further analyzed the movement and contact unbalanced forces of aggregates with different sizes during the compaction process, as shown in Figs. 5(a) and 5(b).

The results indicated that the contact number and vertical unbalanced force increased with aggregate size, resulting in greater displacements for larger coarse aggregate particles. Similar conclusions were reached by Wang et al. [44] and Ren et al. [96]. Wang et al. [97] observed that the content of 9.5 mm aggregates has the greatest impact on the internal structure of OGFC and analyzed its effect on skeleton strength, as shown in Figs. 5(c) and 5(d). Optimal ranges for aggregate size parameters are typically determined through simulation–experiment calibration and statistical analysis, ensuring that selected values reflect both realistic gradation structures and reliable mechanical performance trends. The study suggested setting 40% and 80% as the lower and upper limits for the 9.5 mm aggregate content.

In addition to aggregate size, the influence of aggregate morphology parameters on models is also a significant area of research, as shown in Fig. 6(c). Aggregate shape was usually measured by sphericity, flatness and elongation [98,99]. Researchers have quantitatively analyzed the effects of these parameters on simulation results, as shown in Figs. 6(a) and 6(b). The findings showed that aggregate shape properties have a notably good correlation with skeleton strength, and cubical shape is the recommended shape [98–100].

Researchers have quantitatively analyzed the effects of angularity and texture parameters on asphalt mixture models, as shown in Figs. 6(d)–6(g). The results indicate that aggregate morphology parameters directly influence the number of contact points, contact area, and contact forces between aggregates, thereby affecting the macroscopic performance of asphalt mixtures [104,105]. Higher 3D angularity and surface friction of aggregates lead to improved contact conditions between aggregates [101,106].

Notably, the 3D angularity of aggregates significantly impacts the number of contact points and contact lengths between aggregates, which strongly affects the high-temperature and compaction performance of asphalt mixtures [102]. Souza et al. [107] observed that the angularity of fine aggregates has a more pronounced impact than that of coarse aggregates, primarily due to the influence of fine aggregates on asphalt mortar. Surface roughness has a relatively smaller effect on mixture performance [103]. Furthermore, researchers analyzed the contributions of different types of aggregate morphological parameters to strength within the same model, as shown in Fig. 7.

Within the same simulation model, the flat-elongated parameter and angularity parameter contribute the most to the asphalt mixture strength, as shown in Figs. 7(a) and 7(b). Neural network-based analyses further confirm that, regardless of aggregate size, the flat-elongated parameter and angularity parameter consistently have the highest contributions to strength. The flat-elongated parameter is strongly correlated with aggregate size [95]. Consistent with these findings, and sum up the discussions in Subsection 3.1, this paper concludes that the importance of aggregate parameters is ranked as follows: size parameter > angularity parameter > texture parameter > shape parameter.

3.2 Asphalt mortar simulation parameters

In asphalt mixture simulation studies, fine aggregates smaller than 2.36 mm are typically combined with asphalt binder and regarded as asphalt mastic, constituting approximately 20%–25% of the asphalt mixture [108]. In 3D mesoscopic modeling of asphalt mixtures, asphalt mortar can be represented either implicitly through aggregate contact parameters (contact models) or explicitly as independent, real particle phases with defined geometry and properties [109]. The contact model implicitly simulates asphalt mortar through aggregate interactions, favoring computational efficiency, whereas the real particle model explicitly represents mortar geometry and properties [110]. The primary parameters of real asphalt mastic model are viscoelastic parameters and thickness parameters [111]. The viscoelastic properties of asphalt mastic (Prony series parameters and Burgers model parameters) are typically derived from mechanical performance tests conducted at specific frequencies and temperatures [112,113]. Jiang et al. [114] constructed histograms of mastic thickness distribution in simulation models of asphalt mixtures. Onifade et al. [115] developed a function for asphalt mastic thickness considering the volumes of aggregates, voids, and asphalt absorption. The increase in modulus diminishes as the thickness of the asphalt mastic increases, indicating that its contribution to strength tends to saturate Figs. 8(a) and 8(b). However, You et al. [117] considered extremely small asphalt mastic thicknesses can significantly increase computational time. Therefore, it is not recommended to adopt overly small thickness parameters.

