Physical properties and brittle strength of thermally cracked granite under confinement

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH: SOLID EARTH, VOL. 118, , doi: /2013jb010340, 2013 Physical properties and brittle strength of thermally cracked granite under confinement Xiao-Qiong Wang, 1 Alexandre Schubnel, 2 Jérôme Fortin, 2 Yves Guéguen, 2 and Hong-Kui Ge 1 Received 7 May 2013; revised 17 September 2013; accepted 26 November 2013; published 26 December [1] Effects of thermal crack damage on the rupture processes of a fine-grained granite were investigated under triaxial stress, under water (wet) and argon gas (dry) saturated conditions, and at room temperature. Thermal cracking was introduced by slowly heating and cooling two samples of La Peyratte granite up to 700 ı C, which were compared to two intact specimens. For each rock sample, a hydrostatic test was first carried up to 90 MPa effective pressure (5 MPa constant pore pressure). The samples were then deformed to failure at a constant strain rate of s 1, at 30 MPa effective pressure. Our results show that (1) permeability of heat-treated specimens was 4 5 orders of magnitude larger than that of intact specimens at low effective mean pressure; (2) nevertheless, at our experimental conditions ( s 1 ), thermal cracking had no significant influence on the brittle strength; (3) similarly, no obvious water weakening effect was observed; (4) however, with increasing stress, elastic anisotropy appeared at lower differential stress in heat-treated specimens than in intact ones, but close to failure, the magnitude of P wave anisotropy was approximately the same for both types of specimens; (5) acoustic emission hypocenter locations and P wave velocity anisotropy in the basal plane demonstrate that strain localization started right at the onset of dilatancy for heat-treated specimens, later in the intact specimens; and (6) inverting wave velocities for crack density, we show that failure was reached for vertical crack densities of 0.35 for dry specimens and possibly 0.5 for water-saturated specimens. Citation: Wang, X.-Q., A. Schubnel, J. Fortin, Y. Guéguen, and H.-K. Ge (2013), Physical properties and brittle strength of thermally cracked granite under confinement, J. Geophys. Res. Solid Earth, 118, , doi: /2013jb Introduction [2] In 1965, Walsh [1965a, 1965b, 1965c] published a set of three papers that first provided the conceptual basis of much of our understanding of the influence of cracks on elastic rock deformation. A key point is that the dominant influence on the effective elastic properties of rocks comes from cracks, not pores [Guéguen and Kachanov,2011].Fluids also exert significant mechanical and chemical effects on the properties of rocks. Water weakening, for instance, is such that the brittle strength of a rock is generally reduced in the presence of water, as the result of water adsorption, lower surface energy, subcritical crack growth, and stress corrosion [Atkinson and Meredith, 1987; Costin, 1987; Baud et al., 2000; Brantut et al., 2013]. 1 Unconventional Natural Gas Institute, China University of Petroleum, Beijing, China. 2 Laboratoire de Géologie, CNRS UMR 8538, Ecole Normale Suprieure, Paris, France. Corresponding author: X.-Q. Wang, Unconventional Natural Gas Institute, China University of Petroleum, 18 Fuxue Rd., Changping, Beijing, China. (wxq4526@gmail.com) American Geophysical Union. All Rights Reserved /13/ /2013JB [3] Many studies have concentrated on the effect of crack damage on elastic and transport properties, often by using thermally cracked material [Fredrich and Wong, 1986; Darot and Reuschlé, 2003; Vinciguerra et al., 2005; Nara et al., 2010; Ougier-Simonin et al., 2011a, 2011b; Wang et al., 2012; Faoro et al., 2013]. Some years ago, Friedman et al. [1979] heated Charcoal granodiorite to 1000 ı C, and then deformed the thermally cracked samples at confining pressure of 50 MPa, which turned out to be as strong as an unheated sample deformed at the same pressure. Similar behavior was observed in Cuerbio basalt heated to 750 ı C. However, Friedman et al. [1979] also observed that in unconfined experiments, the uniaxial compressive strengths (UCS) of thermally cracked granodiorite samples could be reduced by as much as a factor of 4 compared to that of the unheated samples. Many studies on UCS of rock as function of temperature confirm this overall weakening trend related to thermal cracking on brittle strength in the absence of confinement. For instance, Nasseri et al. [2007, 2009] demonstrated the decrease of fracture toughness K Ic due to increasing thermal damage in unconfined Chevron notched Brazilian disc (CCNBD) experiments. Similarly, Ougier-Simonin et al. [2011a] and Faoro et al. [2013] have recently shown reduced peak stress with increasing thermal

2 Table 1. La Peyratte Granite Properties Modal composition Grain size Values 38.5% plagioclase, 28.5% quartz, 20% K-feldspar, 8% biotite, 5% muscovite 800 m Porosity Intact <1% Thermally cracked 3% cracking at low confinements in glass and Westerly granite samples, respectively. [4] In this study, the question we want to answer is why does thermal crack damage seem to have a large effect under low confinement, while at high confinement, it seems not to matter? To do so, we revisit the effects of thermal cracking on the physical properties and the mechanical strength of granitic rocks under confining pressure using modern experimental techniques. Here, we performed thermal cracking on fresh granite samples by slowly heating the samples to 700 ı C. We investigate quantitatively the influence of thermal damage on physical properties and mechanical strength and strain localization, under hydrostatic and triaxial stress, using acoustic emission and P and S elastic wave velocities as a monitoring tool, under water (wet) and argon gas (dry) saturated conditions (5 MPa pore pressure), at room temperature. 2. Experimental Setup 2.1. Sample Preparation [5] The material used throughout this study is La Peyratte granite, a granodiorite with an average grain size of 800 m. This rock comes from the same location as that used by Darot et al. [1992] and Darot and Reuschlé [2003] and is similar to Westerly granite in modal composition (Table 1 and Figure 1). Four cylindrical specimens (diameter 40 mm Figure 1. Elemental X-ray mapping on La Peyratte granite. (a) Mg X-ray map emphasize biotite, (b) Fe X-ray map emphasize biotite, (c) K X-ray map shows the K-feldspar and also muscovite and biotite, (d) Na X-ray map indicates plagioclase, (e) Al X-ray map shows all mineral except quartz, and (f) Si X-ray map outlines quartz. 6100

3 and length 80 mm) were cored from the same block. Surfaces were rectified and polished to 10 m to ensure parallelism and minimum friction during testing. [6] Two samples were heat treated at room pressure, up to 700 ı C, at a rate of 5 ı C/min. The samples were kept in the oven at 700 ı C for 2 h, after which the oven was turned off, and the samples were left to cool slowly for an entire night. Because the thermal diffusivity d of the rock is about 10 6 m 2 s 1, the sample radius r being m, the time constant for temperature equilibrium is r 2 /d, i.e., about 400 s (7 min), so that the temperature gradients in the sample were modest/absent during heating. In such a way, thermal cracking arose from differential thermal expansions of neighboring grains and above 550 ı C, from the quartz alpha/beta transformation [Fredrich and Wong, 1986; Nasseri et al., 2007]. Scanning electron microscope (SEM) micrographs of intact and heat-treated samples reveal that the heat treatment leads to homogeneously distributed intragranular and intergranular cracks (Figure 2). Porosity was measured by mercury porosimetry on companion samples. The porosity of the thermally cracked specimen is about 3%, whereas that of the intact specimen is <1%. [7] Eight strain gauges (Tokyo Sokki TML FCB2-11) were mounted on each rock sample in orthogonal pairs to measure directly the axial and radial strains locally, as shown Figure 3a. Volumetric strain was calculated by summing the axial strain and twice the radial strain. Strain measurement accuracy was close to Fourteen P and two S wave piezoelectric ceramic transducers (PI ceramic PI255, 0.5 MHz resonance frequency) were also glued directly on each sample (Figures 3a and 3b). The transducers were positioned with 0.5 mm accuracy and were used in both active mode and passive mode. Inside the vessel, the sample was covered with a neoprene jacket, which insulated it from the confining oil (Figure 3b) Experimental Methods [8] Experiments were performed in the triaxial cell installed in the Laboratoire de Géologie at Ecole Normale Supérieure in Paris. A complete description of this apparatus has previously been given [Brantut et al., 2011; Ougier- Simonin et al., 2011a]. It allows confining and pore pressures up to 100 MPa, deviatoric stresses up to 680 MPa to be servocontrolled independently (accuracy 0.01 MPa) on a cylindrical specimen of 40 mm diameter. Total axial shortening is monitored outside the vessel with an accuracy of 0.3 m using three external gap sensors. External strain measurements are corrected from the machine stiffness. Room temperature was kept constant with an accuracy of 0.5 ı C around 20 ı C Permeability [9] Both argon gas and water were used as pore pressure medium. Permeability measurements along the main axis of compression were performed using the steady state or oscillating pulse methods (Figure 4). The steady state technique (Figure 4a) uses a constant pore pressure gradient. Permeability is inferred using Darcy s law: Q/A = k P/L, whereq is the fluid flow, A is the sample area, L is the sample length, is the dynamic viscosity of the pore fluid, and P is the pressure difference. Switching the flow direction, two measures of permeability were performed at each pressure step. However, this method can only measure 6101 a) 0.5mm b) 0.5mm Figure 2. Scanning electron micrographs of (a) intact and (b) heat-treated specimens. permeability larger than m 2. For lower permeabilities, the oscillating pulse method was used (Figure 4b). In this case, an oscillating pressure is induced at one end of the specimen (upstream). The diffusion of the pressure through the sample results in attenuation and phase shift of the pore pressure oscillation measured in the downstream reservoir (Figure 4b). The permeability value is derived from the amplitude ratio and phase shift between the upstream and downstream pressures. The detailed method is reported in Fischer [1992] and Faulkner and Rutter [2000]. Here, the method was first calibrated at low pressures using pulse transients (Figure 4b). A complete description of the transient method is provided in Brace et al. [1968]. We used a forward model to determine permeability from the measured amplitude ratio and phase shift [Faulkner and Rutter, 2000]. Oscillation periods ranged from 1000 s to a couple of hours, so that permeability measurements took from several hours up to several days. A single measurement was performed on the intact sample, using argon gas. No Klinkenberg [Klinkenberg, 1942] correction was performed, because gas experiments were performed at 5 MPa pore pressure, i.e., a pressure at which the mean free path of argon molecules is orders of magnitudes smaller than the crack hydraulic apertures Elastic Wave Velocities and Acoustic Emissions [10] Acoustic waveforms were amplified at 40 db and recorded at 10 MHz sampling rate using a Richter system (ASC Ltd.). A complete description of the acoustic system is also given in Brantut et al. [2011] and Ougier-Simonin et al. [2011a]. A classical ultrasonic pulse transmission technique was used for P and S wave velocity measurements. The

4 a 1 b P p up 3 P p down c Figure 3. (a) Schematic diagram of the sample. (b) Sample assembly inside the vessel. (c) Angular positions of the piezoelectric transducers. position of the 16 transducers is given on Figure 3c. Independent velocity measurements were measured along three different angles with respect to the vertical: Vp90 (P waves) and Vs90 (S waves) along the horizontal path (dot-dashed line, perpendicular to the symmetry axis), and Vp50 (solid line) and Vp23 (dashed line) along two diagonal paths. For each measurement, 10 waveforms were stacked in order to increase the signal/noise ratio. Note that there are several horizontal and diagonal P wave paths so that, except when explicitly stated otherwise, velocity measurements presented in the following are sample average along those paths. Arrival times were determined using cross 6102 correlations and relative error on velocity measurements is 1%. [11] In passive mode, transducers were used to record acoustic emissions (AE). A trigger logic was applied, generally set at 150 mv on three channels within a 10 s window. AE time arrivals were autopicked. Hypocenter locations were determined using a collapsing grid search algorithm, assuming an evolving (from isotropy to transverse isotropy) homogeneous P wave velocity profile within the sample. A complete description of the technique is given in Ougier- Simonin et al. [2011a]. The total number of AE recorded being significant, up to , we only show AEs that were

