Laboratory determination of the mechanical properties of granite rocks

K. Sosna1 ARCADIS Geotechnika Inc., Prague, Czech Republic

ABSTRACT

This research into the mechanical properties of granite rocks focuses on their porosity and deformability. The study specifically relates to the planned disposal of radioactive waste. Three granitoid types from the Variscan Bohemian Massif of Central Europe have been tested. The investigation boreholes reached depths of up to 100 meters. The porosity was obtained by weighing saturated and dry samples, with saturation provided by water immersion in a vacuum. Young’s modulus and Poisson’s ratio were determined in uniaxial compression. The shear and longitudinal deformation of each sample was measured using aresistive strain gauge fixed directly on the sample. The samples were subjected to five different loads followed by unloading. Aconstant gradient of vertical stress of 1 MPa.s-1 was applied during the loading. P-wave and S-wave velocities were measured in three perpendicular directions. The apparatus consisted of four piezoelectric sensors, an ultrasonic pulsar, receivers, and a digitaloscilloscope recorder. The frequency was 1MHz. Velocities were measured on naturally wet, saturated, and dried samples.Dynamic elastic modulus was calculated from the measured data. The static Young’s modulus varied between 30-60 GPa, while the dynamic modulus rose to 90 GPa. The porosity of the samples varied from 0.6 to 1.4 %. P-wave velocities ranged from 4.4 to 6.9 km.s-1, while S-wave velocities ranged from 2.8 to 3.7 m.s-1. Both P-wave and S-wave velocities generally increase with depth in the borehole. Slight anisotropy was observed in several samples. Keywords: radioactive waste, underground disposal, granite rocks, laboratory tests, seismic waves, elasticity

1 ARCADIS Geotechnika, Geologická 988/4, 152 00 Prague, Czech Republic. sosna@arcadisgt.cz

1 INTRODUCTION

Across the globe, granite massifs are considered to represent a suitable geological reservoir for the strategic storage of gas and liquids. This includes the storage of highly toxic substances and wastes such as high-level radioactive waste and spent fuel.

The physical properties of crustal rocks are strongly influenced by the presence of cracks and fractures. Moreover, the mechanical properties of the rock are dependent on its mineralogy, texture, structure, and weathering [1]. The effects of sample diameter and moisture content on rock

strength and its variability have previously been examined [2]. Changes in elastic moduli measured during increasing amplitude cyclic stressing experiments on dry and water-saturated samples of Etna basalt have previously been studied [3].

The discrepancy between statically and dynamically determined elastic moduli of rock has also been reported [4], [5], and [6]. Furthermore, P-wave velocities in a dry granite rock sample under uniaxial compressions have been measured in the frequency range of 100 kHz to 710 kHz using the pulse transmission technique [7].

2 GEOLOGICAL SETTING

The first locality is situated in a granite quarry close to the village of Panské Dubenky in the southwestern part of Jihlava District, Vysočina, Czech Republic (Figure 1). This part of the central moldanubic pluton comprises medium grained double mica granite with a variable content of feldspar phenocrysts.

The second locality is situated in the Melechov Massif between Humpolec and Světlá nad Sázavou in the northern part of the Pelhřimov District, Vysočina, Czech Republic (Figure 1). This part of the central moldanubic pluton comprises non-porphyric coarse-grained double mica granite.

The third locality is situated close to the village of Pozďátky in the eastern part of the Třebíč District, Vysočina, Czech Republic (Figure 1). The Třebíč pluton comprises porphyric coarse grained amphibole-biotite melasyenite with K-feldspar phenocrysts.

Figure 1. Situation of the localities in the Czech Republic.

3 EXPERIMENTAL METHODOLOGY

3.1 Preparation of the samples

Granite core samples have been taken from the 100 m deep boreholes PDV-1 (Panské Dubenky), MEV-1 (Melechov), and PZV-1 (Pozďátky). The boreholes have diameters of 47 mm. Samples were taken from depths of between 20 to 100 meters, at an interval of approximately 10 meters. Only fresh core, without visible fractures, was sampled. This technique of

sampling allows detailed studies of the parameters within the rock matrix of the borehole. The samples were cut to heights of 50 and 100 mm using a diamond saw.

