# 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
The fitting curve of the logarithmic equation has a better correlation coefficient, R\({}^{2}\), compared to the exponential equation. Additionally, the c value in the exponential equation represents the final attenuation value, and thus, it can only estimate the anti-skid index within the maximum load repetitions of 600,000 times. As a result, this study utilizes the logarithmic equation to anticipate the friction coefficient's attenuation trend and evaluate the anti-skid durability of asphalt mixtures. The fitting curve diagrams of BPN and loading times, represented in Figures 9 and 10, illustrate that after a certain number of load repetitions, the BPN of the anti-skid surface layer exhibits a stable attenuation trend, which is consistent with the actual asphalt pavement's lateral force coefficient attenuation trend. Figure 11 represents the comparison of BPN attenuation stability value and attenuation rate. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Exponential Equation**} \\ \cline{2-9}
**Plan Number** & \multicolumn{2}{c}{\(c\)} & \multicolumn{2}{c}{\(a_{0}\)} & \multicolumn{2}{c}{\(b_{0}\)} & \multicolumn{2}{c}{**Statistics**} \\ \cline{2-9}  & **Value** & **Standard Error** & **Value** & **Standard Error** & **Value** & **Standard Error** & **Residual Sum of Squares** & **Adjusted R\({}^{2}\)** \\ \hline S1 & 46.7 & 2.6 & 18.3 & 2.47 & 0.05 & 0.02 & 4.22 & 0.91 \\ \hline S2 & 48.7 & 1.8 & 13.9 & 2.1 & 0.08 & 0.04 & 7.27 & 0.8  
The anti-skid surface layer made up of various materials exhibits distinct pendulum friction coefficient attenuation rates, while the pendulum friction coefficient that reaches stability differs. The logarithmic equation's A value (\(Y=A-B\times\ln(n)\)) signifies the anti-skid index's initial value, which can typically be replaced by the anti-skid index value during the initial loading stage. The comparative analysis of the test outcomes demonstrates that the A value is quite close to the BPN during the initial loading stage (0.5 million times) with a relative error of less than 8%. Consequently, the BPN at the initial loading stage (0.5 million times) can substitute for the A value of the exponential equation. The B value reflects the decay rate of the anti-skid index, with a higher value indicating faster anti-skid index decay. Figure 12 illustrates a comparison diagram of the BPN decay rate (B value). For the AC-16 asphalt mixture, a greater oil-stone ratio corresponds to a lower pendulum decay rate. S6 (limestone) has the highest pendulum decay rate, while the diabase asphalt mixture's decay rate is intermediate, and the andesite asphalt mixture's decay rate is the lowest. The SMA asphalt mixture's (B = 3.16) pendulum decay rate is superior to that of AC-16 (B = 3.39). Hence, the logarithmic equation's B value can reflect the impact of diverse lithological aggregates, oil-stone ratios, gradations, etc., on the anti-skid durability of asphalt mixtures. Figure 9: Pendulum friction coefficient attenuation fitting curve (AC-16). Figure 11: Comparison of BPN attenuation stability value and attenuation rate. Figure 10: Pendulum friction coefficient attenuation fitting curve (SMA). To investigate the effects of physical indicators of coarse aggregates, gradation, oil-stone ratio, and other parameters on the attenuation rate B value, statistical data of coarse aggregate properties, such as crushing value CSV, abrasion value WSV, polishing value PSV, Pai/Pa (the actual oil-stone ratio to the best oil-stone ratio), as well as gradation scale factor \(\lambda\) and shape factor \(k\), were collected and are presented in Table 8. Based on the analysis, it was found that the oil-stone ratio has a significant impact on the B value. For asphalt mixtures with the same gradation and coarse aggregate, a larger oil-stone ratio leads to a lower pendulum value attenuation rate, while a thicker gradation results in a lower pendulum value attenuation rate at the same oil-stone ratio.