Granular Materials and Criticality:
Predicting Earthquakes and Avalanches

Susan Lehman

Complex systems throughout our world display critical behavior, where there is no simple way to predict the effect which will result from a cause. A butterfly flapping its wings in Africa may or may not cause a hurricane in Florida. A few trades by one person could or could not crash the market. A small change in the strain or stress along a fault line might cause an earthquake, but it might not. The next grain of sand dropped on a pile might or might not start an avalanche. There is no way to tell what a small change will do. Most systems which display this sort of critical behavior are difficult to study in a laboratory due to their size or due to our inability to change their parameters. Our project however deals with an easily accessible physical system – a bead pile. By replacing non-uniform light grains of sand with uniform, slightly larger beads, we can study the dynamics of avalanches under consistent conditions.

Granular systems like sand piles behave in some ways like a liquid with an ability to flow and in some ways like a solid with a stable fixed structure if undisturbed. Although they are neither solids nor fluids, the analysis tool of scaling developed for equilibrium fluid systems near a critical point also work in non-equilibrium granular systems. We conduct experiments on a conical bead pile and measure the resulting distribution of avalanche sizes when using uniform 3mm spheres (“beads”) of various compositions and densities (glass, steel, stainless steel, and zirconium). We have been collaborating with Dr. Karin Dahmen, a theorist at Illinois, who has predicted that clustering from cohesion would change the scaling in the distribution. Our experiment applies an external magnetic field for the bead pile that will induce cohesion among the beads. Such cohesion could cause a larger probability of large avalanches—an effect that is seen in the distribution of earthquake sizes.

We have recently added new data collection capabilities to the pile in order to measure the duration and the spatial extent of individual avalanches. A high speed camera above the pile now records large avalanches as they happen, and we have developed some automated techniques to track the motion on the pile from the movies. We have also added pressure sensors to the base of the pile in order to directly sense the changes in force as an avalanche occurs on the surface of the pile.

Some of the projects we are currently working on include: