# Elastic anisotropy and pore space geometry of schlieren granite: direct 3-D measurements at high confining pressure combined with microfabric analysis.

M Staněk, Yves Géraud, O. Lexa, P Špaček, S Ulrich, Marc Diraison

► To cite this version:

M Staněk, Yves Géraud, O. Lexa, P Špaček, S Ulrich, et al.. Elastic anisotropy and pore space geometry of schlieren granite: direct 3-D measurements at high confining pressure combined with microfabric analysis.. Geophysical Journal International, 2013, 194, pp.383-394. 10.1093/gji/ggt053 . hal-01217035

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# Elastic anisotropy and pore space geometry of schlieren granite: direct 3-D measurements at high confining pressure combined with microfabric analysis

Martin Staněk,<sup>1,2,3</sup> Yves Géraud,<sup>2</sup> Ondrej Lexa,<sup>3</sup> Petr Špaček,<sup>4</sup> Stanislav Ulrich<sup>5</sup> and Marc Diraison<sup>2</sup>

Accepted 2013 February 5. Received 2013 January 24; in original form 2012 August 27

## SUMMARY

Pore space geometry of granitic rocks and its evolution with depth are key factors in large-scale seismics or in projects of enhanced geothermal systems or of deep hazardous waste repositories. In this study, we studied macroscopically anisotropic schlieren-bearing granite by experimental P-wave velocity ($V_P$) measurements on spherical sample in 132 directions at seven different confining pressures in the range 0.1–400 MPa. In order to discriminate the phenomena affecting the rock elastic properties we analysed the orientation of microcracks and of grain boundaries and we measured the anisotropy of magnetic susceptibility of the rock. Three sets of microcracks were defined, with two of them linked to the massif exfoliation process and one to cooling contraction of the massif. During pressurization the measured mean $V_P$ and $V_P$ anisotropy degree at ambient pressure and at highest confinement (400 MPa) yielded 3.3 km s⁻<fnref n="1" /> and 24 per cent, and 6.2 km s⁻<fnref n="1" /> and 3 per cent, respectively. The associated $V_P$ anisotropy pattern was transversely isotropic and governed by the schlieren, with a minimum $V_P$ direction perpendicular to them and a girdle of high $V_P$ directions parallel to them. The highest change in $V_P$ was observed between 0.1 and 10 MPa, suggesting a significant closure of porosity below depths of 500 m. Change of the $V_P$ anisotropy pattern to orthorhombic together with increase of mean $V_P$ and $V_P$ anisotropy degree during depressurization was attributed to inelastic response of one of the sets of microcracks to the loading-unloading cycle.

**Key words:** Magnetic fabrics and anisotropy; Microstructures; Seismic anisotropy; Fractures and faults.

## INTRODUCTION

Over the last three decades, granitic rocks have been prospected as possible host rock massifs for deep (<1 km) radioactive waste repositories (Rempe 2007) and for even deeper (<5 km) enhanced geothermal systems (Tester et al. 2006). In addition, large scale models on continental crust seismicity (Goleby et al. 2006) and strength (DeNosaquo et al. 2009) take granite to be the rock representative of the continental upper crust. In all these applications, understanding of petrophysical properties of granitic rocks, such as permeability, thermal conductivity (TC), elastic wave velocity and mechanical strength, among others, appears to be critical. The anisotropic attributes of the above mentioned physical properties are controlled by the anisotropy of both the rock pore space and the rock solid matrix.

The microporosity in crystalline rocks is represented mainly by microcracks (microfractures, cracks), which can be differentiated according to their position with respect to the rock matrix (inter- or intragranular cracks, grain boundary cracks and cleavages cracks; Kranz 1983). The key microstructural characteristics of the rock matrix affecting the rock elastic properties are grain size, grain shape and shape preferred orientation (SPO) as well as the rock modal composition and crystallographic preferred orientation (CPO) of the constituent phases.

The contribution of each of the above mentioned features to the bulk elastic anisotropy is thoroughly discussed in the literature (see Ullemeyer et al. 2006; Machek et al. 2007 and references therein). The crack-induced porosity is important only at shallow levels of the crust as it is assumed that cracks close progressively with increasing lithostatic pressure and become completely closed at depths of

<footnote n="1"><sup>1</sup>Institute of Geophysics, Czech Academy of Sciences, Boční II 1401, 14131, Praha 4, Czech Republic. E-mail: stanekm@ig.cas.cz</footnote>

<footnote n="2"><sup>2</sup>University of Lorraine, Nancy, France</footnote>

<footnote n="3"><sup>3</sup>Charles University, Praha, Czech Republic</footnote>

<footnote n="4"><sup>4</sup>Masaryk University, Brno, Czech Republic</footnote>

<footnote n="5"><sup>5</sup>Centre for Exploration Targeting, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia</footnote>
3–6 km, that is, at effective pressures of 100–200 MPa. CPO becomes the main parameter controlling rock elastic anisotropy at depths where the crack porosity is closed (Kern & Wenk 1990; Kern 1993), and plays an important role in low porosity (<10 per cent), crystalline rocks. In granitic rocks, even small fractions (<10 per cent) of micas and amphiboles contribute significantly to elastic anisotropy due to their cleavage cracks, which have been shown to stay open even at confining pressures of up to 300 MPa (Babuška & Pros 1984). Especially biotite can contribute to the bulk rock elastic anisotropy significantly (Kern & Wenk 1990), as shows its single crystal elastic anisotropy of 44 per cent (Simmons & Wang 1971). In addition to CPO, biotite and muscovite SPO has been found to contribute significantly to the bulk rock elastic anisotropy (Kern et al. 2009).

In granites containing biotite and muscovite, but no amphibole or ferromagnetic minerals, the orientation of biotite can be easily evaluated by analysis of anisotropy of magnetic susceptibility (AMS; Hrouda 1982; Borradaile & Henry 1997), as the paramagnetic biotite is the principal carrier of the magnetic fabric with single crystal magnetic susceptibility one order of magnitude higher than that of muscovite and two to three orders of magnitude higher than those of diamagnetic quartz or feldspars (Tarling & Hrouda 1993). In the case of dia- and paramagnetic minerals, the AMS is controlled by orientation of the crystallographic axes of minerals (Khan 1962). Isometric crystals of biotite have an AMS ellipsoid that is nearly rotationally symmetric, with its short axis subparallel to the crystallographic c-axis, that is, perpendicular to the cleavage plane (Zapletal 1990; Martín-Hernández & Hirt 2003). For granite containing elongated biotite crystals, strong agreement has been observed between the orientations of the long axis of the biotite crystals and the direction of the highest magnetic susceptibility (Archanjo et al. 1995).

