^a Department of Civil Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia

^b Research Institute, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia

Abstract

Studying fracture toughness behavior at elevated temperatures and confining pressures is valuable for a number of practical situations such as hydraulic fracturing used to enhance oil and gas recovery from a reservoir, and the disposal or safe storage of radioactive waste in underground cavities. Mixed-mode (I–II) fracture toughness under simulated reservoir conditions of high temperature and confining pressure was studied using straight notched Brazilian disk (SNBD) specimens under diametrical compression. Rock samples were collected from a limestone formation outcropping in the Central Province of Saudi Arabia. Tests were conducted under an effective confining pressure (σ₃) of up to 28 MPa (4000 psi), and a temperature of up to 116°C. The results show a substantial increase in fracture toughness under confining pressure. The pure mode-I fracture toughness (K_IC) increased by a factor of about 3.7 under a σ₃ of 28 MPa compared to that under ambient conditions. The variation of K_IC was found to be linearly proportional to σ₃. The pure mode-II fracture toughness (K_IIC) increased by a factor of 2.4 upon increasing σ₃ to 28 MPa. On the other hand, K_IC at 116°C was only 25% more than that at ambient conditions. Some ductile behavior was displayed by the rock samples at a high temperature and confining pressure.

Nomenclature

β

orientation angle of the notch with the direction of loading

σ₃

effective confining pressure [MPa]

a

half crack length

B

thickness of the disk

K_I

mode-I stress intensity factor

K_IC

pure mode-I stress intensity factor

K_IC(σ3)

pure mode-I fracture toughness [MPa m^1/2] under any confining pressure [σ₃]

K_IC(field)

pure mode-I fracture toughness [MPa m^1/2] at field conditions

K_IC(T)

pure mode-I fracture toughness [MPa m^1/2] at any temperature [T]

K_II

pure mode-II stress intensity factor

K_IIC

pure mode-II stress intensity factor

LEFM

linear elastic fracture mechanics

N_I

normalized mode-I stress intensity factor for notched Brazilian disk

N_II

normalized mode-II stress intensity factor for notched Brazilian disk

P

compressive load at failure

R

radius of the Brazilian disk

R²

coefficient of determination

SNBD

straight-notched Brazilian disk

T

temperature

M.Y.B.P.

million years before present

Article Outline

Nomenclature

1. Introduction

2. Theoretical background

3. Experimental investigation

3.1. Rock description

3.2. Sample preparation

3.3. Testing at ambient conditions

3.4. Testing at reservoir conditions

3.4.1. Testing at confining pressure

3.4.2. Testing at high temperature

4. Results and discussion

4.1. Confining pressure

4.1.1. Mode-I

4.1.2. Mixed-mode (I–II)

4.2. Temperature

4.2.1. Mode-I

4.2.2. Mixed-mode (I–II)

4.3. Comparing results at ambient and in situ conditions

5. Conclusions

Acknowledgements

References

1. Introduction

Hydraulic fracturing is a well-known technique used to create fractures in deep-seated rock formations in order to enhance oil or gas recovery from a reservoir of low permeability. The ease of creating fractures is strongly influenced by the rock fracture toughness, which is a measure of the material’s resistance to crack initiation and propagation. The study of rock fracture toughness under in situ conditions at depth (i.e. high temperatures and confining pressures) becomes an important input for designing various aspects of the hydro-fracturing process [1, 2, 3 and 4].

Based on the loading type, there are three basic crack propagation modes in a fracture process, namely: mode-I (extension, opening), mode-II (shear, sliding), and mode-III (shear, tearing). Any combination of these modes can occur as a mixed-mode. Studies in the past have focused on fracture toughness determination under confining pressures only for mode-I failure conditions [5, 6, 7 and 8]. Moreover, specimen types other than the Brazilian disk have been used in these investigations. Nevertheless, due to randomly oriented cracks in rocks and/or in situ stress conditions, cracks tend to propagate under the influence of the combined action of the basic failure modes — called mixed mode [9 and 10]. The combination of mode-I and mode-II (mixed-mode I–II) failure is more common in rocks. Therefore, consideration of mixed mode (I–II) loading in addition to pure mode-I becomes important in fracture toughness investigation.