Researchers have also investigated the effects of surface parameters of asphalt mastic on simulation models [27,36]. Camara et al. [22] conducted a sensitivity analysis and demonstrated that the elastic parameters in the contact model had negligible effects on the dynamic modulus of the mixture. Similar conclusions were drawn by Ren et al. [118]. They found that the generalized Maxwell contact model provides the highest simulation precision at low temperatures, while the generalized Kelvin contact model offers improved accuracy at high temperatures.

Compared to aggregate parameters, researchers often prioritize ensuring that asphalt mastic performance parameters closely align with actual properties and that thickness parameters remain within acceptable error ranges. They pay less attention to analyzing the effects of asphalt mastic parameters on performance. This focus is likely due to the common simplifications in asphalt mixture simulation models, where asphalt mastic is typically treated as a homogeneous material. Additionally, effective methods for accurately determining the internal contact parameters of asphalt mastic are still lacking [22,27]. Yu and Shen [87] introduced the concept of “homogeneous asphalt mortar”, facilitating the conversion of dynamic modulus of asphalt mastic under multi-source coupling conditions.

3.3 Aggregate and asphalt mortar contact type

In mesoscopic simulation of asphalt mixtures, the concept of contact includes both contact models (e.g., Maxwell, Burgers, and Kelvin–Voigt models) and contact types [119]. While comprehensive reviews of contact models and their selection criteria have been provided by previous studies, relatively limited research has systematically compared the significance of various contact types [120,121]. Contact type between aggregates and asphalt mortar are also critical factors influencing asphalt mixture models. These contact can be categorized into three types: aggregate–aggregate contact, asphalt–asphalt mortar contact, and aggregate–asphalt mortar contact [122,123].

Researchers have characterized the distribution of contact forces in asphalt mixtures under different conditions, as shown in Figs. 9(a)–9(c). Zhang et al. [125] demonstrated that the contact forces among these three types are highly uneven, with contact forces in coarse aggregates contributing to over 50% of the total contact forces. However, Nian et al. [113] argued that aggregate–asphalt mortar contact accounts for more than 90% of the bending strength in asphalt mixtures. They also acknowledged, nonetheless, that aggregate–aggregate contact provides the greatest overall strength. Additionally, studies have identified a higher susceptibility to damage at aggregate-to-mastic contacts compared to contacts within the mastic phase [126].

The study summarized the contributions of different contact types to various strengths of asphalt mixtures, as shown in Fig. 9(d). Aggregate–aggregate contact exhibited the highest contribution rates to splitting strength and rutting resistance strength. In contrast, aggregate–asphalt mortar contact contributed the most to flexural tensile strength and three-point bending strength, consistent with the findings of Nian et al. [113]. However, aggregate–aggregate contact forces were still greater overall, as shown in Fig. 9(e). Jiang et al. [124] further demonstrated that the contact force hierarchy in asphalt mixtures is as follows: aggregate–aggregate > aggregate–asphalt mortar > asphalt–asphalt mortar. Based on these findings, this paper concludes that the importance of contact types in asphalt mixtures can be ranked as: aggregate–aggregate > aggregate–asphalt mortar > asphalt–asphalt mortar.

3.4 Air void simulation parameters

In asphalt mixtures, aside from aggregates and asphalt mortar, air voids are the final essential component [67]. In 3D mesoscopic modeling of asphalt mixtures, air voids are typically represented explicitly as independent geometric entities with defined boundaries, size, shape, and spatial distribution. Researchers have created 3D air void models by stacking multiple 2D void layers in both horizontal and vertical directions, as shown in Fig. 10(a). The most prominent parameter of air voids is the air void content [49]. Researchers developed models with varying air void contents and analyzed their impact on mixture performance, as shown in Figs. 10(b)–10(d). This paper found that simulation research in this area primarily focuses on drainage and acoustic absorption performance. Aboufoul et al. [127] and Chen et al. [128] demonstrated that the flow velocity, hydraulic conductivity, and permeability of asphalt mixtures are significantly influenced by air void content. In particular, hydraulic conductivity shows marked changes when the void ratio ranges from 17% to 23%. Jiang et al. [67] and Gao et al. [129] identified air void content as a parameter strongly correlated with noise reduction characteristics, with the sound absorption coefficient being nearly linearly related to air void content. Wu et al. [130] and Feng et al. [131] also found a significant relationship between the uniformity of air void distribution and the indirect tensile strength of asphalt mixture models. However, they noted that the number of air voids has an even greater influence on model performance.