In order to understand the evolution of elastic anisotropy with depth and its relation to rock matrix and microporosity in mesoscopically anisotropic granite, we measured P-wave velocities ($V_p$) of spherical sample of Lipnice granite, Melechov massif, Czech Republic, for confining pressures up to 400 MPa. Furthermore, we analysed the AMS and performed qualitative and quantitative microstructural analysis of microporosity. As such, our experiments provide us with a method to study the pressure compliance with

increasing depth of genetically distinct kinds of microporosity encountered in such rocks. Consequently the results can form a basis to predict the evolution of rock porosity and permeability at depth, though this was outside the scope of the present work. The applied pressure conditions simulate *in situ* depths of up to 10 km, thereby including the typical depths where engineering applications such as radioactive waste repositories or enhanced geothermal systems are commonly envisaged.

## GEOLOGICAL SETTING

### The Melechov massif

The sample material was obtained from the Lipnice granite outcropping near the town of Lipnice nad Sázavou, Czech Republic (49.61484°N; 15.41360°E), situated within the Melechov massif (MM) that has been chosen by the Czech radioactive repository authority (RAWRA) as a research training site. The MM represents the northernmost part of the Central Moldanubian Pluton, which belongs to the Moldanubian zone of the Bohemian Massif (Fig. 1a). The MM covers an area of about 120 km² and reaches down to a depth of 2–17 km (Šrámek et al. 1996; Mlčoch et al. 2000). The columnar batholith of the MM consists of four types of peraluminous two-mica granite disposed in a concentric manner. From the centre outwards these are the Stvořidla, Melechov, Kouty and Lipnice granites (Fig. 1b). Based on the discordance between the magmatic and the host rocks (Chlupáč et al. 2002), the intrusion of the MM granites is considered to be post-orogenic relative to the Variscan events, and formed in a time span of 315 ± 0 Ma, based on radiometric dating of monazites crystals (Breiter & Sulovský 2005). Post-intrusion deformation of the massif is represented by two principal sets of cooling-related and sometimes reactivated subvertical joints (Lexa & Schulmann 2004). Set 1 is characterized by WNW-ESE trending and fractures of several tens of meters in length and by fracture spacing of 1–5 m. Set 2 is NNE-SSW trending and is characterized by fractures of several meters in length and fracture spacing of 0.5–5 m. Another third set is recognized, which is represented by shallowly dipping (<20°) sheeted fractures (exfoliations) related to the exhumation of the massif.

<figure><img src="image_2.png" /><figcaption>**Figure 1.** (a) Map showing the location of the study area, simplified geological map of the Bohemian Massif (modified after Franke 2000) (a – Saxothuringian and Lugian, b – Teplá-Barrandian, c – Variscan granitoids, d – Moldanubian Batholith, e – Gföhl unit, Varied and Monotonous unit, g – Brunovistulian, h – Cretaceous sedimentary cover), (b) Geological map of the Melechov massif with the location of the sampled outcrop (modified after Machek 2011).</figcaption></figure>
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Photograph of the YZ face of the sampled block showing the folded schlieren visible in the upper part of the image. The reference fractures orientation (XY) is perpendicular to the section and parallel to its longer side.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Figure 3.** Photomicrograph of Lipnice granite obtained in polarized (a), cross-polarized (b) and UV (c) light. The thin section (YZ) is perpendicular both to the reference fractures and to the schlieren. Arrows point to representative examples of intragranular cracks in mica (1), in quartz (2) and in feldspar (3).</figcaption></figure>

## The sampled outcrop of the Lipnice granite

The Lipnice granite at L.n.S. displays a clear foliation visible at the mesoscale and defined by quartz- or biotite-rich bands (Fig. 2). The foliation is asymmetrically folded at both the outcrop scale and at the scale of the hand specimen. The long limbs of the folds dip at very moderate E (ESE) angles, while the short limbs are steep and strike N-S, with the fold axis lying subhorizontally in the N-S direction. Fractures observed at the outcrop follow the general characteristics given above except that set 2 is characterized by fracture clusters spaced by one to several tens of metres, with each cluster containing fractures with cm-dm spacing. A block of Lipnice granite 30 cm × 20 cm × 12 cm in size was taken in oriented manner from between two subparallel exfoliation fractures dipping 20° W. These fractures will be referred to as reference fractures in the following text. With

respect to the sample block, the closest fractures of set 1 and set 2 were at distances of 1 and 10 m, respectively.

## Characteristics of the samples

From this block, an oriented spherical sample of 50 mm in diameter was prepared for $V_p$ measurements and six cylindrical cores measuring 25.4 mm in diameter and 21 mm in length were prepared for AMS measurements. After preparation to final shape, the spherical sample was oven-dried during 24 hr at 50 °C and then covered by three thin layers of epoxy resin to protect the material from the confining oil, present in the setup.

Three mutually perpendicular thin sections were also prepared from the block, with one of them perpendicular both to the reference fractures and to the schlieren and another one perpendicular to the reference fractures. As can be seen in thin section photomicrographs (Fig. 3), the sample material features elongated crystals preferentially aligned with the schlieren and ubiquitous microcracks. The quartz shows mostly intra- or transgranular, curved cracks, whereas in micas and feldspars rather straight cracks often follow the mineral cleavages and are interconnected into intergranular cracks.

Microstructural analysis of the three sections was performed to determine the sample mineral composition, grain size and grain aspect ratio. A total of 779 grains was analysed using ESRI ArcGIS software for manual tracing of digital photographs and MATLAB™ PolyLX toolbox (Lexa et al. 2005) for geometric evaluation of the traced objects. The results of our thin section analysis are summarized in Table 1.

Mercury porosimetry yielded a sample density of 2.626 g cm⁻³ and a total porosity of 1.4 per cent, taking into account pores with access diameter between 0.3 and 5 nm. TC was measured by optical scanning method (Popov et al. 1999) along the principal directions of two orthogonal systems defined by the reference fractures and by the schlieren long limb. Independently on the chosen direction, the analysis yielded TC in a narrow range of 2.3–2.5 W m⁻¹ K⁻¹.