Rock specimens should be relatively small in size, requiring minimum machining for sample preparation, particularly when specimens are obtained from large depths (i.e. reservoirs). A centrally notched disk type specimen under diametrical compression (Fig. 1) has been proposed and extensively used in the past for fracture toughness studies of brittle materials including rocks under ambient conditions [10, 11, 12, 13, 14, 15 and 16]. However, the available data for mixed-mode (I–II) fracture toughness under confining pressures is limited. This specimen geometry was chosen in the study because it allows testing under mode-I, mode-II, and mixed-mode (I–II) loading conditions using the same specimen configuration and the same experimental set up. Hence, variations in specimen geometry and testing set up were eliminated. By changing the orientation angle of the notch with respect to the direction of loading (β), any loading condition can be obtained; pure mode-I (β=0°), pure mode-II (β≈30°), or mixed-mode (I–II).

Usually, the fracture toughness of rock is determined at ambient conditions (at room temperature and atmospheric pressure). However, under varying temperatures and confining pressures, the measured fracture toughness has been shown to vary. The fracture toughness behavior of a deep-seated rock formation requires the testing to be conducted in a manner that simulates the in situ conditions such as temperature and confining pressure. Estimates based on field data have indicated that representative hydrofracture toughness parameters are one to two orders of magnitude higher than those determined at ambient conditions [17].

Rock formations at larger depths have temperatures considerably higher than the ambient, which is generally used during a laboratory study. A temperature gradient of about 1°C/30 m exists within the earth’s crust [18]. In the past, little attention has been paid to the fracture toughness determination of rocks with temperatures higher than the ambient. Hoagland et al. [19] studied the effect of temperature on the fracture energy of Indiana limestone and Berea sandstone. They tested double cantilever beam specimens in splitting mode, at 22°C and at 196°C. The results for both rocks indicated that the fracture energy at 196°C was considerably lower than that obtained at room temperature.

Although some studies have been carried out on the effect of temperature on mode-I fracture toughness, little or no attention has so far been focused on mixed-mode (I–II). In the field, however, mode-I may not be dominant, but mode-II and in particular mixed-mode (I–II) is frequently encountered [9]. Therefore, a study of mixed mode fracture toughness behavior at elevated temperature is a matter of significant importance.

The objective of this study is to investigate the effect of temperature and confining pressures on mode-I, mode-II, and mixed-mode (I–II) fracture toughness, using straight-notched Brazilian disk (SNBD) rock specimens collected from the Central Province of Saudi Arabia.

2. Theoretical background

When a notched rock specimen is subjected to an externally applied load, stress concentrates in the vicinity of the crack tip. When this concentrated stress reaches a critical value, failure occurs due to propagation of the pre-existing crack. The fracture toughness is then calculated in terms of the stress intensity factor (SIF) using the failure load, notch size, and other geometrical parameters of the specimen. In this paper, a circular disk with a central straight notch under diametrical compression (Fig. 1) was used to investigate fracture toughness. The following mathematical expressions, proposed by Atkinson et al. [12], were used for the fracture toughness calculation:

(1)

(2)

For linear elastic fracture mechanics (LEFM) to be applicable to the fracture toughness study, the fracture process zone (FPZ) should be as small as possible. This is achieved partly by using specimens of relatively larger thickness [20], and partly by limiting the crack size to a minimum but practical value [21]. Based on that, the small crack approximation proposed by Atkinson et al. [12] can be used to determine the values of N_I, and N_II for half crack to radius ratio (a/R≤0.3), as follows:

(3)

(4)

3. Experimental investigation

3.1. Rock description

Rock blocks were collected from a limestone rock formation outcropping in the Central Province of Saudi Arabia. Geologically, the investigated limestone rock belongs to the ‘Khuff’ formation, which is of early Triassic to late Permain age (215–270 M.Y.B.P.). It outcrops at various places in the Central Province of Saudi Arabia, with an altitude reaching hundreds of meters above the sea level, and it dips toward the east to a depth of about 2000–4000 m below sea level at the Eastern Province. It consists of some members making a total thickness of about 171 m [22]. The generalized lithology consists of layers of limestone, claystone, dolomite, and sandstone.

