Variability in the Natural Frequencies of a Nine-Story Concrete Building from Seconds to Decades

Since 2001, the Southern California Seismic Network has archived continuous waveform data from strong-motion station CI.MIK in Caltech Hall (formerly Millikan Library)—a nine-story reinforced concrete building. Simple spectral analysis of this 20 yr record reveals that the building’s fundamental frequencies have increased gradually by 5.1% (east–west) and 2.3% (north–south), with larger long-term variability up to 9.7% (east–west) and 4.4% (north–south). This finding is unexpected, as previous analysis of forced vibration tests and strong-motion records has shown that between 1968 and 2003 the fundamental frequencies decreased by 22% (east–west) and 12% (north–south), largely attributed to minor structural damage and soil–structure system changes from major earthquakes. Today, the building’s apparent structural stiffness is comparable to what it was in 1986, before the Whittier Narrows earthquake. Using data from earthquakes and forced vibrations, we also document the building’s nonlinear dynamic elasticity, which is characterized by a rapid softening (decrease in apparent frequencies) at the onset of strong motion, followed by a slower, log–linear recovery trend over the scale of minutes. This nonlinear behavior does not appear to have changed with time.