## 5 Discussion and Conclusions  
Quantifying rockfall hazard and risk, as well as the design of rockfall mitigation structures, require information about the falling block volumes (and mass) and their fragmentation during motion. Information on rockfall volumes and fragmentation can be gathered from comprehensive records or through surveying fallen blocks along known rockfall trajectories. However, these methods present challenges where rockfall records are scarce and surveys are not feasible. Rockfall trajectory models in recent years have successfully represented the fragmentation of rockfalls, matching the volume distribution along the rockfall path. This is an important step forward for enhanced rockfall hazard assessments and protection design; however, input information about the fragmented rockfall distribution is still required. A method to estimate fragmented rockfall volume distributions, and fragmented volume-frequency relationships, is therefore needed at locations where rockfall records are scarce or non-existent. This paper presents a method to estimate the fragmented rockfall volume-frequency distribution (relative frequency) in the absence of rockfall records or fallen block surveys. The method takes advantage of photogrammetric techniques to build 3-dimensional surface models of rockfall sources for virtual structural mapping of discontinuities. DFN realizations are developed based on the mathematical representation of structure orientation and spacing variability. The DFN's assume fully persistent discontinuities to define discrete blocks. The volumes of these blocks are used to calculate the DFN fragmented rockfall volume-frequency distribution. This method is based on the hypothesis that fragmentation in strong rocks (Strong to Extremely Strong rocks characterized by Unconfined Compressive Strengths over 50 MPa) will tend to occur through weak planes and by growth of non-persistent discontinuities as the in situ blocks detach, fall, bounce, and roll. This implies that other breakage mechanisms in strong rocks (e.g., breakage of intact rock bridges due to high-energy impacts and abrasion) would have less influence on the fragmented volume distribution of rockfalls, and can be neglected for the purpose of dimensioning rockfall protection structures. The method is tested in this paper at two limestone rock cliffs in the Canadian Cordillera, the Tornado Mountain site and Site S042. The photogrammetry and virtual structural mapping information is representative of the information that is typically available for practical engineering applications. The information available required input of expert judgment when building some of the PDF's to represent the structure orientation and spacing. This included the limited number of observations of dip, dip direction, and spacing for some of the discontinuities, which required selecting shapes for the PDF's based on previous experience. Although this introduces a source of bias, it provided for testing the method under practical constraints commonly encountered in engineering applications. Fragmented rockfall volume distributions obtained through DFN realizations were compared against blocks surveyed along the known rockfall trajectories and toe of talus slopes. These comparisons were made at two scales (in histograms) and provided good approximations, with average errors between 0.02 and 0.08 (probability) and maximum errors between 0.16 and 0.29. These results suggest that the hypothesis that fragmentation in strong rocks will tend to occur through weak planes and by growth of non-persistent discontinuities is an adequate approximation. A statistical evaluation of the hypothesis would require validation at additional locations. Comparison of volume-cumulative relative frequencies between DFN calculated volumes and measured observations highlighted how the number of blocks surveyed and the limited observation period can bias the representation of these relationships. This is a consequence of anchoring the relative distribution to the pair (lowest volume: 1.0).