GoKawiilExperimental set-up
A biaxial apparatus, CrackDyn, was used to perform the experiments (Fig. 1a). The apparatus housed two PMMA plates (40 × 10 × 1 cm and 45 × 10 × 1.8 cm). Experiments were conducted on PMMA rather than natural rocks because it provides three main advantages for scaling laboratory observations to natural fault systems. First, owing to its lower elastic stiffness compared with rocks, the state-evolution slip distance, L, and cohesive zone size, X c , are smaller in PMMA. As a result, a laboratory-scale PMMA fault is dynamically representative of a much larger natural fault, whereas a laboratory rock fault essentially remains of the same scale as its natural counterpart. Second, the reduced elastic properties and fracture energy, G c , of PMMA ensure that nucleation lengths, ℓ c and ℓ ∞ , remain smaller than the total fault dimension in the experiment, which is rarely the case in rocks, in which nucleation patches can be comparable with or larger than the laboratory fault. Finally, the birefringent properties of PMMA allow for photoelastic visualization, enabling direct observation of nucleation growth and subsequent rupture propagation using high-speed imaging.
The plates were characterized by a static Young’s modulus, E, of 3 GPa and a Poisson’s ratio, ν, of 0.35. A normal load was applied by three vertical pistons by means of steel sample holders. The pistons were supplied by a Enerpac P141 hydraulic pump. Similarly, a shearing load was applied by a single horizontal piston. This piston was supplied by a Top Industrie PMHP-35-1000 hydraulic pump. The force applied by each piston was recorded by a Scaime K13 load cell at 500 Hz. Local strains were recorded by 13 350-ohm strain-gauge rosettes (Micro-Measurements C5K-06-S5198-350-33F) located 3 mm from the sample–sample interface. The strain gauges recorded at 2 MHz and were amplified by a factor of 10 by Elsys SGA-2 MK2 amplifiers. Ten PHILTEC model D100-E2H2PQTS displacement sensors were fixed across the sample–sample interface and recorded the local displacement with a recording frequency of 2 MHz. Thirteen Brüel & Kjær Type 8309 accelerometers were glued horizontally approximately 30 mm from the sample–sample interface and recorded at 2 MHz. These signals were amplified by a NEXUS conditioning amplifier 2692. Finally, an EFFILUX EFFI-LINE3-WTR-600-000-POL-PWR-C light source was used to shine linearly polarized light through the sample. This light then passed through a second linear polarizer before reaching a Phantom TMX 6410 high-speed camera, which recorded 1,280 × 32 pixels at 1 MHz. Considering that PMMA is a birefringent material, this allowed for the use of photoelasticity to track changes in stress across the sample–sample interface27,37,38,45. A piezoelectric sensor attached to one of the PMMA samples was used as a trigger for an oscilloscope (Picoscope 4224A), which generated a TLL-like signal that triggered the camera and allowed for the synchronization of the other acquisition systems.
Experimental approach
Experiments were begun by applying 100, 150, 200, 250 or 300 bar nominal normal stress (that is, the pressure indicated on the analogue gauge of the pump supplying the vertical pistons). Next, the shear stress was increased by setting a constant flow rate, 3 cm3 min−1, on the pump supplying the horizontal piston. These conditions were kept constant until enough slip had been accumulated such that the displacement sensors were out of range (approximately 0.5 mm). A 1.3 × 0.3 × 10-cm stopper was placed between the lower-most PMMA sample and the horizontal piston. By adjusting this stopper before the experiment such that it was in either a raised or a lowered position, the local loading conditions could be altered such that a wider variety of events could be produced. Each of the five normal stresses were tested with both stopper positions, resulting in ten total experiments and 94 dynamic events.
Data treatment
As the strain gauges were set up in a quarter-bridge configuration, the strain, ε, could be found for the ith strain gauge as,
$${\varepsilon }_{i}=\frac{-4{U}_{i}}{{U}_{{\rm{ex}}}\left({J}_{{\rm{f}}}{J}_{{\rm{amp}}}\left(1+\frac{2{U}_{i}}{{U}_{{\rm{ex}}}{J}_{{\rm{amp}}}}\right)\right)},$$ (2)
in which U i is the voltage reading of the individual strain gauge, U ex is the excitation voltage, J amp is the amplification gain and J f is the gauge factor of the strain gauge.
In this three-strain-gauge rosette, the strain gauges were oriented at 45° from one another, such that the principal strains were then found as
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