# Interaction between Rockfalls and Vehicles Studied for Speed Limit Zonation along Mountainous Roads
## 3 Materials and Methods
In particular, the decision sight distance (DSD) represents the length of road that a driver needs to make a complex or instantaneous decision. This involves the spatial probability of a vehicle crashing into a fallen boulder laying on the road, which occurs when the driver does not have enough decision time to avoid the impact. For Italian roads, this is a function of the vehicle speed and the longitudinal slope of the road (CNR 1980). The P-DSD can be estimated with Equation (2):  
\[\text{P-DSD}=\left(\frac{\text{ADS}}{\text{DSD}}\right)\text{-}100 \tag{2}\]  
where ASD is the actual sight distance determined for the two directions of travel, since an obstacle on the road will be less visible when it is located just beyond the sharpest part of a curve. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Category**} & \multirow{2}{*}{**Points 3**} & \multicolumn{2}{c}{**Rating Criteria by Score**} & \multirow{2}{*}{**Points 81**} \\ \cline{2-2} \cline{5-5}  & & **Points 3** & & **Points 9** & **Points 27** & **Points 81** \\ \hline Slope height & 7.5 m & 15 m & 22.5 m & \textgreater{}30 m \\ \hline \multirow{4}{*}{Ditch effectiveness} & Good catchment: properly designed according to updates of checking chart + barriers & Moderate catchment: properly designed to updates of checking chart + barriers & Limited catchment: wrongly designed & No catchment \\ \cline{1-1} \cline{2-2} \cline{5-5}  & 25\% & 50\% & 75\% & 100\% \\ \cline{1-1} \cline{2-2} \cline{5-5} P-DSD & Adequate (100\%) & Moderate (80\%) & Limited (60\%) & Very limited (40\%) \\ \hline Roadway width & 21.5 m & 15.50 m & 9.50 m & 3.50 m \\ \hline SMR & 80 & 40 & 27 & 20 \\ \hline Block size & 30 cm & 60 cm & 90 cm & 120 cm \\ \cline{1-1} \cline{2-2} \cline{5-5} Boulder volume & 26 m\({}^{3}\) & 0.21 m\({}^{3}\) & 0.73 m\({}^{3}\) & 1.74 m\({}^{3}\) \\ \hline Volume of rockfall per event & 2.3 m\({}^{3}\) & 4.6 m\({}^{3}\) & 6.9 m\({}^{3}\) & 9.2 m\({}^{3}\) \\ \hline Annual rainfall and freezing periods & h = 300 mm or no freezing period & h = 600 mm or short freezing period & h = 900 mm or long freezing period & h = 1200 mm or long freezing period \\ \hline Rockfall frequency & 1 per 10 years & 3 per year & 6 per year & 9 per year \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters taken into account by the modified Rockfall Hazard Rating System [8]. Figure 3: Schematization of the methodological approach carried out for this study. The sum of scores assigned to each parameter returns a final RHRS value that provides a risk classification according to three classes:  
* High: RHRS scores >500 suggest that the studied road segment has to be considered to have \"immediate need of stabilization measures\";
* Intermediate: 300 < RHRS < 500 suggests that the studied road segment has a \"high priority of remedial work\", although a case-by-case evaluation would be appropriate [8]. * Low: RHRS scores < 300 are an index of \"low urgency\" in designing mitigation measures [14]. The RHRS methodology was applied at 51 road subsegments by taking five different scenarios of vehicle speed into account so as to shed light on the related variation in rockfall risk. This consideration aims at a better understanding of the traffic influence on rockfall risk, and the expected results could be useful for territorial management.