## 3 Methodology for Evaluating the Effectiveness of Rock Fall Protections
### Analysis of the Effectiveness of the Protection Measures
Protection Measures in the Propagation Zone  
Structural measures installed in the propagation zone, such as barrier fences, embankments and retaining walls, aim, on the other hand, at controlling rock fall energy \(E\) and rebound height \(d\) in order to intercept the blocks along their path and prevent them from travelling further downslope--ensuring hazard mitigation beyond their location. The main design features of these structures are the energy absorption capacity and effective height: if \(\mathrm{E_{opt}}\) and \(\mathrm{D_{opt}}\), respectively, denote their nominal values when the measures are in optimal working order, hazard mitigation takes place when both the conditions:  
\[ \begin{cases}\mathrm{E}<\mathrm{E_{opt}}\\ \mathrm{d}<\mathrm{D_{opt}}\end{cases}  \tag{4}\]  
are satisfied. Regarding, more specifically, the effective height of the structure \(\mathrm{D_{opt}}\), this is the parameter that, at a given location, allows us to define, in the first place, the likelihood of intercepting block trajectories (determined, e.g., as the percentage of trajectories that are \"caught\" by the structure over the total number of possible trajectories reaching the protection, according to rock fall simulation results). It is therefore a parameter directly linked to the frequency of reach \(\mathrm{P_{r}}\) as, in principle, the higher the height of the structure, the lower the chance a block will fly over it after a rebound, and travel further. The energy absorption capacity of the structure then completes the intercepting function, by making sure the blocks caught by the protection actually stop their path, losing all their energy at its location. The performance capacity of structural rock fall protections in the propagation zone can be therefore expressed as a function of its parameters (\(\mathrm{E_{opt}}\), \(\mathrm{D_{opt}}\)); accordingly, the penalty coefficients to be used when analysing the actual performance capacity of these measures are: \(\mathrm{e_{n}}\), to be applied to \(\mathrm{E_{opt}}\), and \(\mathrm{t_{n}}\), to be applied to \(\mathrm{D_{opt}}\). Diches and berms, on the other hand, do not directly act against rock fall energy but, strictly speaking, only on the frequency of reach \(\mathrm{Pr}\). These solutions are usually located at areas characterised by low rock fall energy and aim at reducing \(\mathrm{P_{r}}\) thanks to the \"trap\" effect produced by their depth/height, which does not allow rock blocks to jump beyond. The fundamental design parameter for ditches and berms can be therefore also defined as a characteristic dimension D, which for a ditch represents its depth, whereas for a berm its height. Based on considerations similar to those developed on the height of structural measures, the hazard mitigation takes place if:  
\[\mathrm{d}<\mathrm{D_{opt}} \tag{5}\]  
where \(\mathrm{d}\) is again the rebound height of the blocks and \(\mathrm{D_{opt}}\) is the optimal depth (height) of the ditch (berm) for ensuring safety. The performance capacity of these types of protections can thus be defined in terms of \(\mathrm{D_{opt}}\) and the penalty coefficients to be used for evaluating their current performance are the coefficients of type \(\mathrm{t_{n}}\), to be applied to \(\mathrm{D_{opt}}\).