Toppling analysis of the Echo Cliffs precariously balanced rock

Abstract

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.