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.

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.

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.

So, the frequency of the hydraulic shaking motion that must be produced in the centrifuge environment will typically be on the order of 30 Hz to 300 Hz. Since real earthquake signatures as well as test waveforms are being reproduced, the hydraulic controls need to be able to respond very quickly to arbitrary inputs, using closed-loop control to make sure that the motion adequately follows the target inputs. “The motion controller responds by ‘playing back’ recorded stimulus,” said Dan Wilson, Associate Director of the Center for Geotechnical Modeling at UC Davis. “We typically use sine waves to check out the system and then move on to reproduce actual motions recorded in earthquakes such as the 1989 Loma Prieta or 1995 Kobe earthquakes, or just about any other recorded strong ground motion of interest.”

Recently, the UC Davis team upgraded the motion controller they use on their 1-m-radius centrifuge shaker. “Our old hydraulic controller was a homemade device that we couldn’t maintain,” said Wilson. “We wanted a controller that was highly reliable, capable of producing extreme, high-frequency waveforms under closed-loop control, and one that is easy to program for different applications. Plus, we wanted one that would interface easily to a PC running LabVIEW.” The researchers use the LabVIEW program by National Instruments to do filtering and scaling of the earthquake files, as well as collect data from instruments during the experiments.

The shaker on the 1-m radius centrifuge operates at 3000 psi with a peak force of around 4500 pounds, shaking a payload of around 150 pounds. It shakes with a peak stroke of ±6 mm and peak velocity of 0.3 m/s at frequencies up to 400 Hz (not all simultaneously). The high-frequency motions put a stress on hydraulic system components and controls. The frequencies are beyond the resonant frequencies of the oil column and the servo valve being used, and the mass that is being driven is very large compared to the reaction mass available. Plus, the payload (soil sample) can go from something very stiff to very soft during the testing (wet soil can liquefy during an earthquake). This means that the closed-loop controls will be receiving feedback that changes nonlinearly and rapidly during the simulation run.

#### Selecting the Motion Controller

To upgrade the controls in the earthquake simulator, the UC Davis team selected an RMC70 Series motion controller from Delta Computer Systems of Battle Ground, WA. When running a simulation, the controller uses position feedback that it gets from a linear variable displacement transducer (LVDT) to close the position control loop. The motion controller is mounted in a box on the wall outside the centrifuge, and the LVDT and load cell feedback signals and the valve coil drive signal run over slip rings to the actuator on the centrifuge. The UC Davis team has been using Delta’s RMCTools software package to generate motion commands to check out the hardware. The tuning wizard was used as the starting point for all of the tuning. In the case of the shaker, the motion open loop is run at the highest frequencies.

The auto-tuning provided baseline PID coefficients used for feedback control at slower speeds. Typically, the UC Davis team starts out the system with a new model by doing linear motion at relatively slow speeds. Once the system is stabilized, the motion is switched to produce sine waves, and then the researchers switch to using more complex waveforms in proving out the hardware. Full simulation runs are then done using the filtered earthquake waveforms that are downloaded from the PC to the RMC using Modbus TCP/IP over Ethernet. One of the early challenges that needed to be overcome by the team was the ability to manage the high motion frequencies that were being produced. At the frequencies at which they were operating, some of the position feedback was out of phase with the motion.

The team needed to filter out higher-frequency feedback signals in order to keep the motion under control. The new control system has been used so far primarily for a study on using biological grouting methods for liquefaction remediation. In this work, researchers harness naturally occurring biological processes to create cemented sands in the hope they can reduce the risk of liquefaction. The project is a challenge to control because the researchers want to recreate the same motion in models that fully liquefy (i.e. become very soft) to models that are fully cemented (i.e. very stiff). Interesting things that the team has learned include how to tune a system that is very nonlinear in its response. The properties of the system change as it shakes, and soil changes to slurry. Getting the system to respond well under both sets of conditions is a challenge.