5 a at a constant strain rate of s 1. During deformation, strains, elastic wave velocities, and AEs were recorded. 3. Experimental Results 3.1. Hydrostatic: Elastic Velocities and Permeability Data [14] At low effective confining pressure (P e = 5 MPa), thermal cracks have a strong influence on both the P and S initial elastic wave velocities (Figure 5). No significant anisotropy (<5%) was observed, so we present measurements averaged along all raypaths. Values of Vp are b a b Figure 4. Permeability measurements. Fluid pressure in upstream and downstream reservoirs for (a) constant flow method and transient pulse method, and for the (b) oscillation method. accurately located by seven stations at least, with average time residuals of 0.5 s or less. For these, AE hypocenter locations errors were 2 mm Experimental Procedure [12] In the following, we adopt the convention that the compressive stresses and compactive strains are taken positive. The maximum and minimum (compressive) principal stresses are denoted by 1 and 3, respectively, and pore pressure by P p. The difference between the confining pressure (P c = 2 = 3 ) and the pore pressure will be referred to as the effective confining pressure P e. The differential stress is noted Q = 1 3 and the effective mean stress by P =( )/3 P p. Experiments are referred to as dry (argon saturated) or wet (water saturated). [13] At the start of each experiment, confining pressure was increased up to 10 MPa while pore pressure was raised to 5 MPa. Pore pressure remained constant throughout the experiment (nominally drained conditions). The sample was left to reach full saturation for at least 48 h. In each experiment, confining pressure was first slowly raised (0.01 MPa s 1 ) until an effective confining pressure (P c -P p ) of 90 MPa. During this step, volumetric strain, wave velocities, and permeability were measured. The effective confining pressure was then slowly decreased to 30 MPa, conditions under which the sample was deformed to failure, c Figure 5. Wave velocity evolution during the hydrostatic experiments performed on intact samples and heat-treated sample (labeled td). (a) P wave velocities (b) S wave velocities, and (c) Vp/Vs ratio as a function of effective pressure. Open symbols indicate loading, and solid symbols indicate unloading. 6103

6 a Figure 6. Water and argon permeability measurements of heat-treated granite samples in hydrostatic condition. The dashed line is the fitted data. Solid line indicates the transition at P e =30MPa. A single measurement for an intact granite sample is plotted m/s for the dry heat-treated specimen, 4600 m/s for the wet heat-treated specimen and 5600 m/s for the intact ones (Figure 5a). In all cases, Vp increases with increasing effective pressure to reach a maximum value at P e = 90 MPa. Similar behavior was observed for S wave velocities (Figure 5b). Compared to intact specimen, the elastic wave velocities of heat-treated rock samples are not fully recovered at 90 MPa effective pressure but are still 5 10% lower. For the intact samples, the Vp/Vs ratios are similar for the two specimens because of low initial crack density (Figure 5c). For heat-treated specimens, Vp/Vs is larger in the water-saturated specimen (Vp/Vs 2) than in the dry one (Vp/Vs 1.4). Vp/Vs decreases with increasing effective pressure in the wet case, while it increases in the dry case, due to both crack and fluid effects as previously discussed by Wang et al. [2012]. [15] The permeability of the intact rock samples is m 2, at the resolution limit of our system, so that only a single measurement was performed at 5 MPa effective pressure. The permeability measured under hydrostatic conditions in the two heat-treated specimens is m 2 (wet case) and m 2 (dry case) (Figure 6), i.e., 4 5 orders of magnitude larger than that of the intact specimen. Differences between argon and water permeabilities were close to 1 order of magnitude. The mean free path of argon of 0.1 nm is orders of magnitude less than the minimum pore throat radius (20 nm, Figure 13d). Thus, the differences between argon and water permeabilities are due to sample variability and water-rock interactions. Indeed, layers of structured water adsorbed onto mineral surfaces may reduce the effective pore throat aperture and thus reduce the permeability. The permeability decreases with increasing pressure, and the trend is consistent with an exponential law: k = k o e Pe where k o is the initial permeability of the rock sample. The coefficient is a constant, independent of the fluid nature, corresponding to the pressure sensitivity parameter first introduced by David et al. [1994]. For the heat-treated specimen, the slope decreases from 0.06 MPa 1 to 0.01 MPa 1 at Pe =30MPa. At 30 MPa, permeability ranged between m 2 and m 2 in the dry and wet specimen, respectively. Compared to that of intact specimen, the permeability of heat-treated rock samples at 90 MPa effective pressure is still 2 3 orders of magnitude larger. b Figure 7. Mechanical data for granite samples deformed at 30 MPa effective confining pressure: (a) differential stress Q and (b) volumetric strain, plotted versus axial strain Triaxial Experiments: Stress-Strain Data [16] The four granite samples were deformed at P e = 30 MPa and at a constant strain rate of s 1 up to failure. In all experiments, the differential stress attained a peak, beyond which strain softening was observed and differential stress dropped to a residual level (Figure 7a). Overall, the brittle strength of the samples remained at the same level ( MPa differential stress at 30 MPa effective pressure), whether the sample was heat treated or not (Table 2). In addition, no water weakening effect was observed. Visual inspection of postmortem rock samples proved that the rock samples failed by shear localization, with a throughgoing shear fracture across each sample, showing an angle of 30 ı with respect to the vertical. [17] The static Young s modulus, determined using the slope of the stress-strain curve, was reduced by approximately 20% in heat-treated specimens, irrespective of the saturation conditions (Table 2). Initial elastic compaction occurred, but beyond 0.4 to 0.6% shortening, dilatancy [Brace et al., 1966; Hadley, 1975; Brace, 1978; Wong et al., 1997] was systematically observed. Volumetric strain Table 2. Summary of Mechanical Properties Young s Modulus D 0 Peak Stress (GPa) (MPa) (MPa) Thermally cracked, argon Intact, argon Thermally cracked, water Intact, water

