Abstract
To precisely assess the mechanical responses of asphalt pavement structures subjected to heavy-duty traffic loading, a comprehensive finite element modeling framework integrating three-dimensional tire tread patterns and laser-scanned pavement surface textures was developed. A 12R22.5 heavy-duty radial tire finite element model incorporating detailed tread geometry was established, along with a multilayer pavement structural model. Utilizing three-dimensional laser scanning technology, the surface textures of three typical asphalt pavements, namely, AC, SMA, and PAC, were reconstructed to accurately capture realistic surface morphologies, and a realistic tire–pavement contact mechanical model was subsequently established. Based on the analysis of dynamic mechanical responses, the study investigates the distinct mechanical behavior of various pavement structures under real tire loading conditions and reveals the underlying mechanisms of structure-dependent load transfer. Research findings suggest that the non-uniform contact stresses from actual tire loads lead to significant stress concentration in the top layer of pavement. Significant differences are observed among AC, SMA, and PAC structures in terms of the magnitude characteristics and depth distribution of horizontal stress (S11), vertical stress (S22), and vertical displacement (U2). Notably, owing to its high air-void structure, the PAC pavement demonstrates distinct stress diffusion behavior and distribution uniformity compared with AC and SMA pavements. The findings offer a theoretical foundation for the optimization of asphalt pavement structures and material design, tailored to withstand the stresses of heavy-duty traffic.
1 Introduction
With the continuous intensification and development of global transportation and logistics centered around efficiency systems, heavy - duty freight vehicles have emerged as the predominant carriers within highway transportation networks. Concurrently, axle loads and tire inflation pressures have been on the rise (; ; ). These trends impose increasingly stringent requirements on the service performance and structural durability of pavement systems (; ; ). Conventional pavement design theories are primarily based on multilayer elastic system assumptions, in which complex wheel loads are simplified as static, uniformly distributed circular vertical pressures (; ; ). However, extensive field observations and experimental studies have demonstrated that the tire–pavement interaction is inherently a highly nonlinear and dynamic contact process (; ; ). The geometric configuration, tread pattern design, inflation pressure, and operating conditions of heavy-duty tires (e.g., 12R22.5 tires) collectively result in significant non-uniform contact stress distributions at the tire–pavement interface. Such stress concentration phenomena are widely acknowledged as crucial mechanical mechanisms responsible for early pavement distresses, including rutting, shear deformation, and fatigue cracking ().
Considerable research efforts have been dedicated to investigating the mechanical responses of pavement structures under tire loading. In terms of tire load modeling, analyzed the structural characteristics of heavy-duty radial tires (12R22.5) and established a finite element tire model incorporating nonlinear contact boundary conditions between the tire and rim as well as between the tire and pavement. Utilizing ABAQUS software, the static vertical loading process was simulated, and the mechanical relationship between vertical load and deflection was systematically analyzed. developed a coupled interaction model between heavy vehicles and pavements and constructed a three-dimensional finite element model of concrete pavements, demonstrating the applicability and effectiveness of the finite element method (FEM) for multilayer pavement system analysis under heavy vehicle tire loads. Zeng et al. () develops a DE/FE coupling method to investigate off-road tire traction on wet granular terrains, revealing moisture content, friction coefficient, and tire parameters significantly affect sinkage and drawbar pull performance. Based on the above analysis, tire-pavement interaction modeling methods include FEM, CEL, SPH, and DEM-FEM. FEM offers high efficiency and mature material models for conventional analysis, but has limitations in large deformations and nonlinearity. This study adopts FEM for its balance of efficiency and applicability.