Preliminary studies showed that this limestone rock is a homogenous, beige in color, muddy limestone. It is very tight and lacks any pores visible under a polarizing microscope, and therefore it has a negligible porosity. The physical properties include a dry density of 2.586 gm/cm³, a specific gravity of 2.737, a void ratio of 0.055, and a prosoity of 5.4%. The mechanical characteristics of this limestone rock include a uniaxial unconfined compressive strength of 105 MPa and a tensile strength of 2.31 MPa. Also, at 50% of maximum strength, the tangent modulus is about 54 GPa, the secant modulus is about 52 GPa, and the Poisson’s ratio is about 0.276. These mechanical properties are within the ranges reported in the literature for limestone rocks [23]. The mineralogical composition of this rock was determined by X-ray diffraction (XRD) analysis, Fig. 2. Results indicated that this rock is very pure limestone (99% CaCO₃).

3.2. Sample preparation

Cores were obtained from the blocks described above, using 84 mm and 98 mm coring tube pits. These cores were sliced into circular disks using a high-speed circular saw. The thickness (B) of the sliced disks was in the range of 20–24 mm. A straight notch was machined in the center of the disks using a 0.25-mm diamond impregnated wire saw. In the notch making process, a hole was drilled in the center of the disk using a 3-mm drill bit. The wire was passed through the drilled hole and the notch was machined. This technique allows notches of any length to be made, and hence the difficulty associated with machining small notches in Brazilian disks, as reported by Fowell and Xu [15], was overcome. Crack lengths of 25 mm and 29 mm were used for the 84 mm and 98 mm disks, respectively, (i.e. a/R=0.3). Some of the notched disk specimens are shown in Fig. 1(c).

For the testing under confining pressure, the entire disk surface was painted with a glossy spray paint to avoid the penetration of pressurized oil during testing. Also, the notch was sealed by a scotch tape from both sides, to prevent pressure build up inside the notch. Preliminary investigation showed the ability of paint to prevent oil infiltration. Two specimens were confined by pressurized oil for a sufficient period of time, one was painted and the other was not. These two samples were taken out then broken. The painted one showed no sign of oil infiltration, while the unpainted one showed an infiltration of oil to a depth of about 3 mm below the surface. Additionally, the paint was so thin that it will not affect the rock properties, especially the fracture toughness, since the notch itself was not spray-painted.

3.3. Testing at ambient conditions

A strain-controlled loading frame having a capacity of 100 kN was used for the load application with a strain rate of 0.08 mm/min, Fig. 3. SNBD specimens with a 98 mm and 84 mm diameter and a/R=0.3, were diametrically loaded. Specimens were tested with different values of the crack inclination angle (β) ranging from 0° to 75° with a 15° increment. The applied load and load-point displacement were acquired using a computerized data logger.

3.4. Testing at reservoir conditions

Initially, it was proposed to study the fracture toughness variation under the combined influence of temperature and pressure. Unfortunately, the application of confining pressure after heating the sample was not successfully accomplished. During the sample heating stage, the ‘O’ rings in the triaxial chamber became soft and broke during the application of confining pressure, resulting in leakage of oil from the cell. Many attempts were made to remedy the problem, after which it was decided to decouple the application of temperature and confining pressure, and to study their influence on the fracture toughness independently of each other.

