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Theme 1 : Emerging Techniques Laboratory Rock Mechanics Testing Debanjan GuhainRoy and T. N.Singh

Fracture and Tensile Properties of the Layered Crystalline Rocks 1

Debanjan Guha Roy1 and T.N. Singh2

IITB-Monash Research Academy, Indian Institute of Technology Bombay, Mumbai, 400076, India 2 Dept. of Earth Sciences, Indian Institute of Technology Bombay, Mumbai, 400076, India e-mail: [email protected] ABSTRACT: Mechanical and fracture properties of rocks are important for designing and developing the Enhanced Geothermal Systems (EGS), tunnelling, drilling systems etc. But these properties are strongly controlled by the internal heterogeneities (i.e. layers, bedding planes, internal cracks etc.) of the rocks. So, we have studied the mechanical and fracture properties of two high strength heterogenous layered crystalline rocks – granitic gneiss and khondalite in the laboratory. The strength properties were measured using the NX (54.7mm) size core specimen in the Universal Testing Machine (UTM), and the fracture properties were measured using the Semi-circular Bend (SCB) specimens in Three Point Bend (TPB) set-up. The main objectives of the present studies are – a) to see how the pure and mixed mode fracture properties vary with inclination angle b) to see how the Brazilian tensile strength (BTS) of the rocks vary with inclination angle, and c) to develop an empirical relation between the above mentioned properties. The results show that both the BTS and the fracture toughness of the rocks are strongly influenced by the orientation of the rock layers with respect to the loading direction (i.e. inclination angle). Both the Granitic gneiss and Khondalite rock samples show minimum BTS and fracture toughness at 0⁰ and maximum values at 90⁰ inclination angle. From 0⁰ to 90⁰, the BTS values of the granitic gneiss and Khondalite increase by ~34% and ~24%, respectively. The mode-I, mixed-mode and mode-II fracture toughness of Granitic gneiss and Khondalite increases by ~23%, ~16%, ~6% and ~15.3%, ~11%, ~6%, respectively. It was also found that all the pure and mixed-mode fracture toughness are linearly correlated with the BTS of the samples.

1.

INTRODUCTION

A good understanding of the mechanical and fracture properties of the hard crystalline rocks are very important for large scale mining, civil, petroleum engineering projects as well as geothermal energy etc. Since rocks are much weaker in tension than any other kind of stress, therefore the study of rock tensile strength is paramount for the safety of the geomechanical projects. Similarly, the fracture toughness and the fracture energy determines the failure characteristic of the geomaterials and the helps in predicting the critical stress conditions. These are the critical parameters which are essential to build an efficient Enhanced Geothermal System (EGS), to design underground space structures, to construct tunnels and to maintain the stability of the boreholes for nuclear waste or toxic waste disposal. But many rocks contain bedding plains, micro-cracks and oriented micro-structural fabric which make them highly heterogeneous. Both the tensile and fracture properties are strongly dependent on the anisotropy and heterogeneity of the rocks (Douglas and Voight, 1969; Peng and Johnson, 1972; Nasseri et al., 2003; Dan et al.,2013; Nasseri and Mohanty, 2008; Funatsu et al., 2012). So, it is impossible to assign a single value of tensile strength and fracture toughness to heterogeneous rocks without INDOROCK 2017: 7th Indian Rock Conference 25-27 October 2017 130

Fracture and Tensile Properties of the Layered Crystalline Rocks taking the effect of rock layers into account. A complete discussion of the mechanical and fracture property of rock must include direct experimental information on the layer orientation dependent tensile strength and fracture toughness values. Therefore, a laboratory based investigation was carried out on two types of heterogenous crystalline rocks from India – gneissic granite and khondalite. As shown in Figures 1a & b, both of these rocks have visible layering which are characterized by different minerals layers and their distinct colours.The rock cores were retrieved from the blocks and the tensile disc and fracture toughness specimens were prepared from them. These specimens were then tested in the controlled environment for their tensile strength and fracture toughness. The layer orientation with respect to the loading direction (i.e. inclination angle) were varied throughout the experiments to see its effect on the before mentioned parameters.

2.

