# Interaction between Rockfalls and Vehicles Studied for Speed Limit Zonation along Mountainous Roads
## 3 Materials and Methods  
The rockfall risk analysis presented herein cannot be considered only a mere application of a rating method, which would extremely simplify the problem and the related approach of the study. In fact, the risk rating system applied herein, which is presented as a scientific methodology for practical applications, requires an in-depth characterization of the problem from the perspectives of both the rock masses and the road's geometrical features. In fact, it has been widely ascertained that the geomechanical features of a rock mass play a key role in controlling the stabilization and deformation characteristics of rock slopes, especially in seismically active and tectonically complex areas (e.g., [32; 33; 34; 35]), with direct repercussions on slope instability and the resulting risk. Therefore, here, the first step was the complete characterization of the rock mass through field surveys that were performed according to the recommendations of the International Society for Rock Mechanics (ISRM) [36] (Figure 3). The rock mass survey was focused on the road segments surrounded by rock masses that hosted no protective measures and showed signs of potential instability. For each surveyed discontinuity, the orientation, spacing, persistence, opening, in-filling, roughness, uniaxial compressive strength (UCS), and hydraulic were measured and evaluated. Spatial data of the discontinuities were plotted on stereograms and statistically processed to find the most representative discontinuity sets for kinematic purposes. According to the surveyed data, the geomechanical quality of the rock masses was estimated through the Slope Mass Rating approach [37], which relies on the preliminary estimation of the Rock Mass Rating (RMR) value [38], which is then corrected by a factorial adjustment factor depending on the relationships between joints and, if present, on the method of excavation. As a parallel activity, the geometrical features of the road were surveyed in terms of width and visibility conditions, and the road was divided into sub-segments characterized by homogeneous geometrical features (e.g., straight paths, bends). At each sub-segment, the modified Rockfall Hazard Rating System (RHRS) was applied to quantify the rockfall risk according to different scenarios related to the vehicle speed (Figure 2). The principle on which this approach is based is the link between the risk arising from rockfalls and the prioritization of budget allocation for the maintenance and protection of roads. To this purpose, the United States Department of Transportation in Oregon proposed the RHRS classification scheme to identify hazardous slopes requiring urgent remedial work [8; 14; 16]. This methodology consists of assigning a score to nine categories related to rockfall hazard and vehicle vulnerability (Table 1), starting from the slope survey, which is considered an essential feature of the approach [14]. The parameters involved are the slope height, protective measure effectiveness, average vehicle risk (AVR--i.e., the spatial probability of a vehicle's occurrence in the length of the rockfall hazard zone), percentage of sight decision distance (P-DSD), roadway width, geological character (SMR [37]), volume of rockfall/block size, and climate and rockfall history. The sum of the scores expresses the grade of risk exposure along roads. More specifically, the AVR is calculated by using Equation (1):  
\[\text{AVR}=\left(\text{ADT}\cdot\text{SL}\cdot 100\%\right)/\text{PSP} \tag{1}\]  
where ADT is the average traffic volume in one day, SL is the length of the hazard zone expressed in km, and PSP is the road speed limit expressed in km/h. An AVR value of 100% suggests that a vehicle can be expected to be within the hazard zone for 100% of the examined time. A high AVR (>100%) suggests that more than one vehicle is present within the hazard zone [8; 14]. The P-DSD parameter indicates the percentage of decision sight distance.