Regarding pavement structural response analysis, quantitatively investigated the modulus characteristics of asphalt pavements based on field test data and proposed a method for determining the master curve of dynamic response modulus using measured interlayer strain data, combined with finite element inverse analysis techniques. developed a constitutive model for asphalt mixtures using a UMAT subroutine in ABAQUS, The study validated the precision of the numerical model by simulating real traffic conditions and applied it to assess the high-temperature rutting resistance of asphalt pavements across various service stages. conducted combined theoretical and experimental studies on rutting behavior of asphalt pavements, revealing significant differences in rutting development between different base types and highlighting the critical role of base structures in long-term pavement performance.
Although significant advancements have been made in tire modeling and in analyzing pavement structural responses, a detailed investigation into the coupling mechanisms between the non-uniform contact stresses from realistic tire tread structures and the corresponding pavement structural responses is still an area that requires more systematic research. In particular, The differences in mechanical responses among various pavement structures under realistic tire–pavement contact loading conditions have not been fully elucidated. Therefore, this study establishes a finite element model of a realistic tire incorporating tread pattern effects and reconstructs real pavement surface textures based on three-dimensional laser scanning technology. The dynamic mechanical responses of different pavement structures [AC, SMA, and PAC (; )] under realistic heavy-duty tire loading conditions are systematically analyzed, and the influence mechanisms of non-uniform contact stresses on pavement structural behavior are revealed, providing a theoretical basis for structural optimization and material system design of asphalt pavements under heavy-duty traffic conditions.The specific contributions and innovations of this study are:
(1) Integration of realistic tire tread geometry and pavement surface texture; (2) Structure-specific mechanical response characterization; (3) Mechanistic insights for pavement design optimization.
2 Modeling framework and methodology
2.1 Finite element modeling of heavy-duty tire
A three-dimensional finite element model for a 12R22.5 heavy-duty radial tire was established, integrating detailed geometric structures and nonlinear material properties. The model comprises tread, belt layers, carcass layers, sidewalls, and bead regions, creating a multilayer composite structural system as shown in Figure 1. In the specific finite element modeling of the heavy-duty radial tire, the tire geometric elements were created using the axisymmetric method for repetitive structures; subsequently, key regions such as the tire contact zone were subjected to mesh refinement. Based on the validation presented in the following section, the mesh accuracy and quality of the tire finite element model were established.
FIGURE 1
2.2 Constitutive modeling of tire materials
In order to accurately characterize the nonlinear mechanical behavior of rubber materials, a hyperelastic constitutive framework was adopted. Among common hyperelastic models (Mooney–Rivlin, Ogden, Yeoh, Neo-Hookean) (; ), the Neo-Hookean model was selected to describe the rubber material behavior under small-to-moderate deformation conditions. The strain energy density function is expressed as:where is the strain energy function, is the material constant, is the first invariant of the deviatoric strain tensor, is the incompressibility parameter, and is the elastic volume ratio (Table 1).
TABLE 1
| Rimcont | Sanjiao | Inside | Shoulder | Undertread | |
|---|---|---|---|---|---|
| 1.006 | 1.006 | 1.006 | 0.336 | 0.839 | |
| 0.02 | 0.02 | 0.02 | 0.06 | 0.024 |
Shows the parameters of the Neo-Hookean model for tirerubber.
Figure 2 shows the stress contour of the 12R22.5 heavy-duty radial tire finite element model under inflation loading. As can be seen from the figure, the tire inflation area exhibits higher stress values, while other regions show relatively lower stress levels. Meanwhile, the inflation area undergoes slight deformation, whereas other areas experience minimal deformation. This indicates that the 3D finite element tire model possesses favorable stiffness in the inflation region, with adequate strength and supporting capacity to provide stable support and driving performance.
FIGURE 2
2.3 Pavement surface reconstruction and structural modeling
High-resolution pavement surface textures were acquired using a Handyscan 300 three-dimensional laser scanner. The instrument features a resolution of 0.1 mm, an accuracy of 0.025 mm, and a measurement rate of 1,300,000 points/s, yielding a point cloud density of approximately 520,000 points/cm2. After scanning, GEOMAGIC STUDIO was employed for noise reduction processing, with redundant data points exceeding 5 mm in depth eliminated. The texture quality was finally validated through 3D visualization (PAC texture depth > SMA > AC), providing a reliable geometric foundation for subsequent finite element modeling.
