Study of Pavement Macro- and Micro-Texture Evolution Law during Compaction Using 3D Laser Scanning Technology

Abstract

The pavement macro-texture and micro-texture are crucial factors for evaluating pavement performance as they have a significant correlation with friction, water film formation, and driving safety. During pavement construction, the macro-texture and micro-texture are significantly related to compaction operations. However, the current approach for evaluating pavement texture still relies on post-construction acceptance, with few considerations on the evolution patterns of pavement texture during the compaction process. Therefore, this study aimed to investigate the texture evolution law during compaction by implementing a laboratory compaction method. High-precision texture data from various asphalt mixtures were collected using 3D laser scanning during laboratory compaction. Macro-texture and micro-texture parameters were used to evaluate surface texture. Nineteen traditional geometric parameters were calculated at the macro-level to analyze macro-texture characteristics, while a 2D wavelet transform approach was applied at the micro-level to extract micro-texture, and the energy of each level and relative energy were calculated as indicators. This study analyzed the evolution law of parameters and found that certain parameters tend to converge. Moreover, geometric parameters and energy at lower levels of the samples could be utilized as supervising factors to regulate the compaction process.

1. Introduction

The pavement texture refers to the characteristics of the concave–convex structure that exists on the surface of pavements. Several studies have shown [1,2,3] that the pavement texture has a significant relationship with skid resistance, noise mitigation, compaction uniformity, and even driving safety [4,5,6]. Among the many phenomena observed in research and experimentation, the quality of the compaction will affect the surface texture condition of the pavement [7,8]. Furthermore, early damage of asphalt pavement is closely related to the quality of pavement compaction [9]. Despite post-construction testing methods used to ensure proper texture depth, preserving appropriate surface texture during compaction continues to remain a significant challenge in compaction quality control. Hence, it is important to investigate the evolution law of pavement surface texture during the compaction process.

The categorization of pavement surface textures into four groups, namely micro-texture, macro-texture, mega-texture, and unevenness, based on their wavelengths, was proposed by PIARC [10]. Typically, field measurements are used to detect pavement texture; however, the precision of these methods is often inadequate and varied. Variations in the testing methods and texture indicators induce variations in the decision-making process during compact quality control. For instance, to gauge macro-texture, which covers wavelengths between 0.5 mm and 50 mm, the sand patch test method is employed. For evaluating micro-texture within a range of 1 μm to 0.5 mm, testing methods, such as the British Pendulum Tester, Grip Tester, or Locked Wheel Skid Tester, are utilized. Static testing methods can provide measurements of Mean Texture Depth, which are both location-specific and time-consuming. It is also challenging to use these texture indicators without proper validation and site inspection in the construction [11]. Hence, it is important to achieve a more accurate and efficient characterization of the pavement texture using the laser profiler method during the site compaction process. Various sensors, such as high-definition cameras, Lidar, or 3D laser scanners, have been introduced to obtain data more efficiently [12,13]. Among these, the 3D laser scanner stands out as it captures the pavement profile and generates point cloud data containing depth information that describes pavement texture characterization [14]. Indices, such as mean texture depth (MTD) and mean profile depth (MPD), calculated from laser-based data, exhibit a strong correlation with those tested from the sand patch test [15]. Furthermore, high-resolution point cloud data obtained from 3D laser scanners have been utilized to predict friction [16], aggregate gradation [17], and skid resistance [18]. However, current research primarily focuses on the evolution of pavement texture during the maintenance phase, and there is a dearth of studies examining the evolution law of texture during compaction.

Different signal processing methods have been employed to investigate the point cloud data of pavement texture. While Fourier transform methods are widely used, they tend to mask the spatial correlation of the data, which limits their interpretability [19]. Some researchers have applied the Hilbert–Huang transform to investigate the correlation between pavement texture and friction [20]. In addition, pavement texture has been characterized using diverse approaches, including fractal analysis [21], entropy theory [22], power spectral analysis [23], and wavelet analysis [24]. Moreover, the availability of high-density point cloud data, obtained through high-resolution measurements, has made it possible to apply deep learning methods to pavement analysis. For instance, the deep fusion network has emerged as a new tool for efficient and large-scale pavement quality evaluation [3,24], while a domain knowledge-based deep learning network has been used to estimate pavement service life through vast high-definition image data [25,26]. However, it is noteworthy that these advanced signal processing methods have not yet been fully utilized to interpret the pavement texture cloud point data obtained during pavement compaction.

