Stability of clogging arches in a silo submitted to vertical vibrations

Abstract

We present experimental results on the endurance of arches that block the outlet of a two-dimensional silo when subjected to vertical vibration. In a recent paper [C. Lozano et al., Phys. Rev. Lett. 109, 068001 (2012)], it was shown that the arch resistance against vibrations is determined by the maximum angle among those formed between each particle in the bridge and its two neighbors: the larger the maximum angle is, the weaker the bridge. It has also been reported that the breaking time distribution shows a power-law tail with an exponent that depends on the outlet size, the vibration intensity, and the load [I. Zuriguel et al., Sci. Rep. 4, 7324 (2014)]. Here we connect these previous works, demonstrating the importance of the maximum angle in the arch on the exponent of the breaking time distribution. Besides, we find that the acceleration needed to break an arch does not depend on the ramp rate of the applied acceleration, but it does depend on the outlet size above which the arch is formed. We also show that high frequencies of vibration reveal a change in the behavior of the arches that endure very long times. These arches have been identified as a subset with special geometrical features. Therefore, arches that cannot be broken by means of a given external excitation might exist.

Dynamics of breaking arches under a constant vibration

“…It was previously reported [4] that the time needed to break an arch (t b ) follows a probability distribution displaying a power law decay P(t b ) ∝ t −α b . Incidentally, this means that if the exponent α is smaller than two, the first moment of the distribution does not converge and the average breaking time t b will depend on the size of the sample.…”

“…The experimental set-up is the one used by Lozano et al [4]. It consists of a two dimensional silo mounted on top of an electromagnetic shaker (see Fig.…”

“…It is known that under a sustained vibration, arches can be shattered alleviating the problem [2][3][4]. In that scenario flow becomes intermittent, alternating between clogs and flow intervals.…”

“…In previous works [4,15], it was reported that the angle φ between adjacent beads of an arch (see Fig. 1) is an important variable to understand the unclogging process as it affects the robustness of the mechanical structure.…”

“…The first one has been widely studied since 2001 [5] observing that the clogging probability is constant over time yielding an exponential distribution of the flowing times [6][7][8][9][10][11]. The unclogging process, however, has shown temporal dependence and the distribution of breaking times is compatible with a power law decay [1,2,4]. The origin of this is still not fully understood but it could be related with aging, creeping motion or other complex slow dynamics [12].…”