*1.1. Background*

Pavement skid resistance has positive effects on reducing traffic accidents in dry or wet conditions [1]. For example, the skidding risk would increase rapidly when the pavement skid number (SN) from locked-wheel skid testers is below 50 and decrease significantly when the value of SN is over 65 [2]. Additionally, traffic accidents increased 60% when the value of SN decreased from 48 to 33 [3]. Therefore, it is critical to design pavements surface with high skid resistance and wear resistance to ensure driving safety during design life [4].

Skid resistance of pavement surface varies under traffic polishing throughout the design life: It typically increases to a peak at the initial stage and decreases continuously at the following stages of pavement life [5,6]. However, the level of skid resistance is dependent on the wear process of pavement surface texture [7], as the skid resistance of pavement comes directly from the contact between vehicle tires and pavement surface micro- and macro- texture [8]. Pavement surface texture is recognized as the dominating factor influencing pavement skid resistance [9].

Therefore, many studies have been performed to investigate how traffic wear affects pavement texture over time in order to evaluate pavement skid resistance under traffic polish. Pavement texture can be categorized into macro-texture (0.5 mm < wavelength < 50 mm) and micro-texture (wavelength < 0.5 mm) based on the wavelength of its components [10]. The pavement macro-texture provides drainage channels when it rains and comprises the hysteretic component of friction, while the pavement micro-texture provides actual contact with the tire and comprises the adhesion part of friction [11].

**Citation:** Zou, Y.; Yang, G.; Huang, W.; Lu, Y.; Qiu, Y.; Wang, K.C.P. Study of Pavement Micro- and Macro-Texture Evolution Due to Traffic Polishing Using 3D Areal Parameters. *Materials* **2021**, *14*, 5769. https://doi.org/10.3390/ma14195769

Academic Editor: Carlos Morón Fernández

Received: 12 September 2021 Accepted: 30 September 2021 Published: 2 October 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Typically, measurement of pavement macro-texture adopts the sand patch method, the outflow meter, or the circular texture meter (CTM) using a two-dimensional (2D) texture profile [12]. Indicators like mean texture depth (MTD), mean profile depth (MPD), or root mean square depth (RMSD) is customarily applied to characterize pavement macro-texture [13]. Besides, the pavement micro-texture is evaluated by indirect friction measurement devices testing at low speed, such as the British portable tester (BPT), the dynamic friction tester (DFT), and the locked-wheel skid trailer [12].

Recently, pavement surface micro-texture was measured with high-resolution cameras in the laboratory to obtain more texture details [14]. Moreover, the advanced highresolution laser device can conveniently collect three-dimensional (3D) surface texture data from the field and achieve enough accuracy to characterize pavement micro- and macro-texture [15]. The acquisition of high-resolution surface texture information can significantly assist the investigation of the micro- and macro-texture contributions to skid resistance [16].

Further, 3D areal surface texture parameters have been utilized extensively in modern manufacturing industries to control and evaluate the surface finishing of products [17]. The 3D areal texture parameters contain aspects of surface height, spatial, hybrid, function, and feature information, whereas the traditional parameters only contain height information [17]. The areal texture parameters can characterize surface texture functionality and understand texture characteristics in different perspectives that the traditional texture parameter fails to achieve [18]. Therefore, some recent studies attempted to evaluate pavement texture using 3D areal parameters and correlate them with skid resistance [19–21]. The study described in this paper used 3D areal parameters to evaluate pavement texture changes under traffic loading.

Many studies have been performed to investigate how traffic polish affects pavement texture over time so that pavement can be constructed with desired texture features to maintain good skid resistance [22]. Several devices were developed to study the wear-resisting feature of pavements in the laboratory, such as the Wehner/Schulze device (W/S) [23], the Aachen polishing machine (APM) [24], and other accelerated polishing machines [25–28]. These devices evaluate the evolution of pavement texture under simulated traffic polishing in controlled laboratory conditions rather than actual traffic polishing from various vehicles.