In recent years, there has been a growing trend toward the use of intelligent compaction control techniques in pavement field compaction. To measure the compaction of asphalt pavement, the non-nuclear density gauge has gained widespread acceptance due to its efficiency, accuracy, and harmlessness. However, this instrument is limited to measuring the compactness of the pavement and cannot provide information on its texture. Moreover, the advent of Continuous Compaction Monitoring (CCM) and Intelligent Compaction (IC) technologies has presented new opportunities for assessing pavement quality and monitoring temperature in real time [27,28,29]. IC rollers utilize a combination of Global Positioning System, infra-red, and accelerometer sensors to capture and record the speed of the rollers, number of roller passes, temperature of the asphalt pavement, effort applied to compaction, and material response [30]. The CCM method allows for automatic feedback control by modifying the frequency and amplitude of roller vibrations based on real-time measurements [31]. In practical engineering applications, various post-construction acceptance methods, such as the sand patch test, pavement evenness test, and penetration test, are commonly used to monitor pavement compaction [32,33,34]. Despite the benefits of intelligent compaction control techniques, they mainly focus on controlling the rollers and measuring the compactness of the pavement, overlooking the importance of monitoring texture, which is closely related to slip and safety.

This study presents an investigation into the evolution of pavement texture characteristics for five different asphalt mixture types: AC-13, AC-16, AC-25, SMA-13, and OGFC-13. These mixtures were prepared through laboratory compaction experiments, and high-precision pavement texture data were collected using 3D laser measurements. Macro-texture indicators were calculated based on the geometric parameters obtained during laboratory compaction. A 2D wavelet transform approach was then used to separate the micro-texture of each mixture into six levels, with the total energy of each level and the relative energy serving as wavelet-based indicators. The goal of this study is to provide insights into pavement texture evolution during compaction by analyzing the geometric parameters and decomposition results for the five different asphalt mixture types. Figure 1 illustrates the outline of this study.

The remainder of this paper is organized as follows. The materials and test method are presented in Section 2. The methodology is presented in Section 3. The results and discussion are presented in Section 4. The conclusions are presented in the final section.

2. Materials and Test Method

2.1. Preparation of Asphalt Mixture

In this paper, three types of asphalt mixtures, namely asphalt concrete (AC), stone mastic asphalt (SMA), and open-graded friction course (OGFC), were selected for pavement texture characterization. Because of the influence of the maximum nominal particle size on pavement structure, three distinct maximum nominal particle sizes were employed. The AC-13, AC-16, and AC-25 asphalt mixtures with maximum nominal particle sizes of 13.2, 16, and 26.5 mm, respectively, were designed. For the AC mixture, three different nominal maximum aggregate sizes (NMASs) were utilized (AC-13, AC-16, and AC-25), while SMA and OGFC used one NMAS each (SMA-13 and OGFC-13). Figure 2 shows the grading curves for the five different types of mixtures.

In the laboratory, various compaction methods were employed to prepare asphalt concrete specimens, including Marshall compaction, wheel-grind compaction, and Superpave gyratory compaction. Each method possessed distinct compaction characteristics attributed to their specific mold design and loading mode [35]. The Marshall compaction employs the impact force to compact specimens, whereas the wheel-grind compaction and Superpave gyratory compactor utilize kneading forces to form specimens. Among these methods, the kneading compaction method exhibits a closer resemblance to the actual conditions of asphalt pavement construction on site. Although the Superpave gyratory compactor can better replicate the field compaction state, it was observed that asphalt mixtures compacted using this method exhibited higher texture levels compared to field-constructed pavements [36]. Empirical evidence has shown that the laboratory wheel-grind compaction method closely simulates the field construction state in terms of surface texture [37]. Therefore, the present study selected the laboratory wheel-grind compaction method as it resembled best with the field conditions.

