Dynamic Model of Polished Stone Value Attenuation in Coarse Aggregate.

The polished stone value (PSV) of coarse aggregate is closely related to pavement skid resistance and traffic safety. However, the determination of the PSV of coarse aggregate is conventionally a time- and energy-intensive process. To facilitate the test process of PSV in materials selection and pavement design and for the prediction of the service life of aggregate materials in practical service, here a new mathematical model of PSV attenuation in coarse aggregate, which employs a physical polishing process analysis, is proposed. The PSVs of four types of coarse aggregates (calcined bauxite, granite, basalt, and limestone) were analyzed through a polishing experiment, and the corresponding mechanism was investigated via scanning electron microscopy analysis. The modeling results are in good agreement with experimental results. The aggregate PSV is affected by both the macrotexture and microtexture of the aggregate surface. The PSV due to the macrotexture exhibits a strong negative correlation with the Vickers hardness of the aggregates and decreases exponentially as the polishing time increases. The attenuation rate decreases as the fractal box dimension in the aggregate surface morphology increases. The primary factor influencing the macrotexture service life and the half-life is the aggregate surface morphology. The PSV due to the microtexture exhibits a strong positive correlation with the Vickers hardness of the aggregates, whereas there is a poor correlation with the aggregate surface morphology and polishing time. The proportion of the aggregate PSV due to the microtexture increases as the aggregate hardness increases. These results highlight the effectiveness of a new modeling approach that may potentially assist in predicting the anti-slip performance and durability of coarse aggregates.


Introduction
Skid-resistance of a pavement is considered one of the most important factors affecting traffic safety [1], as good anti-skid performance can reduce traffic accidents by providing sufficient adhesion for the vehicle tires, while low skid resistance means poor friction and can increase the risk of accidents. The exposed aggregate on the pavement surface will gradually become polished and worn by traffic, which will reduce its anti-skid performance and eventually create a safety hazard. Investigations show that many highway traffic accidents are related to insufficient pavement skid resistance [2,3], with the particle shape, physical properties, and variations in the coarse aggregate on the pavement surface exerting important effects on its anti-skid performance [4,5].
The polished stone value (PSV) of coarse aggregate is an indicator that reflects the ability of coarse aggregate to resist the polishing action of tires and is used to characterize the ability of coarse aggregate Materials 2020, 13 to maintain a certain coefficient of friction against tire abrasion. The PSV of coarse aggregate is closely related to pavement skid resistance. Pavement surfaces with a larger PSV possess a higher friction coefficient. Pavement surfaces with high PSV coarse aggregate have a higher skid resistance, which improves vehicle safety [6][7][8]. Therefore, the relevant technical specifications of asphalt pavements in China have clear requirements and provisions on the PSV of coarse aggregate, which is a key index for determining whether a certain aggregate can be used in the anti-sliding abrasion layer of an asphalt pavement. However, determining the PSV of coarse aggregate is a time-and energy-intensive process. It is therefore of great significance to study the skid resistance characteristics of coarse aggregate and derive a PSV attenuation law to facilitate better-informed material selection for pavement design and construction and also predict the service life of aggregate materials in practical settings. Numerous research efforts have been reported on the pavement skid resistance problem; these studies investigated the influence of aggregate type [9][10][11], mineral composition [12], particle gradation [13,14], and surface morphology [15,16] on pavement skid resistance. While important advances have been made through these studies, the dynamics of PSV attenuation in coarse aggregate have rarely been reported.
Here a mathematical PSV attenuation model for coarse aggregate was constructed through a theoretical analysis of the polishing process to investigate the sliding-resistance changes in coarse aggregates over time, and experimental observations were analyzed and compared to validate the proposed model, for simplifying the PSV test process and predicting the performance of the coarse aggregates in service.