## EXPERIMENTAL METHODS AND TECHNIQUES

### Experimental P-wave velocity measurement

We performed laboratory $V_p$ measurements on a spherical sample of Lipnice granite described by Pros & Babuška (1968) (see also Pros et al. 1998a, 2003; Machek et al. 2007). The main advantage of using a spherical sample, as opposed to using an orthogonal or multiple cylindrical samples is the possibility to continuously evaluate the spatial distribution of $V_p$ within the studied material. The method inherently eliminates any errors introduced by assumptions

<table><caption>**Table 1.** Modal proportion, grain size and grain shape aspect ratio of the Lipnice granite. Shown are means of values of the three traced thin sections. ALL, all grains; Qtz, quartz; Pl, plagioclase; Kf, K-feldspar; Bt, biotite; Ms, muscovite; $a_1$, $a_3$, long and short axis of grain shape; $Q_1$, $Q_3$, first and third quartile of the population of traced grains.</caption><thead><tr><th rowspan="2">Phase</th><th rowspan="2">Area (per cent)</th><th colspan="4">Equal area diameter (mm)</th><th colspan="4">Axial ratio $a_1/a_3$</th></tr><tr><th>Min</th><th>Mean</th><th>Max</th><th>Q1-Q3</th><th>Min</th><th>Mean</th><th>Max</th><th>Q1-Q3</th></tr></thead><tbody><tr><td>ALL</td><td></td><td>0.17</td><td>0.70</td><td>2.22</td><td>0.45-0.87</td><td>1.0</td><td>1.8</td><td>4.1</td><td>1.4-2.1</td></tr><tr><td>Qtz</td><td>35</td><td>0.15</td><td>0.70</td><td>1.92</td><td>0.49-0.87</td><td>1.0</td><td>1.6</td><td>3.4</td><td>1.3-1.9</td></tr><tr><td>Pl</td><td>33</td><td>0.17</td><td>0.71</td><td>2.78</td><td>0.42-0.89</td><td>1.0</td><td>1.7</td><td>3.4</td><td>1.3-1.9</td></tr><tr><td>Kf</td><td>17</td><td>0.18</td><td>0.70</td><td>2.44</td><td>0.46-0.82</td><td>1.0</td><td>1.9</td><td>4.8</td><td>1.4-2.3</td></tr><tr><td>Bt</td><td>5</td><td>0.19</td><td>0.52</td><td>1.11</td><td>0.36-0.64</td><td>1.0</td><td>2.8</td><td>7.7</td><td>1.8-3.4</td></tr><tr><td>Ms</td><td>9</td><td>0.22</td><td>0.98</td><td>2.42</td><td>0.47-1.37</td><td>1.0</td><td>2.0</td><td>3.7</td><td>1.4-2.4</td></tr></tbody></table>
<figure><img src="image_5.png" /><figcaption>**Figure 4.** (a) Equipment for the laboratory study of P-wave anisotropy on spherical samples under hydrostatic pressure of up to 400 MPa, (b) Sample set up (T – transmitter, R – receiver) and (c, d) Grid of measurement directions with a step of 15°.</figcaption></figure>

regarding the rock texture, modal composition, density and elastic constants. In this light the multidirectional measurements on spherical sample are irreplaceable, even though a recent study using 21 directions of three orthogonally cored subsamples reaches a good fit relative to the measurements on spherical sample (Louis *et al.* 2012).

For our $V_p$ experiments we used the apparatus set up by Z. Pros (see Pros *et al.* 1998a) at the Institute of Geophysics in Prague, which consists of a pressure vessel containing the sample, which is placed in a special positioning unit, a pulse generator, a pulse acquisition unit and an oscilloscope (Fig. 4a). For placement into the positioning unit, two pinions were glued to the poles of the spherical sample. After mounting the sample into the pressure vessel, this enabled rotation of the sample around its vertical axis. Furthermore, a rectangular frame containing two spring-hold piezoelectric transducers, with eigenfrequency of 1 MHz, allows symmetrical rotation of the transducers around a horizontal axis (Fig. 4b). This setup of the sample enables measurement of P-wave traveltime in any direction, with exception of an area of 15° as a result of interference with the pinions. We measured $V_p$ in 132 directions with a step size of 15° (Figs 4c and d), at confining pressure ($P_c$) of 0.1, 10, 20, 50, 100, 200 and 400 MPa). $V_p$ measurements were performed both during stepwise pressurization and depressurization of the sample.

During our experiments P-wave traveltimes were continuously logged using a PC. The measured traveltimes were corrected for any time delay caused by the epoxy layers and by the acquisition elements of the apparatus. The thickness of the epoxy is calculated by subtraction of diameter of the sample before and after epoxy application, typically being 0.05 mm. The delay of the acquisition elements was calibrated by measuring a standard metal sample with known traverse time. The compressional wave velocity was then calculated using the distance given by the sphere diameter.

## Anisotropy of magnetic susceptibility

We measured the AMS on AGICO MFK-1A kappabridge by means of rotating specimen method (Jelínek 1997). Measurements were made at an operating frequency of 976 Hz and peak field intensity of 200 A m⁻¹. A statistical analysis of the AMS data was carried out using the ANISOFT 4.2 MS Windows application. In order to characterize the intensity and shape of the magnetic fabric ellipsoid two parameters (Nagata 1961; Jelínek 1978) were calculated: degree of anisotropy $P = k_1/k_3$, and the shape factor $T = 2 \ln(k_1/k_2) \ln(k_2/k_3) - 1$, where $0 < T < 1$ indicates oblate and $-1 < T < 0$ prolate shapes of magnetic susceptibility ellipsoids. The $k_1 \ge k_2 \ge k_3$ are principal susceptibilities, respectively. The mean magnetic susceptibility $k_m$[($k_m = (k_1 + k_2 + k_3)/3$) reflects the qualitative and quantitative content of magnetic minerals in the rock. In relation to the magnetic fabric the maximum principal susceptibility ($k_1$) represents the magnetic lineation and the minimum principal susceptibility ($k_3$) is considered as a pole to magnetic foliation.

## Tracing of grain boundaries and microcracks

We used microphotographs of three mutually perpendicular, epoxy-saturated thin sections to manually trace grain boundaries, intergranular cracks and intragranular cracks in quartz, feldspars and in micas using ESRI ArcMap 9.3 GIS software. Grain boundaries were traced on microphotographs obtained under cross-polarized light, whereas microphotographs obtained under UV-excited fluorescence light were used for tracing of the cracks. The sample material was epoxy-saturated prior to preparation of the thin-section and so any cracks due to the preparation do not appear in the UV image and are consequently not accounted for during the tracing. The traced networks were processed in MATLAB™ FracnetLX toolbox (Lexa 2010), in order to visualize the orientation distribution functions on rose diagrams and to calculate the bulk anisotropy of preferred orientation [SURFOR ‘A(α)’ function after Panozzo (1984)] for each of the traced features. The presented normalized value of the SURFOR function ranges from 0 for perfect unimodal orientation to 1 for pluri-modal or non-preferred orientation.

## RESULTS

Note that we use the term ‘schlieren’ to refer to the planar structure represented by the long limb of the schlieren fold, as it is the predominant mesoscopic structure in the sample compared to the short limb. Also we will use the terms UP and DOWN to refer to the pressurization and the depressurization stages of the P-wave experiment, respectively.

### Ultrasonic P-wave velocity data

We plotted the results of our $V_p$ measurements on the lower hemisphere of equal area projection using grey scale look up table unique
for each of the plot in order to accentuate the anisotropy evolution throughout the experiment. For easier visual comprehension the plot data are contoured by isolines. In total, we constructed three types of stereo plots that we use for interpretation:

(1) $V_p$ plots for each of the 13 confinement levels (seven during pressurization, six during depressurization). These plots show the $V_p$ range and directional dependence of $V_p$ with confining pressure (depth).

