Modeling to simulate static and dynamic tire-pavement contact: an emphasis on three-dimensional pavement surface texture

Abstract

Tire-pavement contact behavior is closely associated with pavement skid resistance and vehicle safety. However, most existing studies on tire-road contact have overlooked the coupled interaction between tire rubber materials and asphalt pavement texture, particularly the influence of real pavement surface texture characteristics. Therefore, this study employed finite element analysis to investigate the grounding and skid resistance performance of tires under different static and dynamic conditions. A finite element tire-pavement contact model incorporating real pavement surface textures was first established. The contact stress and contact depth of the model were then validated using pressure-sensitive films and carbon papers. Based on the validated model, the tire-pavement contact characteristics and skid resistance performance under different static and dynamic conditions were analyzed. The results show that uneven pavement surface textures lead to non-uniform distributions of contact stress and contact imprints, with more pronounced stress concentration and asymmetric stress distribution observed on surfaces with larger irregularities. In addition, as velocity increases, both the contact area and the average normal contact stress between the tire and pavement gradually decrease. Under ABS braking conditions, pavement surfaces with larger irregularities show more noticeable improvements in skid resistance. This study clarifies tire-pavement contact characteristics under various operating conditions and provides theoretical support for asphalt mixture selection, pavement surface design, and the improvement of vehicle safety.

1 Introduction

In recent years, with the development of the global economy and the acceleration of urbanization, road traffic volume has increased rapidly, leading to a growing number of traffic accidents (Zhu et al., 2019; Li et al., 2026; Zhang et al., 2025). Studies have shown that vehicle skidding on pavement is one of the major causes of traffic accidents (Jalalkamali et al., 2021; Rasol et al., 2021; Praticò, 2025). As the only component directly contacting the pavement surface, tires play a critical role in determining the skid resistance performance of vehicles during operation (Kogbara et al., 2016; Yu et al., 2020).

Pavement surface texture is one of the key factors affecting skid resistance (Ding et al., 2021; Fwa et al., 2012), and extensive research has been conducted on pavement texture characterization (Yun et al., 2025). Previous studies have made substantial progress in the three-dimensional characterization of pavement texture through a variety of reconstruction approaches, including 3D visualization, surface-data-based regression modeling, and image-based texture reconstruction (Kern et al., 2007; Slimane et al., 2008; Wang, 2012). In addition, mixture design factors have also been shown to influence pavement texture characteristics and skid-related performance. For example, larger nominal maximum aggregate size has been reported to increase texture depth and improve skid resistance (Sun et al., 2012). It can therefore be seen that current macro-texture indicators are mainly derived from restoring pavement surface point cloud data, without considering the actual tire–pavement contact depth. Moreover, analyses of the contribution of different texture features to tire–pavement contact remain insufficient, making it difficult to accurately evaluate skid resistance during vehicle operation.

The characteristics of the tire–pavement contact interface are influenced not only by pavement texture, but also closely related to tire properties (Anupam et al., 2014; Zhou et al., 2015) and tire rolling conditions (Rafei et al., 2019; Vu et al., 2017). Previous studies have shown that tire tread design plays an important role in contact and skid-related performance. For example, variations in groove density and tread pattern have been reported to significantly affect braking and traction behavior on snow-covered pavements, indicating that tire structural features can substantially influence interfacial performance (King and Matyja, 1981; Nesbitt and Barron, 1980). In addition, experimental investigations based on pressure-sensitive films have further confirmed the effect of tire structure on contact pressure distribution and contact behavior (Jankowska et al., 2005). Experimental studies have also provided important evidence regarding the stress characteristics of the tire–pavement contact interface. Existing measurements using pressure-sensitive films, triaxial force sensors, and specially developed contact-pressure testing devices have revealed the non-uniform nature of tire contact stress distribution and helped identify typical stress concentration regions under loading (HU and Sun, 2005; Marshek et al., 1986; Tielking and Abraham, 1994).

Under static loading and low-speed rolling conditions, the contact shape and stress–strain distribution between tire and pavement can generally be obtained through experiments. However, under high-speed rolling conditions, the characteristics of the tire–pavement contact interface are difficult to measure directly. Previous studies have used finite element and multibody methods to examine the effects of tire pressure, vertical load, rolling speed, and camber angle on contact stress distribution, footprint characteristics, viscoelastic response, and tire wear (Cho et al., 2011; Faria et al., 1992; Korunović et al., 2011). Although these studies have provided valuable insights into rolling tire behavior, the reliability of the tire model has in many cases been validated mainly through tire stiffness, while the accuracy of the tire–pavement contact interface itself still requires further improvement (Chen et al., 2004; Lu, 2021).

