# Interaction between Rockfalls and Vehicles Studied for Speed Limit Zonation along Mountainous Roads
## 1 Introduction  
Mountainous environments have been attracting settlers for thousands of years thanks to their strategic location in terms of observation spots, territorial surveillance, and controlled accessibility. Over time, such settlements have become hubs for trade and war purposes, and have then turned into villages and gained specific roles in the local territory. Nowadays, the historical value that such villages have gained attracts visitors interested in discovering and enjoying their heritage appeal in peculiar natural environments. Nevertheless, the hard accessibility that represented a defensive feature in remote times represents today a limitation to geotourism because the access routes are usually limited and are characterized by irregular paths to overcome high slope rates. Furthermore, mountainous settings are an expression of a complex geological history, which affects the development of linear infrastructures. These, indeed, often cross different geological formations, thus suffering from specific geological problems related to slope instability. When mountainous roads cross rock masses, the major threat is represented by rockfall occurrence, i.e., rapid kinematic landslides, which represent a serious hazard along roads [1]. In this regard, roads are counted among the most recurrent elements at risk, with rockfalls being some of the most fatal natural events, especially in mountainous areas [1, 2, 3, 4]. This aspect carries arelevant scientific and technical importance, and there are numerous studies in the published literature dealing with this issue (e.g., [5; 6; 7; 8; 9; 10; 11]). In particular, the term risk refers to the expression of the likelihood and impact of an uncertain, sudden, and extreme event that may positively or negatively impact the achievement of a project or program objective [12]. Rockfall risk arises from the probability of causing certain damage to one or more elements at risk (modified after [13]), which, in the case of transportation routes, are represented by both human lives and goods with an economic value, such as passing vehicles and infrastructural elements. For this aspect, numerous risk assessment systems have been proposed to identify, either qualitatively or quantitatively, slopes that are at risk of failure and to allow the arrangement of preventive measures (e.g., [14; 15; 16]). Some authors [17; 18] also proposed a comparison between different rockfall risk rating systems along roads, even highlighting uncertainties and limitations and suggesting that the choice of the most suitable risk assessment methodology can be carried out based on the different planning purposes. Among the multiple aspects that must be taken into account during a rockfall risk analysis along roads, the dynamic presence of elements at risk, represented by vehicular traffic, is a key factor. Traffic safety is one of the most crucial issues, since a large number of people lose their lives in traffic accidents every day, mostly due to inappropriate choice of speed, and there are numerous technical studies aimed at addressing this aspect [19; 20]. It is precisely the dynamism of this element, which involves vehicles traveling at different speeds, that leads to the need for shedding light on how vehicle speed affects rockfall risk. There is indeed a dual relationship between rockfall risk and vehicle speed, which depends on the spatial and temporal correspondence between a falling boulder and a passing vehicle. In particular, the spatial correspondence is related to the possibility that a falling block stops at a roadway and that a driver can see it. In this specific case, the driver needs time to avoid the impact by either changing the vehicle's trajectory or stopping it [2]. The temporal correspondence is linked to the possibility that a vehicle is hit by a falling block due to the intersection of the respective trajectories [2; 7; 21].