Air voids were typically categorized into two types: connected voids and non-connected voids [132,133], as shown in Figs. 11(a)–11(c). Researchers tend to focus more on the effects of connected voids and the characteristics of their axis on the model [135,136]. Chen et al. [137] found a strong correlation between total void content and connected void volume (R² = 0.91). Ling et al. [134] quantitatively analyzed the void and connected axis parameters in models with varying void contents and examined the effects of these parameters on the fluid velocity field in both vertical and horizontal directions. They identified the significance of connected void characteristics on seepage velocity in the following order: connected void content > void size and connected axis size >> connected axis number and tortuosity.

Based on the findings on voids, this paper concludes that simulation models of asphalt mixtures should prioritize connected void content parameters. In cases of limited computational precision, ensuring the correctness and rationality of void content parameters should be the primary focus, with appropriate attention given to void size and distribution parameters.

3.5 Future directions in asphalt mixtures model parameter research

Previous studies have extensively examined individual model parameters; however, interactive effects, particularly between aggregate size and morphological features, remain underexplored. Additionally, asphalt mortar is often oversimplified in existing models, and void representations are commonly limited to bulk content metrics. Future research should enhance the precision of aggregate angularity and texture characterization, as these factors strongly affect inter-particle contact behavior and load transfer efficiency. Explicitly modeling asphalt mortar geometry and viscoelasticity, rather than treating it as a homogeneous filler, will improve simulations of stress dissipation and fatigue resistance. Air void modeling should prioritize connected void content and axis continuity. Finally, aggregate–aggregate contact should remain the primary focus in interface modeling, as it governs the majority of internal contact forces, dominates the development of skeleton structure, and plays a decisive role in simulating splitting and rutting resistance.

4 Different methods for three-dimensional numerical simulation of asphalt mixture

The 3D numerical model of asphalt mixtures includes not only the primary characteristic structural parameters but also various simulation methods, which collectively describe the properties of asphalt mixtures across multiple scales. In the field of asphalt mixture research, the DEM and the FEM are the primary simulation techniques employed [138]. This section focuses on the two most prominent 3D numerical simulation methods for asphalt mixtures: the DEM and the FEM, while also highlighting recent advancements in these techniques.

4.1 Asphalt mixture numerical simulation based on three-dimensional discrete element method

DEM is a numerical simulation technique, in which materials are represented as assemblies of discrete particles interacting via defined contact laws [139]. Particles in DEM are typically modeled explicitly with clear geometric boundaries, and their interactions are computed based on contact detection criteria and force–displacement relationships such as linear elastic, Hertzian, or viscoelastic contact models [140]. DEM is notably proficient in analyzing the mechanical behaviors of granular materials and elucidating the conversion of microscale interactions into macroscale properties [141,142]. The findings in Subsection 3.1 among researchers reflect the capability of the DEM to capture these subtle distinctions, demonstrating its utility as a robust tool in the realm of 3D simulations of asphalt mixtures. The 3D reconstruction of asphalt mixtures based on virtual compaction relies heavily on the advantages of the DEM in simulating the mechanical interactions between particles [143,144]. Researchers show a preference for employing DEM to investigate the force evolution during the compaction of asphalt mixtures or asphalt pavements [145,146].

Researchers analyzed particle displacement and contact forces during the compaction of Marshall and field specimens, as shown in Figs. 12(a) and 12(b). The comparison between virtual compaction height changes and laboratory compaction results demonstrated that the virtual compaction error was within 7% [44,89]. Figure 12(c) depicts the variation in compaction levels under different compaction forces, while Fig. 12(d) presents the compaction degrees for the entire specimen, as well as for the top, middle, and bottom aggregates. Additionally, Figs. 12(e) and 12(f) shown the contributions of aggregates of various sizes to strength during the compaction process in Stone Mastic Asphalt (SMA) and AC models. Similar studies on the compaction process have been conducted by other researchers [43,120]. These studies have provided insights into the compaction mechanisms of asphalt mixtures and have further demonstrated the value of 3D DEM as an essential tool for investigating asphalt mixture behavior.