Wet, water saturated, and dried samples with a height of 50 mm were studied. The term wet is applied to granites in their ‘natural’ state having been stored in an air-conditioned box with 100 % relative humidity. Saturation of the samples was provided by water immersion in a vacuum for 48 hours [8]. After recording all the saturated granite measurements, the samples were oven dried at 105°C for 24 hours. The gradual change of temperature by 0.3°C/min during heating and cooling prevented any cracking of the specimens due to high temperature gradient inside the specimens [9], [10]. During cooling, samples were kept enclosed in a desiccator so as to avoid contact with air humidity until the temperature had fallen to the required level.

3.2 Open porosity

The open porosity was determined in identical conditions, following the methodology suggested by ISRM [8]. The porosity n was obtained through the weighing of saturated msat and dry md samples, respectively (1)

′−

−=

satsat

dsat

mm

mmn (1)

Where msat' is effective weight of the saturated sample in water.

3.3 Ultrasound scanning

P-wave and S-wave velocities were measured in each sample using an apparatus that consisted of two pairs of piezosensors (Olympus V103 and V153) used respectively as transmitter and receiver, a precise impulse generator, and an oscilloscope. The resonance frequency of the sensors was 1 MHz [11] while the contact between the sensors and sample was improved using contact couplant.

The dynamic Young’s modulus Ed (2) was calculated according to [5]:

( )

22

222 43

SP

SPSd

vvvvvE

−

−=ρ

(2)

where ρ is the density of the studied sample, vs is S-wave velocity, and vp is P-wave velocity.

3.4 Deformability in uniaxial compression

Cylindrical wet rock samples with a height of 100 mm were tested. The samples were loaded using uniaxial stress. During the experiment, sample deformations (transverse and longitudinal) were recorded using resistivity tensometers (20/120LY41 Hottinger Baldwin Messtechnik) fixed to the surface of the sample. Loading occurred over five cycles with a constant gradient of 0.5 MPa.s-1. Upper loading limits reached approximately 20, 30, 40, 50, and 60 % of the uniaxial compressive strength. Unloading minimum was set to 5 % of the uniaxial compressive strength. The static Young’s modulus E (3) was determined from hysteresis of the loading loop following methodology of [12].

unloadload

unloadloadEεεσσ

−−

= (3)

where σload is loading stress, is σunload unloading stress, εload is the axial strain at σload and εunload is the axial strain at σunload.

4 RESULTS

4.1 Open porosity

The open porosity of the Panské Dubenky granite (PDV-1) varies between 0.6 % and 1.4 % and decreases with depth down the borehole.

The open porosity of the Melechov granite (MEV-1) varies between 0.6 % and 1.1 % and basically decreases with depth down the borehole.

The open porosity of the Pozďátky melasyenite (PZV-1) varies between 0.5 % and 0.7 %.

4.2 Seismic velocities

The P-wave velocities of the PDV-1 samples vary according to the initial depth of the sample and its level of saturation (Figure 2). Higher values were recorded in saturated samples (5.9 km/s to 6.3 km/s: squares) while the lowest values were recorded in dry samples (4.6 km/s to 5.4 km/s: crosses).

Figure 2 also clearly shows the level of isotropy of the samples. P-wave velocities in the coaxial direction (Direction 1) of the sample (i.e. originally vertical within the borehole) are slightly lower (up to 5 % in the highest velocity samples) than in other directions (i.e. originally horizontal in the borehole).

Figure 2. P-wave velocities of the Panské Dubenky granite samples. Squares: saturated samples; circles: wet samples;

triangles: dried samples. Furthermore, the S-wave velocities (Figure 3)

vary according to the initial depth of the sample and its level of saturation. S-wave velocities were found higher in saturated samples (3.1 km/s

to 3.6 km/s) than in dry samples (2.9 km/s to 3.4 km/s). Both curves again followed a similar trend.

The P-wave velocities in the MEV-1 samples vary according to the initial depth of the sample and its level of saturation (Figure 4). The highest values were recorded in saturated samples (6.0 km/s to 6.5 km/s: squares) while the lowest values were recorded in dry samples (4.4 km/s to 5.5 km/s: crosses).

Figure 4 also clearly shows the level of isotropy of the samples. P-wave velocities in the coaxial direction of the sample are lower (up to 7

% in the highest velocity samples) than in other directions.

Figure 3 S-wave velocities of the Panské Dubenky granite samples. Squares: saturated samples; circles: wet samples;

triangles: dried samples.

Figure 4. P-wave velocities of the Melechov granite samples. Squares: saturated samples; circles: wet samples; triangles:

dried samples. The S-wave velocities (Figure 5) vary

between 3.1 km/s and 3.7 km/s in saturated samples and between 2.9 km/s and 3.5 km/s in dry samples.

