3.4.2. Stratified Parameters

According to the cumulative height distribution curve, the surface topography is stratified into three parts: peak layer, core layer, and valley layer. The three parts of a surface texture are represented by reduced peak height (Spk), core height (Sk), and reduced dale height (Svk), as shown in Figure 5a [10]. The calculation of stratified parameters in this study requires the following steps, as illustrated in Figure 5a:


Generally, the Spk measures the equivalent height of the surface summit, which is the primary and the most worn surface height. The Sk evaluates the long-term contact height of a surface. The Svk measures the equivalent height of deep grooves, which would hold debris from the upper surface [36].

#### 3.4.3. Volume Parameters

The peak material volume (Vmp), core material volume (Vmc), core void volume (Vvc), and dales void volume (Vvv) were calculated as per Equations (13)–(16) [10] as volume parameters and illustrated in Figure 5b. The material ratios, 10% and 80%, are specified as thresholds of the accumulated height to define peak and void of a surface texture [10]. The Vmp represents the material volume that is most likely to be removed by traffic polish. Moreover, the Vmc measures the material volume polished by traffic but not as much as the Vmp is. The Vvc is the surface void volume opposite to the Vmc. The Vvv indicates the void volume with a cumulative height distribution of the lowest 20%.

$$\mathbf{V\_{mp}} = \mathbf{V\_m}(10\%)\tag{13}$$

$$\mathbf{V\_{mc}} = \mathbf{V\_m}(80\%) - \mathbf{V\_m}(10\%) \tag{14}$$

$$\mathbf{V\_{v\cir}} = \mathbf{V\_{v}}(10\%) - \mathbf{V\_{v}}(80\%) \tag{15}$$

$$\mathbf{V\_{VV}} = \mathbf{V\_{V}}(80\%)\tag{16}$$

where Vm(mr) is material volume above the height corresponding to a material ratio mr to the highest peak; Vv(mr) is void volume below the height corresponding to a material ratio mr to the lowest valley.

As shown in Figure 5, stratified parameters and volume parameters divide the surface texture into peak, core, and valley with a different method based on the cumulative height distribution curve. To define surface peak and valley, volume parameters use 10% and 80% material ratios, whereas stratified parameters utilize the tangent line of the cumulative height distribution curve to determine mr1 and mr2. Further, volume parameters calculate these layers' material or void volume, and the stratified parameters estimate equivalent height for surface peak or valley layer.

#### *3.5. Feature Parameters*

The feature parameters can be used to characterize specified features of surface texture. The peak density, Spd, is calculated by dividing the number of peaks by the unit area, and the peak curvature, Spc, is the arithmetic mean curvature of significant peaks. A peak is selected as the highest pixel within a 16 by 16 nearest neighbors. These two feature parameters can be applied in surface contact models [37].

#### **4. Evolution of Micro- and Macro-Texture**

The evolution of pavement micro- and macro-texture was evaluated by comparing 3D areal texture parameters from the three years' data collection on the field site. The Figure 6, Figure 7, Figure 9, and Figures 11–14 summarize the variations of height, spatial, hybrid, function, and feature parameters for pavement micro- and macro-texture under actual traffic polishing. In each figure, the lines with markers display the actual 3D parameters from each data collection, while the bar chart in the upper-right corner shows the average number and standard deviation of each 3D parameter.

#### *4.1. Evolution of Height Parameters*

The variations of height parameters for pavement micro- and macro-texture under actual traffic polish are shown in Figure 6. For macro-texture from 2018 to 2020, (1) both Sa and Sq had no significant distinction in mean value and standard deviation, indicating that traffic polishing was not decreasing the macro-texture's height. This result corresponds to a previous study that the MPD values tended to remain constant under different polishing cycles [31]; (2) the negative Ssk indicates that pavement macro-texture had valley structure; (3) the declined average Sku means that the height variation of surface peaks or valleys was decreasing.