A wheel-grind compaction process was adopted for laboratory experiments, which was similar to the field compaction method. A 300 N/cm line-loaded asphalt slab roller compactor was used for compacting with 12 back-and-forth runs, as shown in Figure 3a. In order to obtain an even mixture of asphalt, the mixture was heated at 155℃. Subsequently, the mixtures were subjected to a two-hour aging process at a temperature of 145 °C to simulate the transportation conditions experienced in the field. Finally, the compacting process was carried out using the wheel-grind method at a temperature of 150 °C. Furthermore, the asphalt–aggregate ratio of AC-13, AC-16, AC-25, SMA-13, and OGFC-13 was 4.4%, 4.5%, 3.7%, 6.1%, and 5.4%, respectively.

The dimensions of the test pieces for each type of asphalt mixture were 300 mm × 300 mm × 50 mm. Each slab was divided into nine parts corresponding to the scanning region of the instrument to measure texture cloud point data accurately, as shown in Figure 3b. The texture cloud point measurement method used in this study employed a laser scanner. It is a non-contact method and measures the surface at a fixed distance and angle.

Texture data were collected at various stages of the compaction process. Specifically, texture data were collected after every two rounds of the roller. The rounds used were 12, 14, 16, 18, 20, 22, and 24. In addition, the compaction of the slabs was detected using a density meter. The data collected from this measurement process were used to generate the compaction curve of the mixture as shown in Figure 4. The compaction curve can determine whether the compaction process is proceeding as intended.

2.2. Data Collection

The data acquisition equipment used to measure the surface texture of the pavement slab samples was the AMES Laser Texture Scanner 9500, which is shown in Figure 5a.

The AMES Laser Texture Scanner 9500 system can acquire highly accurate texture data of the surface. The instrument comprises a laser–camera assembly, which incorporates a camera and a line laser, working in tandem to capture the data. The collection of 3D pavement data was accomplished through the implementation of the laser pulse reflection principle and the laser triangulation method [38].

With a scanning resolution of approximately 0.04 mm for horizontal direction and 0.01 mm for vertical direction, the instrument can detect micro-scale with a resolution of 0.1 mm. The sampling frequency of the scanning is 1 mm. At one time, the horizontal range of the scan is 101.6 mm × 101.6 mm. After scanning, the texture was cropped to the size of 100 mm × 100 mm to ensure that each measurement was taken in the same position.

During data collection, the instrument was not affected by ambient light sources. To display the raw cloud point data, the manufacturer’s software was used, which presented the data on a 3D display, as shown in Figure 5b. The 3D display allowed us to visualize the texture of the pavement surface preliminarily, enabling us to evaluate the quality of the data. The instrument is highly accurate and has a short collection time, making it an effective tool for acquiring pavement texture data.

2.3. Scanning Results

The results of the slab samples’ scanning are presented in Figure 6. Bright areas, such as yellow ones, are the convex parts of slab samples, while dark areas, such as blue ones, are the concave parts of slab samples.

By analyzing Figure 6, we can infer that the compaction process enhances the density of the asphalt mixture by filling in the voids on the surface, leading to a flatter surface. When the roller is flattening the surface, the asphalt mixture experiences considerable deformation, yet it can still compress until all its particles have sufficient contact to generate a compact structure. The compaction process also produces friction, which results in the polishing of the surface and its consequent smoothness. It is worth mentioning that AC-13 asphalt mixtures showed more bright areas than other samples, indicating low void content.

Figure 6 shows that as the compaction proceeds, voids on the asphalt mixture’s surface are filled, which increases the compactness of the concrete and the surface becomes flatter. As the roller compacts the surface, the surface of the asphalt mixture begins to show significant deformation, but there is still compressibility until all particles have been sufficiently touched to form a compact structure. Compaction creates friction, which helps to compact and polish the particles on the surface of the concrete, resulting in a smooth finish. Furthermore, the AC-13 mixtures have more bright areas, indicating a low void content.

