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Soil-Structure System Identification of Millikan Library North–South Response during Four Earthquakes (1970–2002): What Caused the Observed Wandering of the System Frequencies?

Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, California 90089-2531 mtodorov{at}usc.edu

An application is presented of a recently proposed system identification method for buildings that takes into account the effects of soil-structure interaction and the coupling of the horizontal and rocking motions of the foundation. The method gives the uncoupled structural fixed-base frequency f₁ and rigid-body rocking frequency f_R using data only from two horizontal sensors (at base and roof). The fixed-base frequency is estimated from the wave travel time through the structure, the apparent system frequency from Fourier analysis, and the rocking frequency from a relation between these three. The case study is Millikan Library in Pasadena, California. Results are shown for four earthquakes between 1970 and 2002. The method makes it possible to quantify the degree to which the observed changes (wandering) of its resonant frequencies have been due to changes in the structure alone. The results show that (1) both f₁ and f_R are amplitude dependent, (2) significant permanent reduction of frequency occurred over the years, 22% for f₁ and 11% for the apparent frequency f_1,app, mostly caused by the San Fernando earthquake of 1971, while (3) the changes of f_R have been amplitude dependent and recoverable. (4) During the San Fernando earthquake, both f₁ and f_R dropped, respectively, by 24% and 18%, resulting in 21% drop of f_1,app. (5) After this earthquake, the changes in the observed resonant frequencies, which are those of the system, have been due to a much larger degree (4–5 times) to changes of f_R than to changes of f₁. (6) The small permanent changes in f₁ that appear to have occurred after the San Fernando earthquake cannot be deciphered with certainty because of the small number of earthquake records available for this analysis since 1971. Records from the period 1988 to 2002, when released, can be used in future to refine and verify these trends.

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