# Research on the Prediction Model of the Friction Coefficient of Asphalt Pavement Based on Tire-Pavement Coupling

Authors: Miao Yu; Xinquan Xu; Chuanhai Wu; Shanqiang Li; Mingxia Li; Haifeng Chen
Journal: Advances in Materials Science and Engineering
 (2021)

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## Abstract

The correlations between pavement texture and tire pressure with the actual tire-road contact area were first investigated according to the tire-road static contact characteristics; on this basis, the influence mechanisms of speed and pavement texture on the pavement friction coefficient were systematically explored from the angle of tire-road coupling system dynamics via the self-developed dynamic testing system of tire-pavement friction. By integrating the above influence factors, the BP neural network method was applied to the regression of the prediction model for the asphalt pavement friction coefficient. Through the comparison between the model measured value and estimated value, their correlation coefficientR2 reached 0.73, indicating that this model is of satisfactory prediction accuracy and applicable to the antiskid design of asphalt pavement.


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## Body

## 1. Introduction

Pavement skid resistance is closely related to road traffic safety. With good pavement texture as well as hard and wear-resistant aggregates, a pavement will have superior antiskid performance, thus reducing the probability of traffic accidents and increasing traffic safety. The test method and friction mechanism have been investigated frequently in order to accurately evaluate the antiskid performance of asphalt pavements, and on this basis a series of prediction models have been established for the friction coefficient.


### 1.1. Friction Models Based on Material Properties

In the aspect of friction materials, the corresponding rubber friction models have been proposed by quite a few scholars based on the viscoelasticity of rubber materials. The most representative models among these include the binomial friction model (D.F. Moore) [1] and the fractal friction model (B.N.J. Persson) [2], both of which are established based on the analysis of frictional behaviors, adhesion friction, and lag friction, between rubber on tire tread and the pavement. In addition, R. Savkoor [3] conducted a large number of rubber friction tests under different temperature conditions via the linear friction tester and series friction test system and put forward a phenomenological model considering the relationships among the rubber sliding speed, friction coefficient, and static friction coefficient.


### 1.2. Friction Models Based on Tire Friction Behaviors

The structural dynamic response of friction behaviors between tire and asphalt pavement cannot be comprehensively characterized by only the rubber frictional characteristics and tire-road static contact characteristics. In the vehicle-pavement coupling system, the tire will undergo obvious geometric shape changes under the actions of internal pressure as well as external pavement counter-forces like shear force, stretching force, and extruding force, rendering the small-deformation hypothesis no longer applicable [4]; moreover, the force analysis of tire-road contact becomes more difficult due to the complicated mechanical properties of rubber and asphalt pavement. In order to deeply probe the tire-pavement friction mechanism, scholars dedicated to vehicle engineering and road engineering have proposed various evaluation models.In the field of vehicle engineering, Oden [5] proposed an exponential decaying-type friction model (see (1)) for friction behaviors on the tire-road contact surface through mass measured data, conducted a steady-state analysis and verification of tire-road dynamic contact through the finite element method based on this model, and deemed that this model could characterize the adhesion-sliding friction behaviors after the dynamic tire-road contact. H. C. Zhou and G. L. Wang et al. compared the Coulomb friction model with this model via the finite element method and stated that the tire-road frictional contact model played a decisive role in calculating the maximum braking force. Furthermore, in comparison with the Coulomb friction model, the exponential friction model was closer to the dynamic simulation under the braking condition, and the change law of maximum braking force it embodied was more applicable to the antiskid brake system (ABS) [6]:(1)μ=μk+μs+μke−dc⋅s,where μk is the dynamic friction factor corresponding to the maximum slip speed, μs is the static friction coefficient under critical state, dc is the pavement condition attenuation coefficient designated by the user, and s is slip speed.In addition, based on the Grosch rotary-type abrasion machine, Dorsh [7] conducted the friction property test of rubber wheel on dry sandpaper under different load conditions, velocities, and temperatures, proposed the corresponding phenomenological model for the tire friction coefficient, and studied the friction behaviors on the contact surface between the friction model-based tire and smooth pavement via the finite element method. As a function relative to ground pressure intensity, slip speed, and environment temperature, this model can be simply characterized in the form of power exponent as follows:(2)μ=c0pc1vsc2,where c0, c1, and c2 are all material parameters related to tire-road contact.Pavement antiskid principles have been explored by many scholars of road engineering, and several classical models commonly applied to the pavement field measurement have been raised [8, 9].Leu and Henry [10] proposed the Penn State pavement friction coefficient model based on pavement texture and slip speed:(3)μ=μ0e−S/S0,where μ is the friction coefficient under slip speed S; μ0 is a constant characterizing the pavement microstructure, dimensionless; and S0 is a constant characterizing the pavement macrostructure, km/h. A greater μ0 value represents better pavement microstructure, and a greater S0 value denotes better pavement macrostructure. According to this model, the pavement friction coefficient is gradually reduced with the increase of speed.As the average running speed of most vehicles is 60 km/h, the Penn State model is slightly corrected to obtain PIARC model, where two indexes, namely, speed constantSp and standard friction coefficient F60, are used.(4)Sp=a+b⋅Tx,F60=A+B⋅FRs⋅expS−60/a+b·TxC⋅Tx,where Tx is structural parameter of pavement; a and b are regression coefficients; A, B, and C are system calibration parameters of friction coefficient testing equipment; S is slip speed, km/h; and FRs is friction coefficient measured under slip speed S. Theoretically speaking, this model can transform the friction coefficient at any test speed into the friction coefficient F60 at standard testing speed 60 km/h. However, what is characterized by this model is usually the pavement friction coefficient under full-locked state, and large errors exist in the practical application [11]. In addition, the microtexture has not been fully considered in the above commonly used pavement friction coefficient models, which will influence the prediction accuracy of friction coefficient [12–17]. Though applicable to engineering detection, they are not accurate enough when used in evaluation and research on pavement antiskid performance.Given this, prediction models for the pavement friction coefficient have not been fully investigated. In order to further reveal the antiskid mechanism of asphalt pavement, (1) the tire-pavement static characteristic test was first implemented based on the principle of tribology and the influences of factors like pavement texture, load, and tire pressure on the actual tire-road contact area were explored. (2) Next, the single-factor analysis was conducted for the influences of factors like slip rate, speed, contact area, and contact pressure intensity on the dynamic tire-road friction behaviors using the self-developed dynamic tire-road friction system. On this basis, an orthogonal test was conducted for ranking the influence degrees of different factors on the dynamic pavement friction coefficient. (3) Based on the above research results, the BP neural network method was combined to establish the prediction model for the dynamic friction coefficient of asphalt pavement. The above research findings are of certain reference values to the prediction of antiskid mechanism and antiskid performance of asphalt pavement.


## 1.1. Friction Models Based on Material Properties

In the aspect of friction materials, the corresponding rubber friction models have been proposed by quite a few scholars based on the viscoelasticity of rubber materials. The most representative models among these include the binomial friction model (D.F. Moore) [1] and the fractal friction model (B.N.J. Persson) [2], both of which are established based on the analysis of frictional behaviors, adhesion friction, and lag friction, between rubber on tire tread and the pavement. In addition, R. Savkoor [3] conducted a large number of rubber friction tests under different temperature conditions via the linear friction tester and series friction test system and put forward a phenomenological model considering the relationships among the rubber sliding speed, friction coefficient, and static friction coefficient.