In summary, current studies on tire–pavement contact generally lack consideration of the coupled interaction between tire rubber materials and asphalt pavement texture morphology. They often neglect the actual texture characteristics of the pavement and use rigid planes instead of real pavement surfaces to analyze tire deformation and stress behavior, which leads to a certain discrepancy from actual contact performance on textured pavements. In addition, during high-speed rolling, the various performance characteristics of the tire–pavement contact interface are difficult to obtain through direct experimental measurements. Therefore, this study develops a finite element model of tire–pavement contact based on real pavement texture, and comparatively analyzes the skid resistance performance and comprehensive contact performance indices of tires under different operating conditions. The findings are expected to provide theoretical support for the selection of asphalt pavement mixtures and for improving driving safety.

2 Objective

FIGURE 1

3 Material and methodology

3.1 Raw materials and mixture design

This study selected three common asphalt mixture types: porous asphalt pavement (PAC), stone mastic asphalt pavement (SMA), and dense-graded asphalt concrete pavement (AC), all with a nominal maximum aggregate size of 13 mm. For convenience in the following discussion, they are hereafter referred to as PAC-13, SMA-13, and AC-13, respectively. SBS-modified asphalt was used for the SMA-13 and AC-13 pavements, whereas a high-viscosity modified asphalt with greater viscosity was used for the PAC-13 pavement. The performance indices of the two binders are presented in Table 1. Basalt was used as the coarse aggregate, limestone as the fine aggregate, and limestone mineral powder as the filler. Their performance indices are shown in Table 2.

3.2 FE modeling of tire-pavement contact

3.2.1 Acquisition and FE modeling of pavement texture

The initial pavement surface texture was acquired using a HandySCAN 300 handheld three-dimensional laser scanner. A standard rutting slab specimen with dimensions of 300 mm × 300 mm × 50 mm was selected as the scanning object for pavement texture acquisition. To avoid scanning the non-uniform areas near the edges of the rutting slab, a 250 mm × 250 mm frame was used for positioning, and only the central portion was retained, as shown in Figure 2. After scanning, the pavement surface point cloud data were processed and reversely reconstructed using Geomagic software to obtain encapsulated models of the three pavement surfaces. Finally, the three pavement models were meshed in Hypermesh and then imported into Abaqus.

FIGURE 2

3.2.2 Constitutive models and parameters of tire

A 175/70R14 radial tire for a passenger car was selected as the research object (Wang et al., 2005). The tire mainly consists of the tread crown, shoulder, sidewall, and tread, and its cross-sectional structure is shown in Figure 3.

FIGURE 3

Different parts of the tire are composed of various rubber materials, and rubber is an isotropic hyperelastic and viscoelastic material. In this study, the hyperelastic behavior of the tire material was characterized in the finite element software using the Neo-Hookean material model, which can effectively simulate small and moderate strains and exhibits good numerical stability (Zhang, 2020). The Neo-Hookean material model is expressed as Equation 1.where W is the strain energy potential; C₀₁ and C₁₀ are material constants representing the shear behavior of the material; I₁ and I₂ are the first and second invariants, respectively; J denotes the volume change; and D₁ is a material parameter representing the incompressibility of the material.

The viscoelastic behavior of the tire material was defined using the Prony series. The parameters of the Neo-Hookean model for the tire material are listed in Table 4.

The material properties of the tire carcass, belt layers, and other reinforcing components were defined as anisotropic. Some reinforcing layers embedded within the rubber material were mainly described through element material properties. The rebar model can be used to define rubber–cord composite materials (Smith, 2009), in which rebar elements are employed to simulate the cord components and solid elements are used to simulate the rubber components. This modeling approach can effectively reflect the reinforcing effect of the cord layers on the rubber. Therefore, in this study, the Rebar layer model was adopted to characterize the cord plies and belt layers, and the corresponding material parameters are listed in Table 5. To improve computational efficiency, all materials other than the tire carcass, belt layers, and similar reinforcing parts were assumed to be homogeneous and isotropic.

3.2.3 Radial tire FE modeling

Because the internal structure and surface tread pattern of a radial tire are highly complex, the computation is time-consuming and prone to convergence difficulties. Therefore, appropriate simplifications were made to the tire model in this study. During tire modeling, only the longitudinal grooves were considered, while the transverse tread patterns were neglected.

For the three-dimensional tire modeling, the process began with drawing the basic sketch in CAD according to the specific dimensions of the two-dimensional tire cross-section, after which the generated geometry was imported into Hypermesh for cross-sectional meshing. The meshed two-dimensional cross-section was then exported as an INP file recognizable by Abaqus, where material assignment, assembly, and loading were subsequently completed. Since the tire is fully symmetric, the results can also be transferred through symmetry operations. To improve computational efficiency in the early stage, only a half-symmetric model was analyzed, which greatly reduced the computation time. Finally, the complete three-dimensional tire model was generated by applying a symmetry operation to the half model along the axis of symmetry.