Polishing Process Analysis
The PSV of coarse aggregate is its surface friction coefficient, which is measured using a pendulum friction coefficient meter after polishing the coarse aggregate with an accelerated polishing machine and a silicon carbide agent. PSV effectively characterizes both the frictional properties and abrasion resistance of the aggregate.
The surface roughness of coarse aggregate has an important effect on its slip resistance. A rougher surface generally has a better slip resistance and higher corresponding PSV than a smoother surface. However, different rocks with the same roughness often have different slip resistances owing to their varying material properties such as mineral type and particle size and distribution. The slip resistance can also be different in the same rock type due to differences in its mineral composition, crystal size, and weathering degree. Therefore, the PSV of aggregate is related to both the surface roughness and material properties of the aggregate.
The surface roughness of coarse aggregate includes both its macrotexture and microtexture [17]. The macrotexture morphology of coarse aggregate surface forms during the aggregate formation process. This macrotexture morphology is directly in contact with the wheels and is gradually polished off since the aggregate surface is exposed on the pavement surface in actual road applications. It is therefore more appropriate for the aggregate application environment to characterize the aggregate morphology based on the macrotexture height of the aggregate surface.
Both the macrotexture and microtexture of the aggregate affect its PSV. The general observation is that the surface friction performance is primarily influenced by the macrotexture at the beginning of the coarse aggregate polishing process, whereas the microtexture is the primary contributor during the later stage of polishing [18].

General Hypothesis
Coarse aggregate is macroscopically homogeneous; its physical properties are stable during the polishing process; and its hardness and other physical properties do not change with polishing time. The macrotexture morphology of the original coarse aggregate surface is irregularly distributed like mountain peaks, as shown in Figure 1. The vertical coordinate h in the figure represents the macrotexture height of the aggregate; the x-coordinate is the length along the aggregate surface, where h s is the initial maximum macrotexture height and h t is the macrotexture height of the aggregate surface at time t.

Macrotexture Analysis and Hypothesis
The macrotexture of the aggregate surface undergoes a process of constant wear and tear during the aggregate polishing experiment, such that the macrotexture height decreases with increasing polishing cycles. As the number of polishing cycles is a function of the polishing speed and polishing time, the macrotexture height of the aggregate surface is a function of polishing time for a given polishing speed. This means that the macrotexture height decreases with increasing polishing time. The macrotexture height of the aggregate surface is lowered as the polishing time increases until the macrotexture height approaches zero.
The wear area increases and the corresponding wear resistance increases as the macrotexture height decreases during the polishing process since the macrotexture is a distribution of peaks ( Figure  1). This results in a larger area that is subject to wear, greater energy requirements for additional wear, greater abrasion resistance, and a slowdown in the reduction rate of the macrotexture height. Conversely, a higher macrotexture possesses a smaller worn peak area, requires less energy for additional wear, is easier to wear, possesses a smaller wear resistance, and has a higher macrotexture height attenuation rate. This indicates that the macrotexture height attenuation rate is proportional to the macrotexture height.
Furthermore, fractal theory can be used since the aggregate surface roughness has statistical selfsimilarity [19]. Fractal theory is a methodology to measure or describe the complexity of complex systems. Fractal geometry represents the research object with an irregular geometry. The fractal dimension is one of the main parameters in fractal theory, which is a measure of the irregularity of a complex shape. The fractal dimension has many definitions and calculation methods such as the Hausdorff dimension, similarity dimension, information dimension, counting box dimension, and correlation dimension. Here the box-counting dimension, also known as the MinKeFu kiwi number, is measured and calculated using a box of different scales on the surface of the object, which provides a quantitative description of the complexity of the fractal collection. We employ the box dimension to express the complexity of the aggregate surface morphology. The fractal dimension abrasion resistance increases as the surface morphology increases, where the macrotexture height attenuation rate decreases, such that the macrotexture height attenuation rate is inversely proportional to the fractal box dimension of the aggregate surface: where hs and ht are the initial aggregate macrotexture height and macrotexture height after polishing time t, as shown in Figure 1, and D is the fractal box dimension of the initial aggregate surface. The negative sign in Equation (1) means that the rate of change in the macrotexture height exhibits a decreasing trend. Therefore, Equation (1) can be rewritten as

