# Interaction between Rockfalls and Vehicles Studied for Speed Limit Zonation along Mountainous Roads
## 4 Results  
### Rock Mass Survey and Kinematic Analysis  
Rock mass surveys were carried out according to the objective criterion proposed by ISRM [36], which requires the surveying of all discontinuities intersecting a scan line. Measuring stations were placed at six key spots along the studied roadway, on gray dolostone and crystalline limestone outcrops. By analyzing the resulting spatial data of discontinuities, the presence of four main families was highlighted (Figure 4). These were characterized by a medium to high persistence (3 to 20 m) and a close to moderate spacing (60-600 mm). Fractures showed aperture values greater than 5 mm, and the filling material was mostly absent or compact. Joint surfaces were predominantly wavy, with a joint roughness coefficient (JRC) ranging from 2 to 14. The achieved outcomes were used to carry out the estimation of the rock mass geomechanical quality according to the classification systems proposed by [PERSON] [38] and [PERSON] [37]. These procedures returned a homogeneous classification for all of the surveyed rock masses, which could be classified as \"Fair\" rock (geomechanical quality class III), with the RMRb ranging between 42 and 58 and the SMR between 50 and 53. Moreover, based on the empirical relations proposed by this classification system, the main shear strength parameters of the rock mass (Table 2)--namely, cohesion and friction angle--were calculated with Equations (3) and (4), respectively:  
\[\text{c}=5\text{ RMRb} \tag{3}\]  
\[\varphi=0.5\text{ RMRb}+5 \tag{4}\]  
The ranges of cohesion and the internal friction angles of the rock mass were 243-277 kPa and 29-32\({}^{\circ}\), respectively (Table 2). In order to assess the failure predisposition of the rock masses, a kinematic analysis was carried on stereograms out by taking into consideration the angular relationship between the discontinuities and the slope face with reference to different failure patterns. More specifically, planar sliding may occur when lateral-release surfaces are present in a rock mass and the slope face's inclination is greater than that of the sliding surface, which, therefore, daylights on the rock face; moreover, the inclination of the discontinuity plane must exceed the value of the friction angle. In this frame, this kinematic failure pattern was recognized at all of the surveyed stations and it affected the S1 sets, along with some random poles (RD) (Figure 4, Table 3). Wedge failure occurs when two or three discontinuities intersect, releasing a rock volume that can slide either along the intersection line (symmetric wedge) or along the most unfavorable plane (asymmetric wedge). In this case, wedge patterns were found at the intersections of the S1, S2, S3, and S4 sets (Figure 4, Table 3). Toppling failure affected the S2 and S4 sets, and all six stations exhibited this kinematic pattern (Figure 4, Table 3). It must be underlined that, even in this case, the kinematically unstable area also involved RD. This even strengthened the condition of instability of the rock masses along low-recurring discontinuities, which were not grouped into the system but conditioned the threat of rockfall (Figure 4). In order to mathematically prove the instability of the studied kinematic patterns, a numerical analysis was carried out according to the limit equilibrium method, which allows the calculation of a factor of safety as the ratio of the total forces resisting down-slope sliding to the total forces inducing sliding. The resisting forces are mainly represented by the shear strength along the sliding surface, plus artificial reinforcement or other external stabilizing forces, if present. On the other hand, the driving forces consist of the down-slope weight component of a sliding block, seismic acceleration force, water pressures, and external forces on the surface of the upper slope. The results returned factors of safety that were generally lower than 1.3, especially when the seismic force was considered, thus revealing the instability of these kinematic patterns.