MECHANICAL PROPERTIES OF GRANULITE FROM HORNÍ BORY IN BOHEMIAN MASSIF

Granulite represents one of the favourite rock types for the construction of an underground nuclear waste repository in the Czech Republic. Granulite from the Bohemian Massif (locality Horní Bory) was investigated in this study, with a special focus on the evaluation of the rock anisotropy. Investigated rock represents typical fine-grained foliated felsic granulite with principal mineral association: quartz + feldspar (K-feldspar > plagioclase) + garnet + biotite + kyanite and/or sillimanite. Anisotropy was identified in the rock fabric both at macroscopic and microscopic scale. During the laboratory testing, granulite reached considerable high uniaxial compressive strength (UCS) up to 240 MPa; and brittle type (Class II) of failure occurred. We found that variability of the UCS and Young's modulus were relatively low. On the other hand, variability of the Poisson's ratio and the constants in Hoek-Brown failure criterion in triaxial loading were significantly high.


INTRODUCTION
Granulite is light crystalline, highly compact rock with biotite-bearing bands and disseminated garnet. It was originally recognized from the area of Bohemian Massif by von Justi in 1754 [1] under the name "Namiester Stein" on its type locality -Lamberk near Náměšť nad Oslavou (Náměšť Granulite Massif) and 48 years later characterised under the name "Weisstein" (white stone) from the Saxonian Granulite Massif (Sächsisches Granulitgebirge) as a light coloured rock with quartz + feldspar-dominated mineral assemblage [2] (Figure 1; Figure 2A, 2B). Granulites from the Bohemian Massif were more recently characterised in several papers [3,4,5,6,7]. This high-pressure and rarely microdiamond-bearing rocks [8], which holds a potential to record conditions of their formation deep in the Earth's crust, were selected as one of the promising rocks type for the construction of the deep-seated nuclear waste repository in the Czech Republic [9, 10 and references therein].
Foliated structure of granulite as high-pressure metamorphic rock can appear. This macroscopic structure of the rock indicates potential of anisotropy of mechanical properties. Influence of mechanical properties anisotropy regarding the design of nuclear waste repository was investigated in detail on gneiss in Finland [11]. Full description of anisotropy has 36 elastic constants of which 21 are independent in terms of the theory of elasticity by using the generalized form of Hooke's law. However, some simplification can be used in many practical cases. Transverse isotropy (five constants) is usually considered when a rock has isotropic properties in a plane normal to an axis of rotational symmetry. Orthotropy (nine constants) is usually considered, when three orthogonal planes of elastic symmetry exist at each point in a rock and these planes have the same orientation throughout the rock [12]. A comprehensive study of rock anisotropy based on 200 sets of tests results was carried out by Worotnicki [13]. Four groups of anisotropic rocks were established in the study: quartzofeldspathic rocks, basic/lithic rocks, pelitic rocks and carbonate rocks. About 70% of quartzofeldspathic rocks showed a relatively low degree of anisotropy with maximal to minimal Young's modulus ratio less than 1.3. Thus, we can assume that granulite as member of this rock group can show a relatively low degree of anisotropy.
Generally, there is a lack of relevant data about mechanical properties, i.e. combined uniaxial compressive strength, triaxial compressive strength, splitting tensile strength and testing of granulite rock that are accompanied by a detailed petrographic study. The principal aim of our study is to provide combined petrographic and mechanical characteristics of granulite samples from the Horní Bory quarry located within the Bory Granulite Position of the Horní Bory quarry is marked by white asterisk, and the location of the potential site (Kraví Hora) for the construction of underground nuclear waste repository is marked by grey asterisk