## 1.2. Friction Models Based on Tire Friction Behaviors

The structural dynamic response of friction behaviors between tire and asphalt pavement cannot be comprehensively characterized by only the rubber frictional characteristics and tire-road static contact characteristics. In the vehicle-pavement coupling system, the tire will undergo obvious geometric shape changes under the actions of internal pressure as well as external pavement counter-forces like shear force, stretching force, and extruding force, rendering the small-deformation hypothesis no longer applicable [4]; moreover, the force analysis of tire-road contact becomes more difficult due to the complicated mechanical properties of rubber and asphalt pavement. In order to deeply probe the tire-pavement friction mechanism, scholars dedicated to vehicle engineering and road engineering have proposed various evaluation models.In the field of vehicle engineering, Oden [5] proposed an exponential decaying-type friction model (see (1)) for friction behaviors on the tire-road contact surface through mass measured data, conducted a steady-state analysis and verification of tire-road dynamic contact through the finite element method based on this model, and deemed that this model could characterize the adhesion-sliding friction behaviors after the dynamic tire-road contact. H. C. Zhou and G. L. Wang et al. compared the Coulomb friction model with this model via the finite element method and stated that the tire-road frictional contact model played a decisive role in calculating the maximum braking force. Furthermore, in comparison with the Coulomb friction model, the exponential friction model was closer to the dynamic simulation under the braking condition, and the change law of maximum braking force it embodied was more applicable to the antiskid brake system (ABS) [6]:(1)μ=μk+μs+μke−dc⋅s,where μk is the dynamic friction factor corresponding to the maximum slip speed, μs is the static friction coefficient under critical state, dc is the pavement condition attenuation coefficient designated by the user, and s is slip speed.In addition, based on the Grosch rotary-type abrasion machine, Dorsh [7] conducted the friction property test of rubber wheel on dry sandpaper under different load conditions, velocities, and temperatures, proposed the corresponding phenomenological model for the tire friction coefficient, and studied the friction behaviors on the contact surface between the friction model-based tire and smooth pavement via the finite element method. As a function relative to ground pressure intensity, slip speed, and environment temperature, this model can be simply characterized in the form of power exponent as follows:(2)μ=c0pc1vsc2,where c0, c1, and c2 are all material parameters related to tire-road contact.Pavement antiskid principles have been explored by many scholars of road engineering, and several classical models commonly applied to the pavement field measurement have been raised [8, 9].Leu and Henry [10] proposed the Penn State pavement friction coefficient model based on pavement texture and slip speed:(3)μ=μ0e−S/S0,where μ is the friction coefficient under slip speed S; μ0 is a constant characterizing the pavement microstructure, dimensionless; and S0 is a constant characterizing the pavement macrostructure, km/h. A greater μ0 value represents better pavement microstructure, and a greater S0 value denotes better pavement macrostructure. According to this model, the pavement friction coefficient is gradually reduced with the increase of speed.As the average running speed of most vehicles is 60 km/h, the Penn State model is slightly corrected to obtain PIARC model, where two indexes, namely, speed constantSp and standard friction coefficient F60, are used.(4)Sp=a+b⋅Tx,F60=A+B⋅FRs⋅expS−60/a+b·TxC⋅Tx,where Tx is structural parameter of pavement; a and b are regression coefficients; A, B, and C are system calibration parameters of friction coefficient testing equipment; S is slip speed, km/h; and FRs is friction coefficient measured under slip speed S. Theoretically speaking, this model can transform the friction coefficient at any test speed into the friction coefficient F60 at standard testing speed 60 km/h. However, what is characterized by this model is usually the pavement friction coefficient under full-locked state, and large errors exist in the practical application [11]. In addition, the microtexture has not been fully considered in the above commonly used pavement friction coefficient models, which will influence the prediction accuracy of friction coefficient [12–17]. Though applicable to engineering detection, they are not accurate enough when used in evaluation and research on pavement antiskid performance.Given this, prediction models for the pavement friction coefficient have not been fully investigated. In order to further reveal the antiskid mechanism of asphalt pavement, (1) the tire-pavement static characteristic test was first implemented based on the principle of tribology and the influences of factors like pavement texture, load, and tire pressure on the actual tire-road contact area were explored. (2) Next, the single-factor analysis was conducted for the influences of factors like slip rate, speed, contact area, and contact pressure intensity on the dynamic tire-road friction behaviors using the self-developed dynamic tire-road friction system. On this basis, an orthogonal test was conducted for ranking the influence degrees of different factors on the dynamic pavement friction coefficient. (3) Based on the above research results, the BP neural network method was combined to establish the prediction model for the dynamic friction coefficient of asphalt pavement. The above research findings are of certain reference values to the prediction of antiskid mechanism and antiskid performance of asphalt pavement.


## 2. Specimen Fabrication

In view of the major influence of pavement texture on the antiskid performance of asphalt pavement, different types of coarse aggregate-asphalt mixture were selected to prepare slab specimens with the dimensions of 30 × 30 × 5 cm in order to study the influence of macro and microtextures on the antiskid performance of asphalt pavement. Furthermore, gradations originating from the coarse aggregate of basalt, limestone, and granite for asphalt mixtures of AC13, SMA13, and OGFC 13 are shown in Table1. The asphalt-aggregate ratios of AC13, SMA13, and OGFC13 were 4.8%, 5.0%, and 6.2%, respectively.Table 1
The gradation of mineral aggregate of asphalt mixtures.
Sieve size (mm)AC13SMA13OGFC13Coarse aggregate typesCoarse aggregate typesCoarse aggregate typesBasaltLimestoneGraniteBasaltLimestoneGraniteBasaltLimestoneGranite1610010010010010010010010010013.297.998.598.896.997.798.296.397.296.39.580.580.680.570.670.769.764.364.564.34.7561.460.761.629.228.329.918.517.518.52.3644.144.544.224.525.824.510.811.710.81.1830.631.130.919.120.019.08.28.88.20.620.821.421.115.816.215.56.56.76.50.314.515.114.913.914.113.65.35.35.30.1510.110.710.612.612.712.44.44.44.40.0757.47.87.811.411.111.03.73.33.7


## 3. Methods

### 3.1. Pavement Texture

3D texture scanning of the slab specimens was conducted using the linear laser scanning device, with a range of ±10 mm and resolution of ±0.0025 mm. The scanning path is illustrated in Figure1. Additionally, the macrotextures and microtextures were extracted at different precision levels.Figure 1
Route laser scanning on the testing.


#### 3.1.1. Macrotexture Measurement

In full consideration of macrotexture dimensions and workload during the macrotexture measurement, the sampling interval of the laser profile measuring instrument was adjusted to 0.2 mm, each contour line was 100 mm in length (namely, there were 500 sampling points on each contour line), the spacing of contour lines was 0.2 mm, and 200 contour lines were scanned in a rectangular area 40 mm in width. In this way, a total of 500 × 200 (100,000) points were acquired in each scanning area. On this basis, there were 400,000 points in four areas of one rut slab. It was expected that the calculated macrotext parameters would be representative. The scanning path is seen in Figure2.Figure 2
Scanning area on the testing.


#### 3.1.2. Microtexture Measurement

With reference to the macrotexture scanning direction and accuracy, five coarse aggregates, with particle size of 13.2–16.0 mm and even surfaces, were uniformly selected on the surface of a wheel track tape of each specimen for the microtexture scanning of the aggregate surfaces, where the length of contour line was 1 cm, sampling interval was 5μm, and 2,000 point elevations were acquired on each contour line. The distance between adjacent contour lines was 1 mm, and six contour lines were scanned, with a total of 12,000 elevation points for every aggregate.


### 3.2. Static Testing of Tire-Pavement Contact

FUJI pressure film paper with LLW type was pressed on the tire-road contact specimen, and the tire-road static contact test was performed on the TDFA under different pavement textures, upper loads, and tire pressures. More details of TDFA can be found in research by Miao et al. [17]. Furthermore, the tire-road static contact characteristic analysis based on real-time distribution of contact pressure intensity and contact area was carried out with the FPD-8010P pressure film image analysis system. The tire-road static testing conditions are presented in Table 2. The test was repeated three times under each single-factor testing condition.Table 2
Testing conditions of tire-pavement static contact.
Testing itemsSpecific parameter rangePavement textures0.46, 1.29, 1.41Tire load (N)150, 200, 250Tire pressure (bar)1.5, 2.0, 2.5, 3.0Note. The MPD value is obtained from the specimens of AC, SMA, and OGFC by laser scanning.


