Continuously Sheared Granular Matter Reproduces in Detail Seismicity Laws

Abstract

We introduce a shear experiment that quantitatively reproduces the main laws of seismicity. By continuously and slowly shearing a compressed monolayer of disks in a ring-like geometry, our system delivers events of frictional failures with energies following a Gutenberg-Richter law. Moreover foreshocks and aftershocks are described by Omori laws and inter-event times also follow exactly the same distribution as real earthquakes, showing the existence of memory of past events. Other features of real earthquakes qualitatively reproduced in our system are both the existence of a quiescence preceding mainshocks, as well as magnitude correlations linked to large quakes. The key ingredient of the dynamics is the nature of the force network, governing the distribution of frictional thresholds.For more than a century, fracture and stick-slip frictional sliding have tried to explain the behavior of earthquakes. Brittle fracture induced by shear [1] was the most accepted model until the sixties. However, a more precise analysis of the radiated waves [2], the low amount of stress released by an earthquake in relation to the available one, the high energies needed to shear over a fractured surface, and over all, the lack of healing required to generate a second earthquake at the same location and close in time to the first one, set stick-slip sliding mechanisms as a more plausible explanation of earthquakes [3]. Despite these facts, the subcritical fracture of heterogeneous materials shows naturally a jerky behavior that seems closer to earthquake statistics than frictional sliding, which commonly displays a quasi-periodic stick-slip dynamics. Indeed, several fracture experiments [4-8] and numerical models [9, 10] have reported statistics of events following powerlaw distributions of sizes that have been compared to the the Gutenberg-Richter law [11]. The existence of aftershocks that follow the Omori law [12] are also common in fracture experiments [5][6][7][8].Concerning stick-slip frictional sliding, different laboratory experiments have analyzed the sliding dynamics between two solid blocks. From a physical perspective, studies on acrylic blocks have focused on the complex evolution of the frictional strength during the slipping process, describing the behavior as a dynamic fracture problem [13, 14]. Recent friction experiments on rocks have reported results on supershear ruptures [15] and precursory activity prior to stick-slip instabilities [16]. Precursory activity to stick-slip instabilities has been also reported in experiments shearing a layer of granular material [17]. Other relevant results on similar experimental systems include remote triggering [18], and the controlled slowing down of the dynamics [19]. However, one common limitation of many of those laboratory experiments is the fact that they show a main dynamics consisting in a quasi-periodic stick-slip behavior with a narrow distribution of sizes, which * Present address:

Quantitative earthquake-like statistical properties of the flow of soft materials below yield stress

“…We find that the ensemble probability density function of kinetic energies PðEÞ shows a robust power-law decay over more than three decades in E ( Fig. 2a): PðEÞ $ 1=E ϵ , where ϵ ¼ 1 þ ðb=1:5Þ ¼ 1:6 ± 0:1; consistent with the Gutenberg-Richter law for the distribution of earthquake amplitudes 28 , and is close to the value of ϵ obtained in other experiments 2,6,10 . The value of the Gutenberg-Richter exponent b for our system (¼ 0:90 ± 0:15) is very close to the most accepted value for earthquakes (b $ 1), but slightly greater than the reported values for other fracture experiments (b $ 0:60) 8,9,11 .…”

“…To cut through the complexity of such a large-scale reorganization phenomenon, there have been significant recent efforts in mimicking earthquakes in controlled laboratory experiments by studying the deformation and failure in various solid materials under external loads. These include fracture of rock samples under compression [1][2][3][4][5][6] , fracture of artificial rock of sintered polystyrene beads 7 , compression of mesoporous silica ceramics 8 , avalanches in wood compression 9 and stick-slip instabilities under shear in a twodimensional assembly of polymer disks 10 . A recent study 11 demonstrates that charcoal samples damped with ethanol show avalanche events similar to earthquakes due to the internal stresses generated from ethanol evaporation.…”

Micro‐Seismic Monitoring of a Shear Fault Within a Floating Ice Plate

“…In the purpose of exploring the deformation regimes of a natural fault that accommodate slip through a wide range of micro to macro‐ruptures, this experimental set‐up offers interesting advantages: (1) the annular geometry allows sliding over very large distances (up to meters), hence the total imposed slip can be several times the fault's length, implying that the fault goes through several loading/seismic cycles; (2) the fault enters a slowly evolving, quasi steady‐state; (3) because of the geometry of the experiment and the boundary conditions applied the normal stress is low, resulting only from geometrical mismatch between the two sides of the fault; (4) a wide range of torque drops is indeed observed, so that a non‐periodic, complex deformation is the norm. Similar features have also been obtained for granular systems (e.g., Hartley & Behringer, ; Lherminier et al, ; Miller et al, ), but we here reproduce them for a brittle, cohesive medium.…”

Experimental Investigation on Time-Frequency Characteristics of Microseismic Signals in the Damage Evolution Process of Coal and Rock

“…In previous studies, it was confirmed that the MS parameters, such as amplitude, event number and frequency, which could reflect the quantity, size and direction of microcrack propagation, had a great relevance on damage degree of coal and rock [20][21][22][23]. The actual MS signals contain a great amount of noise whose interference often results in the difficulty of the signal processing.…”

“…where, K III is the stress intensity factor of mode-III crack and ν is the Poisson's ratio. According to Formulas (21)- (23), with the increase of stress, the energy release rate increases, which can lead to the widening of MS signals spectrum. This was consistent with experimental results that the high-frequency and low-frequency signals both increased and the band width widened at the late loading stage.…”