1 Introduction

Tensile properties strongly control the deformational characteristics, load bearing capacity, and damage of any kind of geomaterials. This is an important parameter for the design and stability of the underground caverns, geothermal energy system, radioactive and toxic material storage site, hydraulic fracturing, and carbon dioxide sequestration. Since the rock is much weaker under tension than any other kind of stress, so the behavior of rock under tension is of particular interest to the researchers. Particularly, the tensile properties of the igneous and metamorphic rocks are very much important for the toxic fuel and radioactive material storage site selection. Although, due to the low porosity, low permeability and high compressive strength, the crystalline rocks are considered to be an ideal host for the high-temperature radioactive spent fuels, but it has been noticed that with increasing temperature strength of the rock changes. Several researchers have noted that the temperature of the rocks surrounding the underground nuclear disposal sites may vary from 100 to 300 °C over prolonged storage period; the enhanced geothermal systems (EGSs) work at nearly 200 °C and in mechanical drilling the downhole temperature may rise as high as 1000 °C (Paquet and François 1980; Heuze 1983; Shao et al. 2015; Zhao 2015). So, it is worthwhile to conduct experiments at least up to 350 °C, so that the results are applicable to most of the above-mentioned applications. Also, the mechanical properties of rocks are found to be a function of the rock layer orientation. So, it is very important to have a proper understanding of the physical behavior of the layered rocks under elevated temperature.

Several researchers attempted to investigate the temperature-dependent properties of homogeneous sedimentary and crystalline rocks (Wong 1982; Heuze 1983; Homand-Etienne and Troalen 1984; Xu et al. 2008; Vishal et al. 2011; Chen et al. 2012; Wisetsaen et al. 2015; Gautam et al. 2015), and anisotropy-controlled tensile behavior of different rocks under ambient temperature (Amadei 1996; Tavallali and Vervoort 2010, 2013; Dan et al. 2013; Vervoort et al. 2014). A decreasing trend of the rock tensile strength with the increasing temperature has been reported by Bauer and Johnson (1979), Homand-Etienne and Houpert (1989), Dwivedi et al. (2008), Liu and Xu (2014) for granitic rocks and by Vishal et al. (2011) for Khondilites. Dwivedi et al. (2008) reported that the tensile strength of Indian granite decreases nearly 27 % from room temperature to 150 °C, whereas the compressive strength increases by nearly 11.1 %. Bauer and Johnson (1979) found that at higher temperature, different thermal expansion of the feldspar and quartz play a major role behind the thermal crack development and widening. These thermal cracks are the main reason behind the decreasing strength of the rock. Unlike other rocks, Khondalites were found to gain tensile strength at the beginning with temperature increasing till 100 °C, and after that it reduces drastically. But the behavior of the heat-treated-layered crystalline rocks remained a relatively unexplored area. So, in the present paper, we investigated the effect of heating and layer orientation influence on the tensile strength, layer-parallel strain, force-parallel strain and the resulted fracture pattern of a granitic gneiss rock through Brazilian tests.

Here, the tensile properties of the layered gneissic rock are measured under the temperature ranging from room temperature (30 °C) to 350 °C. For each of the temperatures, the layer orientation-dependent tensile properties of the rocks are also measured by varying the angle between the gneissic layers and the loading direction from 0 to 90°. Henceforward, this angle will be termed as ‘inclination angle’ in the rest of the paper. In all the samples, layer-parallel and force-parallel strains are measured, and they are compared with each other to see the effect of temperature and layer orientation on the physical properties of rock and on the distribution of stress in different parts of the sample.

