Rocking Blocks Stability under Critical Pulses from Near-Fault Earthquakes Using a Novel Energy Based Approach

Following the seminal work of Housner, a novel energy based critical pulse theoretical model is derived to assess the seismic stability of rocking rigid blocks under single pulses from near-fault earthquakes. It is shown that overturning is conditional on the availability of sufficient kinetic energy in the exciting pulse and on the inception of rocking. The theoretical model is shown to be in good agreement with discrete element method numerical simulations for similar blocks of sizes 0.5, 1, and 20 m. Similitude rules are established to scale between block sizes and pulse types and tested successfully. The results agree with available experimental data. The proposed stability chart approach provides a practical and simple alternative to the presentation and study of the stability and overturning of blocks published by others in the frequency spectrum domain. For any given rigid block or inverted pendulum structure the model or normalized stability charts provide a method to determine the characteristic period and peak acceleration required for overturning and by extension to identify the critical content of the dominant pulse of a given earthquake signal. Alternatively, the approach could be used in archaeoseismology to identify the characteristics of the dominant pulse content of past earthquakes based on their impacts on various historical and heritage structures.