GEOLOGY OF STUDIED LOCALITY
The state owned company SURAO of the Czech Republic intends to build a deep geological repository for radioactive waste storage. It is a consensus that the waste repository will be located in crystalline rocks, similar to pilot projects in Sweden and Finland [15,16]. The waste is planned to be stored up to a maximum depth of 500 m below surface [10]. Recently, several geologically suitable deposition sites have been identified [9], with two highly favourable sites: Horka near Velké Meziříčí in syenitic rocks [17 and references therein] and Kraví hora near Dolní Rožínka in granulitic rocks. Kraví hora (611 m a.s.l.), located near the village Střítež, is situated within 340 Ma granulite rocks of the lower-crustal Gföhl tectonostratigraphic Unit of the Strážek Moldanubicum [18] ( Figure 1). The depth of the rock complexes is estimated to be several km [9 and references therein], which satisfies the requirements of repository depth. However, surface outcrops of ganulites are very scarce in the surroundings of the Kraví hora site, and the available is not sufficiently fresh for the complex assessment of its mechanical properties ( Figure 2C). Thus, fresh granulite was investigated and sampled from nearby (ca 16 km W from Kraví hora site and 8 km from Velké Meziříčí) active Horní Bory quarry situated within Bory Granulite Massif (10 × 3.5 km in area) of the Strážek Moldanubicum [19] (Figure 1). In the quarry were sampled blocks of fine-grained variably foliated felsic granulites with mineral association: quartz + alkali-feldspar + plagioclase + garnet + biotite + kyanite and/or sillimanite ( Figure 2D).

Petrographic analysis
Tested granulite samples from Horní Bory were described petrographically using conventional optical microscopy. Furthermore, backscatter electron imaging (BSE) and compositional characteristic of main minerals (feldspar, garnet, and mica) were carried out using a CAMECA SX 100 electron microprobe at the Laboratory of Electron Microscopy and Microanalysis, jointly operated by the Masaryk University (Brno) and the Czech Geological Survey. Operating conditions for quantitative WDS analyses involved an accelerating voltage of 15 kV, beam currents 10 nA and a spot size ~5 μm. Both natural and synthetic minerals were used as reference standards. The X-phi correction procedure [20] was used for spectra processing. Mineral compositions and formulae are listed in atoms per formula units (apfu) and XMg [Mg/(Mg + Fe)]. Abbreviations of mineral names are used according to Whitney and Evans [21].

Mechanical parameters
Specimens for mechanical tests were collected and prepared from three blocks of the granulite rock (BO-A, BO-B and BO-C) sampled in quarry Horní Bory. This study is focused on preliminary evaluation of anisotropy of the granulite mechanical properties. However, as it was mentioned in introduction, full description of rock anisotropy is relatively complicated and requires comprehensive testing. Thus, the aim of our study is to describe and compare properties of the rock in two main directions: perpendicular and parallel with foliation planes. Main part of the tests was carried out in Laboratory of rock mechanics at Graz University of Technology. Additional fracturing tests were carried out in laboratory at Institute of Building Testing at Brno University of Technology. Cylindrical specimens were drilled with diameter of 50 mm and L:D ratio of 2.0 for uniaxial compressive strength (UCS) tests and triaxial compression tests. Notation of the specimens and their orientation during testing is summarized and explained in Table 1

BO02a2
Prepared from rock block BO-B.

BO03
Prepared from rock block BO-C.
Ultrasonic velocity was determined on the specimens before destructive tests. Set of measurement profiles was applied on each specimen (see Figure 3) in order to study the influence of foliation on the ultrasonic velocity. Travel time of P-wave ultrasonic impulses was recorded, and velocities were determined. Dynamic elastic modulus Edyn was calculated according to formula (1) derived from equation of P-wave velocity in block specimen as stated in ISRM Suggested Method [22].
where ρ is density, vp is ultrasonic velocity and ν is Poisson's ratio.