7 D =147MPa intact water intact argon D =154MPa td water td argon D =134MPa Volumetric strain (%) D =127MPa Figure 8. Effective mean stress P against volumetric strain of intact and heat-treated (td) granite samples, saturated with water or argon. Hydrostatic loading cycle is represented by the dashed lines. The solid curves indicate the deviatoric stress cycle. Vertical colored bars indicate approximate level of C 0. Absolute value of D 0 is also indicated. reversal marks the transition into dilatancy-dominated deformation. This transition, uniquely defined and noted D 0,was attained for lower axial strain for intact samples (0.5%) than for heat-treated specimens (0.6%). [18] The onset of dilatancy C 0, or onset of crack propagation, was observed at approximately half of the peak strength (Figure 8). We only give here an approximation of the stress values at C 0 (vertical colored bars on Figure 8), because for the heat-treated specimen, the stress-strain curve is so nonlinear during loading that it becomes challenging to define an onset of nonlinearity. In addition, C 0 values may also substantially differ when looking at the onset of dilatancy in the mechanical data, the onset of elastic wave velocities reduction or the onset of AE triggering. Nevertheless, C 0 seems to substantially decrease (by 10% at least) for heat-treated specimen. The transition D 0, which is uniquely defined, was systematically observed to take place at lower differential stress in the heat-treated specimens than in the intact ones (Table 2) Triaxial Experiments: Elastic Wave Velocities [19] In all our experiments, we observed the development of a crack-induced elastic anisotropy well before failure (Figure 9). In contrast, P wave velocities were raypath independent at hydrostatic condition. As differential stress is applied, Vp becomes gradually dependent on the wave propagation direction [Sayers and Kachanov, 1995; Schubnel et al., 2003]. P wave velocities measured perpendicular to the main compressive axis (Vp90) diverge from that measured for a propagation angle of 23 ı (Vp23) and 50 ı (Vp50). Below D 0, Vp23, Vp50, and Vp90 all increase, due to crack closure. However, Vp23 increases faster than Vp50, itself increasing faster than Vp90, because under such stress conditions, mainly horizontal preexisting cracks are closing. Beyond D 0 however, the opposite phenomenon is observed, as wave velocities start to decrease. This time a) Argon b) Water Figure 9. Evolution of three P wave velocities and Vs90 versus differential stress in a thermally damaged sample, water saturated. The measured velocities are indicated by solid lines, and the forward solution derived from the nointeraction approximation is indicated by open circles. Figure 10. P wave velocity measured in the horizontal plane versus differential stress. Vp were measured parallel and perpendicular to the failure plane, for (a) dry samples (b) water-saturated samples. C 0 and D 0 are indicated on the figure. 6105

8 a) intact water b) td Argon Figure 11. Differential stress Q and AE rate versus axial strain in (a) an intact sample and water-saturated sample, and in (b) a sample heat treated and argon saturated. Points II, III, and V correspond to C 0, D 0, and peak stress, respectively. Vp90 decreases faster than Vp50, itself decreasing faster than Vp23, due to the fact that under such stress conditions, mainly vertical cracks propagate. Such a velocity profile can be described as transversely isotropic [Nishizawa, 1982; Sayers and Kachanov, 1995; Schubnel and Guéguen, 2003; Schubnel et al., 2003] and is the one used later for both AE hypocenter location (section 3.4) and crack density inversion (section 4.1 and Appendix A). [20] P wave velocities were also monitored along two different horizontal travel paths: one parallel and one perpendicular to the rupture plane (Figure 10). The strike of the rupture plane was determined post-mortem, using AE locations (section 3.4). In the plane perpendicular to compression, P wave anisotropy appears quite early on during the experiment, around D 0 in intact specimens, and even earlier in heat-treated ones, which is in agreement with Hadley [1975] who showed that volumetric strain became elliptical beyond C 0. The implication is that the strike of the fracture plane has already been selected at that stage, i.e., around C 0 for heat treated specimens and D 0 for intact ones. An important implication is that the horizontal plane is not truly isotropic, which means that the transverse isotropic (TI) approximation is insufficient to describe the elastic fabric. However, for the sake of simplicity and because basal anisotropy is of second order when compared to the one observed between vertically and horizontally propagating P waves, the TI approximation will nevertheless be used in the following. Finally, an important observation is that, approaching peak stress, the magnitude of horizontal P wave anisotropy becomes comparable for all specimens Triaxial Experiments: AE Locations [21] In the case of an intact rock sample, AEs do not occur before C 0, after which the AE rate increased to reach a plateau (Figure 11a). After D 0, it increased exponentially until failure. In a heat-treated specimen, AEs started to occur later on (Figure 11b), so that during phase II-III, dilatancy was the combined result of elastic crack reopening and/or possibly slow crack growth (i.e., not sufficiently dynamic to radiate acoustic waves). In the intact sample, phases II- III and III-IV correspond to an apparent linear elastic phase during which there were few AEs distributed uniformly (Figure 12a). Note that although the cracks were distributed uniformly in the entire sample volume, their direction of propagation was not (cf. Figures 9 and 10). During the phase IV-V (before failure), AEs clustered within a swarm, which turned into a fracture plane. During failure (stage V), all AEs occurred on the fracture plane. [22] In the heat-treated specimen, AE hypocenters were not uniformly distributed (Figure 12b) during any stage of the experiment. Indeed, no AEs were observed during phase II-III, and during phase III-IV, AE clustered, and damage was immediately localized. One should note here that the heat-treated and water-saturated specimens showed similar behavior. During stage III-IV, before failure, AEs were numerous, and a macroscopic fault developed on the right of the specimen. During stage V (failure), all AEs occurred within one of the fracture planes. In both cases, the overall AE location proved again to be in good agreement with the sample postmortem analysis of the fracture planes. a) Intact, water saturated II-III III-IV IV-V after V b) Heat treated, Argon saturated III-IV IV-V afterv Figure 12. AE location time series in (a) an intact sample and water-saturated sample and in (b) a sample heat treated and argon saturated (b). Points II, III, and V correspond to C 0, D 0, and peak stress, respectively. 6106