Subsequently, point cloud data were reconstructed via GEOMAGIC STUDIO to generate realistic surface morphology models for AC, SMA, and PAC pavements, as shown in Figure 3.
FIGURE 3
A multilayer pavement finite element model was established, which comprises a surface layer (AC-13/SMA-13/PAC-13), a middle layer (AC-20), a lower layer (AC-25), a cement-stabilized crushed stone base, a graded crushed stone subbase, and a soil subgrade. The full-scale model dimensions were 6 m × 6 m × 3.76 m as shown in Figure 4. Table 2 is the structural layer parameters (; ; ).
FIGURE 4
TABLE 2
| Layer | Density/g/m3 | Modulus of elasticity/MPa | Poisson’s ratio |
|---|---|---|---|
| AC-20 | 2,400 | 1,454 | 0.3 |
| AC-25 | 2,300 | 1,592 | 0.3 |
| Cement-stabilized crushed stone laye | 2,300 | 1,500 | 0.2 |
| Graded crushed stone layer | 2,100 | 450 | 0.3 |
| Subgrade | 1850 | 45 | 0.4 |
Structural Layer Parameters (; ).
2.4 Tire–pavement contact modeling
The dynamic tire-pavement contact process was simulated by employing the ABAQUS/Explicit solver. Nonlinear contact interactions were established between the realistic tire tread structure and reconstructed pavement surfaces, aiming to capture non-uniform stress distributions at the contact interface, as depicted in Figure 5. The penalty method was adopted, with the pavement set as the rigid master surface and the tire as the slave surface. This setup enables stable acquisition of contact stresses between the tire and pavement, with stress data subsequently extracted from the tire surface for structural analysis.
FIGURE 5
3 Mechanical response analysis under non-uniform contact stress
To ensure mechanical consistency between the tire-pavement contact interface and the structural response domain, the non-uniform contact stress fields obtained from the realistic tire-pavement interaction model were extracted and subsequently applied as boundary conditions to the multilayer pavement structures. Building upon this coupled modeling approach, the mechanical responses of AC, SMA, and PAC pavement structures were systematically analyzed and compared under unified viscoelastic constitutive conditions (; ).
3.1 Horizontal stress response (S11)
Transverse stress S11 is a critical mechanical indicator governing the initiation of fatigue cracking in asphalt pavements, and its spatial distribution directly affects the structural durability and service performance. Figure 6 presents the distribution of transverse stress (S11) at different depths under real tire loading conditions.
FIGURE 6
The results reveal significant differences among PAC, AC, and SMA pavement structures, reflecting the intrinsic influence of material composition and structural morphology on transverse load transfer mechanisms. In the surface layer (approximately 0–120 mm depth), the SMA structure exhibits the most pronounced stress fluctuation, characterized by alternating tensile–compressive stress states. The peak tensile stress reaches approximately 1.45–1.50 MPa, while the minimum compressive stress reaches −0.70 to −0.75 MPa, indicating severe stress concentration. The AC structure shows moderate fluctuations, with tensile peaks around 0.40–0.45 MPa and compressive valleys around −0.30 to −0.35 MPa. In contrast, the PAC structure presents the lowest stress level and the smoothest distribution, demonstrating strong stress dispersion capability.
These differences stem from the distinct structural characteristics. The stone - on - stone skeleton of SMA forms a rigid load - bearing framework that causes transverse stress concentration. AC demonstrates relatively uniform stress transfer because of its dense gradation. Meanwhile, PAC, with high porosity, facilitates stress diffusion and redistribution at the surface. As the depth increases (120–400 mm), the transverse stress in all structures rapidly attenuates and approaches zero. At a depth of approximately 200 mm, the stress in SMA decreases to about 0.15–0.20 MPa, while the stress in AC and PAC approaches near - zero values. This indicates that the effects of transverse stress are mainly confined to the surface and upper layers.