Figure 3. Ultrasonic velocity measuring profiles. The dashed line shows foliation orientation
The samples used for the UCS tests were equipped with two axial strain and one circumferential LVDT strain gauge sensors. Radial strain was calculated from log of the circumferential deformation. One unloading and reloading loop was applied in the beginning of each UCS test. The specimen was loaded to 34 MPa, then unloaded to 10 MPa and reloaded to 34 MPa. The test was stress controlled in this phase with a load rate of 0.4 MPa/s. Thereafter the test was deformation controlled by the circumferential deformation rate of 0.05 mm/min. This control mode allows to obtain the post-peak behaviour for class II rock types.
The unloading and reloading procedure was used in order to determine deformability parameters of the rock. The deformation modulus Edef was determined as secant modulus between two points of stress-strain diagram. The points were considered where 10 MPa and 34 MPa of the axial stress was reached for the first time. Young's modulus E and the Poisson's ratio ν were determined as average from secant value of the unloading and reloading parts of the loop.
Triaxial compression tests were carried out on two specimens with respect to the foliation orientation. Multiple failure state procedure was employed in order to obtain necessary amount of data for failure envelope analysis. The multiple failure procedure is described in ISRM suggested method [23] and it is well established in Laboratory of rock mechanics at Graz University of Technology [24]. Parameters of Hoek-Brown failure criterion (see formula 2) were determined in order to evaluate the influence of the foliation orientation within triaxial load conditions [25]. The parameter values were found by spreadsheet calculation.
where 1 and 3 are major and minor principal stresses, ci is uniaxial compressive strength and mi, s, a are material constants. The ci and mi were determined by method of least squares while conventional values of the s and a were considered for the case of intact rock.
The tensile strength was determined by splitting tensile test. The test was carried out on three disc specimens. The foliation planes were oriented perpendicular to the surface of the load platen and perpendicular to the drilling core longitudinal axis. Average value of the tensile strength was determined.
Fracturing tests were carried out in a set-up of 3-point bending tests according to ISRM Suggested Method [26]. Hence, the tensile mode of fracture, commonly referred to as mode I fracture toughness testing, was investigated. Round bar specimens were used with diameter 50 mm and length 200 mm. A chevron notch was created in the mid-span as the stress concentrator. The test was conducted as deformation controlled with rate 0.01 mm/min. Foliation planes were oriented parallel with the specimen longitudinal axis and transversal inclination of the planes was approximately 45°. Fracture toughness KIC was calculated by the formula (3) [26].
where Fmax is the maximal reached load, D is diameter of the specimen and Amin is calculated according formula (4): where a0 is chevron tip distance from specimen surface and S is distance between supports.

Petrographic characteristics
Principal mineral association of the studied granulites consist of quartz, feldspar (K-feldspar > plagioclase), garnet, biotite, kyanite/sillimanite, with accessory ilmenite, apatite, hercynite and zircon. The granulites from Horní Bory quarry are characterized by porphyroblasts of garnet with predominance of the almandine component (  Table 3). Quartz forms irregular, elongated aggregates and occasionally forms myrmekitic intergrowth with feldspar as well. K-feldspar is anhedral and significantly perthitic. Its compositional range is shown in Figure 6B and listed in Table 3. Plagioclase, by its composition, mainly corresponds to oligoclase. Garnet porphyroblasts are present as rounded, colourless grains, which are sometimes heavily cracked. Kyanite often changes to acicular sillimanite ( Figure 4C and Figure 5D). Rutile creates typical yellow-brown micro-porphyroblasts with striking relief. Ilmenite shows signs of leucoxenization at the edges and breaks down into finer material ( Figure 5A). Apatite is present in the form of elongated grains.