3. Methodology

Characteristics of macro-texture, such as roughness, unevenness, and directionality, can be directly described by geometric parameters. The more abundant the surface macro-texture structure, the more prominent it will be reflected in the geometric parameters based on the calculated 3D information of the road surface. With the improvement in the accuracy of data acquisition of 3D road surface texture and the further development of signal processing technology, micro-texture can be extracted from texture data. We used 2D wavelet transform to decompose and extract micro-texture, then used relevant indicators to characterize, providing new ideas and methods for road construction and design.

3.1. Data Pre-Process

To ensure the accuracy of the data, pre-processing of the scanned data is essential. The first step involved meshing the point cloud data. In this study, a 1600 × 1000 grid was constructed with 0.1 mm intervals in both x- and y-directions. To accurately assign values to the z-direction, an interpolation method was used. Subsequently, normalization was carried out by subtracting the mean value.

However, the presence of bumps and concave data can cause noise in the scanned data. Additionally, diffused or refracted laser light sources through bitumens or aggregates can cause noise. A procedure for pavement texture noise removal was utilized in this study, as depicted in Figure 7. A two-dimensional median filter was employed to remove outliers from the data. For this, a 3 × 3 sliding window was used to detect outliers in both the x- and y-directions, with a step size of 1. Points with z-value variance greater than a defined threshold (0.1 mm) were treated as abnormal points and replaced with the median value of the z-value in the surrounding points of the sliding window.

3.2. Calculation of Geometric Parameters

The characterization of macro-texture in pavements can be described using geometric parameters. In this paper, five categories of geometric parameters were calculated to describe the pavement texture. These categories included profile parameters, height parameters, functional parameters, volume parameters, and hybrid parameters. In order to provide a thorough understanding of these categories, Table 1 outlines the nineteen parameters and the equations that belong to these five categories in a detailed manner.

The surface profile can be characterized by profile parameters [39] as explained by ISO (ISO 1984). Profile parameters are related to the vertical and horizontal extensions of surface profile irregularities. Mean profile depth (MPD) is the distance between the highest point of the profile and the mean line. Roughness average (Ra) is the arithmetic average of the absolute values of the profile heights over the evaluation length. RMS roughness (Rq) is the root-mean-square average of the profile heights over the evaluation length. Ra and Rq provide for easy statistical handling and enable stable results as the parameter is not significantly influenced by measurement noise. Da is the arithmetic mean slope of the surface profile. Dq is the root-mean-square slope of the surface profile. La is the average wavelength of the profile. Lq is the root-mean-square wavelength of the surface profile.

Height parameters [40] specifically pertain to height values along the z-axis and concern height distribution. Skewness of height distribution (Ssk) is a measure of the asymmetry of the profile about the mean line. A negative skewness indicates that a greater percentage of the profile is above the mean line, and a positive value indicates that a greater percentage is below the mean line. Kurtosis of height distribution (Sku) is the quotient of the mean quadratic value of z and the fourth power of Rq within a sampling length. Sku > 3 indicates that the height distribution is sharp, and Sku < 3 indicates that the height distribution is even. Sku relates to the tip geometry of peaks and valleys. Maximum profile peak height (Sp) represents the maximum peak height of a profile within the sampling length. Maximum profile valley height (Sv) represents the maximum valley height of a profile within the sampling length.

Functional parameters [7] and volume parameters [41] expand the material ratio curve parameters of the profile parameter in three dimensions and are suitable for evaluating friction and abrasion. The material volume and void volume were calculated from a material ratio curve as indicated in Figure 8. The position that corresponds to a material ratio of 10% and 80% was regarded as the threshold segmenting the peak, core, and dale. Core height (Sk) is the difference between the upper and lower levels of the core. Reduced peak height (Spk) is the mean height of the protruding peaks above the core. Reduced valley height (Svk) is the mean height of the protruding dales beneath the core. Volume parameters include dale void volume (Vvv), core void volume (Vvc), peak material volume (Vmp), and core material volume (Vmc).

Hybrid parameters [36] integrate both height and spacing characteristics. Developed interfacial area ratio (Sdr) signifies the rate of an increase in the surface area. Sdr values increase as the surface texture becomes rough.