METHODOLOGY

2.1

Specimen Preparation The samples were cored from the rock blocks by maintain the coring direction parallel to the rock layering. Intact and flaw-less cores were dried in the room temperature for 48 hours. The tensile discs were prepared following the ISRM suggested method (ISRM 1978) and the semicircular bend (SCB) fracture toughness samples prepared following the procedure prescribed by ISRM (Kuruppu et al., 2014). All the tensile discs were prepared by maintaining a length/diameter ratio of 0.75. In the SCB specimens, a notch with “notch length/Radius” ratio 0.5 was made using a thin diamond circular saw. For different modes fracture toughness tests, different ‘notch angle’ was chosen.

Fig. 1.(a) Granitic gneiss (b) Khondalite 2.2

Test Procedure Fracture toughness and the tensile strength of the layered samples were measured using the Three-point bend (TPB) setup and the Brazilian cage tool. These two tools are attached to platens of the Universal Testing Machines (UTM) and the loading experiments are performed following a constant loading rate. The TPB tool has two adjustable roller attached at the bottom plate. The distance between these two rollers could be changed to provide proper span support to the specimens. For following test program, a ‘span/diameter’ ratio of 0.5 was chosen. The samples were placed properly on the rollers such that, a line load can be applied at the top of the samples by the upper platen. The Brazilian cage used for the tensile strength tests comprises of two steel curved blocks with Rockwell hardness more than 50 HRC. The sample is placed in between them and a line load is applied on the sample using the UTM. The disc fails due the indirect tensile stress generated in the direction perpendicular to the loading direction. Samples were tested for four different ‘inclination angles’ - 0°, 30°, 60° and 90°. A constant loading rate

INDOROCK 2017: 7th Indian Rock Conference 25-27 October 2017 131

Debanjan Guha Roy and T. N.Singh

of 0.5mm/min is kept for both the experiments to avoid the effect of impact. The specimen and tool details are shown in Figures 2a, b & c. 2.3 Fracture Toughness Calculation Fracture toughness of any SCB specimen is controlled by the loading condition, geometric specification (e.g. notch length, notch angle, radius and thickness of the specimens). The Mode-I fracture toughness of the SCB specimens are calculated by the following equation (Kuruppu, et al. 2014)πa P K IC = Y ' max [1] 2 RB Where,

Y ' = −1.297 + 9.516( s

2R

) − (0.47 + 16.457( s

2R

)) β + (1.071 + 34.401( s

2R

)) β 2

[2]

β =a

R , a=notch length, R=radius of the specimen, s=span. and The mode-II fracture toughness (KIIC) is calculated as:

K IIC = Y "

Pmax πa 2 RB

[3]

The Y’ and Y” are called the non-dimensional strain intensity factors. Following the study of Lim et al. (1993) on the a/R and s/R dependency of the non-dimensional stress intensity factors, a notch angle of 40° were chosen for the mode-II (pure shear) samples. For ‘notch length/radius’ and ‘span/diameter’ of 0.5, at this angle Y’ becomes zero i.e. Mode-I (pure tensile) fracture toughness becomes zero. A notch angle of 30° was chosen for the mixed-mode fracture toughness SCB specimens. This is calculated as –

K eff = K I2 + K II2

Fig. 2 (a)UTM (b). Three-point bend (TPB) tool (c) Brazilian cage


[4]

Fracture and Tensile Properties of the Layered Crystalline Rocks

3.

RESULTS AND DISCUSSION

3.1

Fracture Toughness (FT) All the pure and mixed mode fracture toughness for both the khondalite and the granitic gneiss specimens were tested for four different layer orientations ranging from 0° to 90°. The effect of the ‘inclination angle’ on the fracture toughness of the specimens are shown in Figures 3a and b respectively. The results show that fracture toughness of the rocks are strongly dependent on the layer orientation with respect to the loading direction. As results indicate, all the fracture toughness of the rocks increase with increasing ‘inclination angle’. But this increase is more prominent in the mode-I than the mixed-mode and mode-II fracture toughness. From 0° to 90°, the mode-I fracture toughness of granitic gneiss and khondalite increase by ~23.4% and ~15.3%, respectively. For the same inclination angles, the mixed-mode fracture toughness increase by ~16% and ~10.7% and the mode-II fracture toughness by ~5.6% and ~6.1%. For the comparison purpose, the mode-I fracture toughness of the present experiments were compared with the works of Funatsu et al (2012) and Ghamgosar et al (2015). Although the rock types for both of these works are sandstone, but the trends of the present results are found to be in good agreement with them.

