The existence of the unjamming transition plays a large part in the interest in granular materials. The latter are jammed at rest and can sustain some load, but if a threshold shear stress is exceeded, part of the material starts to flow. In response to some change in external applied forces, the macroscopic activity of a granular system is related to the evolving geometry of its contact network and to the nature of the contacts. It leads to complex behaviors of great interest for industrial and natural processes. In nature, geological processes like landslides or rock avalanches involve an unjamming transition of granular media. Other natural events like earthquakes are often seen as interacting elements that discharge collectively when they reach a trigger threshold. The corresponding models are closely related to avalanches models.
For free surface flows of granular systems under the action of gravity, the unjamming transition above a critical shear stress is evidenced by the existence of an angle of maximum stability of a pile: θM. It is the angle at which the flow starts; the angle of the pile relaxes then towards the smaller angle of repose. Many studies have been devoted to these angles, but most of them focus on the succession of avalanches in a rotating drum, or on a continuously fed pile. In both cases, the heap is built by the successive avalanches, giving a specific contact network geometry to the bulk. An alternative method for investigating avalanche dynamics is to incline gently an undisturbed granular bed in the gravity field.
The exploration of the dynamical response of an inclined granular packing before the avalanche starts is of the greatest interest, as it allows a study of the dynamical transition from a static packing to a flowing one and brings information that may be helpful for the prediction of the occurrence of the avalanche. Obviously, the capability of predicting the probability of occurrence is an important motivation for this area of research.
Freshly prepared piles filling a box were used to study the re-arrangements at the surface before the first avalanche. First, small rearrangements implying only a few grains are detected. The size and the rate of these rearrangements increase with the inclination angle. At some stages, large-amplitude and quasi-periodical events are observed. These events, are called as precursors, consist of collective motions of grains. More recent results confirmed that the precursors are bulk phenomena and allowed to interpret these events as reorganizations of the weak-contact sub-network occurring in the packing. This is in agreement with computer simulations of inclined 2D packings that revealed the occurrence of intermittent rearrangements of grain contacts in the bulk. However, beyond the observation of experimental and numerical evidence of the existence of precursors to avalanches, these regular events have never been explained theoretically.
This oscillating behavior is reminiscent of stick-slips originating from the difference between static and dynamic frictions in frictional system submitted to an increasing load at a small rate. Regular precursors are observed before the onset of frictional motion, and in the mechanical response of amorphous media as metallic glasses and granular materials, before the rupture. More generally, physical systems responding through abrupt events to slowly increasing stresses are rather abundant; earthquakes have already been held up; plastic bursts in crystals are another example. They often can be seen as the depinning of an interface under an external field. Within the waiting intervals between the fast, abrupt events, a slow restructuring of the pinning field can occur; stresses may be relaxed through competing processes, such smooth responses can have effects on the abrupt events properties. These slow processes may be important for intermittency.
Beside the numerical simulations of 2D and 3D inclined granular packings, various experimental methods have been used to expose the secrets of these strange happenings: direct observation of the surface or the side of the box with a camera, X-ray imaging technique, interferometric technique based on diffusive wave spectroscopy, and acoustic methods.
The part of the acoustic wave energy transports through the contact network and the elastic beads of the medium, the probing methods based on the monitoring of acoustic signatures are sensitive to changes in the elastic properties of the granular layer. This class of methods is consequently interesting because it provides sometimes unique, and often complementary, information compared to optical methods.
Passive acoustic probing consists in recording the acoustic emissions originating from the grain and contact local rearrangements. After being to generated by grain motion, the vibrations propagate via the grain contact network and reach the walls of the vessel. By listening to the sound pulses generated by the medium itself during precursors the latter are easily detected with a time resolution of less than a millisecond. These acoustic emissions will become of higher amplitude with the angle of inclination and they have relatively strong energy levels compared to the background noise.
It is worth noticing that low-frequency sound can be generated on some dunes when sand is sheared, a phenomenon known as the song of dunes. It is striking to see that the related acoustic emissions are also asymmetric, similarly to precursor emissions. Yet, no formal link between these two processes has been established to our knowledge.
Conclusion
To conclude, acoustic methods are powerful tools for the understanding of the destabilization leading to the critical state. Sensitivity to the packing elasticity variations with a millisecond time resolution can be achieved. Low-frequency linear propagation allows us to probe the modifications of the average elasticity of the medium. Acoustic measurements give direct information on the bulk mobilization, but the measurement volume is relatively large compared to that of one grain, and the effort required for interpretation can be important. It is thus necessary to combine them with more local characterizing methods. We generally associate them with optical methods, but a combination with numerical simulations is also very promising.
Note: This work is partly presented at International Conference on Physics June 27-29, 2016 New Orleans, USA.