### 3.3. Dynamic Testing of Tire/Pavement Friction Coefficient

The dynamic tire-road friction test was implemented on the basis of TDFA. As listed in Table3, first, the single-factor test of dynamic friction coefficient was conducted based on the running speed and pavement macro-texture, where the test was also repeated three times under each single-factor testing condition.Table 3
The single-factor testing conditions of dynamic friction coefficient.
Testing itemsSpecific parameter rangeSlip ratio20%Vehicle speed10 km/h、30 km/h、50 km/h、70 km/hMacrotextureThe same with Table2


## 3.1. Pavement Texture

3D texture scanning of the slab specimens was conducted using the linear laser scanning device, with a range of ±10 mm and resolution of ±0.0025 mm. The scanning path is illustrated in Figure1. Additionally, the macrotextures and microtextures were extracted at different precision levels.Figure 1
Route laser scanning on the testing.


### 3.1.1. Macrotexture Measurement

In full consideration of macrotexture dimensions and workload during the macrotexture measurement, the sampling interval of the laser profile measuring instrument was adjusted to 0.2 mm, each contour line was 100 mm in length (namely, there were 500 sampling points on each contour line), the spacing of contour lines was 0.2 mm, and 200 contour lines were scanned in a rectangular area 40 mm in width. In this way, a total of 500 × 200 (100,000) points were acquired in each scanning area. On this basis, there were 400,000 points in four areas of one rut slab. It was expected that the calculated macrotext parameters would be representative. The scanning path is seen in Figure2.Figure 2
Scanning area on the testing.


### 3.1.2. Microtexture Measurement

With reference to the macrotexture scanning direction and accuracy, five coarse aggregates, with particle size of 13.2–16.0 mm and even surfaces, were uniformly selected on the surface of a wheel track tape of each specimen for the microtexture scanning of the aggregate surfaces, where the length of contour line was 1 cm, sampling interval was 5μm, and 2,000 point elevations were acquired on each contour line. The distance between adjacent contour lines was 1 mm, and six contour lines were scanned, with a total of 12,000 elevation points for every aggregate.


## 3.1.1. Macrotexture Measurement

In full consideration of macrotexture dimensions and workload during the macrotexture measurement, the sampling interval of the laser profile measuring instrument was adjusted to 0.2 mm, each contour line was 100 mm in length (namely, there were 500 sampling points on each contour line), the spacing of contour lines was 0.2 mm, and 200 contour lines were scanned in a rectangular area 40 mm in width. In this way, a total of 500 × 200 (100,000) points were acquired in each scanning area. On this basis, there were 400,000 points in four areas of one rut slab. It was expected that the calculated macrotext parameters would be representative. The scanning path is seen in Figure2.Figure 2
Scanning area on the testing.


## 3.1.2. Microtexture Measurement

With reference to the macrotexture scanning direction and accuracy, five coarse aggregates, with particle size of 13.2–16.0 mm and even surfaces, were uniformly selected on the surface of a wheel track tape of each specimen for the microtexture scanning of the aggregate surfaces, where the length of contour line was 1 cm, sampling interval was 5μm, and 2,000 point elevations were acquired on each contour line. The distance between adjacent contour lines was 1 mm, and six contour lines were scanned, with a total of 12,000 elevation points for every aggregate.


## 3.2. Static Testing of Tire-Pavement Contact

FUJI pressure film paper with LLW type was pressed on the tire-road contact specimen, and the tire-road static contact test was performed on the TDFA under different pavement textures, upper loads, and tire pressures. More details of TDFA can be found in research by Miao et al. [17]. Furthermore, the tire-road static contact characteristic analysis based on real-time distribution of contact pressure intensity and contact area was carried out with the FPD-8010P pressure film image analysis system. The tire-road static testing conditions are presented in Table 2. The test was repeated three times under each single-factor testing condition.Table 2
Testing conditions of tire-pavement static contact.
Testing itemsSpecific parameter rangePavement textures0.46, 1.29, 1.41Tire load (N)150, 200, 250Tire pressure (bar)1.5, 2.0, 2.5, 3.0Note. The MPD value is obtained from the specimens of AC, SMA, and OGFC by laser scanning.


## 3.3. Dynamic Testing of Tire/Pavement Friction Coefficient

The dynamic tire-road friction test was implemented on the basis of TDFA. As listed in Table3, first, the single-factor test of dynamic friction coefficient was conducted based on the running speed and pavement macro-texture, where the test was also repeated three times under each single-factor testing condition.Table 3
The single-factor testing conditions of dynamic friction coefficient.
Testing itemsSpecific parameter rangeSlip ratio20%Vehicle speed10 km/h、30 km/h、50 km/h、70 km/hMacrotextureThe same with Table2


## 4. Results and Analysis

### 4.1. Static Contact Properties of Tire and Pavement

#### 4.1.1. Correlations of Pavement Texture and Upper Load with Actual Contact Area

As shown in Figure3, the MPD mean values of OGFC, SMA, and AC specimens are 0.46, 1.29, and 1.41, respectively, as seen on the x-coordinate. With the increase of MPD, the actual tire-road contact area is reduced. Although the overall tire-road contact area is significantly enlarged with the increase of upper load, the law “the greater the MPD, the smaller the contact area” remains unchanged.Figure 3
The actual contact area based on different MPD.


#### 4.1.2. Correlation between Tire Pressure and Actual Contact Area

The tire-road actual contact areas of nine specimens under different tire pressures were tested, and a further test was implemented in consideration of the tire pressure. As the specimens presented similar laws, only the AC-13 slab specimen with basalt as the coarse aggregate was analyzed in this paper for the investigation of the actual contact area under the coupled impact of tire pressure and upper load.As shown in Figure4, it can be inferred that, first, under the same tire load, the tire-road contact area started gradually declining after reaching the maximum value at 2.0 bar with the increase of tire pressure, indicating that when the tire pressure was elevated from 1.5 bar to 2.0 bar, the tire was turned from a “deflated” state into a “blown-up” state, and its contact area with the ground was enlarged; however, with the further air inflation loading, the tire-road contact area was reduced, manifesting that the actual tire-road contact was weakened under unchanged external load with the increase of tire strength. Moreover, under the same tire pressure, the tire-road contact area was apparently enlarged with the increase of tire load, that is, the 150–250 N phase. However, as the tire load was further increased from 250 to 300 N, an increased amplitude of the contact area was not obvious, and even presented flat and declining trends. Furthermore, Figure 5 clearly indicates that as the tire load reached up to 300 N, the width of the tire-road contact zone was enlarged, but the disengaging area in the central zone gradually emerged, indicating that the tire strength was insufficient at the status, and the load-carrying area gradually developed from the crown to side wall of the tire. Based on the above analysis, follow-up research should be conducted within reasonable scopes of tire pressure and load. In subsequent tests, the tire pressure was chosen as 2 bar, 2.5 bar, and 3 bar, and the tire load was chosen as 150 N, 200 N, and 250 N.Figure 4
The actual contact area based on different tire loads.Figure 5
The effect of tire speed on the pavement friction coefficient. (a) The AC pavement friction coefficient under different tire speeds. (b) The SMA pavement friction coefficient under different tire speeds. (c) The OGFC pavement friction coefficient under different tire speeds.
(a)(b)(c)


### 4.2. Dynamically Frictional Properties between Tire and Pavement Based on TDFA

#### 4.2.1. Effect of Tire Speed on Dynamic Friction Coefficient

As shown in Figure5, the friction coefficients of AC, SMA, and OGFC pavements all presented an obvious declining trend with the increase of vehicle speed. These phenomena indicate that the acceleration remitted the embedding-squeezing phenomenon between tire and pavement texture, thus leading to the weak tire-pavement adhesion, and, consequently, the effective braking force provided by the pavement to the tire was reduced. In addition, it was found by comparing the different types of pavement that the antiskid performance of OGFC kept the balance with that of SMA, and no obvious advantage of OGFC was found. This can be attributed to the low watering amount during the testing process, so its advantage in keeping good antiskid performance through water drainage was not manifested. In other words, the OFGC could exert its antiskid strength only under large precipitation. By comparing the mixtures with different lithology in the friction coefficient, the antiskid performance of limestone was not significantly different from those of igneous rocks like basalt and granite, indicating that, under the instantaneous braking condition, the abrasion performance of rock had no great impact on its antiskid performance. In the end, the linear regression was conducted for the vehicle speed and friction coefficient on all kinds of pavement, and it was found that the correlation coefficients R2 of vehicle speed-friction coefficients on AC, SMA, and OGFC pavements were 0.79, 0.64, and 0.53, respectively.


