Overturning of Freestanding Blocks Exposed to Earthquake Excitations 1: Numerical Experiment and Parameterization

Matthew D. Purvance

In Preparation 2006, SCEC Contribution #1038

The overturning responses of both symmetric and asymmetric freestanding blocks are investigated through numerical simulations. These results contribute fundamentally to failure analysis and loss estimation applied to freestanding structures/equipment or natural objects (e.g., precariously balanced rocks) exposed to ground shaking. Overturning is quantified in terms of block size, block shape, and the amplitudes of specified excitation intensity measures (IM). Blocks investigated range in height from approximately 54 cm to 3.6 m and have height-to-width ratios ranging from approximately 2.1 to 6.6. The probabilistic formulation regularizes the overturning responses when exposed to ensembles of complex ground motion time histories. Both the lower- and high-frequency amplitudes of the forcing excitation contribute to overturning. The amplitude of the lower-frequency component is parameterized as either the ratio of the peak ground velocity to the peak ground acceleration (PGV/PGA), the ratio of the spectral acceleration at 1 second to the peak ground acceleration (Sa(1)/PGA), or the ratio of the spectral acceleration at 2 seconds to the peak ground acceleration (Sa(2)/PGA). PGA is utilized to measure the high-frequency amplitude of the excitation. The overturning probability is very sensitive to variations in the block slenderness. Small blocks are found to overturn primarily as a result of the high-frequency amplitude of shaking. Tall blocks, on the other hand, require significantly larger high-frequency amplitude to overturn due to exposure to excitations with diminished lower-frequencies. The effect of asymmetry in block slenderness modestly affects the overturning response. The companion paper validates the parameterization via shake table experiments.

Citation
Purvance, M. D. (2006). Overturning of Freestanding Blocks Exposed to Earthquake Excitations 1: Numerical Experiment and Parameterization. Earthquake Engineering and Structural Dynamics, (in preparation).