**Figure 6.** Pavement texture variations via height parameters: (**a**) Macro-texture, and (**b**) Micro-texture.

For micro-texture from 2018 to 2020, (1) the Sa and Sq had an approximate reduction of 20% from 2018 to 2019, and 5% from 2019 to 2020; (2) the Ssk were positive and decreased year after year, suggesting the spike structure of micro-texture was decreasing; (3) the Sku was greater than that of macro-texture and gradually reduced, which means the considerable height variation of micro-texture was decreasing as well. The evolution of these height parameters means the spike structure of pavement micro-texture was gradually polished under traffic, as illustrated in Figure 3b.

#### *4.2. Evolution of Spatial Parameters*

The variation of spatial parameters for pavement micro- and macro-texture is displayed in Figure 7. For macro-texture from 2018 to 2020, (1) the Sal had a 19.5% growth from 2018 to 2019 and stabilized from 2019 to 2020; (2) the Str was around 0.76 during polish, which means the isotropy of macro-texture was unchanged; (3) the Std was fluctuating around zero. Examples of ACF = 0.2 for macro-texture from 2018 to 2020 are shown in Figure 8a: the shape was stable, meaning the spatial characteristics of macro-texture were not changed from 2018 to 2020 under traffic polish.

**Figure 7.** Pavement texture variations via spatial parameters: (**a**) Macro-texture, and (**b**) Micro-texture.

For micro-texture from 2018 to 2020, (1) the Sal had a descent of 62.3% from 2018 to 2019, and 36.7% from 2019 to 2020; (2) the Str decreased year after year, indicating the texture changed from isotropic to anisotropic under traffic polishing; (3) the Std was fluctuating around zero, and its deviation decreased year after year. As shown in Figure 8b, the shape of ACF = 0.2 was round in 2018 and became long and thin in 2020, which corresponded to Str = rmin/rmax decreased from 1.0 to 0.

The spatial evolution of micro-texture can be seen intuitively from Figure 3b. The micro-texture asperities were isotropically distributed in 2018, corresponding to Str = 1. The micro-texture asperities were anisotropic distributed along the driving direction: stripes appeared in 2020, and the Str equals 0. Thus, the spatial parameters successfully characterize how pavement micro-texture evolved from isotropic to anisotropic along driving direction under traffic polish.

**Figure 8.** ACF = 0.2 for pavement macro- and micro-texture: (**a**) Macro-texture, and (**b**) Micro-texture.

#### *4.3. Evolution of Hybrid Parameters*

The variation of hybrid parameters for pavement micro- and macro-texture is displayed in Figure 9. Similar decreasing treads were observed for Sdq and Sdr from 2018 to 2020. For Sdq, a reduction of 46.1% and 32.8% were observed for macro- and micro-texture from 2018 to 2019, and another 16.0% and 11.5% of reduction were observed for macroand micro-texture from 2019 to 2020. As Sdq is getting closer to 0, it means the texture surface is getting close to flat under traffic polish with angular slope decreased. For Sdr, reductions of 43.4% and 32.8% were observed for macro- and micro-texture from 2018 to 2019, and another 16.0% and 113.4% of reduction for macro- and micro-texture from 2019 to 2020. The evolution of hybrid parameters suggests that the steepness and the developed

interfacial area of pavement micro- and macro-texture were decreased year after year under traffic polish.

**Figure 9.** Pavement texture variations via hybrid parameters: (**a**) Macro-texture, and (**b**) Micro-texture.

#### *4.4. Evolution of Function Parameters*

Under traffic polishing, the peak and valley of pavement texture change over time. The cumulative height distribution curve of pavement texture provides an ideal tool to visualize how the texture profile changes due to polishing. Figure 10 shows examples of cumulative height distribution curves for macro- and micro-texture over the years. For example, for macro-texture, the material ratio corresponding to height 8 mm were 41.0% in 2018, 30.1% in 2019, and 16.5% in 2020; for micro-texture, the material ratio corresponding to height 0.05 mm were 4.9% in 2018, 3.4% in 2019, and 2.4% in 2020. This implies that the material of pavement texture was worn due to traffic polish.