Mechanical properties and parameters
UCS testing. An overview of the main mechanical parameters is given in Table 5. Variation of the obtained values can be noticed according to the orientation of foliation. Granulite provided higher UCS when it was loaded perpendicular to foliation than parallel. Vice versa, the rock appeared slightly stiffer in case of loading parallel with foliation. This can be recognized according to the determined deformability parameters.  Investigated granulite has relatively high strength (> 200 MPa) in UCS testing. Brittle failure of the rock was observed in both cases of foliation orientation accompanied by plummet of the peak-stress of the stress-strain curve (Figure 7). The control mode for this test procedure was a constant circumference ramp increase. This enables to control such a test for class II rocks in the post peak area. The plummet magnitude was more noteworthy at BO-1a specimen ( Figure 7A). However, the plummet of the stress-strain curve at BO-1b specimen appeared immediately after reaching the peak strength ( Figure 7B), when large crack formed along one of the foliation planes.
Variability of failure process was recognized by detailed strain analysis as well (Figure 8). Non-linear trend of radial and volumetric strain components appeared prior to peak UCS approaching during the complete test procedure of the two specimens ( Figure 8). The most significant contrast appeared on volumetric strain (   Ultrasonic velocity test results. Determination of the dynamic elastic modulus (Edyn) is based on ultrasonic velocity measurement ( Table 6). Values of the Edyn are summarized in Table 7. Values of density and Poisson's ratio for calculations were derived from Table 5. Foliation direction was considered for selection of value of Poisson's ratio. The general trend shows that Edyn is higher in direction parallel with foliation (64.3 GPa in average) than in perpendicular direction (57.7 GPa in average). Deviation of dynamic modulus for specimen BO-2a is explained by the occurrence of a major crack close to one of the measurement profiles. Ultrasonic velocity was lowered by the crack formation, thus, Edyn value became lower in this case.  (Figure 9). The peak strength shows the same feature regarding foliation orientation dependency as for the UCS test results. Contrast of radial strain curves should be noted in the stress-strain diagrams from the triaxial testing. Radial shrinkage was observed in specimen BO-2b when confining pressure was increased ( Figure 9B). Values of peak axial stresses for different confining pressures reached during triaxial compression tests are listed in Table 8   The data in Table 8 were further analysed in order to determine the parameters of the Hoek-Brown failure criterion and summarised in Table 9. Values of UCS were considered in the analysis as well. The parameter ci is slightly underestimated by the Hoek-Brown criterion compared to directly determined UCS from testing. Variation of UCS is 3% for testing perpendicular to foliation and 2% at loading parallel with orientation of foliation. Material constant mi in the criterion is significantly influenced by foliation orientation. The constant is considerably lower in direction parallel with the foliation. Tensile strength t is estimated to be significantly lower in direction perpendicular to the foliation. Thus, influence of foliation orientation is also evident in case of tensile strength t.

Granulite petrographical features
Based on the observed mineral and petrographic composition we can state that the studied rock material corresponds to fine-grained, variably foliated, felsic granulite with principal mineral association: quartz + feldspar (K-feldspar > plagioclase) + garnet + biotite + kyanite and/or sillimanite and accessory ilmenite, apatite, hercynite and zircon. On the other hand, the rock does not texturally/mineralogically correspond to granulite gneiss, which can form layers, several centimetres to meters thick, in the Horní Bory granulite body [19 and discussion in subchapter 5.2.]. Thus, our tested material corresponds to granulite, which is the same petrographic type as is suggested for the construction of an underground nuclear waste repository [9].