3.2 Vertical stress S22
Vertical stress S22 governs the development of permanent deformation (rutting) and controls the accumulation of compressive strain within pavement layers. Figure 7 shows the vertical stress distribution at different depths.
FIGURE 7
All pavement structures exhibit monotonic attenuation of vertical stress with depth; however, significant differences occur in the surface and upper layers. The maximum compressive stress ranking is: SMA > PAC > AC.
At the surface (0–40 mm), SMA reaches −5.6 to −5.8 MPa, PAC reaches −4.2 to −4.4 MPa, and AC reaches −1.8 to −2.0 MPa. This indicates that rigid skeletal structures concentrate compressive stresses more intensively, while dense - graded mixtures distribute stress more uniformly. Within the 40–200 mm depth range, stresses decay rapidly. At a depth of 100 mm, SMA is approximately −2.5 MPa, PAC is approximately −2.2 MPa, and AC is approximately −1.0 to −1.2 MPa, reflecting different stress diffusion mechanisms. Below 200 mm, stress differences converge, approaching near - zero at 400 mm, indicating that base and subgrade layers dominate load diffusion.
3.3 Vertical displacement U2
Vertical displacement U2 characterizes the global stiffness and deformation capacity of pavement structures. Figure 8 illustrates the displacement profiles with depth.
FIGURE 8
Overall, displacement decreases with depth for all structures, following the ranking: SMA > PAC > AC.
At the surface (0–40 mm), SMA reaches −1.30 to −1.35 mm, PAC reaches −1.10 to −1.15 mm, and AC reaches −0.45 to −0.50 mm, indicating greater surface deformation concentration in rigid skeletal structures. With increasing depth (40–200 mm), SMA maintains high deformation levels (≈−1.0 mm at 100 mm, −0.80 mm at 200 mm), reflecting deep structural participation in deformation. PAC shows moderate attenuation, while AC exhibits the fastest decay, indicating higher overall structural stability. At depths of 200–400 mm, displacement differences gradually diminish, but SMA still maintains larger deep - layer deformation, implying higher demands on base and subgrade bearing capacity.
4 Results and conclusion
This study systematically investigated the mechanical responses of PAC, AC, and SMA pavement structures under real non-uniform tire loading. The main Results are:
Non-uniform real tire loading significantly alters pavement stress and deformation patterns, inducing surface stress concentration and heterogeneous response fields that govern early structural damage development.
Different surface structures form distinct stress–deformation response mechanisms: SMA exhibits strong stress concentration and deep deformation influence; AC shows balanced mechanical response and structural stability; PAC demonstrates effective stress dispersion and buffering behavior.
Pavement structure type fundamentally controls load transfer paths and deformation diffusion patterns, thereby influencing damage modes and structural durability.
This study overcomes the limitations of traditional smooth tire and rigid pavement contact models for obtaining contact stresses, achieves the acquisition and simplified application of real tire-pavement interaction stresses to pavement structures, and enables further exploration of the effects and mechanical responses of real tires on pavement structures under different pavement textures, providing a reference for subsequent research.
Future studies should address the limitations of this research, including the static loading assumption and lack of direct experimental validation, by coupling numerical simulation with Accelerated Pavement Testing (APT) to obtain measured strain/stress data for model validation. Additionally, dynamic tire–pavement interaction and structural optimization-oriented pavement design warrant further investigation.
Statements
Data availability statement
The datasets presented in this article are not readily available because no. Requests to access the datasets should be directed to zhenxuan wang, zhenxuan.wang@ucdconnect.ie.
Author contributions
WZ: Writing – original draft, Writing – review and editing.
Funding
The author(s) declared that financial support was not received for this work and/or its publication.
Conflict of interest
The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Generative AI statement
The author(s) declared that generative AI was not used in the creation of this manuscript.
Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.
Publisher’s note
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
References
1
AssogbaO. C.SunZ.TanY.NondeL.BinZ. (2020). Finite-element simulation of instrumented asphalt pavement response under moving vehicular load. Int. J. Geomechanics20 (3), 04020006. 10.1061/(asce)gm.1943-5622.0001616
2
BaiT.ChengZ.HuX.FuentesL.WalubitaL. F. (2021). Viscoelastic modelling of an asphalt pavement based on actual tire-pavement contact pressure. Road Mater. Pavement Des.22 (11), 2458–2477. 10.1080/14680629.2020.1766545
3
BhattB.WuS. (2025). A comprehensive state-of-art review on the use of rejuvenators in asphalt pavement. J. Road Eng.5 (1), 1–20. 10.1016/j.jreng.2024.10.001
4
CanestrariF.MarianiE.IngrassiaL. P. (2024). Use of wehner-schulze machine to evaluate pavement skid resistance: a review. J. Traffic Transp. Eng. Engl. Ed.11 (5), 896–917. 10.1016/j.jtte.2024.04.006
5
Cannone FalchettoA.MonteparaA.TebaldiG.MarasteanuM. O. (2013). Microstructural characterization of asphalt mixtures containing recycled asphalt materials. J. Mater. Civ. Eng.25 (1), 45–53. 10.1061/(asce)mt.1943-5533.0000544
6
ChengH.LiB.LiuN.SunL. (2020). Study on the dominant curve of dynamic response modulus of pavement asphalt layer under Mobile axle load. China J. Highw. Transp.33 (10), 125–134. 10.19721/j.cnki.1001-7372.2020.10.007
7
DaiJ.MaF.FuZ.LiC.HouY.WenY.et al (2024). Integrated and holistic knowledge map of phase change materials for pavement: a scientometric analysis and bibliometric review. J. Traffic Transp. Eng. Engl. Ed.11 (6), 1317–1339. 10.1016/j.jtte.2024.05.001
8
FathiH.EL-SayeghZ.RenJ.El-GindyM. (2024). Modeling and validation of a passenger car tire using finite element analysis. Vehicles6 (1), 384–402. 10.3390/vehicles6010016
9
LiP.YueL.DingZ.JiangX.LiH.AnL.et al (2025). Review on composition properties, functionalization of bio-oil and its rejuvenation behavior and mechanism on aged asphalt. J. Road Eng.5 (1), 21–34. 10.1016/j.jreng.2024.07.002
10
LiJ.HuiY.ChenQ.YaoN.WangD.JiaM.et al (2026). A comprehensive review of renewable energy utilization in roadway infrastructure. J. Intell. Constr.4, 9180113–9180125. 10.26599/jic.2026.9180113
11
LiuQ.YuB.FalchettoA. C.WangD.LiuJ.BoW. (2026). Characterization and molecular mechanism of the thermal-oxidative gradient aging behavior in asphalt films. Measurement199, 111567. 10.1016/j.measurement.2022.111567
12
MensahR. A.ShanmugamV.NarayananS.RennerJ. S.BabuK.NeisianyR. E.et al (2022). A review of sustainable and environment-friendly flame retardants used in plastics. Polym. Test.108, 107511. 10.1016/j.polymertesting.2022.107511
13
MuhoE. V.BeskouN. D.QianJ. (2025). Models and methods for dynamic response of 3D flexible and rigid pavements to moving loads: a review by representative examples. J. Road Eng.5 (1), 65–91. 10.1016/j.jreng.2024.07.003
14
ZengH.TangX.ChenS.QiH. (2024). Numerical investigations of traction behaviors of a pneumatic tire on wet granular terrains: DE/FE simulations. J. Terramechanics (2024). 113: 100972. 10.1016/j.jterra.2024.100972
15
RiccardiC.FalchettoA. C.WistubaM. P.LosaM. (2025). Fatigue comparisons of mortars at different volume concentration of aggregate particles. Int. J. Fatigue104, 416–421. 10.1016/j.ijfatigue.2017.08.005