In this study, a surface-to-surface contact formulation was adopted to simulate the tire–pavement contact condition. Through displacement control and load control, the pavement was raised by 0.02 m to ensure that, after tire inflation, the tire still had a certain downward displacement allowance, so that the tire and pavement could reach equilibrium during the static loading process. The established tire–pavement contact model is shown in Figure 4.

FIGURE 4

3.3 Measurement of tire-pavement contact

To reduce testing errors, the rolling method was adopted in this study to obtain the tire–pavement contact footprint. For the contact stress and stress distribution characteristics under static tire–pavement contact, a two-sheet pressure-sensitive film was used for testing, as shown in Figure 5. First, the three prepared rutting slab specimens were placed into an actual pavement groove measuring 300 mm × 300 mm × 50 mm. Then, the pressure-sensitive film was fixed in position relative to the specimen to prevent movement during loading. For the contact depth under dynamic tire–pavement interaction at different speeds, the carbon paper method was employed. The selected test speeds were 10, 20, 30, 40, and 50 km/h.

FIGURE 5

After the test, the contact footprints on the test paper were scanned using a high-resolution scanner. The scanned data were then processed in MATLAB through denoising and registration to determine the contact depth (Lu, 2021). The procedure for determining the tire–pavement contact depth is shown in Figure 6.

FIGURE 6

4 Results and discussion

4.1 FE model evaluation

4.1.1 Static test validation

In this study, the effects of test temperature and humidity were taken into account. The C-curve on the LLW pressure-sensitive film calibration chart and the D-curve on the LLLW pressure-sensitive film calibration chart were selected as the reference concentration–stress curves for analysis, and the corresponding two-dimensional and three-dimensional stress maps were obtained, as shown in Figure 7. It can be seen from Figure 7 that there are more high-stress points on the PAC pavement. The maximum contact stress on the different pavements follows the order of PAC > SMA > AC, while the PAC pavement exhibits a smaller contact area. The figure also shows that the distribution of the maximum stress is obviously non-uniform. The regions with the darkest color, indicating the maximum stress, are not completely concentrated in the central area of the tire contact zone, but instead appear at relatively random locations. This is mainly because, during pavement specimen fabrication, the positions of the coarse aggregates are randomly distributed, and aggregate crushing as well as pronounced protrusions of coarse aggregates on some rutting slabs are unavoidable. During tire loading, since the center of the tire load is located at the center of the wheel rim, the stress in the central region of the tire becomes greater than that at the edge of the contact area as the loading time increases. As a result, the compressive contact in the central contact region is more sufficient, leading to a denser distribution of stress concentration points in the center of the contact area than at its edges.

FIGURE 7

Table 6 compares the maximum stress and contact depth measured by the pressure-sensitive film with the corresponding finite element simulation results. It can be seen that the measured contact stress is significantly higher than the simulated value, with the minimum relative error being 13.07% and the maximum relative error being 20.27%. The main reason is that, during loading, friction between the tire and the pressure-sensitive film is unavoidable. In addition, the contact surface is not perfectly smooth, which may cause wrinkling of the film and induce extra sliding between its two rough surfaces, thereby generating additional contact stress in the pressure-sensitive film. As shown in Table 6, the simulated contact depth values are all greater than the measured values, with the minimum relative error being 15.55% and the maximum relative error being 17.51%. This discrepancy is mainly related to the pavement meshing strategy and the selected contact formulation. During the actual scanning process, for coarse aggregates protruding more prominently from the surface, certain cutting and mesh stretching treatments were applied to the highly protruding surface elements; otherwise, excessively large protruding elements on the pavement surface would lead to convergence difficulties. As a result, the simulated tire–pavement contact depth is slightly larger than the measured value. Since the average relative error between the measured and simulated results is within 20%, the finite element model under static contact conditions can be considered to have acceptable accuracy.

4.1.2 Dynamic test validation

The contact depth results of the tire with three types of pavement at different velocities are shown in Table 7. It can be observed that the average relative error of the tire contact depth on the PAC pavement is the smallest, at 15%, while on the SMA, it is 17%. On the AC pavement, the relative error of the contact depth is the largest, at around 30%, and the relative error increases with increasing velocity. This is because vibration generated during vehicle traveling, when the tire contacts the pavement surface, it applies significant impact force to the initially contacted area of the road surface, resulting in deeper coloration of that portion of the carbon paper. Since there is currently no reliable method for measuring contact imprints during the rolling process, based on the comparative results of contact depth at different velocities, it is evident that the measured contact depths on all three types of pavements are significantly greater than the simulated results, with an average relative error of around 20%. This indicates that the finite element dynamic model has a certain level of reliability.