9 4. Discussion WANG ET AL.: STRENGTH OF THERMALLY CRACKED GRANITE 4.1. Crack Density and Aspect Ratio Evolutions [23] In the absence of applied stress, Fredrich and Wong [1986] showed that an upper bound to the total surface of cracks S (per unit volume) created due to mismatch in thermal expansions during heating could be assessed, so that S = E ( T) where E and are the Young s modulus and Poisson s ratio, the difference in mineral thermal expansions, T the temperature of heat treatment (in Celsius) and the surface energy of the minerals. We assume disc shaped cracks and define the crack density as = Nc 3 /V, where N is the number of cracks per unit volume V and c the crack radius. The relationship between the total crack surface and the crack density is such that S = 2/c. Equation (1) can thus be rewritten as follows: = c E ( T) Assuming that the average thermal crack size is that of the grain size l (i.e., c l/2), and taking typical values for a granite [Fredrich and Wong, 1986] such as E 60 GPa, 0.2, K 1,and 10 J/m 2 yields an initial crack density 0.7 for the heat-treated samples. [24] We define now the aspect ratio = w/c, wherew is the crack half aperture. Then, the total crack porosity is equal to =2. Using the value above and an initial porosity of 3% for the heat-treated specimen yields an initial average crack aspect ratio of [25] In the following, using noninteracting crack approximation (NIA) (Appendix A) [Kachanov, 1994; Schubnel et al., 2003, 2006;Fortin et al., 2010], crack density and aspect ratio evolutions were inverted from elastic wave velocity measurements (sections 3.1 and 3.3) for both hydrostatic and triaxial loading conditions Under Isotropic Stress [26] The initial crack density in intact La Peyratte granite is about 0.1 (Figure 13a). At low effective pressure, heattreated specimens display crack densities larger than 0.5, which is consistent with the estimation from thermal strains (equation (2)). Because our heat treatment went to 700 ı C, i.e., beyond the -ˇ transition of quartz 575 ı C, we do know that both intragranular and intergranular cracks exist in our material (Figure 2) [Fredrich and Wong, 1986; Nasseri et al., 2007]. With increasing pressure, the crack density of intact specimen decreases slightly compared to that in the heat-treated specimen, because of gradual crack closure. At 90 MPa, the crack density of heat-treated samples remains higher than that of the intact specimen, which is consistent with the evolution of permeability (Figure 6). At 30 MPa, the crack density of heat-treated specimens is still 0.5. The fact that changes from 0.06 to 0.01 at effective pressure of 30 MPa for the thermally cracked granite has two implications. The initial value of 0.06 is on the high end in comparison with most compact rocks, as can be seen from the compilation in David et al. [1994, Table 3] which implies that the thermal cracks are more compliant than preexisting cracks in a natural rock. This is possibly related to difference (1) (2) 6107 in roughness and aperture statistics as speculated by Wong et al. [1989]. [27] The evolution of crack aspect ratio also highlights the fact that wave velocities and permeability probe, within the microstructure, two different crack populations. Indeed, the crack aspect ratio retrieved from the elastic wave velocity inversion (Figure 13b) is consistent with our estimate above and seems pressure insensitive, i.e., almost constant The crack aspect ratio can also be derived from permeability data (Figure 6). Indeed, is inversely proportional to the pressure of crack closure E,sothat 3/E [David et al., 1994; Ougier-Simonin et al., 2011b]. At P e = 30 MPa, the slope changes from MPa 1 to MPa 1 for both heat-treated specimens. Taking E 60 GPa, the crack aspect ratio inverted from permeability data is below 30 MPa and above. Differences between these values and the previous ones (a factor of 5 to 10) are probably related to the fact that permeability and velocity do not see exactly the same cracks. Indeed permeability is sensitive to connectivity and thus will depend mainly on the hydraulic path. On the other hand, velocity measurements are not very sensitive to crack aspect ratio but mainly dependent on crack density, which means that velocities will see both connected and nonconnected cracks. In consequence, P wave scans all cracks along a prescribed path, while permeability scans cracks along the hydraulic path only, so that wave velocities probably give a better average estimate of crack aspect ratio. [28] From the inverted crack density and aspect ratio evolutions, the total microcrack porosity =2 can be calculated as a function of effective mean pressure (Figure 13c). The initial crack porosity at lower effective pressure is about 2.2%, which is comparable to our mercury porosity results (3%). At high pressure, cracks close so that the porosity decreases. One may argue that the crack porosity data also suggests a change of slope at a pressure of 30 MPa. At 30 MPa, after unloading from 90 MPa effective pressure, the porosity of the heat-treated specimen is still 1%. [29] The permeability k of a cracked material with an isotropic distribution of crack centers and orientations can be written as [Guéguen and Dienes, 1989]: k = 2 15 fw2 (3) where the connectivity f represents the fraction of cracks that are hydraulically connected. Assuming f =1and recalling the respective evolutions of permeability (Figure 6), crack density (Figure 13a), and aspect ratio (Figure 13b), the average hydraulic aperture evolution can also be derived as a function of effective pressure (Figure 13d). The initial crack aperture is about 0.1 m only, smaller than values found in similar conditions for heat-treated Westerly granite by Nasseri et al. [2009] or Takidani granite by Benson et al. [2006]. Using aspect ratios deduced from velocities ( ), the average crack radius is 20 m only, i.e., an order of magnitude smaller than the average grain size. On the other hand, using the crack aspect ratio inverted from permeability would lead to a hydraulic crack apertures 2 to 3 times larger and a corresponding average crack radius of 200 m, i.e., indeed comparable to the grain size and consistent with our initial estimate.

