Materials and Methods
Ailsa Craig micro-granite and thermal
stressing
We used Ailsa Craig micro-granite (ACM) from the island of Ailsa Craig
in the Firth of Clyde, Scotland. ACM is an extremely rare type of
silica-unsaturated, alkali-rich microgranite, known as Blue Hone
(Meredith et al., 2012). As received from the quarry, no pre-existing
microcracks are detectable either by optical or scanning electron
microscopy (Meredith et al., 2005; 2012). Porphyritic in texture with a
groundmass of mean grain size 250 μm, ACM contains sparsely distributed
microphenocrysts (up to 1.5 mm) of alkali feldspar (Odling et al.,
2007). Clint et al. (2001) found it to have extremely low porosity
(<< 1 %) and permeability (1.5 x
10-23 m2 at 10 MPa effective
pressure), indicating that the small amount of pre-existing pores are
predominantly unconnected (e.g., see Fig. 3 top left in Meredith et al.,
2012). These properties make ACM ideal both for its main commercial use
as the running surface of curling stones, and for the purposes of this
study. We chose ACM for two main reasons: (i) its small grain size (250
μm) and (ii) its virtually crack-free nature. The former is essential to
ensure a statistically significant number of grains (>10
grains per diameter) in the small (3 mm diameter x 9 mm long)
cylindrical samples, and so to ensure that such small samples are
representative of the rock as a whole. The latter is essential to allow
comparison between two extreme end-members: (i) an as-received control
sample with the lowest possible (to our knowledge) pre-existing crack
density, and (ii) a second sample (from the same small block) containing
a thermally-induced crack network imprinted over the nominally
crack-free microstructure, thus increasing its heterogeneity compared
with the initially crack-free (untreated) sample.
To introduce a network of micro-cracks, one sample was heated slowly to
600 °C prior to deformation. Thermal stressing is one of the key
fracture-generating mechanisms in crustal rocks and is an effective
method for introducing micro-fractures into rock samples. Heating ACM to
elevated temperatures (>500 °C) induces significant,
permanent micro-crack damage, evident from photomicrographs (Meredith et
al., 2012) and up to 50% and 30% reduction in P- and S- wave
velocities respectively (Clint et al., 2001). Scanning electron
micrograph observations (Odling et al., 2007) show that heating ACM to
900 °C causes the formation of a permanent micro-crack network with
average aperture of 0.3 μm formed by tensile failure, with each crack
nucleating halfway along a previous one to generate fracture
intersections of primarily T-shaped geometry. The thermally-induced
crack network is not discernible in our μCT data because this aperture
is less than one tenth the length of one pixel (2.7 μm). Due to the
partial volume effect, micro-cracks with an aperture smaller than half a
pixel are not visible (e.g., Voorn et al., 2013).
Experimental apparatus, sample assembly and loading
protocol
Synchrotron x-ray microtomography (μCT), in combination with x-ray
transparent pressure vessels (e.g., Fusseis et al., 2014; Renard et al.,
2016; Butler et al., 2017), allow the microstructural evolution of
deforming rock samples to be imaged directly, non-invasively andin-situ during an experiment. This provides a critical advantage
over conventional deformation experiments, where the evolution of
microscopic deformation cannot be inferred from post-test analysis of
the microstructure because it is heavily overprinted by extensive damage
caused during the macroscopic rupture process. Even in the case where
conventional experiments are stopped immediately prior to macroscopic
failure, overprinting occurs when the hydrostatic and differential
stresses are released during extraction of the sample from the
steel-walled pressure vessel, resulting in permanent damage and
hysteresis. In-situ x-ray μCT imaging overcomes both these
issues, as well as providing detailed microstructural information about
the temporal evolution of damage accumulation at a much higher temporal
resolution. A single time-resolved experiment is equivalent to tens of
conventional experiments with ex-situ , post-experiment analysis,
and has the virtue that the same sample is observed at each time-step
rather than a suite of samples, removing the issue of sample
variability.
In our experiments, each sample of ACM underwent tri-axial deformation
to failure. The experiments were conducted using a novel, miniature,
lightweight (<1.3 kg) x-ray transparent tri-axial deformation
apparatus Mjölnir’, developed and tested at the University of Edinburgh.
Mjölnir, named for the hammer of Thor, the Norse god of thunder,
accommodates samples of 3 mm diameter and up to 10 mm in length and is
designed to operate up to confining pressures of 50 MPa and axial stress
in excess of 622 MPa (Butler et al., 2017). For this study, Mjölnir was
installed on the μCT rotation stage at the PSICHE beamline at SOLEIL
Synchrotron, Gif-sur-Yvette, France (Figure 2a,b). Two cylindrical
samples of ACM, one heat-treated and one untreated were cored using a
diamond core drill and the ends ground flat and parallel to achieve 3 mm
outside diameter and 9 mm length, compared to the typical grain size of
250 μm. Even though this sample diameter is very small (required to
obtain high-resolution μCT images), the small grain size means that
there are more than 10 grains per diameter, ensuring that such small
samples are representative of the rock as a whole. The sample was
assembled between the two pistons, jacketed with silicone tubing (3.18
mm internal diameter and 0.79 mm wall thickness), and protected from the
confining fluid using twisted wire loops to seal the jacket against the
piston (Butler et al., 2017). The pressure vessel was lowered over the
sample assembly and fixed into place. A confining pressure of 15 MPa was
then applied and maintained during the test. A hydrostatic starting
pressure condition was achieved by simultaneously increasing the axial
pressure to match the confining pressure. Delivery of the pressurizing
fluid, deionized water, to the hydraulic actuator and pressure vessel
was achieved using two Cetoni neMESYSTM high pressure
syringe pumps operated with QmixElementsTM software.
Experiments were conducted at room temperature under nominally dry
conditions. A reference μCT scan was acquired at zero differential
stress to obtain the initial state of the sample prior to loading. The
sample was then loaded to failure at a constant strain rate of 3 x
10-5 s-1 in a step-wise manner, with
steps of 20 MPa to start with, decreasing to 10 MPa from 70% of the
failure strength and then 5 MPa once the sample started to yield (Figure
2c). At each step the stress was maintained and a μCT volume acquired.
To accommodate the full sample length at maximum resolution, three
sequential scans were acquired at different positions along the length
of the sample and then stacked. For each position the corresponding
projections that comprised the full length of the sample were
tessellated and merged to create a single projection used for
reconstruction of the whole sample in one μCT volume. Each full set of
scans was acquired in approx. 10 minutes. For each sample, 15 sets were
acquired during loading with an additional set acquired after the main
failure. For the heat-treated sample, this included one set at peak
differential stress of 185 MPa. This μCT volume contained the incipient
fault at the critical point of failure, and the sample failed
immediately upon continuation of the loading procedure. The untreated
sample reached a peak stress of 182 MPa but failed before it could be
scanned at this stress. The last pre-failure scan was at 177 MPa (97%
of the critical failure stress, \(\sigma_{c}\)).
The differential stress is \(\sigma=\ \sigma_{1}-\ \sigma_{3}\),
where \(\sigma_{1}\) is the axial stress (the product of the measured
ram pressure and the difference in area between the ram and the sample
cross-section) and \(\sigma_{3}\) is the radially-symmetric confining
pressure. Axial sample strain was calculated as\(\epsilon=\delta L/L_{0}\), where δL is the change in
length of the sample between the starting μCT volume and the volume of
interest and \(L_{0}\) is the initial length of the sample. It was
obtained directly from the reconstructed μCT volumes by measuring the
length change of the rock core between two fixed locations in each
volume.