2 Experimental Procedure

2.1 Sample Preparation

The tensile disks were prepared following the ASTM standard (ASTM D3967–08 2008). NX size cores (54.7-mm diameter) were first retrieved of the rock block using a diamond core bit, and they were thoroughly checked to avoid any visible flaws. The direction of the coring was kept parallel to the layering. Then, the core was cut into several circular tensile disks with thickness-to-diameter ratio 0.5. Disks were carefully prepared so that both the faces were flat; they were parallel to each other and perpendicular to the core axis. After the samples were prepared, the diameter and the length were noted by taking average of three readings for each of the cases. Then, the samples were dried in the room temperature for the next 48 h. The room temperature samples were then tested directly, and rest of the samples were placed in the furnace to be treated at 100, 250, and 350 °C, respectively, for continuous 30 days. The temperature of the furnace was increased gradually to the required level to avoid thermal shock. After the treatment, the samples were taken out of the furnace and were cooled to the room temperature for 24 h before the testing. Slow rate of heating and cooling also allow having homogenous distribution of the heat in the samples. For each combination of temperature and inclination angle, four samples were tested and the results of these four samples were averaged to get a representative value. In total 64, samples were tested for the present research.

2.2 Petrography

To conduct the petrographical studies, representative samples were collected from the blocks and they were grinded and polished to prepare thin sections with 30-µm thickness. These slides were then studied under a Leica microscope and the minerals are identified based on their plain-polarized and cross-polarized optical properties as shown in Fig. 1. The main minerals were identified to be quartz, albite, microcline, and ferro-actinolite. The first three minerals formed the lighter layer and the last one formed the dark gneissic layer. The white gray and dark gray minerals, lacking any visible twinning or cleavage were identified as quartz. Albite grains exhibited distinct lamellar twinning. Microcline grains were identified with its characteristic cross-hatched or tartan twinning. Several feldspar grains were identified with perthitic texture indicating intergrowth of Na- and K-feldspar from a subsolidus exsolution. Actinolite was identified as mineral having light green to blue color under the plain-polarized light and showed pale green to green pleochroism. The slide displayed typical granoblastic texture of the metamorphic rock, where the minerals are anhedral, phaneritic, and equigranular.

Fig. 1
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Photomicrographs of the granitic gneiss samples

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2.3 Physical Properties

The physical properties like uniaxial compressive strength (UCS), density, porosity, and ultrasonic velocity of the untreated samples were measured for all the samples. The density and the porosity of the rock were measured using the buoyancy technique as described by Sharma and Singh (2010). Five samples were tested to determine the average density and porosity. The average density of the granitic gneiss was 2.78 g/cc and the average porosity was 0.55 %. For the UCS and ultrasonic velocity testing, NX size cores with length-to-diameter ratio 2 were prepared. UCS was measured in the uniaxial testing machine (UTM) and the ultrasonic velocity was measured using PUNDIT instrument manufactured by Proceq. Samples with layering parallel to the loading axis have been tested for the UCS and ultrasonic velocities. The average UCS was found to be 124 MPa and the average P-wave velocity was 4654 m/s.

2.4 Brazilian Test

Brazilian test is one of the oldest techniques to measure the indirect tensile strength of the rock. In this process, a cylindrical disk is compressed at diametrically two opposite points and the material fails under tension. This experiment is conducted by placing the sample in the Brazilian cage as shown in Fig. 2. This cage has two steel curved bearing blocks having Rockwell hardness more than 58 HRC. Such configuration allows applying line load on the required areas. This whole system along with sample is then placed in the universal testing machine (UTM). The rate of loading was kept constant at 0.5 mm/min to avoid the effect of impact. However, a continuous measurement of load with time was recorded to ensure that load increased continuously during the testing as shown in Fig. 3. The tensile strength is calculated as follows:

$$\sigma_{t} = 2P/\pi tD$$

\(\sigma_{t}\) tensile strength (MPa), P failure load (KN), t thick ness of the specimen (mm), and D diameter of the specimen (mm).

