How do you test the behavior of different soil structures in an earthquake? Obviously, large earthquakes don’t happen often, and they certainly don’t happen on cue. The solution, of course, is to model earthquakes in a laboratory environment. And that’s exactly what is being done by the Center for Geotechnical Modeling at the University of California, Davis. Since it’s not economical to simulate the forces of an earthquake on fullsize soil structures such as one would find beneath a real bridge or large building, physical models of much smaller size are used. In Figure 1, for example, is a model of the San Francisco Bay Area Rapid Transit transbay tube that was recently tested in Davis1.

Figure 1. The large geotechnical centrifuge at UC Davis was used to study the seismic response of the San Francisco Bay Area’s BART transbay tube and surrounding spoils.

The problem with using small soil models, however, is that material properties of the soil do not scale the same way as the physical dimensions of the model scale. In fact, in order to respond in the same manner to earthquake forces as full-size physical environments, the force of gravity on a smaller model needs to be scaled upward by the same factor that the size of the model is scaled downward from the real-world environment that is being modeled2.

That is, in order to accurately model the gravity loading of a model that is 1/100 the size of the problem in real life, the weight of everything in the model would need to be increased to 100 times its original weight. So how do you simulate a 100-times increase in the force of gravity on an object? You put the object on the end of a centrifuge arm and take it for a spin (Figure 2). Then, if you want to see how the object responds to an earthquake, you shake it while it’s spinning. That’s what’s going on at the UC Davis Center for Geotechnical Modeling. The soil and structure model is placed on a shake table that is affixed to the end of the centrifuge arm. As the centrifuge spins, the table pivots to align itself perpendicular to the arm of the centrifuge.

Figure 2. The model to be tested and the shake table are mounted to a pivoting container at the end of the centrifuge arm. A hydraulic rotary joint in the middle passes high-pressure oil onto onboard accumulators that provide high pressure and high flow to the servo valve.

The rotational velocity of the centrifuge is increased until the desired outward force is reached, at which time a hydraulic cylinder applies the shaking action. The shaking motion is controlled by an electro-hydraulic motion controller under direction from a remote personal computer that can instruct the motion controller to “play back” the shaking motion as recorded from past real earthquakes. The UC Davis lab typically tests models that are between 1/30 and 1/60 the size of their real-life counterparts, but the lab is not studying what happens to buildings or other structures themselves when subjected to earthquakes. Instead, the researchers are focused on learning about how the soils behave and how structures interact with the soil. The soil used for testing is regular soil or sand so that the material properties of the model soil will match the real world. This is possible because the relative size of the sand or soil particles is still sufficiently small compared to the size of the model structures. Getting the stresses correct within the soil is the most important part of getting the soil behavior correct.

Simulation Requirements

The hydraulics that shake the model are mounted on the centrifuge arm (Figure 3). The shaking table that they act on is similar to those used in other laboratory research, except that it needs to operate in an accelerated G-field environment. Earthquake frequencies that are produced in real life typically range from less than 1 to around 10 Hz or more, but the shaking frequency needs to be scaled along with the G level in the model environment.