10 a) b) c) d) Figure 13. (a) Crack density of the four rock samples, (b) aspect ratio (c) crack porosity, and (d) crack aperture of the sample heat treated and water saturated, versus P e during the hydrostatic experiments. Open symbols indicate loading, and solid symbols indicate unloading Under Deviatoric Stress [30] The triaxial compression experiments were conducted at 30 MPa pressure, which, considering the discussion above, is sufficiently high to presumably close the first subset of more compliant (and possibly well-mated) microcracks. Using the effective medium model presented in Appendix A, four independent elastic wave velocities (Vp90, Vs90, Vp50, and Vp23) were inverted in terms of two crack densities: an isotropic crack density i (random crack for abbreviation) and a vertical crack density v (vertical crack for abbreviation). We use a forward solution to invert the two populations of cracks from the four observed velocities (Vp90, Vs90, Vp50, and Vp23) and in general, velocities measured experimentally and that given by our inversion were in good agreement (Figure 9). In intact rock samples (Figures 14a and 14b), the initial random crack density is small, as expected. In heat-treated specimen (Figures 14c and 14d), the random crack density is initially nonnegligible. However, when applying differential stress, random crack density decreases, while the vertical one increases, meaning in fact that the horizontally oriented cracks are gradually closing, inducing elastic crack closure anisotropy. In all cases, the vertical crack density increases sharply at D 0, and failure is reached for vertical crack densities of 0.35 for dry specimens. As for water-saturated specimens, assuming fully saturated cracks, vertical crack density at failure is about 0.5. However, due to low permeability (see Figure 6) and long characteristic time of hydraulic diffusion, the cracks may not be fully saturated, 6108 even at strain rates as low as s 1. Assuming the cracks were dry (Figures 14b and 14d), failure was reached for vertical crack densities of about 0.35 as well. These values are smaller but comparable to that found by Schubnel et al. [2003] on Oshima and Toki granites or in low-porosity basalt by Fortin et al. [2010]. Note that this is a global average, which considers cracks as homogeneously distributed within the rock specimen. Due to strain localization, this is obviously not the case, meaning that the actual crack density close to the fracture plane must be far greater Absence of Water Weakening or Reduction of Peak Strength [31] Previous experimental studies have shown that rocks are weaker in the presence of water [Baud et al., 2000]. In our experiments however, no significant water weakening effect was observed on the mechanical strength. As evoked in the last section, this might simply be due to partial saturation close to failure. In our experiments, the final stage of deformation (Figure 12a, stage IV-V) lasts about 5 10 min only, which is comparable with (for heat-treated specimen) or much smaller than (for intact specimen) the characteristic hydraulic diffusion time in the sample, as estimated from permeability. This means that, in our experiments, as in many experimental studies performed on tight-porosity rocks, full saturation is probably not maintained at failure. Indeed, the characteristic time to get pressure equilibrium is t c = L 2 /D where the hydraulic diffusivity D = k/ˇ, k being the permeability, ˇ being the storage capacity of the sample,

11 a) b) c) d) Figure 14. Evolution of random (red) and vertical (blue) crack densities versus differential stress for (a) an intact sample, argon saturated; (b) an intact sample, water saturated; (c) a heat-treated sample, argon saturated; and (d) a heat-treated sample, water saturated. For water-saturated specimens, the crack density evolution is also given assuming the cracks were dry (dashed line for vertical cracks and solid line for random cracks). L being the sample length, and being the fluid dynamic viscosity. Using L =0.08m, =10 3 Pa s 1, ˇ Pa 1,and k =10 19 m 2 yields a characteristic time of 600 s so that the absence of water weakening in low-permeability rocks at strain rates of 10 6 s 1 and higher is not surprising. [32] More surprising however is the observation that the stress at the onset of dilatancy is reduced while the brittle strength of the samples remains the same ( MPa deviatoric stress at 30 MPa effective pressure) for intact and heat-treated specimens. Following Lehner and Kachanov [1996], the stress at the onset of dilatancy C 0 can be written 1 = p p p 3 K Ic p p (4) 1+2 2c where is the friction coefficient, K Ic the fracture toughness, and c the radius of the longest initial cracks. Our experimental observations suggest that both the onset of dilatancy C 0 and the transition to dilatancy-dominated regime D 0 were observed at lower deviatoric stress in the heat-treated specimens than in intact ones (Figure 8 and Table 2). Using equation (4) and typical values for granite ( = 0.85, K Ic = 1 MPa m 1/2 ), a C 0 value of 250 MPa yields initial flaw size of 800 m approximately, i.e., comparable to the grain size. Reminding that K Ic = (E ) 1/2 where E is the Young s modulus and is the fracture surface energy, and 6109 neglecting possible changes in surface energy or in initial flaw size, equation (4) predicts the stress at the onset of dilatancy will decrease with decreasing Young s moduli. Nasseri et al. [2007] have observed a similar correlation in heattreated Westerly granite samples during unconfined Chevron notched Brazilian disc (CCNBD) experiments. Here, taking the Young s moduli values from Table 2 predicts a 10% reduction of the stress at C 0, a value compatible with our observations on both C 0 and D 0. In other words, in the heat-treated samples, cracks propagate within a damaged material, which behaves as a homogenous elastic solid with reduced stiffness, so that the longest cracks, for which the stress intensification is largest, will start propagating at lower stress. [33] So why is the peak stress not reduced as well? Wing crack models such as Ashby and Sammis s [1990] would predict that if K Ic is reduced, or the initial damage higher, both of which is the case in our experiments, the peak stress should also be reduced. This is not the case in our experiments and several hypotheses can be made. First, thermally treated samples did not show any stage with uniform AE hypocenters distribution, which might be due to the fact that the initial thermal treatment has released the thermal stresses remnant from the crystallization and cooling under stress of the granitic body. In such a way, and counterintuitively, the initial stress heterogeneities might be smaller in