#### 4.2.2. Effect of Pavement Texture on Dynamic Tire-Road Friction Behaviors

It is well known that pavement macrotexture is directly associated with antiskid performance. Furthermore, microtexture also plays a critical role in the antiskid performance, especially the peak value of pavement friction coefficient. The prediction accuracy of pavement antiskid performance can be noticeably improved by incorporating the microtexture into the research on the pavement antiskid performance. Therefore, the aggregate microtextures were characterized using the texture parameterCMT; the physical significance of which was the aspect ratio of microtexture peak, namely, the ratio of altitude difference to horizontal distance of two adjacent points. A greater CMTvalue represents sharp peaked and rich microtextures. The calculation formula is seen in the following equation, and the calculation results are seen in Table 4:(5)CMT=1n∑i=1nΔhΔL,where CMT is the microtexture coefficient, Δh is the vertical distance between crests of two adjacent microtextures (mm), and ΔL is the horizontal distance between crests of two adjacent microtextures (mm).Table 4
The microtexture parameterCMT of coarse aggregate.
Coarse aggregate typesSampling numberAverageCMT12345Basalt0.4660.4060.4240.3620.3970.411Limestone0.4500.4020.4840.3870.4180.428Granite0.3130.3350.3790.3030.2700.320As seen in Table4, limestone has the maximum CMT value, followed by basalt and granite, successively, indicating that limestone has the richest microtextures, and the surface of granite is relatively flat with low roughness in this research.


#### 4.2.3. Pavement Friction Coefficient under Multifactor Coupling

The orthogonal test was designed and implemented using the 7-factor and 3-level orthogonal table to further study the influences of pavement texture, load, tire pressure, speed, and so on on the pavement antiskid performance, and the variable designation is listed in Table5. The macrotextures were controlled via gradation and microtextures controlled using different aggregates. The friction coefficients were tested by TDFA, and four parallel tests were carried out for each group. As the obvious outliers were excluded, the mean value was taken as the test result as seen in the right column of Table 6. The corresponding analysis of variance is displayed in Table 7.Table 5
Levels of the variables of the orthogonal test.
ItemLevel 1Level 2Level 3Macrotexture (mm)(A1) 0.46(A2) 1.29(A3) 1.41Tire load (N)(B1) 150(B2) 200(B3) 250Tire pressure (bar)(C1) 2(C2) 2.5(C3) 3Tire speed (km/h)(D1) 10(D2) 20(D3) 30Microtexture (-)(E1) 0.320(E2) 0.411(E3) 0.428Table 6
The orthogonal test of pavement friction coefficient.
Test no.MacrotextureTire loadTire pressureTire speedMicrotextureCombination of factorsFriction coefficient1A2B2C3D1E3A2B2C3D1E30.5882A3B2C2D3E1A3B2C2D3E10.4883A2B1C3D3E1A2B1C3D3E10.444A1B2C1D3E3A1B2C1D3E30.3535A3B3C3D3E3A3B3C3D3E30.5366A2B3C2D1E1A2B3C2D1E10.5567A1B3C2D2E3A1B3C2D2E30.4118A2B3C1D3E2A2B3C1D3E20.4919A2B1C1D2E3A2B1C1D2E30.5310A1B1C1D1E1A1B1C1D1E10.40511A3B3C1D2E1A3B3C1D2E10.54612A3B2C1D1E2A3B2C1D1E20.62313A3B1C3D2E2A3B1C3D2E20.56514A2B2C2D2E2A2B2C2D2E20.54115A1B3C3D1E2A1B3C3D1E20.45616A1B2C3D2E1A1B2C3D2E10.36317A1B1C2D3E2A1B1C2D3E20.3418A3B1C2D1E3A3B1C2D1E30.62Table 7
ANOVA analysis of the orthogonal test.
FactorsMean squareF valueP valueMacrotexture0.05814261.3120.000Tire load0.001109.0000.000Tire pressure0.0001.0000.415Tire speed0.0014219.7500.000Microtexture0.001825.0620.000It can be seen from Table7 that, within the confidence level of 95%, the P value of tire pressure is 0.415, which is greater than 0.05; therefore, it has insignificant influence on the tire-road friction coefficient, whereas the influence levels of the other four factors on the friction coefficient are all 0.00 (smaller than 0.01), indicating extremely significant correlation. Furthermore, by combining the F value ranking, the influence levels of the above factors on the pavement antiskid performance are ranked as macrotexture > speed > microtexture > load.


## 4.1. Static Contact Properties of Tire and Pavement

### 4.1.1. Correlations of Pavement Texture and Upper Load with Actual Contact Area

As shown in Figure3, the MPD mean values of OGFC, SMA, and AC specimens are 0.46, 1.29, and 1.41, respectively, as seen on the x-coordinate. With the increase of MPD, the actual tire-road contact area is reduced. Although the overall tire-road contact area is significantly enlarged with the increase of upper load, the law “the greater the MPD, the smaller the contact area” remains unchanged.Figure 3
The actual contact area based on different MPD.


### 4.1.2. Correlation between Tire Pressure and Actual Contact Area

The tire-road actual contact areas of nine specimens under different tire pressures were tested, and a further test was implemented in consideration of the tire pressure. As the specimens presented similar laws, only the AC-13 slab specimen with basalt as the coarse aggregate was analyzed in this paper for the investigation of the actual contact area under the coupled impact of tire pressure and upper load.As shown in Figure4, it can be inferred that, first, under the same tire load, the tire-road contact area started gradually declining after reaching the maximum value at 2.0 bar with the increase of tire pressure, indicating that when the tire pressure was elevated from 1.5 bar to 2.0 bar, the tire was turned from a “deflated” state into a “blown-up” state, and its contact area with the ground was enlarged; however, with the further air inflation loading, the tire-road contact area was reduced, manifesting that the actual tire-road contact was weakened under unchanged external load with the increase of tire strength. Moreover, under the same tire pressure, the tire-road contact area was apparently enlarged with the increase of tire load, that is, the 150–250 N phase. However, as the tire load was further increased from 250 to 300 N, an increased amplitude of the contact area was not obvious, and even presented flat and declining trends. Furthermore, Figure 5 clearly indicates that as the tire load reached up to 300 N, the width of the tire-road contact zone was enlarged, but the disengaging area in the central zone gradually emerged, indicating that the tire strength was insufficient at the status, and the load-carrying area gradually developed from the crown to side wall of the tire. Based on the above analysis, follow-up research should be conducted within reasonable scopes of tire pressure and load. In subsequent tests, the tire pressure was chosen as 2 bar, 2.5 bar, and 3 bar, and the tire load was chosen as 150 N, 200 N, and 250 N.Figure 4
The actual contact area based on different tire loads.Figure 5
The effect of tire speed on the pavement friction coefficient. (a) The AC pavement friction coefficient under different tire speeds. (b) The SMA pavement friction coefficient under different tire speeds. (c) The OGFC pavement friction coefficient under different tire speeds.
(a)(b)(c)


## 4.1.1. Correlations of Pavement Texture and Upper Load with Actual Contact Area

As shown in Figure3, the MPD mean values of OGFC, SMA, and AC specimens are 0.46, 1.29, and 1.41, respectively, as seen on the x-coordinate. With the increase of MPD, the actual tire-road contact area is reduced. Although the overall tire-road contact area is significantly enlarged with the increase of upper load, the law “the greater the MPD, the smaller the contact area” remains unchanged.Figure 3
The actual contact area based on different MPD.


