Lubricated soft granular shear explaining an origin of slow-slip phenomena's statistics: Experimental study using fault gouge analogue of spherical hydrogel particles

What makes slow and fast slip phenomena exhibit different statistics, in frequency distribution and temporal rate of moment? [1–3] Here, we experimentally demonstrate an exponential distribution of moment and a proportionality between moment and duration, as slow-slip phenomena. These statistics are realized by our novel rotary shear system using spherical particles floated on a liquid surface. By varying porosity and material of the particle layer, we suggest that low friction and/or low rigidity of particles distinguish slow-slip phenomena from fast slip. Our results imply that the amount and temporal rate of moment is limited by the strain localization and the fraction of pore or ductile phase.

We developed a quasi-two-dimensional rotary shear system using fault gouge analogue lubricated with fluid matrix. A granular layer of spherical particles (~ 4 mm in diameter) was prepared floating on a transparent heavy liquid (density 2.8 g/cm³). We recorded and tracked particle movements while measuring torque in real-time. The porosity of the layer was varied between 0.18 and 1 (pure liquid), using roughly 3900 particles at maximum. These measurements were conducted individually with soft, low-friction hydrogel particles and hard glass beads. A rotating cylinder connected to a torque meter via a torsion spring imposed shear on the layer at 0.6˚/s, 0.01 mm/s on the surface. The same particles were glued onto the cylinder.

Our findings can be summarized in the following three points:

(1) A decrease in porosity results in the transition from stable shear flow to stick-slip behaviors. Using hydrogel particles, the stress drop during slip events follows a scale-limited exponential distribution, irrespective of porosity. Similarly, using glass beads, exponential distributions are observed. Considering previous experimental studies confining dry frictional particles with power law [4–6], low friction by our lubrication might suppress force chain networking across particles and scale-invariant event generation.

(2) The moment of the hydrogel particle layer, calculated from measured torque and visually tracked slip area, also follows an exponential distribution. The characteristic moment increases with porosity decrease (pressure increase). The decrease in porosity is also accompanied by shear band localization. This localization is, thus, caused by compression of a higher porous shear band. The decrease in pore fluid and ductile phase could explain the seismic transition zone from slow to fast earthquakes on updip and downdip side, respectively.

(3) A nearly linear moment-duration scaling with an exponent of 1.0–1.3 is exhibited by hydrogel at any porosity, while glass beads exhibit an exponent of 1.3-2.3. This might correspond to the earthquake scaling: linear for slow-slip phenomena, and cubic for fast ones [2]. Moreover, for soft hydrogel particles, porosity decrease leads to the maximum moment rate, as expected to slow earthquakes [3]. In our analogue system, the maximum moment rate is limited by the minimum width of the localized shear band, suggesting similar mechanisms in natural slip systems.

[1] Chestler & Creager (2017) JGR
[2] Ide et al. (2007) nature
[3] Ide & Beroza (2023) PNAS
[4] Korkolis et al (2021) JGR
[5] Geller et al (2015) PRE
[6] Dalton & Corcoran (2001) PRE