Mechanical and Civil Engineering Seminar
The Gutenberg-Richter law is a power-law in which the majority of tectonic deformation comes from the largest earthquakes; it has fat tails that are difficult to deal with since most of the action comes from infrequent events that are poorly understood; most of them happened long ago and there are no good recordings of shaking. Epidemics and wars are other examples of phenomena that are described by power-law statistics. In contrast, most probabilistic seismic hazard analyses (psha) imply that extreme events are too infrequent to significantly affect the overall hazard. In this talk I am interested in building collapse and I will concentrate on shaking close to large earthquakes. I show that high-frequency near-source ground motions are log-normally distributed and reasonably described with standard actuarial statistics. Log-normal statistics describe the occurrence of independent events, such as auto accidents or heart attacks. In contrast, low-frequency ground motions are a difficult-to-characterize power law.
I also show that the collapse of tall buildings can be predicted from peak ground velocity and displacement (pgv, pgd). For 20-story steel-moment-resisting-frame buildings, pgd's greater than m combined with pgv's greater than m/s can cause collapse. While tall buildings have not experienced these conditions; they will in the future. Simulations of the 1906 San Francisco earthquake indicate a strong potential for collapse in urban parts of the Bay Area. That 1906-like earthquakes will collapse tall buildings seems incompatible with the widespread belief that these systems are designed to withstand the largest shaking in two millennia.
Currently, psha measures the size of an earthquake using magnitude, but (pgv, pgd) is not well described by magnitude. The amplitude of fault slip is a better parameter; doubling the slip, doubles long-period motions. Slip distributions are best described by power-laws. The current use of log-normal statistics is significantly underestimating the probability that long-period buildings will fail in future large earthquakes.