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:

  • Pressure sensor development: How do we analyze and understand the new data we obtain from the pressure sensors? The data from the sensors need to be compared to data from the video and the mass data so that we understand how to process this information. We should then be able to tackle the problem of characterizing avalanches by some aspect of their dynamic behavior rather than only their size.
  • Probability of avalanche occurrence and the time between avalanches: investigating the changes in the probability distribution function as the cohesion is varied, including using scaling analysis to better understand what parts of the pile behavior are universal. Analysis by our collaborators at Illinois have recently suggested that our small avalanches cluster together in time while large avalanches recur quasi-periodically. We want to investigate the time behavior in detail, particularly how this inter-event time scales with cohesion. These questions about scaling and inter-event time lend themselves to a more mathematical treatment.
  • Video-tracking: Continuing to use the MATLAB routines for PIV analysis and particle tracking analysis. We now have velocity information about avalanches on the pile, and we have begun using the information to analyze the avalanches. Like the questions in the pressure sensor project, we need to understand what the results we are seeing mean in terms of avalanche behavior, and need to develop ways to process and understand the vast amount of information about an individual avalanche that we are now able to observe.
  • Angle of Repose: An open question in the bead pile system is how large and how frequent surface-only avalanches are. How do beads move down from the apex to the edge of the pile? By capturing an image of the pile profile between each bead drop, we are starting to answer these questions. So far, we have been analyzing select sets of images by hand to get an idea of the information they contain. Ideally, we will develop an automated video analysis for the set of images.