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Home>Research Projects>Earthquake Modeling Laboratory "Foam Lab"

Earthquake Modeling Laboratory "Foam Lab"

James N. Brune and Rasool Anooshehpoor

At the earthquake modeling laboratory, polyurethane foam (foam rubber) is used to study earthquake related problems such as fault rupture mechanism, seismic site effects and soil-structure interaction. Scale physical models of faulting are guaranteed to obey static and dynamic mechanical laws. They act as analog computers that automatically account for all of the complicated effects of seismic wave propagation and thus can be used to gain insight into possible physical processes involved. Of course, there are inherent problems of scaling laboratory models to the real Earth. Such models can nonetheless provide important insight and constraints on numerical and theoretical models.

Stick-slip fault rupture modeling apparatus of two large foam-rubber blocks

Foam-rubber is very flexible, that is, it has a low rigidity, making it is easy to produce large strains and particle motions. Since foam-rubber is light-weight, relatively large models can be constructed, enabling the scale of dynamic phenomena to be enlarged. This allows dynamic features to be more easily observed and recorded using relatively simple electronic devices.

Another view of the stick-slip fault rupture model, with photographic recorder

Great effort has been expended in rock mechanics laboratories to determine the properties of slip along interfaces between small blocks (centimeters to meters) of rock in hopes that these results could somehow be scaled up to the dimensions of rocks involved in real earthquakes (tens of kilometers or more). However, such scaling has never been justified. There are two dynamic scaling considerations not satisfied by ordinary rock mechanics experiments which are satisfied by the foam-rubber model. First, the stressing apparatus for the foam model has effectively infinite rigidity compared to the rigidity of the model, assuming that the dynamics of the model are not influenced by interaction with the stressing apparatus. Secondly, the overall dimensions of the foam rubber model are large compared to the dimension of dynamic slip pulse which propagates along the interface between the two blocks. This allows the slip pulse to propagate predominantly under the influence of conditions local to the slip pulse itself, with minimized effects of the boundaries of the model and the stressing apparatus. This corresponds better to the conditions in the earth, for which the length of slip pulse is small compared to the dimensions of the fault.

Some of the major limitations of foam-rubber modeling include:

Intrinsic Q is on the order of 10 (high damping) and cannot be controlled. This constrains the usefulness of foam-rubber modeling to wave propagation distances which are not too large compared to the wavelengths involved. Thus it is most useful to gain insight into near-source phenomena.
The fault surface friction conditions are difficult to control. The lattice of foam-rubber vesicles produces extreme roughness on a small scale (of the order of a millimeter). The coefficient of friction is on the order of 10, whereas that for rocks is of the order of 0.5. Thus to produce fault slip, the strains must be very large, of the order of 10-2, whereas in the earth the corresponding strains are of the order of 10-4. However, as long as strains are approximately linear, the difference can be adjusted for.

The 1/816 scale foam rubber model of the topography around Pacoima Dam used to study the topographic amplification during the February 9, 1971 San Fernando, California earthquake. The strong motion accelerometers, near the left abutment of the dam, recorded exceptionally large horizontal ground accelerations (peak acceleration of about 1.25 g near 10 hz). However, the location of the recording instrument on top of a steep ridge raised questions about the possible effects of topography on the recorded ground motion. But, results from the 3-D foam rubber model showed about 50 percent amplification near 6 hz (normal mode of the ridge) and a slight de-amplification near 10 hz.

Foam-rubber model of topography around Pacoima Dam, in the San Gabriel Mountains of southern California

Closeup of Pacoima Dam's representation in the model

Bibliography

Anooshehpoor, A., J.N. Brune (1989): Foam rubber modeling of topographic and dam interaction effects at Pacoima Dam, Bull. Seis. Soc. Am., vol. 79, pp 1347-1360.
Brune, J. N. and A. Anooshehpoor (1991): Foam rubber modeling of the El Centro terminal substation building, EERI: Earthquake Spectra, vol. 7, pp 45--79.
Brune, J. N. and A. Anooshehpoor (1991): Foam rubber modeling of the Lotung Large-Scale Seismic Experiment, EERI: Earthquake Spectra, vol. 7, pp 165--178.
Anooshehpoor, A., J. N. Brune (1994), Frictional Heat Generation and Seismic Radiation in a Foam Rubber Model of Earthquakes, PAGEOPH, vol. 142, No. 3/4.

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