(2) $\Delta V_p(\Delta p)$ plots showing changes of $V_p$ pattern between successive levels of confining pressure, for both pressurization and depressurization. Changes in $V_p$ are correlated to the closing or opening of microporosity as a function of confining pressure (depth).

(3) Hysteresis $\Delta V_p$ plots showing differences in $V_p$ pattern at the same constant confinement level between pressurization and depressurization. Hysteresis is a measure for any irreversible deformation induced by pressure loading and unloading.

In addition to the $V_p$ scale, all plots also show the degree of $V_p$ anisotropy $k$, defined as (Babuška 1968)

$$k = (V_{Pmax} - V_{Pmin}) / [(V_{Pmax} + V_{Pmin}) / 2], \quad (1)$$

where $V_{Pmax}$ and $V_{Pmin}$ are, respectively, the maximum and the minimum $V_p$ values.

We constructed stereo plots visualizing the anisotropy of $V_p$, at different confining pressures (Fig. 5). At ambient pressure (0.1 MPa) the anisotropy is nearly transversely isotropic, with high $V_p$ directions parallel to the schlieren and the lowest $V_p$ direction perpendicular to them. This pattern persists over the entire pressurization, though a rapid decrease of anisotropy is observed between 0.1 and 50 MPa from 24 to 8 per cent, which further decreases to 3 per cent towards peak confinement. Note that for the depressurization a progressive transition from transversely isotropic to orthorhombic pattern can be seen, with the minimum $V_p$ direction perpendicular to the schlieren and the higher values arranged in an elliptical pattern with the long axis lying in the plane of the schlieren. The orthorhombic pattern persists for the remainder of the DOWN part. An increase of the degree of anisotropy is observed reaching a value of 36 per cent at ambient pressure, that is, a value 1.5 times the value at the onset of the experiment (0.1 MPa UP). The evolution of the minimal, mean and maximal $V_p$ values ($V_{Pmin}$, $V_{Pmean}$, $V_{Pmax}$) as a function of confining pressure is plotted in Fig. 6(a), for both UP and DOWN sequence and the pressures of 0.1–100 MPa. Note that the slope $\Delta V_p/\Delta p$ becomes successively gentler going from the ambient to the highest pressure. Whilst the values of $V_{Pmin}$ UP and $V_{Pmin}$ DOWN at ambient pressure are similar, they differ strikingly for the $V_{Pmax}$ UP and $V_{Pmax}$ DOWN. Comparison of the six $V_p$ curves on the entire displayed pressure interval reveals a strongly deviatory $V_{Pmax}$ DOWN function, which, contrarily to the others, features only slight breaks at the levels of 20, 50 and even 100 MPa.

Stereo plots displaying the changes in $V_p$ with pressure, $\Delta V_p(\Delta p)$, for each of the pressure steps, are shown in Fig. 7. As can be seen, the pressure step between 10 and 0.1 MPa shows similar values of mean $\Delta V_p(\Delta p)$ for both the UP (94 m s$^{-1}$ MPa$^{-1}$) and the DOWN (99 m s$^{-1}$ MPa$^{-1}$) sequences. Furthermore, these mean values of $\Delta V_p(\Delta p)$ are the highest of all the pressure steps. For the low pressure steps (0.1–100 MPa), the steps 20–10 MPa display the least anisotropy, whereas the steps 50–20 MPa [mean $\Delta V_p(\Delta p)$ of 18 and 14 m s$^{-1}$ MPa$^{-1}$ for the UP and DOWN sequence, respectively] show a marked difference in anisotropy of $\Delta V_p(\Delta p)$. A clear transition from transversely isotropic to an orthorhombic anisotropy pattern is observed in the DOWN step, whereas this change in anisotropy is not observed in the UP step. The orthorhombic anisotropy can

<figure><img src="image_6.png" /><figcaption>Figure 5. Results of measurements of P-wave velocity spatial distribution at confining pressures 0.1–400 MPa for pressurization (UP) and depressurization (DOWN) plotted on lower hemisphere of equal area projection. For each step, minimum, mean and maximum $V_p$ (m s$^{-1}$) are shown near the grey scale and $V_p$ anisotropy degree $k$ (per cent) is shown below the grey scale. The directions of maximum and minimum $V_p$ are represented by white and black dot, respectively. Orientations of the schlieren (S) and of the reference fractures (F) are represented by dashed and full line, respectively.</figcaption></figure>

be also seen in the DOWN steps of 100–50 MPa and 200–100 MPa. Striking information on the evolution of the $V_p$ anisotropy degree $k$ is visible through the curve of its hysteresis plotted in Fig. 6b. One can see that there is hardly any hysteresis of $V_p$ anisotropy for pressure 100 MPa (and higher), whereas there is a gradual increase of $V_p$ anisotropy hysteresis towards the ambient pressure defining three intervals 100–50, 50–10 and 10–0.1 MPa as progressively more hysteretic ones.
<figure><img src="image_7.png" /><figcaption>**Figure 6.** Evolution of minimum, mean and maximum $V_p$ (a), $V_p$ anisotropy (b) and hysteresis of minimum, mean and maximum $V_p$ (c) with hydrostatic pressure for pressurization (UP) and depressurization (DOWN).</figcaption></figure>

Stereo plots showing $V_p$ hysteresis, $\Delta V_p$, that is, the difference $V_p$ UP minus $V_p$ DOWN at a given confining pressure, are shown in Fig. 8, for $P_c$ of 0.1, 50, 100 and 200 MPa. As can be seen, hysteresis anisotropy is negligible at high pressures (100 and 200 MPa), whereas it is striking for the low pressures (0.1 and 50 MPa), show-

<figure><img src="image_8.png" /><figcaption>**Figure 7.** Spatial distributions of calculated differences $\Delta V_p(\Delta p)$ for pressurization (UP) and depressurization (DOWN) plotted on lower hemisphere of equal area projection. For each step, minimum, mean and maximum $\Delta V_p(\Delta p)$ (m s$^{-1}$) are shown near the grey scale. The directions of maximum and minimum $\Delta V_p(\Delta p)$ are represented by white and black dot, respectively. Orientations of the schlieren (S) and of the reference fractures (F) are represented by dashed and full line, respectively.</figcaption></figure>

ing a clear transversely isotropic pattern. This is confirmed by the larger interval $V_{Pmax} - V_{Pmin}$ at lower pressures, compared to higher pressures. The hysteresis stereo plots show that there is an irreversible change within the sample material, as a result of pressurization. During depressurization, down to $P_c$ of 100 MPa, the rock responds in an elastic fashion, while further depressurization suggests non-elastic response, resulting from irreversible deformation. The hystereses of $V_{Pmin}$, $V_{Pmean}$ and $V_{Pmax}$ are plotted in Fig. 6c as a
<figure><img src="image_9.png" /><figcaption>**Figure 8.** Spatial distributions of calculated hystereses ($\Delta V_p$) plotted on lower hemisphere of equal area projection. For each step, minimum, mean and maximum $\Delta V_p$ (m s$^{-1}$) are shown near the grey scale. The directions of maximum and minimum $\Delta V_p$ are represented by white and black dot, respectively. Orientations of the schlieren (S) and of the reference fractures (F) are represented by dashed and full line, respectively.</figcaption></figure>

function of confining pressure for $P_c$ of 0.1–100 MPa. Note that the hysteresis of $V_{Pmax}$ is higher than that of $V_{Pmin}$ for all the pressure levels and that all the three functions culminate at the pressure level of 10 MPa.

