Rockfall Magnitude-Frequency Relationship Based on Multi-Source Data from Monitoring and Inventory

Abstract

Quantitative hazard analysis of rockfalls is a fundamental tool for sustainable risk management, even more so in places where the preservation of natural heritage and people’s safety must find the right balance. The first step consists in determining the magnitude-frequency relationship, which corresponds to the apparently simple question: how big and how often will a rockfall be detached from anywhere in the cliff? However, there is usually only scarce data on past activity from which to derive a quantitative answer. Methods are proposed to optimize the exploitation of multi-source inventories, introducing sampling extent as a main attribute for the analysis. This work explores the maximum possible synergy between data sources as different as traditional inventories of observed events and current remote sensing techniques. Both information sources may converge, providing complementary results in the magnitude-frequency relationship, taking advantage of each strength that overcomes the correspondent weakness. Results allow characterizing rockfall detachment hazardous conditions and reveal many of the underlying conditioning factors, which are analyzed in this paper. High variability of the hazard over time and space has been found, with strong dependencies on influential external factors. Therefore, it will be necessary to give the appropriate reading to the magnitude-frequency scenarios, depending on the application of risk management tools (e.g., hazard zoning, quantitative risk analysis, or actions that bring us closer to its forecast). In this sense, some criteria and proxies for hazard assessment are proposed in the paper.

High-Temporal-Resolution Rock Slope Monitoring Using Terrestrial Structure-from-Motion Photogrammetry in an Application with Spatial Resolution Limitations

“…We observed variations in the scaling exponent from 0.5 to 1.3 on a month-to-month basis, with one anomalous value over 2.5. This variability is generally consistent with the findings of Janeras et al [45], who showed a fluctuation of the scaling exponent from about 0.25 to 0.81 at one location and from about 0.38 to 0.78 at another location, although their rockfall database monitoring intervals were in the order of a year rather than monthly. Both of these findings show that rockfall hazard is not constant through time over all time intervals.…”

Lidar-Derived Rockfall Inventory—An Analysis of the Geomorphic Evolution of Rock Slopes and Modifying the Rockfall Activity Index (RAI)

“…As shown in Figure 7, cumulative rockfall magnitude-frequency plots relatively linearly on a log-log graph over three (Sites B and D), four (Site C), or five (Site A) orders of magnitude, an effect that is similarly observed in rockfall inventories collected by other researchers [20][21][22][23][24][25]34,36]. This observation indicates that rockfall at the study sites follows a power-law magnitude-frequency distribution, as observed frequently in nature.…”

“…The statistical analysis of an inventory of past mass-wasting events is a rigorous method to inform models that project the future likelihood of mass-wasting [17]. Masswasting events, such as landslides and rockfalls, have been shown to self-organize into a power-law magnitude-frequency distribution [18][19][20][21][22][23][24]. Researchers have recently compiled lidar-based inventories of hundreds to thousands of rockfall events over multi-year periods [20][21][22][23][24][25][26] that have demonstrated power-law magnitude-frequency relationships over several orders of magnitude.…”

“…Masswasting events, such as landslides and rockfalls, have been shown to self-organize into a power-law magnitude-frequency distribution [18][19][20][21][22][23][24]. Researchers have recently compiled lidar-based inventories of hundreds to thousands of rockfall events over multi-year periods [20][21][22][23][24][25][26] that have demonstrated power-law magnitude-frequency relationships over several orders of magnitude. Some authors have recommended frameworks for informing hazard assessment methodologies using their lidar-based rockfall inventories [26].…”

“…Mass-wasting events, such as landslides and rockfalls, have been shown to self-organize into power-law magnitude-frequency distributions [18][19][20][21][22][23][24] with a lower-end rolloff related to sampling resolution for rockfall [35,36], and an upper-end roll-off related to slope morphology, vertical relief, and the temporal extent of the surveys [34,35]. For this study, we use the negative power-law scaling relationship between the cumulative frequency of events (F) and the event magnitude (V), given by the following equation: We also use the rockfall inventory to calculate annual failure rate and average failure depth for cells associated with each RAI class.…”