Macrotexture Analysis and Hypothesis
The macrotexture of the aggregate surface undergoes a process of constant wear and tear during the aggregate polishing experiment, such that the macrotexture height decreases with increasing polishing cycles. As the number of polishing cycles is a function of the polishing speed and polishing time, the macrotexture height of the aggregate surface is a function of polishing time for a given polishing speed. This means that the macrotexture height decreases with increasing polishing time. The macrotexture height of the aggregate surface is lowered as the polishing time increases until the macrotexture height approaches zero.
The wear area increases and the corresponding wear resistance increases as the macrotexture height decreases during the polishing process since the macrotexture is a distribution of peaks ( Figure 1). This results in a larger area that is subject to wear, greater energy requirements for additional wear, greater abrasion resistance, and a slowdown in the reduction rate of the macrotexture height. Conversely, a higher macrotexture possesses a smaller worn peak area, requires less energy for additional wear, is easier to wear, possesses a smaller wear resistance, and has a higher macrotexture height attenuation rate. This indicates that the macrotexture height attenuation rate is proportional to the macrotexture height.
Furthermore, fractal theory can be used since the aggregate surface roughness has statistical self-similarity [19]. Fractal theory is a methodology to measure or describe the complexity of complex systems. Fractal geometry represents the research object with an irregular geometry. The fractal dimension is one of the main parameters in fractal theory, which is a measure of the irregularity of a complex shape. The fractal dimension has many definitions and calculation methods such as the Hausdorff dimension, similarity dimension, information dimension, counting box dimension, and correlation dimension. Here the box-counting dimension, also known as the MinKeFu kiwi number, is measured and calculated using a box of different scales on the surface of the object, which provides a quantitative description of the complexity of the fractal collection. We employ the box dimension to express the complexity of the aggregate surface morphology. The fractal dimension abrasion resistance increases as the surface morphology increases, where the macrotexture height attenuation rate decreases, such that the macrotexture height attenuation rate is inversely proportional to the fractal box dimension of the aggregate surface: where h s and h t are the initial aggregate macrotexture height and macrotexture height after polishing time t, as shown in Figure 1, and D is the fractal box dimension of the initial aggregate surface. The negative sign in Equation (1) means that the rate of change in the macrotexture height exhibits a decreasing trend. Therefore, Equation (1) can be rewritten as where k (s −1 or min −1 ) is a constant related to the equipment conditions during aggregate wear. We then integrate Equation (2) to obtain As the polished value owing to the macrotexture corresponds to the macrotexture height, the polished value at time t (P t ) owing to the macrotexture can be defined as where P t is the polished value at time t and P s is the polished value for h s . As P t is related to both the surface morphology and material properties of the aggregate, the exponential and P s in Equation (4) capture the influence of the surface morphology and material properties of the aggregate, respectively.
Given that e −kt/D is a number between 0 and 1, P t tends to 0 with increasing polishing time, with P s representing the maximum macrotexture polished value during the polishing process.

Microtexture Analysis and Hypothesis
The microtexture of coarse aggregate presents a different situation during the polishing process. The polished value owing to the microtexture of the aggregate is influenced by the mineral composition and properties, grain size, defect size, and their respective distributions during the polishing process since the rock is formed of crystals with different strengths, grain sizes, and defects [20], this highlights that the aggregate hardness is one of the primary factors that affects its polished value [21].
The soft grains and defects in high-hardness aggregates are constantly worn down during the polishing process, whereas the hard grains are more difficult to grind and are the main components that hinder abrasion and friction. The hard particle bulges will gradually form a smooth macrostructure area, but as an uneven microstructure area, as the polishing process progresses. The smooth macrostructure area formed by abrasion decreases as the aggregate hardness increases. Therefore, the smooth macrostructure area that is formed by hard grains is the primary surface morphology feature during the polishing process.
Conversely, the grains in low-hardness aggregates are easier to grind down because the grains are softer. The abrasive will usually form abrasive wear on the aggregate surface if the aggregate hardness is much lower than the particle hardness of the abrasive. Therefore, the continuously grinding down of the grains and the formation of wear furrows on the surface of soft aggregates are the main surface morphology characteristics during the polishing process.
A microtexture will always exist during the aggregate polishing process, regardless of whether the aggregate is hard or soft. A new surface is constantly forming along the aggregate surface, such that its friction capacity is unaffected, even as the height of the aggregate surface continues to decrease. Therefore, the polished value owing to the microtexture is largely unrelated to the microtexture height of the aggregate surface and polishing time.
However, the friction effect on the abrasives is different owing to the different morphologies of the new surface, which are formed by the hard and soft aggregates. Therefore, the PSV due to the microtexture is related to the aggregate material hardness.
Hardness is an important performance index for measuring the degree of hardness or softness in materials. It is a comprehensive index of mechanical properties of the material, such as elasticity, plasticity, strength, and toughness. Studies have shown that the hardness of the material itself is related to the chemical bonds of the crystal. The aggregate material with higher hardness is the harder Materials 2020, 13, 1875 5 of 15 material and exhibits greater resistance to friction between the abrasives during the aggregate polishing process. Conversely, the aggregate material with lower hardness is the softer material and exhibits a weakened ability to prevent friction and wear of the abrasives. Therefore, the polished value owing to the microtexture is proportional to the aggregate hardness: where P x is the polished value owing to the microtexture and H v is the Vickers hardness of the aggregate. This can be rewritten as where b 0 and b 1 are adjustment coefficients related to the test environment and polishing conditions.