16
ShaA.LiuZ.JiangW.QiL.HuL.JiaoW.et al (2021). Advances and development trends in eco-friendly pavements. J. Road Eng.1, 1–42. 10.1016/j.jreng.2021.12.002
17
SunZ.PremarathnaW. A. A. S.AnupamK.KasbergenC.M.J.G. ErkensS. (2024). A state-of-the-art review on rolling resistance of asphalt pavements and its environmental impact. Constr. Build. Mater.411, 133589. 10.1016/j.conbuildmat.2023.133589
18
ValaškováV.VlčekJ. (2018). Stress response analysis of concrete pavement under tire of heavy vehicle. Civ. Environ. Eng.14 (2), 146–152. 10.2478/cee-2018-0019
19
WangD.FalchettoA. C.PoulikakosL.HofkoB.PorotL. (2026). RILEM TC 252-CMB report: rheological modeling of asphalt binder under different short and long-term aging temperatures. Mater. Struct.52 (4), 73. 10.1617/s11527-019-1370-9
20
WangW.YanS.ZhaoS. (2013). Experimental verification and finite element modeling of radial truck tire under static loading. J. Reinf. Plastics Compos.32 (7), 490–498. 10.1177/0731684412474998
21
WangD.Cannone FalchettoA.AlisovA.SchraderJ.RiccardiC.WistubaM. P. (2019a). An alternative experimental method for measuring the low temperature rheological properties of asphalt binder by using 4mm parallel plates on dynamic shear rheometer. Transp. Research Record2673 (3), 427–438. 10.1177/0361198119834912
22
WangD.Cannone FalchettoA.MoonK. H.RiccardiC.PeiJ.WenY. (2019b). Artificially prepared reclaimed asphalt pavement (RAP)—An experimental investigation on re-recycling. Environ. Sci. Pollut. Res.26 (35), 35620–35628. 10.1007/s11356-019-05970-w
23
WangW.JiaoW.ShaA.LiX.ZhangF.JiangW.et al (2025). Evaluating the driving comfort on urban self-luminous pavements based on human-machine interaction. J. Traffic Transp. Eng. Engl. Ed.12 (5), 1210–1227. 10.1016/j.jtte.2023.04.011
24
YangZ. (2023). Material modeling in finite element analysis[M]. 2nd ed. CRC Press. 10.1201/9781003436317
25
YangL.HuY.ZhangH. (2020). Comparative study on asphalt pavement rut based on analytical models and test data. Int. J. Pavement Eng.21 (6), 781–795. 10.1080/10298436.2018.1511781
26
ZhangJ.ZhuC.LiX.PeiJ.ChenJ. (2017). Characterizing the three-stage rutting behavior of asphalt pavement with semi-rigid base by using UMAT in ABAQUS. Constr. Build. Mater.140, 496–507. 10.1016/j.conbuildmat.2017.02.152
Summary
Keywords
asphalt pavement structure, FEM, mechanical response, real tire loading, tire–pavement contact
Citation
Zhenxuan W (2026) Mechanical response characteristics of different asphalt pavement structures under realistic tire loading conditions. Front. Mater. 13:1821090. doi: 10.3389/fmats.2026.1821090
Received
02 March 2026
Revised
09 April 2026
Accepted
22 April 2026
Published
25 May 2026
Volume
13 - 2026
Edited by
Jiasheng Dai, Guangxi University, China
Reviewed by
Augusto Cannone Falchetto, University of Padua, Italy
Jie Gao, East China Jiaotong University, China
Fucheng Guo, Lanzhou Jiaotong University, China
Updates
Copyright
© 2026 Zhenxuan.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Wang Zhenxuan, zhenxuan.wang@ucdconnect.ie
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.