Static Avalanches and Giant Stress Fluctuations in Silos

We propose a simple model for arch formation in silos. We show that small pertubations (such as the thermal expansion of the beads) may lead to giant stress fluctuations on the bottom plate of the silo. The relative amplitude $\Delta$ of these fluctuations is found to be power-law distributed, as ${\Delta }^{-\tau }$, $\tau \simeq 1$. These fluctuations are related to large-scale “static avalanches,” which correspond to long-range redistributions of stress paths within the silo.