## Anisotropy of magnetic susceptibility

The mean magnetic susceptibility ($k_m$) in the analysed samples ranges from 70.2 to 97.8 × 10$^{-6}$ SI. Such mean magnetic susceptibility is at the lower limit of susceptibilities typical of the Variscan biotite granites of the Bohemian Massif. As can be seen on P–T diagram in Fig. 9(a), the magnetic anisotropy degree parameter $P$ ranges from 1.093 to 1.109 and the shape parameter $T$ varies between 0 and 0.7, suggesting oblate susceptibility ellipsoid. Stereo plot relating the principal susceptibility directions to the orientation of the sample mesostructures (Fig. 9b) shows that the maximum susceptibility ($k_1$) direction is parallel with the schlieren and the minimum susceptibility ($k_3$) direction is perpendicular to them.

<figure><img src="image_10.png" /><figcaption>**Figure 9.** Results of AMS analysis. (a) P–T plot, (b) Orientation of principal axes of the AMS ellipsoid ($k_1, k_2, k_3$) plotted on lower hemisphere of equal area projection. Orientations of the schlieren and of the reference fractures are represented by dashed and full line, respectively.</figcaption></figure>

## Tracing of grain boundaries and microcracks

The results of the tracing for each of the defined microstructural feature are shown in Figs 10(b)–(f), in the form of rose diagrams and values of normalized SURFOR $A(\alpha)$ value for each of the three sections.

It is clear that the section (YZ) perpendicular to both mesoscopic structures, that is, the schlieren and the fractures, bears the most anisotropy. A clear pattern was obtained for all features with exception of the feldspar cracks, for which a dominant orientation is accompanied by two subdominant ones. Overall, XY section shows less anisotropy, though one dominant orientation can still be seen for all the features, with the exception of the feldspar cracks. In case of the least anisotropic section XZ, a clear dominant orientation for grain boundaries and mica and feldspar cracks is observed, whereas several directions of similar strength can be discerned in the cases of intergranular and quartz cracks.

## SUMMARY AND DISCUSSION

The schlieren represent a dominant structure for both of the petrophysical methods and are reflected by the preferred orientation of grain boundaries. The effect of microcracks on elastic properties is expressed by the rapid increase in bulk $V_p$ during the low-pressure stages of pressurization and by the anisotropy of some of the $V_p$ measurements and calculations. We will now discuss the orientation of the traced features and of the magnetic fabric and we will examine their relation to the $V_p$ data. We will also discuss the relation of the microcracks to the massif fracture system and compare the bulk elastic properties of our sample with those of other granitic rocks reported in the literature. Finally, we will consider implications of the presented data for the evolution of the rock porosity, permeability and TC with confining pressure.

### Orientation of grain boundaries, cracks and magnetic fabric

Based on the preferred orientation of the 2-D traces acquired by tracing of the thin sections shown above (Fig. 10), we derived the orientation of planes representing each of the traced features (Fig. 11). The YZ section, which is perpendicular to both the schlieren and the fractures, displays the highest preferred orientation for all the traced features and was therefore attributed the main importance. The 3-D orientation of grain boundaries and of intragranular feldspar cracks
<figure><img src="image_11.png" /><figcaption>**Figure 10.** Results of photomicrograph tracing. (a) Orientation of thin sections with respect to the sample mesostructures, (b–f) orientation rose diagrams for grain boundaries, intergranular cracks, and intragranular cracks in quartz, mica and feldspar featuring the normalized value of SURFOR 'A(α)' function [after Panozzo (1984)] on the bottom right.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Figure 11.** Interpretation of the traced features 3-D orientation. Lower hemisphere equal area projections showing orientation of the sample mesostructures (a) and of the traced features (b). For easier comparison with the *V*<sub>P</sub> data both great circles (lines) and poles to the planes (symbols) are plotted to represent the orientation of the traced features.</figcaption></figure>

are each represented by one plane, whereas for intergranular cracks and intragranular cracks in quartz and micas, the 2-D patterns could not be reasonably combined into one plane and they are therefore represented by two differently oriented planes. Although other interpretations of the 2-D patterns are possible, for the sake of clarity we present only the simplest solution reflecting the sample mesostructures and the results of the two petrophysical methods.

Comparison of the stereo plots displaying the orientation of the sample mesostructures and of the traced features in Figs 11(a) and (b) shows that the grain boundaries, mica and feldspar cracks and one of two populations of intergranular cracks are subparallel to the schlieren. The other population of intergranular cracks and one population of quartz cracks are subperpendicular both to the schlieren and to the reference fractures. Finally, the other population of intraquartz cracks is subparallel to the reference fractures.

The AMS analysis results indicate that the rock magnetic fabric is controlled by biotite and that the magnetic susceptibility ellipsoid is rather oblate, with the symmetry axis ($k_3$) oriented perpendicular to the schlieren, that is, that the biotite basal planes are coplanar with them (Fig. 9b). This observation is coherent with the evaluated

preferred orientation of mica cracks (Fig. 11b), taking into account that the mica cracks predominantly follow the mica cleavage planes.

## Pore fabric effect on elastic properties

The ultrasonic experiment characterizes the sample at ambient pressure before pressurization by a transversely isotropic pattern with minimum $V_p$ direction perpendicular to the schlieren. In terms of the traced features, the minimum $V_p$ direction is sub-parallel to the poles to grain boundaries, feldspar cracks and one population of intergranular cracks. Also poles to both of the mica crack populations are close (<20°) to the minimum $V_p$ directions. Detailed look on the corresponding $V_p$ stereo plot (Fig. 5, 0.1 MPa UP) reveals that the distribution of the low $V_p$ directions surrounding the absolute minimum is slightly deviated towards the direction of pole to the population of quartz cracks that are subparallel to the reference fractures. The interference of the quartz cracks at low pressures is accentuated by the first step 10–0.1 MPa of the pressurization part, where two separate directions of high $\Delta V_p(\Delta p)$ partly coincide with the 0.1 MPa level low $V_p$ directions (compare Figs 5 and 7). The high mean $\Delta V_p/\Delta p$ value (93 m s⁻¹ MPa⁻¹) during this first pressurization step suggests major closing of porosity below pressure of 10 MPa. It is likely that the porosity reduction is linked to the closing of the quartz cracks and the schlieren-related cracks given that the two high $\Delta V_p(\Delta p)$ directions coincide with poles to these two cracks populations.