Fig. 2
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Brazilian test configuration

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Fig. 3
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Stress vs time graph of the 90° ‘inclination angle’ samples at different temperature

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Two 10-mm-long strain gage are also attached on one of the planes of the tensile disk. One was placed parallel to loading direction and other one was attached parallel to the gneissic layer. They recorded the force-parallel strain (F-strain) and layer-parallel strain (L-strain), respectively. These micro-strain data were recorded in the data logger while loading the specimen.

3 Results

3.1 Effect of Layer Orientation

3.1.1 Tensile Strength

Effect of gneissic layer orientation with respect to the loading axis on the tensile strength of the rocks is demonstrated in Fig. 4. It is observed that at the room temperature (30 °C), 100 and 250 °C, the tensile strength is highest at the 60° inclination angle, and at 350 °C it is at 30°. Similar trends have also been observed by Tavallali and Vervoort (2010) for sandstone and by Dan et al. (2013) for the gneissic rocks. The sandstones of Tavallali and Vervoort show two uphills in the tensile strength, one at 30° and other one at 60°, with later one being of higher value. But Dan et al. (2013) found a positive bulge between 20° and 40° inclination angles. Vervoort et al. (2014) also reported that in Leubsdorfer gneiss, Asan gneiss and Yeoncheon schist tensile strength increases with increasing inclination angle. Among these three rocks, the tensile strength of Leubsdorfer gneiss and Asan gneiss increases continuously till 90° inclination, but in Yeoncheon schist a relatively higher tensile strength is observed at 60° inclination angle. From these observations, it is interpreted that the tensile strength of the layered rocks are strongly dependent on the layer orientations; in most of the cases, an increased tensile strength is observed at the inclination angles between 30° and 60°. But, contrary to the findings of Dan et al. (2013), Tavallali and Vervoort (2013) and Vervoort et al. (2014) reported that a maximum tensile strength is found at the inclination angle 90°, in the present study, highest tensile strength is found near 60° inclination angle. The tensile strength at the 90° inclination angle is nearly similar to that of 0°.

Fig. 4
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Inclination angle-dependent tensile strength at four temperatures

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3.1.2 Layer-Parallel Strain

The layer-parallel strain evolution with increasing stress for different inclination angles at different temperatures are shown in Fig. 5a–d. It is observed that in all the temperatures, samples at inclination angle 60° show the highest gradient of the stress vs L-strain curve, followed by 30° and 90° inclination angles, and inclination angle 0° shows the minimum. It shows that where the rock layers are parallel to the loading axis, the sample experiences maximum deformation. It is followed by the samples, where rock layers are perpendicular to the loading axis i.e., parallel to the direction of the acting indirect tensile stress. Among 30° and 60° inclination angles, the 30° inclination angle samples experience relatively higher amount of layer-parallel strain.

Fig. 5
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Layer-parallel strain for all the inclination angles at a room temperature (30 °C), b 100 °C, c 250 °C, and d 350 °C

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3.1.3 Force-Parallel Strain

The F-strain acting upon the samples with different layer orientations are shown in Fig. 6a–d. It is seen that, the F-strain was affected deeply by the increasing exposure of the rock to the higher temperature for a long time. At the room temperature, only the inclination angle 0° samples showed the maximum and relatively higher force-parallel deformation. But as the temperature was increased to 100, 250, and 350 °C, other inclination angles also show considerable amount of deformation. At these temperatures, the deformation patterns are nearly similar and closely spaced for all the inclination angles. But no particular pattern of the effect of layer inclination angles on the F-strain can be observed. The difference between the lowest and highest F-strain reduces from 95 % at the room temperature to nearly 3.7 % at 350 °C temperature.

Fig. 6
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Force-parallel strain for all the inclination angles at a room temperature (30 °C), b 100 °C, c 250 °C, and d 350 °C

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3.1.4 Strain Ratio

The strain ratio at different layer orientations is shown in Fig. 7a–d for different temperatures. The strain ratio of inclination angle 0° is always 1 for having same L- and F-strain values. As can be seen from figures, at room temperature the strain ratio ranges from 2 to 14 for all the inclination angles, where 60° shows the maximum strain ratio, followed by 90° and 30°. For the higher temperatures (100, 250, and 350 °C), all the strain ratio came down below 1 as the F-strain becomes a dominant factor in the sample deformation. In these two temperatures, highest and lowest strain ratios are displayed by 90° and 60° inclination angles, respectively.