## 4.1.2. Correlation between Tire Pressure and Actual Contact Area

The tire-road actual contact areas of nine specimens under different tire pressures were tested, and a further test was implemented in consideration of the tire pressure. As the specimens presented similar laws, only the AC-13 slab specimen with basalt as the coarse aggregate was analyzed in this paper for the investigation of the actual contact area under the coupled impact of tire pressure and upper load.As shown in Figure4, it can be inferred that, first, under the same tire load, the tire-road contact area started gradually declining after reaching the maximum value at 2.0 bar with the increase of tire pressure, indicating that when the tire pressure was elevated from 1.5 bar to 2.0 bar, the tire was turned from a “deflated” state into a “blown-up” state, and its contact area with the ground was enlarged; however, with the further air inflation loading, the tire-road contact area was reduced, manifesting that the actual tire-road contact was weakened under unchanged external load with the increase of tire strength. Moreover, under the same tire pressure, the tire-road contact area was apparently enlarged with the increase of tire load, that is, the 150–250 N phase. However, as the tire load was further increased from 250 to 300 N, an increased amplitude of the contact area was not obvious, and even presented flat and declining trends. Furthermore, Figure 5 clearly indicates that as the tire load reached up to 300 N, the width of the tire-road contact zone was enlarged, but the disengaging area in the central zone gradually emerged, indicating that the tire strength was insufficient at the status, and the load-carrying area gradually developed from the crown to side wall of the tire. Based on the above analysis, follow-up research should be conducted within reasonable scopes of tire pressure and load. In subsequent tests, the tire pressure was chosen as 2 bar, 2.5 bar, and 3 bar, and the tire load was chosen as 150 N, 200 N, and 250 N.Figure 4
The actual contact area based on different tire loads.Figure 5
The effect of tire speed on the pavement friction coefficient. (a) The AC pavement friction coefficient under different tire speeds. (b) The SMA pavement friction coefficient under different tire speeds. (c) The OGFC pavement friction coefficient under different tire speeds.
(a)(b)(c)


## 4.2. Dynamically Frictional Properties between Tire and Pavement Based on TDFA

### 4.2.1. Effect of Tire Speed on Dynamic Friction Coefficient

As shown in Figure5, the friction coefficients of AC, SMA, and OGFC pavements all presented an obvious declining trend with the increase of vehicle speed. These phenomena indicate that the acceleration remitted the embedding-squeezing phenomenon between tire and pavement texture, thus leading to the weak tire-pavement adhesion, and, consequently, the effective braking force provided by the pavement to the tire was reduced. In addition, it was found by comparing the different types of pavement that the antiskid performance of OGFC kept the balance with that of SMA, and no obvious advantage of OGFC was found. This can be attributed to the low watering amount during the testing process, so its advantage in keeping good antiskid performance through water drainage was not manifested. In other words, the OFGC could exert its antiskid strength only under large precipitation. By comparing the mixtures with different lithology in the friction coefficient, the antiskid performance of limestone was not significantly different from those of igneous rocks like basalt and granite, indicating that, under the instantaneous braking condition, the abrasion performance of rock had no great impact on its antiskid performance. In the end, the linear regression was conducted for the vehicle speed and friction coefficient on all kinds of pavement, and it was found that the correlation coefficients R2 of vehicle speed-friction coefficients on AC, SMA, and OGFC pavements were 0.79, 0.64, and 0.53, respectively.


### 4.2.2. Effect of Pavement Texture on Dynamic Tire-Road Friction Behaviors

It is well known that pavement macrotexture is directly associated with antiskid performance. Furthermore, microtexture also plays a critical role in the antiskid performance, especially the peak value of pavement friction coefficient. The prediction accuracy of pavement antiskid performance can be noticeably improved by incorporating the microtexture into the research on the pavement antiskid performance. Therefore, the aggregate microtextures were characterized using the texture parameterCMT; the physical significance of which was the aspect ratio of microtexture peak, namely, the ratio of altitude difference to horizontal distance of two adjacent points. A greater CMTvalue represents sharp peaked and rich microtextures. The calculation formula is seen in the following equation, and the calculation results are seen in Table 4:(5)CMT=1n∑i=1nΔhΔL,where CMT is the microtexture coefficient, Δh is the vertical distance between crests of two adjacent microtextures (mm), and ΔL is the horizontal distance between crests of two adjacent microtextures (mm).Table 4
The microtexture parameterCMT of coarse aggregate.
Coarse aggregate typesSampling numberAverageCMT12345Basalt0.4660.4060.4240.3620.3970.411Limestone0.4500.4020.4840.3870.4180.428Granite0.3130.3350.3790.3030.2700.320As seen in Table4, limestone has the maximum CMT value, followed by basalt and granite, successively, indicating that limestone has the richest microtextures, and the surface of granite is relatively flat with low roughness in this research.


### 4.2.3. Pavement Friction Coefficient under Multifactor Coupling

The orthogonal test was designed and implemented using the 7-factor and 3-level orthogonal table to further study the influences of pavement texture, load, tire pressure, speed, and so on on the pavement antiskid performance, and the variable designation is listed in Table5. The macrotextures were controlled via gradation and microtextures controlled using different aggregates. The friction coefficients were tested by TDFA, and four parallel tests were carried out for each group. As the obvious outliers were excluded, the mean value was taken as the test result as seen in the right column of Table 6. The corresponding analysis of variance is displayed in Table 7.Table 5
Levels of the variables of the orthogonal test.
ItemLevel 1Level 2Level 3Macrotexture (mm)(A1) 0.46(A2) 1.29(A3) 1.41Tire load (N)(B1) 150(B2) 200(B3) 250Tire pressure (bar)(C1) 2(C2) 2.5(C3) 3Tire speed (km/h)(D1) 10(D2) 20(D3) 30Microtexture (-)(E1) 0.320(E2) 0.411(E3) 0.428Table 6
The orthogonal test of pavement friction coefficient.
Test no.MacrotextureTire loadTire pressureTire speedMicrotextureCombination of factorsFriction coefficient1A2B2C3D1E3A2B2C3D1E30.5882A3B2C2D3E1A3B2C2D3E10.4883A2B1C3D3E1A2B1C3D3E10.444A1B2C1D3E3A1B2C1D3E30.3535A3B3C3D3E3A3B3C3D3E30.5366A2B3C2D1E1A2B3C2D1E10.5567A1B3C2D2E3A1B3C2D2E30.4118A2B3C1D3E2A2B3C1D3E20.4919A2B1C1D2E3A2B1C1D2E30.5310A1B1C1D1E1A1B1C1D1E10.40511A3B3C1D2E1A3B3C1D2E10.54612A3B2C1D1E2A3B2C1D1E20.62313A3B1C3D2E2A3B1C3D2E20.56514A2B2C2D2E2A2B2C2D2E20.54115A1B3C3D1E2A1B3C3D1E20.45616A1B2C3D2E1A1B2C3D2E10.36317A1B1C2D3E2A1B1C2D3E20.3418A3B1C2D1E3A3B1C2D1E30.62Table 7
ANOVA analysis of the orthogonal test.
FactorsMean squareF valueP valueMacrotexture0.05814261.3120.000Tire load0.001109.0000.000Tire pressure0.0001.0000.415Tire speed0.0014219.7500.000Microtexture0.001825.0620.000It can be seen from Table7 that, within the confidence level of 95%, the P value of tire pressure is 0.415, which is greater than 0.05; therefore, it has insignificant influence on the tire-road friction coefficient, whereas the influence levels of the other four factors on the friction coefficient are all 0.00 (smaller than 0.01), indicating extremely significant correlation. Furthermore, by combining the F value ranking, the influence levels of the above factors on the pavement antiskid performance are ranked as macrotexture > speed > microtexture > load.


