Influence of Monitoring Time on Rockfall Magnitude-Frequency Uncertainty

ABSTRACT: Rockfall along mountainous roadways poses a hazard to transportation infrastructure, commercial traffic, and the public. Lidar scanning and photogrammetry are powerful tools to create high-resolution point cloud models of rock slopes and quantify change, facilitating rockfall volume estimation. The empirical magnitude-cumulative frequency (MCF) distribution of rockfall defines the number of rockfalls of various sizes that occur for a certain study area over a given period of time. The time required for the MCF curve fit parameters to stabilize varies for different slopes depending on source area size and rockfall frequency. Four Colorado rock slopes with remote-sensing-based rockfall inventories were studied to determine the typical length of monitoring necessary to produce an MCF power law that accurately reflects long-term slope rockfall activity. Bootstrapped confidence intervals on the MCF fit parameters were used to quantify the power law variability for each slope over time (as additional monitoring periods are added) and with the sequential addition of rockfalls to the database. The results of this research include guidelines for minimum rock slope monitoring time and database size to accurately constrain the rockfall magnitude-frequency relationship. 1. INTRODUCTION Empirical distribution fitting is commonly used to model natural, difficult to predict phenomena in the geosciences. Many natural processes follow an empirical power-law to describe the relative frequency of their size or energy over a certain range, including earthquakes, forest fires, landslides, rockfall, and volcanic eruptions (Corral & González, 2019). In rockfall hazard analysis, an inverse relationship of decreasing rockfall frequency with increasing size has been consistently observed from rockfall records (Benjamin et al., 2020; Guerin et al., 2020). A power law model fit to this magnitude-frequency distribution is commonly used to predict the exceedance probability of a given rockfall volume (Dussauge-Pessier et al., 2002; Graber & Santi, 2022; Hungr et al., 1999; Janeras et al., 2023). Use of this model as a predictive tool is dependent on the accuracy and completeness of the rockfall inventory used to define the power law.