Further, Kane et al. proposed a polishing model to predict the surface variation with polishing cycles based on laboratory testing using the W/S machine and adopted the roughness parameters (Rq) to validate the model [29]. Druta et al. conducted accelerated polish testing on stone matrix asphalt (SMA) species and found that MPD had completely different changing trends with BPN during the polish process [30]. Wang et al. tried to quantify the effect of aggregate size with W/S device on polishing resistance, and the texture variation characterized by power spectral density (PSD) showed that the coarser aggregate had a significantly rougher texture [5]. Wu and Abadie simulated the wearing process with an accelerated polishing machine and measured MPD with a CTM, and the results indicated that the MPD values tended to remain constant under different polishing cycles [31]. Plati and Pomoni investigated the long-term field data of skid resistance and macro-texture and found that the MPD and grip number (GN) presented a contrary trend under traffic polish [32].

#### *1.2. Research Need*

Several limitations in previous studies have been identified and summarized as follows:


ment of pavement data collection, high-resolution 3D texture data should be applied to understand better the evolution of asphalt pavement micro- and macro-texture under traffic polish.

(3) Traditional pavement texture parameters only consider texture height distribution while miss other texture characteristics (such as spatial, hybrid, and so on). Hence, different categories of 3D areal parameters should be explored to characterize pavement micro- and macro-texture under traffic polishing from different aspects.

Therefore, it is necessary to conduct field studies to understand pavement micro- and macro-texture evolution under actual traffic polish using different 3D areal texture parameters.

#### *1.3. Objective*

In this study, a field asphalt pavement site was monitored from 2018 to 2020 to study the influence of traffic polish on the evolution of pavement micro- and macro-texture. Pavement 3D texture images were collected using an LS-40 3D laser scanner (HyMIT Measurement Instrument Technology, Austin, TX, USA) for three years. Then, pavement micro- and macro-texture were separated from the obtained 3D texture data using twodimensional discrete Fourier Transform method and Butterworth filters method 21. Next, twenty 3D areal parameters from five categories (height, spatial, hybrid, function, and feature) were calculated for pavement 3D micro- and macro-texture. The obtained microand macro-texture parameters in three years were analyzed to describe the evolution of surface texture under actual traffic polish from different perspectives.

#### **2. Field Data Collection**

This study selected the field site on a suburb road paved with dense-graded asphalt mixture (HMA-13) in Yongning avenue, located in an industrial district of Chengdu, China. There were about 3 million passage cars on this site in 2019, and the traffic volume had an 11.9% growth in 2020. The site was constructed in 2018 and monitored until 2020 for pavement texture variations under actual traffic polishing.

Figure 1 shows example pavement images from this site in 2018, 2019, and 2020, individually. Most of the aggregates were coated with bitumen in 2018 when the pavement was just constructed (Figure 1a). After traffic polish from 2018 to 2019, the bitumen layer was gradually removed, and the coarse aggregate was exposed to field environmental effect and traffic polishing and compacting, as shown in Figure 1b. Further, the texture of coarse aggregates in 2020 looked smoother and more aging than that in 2019 due to traffic polish (see Figure 1c).

Figure 2a shows the LS-40 Portable Surface Analyzer (LS-40, HyMIT Measurement Instrument Technology, Austin, TX, USA) that was used to record 3D texture images on this site to quantify pavement texture evolution due to traffic polish. The LS-40 scans a 102.4 × 102.4 mm pavement surface area with height resolution (z) at 0.01 mm and lateral resolution (x, y) at 0.05 mm. From 2018 to 2020, a total number of 42 3D texture images were obtained from the wheel path during each data collection from previously marked locations on this site.

The 3D texture data collected by LS-40 was denoised (see Figure 2b) by a Gaussian smoothing filter with a kernel size of 5 × 5. Then the Fourier transform converted the texture height data into the frequency domain, and the Butterworth filter separated texture components in the frequency domain into micro-texture and macro-texture at a boundary of 2 Hz. Subsequently, the inverse Fourier transform converted the frequency domain micro-texture and macro-texture data back to texture height data, respectively, as shown in Figure 2c,d. The detailed procedure of texture data processing was published in a previous research [21].

**Figure 1.** Pavement surface pictures from the field site: (**a**) May 2018, (**b**) June 2019, and (**c**) July 2020.

Figure 3 shows an example of how 3D pavement micro- and macro-texture changed from 2018 to 2020. It is noteworthy that the height of macro-texture was decreasing over time and tiny stripes formed on the micro-texture along driving direction in 2020. To characterize the evolution of micro- and macro-texture, quantitative analysis is conducted in the following section via 3D areal parameters.