## 4.2.1. Effect of Tire Speed on Dynamic Friction Coefficient

As shown in Figure5, the friction coefficients of AC, SMA, and OGFC pavements all presented an obvious declining trend with the increase of vehicle speed. These phenomena indicate that the acceleration remitted the embedding-squeezing phenomenon between tire and pavement texture, thus leading to the weak tire-pavement adhesion, and, consequently, the effective braking force provided by the pavement to the tire was reduced. In addition, it was found by comparing the different types of pavement that the antiskid performance of OGFC kept the balance with that of SMA, and no obvious advantage of OGFC was found. This can be attributed to the low watering amount during the testing process, so its advantage in keeping good antiskid performance through water drainage was not manifested. In other words, the OFGC could exert its antiskid strength only under large precipitation. By comparing the mixtures with different lithology in the friction coefficient, the antiskid performance of limestone was not significantly different from those of igneous rocks like basalt and granite, indicating that, under the instantaneous braking condition, the abrasion performance of rock had no great impact on its antiskid performance. In the end, the linear regression was conducted for the vehicle speed and friction coefficient on all kinds of pavement, and it was found that the correlation coefficients R2 of vehicle speed-friction coefficients on AC, SMA, and OGFC pavements were 0.79, 0.64, and 0.53, respectively.


## 4.2.2. Effect of Pavement Texture on Dynamic Tire-Road Friction Behaviors

It is well known that pavement macrotexture is directly associated with antiskid performance. Furthermore, microtexture also plays a critical role in the antiskid performance, especially the peak value of pavement friction coefficient. The prediction accuracy of pavement antiskid performance can be noticeably improved by incorporating the microtexture into the research on the pavement antiskid performance. Therefore, the aggregate microtextures were characterized using the texture parameterCMT; the physical significance of which was the aspect ratio of microtexture peak, namely, the ratio of altitude difference to horizontal distance of two adjacent points. A greater CMTvalue represents sharp peaked and rich microtextures. The calculation formula is seen in the following equation, and the calculation results are seen in Table 4:(5)CMT=1n∑i=1nΔhΔL,where CMT is the microtexture coefficient, Δh is the vertical distance between crests of two adjacent microtextures (mm), and ΔL is the horizontal distance between crests of two adjacent microtextures (mm).Table 4
The microtexture parameterCMT of coarse aggregate.
Coarse aggregate typesSampling numberAverageCMT12345Basalt0.4660.4060.4240.3620.3970.411Limestone0.4500.4020.4840.3870.4180.428Granite0.3130.3350.3790.3030.2700.320As seen in Table4, limestone has the maximum CMT value, followed by basalt and granite, successively, indicating that limestone has the richest microtextures, and the surface of granite is relatively flat with low roughness in this research.


## 4.2.3. Pavement Friction Coefficient under Multifactor Coupling

The orthogonal test was designed and implemented using the 7-factor and 3-level orthogonal table to further study the influences of pavement texture, load, tire pressure, speed, and so on on the pavement antiskid performance, and the variable designation is listed in Table5. The macrotextures were controlled via gradation and microtextures controlled using different aggregates. The friction coefficients were tested by TDFA, and four parallel tests were carried out for each group. As the obvious outliers were excluded, the mean value was taken as the test result as seen in the right column of Table 6. The corresponding analysis of variance is displayed in Table 7.Table 5
Levels of the variables of the orthogonal test.
ItemLevel 1Level 2Level 3Macrotexture (mm)(A1) 0.46(A2) 1.29(A3) 1.41Tire load (N)(B1) 150(B2) 200(B3) 250Tire pressure (bar)(C1) 2(C2) 2.5(C3) 3Tire speed (km/h)(D1) 10(D2) 20(D3) 30Microtexture (-)(E1) 0.320(E2) 0.411(E3) 0.428Table 6
The orthogonal test of pavement friction coefficient.
Test no.MacrotextureTire loadTire pressureTire speedMicrotextureCombination of factorsFriction coefficient1A2B2C3D1E3A2B2C3D1E30.5882A3B2C2D3E1A3B2C2D3E10.4883A2B1C3D3E1A2B1C3D3E10.444A1B2C1D3E3A1B2C1D3E30.3535A3B3C3D3E3A3B3C3D3E30.5366A2B3C2D1E1A2B3C2D1E10.5567A1B3C2D2E3A1B3C2D2E30.4118A2B3C1D3E2A2B3C1D3E20.4919A2B1C1D2E3A2B1C1D2E30.5310A1B1C1D1E1A1B1C1D1E10.40511A3B3C1D2E1A3B3C1D2E10.54612A3B2C1D1E2A3B2C1D1E20.62313A3B1C3D2E2A3B1C3D2E20.56514A2B2C2D2E2A2B2C2D2E20.54115A1B3C3D1E2A1B3C3D1E20.45616A1B2C3D2E1A1B2C3D2E10.36317A1B1C2D3E2A1B1C2D3E20.3418A3B1C2D1E3A3B1C2D1E30.62Table 7
ANOVA analysis of the orthogonal test.
FactorsMean squareF valueP valueMacrotexture0.05814261.3120.000Tire load0.001109.0000.000Tire pressure0.0001.0000.415Tire speed0.0014219.7500.000Microtexture0.001825.0620.000It can be seen from Table7 that, within the confidence level of 95%, the P value of tire pressure is 0.415, which is greater than 0.05; therefore, it has insignificant influence on the tire-road friction coefficient, whereas the influence levels of the other four factors on the friction coefficient are all 0.00 (smaller than 0.01), indicating extremely significant correlation. Furthermore, by combining the F value ranking, the influence levels of the above factors on the pavement antiskid performance are ranked as macrotexture > speed > microtexture > load.