Fig. 7
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‘Strain ratio’ for different ‘inclination angle’ samples at a room temperature (30 °C), b 100 °C, c 250 °C, and d 350 °C

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3.1.5 Strain at Failure

Figure 8a, b show the L- and F-strain at failure at different inclination angles for all the temperatures. As can be seen from Fig. 8a, for all the temperatures except room temperature, inclination angle 60° shows the minimum L-parallel strain at failure load and 0° shows the maximum. At the room temperature, inclination angle 30° shows the minimum L-strain at failure. But in Fig. 8b, for all the temperatures except 100 °C, the maximum F-strain at failure is found at the 0° and then it reduces to a minimum value at 90° inclination angle. At 100 °C, the maximum F-strain at failure is recorded at 60° inclination angle and lowest at 0°. At the room temperature, the reduction of the F-strain at failure is rapid but at higher temperatures (250 and 350 °C), the reduction is very slow. Additionally, at the room temperature, inclination angle 0°, 30°, 60°, and 90° have nearly similar F-strain at failure values.

Fig. 8
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a ‘L-strain at failure’ for different ‘inclination angle’ samples. b ‘F-strain at failure’ for different ‘inclination angle’ samples

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3.1.6 Fracture Geometry

Fracture geometry and fracture pattern are strongly controlled by the anisotropy of the rock structure and stress distribution. So, in the layered rock, depending upon the orientation of the layers, a different amount of shear and tensile stress can act on the layers. As shown in Fig. 9, this heterogeneous distribution may lead to deviation of the tensile fracture pattern from its original straight path to form “non-central” fractures. To identify the presence of such phenomena in the present experiments, the ‘crack length ratio’ has been calculated for all the tensile fractures. The ‘crack length ratio’ is defined as the ratio of tensile crack length to the sample diameter. Deviation of the tensile crack from its original straight path will result “crack length ratio” to be more than 1. The ‘crack length ratio’ at different inclination angles for all the temperatures has been plotted in Fig. 10. Results show that at the room temperature and 350 °C, the maximum “crack length ratio” is obtained at the inclination angle 30°; at the 100 and 250 °C, the maximum ‘crack length ratio’ is found at 60°. These increased ‘crack length ratio’ is resulted due to the activation of the gneissic layers during the tensile fracture propagation.

Fig. 9
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Crack geometries at different ‘inclination angles’

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Fig. 10
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‘Crack length ratio’ at different inclination angles for different temperatures

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3.2 Effect of Heat Treatment

3.2.1 Mineralogical and Microstructural Changes

Changes in the physical properties of rock under the influence of temperature are often accompanied by the concurrent changes in the mineralogical and microstructural properties of the rocks. To investigate these properties deeply, both the X-ray diffraction (XRD) and scanning electron microscopy (SEM) studies have been conducted on the untreated and treated samples. The XRD study did not indicate any significant change in the mineralogical composition of the rock. Only a slight decrease in the intensity of the rock was noticed, and it was interpreted to be due to the possible damage of the ferro-actinolite crystal structure on releasing of small amount of water. High-resolution SEM photographs (Fig. 11a, b) showed that the rock has gone through micro-mechanical changes due to the exposer to the high temperature. Most noticeably, several isolated and branched micro-cracks appeared, which were not present in the untreated samples. These micro-cracks mostly generated at the boundary of the harder minerals and propagated either through the bi-mineral boundaries, or through the adjacent weaker crystals. These thermal stress induced micro-cracks are interpreted to be the main reason behind the tensile strength decline of the heat-treated rock.