Assumption of the PSV Attenuation Law for Coarse Aggregate during Polishing
PSV comprises the macrotexture and microtexture influences as follows: The initial total polished value simplifies to P 0 = P s + P x when t = 0, such that the relationship between the initial total polished value P 0 and maximum P s value is The substitution of Equation (8) into Equation (7) yields: P 0 is the total friction coefficient of the aggregate at t = 0 and the maximum PSV during aggregate polishing. P 0 is also related to the aggregate material properties (hardness) since it is the sum of P s and P x , both of which are related to the aggregate material properties (hardness). P 0 is proportional to the aggregate hardness: which can be rewritten as, where a 0 and a 1 are adjustment factors. The substitution of Equations (6) and (11) into Equation (9) yields Equation (12) is the mathematical model of aggregate PSV as a function of time. This tells us that the aggregate PSV is affected by both the macrotexture and microtexture, such that its value is related to H v and D and decreases exponentially with polishing time. k, a 0 , a 1 , b 0 , and b 1 are constants for a given test equipment condition. These constants can be obtained by measuring the P 0 , H v , and D values of the coarse aggregates and PSV values of the partial polishing time, which then allows the aggregate PSV attenuation over time to be obtained.

Test Materials
The experimental materials used for the model verification are the same as those in the literature [22], with calcined bauxite, granite, basalt, and limestone chosen as the test aggregates. The basic physical and mechanical properties of these aggregates are listed in Table 1.

Experimental Methods
PSV test data from the literature [22] were used in the model, where the rotation of the polishing machine was 320 ± 5 rpm. The polishing time was obtained by dividing the number of polishing cycles by the rotational speed of the polishing machine.
A VK-9700 color 3D laser microscope (Keyence; Osaka, Japan) and S-4800 scanning electron microscope (Hitachi; Tokyo, Japan) were used to observe the aggregate morphology during polishing.

Determination of the Fractal Box Dimension D of the Aggregates
Laser microscope images of the sections from the aggregate samples used in the experiment are shown in Figure 2. MATLAB (R2017b, MathWorks, Natick, MA, USA) was used to binarize the photos in Figure 2; then the square box was taken as the counting cell to calculate the fractal box dimension. The binarization image of each laser microscope image is shown in Figure 3. The fractal box dimensions of the four aggregates are listed in Table 2.

Experimental methods
PSV test data from the literature [22] were used in the model, where the rotation of the polishing machine was 320 ± 5 rpm. The polishing time was obtained by dividing the number of polishing cycles by the rotational speed of the polishing machine.
A VK-9700 color 3D laser microscope (Keyence; Osaka, Japan) and S-4800 scanning electron microscope (Hitachi; Tokyo, Japan) were used to observe the aggregate morphology during polishing.

Determination of the Fractal Box Dimension D of the Aggregates
Laser microscope images of the sections from the aggregate samples used in the experiment are shown in Figure 2. MATLAB (R2017b, MathWorks, Natick, MA, USA) was used to binarize the photos in Figure 2; then the square box was taken as the counting cell to calculate the fractal box dimension. The binarization image of each laser microscope image is shown in Figure 3. The fractal box dimensions of the four aggregates are listed in Table 2.      [22] were selected to determine the k value, which are listed in Table 3. Table 3 indicates that P0 = 67.7. We assume that t→∞ at t ≈ 52,500 min, such that P∞ = Px ≈ 29.7. The k value is then derived from Equation (9), where PSV = 38.4 at t = 15,000 min (Table 3), and D = 1.9562 for limestone (