4.2 Force analysis of static contact simulation

4.2.1 Contact area

The contact area is defined as the sum of the areas of all contact elements when the tire and pavement reach an equilibrium state. In this study, the tire load was fixed at 3.3 kN, and the tire inflation pressure was varied to obtain the contact area under different inflation pressures, as shown in Figure 8a. It can be seen that, within the inflation pressure range of 0.18–0.26 MPa, the average contact area of the tire on the AC pavement was 20.56% larger than that on the SMA pavement and 30.52% larger than that on the PAC pavement. Under the same inflation pressure, the contact area on the three pavements followed the order AC > SMA > PAC. With a constant load, the tire contact area gradually decreased as the inflation pressure increased. For every 0.01 MPa increase in inflation pressure, the contact area decreased by 1.360 cm², 1.905 cm², and 2.115 cm² on the PAC, SMA, and AC pavements, respectively. The rate of decrease in contact area was the highest on the AC pavement and the lowest on the PAC pavement. This is because tire contact with the PAC pavement is inherently less sufficient; as the inflation pressure increases, the tire stiffness also increases, resulting in a smaller effect on pavements with more pronounced surface texture.

FIGURE 8

Figure 8b shows the variation in tire contact area with load at a fixed inflation pressure of 0.22 MPa. It can be seen that, within the load range of 2.8–3.8 kN, the average contact area of the tire on the AC pavement was 19.91% larger than that on the SMA pavement and 30.80% larger than that on the PAC pavement. Under the same load, the contact area on the three pavements also followed the order AC > SMA > PAC. With a constant inflation pressure, the tire contact area gradually increased as the load increased. For every 0.1 kN increase in tire load, the contact area increased by 2.044 cm², 2.485 cm², and 2.813 cm² on the PAC, SMA, and AC pavements, respectively. Among the three pavements, the contact area on the AC pavement was most sensitive to load variation. This is because the tire contact on the AC pavement was more sufficient, which is consistent with the effect of inflation pressure on contact area.

4.2.2 Contact footprint

When the load was fixed at 3.3 kN, the tire contact footprints on the three pavements under different inflation pressures are shown in Figure 9. It can be seen that, under a constant load, the maximum contact stress increased with increasing inflation pressure. When the inflation pressure increased from 0.18 MPa to 0.26 MPa, the contact contour area of the tire on the PAC pavement decreased, while the maximum contact stress increased from 1.534 MPa to 1.972 MPa, representing an increase of 28.55%. On the SMA pavement, the maximum contact stress increased from 1.200 MPa to 1.223 MPa, showing only a slight change with inflation pressure, with an increase of merely 1.92%. On the AC pavement, the maximum contact stress increased from 5.944 MPa to 6.415 MPa, corresponding to an increase of 7.92%. Among the three pavements, the tire exhibited the smallest contact area and the largest maximum contact stress on the PAC pavement. On the SMA pavement, the point of maximum contact compressive stress remained located at the same protruding position on the pavement surface. Therefore, such local prominent protrusions on the pavement should be avoided as much as possible, because long-term stress concentration at these locations will accelerate local wear and lead to premature damage. From the contact footprints on the AC pavement, it can be observed that, as the inflation pressure gradually increased, the tendency of the maximum vertical stress to migrate toward both tire shoulders was alleviated. This is because higher inflation pressure increases tire stiffness and thereby suppresses tire deformation to a certain extent.

FIGURE 9

At a constant inflation pressure of 0.22 MPa, the tire contact footprints under different loads are shown in Figure 10. As the load increased, the maximum tire contact stress also increased. The effects of increasing load on the contact footprint were generally similar to those of increasing inflation pressure. When the load increased from 2.8 kN to 3.8 kN, the contact contour area of the tire on the PAC pavement increased, while the maximum contact stress rose from 1.445 MPa to 2.006 MPa, representing an increase of 38.82%. On the SMA pavement, the maximum contact stress increased from 1.098 MPa to 1.312 MPa, corresponding to an increase of 19.49%. On the AC pavement, the maximum contact stress increased from 5.910 MPa to 6.381 MPa, an increase of 7.97%. The greater the load, the higher the stress on both sides of the tire. This is mainly because a higher load causes the tire to warp toward its longitudinal centerline, making stress concentration more likely to occur at the two shoulders. From the contact footprints on the AC pavement, it can be clearly observed that, with increasing load, the entire contact region tends to expand toward both sides. This is because, during the loading process, the tire centerline is subjected to inward compressive forces, which cause the tire to deform inward and distribute symmetrically along the centerline, a phenomenon that becomes more pronounced under higher loads.