**Figure 10.** Cumulative height distribution curve of pavement macro- and micro-texture: (**a**) Macrotexture, and (**b**) Micro-texture.

Notably, the cumulative height distribution curve of macro-texture in 2019 was lower than that of 2018. It means that the texture material was worn, and the texture valley was increased from 2018 to 2019, which should correspond to the bitumen removal process. The cumulative height distribution curve of macro-texture in 2020 was lower at the peak layer and core layer but higher at the valley layer than that of 2019. This phenomenon illustrates that the upper part of macro-texture was removed by traffic polishing and field environmental erosion, and the valley void collected dust, debris, or chipping under traffic polishing. Besides, micro-texture's cumulative height distribution curve was getting lower year after year, suggesting micro-texture was consistently polished by traffic.

#### 4.4.1. Evolution of Material Ratio Parameters

The variation of material ratio parameters for pavement micro- and macro-texture is displayed in Figure 11. For macro-texture from 2018 to 2020, (1) the Sxp slightly increased from 2018 to 2019 and remained stable after the second polish year; (2) the Sdc kept almost unchanged. For micro-texture from 2018 to 2020, (1) the Sxp had a 20% decrement from 2018 to 2019 and another 7.5% decrement from 2019 to 2020; (2) the Sdc decreased by20% and 6.9%, respectively, after the first and second years of polishing. The material ratio parameters of micro-texture changed more than that of macro-texture by traffic polish, suggesting traffic polish mainly affects materials of micro-texture.

**Figure 11.** Pavement texture variations via material ratio parameters: (**a**) Macro-texture, and (**b**) Micro-texture.

#### 4.4.2. Evolution of Stratified Parameters

The variation of stratified parameters for pavement micro- and macro-texture is displayed in Figure 12. For macro-texture from 2018 to 2020, (1) the Spk increased by 17.6% from 2018 to 2019 and remained unchanged roughly after the second year of polishing, indicating that the peak layer remained unchanged after the bitumen layer was removed; (2) the Svk of macro-texture decreased by 10% and 5.7% for each polishing year, which implies that the valley structure of macro-texture was gradually filled by dust, debris, or residue under traffic polishing; (3) the Sk showed minor variance after two years of traffic polish, which means the core layer of macro-texture was stable under traffic polish. Therefore, the variation of stratified parameters for macro-texture reveals that the traffic polish mainly affects the peak and valley layers but not the core layer of pavement macrotexture.

For micro-texture from 2018 to 2020, (1) the Spk and Sk had significant decrement after the first year's polish and minor change after the second year's polish; (2) the mean value and standard deviation of micro-texture Svk was almost zero, because the dale stratification did not exist in the cumulative height distribution curve of micro-texture, as shown in Figure 10b. It means traffic polish affects peak, core, and valley layers of pavement micro-texture.

#### 4.4.3. Evolution of Volume Parameters

Figure 13 shows the variation of volume parameters in three years for pavement micro- and macro-texture. For macro-texture from 2018 to 2020, (1) the Vmp increased 9.9% and 5.9% after each polishing year, suggesting more material from the peak layer was exposed under traffic polish; (2) the Vmc and Vvc remained unchanged, indicating the material and void volume of core layer was unaffected by traffic polish; (3) the Vvv slightly

decreased 8.5% and 3.9% sequential under traffic, meaning the void volume of valley layer was gradually reduced by collecting dust, debris, or residue under traffic polishing.

