Estimates of rare seismic hazard are essential for the resilience of critical infrastructure and facilities. However, these estimates are highly uncertain at long return periods due to the lack of observed earthquake records. Several ground motion prediction equations have been proposed to close this gap and estimate rare seismic demands; however, these models were developed based on more moderate earthquake records and can yield physically unrealizable ground motions when extrapolated to long return periods. For this reason, seismologists have proposed using precariously balanced rocks (PBRs) as a way to constrain rare seismic hazard. PBRs are a type of fragile geologic structure whose upright existence indicates that a seismic event powerful enough to cause the structure to overturn has not yet occurred. PBRs are individual or stacks of freestanding rocks that tend to respond in rigid body modes, such as rocking and sliding, when subjected to earthquake loads. The behavior of these freestanding structures is very sensitive to small changes in geometry, position, and ground motion characteristics. As a result, reliable probabilistic relationships for the seismic response of freestanding structures are lacking. To this end, this thesis aims to rigorously evaluate and identify a robust probabilistic relationship between the intensity of a ground motion and the dynamic behavior of freestanding structures, including both rocking and sliding demands, such that PBRs can be used to constrain seismic hazard. The dynamic response of freestanding structures is modeled analytically via two-dimensional equations of motion. Various ground motion intensity measures are evaluated in both scalar and vector forms to identify an optimal predictor of structural response. After thorough analysis, a vector combination of Cumulative Absolute Velocity and Response Spectrum Intensity is selected. This relationship is then used in a case study to demonstrate the applicability of the vector intensity measure in a PBR analysis and comparison with current seismic hazard in the New Madrid Seismic Zone.
Advisor: Christine E. Wittic
