Toppling Analysis of the Echo Cliffs Precariously Balanced Rock
Toppling analysis of a precariously balanced rock (PBR) can provide insight into the nature of ground motion that has not occurred at that location in the past and, by extension, can constrain peak ground motions for use in engineering design. Earlier approaches have targeted 2D models of the rock or modeled the rock–pedestal contact using spring‐damper assemblies that require recalibration for each rock. Here, a method to model PBRs in 3D is presented through a case study of the Echo Cliffs PBR. The 3D model is created from a point cloud of the rock, the pedestal, and their interface, obtained using terrestrial laser scanning. The dynamic response of the model under earthquake excitation is simulated using a rigid‐body dynamics algorithm. The veracity of this approach is demonstrated through comparisons against data from shake‐table experiments. Fragility maps for toppling probability of the Echo Cliffs PBR as a function of various ground‐motion parameters, rock–pedestal interface friction coefficient, and excitation direction are presented. These fragility maps indicate that the toppling probability of this rock is low (less than 0.2) for peak ground acceleration (PGA) and peak ground velocity (PGV) lower than 3 m/s^2 and 0.75 m/s, respectively, suggesting that the ground‐motion intensities at this location from earthquakes on nearby faults have most probably not exceeded the above‐mentioned PGA and PGV during the age of the PBR. Additionally, the fragility maps generated from this methodology can also be directly coupled with existing probabilistic frameworks to obtain direct constraints on unexceeded ground motion at a PBR's location.
Additional Information© 2016 Seismological Society of America. Manuscript received 29 May 2016; Published Online 13 December 2016. We thank James Brune, Richard Brune, Glenn Biasi, and Matthew Purvance for the results from the shake-table experiments and for sharing their insights and experiences with precariously balanced rocks (PBRs). We would also like to thank David Phillips of UNAVCO for supporting laser scanning of the Echo Cliffs PBR, as well as the field crew that included D. Haddad, D. Rood, A. Limaye, W. Amidon, D. Lynch, and E. Pounders, and also G. Bawden and S. Bond who helped process the data. In addition, we thank Robert Graves, Thomas Hanks, and Patricia McCrory of U.S. Geological Survey (USGS), Jack Baker, and an anonymous reviewer for providing reviews of earlier versions of this article. This research project has been supported by the National Science Foundation (NSF Award EAR-1247029), the USGS, and the Southern California Earthquake Center (SCEC). Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.
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