**Figure 12.** Pavement texture variations via stratified parameters: (**a**) Macro-texture, and (**b**) Micro-texture.

**Figure 13.** Pavement texture variations via volume parameters: (**a**) Macro-texture, and (**b**) Micro-texture.

For micro-texture from 2018 to 2020, (1) the Vmp decreased by 42.9% and 14.0%; (2) the Vmc decreased by 16.7% from 2018 to 2019, and changed minor (2.9%) after the second year's traffic polish; (3) the Vvc had a large descend of 17.8% from 2018 to 2019, and minor change (4.7%) from 2019 to 2020; (4) the Vvv also had consecutive drops of 16.0% and 1.9%. This result implies that traffic polish affects the material and void volume of pavement micro-texture.

Therefore, the volume parameters suggest that traffic polish influences pavement macro-texture in the following aspects: (1) exposed more material from the peak layer into contact; (2) filled up the valley layer with dust, debris, or residue; (3) had a minor impact on the core layer. Additionally, traffic polish consistently reduced the height or volume of pavement micro-texture peak, core, and valley layers.

#### *4.5. Evolution of Feature Parameters*

The evolution of feature parameters for macro- and micro-texture is shown in Figure 14. Generally, the Spd of macro-texture had a tiny descend of around 5%, which means the number of contact peaks was reduced by abrasion. The average number of Spc dropped 26.3% after the first year's polish, corresponding to the removal of the bitumen layer and fine aggregate. Then the Spc had only a 7% drop from 2019 to 2020, because the coarse aggregate in pavement structure was gradually exposed and was harder to get worn than bitumen layer under traffic polish.

**Figure 14.** Pavement texture variations via feature parameters: (**a**) Macro-texture, and (**b**) Micro-texture.

Unlike the macro-texture, the Spd of micro-texture was slightly increased year after year, as displayed in Figure 14b. The enlarged micro-texture in Figure 3b also shows more peaks existed on micro-texture over time due to traffic polish. The coarse aggregate exposure from 2018 to 2019 and the new micro-texture generated in the wearing process of coarse aggregates from 2019 to 2020 may contribute to the increased Spd. However, the Spc was lessening by 33% and 17% after each year's polish, which means the pavement micro-texture was gradually rounded by polish.

#### **5. Conclusions**

This paper applies 3D areal parameters to investigate asphalt pavement micro- and macro-texture evolution under actual traffic polish and environmental conditions. The portable 3D laser scanner LS-40 collected high-resolution 3D pavement texture data from predefined locations on a field site in 2018, 2019, and 2020, respectively. The obtained LS-40 data was decomposed into pavement micro- and macro-texture data sets to calculate 3D areal texture parameters. A total number of twenty parameters under five categories (height, spatial, hybrid, functional, and feature) were calculated to study the evolution of pavement micro- and macro-texture under actual traffic polish. The conclusions are summarized as follows:


The results demonstrate the advantage of 3D areal parameters to describe the evolution characterization of pavement micro- and macro-texture under traffic polish. However, this paper only recorded texture data from one asphalt mixture in three years. Thus, it is expected that more asphalt pavement texture categories could be collected for a longer time frame in a future study to understand how traffic polish affects pavement micro- and macro-texture for different pavements. Furthermore, the relationship of texture wear and skid resistance should be studied in the future as well.

**Author Contributions:** Conceptualization, Y.Z.; methodology, Y.Z. and G.Y.; software, Y.Z.; validation, Y.Z. and G.Y.; formal analysis, Y.Z. and G.Y.; investigation, Y.Z.; resources, W.H., Y.L., Y.Q., K.C.P.W.; data curation, Y.Z. and G.Y.; writing—original draft preparation, Y.Z.; writing—review and editing, Y.Z. and G.Y.; visualization, Y.Z.; supervision, W.H., Y.L., Y.Q., K.C.P.W.; project administration, Y.Z.; funding acquisition, W.H., Y.L. and Y.Q. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by [National Natural Science Foundation of China] grant number [51778541 and 51878574], [Sichuan Province Science and Technology Project] grant number [2020YFS0362], and [Sichuan Province Youth Science and Technology Innovation Team] grant number [2021JDTD0023]. The APC was funded by [National Natural Science Foundation of China] grant number [51778541].

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