Anisotropy of mechanical properties
Anisotropy of mechanical properties of the granulite from Horní Bory quarry was expected considering the foliation observed in microscopic and macroscopic scale. Some variation of the compressive strength and deformability parameters exist in the specimens studied. The UCS was of 6.3% higher in loading direction perpendicular to the foliation compared with the specimens loaded parallel with the foliation (see Table 5). Peak strengths reached from triaxial compression testing were much higher from loading perpendicular the foliation orientation (see Table 8). Parameter mi of the Hoek-Brown failure criterion varied most significantly (78%).
However, variation of the estimated tensile strength t was also high (76%), but having an opposite trend -the strength was higher in tension from bending in the direction parallel with the foliation (see Table 9). When we compare deformability parameters, E (1.8%), Edef (3.4%) (see Table 5) and average of Edyn (10%) (see Table 7) we observed slightly higher values when the foliation is oriented parallel with loading. The Poisson's ratio ν is 26% lower when the orientation of foliation is parallel with loading direction (see Table 5). Other findings of this study about tensile strength t, modulus of elasticity and the Poisson's ratio with respect to influence of foliation orientation are in accordance with previous study of anisotropic metamorphic rocks presented by Brosch et al. [28]. To sum up, the degree of anisotropy of the specimen studied is relatively low, except for the mi and t parameters. The compressive strength under uniaxial and triaxial loading conditions decrease when the rock is loaded parallel with foliation, while E modules are slightly increased.
The tested granulite reached relatively high UCS (225 resp. 240 MPa -see Table 5). Hence, the rock belongs to grade "R5 -Very strong" of the ISRM classification [29] and the obtained UCS value is close to the upper limit of this grade (100-250 MPa). Brittle failure occurred especially during the UCS tests and agrees with the post-failure phase of the stress-strain diagrams presented in Figure 7. The obtained fracture toughness KIC value is exceptionally high, as well. The reached value of 2.19 MPa.m 0.5 is significantly higher compared to the values reported for the 3-point bending experimental setup presented in the comprehensive list of results by Ouchterlony [26]. Fracture toughness of granulite is comparable with KIC of igneous rocks like tonalite (2.21 MPa.m 0.5 ), dolerite (2.48 MPa.m 0.5 ) and basalt (2.01 MPa.m 0.5 ) [30].
Mechanical properties of granulite from the Bohemian Massif are reported in a recent study by Petružálek [31]. The study presents the UCS = 215 MPa, Young's modulus E = 49.8 MPa, and the Poisson's ratio ν = 0.19.
The peak strength in triaxial compression testing is 310 MPa at confining pressure 3 = 13 MPa and the splitting tensile strength 10.5 MPa. The UCS, E and splitting tensile strength are lower than we obtained in our experiments. The Poisson's ratio reached the same value as in our study when the foliation was oriented perpendicular to loading direction. Peak strength in the triaxial tests is between values which we obtained (272 and 391 MPa - Table 8) at the most similar confinement (3 = 13.5 MPa). Below we present a likely explanation of the difference in results of the two studies:  Pertužálek [31] tested samples directly from Kraví Hora -potential location of the nuclear waste repository (see grey asterisk in Figure 1). The rock was sampled from available outcrops; thus, the rock could be weathered (cf. Figure 2C and 2D).
 Samples from Kraví hora site are strongly foliated [31 and figures therein] and more melanocratic than is characteristic for typical felsic granulite (cf. Figure 2). Higher content of dark minerals in the rock from Kraví hora site is indicated by its higher density (2655 kg/m 3 ) than we obtained in our study (Table 5). Hence, the rock from Kraví hora site resembles granulite gneiss, rather than granulite. This

CONCLUSIONS
Fine-grained variably foliated felsic granulite from the Bohemian Massif (locality Horní Bory) was investigated in this study, with a special focus on the evaluation of the rock anisotropy. Detailed study of petrography and mineralogy was done together with a set of mechanical tests. This rock represents one of the favourite rock types for the construction of underground nuclear waste repositories in the Czech Republic.
The main conclusions are summed up: 1. Anisotropy of granulite was identified in the rock fabric both at macroscopic and microscopic scale.
Anisotropy of the mechanical properties appeared from testing the rock, as well. Variability of UCS and E modules was found to be relatively low. On the other hand, the variability of Poisson's ratio and the parameters of the Hoek-Brown failure criterion in triaxial load conditions is significantly high.
2. The tested granulite reached considerable high UCS (up to 240 MPa) and brittle type of failure (Class II) was observed during the laboratory testing. Brittleness of rock can lead to specific problems such as rock burst, thus, it should be considered as a potential risk during construction of underground openings of repositories.
3. Determination of mechanical properties of anisotropic rock requires considerably more laboratory data than could be presented in this study. Therefore, the presented quantification of the granulite anisotropy of the Horní Bory quarry should be considered as work in progress.