# Evaluation of Anti-Skid Performance of Asphalt Mixture Based on Accelerated Loading Test
## 3 Result and Discussion
### Anti-Skiid Performance and Durability Evaluation
#### 3.3.1 Anti-Skiid Attenuation Equation
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number** & **B Value** & **Predicted B Value** & **Relative Error** \\ \hline S1 & 3.6 & 3.55 & 1.6 \\ \hline S2 & 2.94 & 3.23 & \(-9.8\) \\ \hline S3 & 2.69 & 2.91 & \(-8\) \\ \hline S4 & 3.81 & 3.43 & 10.2 \\ \hline S5 & 3 & 2.74 & 8.5 \\ \hline S6 & 4.27 & 4.35 & \(-1.7\) \\ \hline S7 & 3.6 & 3.21 & 10.7 \\ \hline S8 & 3.51 & 3.1 & 11.5 \\ \hline S9 & 3.24 & 3 & 7.7 \\ \hline S10 & 2.81 & 3.16 & \(-12.1\) \\ \hline S11 & 2.27 & 2.43 & \(-7.2\) \\ \hline S12 & 3.56 & 3.73 & \(-4.9\) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Attenuation rate B value comparison. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**B1** & **B2** & **B3** & **B4** & **B5** & **B6** & **B7** \\ \hline
0.194 & 0.117 & \(-0.236\) & \(-0.101\) & \(-3.136\) & 0.500 & 0.986 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Regression analysis results for various parameters. cross-section of the lane. In the case of expressways, the lateral distribution frequency curve of the wheel track exhibits a hump-shaped distribution, as demonstrated in Figure 13.  
The findings presented in Figure 13 indicate that the peak frequencies of wheel loads occur at the 4 th and 12 th units from the edge of the lane, which correspond to the midpoint of the wheel track belt on the road surface. This region is subjected to the most wear and abrasion and is the primary test position for the pavement lateral force coefficient. Consequently, we have identified the 30.4% and 29.2% lateral distribution frequency points as the locations where the anti-skid performance deteriorates the most. Based on this information, we propose to define the lateral distribution coefficient of wheel tracks as follows:  
\[\varphi=\frac{\left(30.4\%+29.2\%\right)}{2}=29.8\% \tag{7}\]  
By means of the preceding analyses and computations, we have derived Equation (8), which characterizes the conversion correlation between the cumulative load repetitions (n) of PAVEMLS11 and the actual cumulative axle load repetitions (Ne) on the road surface. \[\text{n}=0.298N_{e} \tag{8}\]  
Based on the measured SFC and BPN values and the correlation analysis results presented in this article, it is evident that BPN and SFC exhibit a strong linear correlation. A linear regression analysis was performed to establish the equation between SFC and BPN, which is depicted in Equation (9), and the correlation coefficient R was found to be 0.94, indicating a strong correlation between these two parameters. \[SFC=1.07\times BPN-4.6 \tag{9}\]  
Accordingly, the substitution of Equations (6) and (8) into Equation (9) leads to the derivation of the prediction equation for actual asphalt pavement SFC, as presented in Equation (10). Both Equations (10) and (11) are the outcomes of regression analyses. \[SFC=1.07\cdot(A-(0.194\cdot WSV+0.117\cdot PSV-0.236\cdot\lambda+0.101\cdot k+3.136P_{a}/P_{ai}+0.5)ln(0.298N_{e}))-4.6 \tag{10}\]  
\[SFC=10-3.085\times\ln(CNAT)+1.650\times PSV+0.730\times\lambda+6.552\times k \tag{11}\]  
Figure 13: Wheel track transverse frequency distribution curve. The presented equation includes various factors relevant to predicting the lateral force coefficient of asphalt pavement, denoted as _SFC_. These factors include \(A\), representing the initial value of the pendulum value of indoor slab specimens for rutting test blocks; \(WSV\), referring to the loss rate of the coarse aggregate Los Angeles abrasion, expressed as a percentage; \(PSV\), indicating the coarse aggregate polishing value; \(\lambda\), the graded scale factor; \(k\), the gradation form factor; and Ne, the cumulative number of axle loads of trucks, measured in ten thousand repetitions.