Fig. 11
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Micro-cracks in the heat-treated samples (SEM images)

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3.2.2 Tensile Strength

For each of the temperatures, samples were tested for four ‘inclination angles’. These angles were 0°, 30°, 60°, and 90°. The variation of tensile strength with the temperature is shown in Fig. 12. It is observed that for all the inclination angles, the tensile strength of the rock decreases with increasing heat treatment temperature. The reduction of the tensile strength is nearly negligible up to 250 °C temperature, after which it reduces rapidly. The reduction of the average tensile strength from room temperature to 350 °C for different inclination angles are shown in Table 1.

Fig. 12
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Tensile strength of the samples at four different temperatures for four ‘inclination angles’

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Table 1 Reduction of the average tensile strength from room temperature (30 °C) to 350 °C
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3.2.3 Layer-Parallel Strain

Strain indicates the deformational behavior of any material in response to the stress, temperature, and other parameters. Continuous measurement of strain with increasing stress gives an insight to the development of deformation. In the present experiments, the layer- and force-parallel strains were measured simultaneously to see the effect of the forces on the samples treated at different temperature. Changing strain values with temperature often indicate change in the material behavior as well as activation of the rock layers under the effect of temperature. Figure 13a–d show the development of layer-parallel strains at different temperatures. It should be noted that for the inclination angle 0°, both the layer- and force-parallel strain are same. It is observed that, for all the inclination angles, temperature has a significant effect on the rock material properties. As the temperature of the heat treatment increases, the L-strain value increases and the stress vs L-strain graph becomes inclined toward the L-strain axis. This behavior of L-strain with temperature indicates an increasing ductile behavior and degrading Young’s modulus of the rock.

Fig. 13
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Stress-layer-parallel strain curves for four different temperatures at a 0°, b 30°, c 60°, and d 90° inclination angles

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3.2.4 Force-Parallel Strain

Along with the layer-parallel strain, force-parallel strain also indicates the evolution of the deformational behavior along the loading direction. Similar to the layer-parallel strain, the force-parallel strain evolution also confirms the increasing ductility of the rock with the temperature. But, unlike the layer-parallel strain, the change in force-parallel strain with temperature is drastic in nature as seen in Fig. 14a–d. The gradients of the stress vs F-strain curve at 250 and 350 °C are nearly similar to each other but significantly less than that of the room temperature.

Fig. 14
figure 14

Stress-force-parallel strain curves for four different temperatures at a 0°, b 30°, c 60°, and d 90° inclination angles

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3.2.5 Strain Ratio

‘Strain ratio’ is defined as the ratio of the layer-parallel strain to the force-parallel strain during a tensile strength experiment. It gives a comparative understanding of how the sample is getting deformed along and across the layers of the samples while loading. A value more than 1 indicates a dominant layer-parallel deformation and less than 1 indicates the opposite. While comparing the rocks treated in different temperatures, this ratio is particularly helpful to see if the temperature has any significant effect on the strain distribution across the samples. The results are shown in Fig. 15a–d. As the L- and F-strain are same at the inclination angle` 0°, so the strain ratio remains 1 for all the temperature. For the rest of the inclination angles, the strain ratio decrease with increasing heat treatment temperature. At room temperature, for all the inclination angles, the strain ratio varies between 2 and 14 and shows relatively high-frequent variation at different stages of deformation. But at 250 and 350 °C, the strain ratios are below 1 and show nearly linear pattern with stress. The reduction of the average strain ratio with increasing heat treatment temperature is given in Table 2. These indicate that at room temperature layer-parallel strain is the dominant strain, and the variation is resulted from the series of small scale brittle fracturing resulted from the tensile tests. But, as rock becomes more ductile with heat treatment, force-parallel strain increases and becomes relatively higher than the layer-parallel strain. This is why the strain ratios reduce to less than 1 and show the linear pattern.