**Figure 2.** LS-40 and examples 3D texture data: (**a**) LS-40 Portable Surface Analyzer, (**b**) Denoised original image, (**c**) Macrotexture, and (**d**) Micro-texture.

**Figure 3.** Evolution of pavement micro- and macro-texture: (**a**) Macro-texture, and (**b**) Micro-texture.

#### **3. Three Dimensional Areal Parameters**

In this section, twenty 3D areal texture parameters from five categories (height, spatial, hybrid, functional, and feature) were calculated for both 3D micro- and macro-texture to investigate the evolution of pavement surface texture under actual traffic polishing and environmental impacts. The category, name, and unit of these 3D areal parameters are summarized in Table 1. The detailed definition of these parameters is introduced as follows.


**Table 1.** Summary of 3D areal parameters.

#### *3.1. Height Parameters*

The height parameters consider the surface height information, but neglect the horizontal input. In this section, four height parameters, including arithmetic mean height (Sa), root mean square height (Sq), skewness (Ssk), and kurtosis (Sku), were calculated per Equations (1)–(4) [10]. The Sa and Sq measure the overall height of a surface and correlate intensely with each other, and the Ssk and Sku describe the shape of the surface probability density [10]. The Ssk indicates the symmetry of the height probability density curve, and the Sku characterizes the kurtosis of the probability density curve. Pavement surface with positive Ssk would have spike structure, and surface with negative Ssk would have valley structure. Moreover, a higher Sku implies more significant height variation of surface peaks or valleys. Significantly, the Ssk is 0.0 and the Sku is 3.0 when the surface probability density function is Gaussian distribution [33].

$$\mathbf{S\_{a}} = \sqrt{\frac{1}{\mathbf{A}} \iint |\mathbf{z(x,y)}| \mathrm{d}x \mathrm{d}y} \tag{1}$$

$$\mathbf{S\_{q}} = \sqrt{\frac{1}{\mathbf{A}} \iint \mathbf{z(x,y)^{2}} \, \mathrm{d}x \mathrm{d}y} \tag{2}$$

$$\mathbf{S}\_{\rm sk} = \frac{1}{\mathbf{A} \, \mathbf{S}\_{\rm q}^{\rm 3}} \iint \mathbf{z}(\mathbf{x}, \mathbf{y})^{\rm 3} \, \mathbf{dx} \, \mathbf{dy} \tag{3}$$

$$\mathbf{S}\_{\rm ku} = \frac{1}{\rm AS\_{\rm q}^4} \iint \mathbf{z}(\mathbf{x}, \mathbf{y})^4 \, d\mathbf{x} d\mathbf{y} \tag{4}$$

where A is the area of a 3D image; z is the height value of pixels in a 3D image; x and y are the horizontal coordinates of pixels in a 3D image.

#### *3.2. Spatial Parameters*

The calculation of spatial parameters involves the autocorrelation function (ACF) of a 3D texture surface. The ACF calculates the similar degree of a surface z(x, y) and the duplicate surface z(x-τx, y-τy) with a horizontal shift (τx, τy) [17]. Equation (2) shows the function to calculate ACF, and Figure 4a shows the ACF of an obtained LS-40 data as an example. For instance, the ACF is 1.0 when the LS-40 data has a horizontal shift (0, 0), the ACF equals 0.2 when the LS-40 data has a horizontal change along the red circle highlighted in Figure 4a.

**Figure 4.** Calculation of spatial parameters: (**a**) ACF of an LS-40 data, and (**b**) rmin, rmax, and θ when ACF = 0.2.

The spatial parameters, including autocorrelation length (Sal), texture aspect ratio (Str), and texture direction (Std), were obtained for each LS-40 data per Equations (5)–(8) using 0.2 as the threshold of ACF. Figure 4b illustrates an example of how to calculate rmin, rmax, and θ from the red circle when ACF = 0.2 [10]. The Sal is defined as the horizontal distance rmin that has the fastest decay to ACF = 0.2 [34]. Additionally, the Str is calculated as the ratio of the fastest decay distance rmin to the slowest decay distance rmax, which is the most critical indicator to characterize isotropy of surface texture in the horizontal direction. The surface is isotropic when Str equals 1, and the surface is anisotropic when Str equals 0. Further, the Std gives the angle of rmax for a surface texture, as shown in Figure 4b.