3.3. 2D Wavelet Decomposition

Pavement textures refer to the surface characteristics of pavement, which are composed of micro-texture that is extremely intricate and difficult to analyze through naked eyes. To overcome this challenge, researchers have utilized various approaches, such as Fourier transform [19] and one-dimensional wavelet transform [42,43,44], to decompose the data for analysis. However, in this paper, a 2D wavelet transform algorithm was utilized for decomposition, which has the potential to provide more comprehensive and accurate results. We carried out the analysis using the powerful MATLAB Wavelet Toolbox, which provides numerous functionalities for signal processing and decomposition that are essential to our research.

While working with different mother wavelets, it is crucial to choose the most suitable one for the analysis, as different wavelets can produce unique effects on the decomposition results. The different types of mother wavelets that can be selected include Haar, Morlet, Daubechies (db), and Symlets. Among these options, the db wavelet, which is composed of ten compactly supported orthonormal wavelet functions, has been proven to be the most-applied one for surface texture analysis. For instance, previous studies have used db3 to analyze surface texture due to its sharp spikes and close resemblance to a profile signal.

However, other options, such as db4 to db10, exhibit smooth signal characteristics and are not suitable for texture analysis. As such, in this paper, we used db3 as the mother wavelet for conducting texture analysis. This is because it provides better resolution at high frequencies and enhances the accuracy of texture feature extraction. Overall, our approach to pavement texture analysis using the 2D wavelet transform algorithm and the appropriate mother wavelet selection was expected to deliver more detailed insights into the characteristics and properties of road surfaces.

The data were decomposed into six levels, of which five were detail levels denoted as Level 1 (<0.3 mm), Level 2 (0.3~0.6 mm), Level 3 (0.6~1.2 mm), Level 4 (1.2~2.4 mm), Level 5 (2.4~4.8 mm), and Level 6 (>4.8 mm). According to the definition specification, the wavelengths range of micro-texture typically ranges from 1 μm to 0.5 mm, whereas macro-texture typically ranges from 0.5 mm to 50 mm. In this regard, Levels 1 and 2 represent micro-texture, while Levels 3, 4, 5, and 6 represent macro-texture.

In the x- or y-direction, each texture data were decomposed into six components using the 2D wavelet transform algorithm. Additionally, this algorithm decomposed the texture data into 6 × 6 parts. Figure 9 shows the decomposition results after using the 2D wavelet transform algorithm.

The energy (E) is an indicator that measures the overall condition of each part, and it can be calculated as:

(1)$E=\sum _x\sum _y{\left|Z_{x,y}\right|}^2$

The energy characteristic represents the overall roughness, which exhibits significant variations among different specimens. Additionally, for the same specimen, the energy is sensitive to slight changes in the detection position. Therefore, to address this issue, the concept of relative energy (RE) was introduced. RE represents the proportion of energy at each scale in relation to the total energy and is defined as follows:

(2)${RE}_{ij}=\frac{E_{ij}}{{\sum }_{i=1}^6{\sum }_{i=1}^6{E}_{ij}},(1\le i\le \mathrm{6,1}\le j\le 6)$

RE was used in this paper to characterize pavement texture at multiple scales due to its comparability between different samples.

4. Results and Discussion

During the indoor testing phase, five types of asphalt mixtures were prepared. To enrich the data, each mixture was used to prepare seven pavement slabs. Each pavement slab sample was further divided into nine areas measuring 10 cm × 10 cm each, facilitating data collection.

4.1. Evolution Law of Macro-Texture Characteristics

According to Section 3.2, nineteen texture geometric parameters were calculated. These geometric parameters can be directly used to characterize macro-texture of the pavement. To investigate the potential relationship between pavement macro-texture and pavement compaction, this study conducted a correlation analysis between the compactness of the asphalt mixtures (measured by degree of compaction and number of roller passes) and the geometric parameters. The correlation coefficient (r) was commonly utilized to analyze the correlation between the two variables, and its calculation formula is as follows:

(3)$r=\frac{\sum _i^n(x_i-\stackrel{-}{x})(y_i-\stackrel{-}{y})}{\sqrt{{\sum _i^n(x_i-\stackrel{-}{x})}^2}\sqrt{{\sum _i^n(y_i-\stackrel{-}{y})}^2}}$

where the x_i is the geometric parameter value of the i-type asphalt mixture, and $\stackrel{-}{x}$ is the average geometric parameter value of the asphalt mixtures; y_i is the compactness value of the i-type asphalt mixture, and $\stackrel{-}{y}$ is the average compactness value of the i-type asphalt mixtures.