At higher confinement levels the elastic anisotropy pattern stays transversely isotropic and schlieren-controlled, the most important phenomenon being a strongly anisotropic $V_p$ change during the 50–20 MPa step with mean $\Delta V_p/\Delta p$ value of 18 m s⁻¹ MPa⁻¹. Differently to the major $V_p$ change during the 10–0.1 step, in this case the directions of high $\Delta V_p(\Delta p)$ are concentrated in proximity of the poles to the schlieren-oriented cracks only, suggesting that the quartz cracks do not comply significantly. The step 100–50 MPa
exhibiting low $\Delta V_p/\Delta p$ value of 9 m s⁻¹ MPa⁻¹, indicates compliance of quartz and intergranular cracks as the $\Delta V_p(\Delta p)$ maximum direction is close to the poles to both of them.

The populations of quartz and intergranular cracks that are sub-perpendicular to both the schlieren and the reference fracture seem to respond to the loading only very subtly as hardly any particular direction of $V_p$ increase can be linked to their orientation. On the other hand, their presence is manifested during the depressurization sequence of the ultrasonic experiment by the high $V_p$ hysteresis directions clearly oriented about poles to these two crack populations. The hysteresis is thus linked to irreversible closing of the cracks in reaction to the pressure loading, probably due to collapse of the cracks or due to crushing of the crack wall asperities. As a consequence, during sample unloading the $V_p$ anisotropy degree $k$ at each pressure level is greater than at its pressurization equivalent and reaches 36 per cent after complete unloading with hand-in-hand change of anisotropy pattern from transversely isotropic to orthorhombic.

Taking into account that the hysteresis can be clearly seen only at pressures of 100 MPa or lower, there is only elastic response (in all directions) at pressures higher than 100 MPa. Furthermore, the fact that the UP and DOWN steps of 10–0.1 MPa agree quite precisely in values of minimum and maximum $\Delta V_p(\Delta p)$ as well as in the anisotropy pattern implies that the rock reacted in elastic manner also at confining pressures below 10 MPa, which can be seen from a different point of view via the plot of $V_p(p)$ curves (Fig. 6). The values of $V_{Pmax}$ DOWN, which correspond to the directions of the highest $V_p$ hysteresis, decreased over the pressure interval 100–10 MPa during depressurization at clearly lower rate than the corresponding $V_p$ means and minima, whereas for the last step (10–0.1 MPa) the three values decreased at similar rate. Synthesizing the above observations, the pressure interval where irreversible change dominantly takes place can be constrained to 10–100 MPa.

It should be noted that the $V_p$ measurements were carried out on a dry rock sample, that is, with the air as pore fluid. However, in *in situ* conditions, the rock pore space can be filled by another fluid (e.g. water solution) as a consequence of high pore fluid pressure. In such a setting, one can expect increase of bulk rock $V_p$ and decrease of $V_p$ anisotropy with respect to the presented values. Both the effects would then be proportional to the *in situ* total porosity and to the $V_p$ ratio of the air and of the *in situ* pore-filling fluid.

## Comparison of the $V_p$ data to previous studies

In Table 2, we have displayed the mean $V_p$ and $V_p$ anisotropy at different confining pressures for granitic rocks of similar density as the Lipnice granite (2.627 ± 0.05 g cm⁻³). As can be seen, at ambient pressure the Lipnice granite shows very low minimum $V_p$ and strong anisotropy. Although studies report samples with similar $V_p$ and $k$ values, these samples feature two or three times higher bulk porosity. Furthermore, in comparison with the slowest reported granites, the mean $V_p$ of the Lipnice granite at high confining pressures (≥100 MPa) yields only slightly lower (~0.1 km s⁻¹) values. The low mean $V_p$ at ambient pressure coupled with the low porosity, as well as the regain of ‘normal’ $V_p$ at high confining pressures of Lipnice granite indicates that its porosity is mainly composed of low aspect ratio pores, that is, cracks, which are more susceptible to decelerate a propagating elastic wave and to comply at lower confining pressure as compared to equant pores. This hypothesis is supported by the observation that the minimum $V_p$ in our sample was measured in direction perpendicular to intergranular cracks

