## 3 Methods for the Characterisation and Evaluation of the Skid Resistance of Asphalt Pavements
### Asphalt Pavement Skid Resistance Evaluation Model
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt}} \hline Model Type & Parametric Expression \\ \hline Empirical Formula Model & \((1)\) Y = Alnx + B (2) Y = A e B x \\ \cline{2-3}  & Y is the slip resistance index or the depth of construction, x is the number of axle loads (10,000), and A and B are regression coefficients. \\ \hline Penn State Model & \(\text{F(S)}=\text{F}_{0}\exp\left(1-\frac{\text{S}}{\text{S}_{0}}\right)\) \\ \cline{2-3}  & F(S) represents the friction factor of the wheel at a slip speed of S; F0, S0 are the characteristic parameters of the test apparatus; F0 is the friction factor at a slip velocity of 0; and S0 is a function that depends on the macroscopic texture of the pavement. \\ \hline Modified Penn State Model & \(\text{F(S)}=\text{F}_{10}\exp(\frac{10-\text{S}}{\text{S}_{0}})\) \\ \cline{2-3}  & F10 is the friction factor for a slip velocity of 10 km\(\cdot\)h\({}^{-1}\), and the rest of the parameters have the same meaning as in the Penn State Model. \\ \hline Asymptotic Model & \(\text{y}=\text{A}\text{e}^{\text{B}_{*}}+\text{C}\) \\ \cline{2-3}  & A is the attenuation amplitude, B is the attenuation rate, C is the final attenuation value, and x is the number of axial loads. \\ \hline PIARC Model & \(\text{F}_{60}\)= A\({}^{\prime}+\text{B}^{\prime}\mu_{y}^{\prime}\text{exp}[\frac{\text{S}-60}{ \text{S}_{0}+\text{S}_{0}+\text{S}_{0}}]+\text{C}^{\prime}\text{T}_{\text{x}}\) \\  & S\({}_{\text{p}}\)= a + bT\({}_{\text{x}}\) \\  & I\({}_{\text{IFI}}(\text{F}_{60},\text{S}_{\text{p}})=\text{F}_{60}\exp(\frac{\text{S}-60}{ \text{S}_{0}})\) \\ \hline \(S_{\text{p}}\) is the speed number; \(F_{60}\) is the friction factor corresponding to a slip speed of 60 km\(\cdot\)h\({}^{-1}\); \(A^{\prime}\), \(B^{\prime}\), \(C^{\prime}\) are the influence coefficients; \(T_{\text{x}}\) is the pavement construction parameter (MTD when measured by the sand-laying method, and MPD when measured by the laser method); \(a,b\) are the calibration parameters of the instrument; \(\mu^{\prime}\) is the friction factor at a slip speed of the s friction factor when the slip velocity is \(s\); and IFlis the international friction index. \\ \hline Pavement Skid Resistance & \(\text{y}=-\text{Aln(x)}+\text{C},\text{A}=0.178\text{s}+1.9054\) \\ Prediction Model & \(\text{y}\) is the pendulum value; A is the attenuation rate; X is the cumulative number of axle loads, i.e., 10,000 times; C is the initial value of attenuation related to asphalt mix gradation; and s is the aggregate polishing value. \\ \hline Friction and Texture Models & \(\text{BPN}=\text{$\alpha$}+\beta_{\text{MPD}_{\text{max}}}\text{Macro}_{ \text{MPD}}+\beta_{\text{treat}}\text{Treat}+\beta_{\text{treat}}\text{ Micro}_{\text{param}_{i}}^{\text{baseline}}\) \\ \hline Macro\({}_{\text{MPD}}\) is the MPD; Treat is a virtual variable that takes 1 when the cross-section receives an optical texture and 0 otherwise; and \(\text{Micro}_{\text{param}_{i}}^{\text{baseline}}\)) is the microtexture baseline space parameter. \\ \hline \end{tabular}
\end{table} 
Table 3: Evaluation models for pavement skid resistance. The PIARC model was developed by the World Road Association following a comprehensive study of 54 road sections in Belgium and Spain, utilising 47 types of pavement macro- and microtexture testing equipment. The PIARC model incorporates all test variables and enables the conversion of measured pavement friction coefficients at various test parameters to the friction coefficient at 60 km/h [69; 91]. Where the International Friction Index (IFI) consists of two parameters, i.e., speed Sp and the friction factor F\({}_{60}\), at the standard speed, where Sp\(=\) a + bT\({}_{x}\); a and b are regression coefficients; and T\({}_{x}\) is the depth of the pavement construction. The skid resistance of most pavements can be evaluated by the PIARC model, as shown in Figure 15. It has been divided into four distinct zones in Figure 15. Zone I exhibits excellent skid resistance.