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Flying circus of physics

Nimitz Freeway collapse

Wednesday, October 01, 2014

 

Nimitz Freeway collapse
Jearl Walker  www.flyingcircusofphysics.com
October 2014  In 1989, minutes before the start of the third game of the baseball World Series in Oakland, California, an earthquake of magnitude 7.1 erupted 100 kilometers away. When the seismic waves reached the Oakland-San Francisco area, collapsing structures killed 67 people and did extensive damage. Perhaps the most dramatic damage occurred on a long stretch of the Nimitz Freeway: an upper deck fell onto a lower deck, crushing vehicles and motorists. Obviously the upper deck collapse was due to the severe oscillations produced by the seismic waves, but why was the collapse of the upper deck restricted to that certain length of the freeway, with no collapse along the rest of the freeway which was almost identical in construction?

https://www.youtube.com/watch?v=zGFtcJI8MiM

https://www.youtube.com/watch?v=w3MhymxLS60 Warning: some of the video is explicit in showing injuries.

The Nimitz Freeway collapse was confined to the stretch built on a loosely structured mudfill, which underwent liquefaction (or fluidization) during the shaking. That is, when the particles in the mudfill were shaken, the average distance between them increased and the mudfill became more fluid (it could flow) than solid. With the mudfill in a fluid state, the seismic waves had a much greater effect than in the surrounding regions where the freeway was anchored in rock deposits.

We can measure how devastating seismic waves can be in at least two ways.

Maximum speed of oscillations. We can calculate the maximum speed that the waves gave to the ground particles as they made the particles oscillate. In the mudfill regions, the maximum speed was at least five times what it was in the rock-deposit regions. Thus, the ground shake was much more severe in the mudfill regions than in the rock-deposit regions.

Resonance. We can determine the resonant frequencies of the deck sections of the bridge. Those sections can oscillate both horizontally (due to longitudinal waves) and vertically (due to transverse waves) in certain frequency ranges. If the sections are shaken at one of those frequencies, the oscillation of the section builds. You do something similar with a child in a playground swing. The swing will swing with a certain frequency of oscillation. If you repeatedly push on the child with that frequency, the extent of swinging (the amplitude) increases. The frequency matching and resulting increase in amplitude is said to be resonance. For the bridge sections, the resonant frequencies for horizontal oscillations ranged from 1.6 to 4.5 hertz and the resonant frequency for vertical oscillations was 2.5 hertz. Seismograph recordings of the seismic waves that hit the region showed that the greatest ground oscillations were in the frequency range of 2 to 5 hertz. Thus, the bridge sections were shaken in resonance, and the oscillation amplitudes quickly built up to the point where the support structures failed.

For both reasons, greater maximum oscillation speed and resonance, the bridge sections were shaken so severely that they collapsed.

References
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Journal reference style: author, title, journal, volume, pages (date)
· Hough, S. E., P. A. Friberg, R. Busby, E. F. Field, K. H. Jacob, and R. D. Borcherdt, “Sediment-induced amplification and the collapse of the Nimitz Freeway,” Nature, 344, 853-855 (26 April 1990)

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