<table><caption>**Table 2.** Comparison of mean $V_p$ ($V_{Pmax}$) and anisotropy degree ($k$) of the Lipnice granite and of previously studied granitic rocks as a function of confining pressure ($P_c$). Sample superscript numbers refer to: 1 – this study, 2 – Machek (2011), 3 – Pros et al. (1998b), 4 – Nur & Simmons (1969).</caption><thead><tr><th rowspan="3">Sample</th><th rowspan="3">Grain size<br>(mm)</th><th colspan="8">P<sub>c</sub> (MPa)</th><th colspan="8">V<sub>P</sub> (km s<sup>-1</sup>)</th></tr><tr><th colspan="2">0.1</th><th colspan="2">10</th><th colspan="2">20</th><th colspan="2">50</th><th colspan="2">100</th><th colspan="2">200</th><th colspan="2">400</th></tr><tr><th>Density<br>(g cm<sup>-3</sup>)</th><th>Porosity<br>(per cent)</th><th>k</th><th>V<sub>P</sub><br>(km s<sup>-1</sup>)</th><th>per cent</th><th>k</th><th>V<sub>P</sub><br>(km s<sup>-1</sup>)</th><th>per cent</th><th>k</th><th>V<sub>P</sub><br>(km s<sup>-1</sup>)</th><th>per cent</th><th>k</th><th>V<sub>P</sub><br>(km s<sup>-1</sup>)</th><th>per cent</th><th>k</th><th>V<sub>P</sub><br>(km s<sup>-1</sup>)</th><th>per cent</th></tr></thead><tbody><tr><td>Lipnice<sup>1</sup></td><td>0.7</td><td>2.626</td><td>1.4</td><td>3.3</td><td>23.8</td><td>4.1</td><td>13.0</td><td>4.5</td><td>11.2</td><td>5.1</td><td>7.6</td><td>5.5</td><td>5.7</td><td>5.9</td><td>3.5</td><td>6.1</td><td>3.0</td><td>—</td><td>—</td></tr><tr><td>Kouty-<sup>2</sup></td><td>0.7</td><td>—</td><td>1.7</td><td>4.4</td><td>12.4</td><td>5.0</td><td>10.4</td><td>5.3</td><td>8.5</td><td>5.6</td><td>5.7</td><td>5.8</td><td>4.8</td><td>6.0</td><td>3.9</td><td>6.2</td><td>3.2</td><td>—</td><td>—</td></tr><tr><td>Kouty-m<sup>2</sup></td><td>0.9</td><td>—</td><td>2.2</td><td>—</td><td>—</td><td>4.6</td><td>7.3</td><td>4.9</td><td>6.2</td><td>5.4</td><td>4.9</td><td>5.7</td><td>3.9</td><td>6.0</td><td>2.8</td><td>6.1</td><td>2.8</td><td>—</td><td>—</td></tr><tr><td>Melechov<sup>2</sup></td><td>1.5</td><td>—</td><td>3.3</td><td>—</td><td>—</td><td>4.2</td><td>24.0</td><td>4.7</td><td>16.7</td><td>5.3</td><td>10.8</td><td>5.7</td><td>8.2</td><td>6.0</td><td>5.8</td><td>6.1</td><td>5.2</td><td>—</td><td>—</td></tr><tr><td>KVP G5<sup>3</sup></td><td>0.4</td><td>2.651</td><td>—</td><td>5.5</td><td>6.0</td><td>—</td><td>—</td><td>—</td><td>4.0</td><td>6.0</td><td>—</td><td>—</td><td>3.6</td><td>6.1</td><td>3.3</td><td>6.3</td><td>—</td><td>—</td><td>—</td></tr><tr><td>SP G6<sup>3</sup></td><td>0.3</td><td>2.627</td><td>2.9</td><td>3.7</td><td>23.8</td><td>—</td><td>—</td><td>—</td><td>4.7</td><td>14.6</td><td>5.3</td><td>—</td><td>5.8</td><td>4.7</td><td>6.1</td><td>2.8</td><td>6.3</td><td>—</td><td>—</td></tr><tr><td>SP G8<sup>3</sup></td><td>0.9</td><td>2.621</td><td>3.0</td><td>3.2</td><td>24.6</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>5.3</td><td>—</td><td>5.7</td><td>5.8</td><td>6.0</td><td>6.0</td><td>6.2</td><td>—</td><td>—</td></tr><tr><td>KVP G9<sup>3</sup></td><td>0.6</td><td>2.608</td><td>4.1</td><td>3.3</td><td>38.6</td><td>—</td><td>—</td><td>—</td><td>4.8</td><td>8.1</td><td>5.3</td><td>—</td><td>5.6</td><td>5.2</td><td>5.9</td><td>3.4</td><td>6.0</td><td>—</td><td>—</td></tr><tr><td>KVP ZC19<sup>3</sup></td><td>—</td><td>2.578</td><td>—</td><td>5.1</td><td>14.7</td><td>—</td><td>—</td><td>—</td><td>5.6</td><td>15.8</td><td>6.0</td><td>—</td><td>6.2</td><td>6.2</td><td>5.8</td><td>6.3</td><td>—</td><td>—</td><td>—</td></tr><tr><td>Casco<sup>4</sup></td><td>5.0</td><td>2.626</td><td>0.7</td><td>3.3</td><td>—</td><td>5.1</td><td>—</td><td>—</td><td>5.7</td><td>—</td><td>—</td><td>—</td><td>6.5</td><td>—</td><td>6.6</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>Westerly<sup>4</sup></td><td>0.8</td><td>2.646</td><td>0.9</td><td>3.8</td><td>—</td><td>5.0</td><td>—</td><td>—</td><td>5.3</td><td>—</td><td>—</td><td>—</td><td>5.9</td><td>—</td><td>6.1</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>Troy<sup>4</sup></td><td>4.0</td><td>2.670</td><td>0.2</td><td>4.4</td><td>—</td><td>5.9</td><td>—</td><td>—</td><td>6.2</td><td>—</td><td>—</td><td>—</td><td>6.5</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr></tbody></table>
and mica cracks. In this regard, the schlieren-bearing Lipnice gran-
ite is similar to the orthogneiss sample RP3 studied by Přikryl et al.
(2005), which was characterized by similar modal proportions (in-
cluding a similar mica content of 15 per cent) and by high preferred
orientation of mica and which yielded a V<sub>Pmin</sub> value of 2.7 km s<sup>-1</sup> in
a direction perpendicular to mica basal planes. Compared to gran-
ite samples from the Melechov massif studied by Machek (2011),
the Lipnice granite corresponds the best to the fine-grained variety
of Kouty granite (Table 2). Compared to West Bohemian granites
(Pros et al. 1998b) in terms of mean V<sub>P</sub> and grain size it is similar
to the muscovite granite from the Smrčiny massif (sample G8) and
the two-mica granite from the Karlovy Vary massif (sample G9).

Microcracks origin and its relation to the fracture system
of the granitic massif

Microcracks in rock form generally in response to differential
stress which can be provoked by larger-scale fractures propaga-
tion (Lespinasse & Pêcher 1986; Scholz et al. 1993; Faulkner et al.
2010), thermally induced volumetric changes (Géraud 1994; Chaki
et al. 2008) or volumetric changes due to phase transition (Angerer
et al 2011; Lachassagne et al. 2011). If no former discontinuity
exists, their orientation is normal to the local minimum principal
stress acting during their formation. The orientations of the remote
and of the local stress may or may not be the same, which distin-
guishes shear fractures (faults), where remote stress is oblique to the
local one, and tensile fractures (joints), where the two correspond
in orientation.

The sampled outcrop of Lipnice granite shows an orthogonal
fracture system formed by two sets of steep and one set of flat joints.
At the scale of the granitic massif, the steep and the flat joints were
related to the post-magmatic cooling of the granitic massif and to the
exhumation-induced exfoliation, respectively (Lexa & Schulmann
2004). The proposed tectonic setting of the joints formation is valid
also for our sample outcrop, given that the observed joints do not
display any sign of faulting and that no important mineral alteration
was observed in the sample material.

Taking into account the above facts, we refer to the mutual ori-
entation of the microcracks and the outcrop fractures to decipher
their genetic relation. Hence, the steep E–W trending intergranu-
lar and quartz cracks are linked to the subvertical E–W trending
cooling-related joints of set 1 and the flat-lying quartz cracks to the
shallowly W dipping exfoliation joints. The intergranular cracks
oriented at low angle to the reference exfoliation fractures were
induced by the exfoliation process as well. The formation of two
differently oriented populations of microcracks by the exfoliation
process can be attributed to the absence of cleavage in quartz, and,
on the other hand, to the strong cleavage in anisometric crystals of
micas oriented subparallel to the schlieren. Hence, in the cleavage-
free crystals of quartz the exfoliation-related stress field induced
cracks oriented perpendicular to the minimum compressive stress,
whereas in micas the cleavage planes represented favourably ori-
ented zones of weakness and were therefore privileged sites for the
intergranular cracks propagation.