Determination of the Px Values
The PSVs of the four aggregate samples at t = 0 and 15,000 min were selected to determine the Px values, with the analyzed experimental values [22] listed in Table 4. The Px values for the four aggregates were then determined by rearranging Equation (9):

Determination of the k Value
Some of the experimental polished values for limestone [22] were selected to determine the k value, which are listed in Table 3. Table 3 indicates that P 0 = 67.7. We assume that t→∞ at t ≈ 52,500 min, such that P ∞ = P x ≈ 29.7. The k value is then derived from Equation (9), where k = −D/t × ln((PSV − P x )/(P 0 − P x )) (13) PSV = 38.4 at t = 15,000 min (Table 3), and D = 1.9562 for limestone (

Determination of the P x Values
The PSVs of the four aggregate samples at t = 0 and 15,000 min were selected to determine the P x values, with the analyzed experimental values [22] listed in Table 4. The P x values for the four aggregates were then determined by rearranging Equation (9): Materials 2020, 13, 1875 8 of 15 with the determined k value, PSV values at t = 0 and 15,000 min, and D values of the four aggregates used to calculate the P x values, which are listed in Table 5. The H v values in Table 1, P x values in Table 5, and Equation (6)  The correlation coefficient R between P x and H v is 0.956 at the 95% confidence interval, indicating that P x exhibits a strong linear correlation with H v , where: The H v values in Table 1, P 0 values in Table 4, and Equation (11) were used to determine the a 0 and a 1 values, with a regression analysis yielding a 0 = 63.39083 and a 1 = 0.007985 The correlation coefficient R between P 0 and H v is 0.981 at the 95% confidence interval, indicating that P 0 exhibits a strong linear correlation with H v , where: The substitution of Equations (15) and (16) into Equation (12) yields the total PSV:

PSV Validation
PSV test data for the four aggregates in the literature [22] were selected to validate the model, which are listed in Table 6. The PSVs of the aggregates at different polishing times t are calculated using Equation (17), with comparisons between the modeled and experimental values for the four aggregates shown in Figures 4-7. The maximum relative deviation between the modeled and experimental PSVs, relative deviation of the maximum P 0 values, and relative deviation of the P x values, which are derived from Figures 4-7, are listed in Table 7. The accuracy of the modeled PSV results, ranging from high to low, is calcined bauxite > basalt > granite > limestone. The relative PSV deviation due to the microtexture, ranging from high to low, is limestone > basalt > calcined bauxite > granite. The maximum relative deviation between the modeled and experimental PSVs, relativ deviation of the maximum P 0 values, and relative deviation of the P x values, which are deri from Figs. 4-7, are listed in Table 7. The accuracy of the modeled PSV results, ranging fro to low, is calcined bauxite > basalt > granite > limestone. The relative PSV deviation due to microtexture, ranging from high to low, is limestone > basalt > calcined bauxite > granite. The results in Table 7 show that the differences between the modeled and experimenta are not large, with a maximum deviation of only 12.3%, which indicates that the our hypo  and tested PSV results for basalt. Fig. 7 Modeled and tested PSV results for limestone.
aximum relative deviation between the modeled and experimental PSVs, relative f the maximum P 0 values, and relative deviation of the P x values, which are derived 4-7, are listed in Table 7. The accuracy of the modeled PSV results, ranging from high  The maximum relative deviation between the modeled and experimental PSVs, relativ deviation of the maximum P 0 values, and relative deviation of the P x values, which are deri from Figs. 4-7, are listed in Table 7. The accuracy of the modeled PSV results, ranging fro to low, is calcined bauxite > basalt > granite > limestone. The relative PSV deviation due to  tested PSV Results for calcined bauxite. Fig. 5 Modeled and tested PSV results for granite. and tested PSV results for basalt. Fig. 7 Modeled and tested PSV results for limestone.
aximum relative deviation between the modeled and experimental PSVs, relative of the maximum P 0 values, and relative deviation of the P x values, which are derived 4-7, are listed in  Table 7 show that the differences between the modeled and experimental results ge, with a maximum deviation of only 12.3%, which indicates that the our hypothesis is . Therefore, our proposed model can adequately describe the PSV attenuation law for The results in Table 7 show that the differences between the modeled and experimental results are not large, with a maximum deviation of only 12.3%, which indicates that our hypothesis is reasonable. Therefore, our proposed model can adequately describe the PSV attenuation law for coarse aggregates.