## 5. Prediction Model Research on Tire-Asphalt Pavement Friction Coefficient

### 5.1. Modelling for Prediction of the Asphalt Pavement Friction Coefficient Based on BP Neural Network

The BP neural network was used to construct the prediction model for the friction coefficient. The testing samples were selected based on their influence on the pavement friction in the orthogonal test. In consideration of the insignificant correlation of tire pressure with the friction coefficient, the number of input-layer nodes (number of independent variables) was 4 and the number of output-layer nodes (number of dependent variables) was 1 in the neural network after the tire pressure was excluded. On this basis, the number of hidden nodes was finally confirmed as 4 through the cut-and-trial method. There was one input layer in the BP neural network, containing 4 nodes; one hidden layer, containing 4 nodes; and one output layer, containing 1 node, and thus the model solving was realized in the program via the MATLAB programming according to the network structure needed. The steps are as follows.Step I. The orthogonal test data were saved in the data file to complete the input of sample data. The data were first standardized by converting the input data into numbers within 0–1 to avoid the inaccurate prediction caused by the difference in order of magnitudes, and the processing methods included the max-min method (see (6)) and average number method (see (7)):(6)xi=xk−xminxmax−xmin,where xmin is the minimum data in the input data and xmax is the maximum data in the input data, and (7)xi=xk−xmeanxvar,where xmeanis the mean value of the input data and xvar is the variance of the input data.Step II. The threshold and weight value between layers were randomly initialized according to the determined network structure.Step III. The neural network was trained according to the standard training process, the weight value and threshold were continuously modified, and the model training was implemented using 80% of the sample number in the program.Step IV. The network model-based prediction, namely, 20% of the sample data, were reserved in the neural network training to predict model precision and ensure the accuracy of the trained neural network model.The learning sample data obtained through the test (the comparison chart of sample data training set and test set with the prediction results) were input into the BP neural network, and the equation of factors and friction coefficient were obtained through the MATLAB operation. The coefficients can be seen in Table8, and the derived equation is seen in the following equation:where x1 is the macrotexture parameter value (mm), x2 is the load value (N), x3 is the speed value (km/h), x4 is the microtexture parameter value (/), and y is the predicted value of friction coefficient (/).Table 8
Coefficients used for the predictive model of friction coefficient of asphalt pavement.
abcdX1−5.2989＋8.4980＋9.3854−2.7174X2＋0.0169＋0.0223−0.0051＋0.0192X3＋0.1430−0.1258−0.0398−0.1556X4−22.6687＋27.9335＋3.0993−0.0219C＋5.1314−16.7806−12.0751＋3.9483K1＋0.1696−0.0440−0.1741−0.1181K2＋1(8)y=0.1696ea+1−0.0440eb+1−0.1741ec+1−0.1181ed+1+1↓,a=−5.2989x1+0.0169x2+0.1430x3−22.6687x4+g.1314↓,b=+8.4980x1+0.0223x2−0.1258x3+27.9335x4−16.7806↓,c=+9.3854x1−0.0051x2−0.0398x3+3.0993x4−12.0751↓,d=−2.7174x1+0.0192x2−0.1556x3−0.0219x4+3.9483↵.As shown in Figure6, 80% of the 18 training sample data, namely, 14 data in the training set, were totally consistent with the predicted value of the neural network, the result error was between 20% of the training sample data, namely, 4 data in the test set, and the output value was small, and the absolute error was within 0.05, indicating that the prediction effect of the neural network was accurate, and the neural network model was effective when used to predict the training sample data. To further investigate the validation of the model, the untrained sample data were tested and compared with the measured values.Figure 6
Predictive accuracy of the pavement friction coefficient based on BP neural network. (a) Comparison between the predictive set value and the training set value. (b) Comparison between the predictive set value and the testing set value.
(a)(b)


### 5.2. Model Precision Test

To verify the prediction accuracy of this friction coefficient model, the slab specimens were fabricated for the friction coefficient test. First, the microtexture parameterCMTwas calculated after the microtextures on the aggregate surface were scanned, followed by calculation of macrotexture parameter MPD after the macrotexture scanning. In the end, the friction coefficients of the slab specimens measured under different operating conditions were compared with the model predicted values to verify the model precision, and the testing conditions, measured values, and predicted values are shown in Table 9.Table 9
The precision test for the predictive model of the pavement friction coefficient.
No.Macrotexture (mm)Tire speed (km/h)Microtexture (mm)Tire load (N)Predictive value (/)Measured value (/)Error (-)Relative error (%)10.556200.4112000.4420.41−0.032−7.8020.569200.4282000.4590.40−0.059−14.7531.293200.3202000.5210.50−0.021−4.2041.917200.4112000.6040.610.0060.9851.900200.3202000.6040.53−0.074−13.9660.556100.4112000.4860.520.0346.5470.556300.4112000.3570.380.0236.0580.569100.4282000.4920.510.0183.5390.569300.4282000.3820.34−.0420−12.35100.556300.3202000.2870.290.0031.03111.609100.4112000.6540.660.0060.92121.353100.4282000.6060.650.0446.77131.353300.4282000.5020.45−0.052−11.56141.293300.3202000.4380.40−0.038−9.50151.917100.4112000.6470.660.0131.97162.123100.4282000.6330.640.0071.09171.900100.3202000.6480.660.0121.82180.556200.4112500.4170.40−0.017−4.25190.569200.4282500.4370.39−0.047−12.05200.559200.3201500.3550.32−0.035−10.94210.559200.3202500.3320.370.03810.27221.609200.4112500.5900.51−0.080−15.69231.353200.4282500.5700.54−0.030−5.56241.917200.4111500.5820.55−0.032−5.82251.917200.4112500.6310.59−0.041−6.95262.123200.4281500.5740.53−0.044−8.30272.123200.4282500.6160.61−0.006−0.98281.900200.3201500.5820.56−0.022−3.93291.900200.3202500.6310.62−0.011−1.77300.559200.3202000.3380.470.13228.09311.609200.4112000.6150.46−0.155−33.70321.353200.4282000.5650.45−0.115−25.56332.123200.4282000.5900.45−0.140−31.11340.559100.3202000.4100.540.13024.07351.609300.4112000.5670.41−0.157−38.29361.293100.3202000.5660.45−0.116−25.78371.917300.4112000.5720.45−0.122−27.11381.900300.3202000.5710.41−0.161−39.27391.293200.3202500.5160.49−0.026−5.31400.556500.4112000.2040.340.13640.00410.556700.4112000.1760.220.04420.00420.569500.4282000.2090.330.12136.67430.569700.4282000.1760.220.04420.00440.559500.3202000.1960.310.11436.77450.559700.3202000.1750.250.07530.00461.609500.4112000.5080.38−0.12833.68471.609700.4112000.3820.34−0.042−12.35481.353500.4282000.3950.37−0.025−6.76491.353700.4282000.2650.290.0258.62501.293500.3202000.2630.350.08724.86511.293700.3202000.1970.320.12338.44521.917500.4112000.5560.41−0.146−35.61531.900700.3202000.4210.35−0.071−20.26As presented in Table8, the data with the absolute value of relative error being smaller than 10% accounted for 45.28%, those with the absolute value of relative error being smaller than 20% accounted for 66.04%, and those with the absolute value of relative error being smaller than 30% accounted for 81.13%. Additionally, the absolute values of relative errors of all data were within 40%. The correlation between predicted value and measured value of friction coefficient was established as shown in Figure 7 based on Table 8, and their correlation coefficient was obtained as R2 = 0.73, manifesting the favorable model prediction accuracy.Figure 7
Correlation between the predictive value and the measured value of friction coefficient.