12 the heat-treated specimens than in the intact ones during the early part of the load history. Second, if the medium has a reduced stiffness, then stress interactions will also become less effective [Lawn, 1993], which is particularly true for aligned/parallel crack distributions [Kachanov, 1994], for which stress shielding is an important phenomenon. One should note, if this is true, that wing crack models [Ashby and Sammis, 1990; Bhat et al., 2011, 2012; Brantut et al., 2012] will not be able to grasp such a behavior, as they consider only positive stress interactions and single sized initial flaws [Bhat et al., 2011]. In our heat-treated specimens however, crack-induced anisotropy appears very early on (cf. Figures 9 and 10), and stress shielding may be playing an important role, which could potentially explain why the onset of AE triggering comes later on and closer to failure in the heat-treated specimen compared to the intact specimen (cf. Figure 11). In consequence, cracks will propagate only once stress interactions become positive, which could explain the fact that the apparent stress domain for which cracks propagate is clearly reduced and also why crack damage is immediately localized. [34] Third, our microstructural analysis, as well as the evolution of physical properties during hydrostatic loading, have revealed the existence of two distinct populations of cracks in our samples: short and narrow intragranular ones, to which velocities are sensitive, and long and opened intergranular ones, controlling the permeability. It is possible that the latter ones, which certainly also control the peak strength of the material, might be inherited fractures present in the intact material and which only opened-up during thermal treatment. This observation should be put in perspective with the recent works of Ougier-Simonin et al. [2011a], who have shown a dramatic reduction of peak stress in thermally shocked glass. However, in their study, Ougier-Simonin et al. [2011a] noticed that if the reduction of peak stress was significant (a factor of 2) between untreated glass and thermally shocked glass samples, increasing the magnitude of the thermal shock did not have subsequent systematic effects on the peak strength. That is, after cracks were introduced in the sample, the overall strength remained the same. 5. Conclusions [35] Thermal damage had a significant influence on the rock elastic and transport properties of La Peyratte granite, and our experimental observations could be well reconciled using simple crack models. We showed that wave velocities see intragranular short and narrow cracks, while permeability sees long and opened ones. Hence, these two physical properties probe, within the microstructure, different crack populations. It is very well possible that a rather continuous distribution of crack properties is convoluted by two different sensitivities and therefore yielding different results, so that the crack distribution in our sample is not necessary a bimodal distribution. [36] The effects of thermal crack damage on the rupture processes of La Peyratte granite under confinement were counterintuitive. The onset of dilatancy was observed at lower differential stress in heat-treated specimen. We interpret this reduction in terms of reduced critical stress intensity factor. In other words, in the heat-treated samples, cracks propagate within a damaged material, which behaves as 6110 a homogenous elastic solid with reduced stiffness, so that cracks start propagating at lower stresses. In intact specimen, the onset of dilatancy coincided with randomly localized AE hypocenters. Elastic wave velocities show that, although randomly located, these cracks were not randomly oriented. In heat-treated specimen, no random AE location stage was observed. AEs immediately clustered within a swarm, which eventually turned into the main fracture. Interestingly, in all our experiments, we observed the development of an elastic fabric well before rupture. The implication is that the determination of the final orientation of the failure plane is an early step of strain localization. [37] But our main experimental result shows that the initial crack damage had no influence on the mechanical strength, at least at the strain rate s 1 investigated in this study. We interpret this as due to stress shielding and the existence of preexisting flaws which control the peak strength and are longer than those introduced by the thermal treatment. This counterintuitive result is probably not universal. Confinement, initial grain size, strain rate, and cyclic loading certainly play important roles, which need to be thoroughly investigated. Nevertheless, our results, like that of Friedman et al. [1979], suggest that, under confinement (here 30 MPa, 50 MPa in the case of Friedman et al. [1979]), the peak strength of fine grain-size crystalline rocks are actually quite insensitive to initial damage. An unanswered question then remains: How high is the pressure required to negate the effect of thermal cracking? In other words, what is the threshold pressure at which the brittle failure envelopes of unheated and thermally cracked samples of the same rock start to overlap? Our experimental results suggest that the weakening is inhibited once the first subset of high aspect ratio thermal cracks are completely closed. Appendix A: No-Interaction Approximation [38] In the no-interaction approximation (NIA), each crack is considered to be isolated, and crack interactions are assumed to compensate each other on average [Kachanov, 1994], so that an elastic solid containing N cracks can be treated as the sum of individual sources of extra strains due to each singular crack. For penny-shaped cracks of radius c, the extra compliance S ijkl due to cracks has a simple form [Kachanov, 1994; Sayers and Kachanov, 1995]: 1 S ijkl = h 4 (ı ik jl + ı il jk + ı jk il + ı jl ik )+ ˇijkl (A1) where the scalar h h = 32(1 2 o ) 3(2 o )E o (A2) E o and o being the Young s modulus and Poisson s ratio of the crack-free matrix, respectively. The Kronecker symbol is ı ij, ij and ˇijkl are the second rank and fourth rank crack density tensors, respectively, defined as follows: ij = n i n j ; ˇijkl = n i n j n k n l (A3) where is the scalar crack density and n is the unit normal to a crack. Tensors ij and ˇijkl represent respectively the second order and the fourth order moment of the crack orientation distribution function, standing for a statistical angular