3D DEM has been widely used to study the mechanical behavior of asphalt mixtures [148,149]. Researchers have investigated the effects of temperature, loading rate, and aggregate size on the shear strength of asphalt mixtures based on 3D DEM [150,151]. Results have shown that reliable 3D DEM models can effectively predict the low-temperature cracking behavior of asphalt mixtures, significantly reducing the need for expensive and time-consuming experimental tests [152]. 3D DEM models have proven effective in accurately predicting the dynamic modulus and fatigue resistance of asphalt mixtures at various temperatures and loading frequencies [153–155]. The rapid advancement of GPU technology over the past 3–5 years has enabled researchers to construct more complex and detailed 3D DEM models. These developments facilitate simulations involving increased particle interactions and longer collision durations [156,157].

4.2 Asphalt mixture numerical simulation based on three-dimensional finite element method

Unlike the DEM, the FEM is distinctively characterized by its “continuous” approach [158]. FEM is a numerical simulation method in which continuous domains are discretized into finite elements interconnected through nodal points, governed by established equilibrium equations and constitutive relationships. Due to its inherent characteristics, FEM is commonly utilized in continuum macroscale research. However, continuum macroscale modeling is beyond the scope of this paper. This paper focuses on 3D FEM modeling at the mesoscopic scale. Asphalt mortar and aggregate particles in the FEM models are represented as solid entities, as shown in Figs. 13(a)–13(c). Han et al. [160] analyzed the brittle fracture process based on the Cohesive Zone Model (CZM) and the Phase Field Method (PFM), as illustrated in Figs. 13(d) and 13(e). Their findings indicate that 3D FEM provides significant advantages in simulating and predicting fracture behaviors of asphalt mixtures. Gao et al. [162] and Zhao et al. [163] reached similar conclusions. Other researchers have also employed 3D FEM to analyze changes in asphalt mixtures under various loading conditions, including compaction, creep, and wheel loading processes [159,164,165]. Zhang et al. [166] predicted the rutting performance and rutting evolution curves of recycled asphalt mixtures under complex conditions using FEM simulations combined with mechanistic-empirical models.

In addition to mechanical analysis, FEM, as a continuum-based modeling approach, enables researchers to accurately simulate heat transfer within complex materials, as presented in Table 2. These studies have demonstrated the effectiveness of 3D FEM models in predicting internal temperature distributions and variations within asphalt mixtures, and in guiding optimized material design.

Beyond the conventional FEM and DEM, researchers have begun to explore alternative methodologies for developing 3D numerical models of asphalt mixtures to facilitate research in specific thematic areas [171]. Lattice Boltzmann method focuses on simulating fluid flow within asphalt mixtures [172,173]. While the molecular dynamics method emphasizes modeling the microscopic structure of asphalt [174,175]. Since these methods are not primarily designed to simulate asphalt mixtures themselves, they are not discussed in detail in this paper.

4.3 Asphalt mixture coupling three-dimensional numerical simulation

Both 3D DEM and 3D FEM offer distinct advantages in studying specific aspects of asphalt mixtures. However, each method also has inherent limitations, making it difficult for a single 3D simulation approach to fully capture the complexity of asphalt mixtures. In recent years, with advancements in computational technology, researchers have explored combining the strengths of FEM and DEM to develop more realistic numerical models of asphalt mixtures [176,177]. The principle of DEM-FEM coupling simulation as shown in Fig. 14(a). The key to a coupling model lies in the method used to transfer displacement and stress data between the DEM and FEM models. A straightforward example of a DEM-FEM coupled model involves using both methods to create a composite structure, as shown in Fig. 14(b). The DEM model and the FEM model entered into the next time step analysis together to ensure the continuity of force and velocity on the contact boundary [178]. Fang et al. [138] and Liu et al. [179] employed similar DEM-FEM coupling methods in their studies, demonstrating that composite models built with DEM-FEM coupling can achieve computational efficiency by selectively applying appropriate methods to different model regions, while maintaining accuracy comparable to that of single-method models applied at finer resolutions.