FIGURE 10

The tire contact footprints on different pavements generally exhibited an elliptical distribution. However, when the tire contacted the PAC and SMA pavements, some areas within the footprint showed limited contact, and the contact stress contours were not clearly visible. This may be attributed to the excessively pronounced surface asperities captured during pavement scanning. When the tire reached an equilibrium state, contact occurred only at the protruding parts of the pavement surface. Because the texture depth was too large, the tread rubber was unable to fully penetrate into the surface depressions, resulting in no contact with some pavement elements and, consequently, less distinct stress contours. In addition, obvious stress concentration was observed in the contact footprint maps for the PAC and SMA pavements, which may be caused by the presence of large protruding coarse aggregates on the rutting slab specimens.

4.2.3 Evaluation of static contact characteristics

The static contact performance of a tire can be evaluated by the contact coefficient C and the hardness coefficient H. The contact coefficient is defined as the ratio of the longitudinal axis length to the transverse axis length of the tire footprint. The closer the contact coefficient is to 1, the more rectangular the tire contact footprint is. The deformation of the tire under an external vertical load is jointly sustained by the tire structure itself and the inflation pressure. The closer the hardness coefficient is to 1, the more the external load is borne by the inflation pressure, which is more favorable for the tire stress condition. When the hardness coefficient is less than 1, the entire applied load is borne by the inflation pressure. When the hardness coefficient is greater than 1, the external load is jointly borne by the inflation pressure and the tire structure. The hardness coefficient is calculated as Equation 2:

Where H is the hardness coefficient; F is the vertical load (N); A is the contact area (c ); and P is the tire inflation pressure (N/m²).

As shown in Figure 11a, at a constant inflation pressure, when the load increased from 2.8 kN to 3.8 kN, the contact coefficient of the tire on the PAC, SMA, and AC pavements increased by 21.54%, 21.62%, and 9.30%, respectively. Among them, the contact coefficient on the AC pavement increased from 0.86 to 0.94, indicating that its contact footprint was the closest to a rectangle. As shown in Figure 11b, at a constant load, when the inflation pressure increased from 0.18 MPa to 0.26 MPa, the contact coefficient of the tire on the PAC, SMA, and AC pavements decreased by 12.99%, 10.34%, and 9.57%, respectively, and the contact footprint gradually became more elliptical. This is because, under low inflation pressure and high load conditions, the tire has greater longitudinal and transverse contact lengths. From the results of the tire footprint variation with inflation pressure and load, it can be found that the increase in longitudinal contact length with load is significantly greater than that in transverse contact length. This is related to the inward concave deformation of the tire: as the load increases, the stress is squeezed toward the tire centerline, causing the tire to deform mainly in the longitudinal direction, and thus resulting in a larger variation in longitudinal contact length. An increase in the contact coefficient indicates that the contact shape changes from an ellipse toward a rectangle. As the load increases, the contact coefficient gradually approaches 1, suggesting that within a certain load range, increasing the load leads to a more favorable contact stress distribution on pavements with less pronounced surface texture.

FIGURE 11

As can be seen from Figures 11c,d, at a constant inflation pressure, the hardness coefficient increased with increasing load. When the load increased from 2.8 kN to 3.8 kN, the hardness coefficient of the tire on the PAC, SMA, and AC pavements increased by 4.89%, 3.70%, and 5.56%, respectively. At a constant load, the hardness coefficient decreased with increasing inflation pressure. When the inflation pressure increased from 0.18 MPa to 0.26 MPa, the hardness coefficient of the tire on the PAC, SMA, and AC pavements decreased by 20.83%, 17.93%, and 19.46%, respectively. The influence of load variation on the hardness coefficient was clearly smaller than that of inflation pressure variation, and the hardness coefficient was generally greater than 1. Under conditions of high inflation pressure and low load, the tire hardness coefficient was closer to 1. In this case, most of the external load was mainly borne by the inflation pressure, while the tire structure itself carried a smaller portion of the external load. As a result, the deformation of the tread rubber caused by the external load was smaller, suggesting that the rolling resistance generated under the corresponding rolling conditions would also be lower.

4.3 Force analysis of dynamic contact simulation

4.3.1 Effect of inflation pressure on tire in free-rolling status

Free rolling refers to the process in which a tire rolls at a constant speed without the action of external driving or braking forces. Under free-rolling conditions, the tire rolls without slipping, and the torque at the tire center is zero. Figure 12 presents the contact area and maximum normal contact stress of the tire on the three pavements at a free-rolling speed of 10 km/h under different load and inflation pressure conditions. It can be seen that the variation patterns of contact area and contact stress on the three pavements with inflation pressure and load are generally consistent with those under static contact conditions.

