Seismicity in sheared granular matter

Aghil Abed Zadeh, Jonathan Barés, Joshua E. S. Socolar, and Robert P. Behringer

Phys. Rev. E 99, 052902 – Published 20 May 2019

Abstract

We report on experiments investigating the dynamics of a slider that is pulled by a spring across a granular medium consisting of a vertical layer of photoelastic disks. The motion proceeds through a sequence of discrete events, analogous to seismic shocks, in which elastic energy stored in the spring is rapidly released. We measure the statistics of several properties of the individual events: the energy loss in the spring, the duration of the movement, and the temporal profile of the slider motion. We also study certain conditional probabilities and the statistics of mainshock-aftershock sequences. At low driving rates, we observe crackling with Omori-Utsu, Båth, and waiting time laws similar to those observed in seismic dynamics. At higher driving rates, where the sequence of events shows strong periodicity, we observe scaling laws and asymmetrical event shapes that are clearly distinguishable from those in the crackling regime.

Received 13 November 2018
Revised 11 April 2019

DOI:https://doi.org/10.1103/PhysRevE.99.052902

Physics Subject Headings (PhySH)

Granular materials

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Aghil Abed Zadeh^1,*, Jonathan Barés², Joshua E. S. Socolar¹, and Robert P. Behringer^1,†

¹Department of Physics & Center for Non-linear and Complex Systems, Duke University, Durham, North Carolina 27708, USA
²Laboratoire de Mécanique et Génie Civil, Université de Montpellier, CNRS, Montpellier, France

^*aghil.abed.zadeh@duke.edu
^†Deceased.

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 99, Iss. 5 — May 2019

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Stick-slip event statistics for loading speed $c = 0.1$ mm/s. (a) Schematic of the experiment at loading speed $c$ . (b) Time series of the spring energy $E$ (blue) and radiated power $P$ (black). (c) An enlarged view of a single peak in $P$ with starting time $t_{i}$ , duration $D_{i}$ , and size $S_{i}$ . The horizontal line indicates the threshold used for event detection. (d) PDF of the event sizes. The blue dashed line is a fit to the form of Eq. (1) with $β = 1.22 \pm 0.07$ and $S_{max} = 6.1 \times 10^{- 4} \pm 0.7 \times 10^{- 4} J$ . Error bars show 95% confidence intervals. (e) Average event shape for $D \in [0.01, 0.02]$ s. The black solid line is computed from the experimental data, and the blue dashed line is a fit to Eq. (2) with $σ = 1.09 \pm 0.02$ . (f) Event duration as a function of event size. Gray dots are individual events; the black line is the binned average. The dashed line shows a power-law corresponding to $1 / γ = 0.79$ .
Reuse & Permissions
Figure 2
Waiting time law, productivity law, Omori-Utsu law, and Båth's for $c = 0.1$ mm/s. (a) Waiting time law: PDF of the waiting time between two consecutive events larger than $S_{c}$ , rescaled by $T_{c}$ , the average waiting time between events larger than $S_{c}$ . The dashed line is a fit to the form of Eq. (3) with $ν = 1.10 \pm 0.08$ and $u_{max} = 3.04 \pm 0.15$ . Inset: The number of AS's as a function of the MS energy, $S_{MS}$ . Blue dots are from experiment; cyan crosses are obtained from random permutations of the experimental events, and the black dashed line is obtained from Eq. (4). (b) The rate of AS events corresponding to a MS of energy $S_{MS}$ . Time is rescaled by $N_{AS} (S_{MS})$ . The straight dashed line with slope 0.7 is a guide to the eye. Inset: Ratio between MS size, $S_{MS}$ , and size of the largest AS. Black dots are experimental data; cyan crosses are obtained from a randomly mixed sequence of events.
Reuse & Permissions
Figure 3
(a) PDF of the event energy, $P (S)$ , for loading speeds $c \in [0.02, 100]$ mm/s. Inset: Logarithmic decay of the exponent $β$ with increasing $c$ . The fit for $10^{- 1} < c < 20$ mm/s has a slope $- 0.55 \pm 0.06$ . (b) PDF of the waiting time between two consecutive events larger than $S_{c} = 10^{- 6}$ J for different $c$ . Inset: Evolution of the upper cutoff, $Δ t_{max}$ [see Eq. (3)] as a function of $c$ . The fitted power law for $c < 20$ mm/s shows an exponent of $- 0.75 \pm 0.03$ .
Reuse & Permissions
Figure 4
(a) Evolution of avalanche duration, $D (S)$ , for loading speeds $c \in [0.02, 100]$ mm/s. Inset: Evolution of the exponent, $1 / γ$ . (b) Average shape ${\bar{P}}_{D}$ for events with $D_{i} \in [0.01, 0.02] s$ . Insets: Evolution of the exponent, $σ$ , and asymmetry parameter, $a$ , for event shapes as a function of $c$ showing that events develop left-shifted asymmetry as $c$ increases. In all graphs, error bars stand for 95% confidence level and vertical gray lines show $c = c_{c} = 20$ mm/s.
Reuse & Permissions

Physical Review E

covering statistical, nonlinear, biological, and soft matter physics