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.