Factors Influencing the P x Values
The P x values for the four aggregates at different times t are shown in Figure 8. The Px values for each aggregate are generally constant over time, with the exception of some individual points, which indicates that the Px value is not a function of polishing time, such that any changes in Px are likely unrelated to the polishing time. However, there are obvious differences among the aggregates, which means that the material properties have a major influence on Px. The The P x values for each aggregate are generally constant over time, with the exception of some individual points, which indicates that the P x value is not a function of polishing time, such that any changes in P x are likely unrelated to the polishing time. However, there are obvious differences among the aggregates, which means that the material properties have a major influence on P x . The average P x value of each aggregate is listed in Table 8. The correlation coefficient R between the average P x value and H v for each aggregate is 0.984 at the 95% confidence interval, which indicates that P x does have a strong linear correlation with the aggregate hardness [23], such that the P x value will increase as the aggregate hardness increases.

P x /P s Ratio
The influence of the microtexture is analyzed by comparing P x with P s ; the results are listed in Table 9. The P x /P s ratios of the aggregates exhibit the following trend (ranging from high to low): calcined bauxite > granite > basalt > limestone ( Table 9). The first three values are much higher than the last value. As P 0 , which is the maximum PSV, is composed of P x and P s , the high P x /P s ratios indicate that a high proportion of P x values is derived from the high-hardness aggregate, whereas a low proportion of P s values is derived from the low-hardness aggregate, and vice versa. Table 9. P x /P s ratios for the different aggregates.

Aggregate
Calcined The correlation coefficient R between the P x /P s ratio and H v for the four aggregates is 0.985 at the 95% confidence interval, demonstrating a strong linear correlation between the P x /P s ratio and H v . This means that the P x /P s ratio increases as the hardness of the aggregate material increases, which indicates that the microstructure exerts a greater influence on PSV. Here the P x value for calcined bauxite, which possesses high hardness, accounted for more than 2/3 of the P 0 value, whereas the P x value of limestone, which possesses low hardness, accounted for less than 1/2 of the P 0 value. Therefore, the PSV of the high-hardness aggregates is primarily controlled by P x , whereas the PSV of the low-hardness aggregates is affected by both P x and P t [24].

Changes in Maximum P s
The P s values for each aggregate are calculated using Equation (8) and are listed in Table 10. The P s values of the high-hardness aggregates (calcined bauxite and granite) are small, whereas the P s values of the low-hardness aggregates (basalt and limestone) are large. The correlation coefficient between P s and H v for the four aggregates is −0.883, which indicates that there is a strong negative correlation between P s and H v . Equations (15) and (16) show that P s = (a 0 − b 0 ) + (a 1 − b 1 )H v = 36.236 − 0.00715H v , where the negative change in slope means that P s decreases as the aggregate hardness increases. This is consistent with the calculated results in Table 10, which indicates that the macrotexture is preserved, the height value is high, the corresponding aggregate surface macroscopic peak friction and wear area are small, and the friction and wear resistance are small for high-hardness aggregates during polishing, such that their P s values are also small. The opposite trend occurs for low-hardness aggregates. 4.2.2. Macrotexture Service Life t 0.05 and Half-Life t 0.5 Equation (4) highlights that the P t value of the macrotexture decreases exponentially with increasing polishing time t, and is related to the maximum P s and D. Note that the P t decay rate will decrease as D increases.
The macrotexture reaches the maximum service life during the aggregate polishing process when the P t value owing to the macrotexture height approaches zero. However, a long polishing time is required for the P t value to approach zero in practical engineering. Therefore, we assume that the P t service life has been reached when P t = 0.05P s . Equation (4) is simplified to e −kt/D = 0.05, and solved as follows: where t 0.05 is the service life.
Similarly, we assume that the P t half-life has been reached when P t = 0.50P s , such that where t 0.5 is the half-life. The t 0.05 and t 0.5 values for the four aggregates were calculated using Equations (18) and (19), respectively, and are listed in Table 11. The t 0.05 and t 0.5 values for the four aggregates follow the same decreasing trend, where calcined bauxite > basalt > granite > limestone, but they do exhibit small differences. The maximum deviation occurred between calcined bauxite and limestone, although the value did not exceed 4.6%. However, there is a >3-fold difference in H v between these two aggregates, which indicates that the aggregate material properties have little influence on the t 0.05 and t 0.5 of the macrotexture. The main factor influencing the t 0.05 and t 0.5 of the P t value should be the aggregate surface morphology, which is represented by the D value of the aggregate surface in this paper. Both t 0.05 and t 0.5 are linearly related to D, as shown in Equations (18) and (19), which indicates that both t 0.05 and t 0.5 increase as the aggregate surface morphology becomes more complex. Furthermore, the slope of t 0.05 is more sensitive to changes in D than that of t 0.5 , which reveals that increasing the box dimension (increasing the complexity of the aggregate surface morphology, such as increasing its angularity) is an effective way to extend the service life of the aggregate macrotexture [25].