Figure 10 presents the results of the calculation for the correlation between the geometric parameters and pavement compaction. The correlation coefficient ranges from −1 to 1, where more positive values indicate a deeper yellow color in the correlation matrix, while more negative values appear as darker blue. Figure 11 presents the detailed evolution law for the texture geometric parameters during compaction, realized through linear and polynomial relations.

(1) Figure 10 illustrates that most of the indicators display a negative or weak positive correlation with compaction. A larger geometric parameter value typically indicates a rougher surface texture. Theoretically, as compaction progresses, the macro-texture is influenced by applied forces resulting in a smoother surface and a decrease in the values of geometric parameters. However, some indicators present anomalous behavior in the case of large NMAS asphalt mixtures. Coarse aggregates occupy a significant proportion of mixtures, and their macro-texture is hard to alter during the compaction process.

(2) Figure 10 reveals that the asphalt mixtures with a lower void content exhibit stronger correlations with a larger number of indexes. The changes in geometric parameters of macro-texture exhibit regularity. This suggests that these mixtures form a denser structure early in the compaction process where aggregates are fixed in place and the macro-texture is not affected during the later stages of compaction. Therefore, the formation and alteration of macro-texture in compacted asphalt mixtures exhibit regularity when the void content is low. Monitoring geometric parameters of the macro-texture can enable real-time control of compaction quality.

(3) Figure 11 shows that the MPD curve decreases almost linearly throughout the compaction process, with R² values of 0.9452 for AC-13, 0.885 for AC-16, and 0.8703 for SMA-13. This phenomenon explains the common occurrence of insufficient MPD resulting from over-compaction in the field. Because MPD is an indicator of skid resistance, caution should be exercised to prevent over-compaction during field compaction procedures.

(4) Additionally, Figure 12 shows that the convergence of the sp (maximum peak height) and vmp (peak material volume) parameters implies that they can be used to monitor compaction progress. The convergence of these two parameters signifies that the compaction process has essentially been completed, particularly in asphalt mixtures AC-16 and VMA-13, where this phenomenon is more pronounced. Furthermore, the variation in the sp and vmp parameters is similar to that of the compaction degree curve. It indicates that the reduction in volume and height of the macro-texture peaks is regular during the compaction process.

4.2. Evolution Law of Micro-Texture Characteristics

The wavelet energy for each of the decomposition levels can be used to explain the differences in the properties of pavement surfaces. Figure 13 shows the energy results for Level 1 and Level 2, representing the micro-texture. The results of the RE distribution for Levels 1 to 6 after the roller passes 12 and 24 times of the five types of mixtures are shown in Table 2.

(1) As shown in Figure 13, on the micro-scale, the AC-13 slab sample shows the lowest energy, and the OGFC-13 and AC-25 slab samples show the highest energy, which is nearly twice the energy of the AC-13 sample. This indicates that micro-texture is closely related to the surface of the aggregate and structure of mixtures. When more coarse aggregates are used or polyporous structures are employed, the micro-texture will have a convex and concave texture, resulting in large energy values.

(2) Figure 13 shows that in the original surface, the micro-texture is complex and has large energy values at Level 1 and Level 2. Compaction has a filling effect on asphalt mixtures, polishing the surface of the aggregate and compacting the structure, resulting in a reduction in the energy value of the micro-texture. Moreover, the energy can be chosen as the index to supervise the micro-texture, because the curves converge strongly after the roller passes 18 times.