Further advancing the integration of these simulation techniques, Ge et al. [112,180] proposed a DEM-FEM coupling model to investigate the tire-pavement interaction mechanism, as shown in Figs. 14(c)–14(e). They developed a DEM model of asphalt mixtures incorporating irregularly shaped particles, while the tire contact stresses were captured through FEM model. The coupling method incorporating both FEM and DEM provides a promising way for analyzing at the mesoscale asphalt mixture responses under realistic rolling tire loads.

Another category of coupling simulation research focuses on multiscale coupling simulations of asphalt mixtures [46,181]. The basic process is shown in Figs. 15(a) and 15(b). First, full-size pavement and mixture models are constructed to represent macroscale and mesoscale models, respectively. Secondly, two distinct FEM models were established and interconnected using the upscaled homogenization theory and downscaled mechanistic transfer procedures. Allen et al. [176] and Kim et al. [177] applied a similar approach to develop bidirectional coupling models that account for macro (pavement level) and meso (mixture level) interactions. Additionally, integrating the temperature field in FEM research enables the analysis of temperature-induced stresses and their impacts on pavement service life [185,186]. Such cross-scale simulation models have been proven to more effectively predict the properties of asphalt mixtures and the mechanical responses of asphalt pavements under complex conditions [187–189]. It is noteworthy that accurate DEM-FEM coupling requires explicit definition of interface mechanics and optimized contact models to ensure precise data transfer. Iterative or sub-stepping coupling algorithms address synchronization issues in data exchange [178]. Recently, researchers have integrated numerical models with Convolutional Neural Networks (CNN) and introduced additional stochastic elements into simulations [190,191]. This approach has produced models that better reflect actual mechanical behaviors. These efforts preliminarily demonstrate the feasibility of applying artificial intelligence in numerical simulation research.

4.4 Future directions in three-dimensional numerical simulation

Although 3D simulation methods have advanced asphalt mixture modeling, DEM remains limited by high computational cost and parameter sensitivity, especially in large-scale. FEM simulations relies heavily on interface and constitutive assumptions. Coupled DEM-FEM and multiscale approaches show great potential but continue to face key challenges related to force–displacement data transfer, time synchronization, and algorithmic stability. Future numerical simulation studies of asphalt mixtures should flexibly select or combine modeling approaches based on specific application needs, while further optimizing data consistency and exchange mechanisms in DEM-FEM coupling models, with a focus on improving interface accuracy and computational stability under complex loading conditions. With the continuous advancement of computing hardware and software, researchers should develop more refined and realistic numerical models supported by techniques such as CNN.

5 Validation of three-dimensional simulation model of asphalt mixture

Validation is a critical step to ensure that simulation models accurately reflect real-world conditions. Through validation, researchers can confirm whether the model’s predictions align with experimental data or actual observations. Validation can be categorized into two types: laboratory-based validation and field-based validation.

5.1 Validation of models based on laboratory testing

Most studies validate 3D simulation models by comparing simulation results with indoor experimental outcomes, as shown in Fig. 16(a). It is generally considered acceptable for model reliability if the deviation falls within the range of 5% to 10% [192,193]. Some researchers have also identified parameter sensitivities and determined the scope or limitations of the model [88,193]. Some researchers have adopted more precise methods to guide the revision and optimization of model parameters. Liu et al. [71] innovatively applied a Genetic Algorithm-Back Propagation (GA-BP) neural network to study the sensitive impact of coarse aggregate morphology on the skeleton strength of asphalt mixtures, as shown in Fig. 16(b). They designated 76% of the data as training sets, 12% as verification sets, and 12% as testing sets, using this approach to adjust the model’s parameters and validate its appropriateness.