Influence of the Material Property Difference on the PSV Mechanism
Scanning electron microscopy (SEM) microstructure analysis was conducted on four types of aggregates to investigate how the aggregate material properties influence the polished value, with SEM photos at t = 37,500 min (200,000 cycles of polishing) shown in Figure 9. The aggregate surface morphologies exhibit key differences after polishing. way to extend the service life of the aggregate macrotexture [25].

Influence of the Material Property Difference on the PSV Mechanism
Scanning electron microscopy (SEM) microstructure analysis was conducted on four types of aggregates to investigate how the aggregate material properties influence the polished value, with SEM photos at t = 37,500 min (200,000 cycles of polishing) shown in Figure 9. The aggregate surface morphologies exhibit key differences after polishing. Obvious smooth macrostructure areas and uneven microstructure points (point a in Figure 9) formed on the surface of the hard particles in the high-hardness aggregates (calcined bauxite and granite) during polishing, which are the primary structures that inhibit abrasion and further surface wear, such that hs and Ps are lower. The hardness of granite is lower than that of bauxite, so its smooth macrostructure area is clearly larger than that of bauxite, which is consistent with the previous analysis results. Conversely, the surfaces of the low-hardness aggregates (basalt and limestone) were Obvious smooth macrostructure areas and uneven microstructure points (point a in Figure 9) formed on the surface of the hard particles in the high-hardness aggregates (calcined bauxite and granite) during polishing, which are the primary structures that inhibit abrasion and further surface wear, such that h s and P s are lower. The hardness of granite is lower than that of bauxite, so its smooth macrostructure area is clearly larger than that of bauxite, which is consistent with the previous analysis results. Conversely, the surfaces of the low-hardness aggregates (basalt and limestone) were obviously worn after polishing, such that abrasion could not be effectively inhibited, yielding higher h s and P s values.
The smooth points that formed on the bauxite and granite surfaces also exhibited a strong resistance to friction during polishing, indicating a high P x value. However, the abrasives in basalt and limestone adopted high-hardness emery (SiC) particles during the polishing experiments, with the emery particles forming obvious wear furrow scratches on the soft aggregate surface (point b in Figure 9). These soft aggregates are easy to wear, such that their resistance to the frictional movement of the abrasives is low, indicating a low P x value. Regardless, the P x value of the aggregates does not change with polishing time due to a new worn surface being formed repeatedly during the polishing process, such that P x is only related to the aggregate material.

Conclusions
(1) Through a physical polishing process analysis, a new mathematical model of PSV attenuation in coarse aggregate is proposed. In the model, the PSV of coarse aggregate is affected by both the macrotexture and microtexture. Its value is related to the material properties, aggregate surface morphology, and polishing time. The calculated data of the proposed PSV model are in good agreement with the experimental results.
(2) The polished value owing to the macrotexture is negatively correlated with the coarse aggregate hardness and decreases exponentially as the polishing time increases. The decay rate decreases as the fractal box dimension of the aggregate surface morphology increases. The primary factor influencing the service life and half-life of the macrotexture is the aggregate surface morphology. Both the service life and half-life increase as the fractal box dimension increases.
(3) The polished value owing to the microtexture is positively correlated with the Vickers hardness of coarse aggregate and is less correlated with the surface morphology and polishing time. The proportion of the PSV that consists of the polished value owing to the microtexture increases with increasing aggregate hardness.

Conflicts of Interest:
There are no conflicts of interest to declare.