Communities living at the foot of the Alps need a way to predict the occurrence of avalanches for timely evacuation, but monitoring the entire Alpine range is impossible. Fortunately for those near the Alps, the study of granular materials has allowed scientists to move mountains into labs and use small, contained systems (like piles of rice) to simulate real-world avalanche conditions. Granular materials, by definition, are conglomerates of discrete visible particles that lose kinetic energy during internal collisions; they are neither too small to be invisible to the naked eye, nor too big to be studied as distinct objects.1 The size of granular material situates them between common objects and individual molecules.
While studying extremely small particles, scientists stumbled upon an unsettling contradiction: the classical laws governing the macroscopic universe do not always apply at microscopic scales. For example, Niels Bohr sought to apply classical mechanics to explain the orbits of electrons around nuclei by comparing them to the rotation of planets around stars. However, it was later discovered that an electron behaves in a much more complicated way than Bohr had anticipated. At its size, the electron gained properties that could only be described through an entirely new set of laws known as quantum mechanics.
Though granular materials do not exist at the quantum level, their distinct size necessitates an analogous departure from classical thought. A new category of physical laws must be created to describe the basic interactions among particles of this unique size. Intuitively, this makes sense; anyone who has cooked rice or played with sand knows that the individual grains behave more like water than solid objects. Scientists are intrigued by these materials because of the variation in their behaviors in different states of aggregation. More importantly, since our world consists of granular materials such as coffee, beans, dirt, snowflakes, and coal, their study sheds new light on the prediction of avalanches and earthquakes.
The physical properties of granular flow vary with the concentration of grains. At different concentrations, the grains experience different magnitudes of stress and dissipate energy in different ways. Since it is hard to derive a unifying formula to describe granular flows of varying concentrations, physicists use three sets of equations to fit their states of aggregation, resembling the gaseous, liquid, and solid phases. When the material is dilute enough for each grain to randomly fluctuate and translate, it acts like a gas. When the concentration increases, particles collide more frequently and the material functions as a liquid. Since these particles do not collide elastically, a fraction of their kinetic energy dissipates into heat during each collision. The increased frequency of inelastic collisions between grains in the analogous liquid phase results in increasing energy, dissipation, and greater stress. Finally, when the concentration increases to 50% or more, the material resembles a solid. The grains experience significant contact, resulting in predominantly frictional stress and energy dissipation.1
Avalanches come in two types, flow and powder, each of which requires a specific combination of the gas, liquid, and solid granular models. In a flow avalanche, the descending layer consists of densely packed ice grains. The solid phase of granular materials best models this, meaning that friction becomes the chief analytical aspect. In a powder avalanche, particles of snow do not stick together and descend in a huge, white cloud.2 The fluid and solid models of granular materials are equally appropriate here.
Physicists can use these avalanche models to investigate the phenomena leading up to a real-world avalanche. They can simulate the disturbance of a static pile of snow by constantly adding grains to a pile, or by perturbing a layer of grains on the pile’s surface. In an experiment conducted by statistical physicists Dr. Daerr and Dr. Douady, layers of glass beads of 1.8 to 3mm in diameter were poured onto a velvet surface, launching two distinct types of avalanches under different regimes decided by the tilt angle of the plane and the thickness of the layer of glass beads.3
For those of us who are not experts in avalanches, there are a few key points to take away from Daerr and Douady. They found that a critical tilt angle exists for spontaneous avalanches. When the angle of the slope remained under the critical angle, the size of the flow did not grow, even if a perturbation caused an additional downfall of grains. Interestingly, when the angle of the slope was altered significantly, the snow uphill from the perturbation point also contributed to the avalanche. That means that avalanches can affect higher elevations than their starting points. Moreover, the study found that the angle of the remaining slope after the avalanche was always less than the original angle of the slope, indicating that after a huge avalanche, mountains would remain stable until a change in external condition occured.3 A. Often, a snow mountain with slopes exceeding the critical angle can remain static and harmless for days, because of the cohesion between particles.
Situations become complicated if the grains are not completely dry, which is what happens in real snow avalanches. In these scenarios, physicists must modify existing formulas and conduct validating experiments to predict the behaviors of these systems. Granular materials are not limited to predicting avalanches. In geophysics, scientists have investigated the relation of granular materials to earthquakes. For instance, one study used sound waves and glass beads to study the effects of earthquake aftershocks.4 Apart from traditional modeling with piles of rice or sand, the understanding of granular materials under different phases paves the way for computational modeling of large-scale natural disasters like avalanches and earthquakes. These studies will not only help us understand granular materials themselves, but also help us predict certain types of natural disasters.
- Jaeger, H. M., Nagel, S. R., and Behringer, R. P. Granular Solids, Liquids and Gases. Rev. Mod. Phys., 1996, 68, No.4, 1259-1273.
- Frankenfield, J. Types of Spring and Summer Avalanches. http://www.mountain-guiding.com/avalanche/info/spring-types.html (accessed Oct. 29, 2015).
- Daerr, A. and Douady, S. Two Types of Avalanche Behaviour in Granular Media. Nature, 1999, 399, 241-243.
- Johnson P. A., et al. Effects of acoustic waves on stick–slip in granular media and implications for earthquakes. Nature, 2008, 451, 57-60.