Fig.3 (a). Mode-I fracture toughness (b) Mixed-mode and Mode-II fracture toughness Brazilian Tensile Strength (BTS) The effect of layer orientation on the Brazilian tensile strength of the granitic gneiss and khondalite is shown in Figure 4. As the results indicate, the BTS of both the rocks increase with increasing ‘inclination angle’. So, the minimum BTS is registered when the rock layers are parallel to the loading direction (0°) and maximum is BTS is found when the layers are at the perpendicular to the loading direction (90°). From 0° to 90°, the BTS of granitic gneiss increases from 13MPa to 19.7 MPa, and in khondalite BTS increases from 14.4MPa to 18.9MPa. The rate of increase was found to be higher in granitic gneiss than the khondalite. So, with increasing ‘inclination angle’ BTS of granitic gneiss and khondalite increase by nearly ~34% and ~25.9%. Similar results of increasing tensile strength with increasing ‘inclination angle’ are also reported for other rocks like Assan gneiss and Freiberger gneiss (Vervoort et al., 2014). 3.2


Debanjan Guha Roy and T. N.Singh

Fig. 4. Brazilian tensile strength of granitic gneiss and khondalite 3.3 Relationship between BTS and FT Tensile strength of any rock shows the resistance of the material against the initiation and propagation of tensile cracks/fractures. Similarly, fracture toughness indicate the resistance of any material against propagation of any fracture from an already existing crack. So, both of these resistances of the material against the crack can be correlated to understand their internal relationship. Therefore, the fracture toughness of the layered granitic gneiss and khondalite have been plotted against their BTS values in Figures 5a & b respectively. As can be seen from the figures, these two parameters correlate well and predictable empirical relationships can be postulated for each of the rocks. For granitic gneiss, the relationships are expressed as –

FTI = 0.0427 * BTS + 0.3359 ; R2=0.9 FT( I − II ) = 0.018 * BTS + 0.4053 ; R2=0.93

[5] [6]

R2=0.82

[7]

FTII = 0.0054 * BTS + 0.5121 ;

For khondalite, the relationships can be expressed as –

R2=0.78 FTI = 0.0209 * BTS + 0.3356 ; FT( I − II ) = 0.0137 * BTS + 0.3067 ; R2=0.9

[8] [9]

R2=0.96

[10]

FTII = 0.0071 * BTS + 0.375 ;

The results show that in both the layered rocks, mode-I fracture toughness is most sensitive to the BTS of the rocks followed by mixed-mod and mode-II fracture toughness. The mode-II fracture toughness could be considered nearly independent of the BTS and remains largely constant.


Fracture and Tensile Properties of the Layered Crystalline Rocks

Fig. 5.Relationship between fracture toughness and tensile strength of (a) Granitic gneiss and (b) Khondalite.

4.

CONCLUSION

In order to investigate the effect of layer orientation on the tensile and fracture toughness of the specimen, series of laboratory tests were performed in the Brazilian cage set up and Threepoint bend (TPB) tool. All the results were expressed as a function of the ‘inclination angle’ to visualize the effect. Moreover the BTS of the samples were compared with the all the pure- and mixed-mode fracture toughness of the samples and mathematical relationships were constructed. The main findings are summarized as: i. Pure- and mixed-mode fracture toughness are dependent on the ‘inclination’ angle of the layers and the toughness values increase with increasing ‘inclination angle’. ii. Among all the modes, mode-I fracture toughness is more sensitive towards the ‘inclination angle’ than the mixed-mode and mode-II fracture toughness. iii. Tensile strength of the rocks are layer orientation dependent and the BTS increases with increasing ‘inclination angle’. iv. Between granitic gneiss and khondalite, both the BTS and FT of the granitic gneiss are more sensitive toward the ‘inclination angle’ than the khondalite. v. Tensile strength and fracture toughness of the rocks are linearly correlated with each other, however mode-I FT is more sensitive compared to other modes.

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