Fig. 15
figure 15

‘Strain ratio’ at different temperature for different inclination angle—a 0°, b 30°, c 60°, and d 90°

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Table 2 Reduction of the average strain ratio from room temperature (30 °C) to 350 °C
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3.2.6 Strain at Failure

The ultimate strain at failure is one of the important parameter to comment on the temperature influenced physical behavior of the samples. Along with the L-strain and F-strain curves, L-strain and F-strain at failure act as the complimentary data to assert the fact those samples have actually displayed ductile behavior. These data have been plotted in Figs. 16a–d and 17a–d. Results show that except the 0° inclination angle, for all the other samples both the L- and F-strain at failure increase with the increasing temperature. For the 30°, 60°, and 90° inclination angles, the L-strain at failure and F-strain at failure increases by 77.69 and 94.9, 39.85 and 96.84 %, and 77.16 and 93.29 %, respectively, from the room temperature to 350 °C. It is evident from the above values that as the samples are treated at increasingly higher temperatures, the F-strain at failure increases rapidly than the L-strain at failure. This is visualized in Fig. 18, which shows that only at room temperature the L-strain at failure load is larger than the F-strain at failure and the difference is positive. But, with the increasing temperature, F-strain at failure becomes higher than the L-strain at failure and the difference becomes highly negative.

Fig. 16
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‘L-strain at failure’ at different temperature for different inclination angle—a 0°, b 30°, c 60°, and d 90°

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Fig. 17
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‘F-strain at failure’ at different temperature for different inclination angle—a 0°, b 30°, c 60°, and d 90°

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Fig. 18
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Difference between L- and F-strain at failure at all the temperatures for all the inclination angles

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4 Discussion and Conclusion

Experimental results indicate that temperature affects rock in two ways—first, it makes rock weaker by creating micro-cracks, and second, rocks treated at higher temperature start showing ductile behavior. These are the main reasons behind the reduction of the tensile strength with increasing treatment temperature. The L- and F-strain distributions show that at room temperature, rock behaves like a brittle material and experience brittle tensile fracturing. This is why a variable but higher “strain ratio” is observed with the increasing tensile load at this temperature. But, as the temperature is increased to 250 and 350 °C, the ductile behavior starts affecting the rock properties, and F-strain becomes the major component of deformation than the L-strain. This dominance of F-strain results in a low value of “strain ratio” at higher temperatures. By comparing the L-strain and F-strain, it can be interpreted that increasing temperature has more effect on the evolution of the force-parallel strain than the layer-parallel strain.

The rock layer orientation also has a profound effect on the tensile properties of the rocks at different temperatures. In the granitic gneiss, the tensile strength is highest between the 30° and 60° inclination angles. Along with that, inclination angle also controls the fracture path of the failed samples. For the inclination angle between 30° and 60°, a high number of noncentral fractures are observed. In samples with inclination angles less than 30° and more than 60°, generally central fractures appear. This behavior is similar to the observation of Szwedzicki (2007) and Tavallali and Vervoort (2010). As the rock layer orientation changes with respect to the loading direction, a considerable amount of shear stress appears parallel to the layers. But, depending upon the inclination angle, the intensity of the shear stress vary. And depending upon the ratio of the shear stress to the tensile stress working on the rock layer, either central or noncentral fractures appear. As reported by the other researchers, in extreme cases, complete layer activations are observed, where the material fails predominantly along the direction of anisotropy.

Present study clearly indicates that the behavior of the layered rock under high temperature is considerably different than that of the homogenous, isotropic rock. So, while designing the nuclear or toxic material repository, a close look must be given on the combined effects of layering and temperature on the tensile properties of the host rocks to make it safe and secure for the long-term stability. It must also be noted that, under Brazilian test conditions, layered rock not only fails under tension, but depending upon the layering angle shear components also appear. So the conventional tensile strength formula may not be entirely applicable for such cases. Although for the comparison purpose, it appears to be quite useful.