GEOLOGICAL AND ENVIRONMENTAL CONSTRAINTS ON THE NEGATIVE POWER LAW SCALING OF ROCKFALLS, YORKSHIRE, UK

A large body of evidence within the research literature indicates that mass movements follow a negative power law scaling in their magnitude-frequency distributions over several orders of magnitude. Questions remain as to: (1) Whether this relationship holds for the entire range of the magnitude-frequency distribution. The existence of a rollover in the distribution for smaller events has been the topic of much discussion in the research literature with authors regarding it is a geophysical property of mass movements or as caused by data censoring of smaller magnitude events. (2) The effect that different geological and environmental boundary conditions have on constraining the power law. This research makes use of an ongoing sea cliff monitoring project at Boulby, UK to answer these questions. Monthly surveys using terrestrial laser scanning (TLS) over a period of 7 yrs provides one of the most comprehensive datasets for rock fall in existence. Here we demonstrate that the negative power law scaling holds over six orders of magnitude from 0.01m3 up to 1000 m3 with a characteristic rollover in the distribution for smaller failures. The rollover for the Boulby dataset occurs for rock falls that are three orders of magnitude smaller than other mass movements reported in the research literature and supports the view that it is the result of data censoring rather than a geophysical property inherent to mass movements. Furthermore, we can conclude that our TLS method has a resolution that allows the identification of events from as small as 0.01 m3 to those involving the entire cliff face. Previous research demonstrates that the scaling parameter associated with the slope of the negative power law varies considerably according to regional differences in geology, morphology, hydrology, and climate. At Boulby, the cliffs are composed of horizontally interbedded shales, sandstones, and carbonates allowing for detailed investigation into the geological controls on rock fall occurrence under a wide range of environmental conditions. Stratifying the data in this way gives insight into the constraining influence that these factors have on the magnitude-frequency of rock falls in the area. For example, our results indicate that a decrease in the strength of a rock mass has the effect of steepening the magnitude frequency relation when plotted on logarithmic axes. To date, no project has quantified the geological and environmental constraints on the negative power law scaling of mass movements in this way. Such data will be useful for models of landscape evolution and as a management tool for coastal erosion defences.