(3) Table 2 shows that the SMA-13 and AC-13 are primarily distributed on Level 4, the AC-16 on Level 5, and the AC-25 and OGFC-13 on Level 6. A comparison with the RE results shows that compaction did not have much effect on the RE distribution. The reason for this result may be because the RE results are related to the gradation of mixtures, and compaction did not change the gradation.

5. Conclusions

In this study, geometric parameters were computed to analyze macro-texture, and a 2D wavelet transform approach was proposed to decompose texture for the analysis of micro-texture. Geometric parameters, energy, and relative energy were utilized as indicators. Through observation and data analysis of experimental results, the pavement macro- and micro-texture evolution laws were found, leading to the following conclusions:

(1) Geometric parameters can characterize macro-texture, while energy-based indicators after 2D wavelet transform decomposition can observe micro-texture. Because of the binder masking effect at the initial stages, micro-texture evolution law was not expected to be fully revealed compared with macro-texture in this study. Macro-texture was more critical and easier to control during the construction phase. These results can establish a foundation for the real-time monitoring of pavement texture during field compaction.

(2) On a macro-scale, geometric parameters can serve as description indices with a strong relationship with compaction. Among these parameters, Sp and Vmp can monitor compaction quality in all types of mixtures, including those with different sizes and structures. The R-square values of polynomial fit with Sp or Vmp values and number of roller passes are greater than 0.90 in all mixtures. Other geometric parameters can also provide valuable information about macro-texture characteristics, and the evolution law of macro-texture can regulate the compaction process and optimize mixture properties for its intended use.

(3) On a micro-scale, the 2D wavelet transform approach is suitable for characterizing micro-texture properties, and energy can supervise the compaction process. The end energy of Level 1 is about 45% of the initial energy, and the end energy of Level 2 is about 50% of the initial energy. As the compaction is gradually completed, the energy will also tend to be stable, such as Level 1 energy of AC-13 convergence to 20 and Level 2 energy of SMA-13 convergence to 650. By using energy as a supervising factor, we can control the compaction process and ensure efficient material compaction.

In our follow-up study, these indicators can be combined with a mechanical model to evaluate the compaction process adequately. Further research can focus on the evolution law of texture under different gradations during field compaction. Based on the findings of this study, it is suggested that by setting suitable thresholds for certain indices, texture can be controlled during the compaction process. These indices can also be linked to other advanced techniques used for monitoring the compaction process, which can help improve the quality of compaction control.

Author Contributions

Conceptualization, C.D. and D.W.; Formal analysis, Y.L. and H.X.; Investigation, Y.L., H.X. and C.D.; Methodology, Y.L., D.W., S.J. and Z.W.; Software, Y.L. and Z.W.; Validation, H.X.; Writing—original draft, Y.L.; Writing—review and editing, D.W., C.D. and S.J. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

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Figures and Tables

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Figure 1. Methodology outline.

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Figure 2. Grading curves for five asphalt mixtures.

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Figure 3. (a) Laboratory compaction with wheel-grind method. (b) Asphalt mixture slabs with 300 mm × 300 mm × 50 mm, then divided into 9 parts.

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Figure 4. Relationship between degree of compaction and number of roller passes.

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Figure 5. (a) Texture data acquisition using AMES Laser Scanner 9500; (b) Three-dimensional display of data on software.

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Figure 6. Texture scanning results of AC-13 asphalt mixtures, grind times 14, 16, 18, 20, 22, and 24.

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Figure 7. Data pre−process to remove the outliers.

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Figure 8. The areal material ratio curve and functional and volume parameters.

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Figure 9. Decomposition by 2D wavelet transform algorithm.

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Figure 10. Correlation coefficient matrix between nineteen geometric parameters and compactness.

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Figure 11. (a–i) The linear and polynomial relations between AC−13−MPD/AC−16−MPD/ SMA−13−MPD/AC−13−Sp/AC-16-Sp/SMA-13-Sp/AC−13−Vmp/AC−16−Vmp/SMA−13−Vmp and number of roller passes.

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Figure 12. (a,b) Fitted curve of compaction and Sp/Vmp from AC-16; (c,d) Fitted curve of compaction and Sp/Vmp from SMA-13.

