# 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  
At present, logarithmic and exponential equations are predominantly employed by both domestic and foreign researchers to anticipate the attenuation condition of anti-skid properties in asphalt mixtures [24]. The utilization of exponential and logarithmic equations to signify the attenuation pattern of the anti-skid index for asphalt pavements is denoted by Equations (2) and (3), respectively. \[y=a_{0}e^{-b_{0}n}+c \tag{2}\]  
\[y=a_{1}-b_{1}\text{log}(n) \tag{3}\]  
where:  
\(y\) is the anti-skid index of the asphalt surface. \(n\) is the number of axle loads (times). \(a_{0}\), \(b_{0}\), \(c\), \(a_{1}\), and \(b_{1}\) are equation parameters. To assess the suitability of Equations (2) and (3) for anti-skid surface layers in both AC and SMA, a comparison of anti-skid index BPN and MTD values of asphalt mixtures gathered during accelerated loading conditions was conducted utilizing the least squares principle. Nonlinear fitting was then utilized to examine the correlation between loading times and the anti-skid index of the asphalt surface, and the equation parameters are presented in Tables 6 and 7. The results in Table 6 indicate that the correlation coefficient R\({}^{2}\) for the exponential equation and the logarithmic equation in MTD attenuation estimation are virtually identical. Furthermore, the prediction accuracy for the structural depth attenuation trend is relatively high. However, the effectiveness of predicting the structural depth attenuation trend in the SMA mixture is suboptimal, with the minimum value of the correlation coefficient R\({}^{2}\) at only 0.24. This outcome is primarily due to wave-like changes in the structural depth of the SMA mixture with an increasing number of loads, resulting in the equations' failure to deliver better outcomes. \begin{table} \begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Exponential Equation**} \\ \hline \multirow{2}{*}{**Plan Number**} & \multicolumn{2}{c}{_c_} & \multirow{2}{*}{_c_} & \multirow{2}{*}{_a_0} & \multirow{2}{*}{_b_0} & \multirow{2}{*}{_Adjusted R\({}^{2}\)_} \\ \cline{2-2} \cline{6-8}  & & & & & & \\ \cline{2-2} \cline{6-8}  & **Value** & **Standard Error** & **Value** & **Standard Error** & **Value** & **Standard Error** \\ \hline S1 & 0.91 & 0.01 & 0.22 & 0.01 & \(-\)0.13 & 0.02 & 0.98 \\ \hline S2 & 0.79 & 0.01 & 0.21 & 0.01 & \(-\)0.07 & 0.01 & 0.97 \\ \hline S3 & 0.76 & 0.01 & 0.14 & 0.01 & \(-\)0.05 & 0.01 & 0.96 \\ \hline S4 & 0.52 & 0.01 & 0.19 & 0.03 & \(-\)1.17 & 0.36 & 0.84 \\ \hline S5 & 0.98 & 0.02 & 0.15 & 0.02 & \(-\)0.07 & 0.03 & 0.8 \\ \hline S6 & 0.77 & 0.03 & 0.23 & 0.03 & \(-\)0.07 & 0.03 & 0.81 \\ \hline S7 & 0.93 & 0.00 & 0.28 & 0.00 & \(-\)0.59 & 0.02 & 1 \\ \hline S8 & 0.97 & 0.02 & 0.19 & 0.05 & \(-\)0.79 & 0.51 & 0.56 \\ \hline S9 & 0.58 & 0.01 & 0.11 & 0.02 & \(-\)0.59 & 0.24 & 0.8 \\ \hline S10 & 1.31 & 0.02 & 0.21 & 0.03 & \(-\)0.20 & 0.09 & 0.82 \\ \hline S11 & 1.15 & 0.02 & 0.23 & 0.06 & \(-\)0.71 & 0.43 & 0.61 \\ \hline S12 & 0.73 & 0.01 & 0.06 & 0.02 & \(-\)0.16 & 0.18 & 0.34 \\ \hline \hline \end{tabular} 
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Logarithmic Equation**} \\ \hline \multirow{2}{*}{**Plan Number**} & \multicolumn{2}{c}{_a_1} & \multicolumn{2}{c}{_b_1} & \multirow{2}{*}{_Adjusted R\({}^{2}\)_} \\ \cline{2-2} \cline{6-8}  & **Value** & **Standard Error** & **Value** & **Standard Error** & **Adjusted R\({}^{2}\)** \\ \hline S1 & 1.085 & 0.006 & 0.049 & 0.002 & 0.98 \\ \hline S2 & 0.992 & 0.008 & 0.046 & 0.003 & 0.96 \\ \hline S3 & 0.903 & 0.007 & 0.030 & 0.003 & 0.93 \\ \hline S4 & 0.587 & 0.007 & 0.023 & 0.003 & 0.89 \\ \hline S5 & 1.105 &Table 7 reveals that the correlation coefficient R\({}^{2}\) for BPN attenuation estimation is essentially the same for the exponential equation and the logarithmic equation. However, the two equations emphasize the decay trend of asphalt mixture BPN in their respective ways.