Dynamical stress in force chains of granular media traveling on a bumpy terrain and the fragmentation of rock avalanches
The paper discusses dynamical granular fragmentation in rock avalanches suggesting that the stress may increase along a sequence of force chains formed by the granular material. As a starting point, on the base of Bond's relation, the author studies the energy necessary to break an intact grain into smaller particles. Moreover, the author considers the granular medium inside a rock avalanche as a thermalized ensemble of grains with inter-granular impacts due to thermal-like fluctuations in particle speeds, and he also investigates the role of static force chains in the process of fragmentation. All these models show evident discrepancies between observed and predicted final grain sizes, suggesting that static chains are insufficient to explain the observed fragmentation. Due to this, the author proposes a simple model of dynamic fragmentation based on the consideration of force chains on a bumpy topography. It is assumed that force chains form continuously within a rock avalanche and produce a pile of spherical particles representing a force chain. The spheres collide in the vertical direction with neighbors, and dissipate the energy upon each collision. The motion equations are written for each particle along the direction perpendicular to the terrain, but the terrain topography is assigned with a parametric equation for height. Then, the author derives the motion equation for frictional materials with constant friction coefficient. To introduce a bumpy topography, simple sinusoidal fast-changing perturbations are superimposed on the basic exponential slope path. In order to estimate the fragmentation rate, the paper focuses on the compressive stress between particles. Only one single pile is considered, that is, the paper neglects interactions between various piles. To estimate the breakage probability of grains along a pile, the compressive stress through each grain is calculated, and this quantity is compared to the stress necessary for grain breakage. The calculations show correlation between breakage locations and topographic bumps. Fragmentation efficiency is found to increase with both amplitude and wave number of the topographic bumps, reaching a limit behavior.
scientific article; zbMATH DE number 5963703