## 2 Materials and Methods
### Prediction of IFI for Skid-Resistance Analysis  
As mentioned before, the pavement surface's microtexture and macrotexture have a major impact on the friction or skid resistance it offers. A standardized friction number suggested by the International Friction Index (IFI) is used to measure the combined effect of different surface textures [16]. In order to compare texture and friction measures, the World Road Association (Permanent International Association of Road Congresses) conducted a number of tests. The IFI, the international standard for evaluating pavement surface friction, was created as a result of these efforts (ASTM E1960-07) [18]. The IFI consists of two key components: F (60) and Sp. The index is denoted and reported as IFI (F (60), Sp), and it is a mathematical model that describes the friction coefficient in terms of slip speed and macrotexture. To compute the IFI speed number (Sp) and friction number (F60), the following Equations (1)-(3) were used, as outlined in ASTM E 1960:  
\[\text{Sp}=\text{a}+\text{(b}\times\text{TX)} \tag{1}\]  
Sp is the IFI speed number.  
a and b are calibration constants that depend on the method used to measure macrotexture for this research, and using MPD measured according to ASTM E1960, a = 14.2 and b = 89.7.  
TX is the macrotexture measurement in millimeters (mm), which in this study conducted by CTM.  
\[\text{FR}\left(60\right)=\text{FR}(\text{S})\times\text{exp}[\text{(S}-60)/ \text{Sp}] \tag{2}\]  
FR (60) is the adjusted friction value at a slip speed of 60 km/h, FR(S) is the friction value at the selected slip speed, and S is the selected slip speed in km/h.  
These equations enable a comprehensive assessment of the pavement's frictional properties, incorporating the effects of both microtexture and macrotexture.  
\[\text{F}\left(60\right)=\text{A}+\text{B}\times\text{FR}\left(60\right)+\text {C}\times\text{TX} \tag{3}\]  
F (60) is the IFI friction number, which is derived from the correlation.  
A, B, and C are calibration constants dependent on the friction measuring device used.  
TX is the macrotexture measurement in millimeters (mm).  
According to PIARC findings, ASTM E1960-07 recommends utilizing the DFT reading at 20 km/h in conjunction with measurements from the CTM as the standard instruments for calibrating the IFI. Using these devices, Sp and the friction at 60 km/h, F (60), are determined based on Equations (4) and (5):  
\[\text{Sp}=14.2+89.7\text{MPD} \tag{4}\]\[\text{F}\left(60\right)=0.081+0.732\ \times\text{DFT20}\ \times\text{exp}[(-40)/\text{ Sp}] \tag{5}\]  
The foundation of the IFI concept is the notion that the friction of a pavement is dependent on the texture properties of the surface, such as microtexture and macrotexture, as well as the slip speed at which measurements are made. However, it might not be appropriate to apply Equation (2) to ribbed pavements or certain surface treatments. Regardless of the measured slip speed, these surfaces often retain constant friction levels, with friction values essentially staying constant throughout a range of slip speeds. In these situations, the parameter (Sp) loses significance since the slip speed (S) in Equation (2) does not take into consideration changes in friction measurements [34; 35]. According to ASTM E1960-07, the IFI concept is validated for pavements with profile depths of 0.25 \(\leq\) MPD \(\leq\) 1.5 and friction values of 0.30 \(\leq\) DFT20 \(\leq\) 0.90. This illustrates how sensitive the Sp parameter is to high levels of macrotexture, exposing a major drawback in the application of the IFI principle for surface treatments. The IFI should be optimized utilizing Sp values or modified in accordance with the MPD of various surfaces in order to increase its accuracy and usefulness across a range of pavement textures.