Résumé
In the absence of thermal agitation, granular materials are often found in a metastable state in the sense that a partial flow of grains may occur in response to a small perturbation. The flow is transient in nature and stops as the grains get jammed in a new metastable state. The prediction of the onset and propagation of such transient granular flows and their arrest is crucial to practical issues such as risk assessment with respect to landslides and granular avalanches in geotechnics, silo discharge and plug flow in pipelines. The fragile nature of metastable states leads to a fluctuating behavior with marked spatial correlations and broad distributions of the number of mobilized grains, flow lifetimes or resulting macroscopic deformations. In this talk, I discuss the stochastic nature of these dynamic events and their spatial correlations in two different systems by mean of extensive contact dynamics simulations. The first system is a silo in the jamming regime, i.e. a silo with an opening sufficiently small that the flow stops in finite time. The temporal behavior will be analyzed with the outlet size R as control parameter. Our numerical data are consistent with a stationary Poisson process: 1) for the sequence of passing grains with the flow rate Q(R) as parameter, and 2) for the sequence of jamming events with the mean number ⟨N⟩(R) of passing grains between consecutive jams as parameter. This feature reveals the absence of memory in the process as a consequence of chaotic dynamics in the fluidized zone above the outlet. We show that the function ⟨N⟩(R) is dictated by the Beverloo law at small R and by a diverging mean flow lifetime ⟨T ⟩ as a critical opening is approached. The second system that will be considered in this talk is a granular bed subjected to gradual rotation. The principal stress directions rotate with respect to the free surface until a surface avalanche is initiated. However, as long as the slope angle is below the avalanche angle, the granular layer undergoes a gradual plastification as a result of local instabilities and rearrangement events. I will focus for this system on the spatial correlations. We introduce an order parameter defined as the density of critical contacts, i.e., contacts where the friction is fully mobilized. The spatial correlation of critical contacts reveals the occurrence of ʻʻfluidizedʼʼ clusters which exhibit a power-law divergence in size at the approach of the avalanche limit. At the same time, an increasingly large number of grains are overloaded in the sense that they are found to carry a stress ratio above the Coulomb yield threshold of the whole packing. Using this property, a coarse-graining length scale is introduced at which all stress ratios are below the packing yield threshold. This length increases with the slope angle and jumps to a length comparable to the depth of the granular bed at an angle below the avalanche angle. This transition coincides with the onset of dilation in the packing. We map this transition into a percolation transition of the overloaded grains.