5.2 Validation of models based on field testing

Obtaining data from actual roads and construction sites is crucial for validating 3D models of asphalt mixtures. Wan et al. [173] highlighted that specimens sampled from actual sites can more effectively validate the 3D models of mixtures and efficiently guide modifications to model parameters. Beyond merely aligning more closely with real-world conditions than indoor experimental specimens, the primary aim of researchers employing field tests to validate 3D models of asphalt mixtures is to ensure the models accurately reflect the scenarios encountered during actual construction. Researchers have utilized 3D simulation techniques to replicate various aspects of the asphalt pavement construction process, as shown in Fig. 17.

5.3 Future directions in model validation

Current studies primarily focus on matching simulation outputs with experimental results, but often lack transparent and quantitative analysis of parameter calibration, iterative optimization, and error control processes. This omission hinders reproducibility and limits the broader applicability of simulation models. Future research should emphasize detailed documentation of model parameter calibration and validation procedures. Integrating neural networks and related techniques can automate the identification of key influencing parameters, enhancing calibration efficiency and accuracy. Developing standardized procedures for parameter calibration and validation is also essential for advancing model verification from qualitative assessments to quantitative analysis.

6 Conclusions

Asphalt mixtures are inherently complex and heterogeneous composite materials. The advancement of 3D mesoscopic modeling and simulation techniques has significantly enhanced the understanding of the composition and behavior of asphalt mixtures. This paper provides a structured synthesis of recent advancements in 3D mesoscopic modeling of asphalt mixtures. It reviews the latest developments in 3D model generation techniques, identifies key parameters influencing model accuracy and reliability, and summarizes major advancements in numerical simulation approaches. The main findings of this paper are summarized as follows.

1) Image-based 3D models based on CT scans yield high-fidelity mesostructures and are ideal for void and permeability analysis, though limited by cost and reproducibility. User-defined methods rely on assumed parameters and artificial filling algorithms, offering higher efficiency but reduced structural realism. Among them, the virtual compaction best approximating actual compaction processes and is well-suited for simulating particle rearrangement and contact evolution.

2) In asphalt mixtures 3D simulation, aggregate size and flat–elongated ratio are the primary contributors to mechanical strength, exerting significant influence on skeleton integrity, inter-particle interlock, and internal stress distribution, followed by angularity and surface texture. Furthermore, the type of contact between aggregates and other components critically shapes model outcomes. Aggregate–aggregate contact exerts the highest mechanical performance contribution, accounting for over 50% of the internal contact force.

3) Current simulations of asphalt mortar primarily target thickness and viscoelasticity, yet often oversimplify it as a homogeneous phase or represent it implicitly via contact models, limiting accurate description of binder–aggregate and binder–binder interfaces. In air void modeling, the connected void content, void size, and length of connected void axes have been identified as critical parameters for accurately simulating the permeability and acoustic characteristics of asphalt mixtures.

4) 3D DEM simulation is highly effective for modeling particle interactions and compaction behavior, whereas FEM is more suitable for continuum-scale mechanical analyses. DEM-FEM coupling integrates the strengths of both methods, enabling multiscale modeling capabilities. However, current coupling techniques face challenges, including inconsistent data transfer across interfaces and difficulty in synchronizing force–displacement responses.

5) Most studies validate 3D asphalt mixture models by comparing simulation outputs with laboratory or field results, typically considering errors within 5%–10% as acceptable. However, detailed procedures for parameter calibration and iterative optimization are rarely reported, limiting model reproducibility and applicability across broader engineering contexts.

Significant achievements have been made in the field of 3D simulation of asphalt mixtures. First, future studies should prioritize the development of reusable digital aggregate libraries and the refinement of virtual compaction methods to enhance the realism and efficiency of 3D model generation. Secondly, model parameters, particularly those related to aggregate morphology and contact types, require more precise characterization, with greater emphasis on aggregate–aggregate contact mechanisms. The representation of asphalt mortar also needs to be improved. Thirdly, simulation approaches should be flexibly selected or coupled based on application needs, while optimizing DEM-FEM coupling techniques to ensure data consistency and force–displacement synchronization under complex loads. Lastly, researchers should also provide more transparent documentation of parameter calibration, iterative optimization, and error control processes to improve model reproducibility. These efforts will offer more accurate, reliable, and comprehensive insights into the design and analysis of asphalt mixtures.

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