## 5.1. Modelling for Prediction of the Asphalt Pavement Friction Coefficient Based on BP Neural Network

The BP neural network was used to construct the prediction model for the friction coefficient. The testing samples were selected based on their influence on the pavement friction in the orthogonal test. In consideration of the insignificant correlation of tire pressure with the friction coefficient, the number of input-layer nodes (number of independent variables) was 4 and the number of output-layer nodes (number of dependent variables) was 1 in the neural network after the tire pressure was excluded. On this basis, the number of hidden nodes was finally confirmed as 4 through the cut-and-trial method. There was one input layer in the BP neural network, containing 4 nodes; one hidden layer, containing 4 nodes; and one output layer, containing 1 node, and thus the model solving was realized in the program via the MATLAB programming according to the network structure needed. The steps are as follows.Step I. The orthogonal test data were saved in the data file to complete the input of sample data. The data were first standardized by converting the input data into numbers within 0–1 to avoid the inaccurate prediction caused by the difference in order of magnitudes, and the processing methods included the max-min method (see (6)) and average number method (see (7)):(6)xi=xk−xminxmax−xmin,where xmin is the minimum data in the input data and xmax is the maximum data in the input data, and (7)xi=xk−xmeanxvar,where xmeanis the mean value of the input data and xvar is the variance of the input data.Step II. The threshold and weight value between layers were randomly initialized according to the determined network structure.Step III. The neural network was trained according to the standard training process, the weight value and threshold were continuously modified, and the model training was implemented using 80% of the sample number in the program.Step IV. The network model-based prediction, namely, 20% of the sample data, were reserved in the neural network training to predict model precision and ensure the accuracy of the trained neural network model.The learning sample data obtained through the test (the comparison chart of sample data training set and test set with the prediction results) were input into the BP neural network, and the equation of factors and friction coefficient were obtained through the MATLAB operation. The coefficients can be seen in Table8, and the derived equation is seen in the following equation:where x1 is the macrotexture parameter value (mm), x2 is the load value (N), x3 is the speed value (km/h), x4 is the microtexture parameter value (/), and y is the predicted value of friction coefficient (/).Table 8
Coefficients used for the predictive model of friction coefficient of asphalt pavement.
abcdX1−5.2989＋8.4980＋9.3854−2.7174X2＋0.0169＋0.0223−0.0051＋0.0192X3＋0.1430−0.1258−0.0398−0.1556X4−22.6687＋27.9335＋3.0993−0.0219C＋5.1314−16.7806−12.0751＋3.9483K1＋0.1696−0.0440−0.1741−0.1181K2＋1(8)y=0.1696ea+1−0.0440eb+1−0.1741ec+1−0.1181ed+1+1↓,a=−5.2989x1+0.0169x2+0.1430x3−22.6687x4+g.1314↓,b=+8.4980x1+0.0223x2−0.1258x3+27.9335x4−16.7806↓,c=+9.3854x1−0.0051x2−0.0398x3+3.0993x4−12.0751↓,d=−2.7174x1+0.0192x2−0.1556x3−0.0219x4+3.9483↵.As shown in Figure6, 80% of the 18 training sample data, namely, 14 data in the training set, were totally consistent with the predicted value of the neural network, the result error was between 20% of the training sample data, namely, 4 data in the test set, and the output value was small, and the absolute error was within 0.05, indicating that the prediction effect of the neural network was accurate, and the neural network model was effective when used to predict the training sample data. To further investigate the validation of the model, the untrained sample data were tested and compared with the measured values.Figure 6
Predictive accuracy of the pavement friction coefficient based on BP neural network. (a) Comparison between the predictive set value and the training set value. (b) Comparison between the predictive set value and the testing set value.
(a)(b)


## 5.2. Model Precision Test

To verify the prediction accuracy of this friction coefficient model, the slab specimens were fabricated for the friction coefficient test. First, the microtexture parameterCMTwas calculated after the microtextures on the aggregate surface were scanned, followed by calculation of macrotexture parameter MPD after the macrotexture scanning. In the end, the friction coefficients of the slab specimens measured under different operating conditions were compared with the model predicted values to verify the model precision, and the testing conditions, measured values, and predicted values are shown in Table 9.Table 9
The precision test for the predictive model of the pavement friction coefficient.
No.Macrotexture (mm)Tire speed (km/h)Microtexture (mm)Tire load (N)Predictive value (/)Measured value (/)Error (-)Relative error (%)10.556200.4112000.4420.41−0.032−7.8020.569200.4282000.4590.40−0.059−14.7531.293200.3202000.5210.50−0.021−4.2041.917200.4112000.6040.610.0060.9851.900200.3202000.6040.53−0.074−13.9660.556100.4112000.4860.520.0346.5470.556300.4112000.3570.380.0236.0580.569100.4282000.4920.510.0183.5390.569300.4282000.3820.34−.0420−12.35100.556300.3202000.2870.290.0031.03111.609100.4112000.6540.660.0060.92121.353100.4282000.6060.650.0446.77131.353300.4282000.5020.45−0.052−11.56141.293300.3202000.4380.40−0.038−9.50151.917100.4112000.6470.660.0131.97162.123100.4282000.6330.640.0071.09171.900100.3202000.6480.660.0121.82180.556200.4112500.4170.40−0.017−4.25190.569200.4282500.4370.39−0.047−12.05200.559200.3201500.3550.32−0.035−10.94210.559200.3202500.3320.370.03810.27221.609200.4112500.5900.51−0.080−15.69231.353200.4282500.5700.54−0.030−5.56241.917200.4111500.5820.55−0.032−5.82251.917200.4112500.6310.59−0.041−6.95262.123200.4281500.5740.53−0.044−8.30272.123200.4282500.6160.61−0.006−0.98281.900200.3201500.5820.56−0.022−3.93291.900200.3202500.6310.62−0.011−1.77300.559200.3202000.3380.470.13228.09311.609200.4112000.6150.46−0.155−33.70321.353200.4282000.5650.45−0.115−25.56332.123200.4282000.5900.45−0.140−31.11340.559100.3202000.4100.540.13024.07351.609300.4112000.5670.41−0.157−38.29361.293100.3202000.5660.45−0.116−25.78371.917300.4112000.5720.45−0.122−27.11381.900300.3202000.5710.41−0.161−39.27391.293200.3202500.5160.49−0.026−5.31400.556500.4112000.2040.340.13640.00410.556700.4112000.1760.220.04420.00420.569500.4282000.2090.330.12136.67430.569700.4282000.1760.220.04420.00440.559500.3202000.1960.310.11436.77450.559700.3202000.1750.250.07530.00461.609500.4112000.5080.38−0.12833.68471.609700.4112000.3820.34−0.042−12.35481.353500.4282000.3950.37−0.025−6.76491.353700.4282000.2650.290.0258.62501.293500.3202000.2630.350.08724.86511.293700.3202000.1970.320.12338.44521.917500.4112000.5560.41−0.146−35.61531.900700.3202000.4210.35−0.071−20.26As presented in Table8, the data with the absolute value of relative error being smaller than 10% accounted for 45.28%, those with the absolute value of relative error being smaller than 20% accounted for 66.04%, and those with the absolute value of relative error being smaller than 30% accounted for 81.13%. Additionally, the absolute values of relative errors of all data were within 40%. The correlation between predicted value and measured value of friction coefficient was established as shown in Figure 7 based on Table 8, and their correlation coefficient was obtained as R2 = 0.73, manifesting the favorable model prediction accuracy.Figure 7
Correlation between the predictive value and the measured value of friction coefficient.


## 6. Conclusions

The tire-road static contact characteristics were first investigated, the asphalt pavement antiskid performance was tested based on the tire-road coupling friction behaviors, and the prediction model for the asphalt pavement friction coefficient was constructed with the BP neural network in consideration of the pavement macro- and microtexture parameters. The specific conclusions were drawn as follows.The actual tire-road contact area is reduced with the increase of MPD. However, considering the difference of the pavements with multiple gradations, this conclusion is more applicable for evaluating the relation between the pavements belonging to the same type and friction coefficient.The ground pressure intensity of tire is increased gradually with the increase of upper load. Nevertheless, it can be known by adding the pressure film scanning analysis that when the upper load is too large, the tire-road ground pressure intensity is gradually migrated from the crown to side wall of the tire. Therefore, the tire pressure should be correspondingly adjusted under different loads to ensure the service life of the tire and driving safety.As the vehicle speed is accelerated, the friction coefficients of all pavements present a significant declining trend. It was found through the comparison that the OGFC has equivalent antiskid performance to SMA, and no advantage of OGFC is found in the aspect of antiskid performance. It is inferred that no obvious water film is formed on either of the pavements, so the advantage of OGFC in drainage-based skid resistance is not fully embodied. In other words, the OGFC can give full play to its antiskid advantage only under large precipitation.In comparison with igneous rocks like basalt and granite, the limestone shows no significant difference in the aspect of instantaneous antiskid performance, indicating that when the aggregates are of favorable angularity, their difference in abrasion performance is not closely related to the antiskid performance.Based on the orthogonal test of tire-road friction coefficient in full consideration of aggregate texture, tire pressure, speed, and load, the influence degrees of these factors on the asphalt pavement antiskid performance are sorted as macrotexture > speed > microtexture > load.Based on the influence factors of pavement antiskid performance obtained by the previous conclusion, the BP neural network is added for the regression of the prediction model for the asphalt pavement friction coefficient. The model effectiveness is then verified, and the correlation coefficientR2 between predicted value and measured value is obtained as 0.73, representing the good prediction accuracy of this model for the friction coefficient.



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*Source: 6650525-2021-02-11.xml*