$$\text{ACF}(\tau\_{\text{x}}, \tau\_{\text{y}}) = \frac{\iint \mathbf{z}(\mathbf{x}, \mathbf{y}) \mathbf{z} (\mathbf{x} - \tau\_{\text{x}}, \mathbf{y} - \tau\_{\text{y}}) \, \text{dxdy}}{\iint \mathbf{z}^{2}(\mathbf{x}, \mathbf{y}) \, \text{dxdy}} \tag{5}$$

$$\mathbf{S\_{sl}} = \min\_{\tau\_{\mathbf{x}\_{\mathbf{x}}}, \tau\_{\mathbf{y}} \in \mathbb{R}} \sqrt{\tau\_{\mathbf{x}}^2 + \tau\_{\mathbf{y}}^2} = \mathbf{r\_{min}} \tag{6}$$

where R = τx, τ<sup>y</sup> : ACF τx, τ<sup>y</sup> ≤ 0.2 .

$$\mathbf{S}\_{\rm tr} = \frac{\mathbf{r}\_{\rm min}}{\mathbf{r}\_{\rm max}} \tag{7}$$

$$\mathbf{S}\_{\rm td} = \boldsymbol{\Theta} \tag{8}$$

where τ<sup>x</sup> and τ<sup>y</sup> are the shifting along and perpendicular to the driving direction, respectively; rmax and rmin are the slowest and fastest decay distance to ACF = 0.2, respectively; θ is the angle between rmax and driving direction.

### *3.3. Hybrid Parameters*

The hybrid parameters describe the height and spacing information of a surface texture. They measure the angular slope of the 3D profile and are handy for assessing friction, adhesion, vibration, etc. The root mean square gradient (Sdq) and developed interfacial area ratio (Sdr) were calculated per Equations (9) and (10) as the hybrid parameters based on the surface local gradient. The Sdq and Sdr can be utilized to assess surface cosmetic flatness and correlate to adhesion property [35]. A flat surface would have both Sdq, and Sdr value equals 0. Besides, a 45◦ inclined surface would have a Sdq value of 1 and a Sdq value of 41.4%.

$$\mathbf{S\_{dq}} = \sqrt{\frac{1}{\mathbf{A}} \iint \left(\frac{\partial \mathbf{z}}{\partial \mathbf{x}}\right)^2 + \left(\frac{\partial \mathbf{z}}{\partial \mathbf{y}}\right)^2 \mathbf{d} \mathbf{x} \mathbf{d} \mathbf{y}} \tag{9}$$

$$\mathbf{S\_{dr}} = \frac{1}{\mathbf{A}} \{ \iint \left[ \sqrt{1 + \left( \frac{\partial \mathbf{z}}{\partial \mathbf{x}} \right)^2 + \left( \frac{\partial \mathbf{z}}{\partial \mathbf{y}} \right)^2} - 1 \right] \mathbf{d} \mathbf{x} \mathbf{d} \mathbf{y} \} \times 100\% \tag{10}$$

#### *3.4. Function Parameters*

The function parameters are strongly associated with surface functions, such as wearing, bearing, and hydroplaning. Three sub-categories of functional parameters, material ratio, stratified, and volume, were calculated for 3D micro- and macro-texture data based on the cumulative height distribution curve or material ratio curve. The dashed line in Figure 5 shows examples of the cumulative height curve of the 3D texture. The ordinate is the surface height, and the abscissa is the cumulative probability above a certain height. The function parameters characterize peak, core, and valley features of pavement microand macro-texture. Details of how to calculate stratified and volume parameters per the cumulative height curve are introduced as follows.

#### 3.4.1. Material Ratio Parameters

The areal material ratio parameters employ the peak extreme height (Sxp) and the surface section difference (Sdc) to characterize the upper half part and the general height of a surface, respectively [18]. The calculation of Sxp considers the surface part among the mean plane (50%) and the summit (2.5%). The parameter Sdc defines the general height difference of the surface without taking the highest peaks (below 2%) and the lowest valleys (above 98%) into account, as shown in Equations (11) and (12).

$$\mathbf{S\_{xp}} = \mathbf{S\_{mc}}(2.5\%) - \mathbf{S\_{mc}}(50\%) \tag{11}$$

$$\mathbf{S\_{dc}} = \mathbf{S\_{mc}}(2\%) - \mathbf{S\_{mc}}(98\%) \tag{12}$$

where Smc(p) is the height value c corresponding to a material ratio p in Figure 5a.