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Figure 13. (a,b) Energy results of Level 1 and Level 2; (c,d) Comparison of energy results of Level 1 between AC mixtures/NMAS-13 mixtures; (e,f) Comparison of energy results of Level 2 between AC mixtures/NMAS-13 mixtures.

Table 1

Geometric parameters of macro-texture.

Parameters	Meaning	Equation
Profile parameters
MPD (mm)	Mean profile depth	$\mathrm{M}\mathrm{P}\mathrm{D}=\frac{\sum _1^n(\frac{h_1+h_2}{2}-h)}{n}$
Ra (mm)	Roughness average	$Ra=\frac{1}{n}·{\displaystyle \sum _{i=1}^n}\left|y_i\right|$
Rq (mm)	RMS roughness	$Rq=\sqrt{\frac{1}{n}·{\displaystyle \sum _{i=1}^n}({y_i)}^2}$
Da	Arithmetic mean slope	$Da=\frac{1}{n}·{\displaystyle \sum _{i=1}^n}\left|\frac{\Delta y}{\Delta x}\right|$
Dq	RMS slope	$Dq=\sqrt{\frac{1}{n}·{\displaystyle \sum _{i=1}^n}{(\frac{\Delta y}{\Delta x})}^2}$
La (mm)	Average wavelength	$La=2\pi \times \frac{Ra}{Da}$
Lq (mm)	RMS wavelength	$Lq=2\pi \times \frac{Rq}{Dq}$
Height parameters
Ssk	Skewness of height distribution	$Ssk=\frac{1}{{Lq}^3}·\frac{1}{A}{\displaystyle \sum _A}{Z}^3(x,y)$
Sku	Kurtosis of height distribution	$Sku=\frac{1}{{Lq}^4}·\frac{1}{A}{\displaystyle \sum _A}{Z}^4(x,y)$
Sp (mm)	Maximum peak height	$Sp=maxZ(x,y)$
Sv (mm)	Maximum valley height	$Sv=\left|minZ(x,y)\right|$
Functional parameters
Sk (mm)	Core height	$Sk=Sk1-Sk2$
Spk (mm)	Reduced peak height	$Spk=Sp-Sk1$
Svk (mm)	Reduse valley height	$Svk=Sk2-Sv$
Volume parameters
Vvv (mm3/mm2)	Dale void volume	$Vvv=V_v\left(mr2\right)$
Vvc (mm3/mm2)	Core void volume	$Vvc=V_v\left(mr1\right)-V_v\left(mr2\right)$
Vmp (mm3/mm2)	Peak material volume	$Vmp=V_m\left(mr1\right)$
Vmc (mm3/mm2)	Core material volume	$Vmc=V_m\left(mr1\right)-V_m\left(mr2\right)$
Hybrid parameters
Sdr	Developed interfacial area ratio	$Sdr=\frac{1}{A}\{{\displaystyle \sum _A}\sqrt{1+{[(\frac{\partial z(x,y)}{\partial x})]}^2+{[(\frac{\partial z(x,y)}{\partial x})]}^2}-1\}$

Table 2

RE distribution results.

RE of Mixtures after Roller Passes 12 Times		AC-13	AC-16	AC-25	SMA-13	OGFC-13
Decomposition Level	Level 1	0.2	0.2	0.3	0.1	0.3
	Level 2	4.1	5.1	7.6	3.1	6.5
	Level 3	6.6	7.2	9.3	14.2	7.5
	Level 4	24.4	14.3	9.5	24.9	10.2
	Level 5	12.5	26.5	12.4	16.5	16.3
	Level 6	52.1	46.7	60.9	41.2	59.1
RE of Mixtures after Roller Passes 24 times		AC-13	AC-16	AC-25	SMA-13	OGFC-13
Decomposition Level	Level 1	0.1	0.2	0.3	0.1	0.4
	Level 2	3.0	5.5	8.2	3.9	8.5
	Level 3	5.2	12.4	9.0	16.2	8.5
	Level 4	26.5	13.8	9.7	t.3	13.0
	Level 5	14.2	23.9	12.4	17.3	13.2
	Level 6	50.9	44.2	60.3	42.2	56.4

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