FIGURE 12

At a fixed load of 3.3 kN, as the tire inflation pressure increased, the contact area under rolling conditions decreased, while the maximum normal contact stress increased accordingly. When the tire was in free rolling at a speed of 10 km/h, increasing the inflation pressure from 0.18 MPa to 0.26 MPa reduced the contact area on the PAC, SMA, and AC pavements by 13.44%, 13.63%, and 15.21%, respectively. Compared with the static contact condition, the average contact area of the tire in free rolling at 10 km/h decreased by 18.82%, 17.05%, and 8.56% on the PAC, SMA, and AC pavements, respectively. For every 0.01 MPa increase in inflation pressure, the maximum normal contact stress increased by 0.071 MPa, 0.060 MPa, and 0.033 MPa on the PAC, SMA, and AC pavements, respectively. The rate of increase in contact stress on the PAC pavement was clearly greater than that on the other two pavements, whereas the increase on the AC pavement was the smallest. The decrease in contact area and increase in contact stress essentially indicate an upward shift of the tire centroid and a reduction in the tire embedment depth into the pavement. On pavements with more pronounced surface texture, fewer surface asperities bear the tire load, resulting in higher contact stress.

Figure 13 shows the contact stress distributions extracted along the centerline of the tire contact region under different inflation pressures, with the tire load fixed at 3.3 kN and the free-rolling speed set at 10 km/h. It can be seen that, along the longitudinal direction of the tire, the tire–pavement contact stress distribution tends to shift in the rolling direction, indicating that the stress is greater in the leading part of the contact region during tire rolling. This forward-leaning stress concentration becomes more pronounced on pavements with more prominent surface texture. Along the transverse direction of the tire, the contact stress distribution becomes more non-uniform as the pavement texture becomes rougher, whereas on pavements with less pronounced texture, the contact stress distribution tends to be more symmetric, as shown by the stress distribution on the AC pavement.

FIGURE 13

In the central contact region of the tire, a higher inflation pressure corresponds to a higher contact stress, whereas at the peak stress location in the rolling direction, the opposite trend is observed, namely, that a lower inflation pressure leads to a higher contact stress. The relationship between inflation pressure and contact stress in the tire central region is consistent with that under static conditions. However, in the forward-leaning region along the rolling direction, the opposite pattern appears. On the one hand, under low inflation pressure, more contact elements are engaged in the forward-leaning region under external loading, resulting in higher contact stress. On the other hand, at high inflation pressure, the tire stiffness increases, which imposes greater restraint on tire deformation and thus leads to lower contact stress in the forward-leaning region.

Under high inflation pressure conditions, the increased tire stiffness produces a typical inward concave deformation. The tire shoulders on both sides compress the central contact region, resulting in a reduced longitudinal contact length and an increase in contact stress in the central contact area. At the two side peaks, the distance between the peak stresses is greater under low inflation pressure, indicating that the tire has a larger longitudinal contact length and a larger contact area under low inflation pressure conditions.

4.3.2 Effect of tire load on tire in free-rolling status

As shown in Figure 14, at a constant inflation pressure of 0.22 MPa, both the contact area and the maximum normal contact stress of the tire increased significantly with increasing load. When the tire was in free rolling at a speed of 10 km/h, increasing the load from 2.8 kN to 3.8 kN increased the contact area on the PAC, SMA, and AC pavements by 29.24%, 34.20%, and 29.04%, respectively. Compared with the static contact condition, the average contact area of the tire in free rolling at 10 km/h decreased by 18.72%, 17.83%, and 9.75% on the PAC, SMA, and AC pavements, respectively. For every 0.1 kN increase in load, the maximum normal contact stress increased by 0.082 MPa, 0.052 MPa, and 0.024 MPa on the PAC, SMA, and AC pavements, respectively. As the load increased, the rate of increase in the maximum normal contact stress remained the highest on the PAC pavement and the lowest on the AC pavement. The increase in contact area and contact stress with increasing load essentially reflects a downward shift of the tire centroid and an increase in the tire embedment depth into the pavement, which leads to higher stress being distributed to each protruding point on the pavement surface.