The P-wave velocities in the PZV-1 samples vary according their level of saturation (Figure 6). The highest values were recorded in saturated samples (6.1 km/s to 6.9 km/s: squares) while the lowest values were recorded in dry samples (4.4 km/s to 5.8 km/s: crosses). P-wave velocities in the coaxial direction of the sample are lower (up to 20 % in the highest velocity samples) than in other directions. The S-wave velocities (Figure 7) vary between 3.1 km/s and 3.6 km/s in saturated samples and between 2.8 km/s and 3.3 km/s in dry samples.

Figure 5. S-wave velocities of the Melechov granite samples. Squares: saturated samples; circles: wet samples; triangles:

dried samples.

Figure 6. P-wave velocities of the Pozďátky melasyenite

samples. Squares: saturated samples; circles: wet samples; triangles: dried samples.

Figure 7. S-wave velocities of the Pozďátky melasyenite

samples. Squares: saturated samples; circles: wet samples; triangles: dried samples.

The level of saturation affects both P-wave

and S-wave velocities. While the difference between P-wave velocities in dry and saturated samples was observed to be as much as 30 % (PZV-1), the difference between S-wave

velocities in dry and saturated samples was observed to be slightly less than 15 %. The anisotropy of P-wave velocities is well perceptible on dry samples.

4.3 Young’s modulus

The trend of dynamic Young’s modulus is characteristically similar to those of the seismic wave velocities. Its variation is given in Table 1. Directional anisotropy of the modulus is present in the samples, but it remains rather insignificant. As with the velocities, the modulus was found to be higher in the saturated samples than in dry samples. The difference in moduli between the saturated and dry samples is about 20 %.

Table 1. Highest and lowest dynamic Young’s moduli of Panské Dubenky, Melechov, and Pozďátky granitoids on oven dried and saturated samples.

Lowest Ed [GPa]

Highest Ed [GPa]

PDV-1 dried 51.3 69.5 PDV-1 saturated 67.2 84.0 MEV-1 dried 50.7 73.4 MEV-1 saturated 67.4 88.2 PZV-1 dried 50.8 70.7 PZV-1 saturated 72.2 90.2

Wet samples with a height of 100 mm were

used to assess static Young’s modulus. Its variations are given in Table 2.

Table 2. Highest and lowest static Young’s moduli of Panské Dubenky, Melechov, and Pozďátky granitoids on wet samples.

Lowest Ed [GPa]

Highest Ed [GPa]

PDV-1 39.5 57.6 MEV-1 43.6 57.5 PZV-1 34.8 46.6

A comparison of the statically and

seismologically determined Young’s moduli is shown in Figure 8. The horizontal axis shows Young’s modulus determined from uniaxial cyclical loading, while the vertical axis shows Young’s modulus determined from seismic measurements on wet samples from the same depths as the loaded samples in the coaxial direction. Dynamic Young’s modulus is

approximately 1.2-1.5 times greater than static Young’s modulus. This discrepancy is probably caused by differences the in axial strain of each method [13].

Figure 8. A comparison of the statically and seismologically

determined Young’s moduli on wet samples in a coaxial direction.

5 CONCLUSIONS

The main advantage of the ultrasound scanning method is that it is comparatively inexpensive when set against other methods (e.g. uniaxial loading, logging). Seismic measurements are able to determine small anomalies in the physical parameters, even within a single monotonous borehole. A further advantage is that it provides an assessment of deformation parameters in directions perpendicular to the well. It is not possible to measure these two directions in small-profiled cores using uniaxial loading [14].

The porosity of the samples varied from 0.6 to 1.4 %. P-wave velocities ranged from 4.4 to 6.9 km/s, while S-wave velocities ranged from 2.8 to 3.7 km/s. The saturation level affects both P-wave and S-wave velocity. While the difference between P-wave velocities in dry and saturated samples was observed to be as much as 30 %, the difference between S-wave velocities in dry and saturated samples was observed to be slightly less than 15 %. Slight anisotropy was observed in several samples. The static Young’s modulus varied between 30-60 GPa, while the dynamic modulus rose to 90 GPa. Dynamic Young’s modulus Ed is approximately 1.2-1.5 times greater than static Young’s modulus.

ACKNOWLEDGEMENT

This work has been funded by the Ministry of Industry and Trade of the Czech Republic (FR-TI1/367).

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