## 3 Methodology for Evaluating the Effectiveness of Rock Fall Protections
### Analysis of the Effectiveness of the Protection Measures
If, in general, n factors (among those listed in Tables 1 and 2) can negatively affect the performance of a protection, penalty coefficients are defined for each of them, for modelling:
* A reduction in the capacity of the protection in terms of energy and return period retention all over the threatened areas (coefficients \(\mathrm{r_{n}}\)), the energy and return period retention capacity being hereby defined as the capacity of a protection measure of preventing a given location on the slope from being affected by values of energy \(\mathrm{E>E_{m}}\) and return period \(\mathrm{T<T_{m}}\), which is not compatible with the desired mitigation effect \(\mathrm{H(E_{m},T_{m})}\);
* A reduction of the nominal energy absorption capacity \(\mathrm{E_{opt}}\) established at the time of the design (coefficients \(\mathrm{e_{n}}\));
* A reduction of the nominal effective height \(\mathrm{D_{opt}}\) established at the time of the design, preventing a given location on the slope--and, possibly, beyond--from being affected by a value of frequency of reach \(\mathrm{P_{r}}\) higher than a desired value (coefficients \(\mathrm{t_{n}}\)). The appropriate coefficients are used as a function of the type of protection measure analysed, that is, protection systems conceived to act against the detachment of blocks from the cliff, at the source area, or structural measures and topographic modifications acting directly against the rock fall trajectories, in the propagation zone. 2.1 Types of Protections, Performance Capacity and Penalty Coefficients Protection Measures at the Rock Fall Source Area  
Protection measures at the rock fall source area, such as wire mesh/cable nets, anchors and nails, aim at completely preventing the blocks from leaving the cliff (e.g., anchors, nails) or drastically reducing their paths (e.g., blocks possibly falling behind wire mesh nets). As their objective is essentially that no propagation of the blocks develops far away from the cliff, these works can be considered to act on the frequency of reach \(\mathrm{P_{r}}\) of the blocks (as they do not actually influence the failure mechanisms developing within the rock mass, responsible for the potential release of blocks). The main parameters defining their action against potential hazards are the resistance of the materials constituting the protection system and the rock cliff, i.e., the strength parameters of the elements involved in the safety proofs to be conducted when designing the system itself (e.g.,: proof of bearing resistance of the nets, proof of bearing resistance of the anchors, proof against sliding-off of blocks beneath the nets, proof of the mesh against puncturing, etc., as a function of the specific type of system). When the measure is in optimal working order, the hazard is mitigated if:  
\[\mathrm{A_{(i)}<R_{opt(i)}}\qquad\quad\mathrm{with\;i=1\,\dots\;n} \tag{3}\]  
where \(\mathrm{A_{(i)}}\) is the destabilising action of the block on the protection system, specific to proof i (among the n proofs of safety required by the specific system), and \(\mathrm{R_{opt(i)}}\) the resistance of the protection system in optimal working order to action \(\mathrm{A_{(i)}}\). The performance capacity for these measures can therefore be expressed in terms of these values of resistance \(\mathrm{R_{opt(i)}}\); the penalty coefficients defining the current performance of the system in its actual conditions are in this case the coefficients \(\mathrm{r_{n}}\), applied to \(\mathrm{R_{opt(i)}}\). As they reduce the values of materials' strength parameters (or associated resisting forces) in order to define corresponding design values to be used in the proofs of safety, it can be noticed that, in this case, the penalty coefficients act basically the same way as partial safety factors in current civil and mechanical engineering practices.