FIGURE 14

Figure 15 shows the contact stress distributions extracted along the centerline of the tire contact region under different loads, with the tire inflation pressure fixed at 0.22 MPa and the free-rolling speed set at 10 km/h. It can be seen that, on all three pavements, the contact stress generally increased with increasing tire load. This trend was more pronounced at the peak stress locations on both sides of the tire. Owing to pavement surface irregularity, in regions with relatively low contact stress, the tire contact stress under different loads did not show obvious differences. The contact stress distribution of the tire under rolling conditions was generally similar to that under static contact conditions. At the peak stress locations on both sides of the tire, it can be observed that the distance between the two stress peaks increased with increasing load, indicating that the tire had a greater contact length and a larger contact area under higher loads, which is consistent with the static contact pattern. The smaller the pavement surface relief, the better the symmetry of the stress distribution. Compared with static contact, under rolling conditions the contact area decreased while the contact stress increased. Moreover, the more pronounced the pavement surface texture, the greater the influence on contact stress and the smaller the influence on contact area.

FIGURE 15

4.3.3 Tire in traction and braking status

Figure 16 shows the tire contact footprints on the three pavements under braking and traction conditions at a speed of 70 km/h. It can be seen that the maximum contact stress under braking was 9.01%, 11.50%, and 9.80% higher than that under traction on the PAC, SMA, and AC pavements, respectively. Under both braking and traction conditions on the different pavements, the tire stress under braking was clearly greater than that under traction, and the stress concentration region under braking tended to shift downward in the rolling direction. As can be seen from the contact footprint on the AC pavement, under the traction condition, the number of stress concentration regions increased, and stress concentration points also appeared in the direction opposite to rolling. This may be attributed to the fact that, under the action of external driving torque, the tire rubber is subjected to compression during tire–pavement contact under external loading. When the tire rolls out of the compressed state, the viscoelastic recovery of the rubber generates relatively large adhesive forces that promote tire rolling, thereby increasing the occurrence of local stress concentration. Compared with the contact stress under the same static conditions, the increase in contact stress during braking and traction was greater on pavements with more pronounced surface texture. According to friction theory, larger contact stress leads to greater rolling resistance. Therefore, the tire exhibits greater rolling resistance and better skid resistance on pavements with more pronounced surface texture.

FIGURE 16

To analyze the effect of speed on the contact footprint, the AC pavement, which exhibited a relatively symmetric contact footprint, was selected, and the braking contact footprints at different speeds are shown in Figure 17. It can be seen that, under braking conditions, the high-stress region appeared at the leading edge of the tire contact area in the rolling direction. Compared with the free-rolling condition, the contact area between the tire and pavement decreased, while the contact stress increased. The contact footprint maps also show that, as the speed increased, the contact region in the direction opposite to rolling decreased more noticeably. On the AC pavement, it can be clearly observed that the stress concentration region below the tire centerline moved significantly downward compared with the static contact footprint, while the stress concentration on both sides of the tire was no longer obvious. Therefore, pavements with less pronounced surface texture are more favorable for achieving a more uniform stress distribution during tire rolling and also lead to lower contact stress, which can help prevent local tire damage caused by stress concentration.

FIGURE 17

It can be seen from Table 8 that, as the speed increased, the average normal contact stress between the tire and pavement gradually decreased. When the speed increased from 10 km/h to 110 km/h, the average contact stress decreased by 21.05% on the PAC pavement, 14.81% on the SMA pavement, and 9.09% on the AC pavement, indicating that changes in speed had a greater influence on the average normal contact stress on pavements with more pronounced surface texture. This is because contact stress is mainly related to the contact area, and the tire contacts more fully with pavements having less pronounced surface texture.

4.4 Skid resistance analysis of dynamic contact simulation

4.4.1 Tire in ABS braking status

The ABS braking system refers to a control system that regulates the front and rear tires of a vehicle according to the select-low principle, thereby greatly improving vehicle stability during emergency braking. During tire braking, the braking intensity is generally described by the slip ratio. In the Abaqus finite element software, the slip ratio of the tire can be controlled by modifying the combination of tire angular velocity and linear velocity through keywords in the INP file. The relationship among tire slip ratio, slip velocity, and angular velocity (Guo, 2016) is given as Equation 3

Where is the slip ratio during tire braking; is the translational linear velocity of the tire (m/s); the angular velocity of the tire (rad/s); is the rolling radius of the tire (m).

The slip ratio of 15% was adopted to represent the ABS braking condition, as previous studies indicate that the optimal braking slip on dry asphalt typically falls within the range of 10%–20% (Boisvert and Micheau, 2016). The rolling angular velocity and translational linear velocity of the tire were then calculated based on the corresponding rolling radius under different operating conditions. The adhesion coefficient is generally used to evaluate the skid resistance between the tire and pavement during braking. A larger adhesion coefficient indicates better skid resistance. The adhesion coefficient, expressed in Equation 4, is defined as the ratio of the tangential reaction force at the tire contact surface to the vertical load (Yang et al., 2016).

