# Road Safety Management of Uncontrolled Access Points:
## 2 Materials and Methods
### Access Density vs. Traffic Accidents: Consideration of the Effects of the Functional Area Filter  
The assessment of the functional area for each access point allowed for defining a selection law to filter only traffic crashes located in a delimited area. It is necessary to note that it has been assumed that an access point can be a contributing factor or a concomitant cause of a collision; as a consequence, all the crashes located within the functional area are potentially attributable to the presence of the selected access point based on the main hypothesis that the effects related to its presence are recordable in the functional area. The assumption of this hypothesis is required as this analysis is focused on road infrastructure conditions in order to quantify the effect of access-related properties on the safety level; however, it is well known that the cause-effect link can be affected by other unmeasured variables such as the incorrect and distracted driver behaviour which can be a substantial contributing factor in most collisions at driveways according to the literature [3]. Vehicle type was not considered in this study as the percentage of crashes involving a personal car is more than 90%; furthermore, the focus is on the risk of collision which is strictly related to the interference among the vehicle's trajectories rather than the type of vehicle. The GIS project facilitated data management and supported the process of assigning access-related crashes to each specific access point. At the end of the implementation of this process for the case study, the filtered crashes are 371 (about 77% of the total crashes of the initial database (482 crashes)). The number of injuries recorded is 261 for the rural area and 374 for the urban one; the number of fatalities collected for the rural area and urban area is approximately comparable (9 and 10 for the rural and urban environment, respectively). The analysis of the collision type of the filtered crashes allowed the discovery of the main types of access collisions. The data showed the following accident types [41]: right-angle (103 crashes), rear-end (101 crashes), side-by-side (39 crashes), and head-on angle (28 crashes). The study of the cause-effect relationship (access-traffic accidents) highlighted the highest level of accuracy of the analysis obtained by implementing the filter described above. More specifically, the potential correlation between Access Density (number of access points per kilomet) and Accident Density (accidents per kilomet) is carried out for two cases with two different orders of detail. Access Density is considered the most influential factor in the occurrence of crashes according to the literature [42]. Figure 5 provides an overview of the analysed scenarios. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Functional Area Parameters** & **Characteristic** & **Rural Area** & **Urban Area** \\ \hline \multirow{8}{*}{L\({}_{\text{dxTOT}}\)} & v\({}_{1}\) [m/s] & 19.44 & 13.89 \\  & v\({}_{2}\) [m/s] & 0 & 0 \\  & a [m/s\({}^{2}\)] & 2.00 & 2.00 \\  & L\({}_{\text{dx}}\) [m] & 95 & 48 \\  & t\({}_{\text{pr}}\) [s] & 2.8 & 1.5 \\  & v\({}_{1}\) [m/s] & 19.44 & 13.89 \\  & L\({}_{\text{pr}}\) [m] & 54 & 21 \\  & L\({}_{\text{dxTOT}}\) [m] & 149 & 69 \\ \hline \multirow{4}{*}{L\({}_{\text{ex}}\)} & v\({}_{1}\) [m/s] & 0 & 0 \\  & v\({}_{2}\) [m/s] & 15.56 & 11.111 \\ \cline{1-1}  & a [m/s\({}^{2}\)] & 1.00 & 1.00 \\ \cline{1-1}  & L\({}_{\text{ex}}\) [m] & 121 & 62 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: L\({}_{\text{dxTOT}}\) and L\({}_{\text{ex}}\) assessment for the test site for the rural and urban areas. Data is aggregated per kilomet for both Scenarios, but for Scenario-ii the implementation of the functional area filter implied that the cause-effect relationship was first investigated for the single access point. The experimental distributions are shown in Figure 6. Despite the slightly increasing trend, a great dispersion of data is registered for Scenario-i, especially for high access density values.