The presence of microcracks subparallel to one of the sets of ver-
tical joints (set 1) and, on the other hand, the absence of microcracks
parallel to the other one (set 2), reflects the difference in the fracture
sets characteristics and the distances of the closest fractures of the
respective sets from the sample block. We remind that the set 1 is
represented by decametric factures and the closest fracture of this
set was 1 m distant from the sample block, whereas the set 2 is char-

acterized by metric fractures with the closest one 10 m distant from
the sample block. Assuming that the width of the facture process
zone scales with fracture length this means that only the fracture of
the set 1 was large and/or close enough to induce cracking in the
sampled material.

Implications on the rock physical properties

The presented data and observations enable us to formulate sev-
eral implications on physical properties of the studied rock and
their evolution with depth. However, we propose rather qualitative
constraints as exact quantification is beyond the scope of this paper.

We have shown that the rock crack-related porosity decreased
markedly in the pressure interval 0.1–100 MPa, in which the effect
of cracks was clearly discernible by important, anisotropic change in
Vp. For approximate evaluation of the porosity reduction we follow
the approach of Pros et al. (1998a) to estimate the state of openness
of cracks as a function of confining pressure. The author proposes an
equation, which combines linear and exponential terms to account
for increase of Vp with increasing confinement due to elastic param-
eters and due to closing of cracks, respectively. This approach allows
calculating the relative crack-induced deceleration of Vp as the dif-
ference between a hypothetic Vp of an ideal non-cracked medium
and the experimentally measured values. The hypothetic Vp of the
non-cracked medium is a linear function of hydrostatic pressure
defined by the measured Vp values at the two high-pressure levels
(200 and 400 MPa), where all the cracks are supposed to be closed.
Assuming that there is a linear proportionality between the change
in Vp due to cracks closing and the change in the crack porosity
volume, the two pressure steps 0.1–10 MPa and 20–50 MPa indi-
cating important closing of cracks are related to relative decrease
in crack porosity to 61 and 26 per cent of its initial value at ambient
pressure. The strong assumption on the cracks closure at the two
highest pressure levels is surely questionable if no direct porosity
measurement is available. On the other hand, in our results we see
two strong arguments for its plausibility. Firstly, the pressure step
200–400 MPa features very low mean ΔVp(Δp) (1 m s⁻¹ MPa⁻¹)
and low anisotropy (see Fig. 7). Such characteristics are hardly as-
sociable with crack closure. Secondly, the Vp anisotropy at the two
highest pressure levels is very low (3–4 per cent) and the Vp minima
are oriented subperpendicular to the grain boundaries. Therefore
this Vp anisotropy reflects rather the material SPO than any open
cracks.

Many studies have shown that microcracks closure induces im-
portant reduction of fluid permeability (Benson *et al.* 2006, and
references therein). Given that cracks represent an important part
of the porosity of our sample material, it is likely that its perme-
ability would decrease with confining pressure progressively with
the crack porosity reduction. Simultaneous measurements of poros-
ity and permeability of a cracked granite by Benson *et al.* (2006)
show that a relative decrease in porosity of 10 per cent may re-
duce the bulk permeability by one order of magnitude and that
the permeability along the cracks is several times higher than per-
pendicular to them. We have observed three differently oriented
sets of microcracks, with majority of the crack populations sub-
parallel to the schlieren. We therefore suppose that the perme-
ability anisotropy is controlled by the schlieren, with high per-
meability directions parallel to them. Particularly the intersections
of the schlieren-related cracks with the cracks of the two other
sets are likely to represent the most permeable conduits. Taking
into account the irreversible closing of cracks perpendicular to the
schlieren and to the reference fractures, the principal permeability
direction after a possible loading-unloading cycle would be defined
by the intersection of the other two crack sets that reopen during
depressurization.

Both the schlieren and the microcracks can be expected to affect markedly the thermal properties of the studied granite. For TC of granite, the quartz content and distribution are crucial as quartz features two to three times higher TC than the other rock constituent phases (Clauser & Huenges 1995). In this light the schlieren-related quartz bands represent principal heat conductors and their orientation defines the principal TC anisotropy. Concerning *in situ* rock thermal properties, higher confinement leads also to higher TC of minerals. Although for rocks the rate of pressure change of the TC is generally very small (0.03–0.9 W m⁻¹ K⁻¹ GPa⁻¹; Abdulagatov *et al.* 2006, and references therein), it is worth noting that the highest TC dependence is featured by quartz (3.3 W m⁻¹ K⁻¹ GPa⁻¹, Horai & Susaki 1989) highlighting the impact of the schlieren.

Géraud (1994) has shown that granitic rock submitted repeatedly to heating-cooling cycle with maximum temperatures of 100 °C became less porous, whereas at higher maximum temperatures it became progressively more cracked. From this point of view it is the quartz that features the highest thermal expansion (Fei 1995). Consequently, the schlieren-related quartz bands would expand the most and cracking would preferentially take place along their boundaries.

It has been shown experimentally that the *V*<sub>p</sub> of granite and other quartz-rich rocks tested at 200 and 600 MPa confining pressure decreases significantly in the temperature range of 500–700 °C and that this *V*<sub>p</sub> decrease is less important at higher confinement (Kern 1979, 1982). This phenomenon caused by thermal cracking and by the α-β quartz transition should be taken into account when considering the *in situ* elastic properties of the studied rock.

The role of cracks on the rock TC is twofold. On one hand, at dry conditions, open cracks represent a barrier for the heat conduction in granite (Géraud *et al.* 2010) and therefore the inferred reduction of crack porosity with confining pressure in our sample would be associated with higher bulk TC and lower TC anisotropy. On the other hand, open cracks filled by another fluid than air, for example, water solution, may enhance the bulk TC of the rock and reduce the TC anisotropy proportionally to the TC of the pore fluid. In addition, well-interconnected system of open cracks enables heat transfer by convection.

CONCLUSIONS

We have characterized a schlieren-bearing sample of the Lipnice
granite using three independent methods: multi-directional mea-
surements of P-wave velocity at confining pressure up to 400 MPa,
AMS analysis and manual tracing of grain boundaries and mi-
crocracks. The schlieren have been demonstrated to control the
anisotropy pattern of the sample elastic properties and of its mag-
netic fabric. Three sets of microcracks differing in orientation have
been genetically related to the fracture system of the granitic massif.
High pressure loading-unloading cycle has been shown to induce
irreversible closure of microcracks associated with joints related
to post-magmatic thermal cooling, whereas microcracks associated
with sheeted fractures have been shown to react to the pressure cy-
cle in elastic manner. Major crack closing characterized by rapid Vp
increase of 93 m s⁻¹ MPa⁻¹ has been observed in the pressure range
0.1–10 MPa, corresponding to depths less than 500 m. Implications
on the evolution with depth of the rock porosity, permeability and
TC have been discussed and the importance of the schlieren struc-
ture has been accentuated.

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