Where is the tire adhesion coefficient, is the tangential reaction force at the contact interface, is the normal reaction force from the pavement.

As can be seen from Figure 18a, under ABS braking conditions, the maximum shear stress between the tire and pavement showed a decreasing trend with increasing speed. As the speed increased from 10 km/h to 110 km/h, the maximum shear stress decreased by 9.65%, 12.75%, and 17.65% on the PAC, SMA, and AC pavements, respectively, with the smallest reduction occurring on the PAC pavement. Therefore, the skid resistance of the tire on the three pavements followed the order PAC > SMA > AC, indicating that pavements with more pronounced surface texture provide better skid resistance. As shown in Figure 18b, the variation pattern of contact area on different pavements was the same as that under free-rolling conditions, which was mainly related to the pavement surface texture. Compared with the free-rolling state, the contact area of the tire under ABS braking was slightly smaller on all three pavements. As the speed increased from 10 km/h to 110 km/h, the contact area of the tire decreased by 8.49%, 9.98%, and 9.40% on the PAC, SMA, and AC pavements, respectively. According to the previous analysis, a smaller contact area corresponds to a larger normal contact stress, which in turn leads to a greater friction force during relative motion. Therefore, the friction force under ABS braking is greater than that under free-rolling conditions.

FIGURE 18

As can be seen from Figure 19a, under ABS braking conditions, the friction force between the tire and pavement increased significantly compared with that under full braking. When the speed increased to 110 km/h, the friction force under ABS braking increased by 3.73% on the PAC pavement and by 1.42% on the AC pavement. This indicates that, at high speeds, ABS braking leads to a greater improvement in skid resistance on pavements with more pronounced surface texture. For the AC pavement, the friction force did not decrease significantly when the speed increased from 10 km/h to 30 km/h. However, when the speed increased from 10 km/h to 110 km/h, the friction force decreased by 9.47%, 10.42%, and 12.89% on the PAC, SMA, and AC pavements, respectively. Under ABS braking conditions, for every 10 km/h increase in vehicle speed, the friction force of the tire decreased by 20.11 N, 21.62 N, and 27.97 N on the PAC, SMA, and AC pavements, respectively. As shown in Figure 19b, the variation trend of the adhesion coefficient with speed was consistent with that of the friction force. As the speed increased from 30 km/h to 110 km/h, the adhesion coefficient decreased by 12.94%, 16.67%, and 20.00% on the PAC, SMA, and AC pavements, respectively. Changes in speed had the smallest effect on the adhesion performance of the tire on the PAC pavement and the greatest effect on that on the AC pavement.

FIGURE 19

4.4.2 Effect of changes in the friction coefficient

The friction coefficient is mainly related to the pavement surface composition and texture characteristics, as well as tire parameters. A friction coefficient of 0.7 was adopted in the baseline simulations to represent a typical dry asphalt–rubber contact condition (Ni et al., 2026; Premarathna et al., 2026). To further investigate the influence of the friction coefficient on the skid resistance of the tire on the three pavements, this section compares the skid resistance performance under a fixed tire load of 3.2 kN, an inflation pressure of 0.25 MPa, and a tire speed of 50 km/h, while varying the friction coefficient from 0.4 to 0.9.

Figure 20 presents the variation patterns of contact area, average normal contact stress, and friction force on the three pavements under different friction coefficients. It can be seen that the variation trends on the different pavements were generally similar. As the friction coefficient increased, the contact area of the tire on all three pavements gradually decreased, while the average normal contact stress and friction force gradually increased. However, the variation in contact area was relatively small, indicating that, at a constant speed, the friction coefficient had little effect on tire contact area. As the friction coefficient increased, the average normal contact stress increased most rapidly on the AC pavement and most slowly on the PAC pavement. For every 0.1 increase in the friction coefficient, the friction force of the tire increased by an average of 17.72%, 15.66%, and 15.01% on the PAC, SMA, and AC pavements, respectively. The increase in friction force on the PAC pavement was clearly greater than that on the other two pavements. At the same friction coefficient, pavements with more pronounced surface texture produced greater friction force. Therefore, the influence of the friction coefficient was greater on pavements with more pronounced surface texture, and larger friction coefficients together with more pronounced pavement texture resulted in better skid resistance. Increasing the friction coefficient on pavements with more pronounced surface texture led to a more substantial improvement in skid resistance.

FIGURE 20

5 Main conclusions

Overall, pavement texture significantly influenced tire–pavement contact behavior and skid resistance. Pavements with more pronounced macrotexture showed stronger local interaction and greater sensitivity to speed and friction-related parameters. The present model was limited to dry conditions and should be extended in future work to include wet conditions, temperature variation, wear evolution, complex tread patterns, and material heterogeneity.

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