# Critical Systems: An Exploration of Cohesion and the Moments of Distribution

## Nate Stone

### 2016

In this thesis, cohesion and its ability to affect the probability that an avalanche will occur on a conical bead pile were investigated. Cohesion was found to be related to the probability that an avalanche will occur through two universal variables, τ and σ, which were experimentally found and compared to past predictions. In order to find τ and σ, the moments of distribution were used. The moments for both small and large avalanches were calculated over a number of different cohesions. When using data for the moment calculations, it was important that there were no double drops when two beads fall at the same time. Double drops have higher impacts and a higher probability of causing an avalanche. In order to minimize the effects of double drops, only data runs with less than 2% double drops were used. As the cohesion was increased, the small avalanche moments decreased by a power law function dependent on both τ and σ. The values of τ and σ were found to be 1.34 and 4.43. The predicted values of τ and σ were 1.5 and 0.5. The large moments increased as the cohesion increased. Each of the data sets were then collapsed. The collapsed data provided a method, different from moment analysis, to determine τ. The collapsed data showed τ = 1.5.

The velocities of a falling bead were also calculated in order to determine if the beads were falling straight towards the pile and whether they were starting at the correct position. We found that the beads did have horizontal velocity and they were not falling directly onto the apex of the pile. The beads would fall within a 2cm radius of the apex of the pile. It was also found that the beads, more often than not, were starting at positions much different from the intended start. The beads were typically falling from heights that were within 1cm of the drop point.