A sandpile experiment and its implications for self-organized criticality and characteristic earthquake

Abstract

We have performed an experiment in which a conical sandpile was built by slowly dropping sand onto a circular disk through a funnel with a small outlet. Avalanches (sand dropping off the disk) occurred, the size and the number of which were observed. It was seen that the behavior of avalanches (frequency-size distribution) was determined solely by the ratio of grain size to disk size, which is consistent with earlier studies. We categorize the behavior into three types: (1) the self-organized criticality (SOC) type (obeying Gutenberg-Richter's law), (2) the characteristic earthquake (CE) type where only large avalanches are almost periodically generated, and (3) the transition type. The transition from SOC to CE type drastically occurs when the ratio of grain diameter to disk radius is reduced to about 0.02. The underlying mechanism to cause the transition is considered. Results of simulation by cellular automaton models, an experimental result showing that a conical pile has a stress dip near its center, and a two-dimensional simulation building up a conical pile, all suggest that the transition occurs due to a change in stress profile inside and near the surface of the pile. Although we are unfortunately not able to understand the detailed mechanism at the present stage, it seems very important to further investigate the underlying physics of the transition because it presumably provides us a clue to understand the mechanism of the periodicity of large characteristic earthquakes and may open a way for earthquake prediction.

Step‐pool stability: Testing the jammed state hypothesis

“…This behavior suggests that the bed does not rearrange itself to attain a state that is just at the limit of stability, but rather can jump to a new state that is capable of withstanding further flow increases. We believe the “jumpy” nature of the channel response, analogous to phenomena associated with critical limit states in other media [e.g., Yoshioka , 2003], contributes significantly to the variability observed in the jamming plot.…”

Self-Organized Bistability Associated with First-Order Phase Transitions

“…Instead, they found anomalously large quasi-periodic avalanches, that exceeded the expectations for large events in SOC (see, e.g. Fig.4 in [28]). The reason for this is that real sandgrains have a tendency to keep on moving once they start doing so, dragging other grains, and facilitating the emergence of huge avalanches.…”

Hydromechanical triggering of landslides: From progressive local failures to mass release

“…It can be shown that avalanche size and frequency follow a power law with exponent of close to −1 [ Hergarten , 2002]. The notion that addition of a single grain may induce avalanches with a wide range of size distributions have been confirmed in laboratory experiments using sand or rice grains [ Yoshioka , 2003; Held et al , 1990; Lörincz and Wijngaarden , 2007], however, the resulting values of power laws were typically higher (between 1.1 and 2.5) than predicted by the theoretical BTW‐sandpile model. This difference in power law values indicates that the frequency of large avalanches is lower in real systems and the redistribution mechanism in the sandpile model is too simplified, mainly due to frictional forces reducing stress release in real sandpiles [ Hergarten , 2003].…”