13 average, based on the continuous distribution of the cracks orientation. The parameter = 1 o 2 ıf 1+ı f 1 (A4) where ı f compares the crack and fluid compressibilities, and thus accounts for the effect of fluid pressure ı f = E o 4(1 2 o ) (1/K f 1/K o ) (A5) Here, K f and K o are the fluid and matrix bulk moduli respectively. From equation (A5), under dry condition, K f << K o so that ı f >> 1 and o. Note that ı 2 f also depends on the crack geometry, in particular on the crack aspect ratio, sothatˇijkl cannot be neglected when considering a fluid such that E o and K f are comparable. Equations (A1) (A5) are valid for any distribution of crack orientations, assuming that all cracks are identical in size and shape. [39] Using the effective medium model presented above, four independent elastic wave velocities (Vp90, Vs90, Vp50, and Vp23) were inverted in terms of two crack densities: an isotropic crack density i (random crack for abbreviation) and a vertical crack density v (vertical crack for abbreviation). In this case, the extra compliance S ijkl due to two populations of cracks can be written as follows: S = S i + S v (A6) where S i is the extra compliance induced by random cracks (isotropic case), and S v is the extra compliance induced by vertical cracks (transverse isotropic case). This method is described in more details in Fortin et al. [2010]. [40] At high differential stress, the horizontal plane was no longer isotropic (Figure 10) so that the transversely isotropic (TI) symmetry was broken. However, more complicated anisotropic symmetries are difficult to use because more independent raypaths would be needed. Consequently, we use the TI symmetry, even approaching failure, as an approximation. [41] Acknowledgments. The authors would like to thank Joerg Renner and Teng-Fong Wong for their reviews which greatly enhanced the quality of this manuscript. We acknowledge the help of Yves Pinquier with the experimental device and Damien Deldicque with the SEM. This work was supported by the Key Laboratory of Seismic Observation and Geophysical Imaging, CEA(SOGI2013FUDB01); the Institut National des Sciences de l univers(programme INSU-CNRS Faille Fluide Flux); the NSFC (National Natural Science Foundation of China, grant ); and the Research Funds Provided to New Recruiments of China University of Petroleum- Beijing (YJRC ) and the Science Foundation of China University of Petroleum, Beijing (YJRC ). References Ashby, M. F., and C. G. Sammis (1990), The damage mechanics of brittle solids in compression, Pure Appl. Geophys., 133, Atkinson, B. K., and P. G. Meredith (1987), The theory of subcritical crack growth with applications to minerals and rocks, in Fracture Mechanics of Rock, edited by B. K. Atkinson, pp , Academic Press, London. Baud, P., W. Zhu, and T. F. Wong (2000), Failure mode and weakening effect of water in sandstones, J. Geophys. Res., 105, 16,371 16,389. Benson, P., A. Schubnel, S. Vinciguerra, C. Trovato, P. Meredith, and R. P. Young (2006), Modeling the permeability evolution of microcracked rocks from elastic wave velocity inversion at elevated isostatic pressure, J. Geophys. Res., 111, B04202, doi: /2005jb Bhat, H. S., C. G. Sammis, and A. J. Rosakis (2011), The micromechanics of westerley granite at large compressive loads, Pure Appl. Geophys., 168, Bhat, H. S., A. J. Rosakis, and C. G. Sammis (2012), A micromechanics based constitutive model for brittle failure at high strain rates, J. Appl. Mech., 79, Brace, W. F. (1978), Volume changes during fracture and frictional sliding: Areview,Pure Appl. Geophys., 116, Brace, W. F., B. W. Paulding, and C. H. Scholz (1966), Dilatancy in the fracture of crystalline rocks, J. Geophys. Res., 71, Brace, W. F., J. B. Walsh, and W. T. Frangos (1968), Permeability of granite under high pressure, J. Geophys. Res., 73, Brantut, N., P. Baud, M. J. Heap, and P. G. Meredith (2012), Micromechanics of brittle creep in rocks, J. Geophys. Res., 117, doi: /2012jb Brantut, N., M. J. Heap, P. G. Meredith, and P. Baud (2013), Timedependent cracking and brittle creep in crustal rocks: A review, J. Struct. Geol., 52, Brantut, N., A. Schubnel, and Y. Guéguen (2011), Damage and rupture dynamics at the brittle-ductile transition: The case of gypsum, J. Geophys. Res., 116, B01404, doi: /2010jb Costin, L. S. (1987), Time-dependent deformation and failure, in Fracture Mechanics of Rock, edited by B. K. Atkinson, pp , Academic Press, London. Darot, M., Y. Guéguen, and M.-L. Baratin (1992), Permeability of thermally cracked granite, Geophys. Res. Lett., 19, Darot, M., and T. Reuschlé (2003), Wood s metal dynamic wettability on quartz, granite, and limestone, Pure Appl. Geophys., 160, David, C., T.-F. Wong, W. Zhu, and J. Zhang (1994), Laboratory measurement of compaction-induced permeability change in porous rocks: Implications for the generation and maintenance of pore pressure excess in the crust, Pure Appl. Geophys., 143, Faoro, I., S. Vinciguerra, C. Marone, D. Elsworth, and A. Schubnel (2013), Linking permeability to crack density evolution in thermally stressed rocks under cyclic loading, Geophys. Res. Lett., 40, , doi: /grl Faulkner, D. R., and E. H. Rutter (2000), Comparisons of water and argon permeability in natural clay-bearing fault gouge under high pressure at 20 ı C, J. Geophys. Res., 105, 16,415 16,426. Fischer, G. J. (1992), The determination of permeability and storage capacity: Pore pressure oscillation method, in Fault Mechanics and Transport Properties of Rocks, edited by B. Evans, and T. F. Wong, pp , Academic Press, San Diego, Calif. Fortin, J., S. Stanchits, S. Vinciguerra, and Y. Guéguen (2010), Influence of thermal and mechanical cracks on permeability and elastic wave velocities in a basalt from Mt. Etna volcano subjected to elevated pressure, Tectonophysics, 503, Fredrich, J. T., and T. F. Wong (1986), Micromechanics of thermally induced cracking in three crustal rocks, J. Geophys. Res., 91, 12,743 12,764. Friedman, M., J. Handin, N. G. Higgs, and J. R. Lantz (1979), Strength and ductility of four dry igneous rocks at low pressures and temperatures to partial melting, paper presented at 20th U.S. Symposium on Rock Mechanics (USRMS), Am. Rock Mech. Assoc., Austin, Tex., 4 6 June. Guéguen, Y., and J. Dienes (1989), Transport properties of rocks from statistics and percolation, Math. Geol., 21, Guéguen, Y., and M. Kachanov (2011), Effective elastic properties of cracked rocks An overview, in Mechanics of Crustal Rocks, CISM Courses and Lectures, vol. 533, edited by Y. Leroy, and F. K. Lehner, pp , Springer, New York. Hadley, K. (1975), Azimuthal variation of dilatancy, J. Geophys. Res., 80, Kachanov, M. (1994), Elastic solids with many cracks and related problems, in Advances in Applied Mechanics, vol. 32, edited by J. W. Hutchinson, and T. Y. Wu, pp , Academic Press, New York. Klinkenberg, L. J. (1942), The permeability of porous media to liquids and gases, Am. Petrol. Inst. Drill. Prod. Pract., 2, Lawn, B. (Ed.) (1993), Fracture of Brittle Solids, 2nd ed., Cambridge Univ. Press, Cambridge, U. K. Lehner, F., and M. Kachanov (1996), On modelling of winged cracks forming under compression, Int. J. Fract., 77, R69 R75. Nara, Y., P. G. Meredith, T. Yoneda, and K. Kaneko (2010), Influence of macro-fractures and micro-fractures on permeability and elastic wave velocities in basalt at elevated pressure, Tectonophysics, 503, Nasseri, M. H. B., A. Schubnel, P. M. Benson, and R. P. Young (2009), Common evolution of mechanical and transport properties in thermally cracked Westerly granite at elevated hydrostatic pressure, Pure Appl. Geophys., 166, Nasseri, M. H. B., A. Schubnel, and R. P. Young (2007), Coupled evolutions of fracture toughness and elastic wave velocities at high crack density in thermally treated Westerly granite, Int. J. Rock Mech. Min. Sci., 44,