# Impact of Putting on Traffic Safety: A Synthesis of Research Findings
## 3 Results and Discussion
### Prediction Model  
Data points representing the relationship between rut depth and accident rate were extracted from field observation studies. A total of 167 data points were extracted from \begin{table}
\begin{tabular}{c c c c} \hline
**Reference** & **Study Type** & **Special Factors** & **Speed (km/h)** & **Critical RD** \\ \hline [PERSON] et al. [42] & Field observation & Wetness & - & 7.6 mm \\ [PERSON] et al. [11] & Field observation & - & - & 8.9–10.1 mm \\  & & & 90 & 5 \\ [PERSON] et al. [37] \({}^{\star}\) & Simulation & Wetness (hydroplanning) & 83 & 15 \\  & & & 75 & 20 \\ [PERSON] et al. [30] & Simulation & - & 120 & 6 mm \\ [PERSON] et al. [28] & Simulation & Water-filled rut, rut length = 220 & 100 & 7 mm \\ [PERSON] et al. [27] & Simulation & Water-filled rut (hydroplanning) & 80 & 13 mm \({}^{\star}\) \\ [PERSON] et al. [35] & Simulation & Dry & 100 & 20 mm \\  & Simulation & Water-filled rut & 120 & 10 mm \\ [PERSON] et al. [48] & Simulation & Wet weather, SN = 30 & 60 & 6 \\  & Simulation & Wet weather, SN = 25 & 60 & 25 \\ \hline \end{tabular} \({}^{\star}\) Total water depth; RD: rut depth; SN: Skid number.  
\end{table} 
Table 6: Rut limits suggested by various field observation and simulation studies. \begin{table}
\begin{tabular}{c c c c} \hline
**Highway Agency** & **Low (mm)** & **Medium (mm)** & **High (mm)** \\ \hline Pavement Condition Index & 6.3–12.7 & 12.7–25.4 & \textgreater{}25.4 \\ Pavement surface evaluation and rating manual, & & 0–12.7 & 12.7–25.4 & \textgreater{}25.4 \\ asphalt roads & & & \\ Washington State Department of Transportation & 6.3–12.7 & 12.7–19.1 & \textgreater{}19.1 \\ Ohio Department of Transportation & 3.2–9.5 & 9.5–19.1 & \textgreater{}19.1 \\ Massachusetts Highway Department & 6.3–9.5 & 12.7–38.1 & \textgreater{}38.1 \\ Ministry of Transportation and Infrastructure, & 3–10 & 10–20 & \textgreater{}20 \\ British Columbia & & & \\ Malaysia & 0–10 \({}^{\star}\) & 5–20 & \textgreater{}20 \\ \hline \end{tabular} \({}^{\star}\) Combine good and fair condition.  
\end{table} 
Table 5: Rut severity classification by highway agencies based on rut depth [8; 37]. eleven studies, as presented in Table 7. For each data point, information was searched based on ten prediction features and a prediction label. The prediction features constitute rut depth value in addition to ten previously identified factors. The constructed dataset was validated to check the completeness of the data and the usability of the different attributes. Consequently, the study type was excluded since all considered studies were of the field observation type. Driving trajectory, lighting conditions, speed, and vehicle type were also excluded due to limited data availability. The prediction label was set as the accident rate per 100 MVkm. This dataset was utilized to develop ML-based prediction models that explain the relationship between rut depth and accident rates. The frequency distribution of the prediction inputs and outputs is presented in Figure 10. As shown in Figure 10, the data exhibit substantial diversity in rut depth values (0-30 mm) and accident rate values (0-250 accidents per 100 MVkm), as illustrated in Figure 10a and b, respectively. Additionally, the dataset includes information from seven countries, as depicted in Figure 10c. The data also encompass various road types, traffic volumes, and weather conditions, as presented in Figure 10d, e, and f, respectively. The considerable diversity within the dataset supports the development of more comprehensive models. However, it is important to note that the data are imbalanced for both the inputs and outputs. For instance, only a limited number of data points correspond to road sections with rut depths exceeding 12 mm, as shown in Figure 10a. Similarly, the majority of data points pertain to accident rates below 50 accidents per 100 MVkm, as indicated in Figure 10b. This limited availability of data for severe rut depths and the imbalance in accident rates may affect the reliability of the developed models.