3.4.1. Testing at confining pressure

Specimens were tested inside a triaxial cell made of stainless steel, manufactured locally for this purpose, Fig. 4(a) and (b). The cell was mounted into the apparatus shown in Fig. 3. The notched disk was placed, with the desired crack inclination to the loading direction (β), on a sample holder fixed to the base of the triaxial cell. Two lateral screws on each side of the sample holder were made to gently touch the sample to ensure its verticality. The disk was then fixed to the base of the sample holder using quick-setting glue, Fig. 4(c). A flat circular base snugly attached to a circular rod was fixed on top of the specimen to precisely control the loading angle as shown in Fig. 3. The triaxial chamber was tightly screwed to the base, and the whole assembly placed under the loading frame used for testing at ambient conditions. The chamber was filled with a light oil, and confining pressure was applied by a hydraulic pump. A confining pressure of up to 28 MPa (4000 psi) was used in this investigation, which is equal to the anticipated effective confining pressure in a reservoir. The confined rock specimen was then diametrically loaded in compression, while load and load-point displacement were recorded using a computerized data acquisition system.

To study the variation in mode-I fracture toughness from ambient to a confining pressure of 28 MPa (4000 psi), specimens were tested under various values of confining pressure ranging from 0 to 28 MPa, with an increment of 7 MPa (1000 psi). To investigate the effect of disk size on mode-I fracture toughness, SNBD specimens 98 mm and 84 mm in diameter were tested in mode-I under a confining pressure of 28 MPa (4000 psi).

SNBD specimens with a diameter of 98 mm, 22 mm thick, and a/R=0.3 were used to investigate the effect of confining pressure on mixed-mode (I–II) fracture. Confining pressures of 0 and 28 MPa were used for this purpose. Specimens under various values of confining pressure were tested with different values of crack inclination angle (β) ranging from 0° to 75° with an increment of 15°. The effect of specimen size on mixed-mode (I–II) fracture toughness was investigated using additional SNBD specimens with a diameter of 84 mm and a normalized crack (a/R=0.3). The thickness to diameter ratio (B/D) was the same as that of the 98 mm specimens (i.e. 0.2), which resulted in a thickness of 17 mm.

3.4.2. Testing at high temperature

SNBD specimens with a diameter of 98 mm, 22 mm thick, and a/R=0.3, were used to investigate the effect of temperature on fracture toughness. Specimens were tested inside a rectangular box fabricated from a heat and electrical insulating material (Bakelite), Fig. 5, to study the fracture toughness behavior at temperatures simulating field conditions. The inside dimensions of the box were 200×300×200 mm height, and the wall thickness was 14 mm. Specimens were placed inside the box at particular values of β, and precisely secured in position with the help of two lateral screws. Then the box was filled with coarse sand in a loose state, covered with a cap, and the whole assembly placed in an oven for heating to the desired temperature. After reaching the required temperature, the whole assembly was removed from the oven, and the sample was diametrically compressed by the loading frame shown in Fig. 3. Due to the long time required for the samples to reach a uniform temperature, only two samples per day could be tested. Load and load-point displacement were recorded during testing.

Preliminary investigation was made in which the temperature was monitored directly on the specimen surface. The temperature was found to drop by only 2°C in half an hour for the highest temperature. Since the time for each test was only 5 min, it was concluded that the slight drop (0.3°C) in temperature is negligible.

The samples were tested both in mode-I and mixed-mode (I–II) loading conditions. For mode-I, the specimens were tested at temperatures of 27°C, 50°C, and 116°C (reservoir temperature); and only one sample for each condition was tested. For mixed-mode (I–II) fracture toughness, the specimens were tested at temperatures of 27°C and 116°C, with a crack inclination of 0° to 75°, and two specimens were tested for each inclination.

4. Results and discussion

4.1. Confining pressure

4.1.1. Mode-I

Load-displacement curves for the specimens tested under confining pressures (σ₃) of 0, 7, 14, 21 and 28 MPa (0, 1000, 2000, 3000, and 4000 psi) for mode-I, are shown in Fig. 6. The failure load increases as the confining pressure increases. Moreover, load-deformation curves are progressively shifted to the right as the pressure increases, i.e. the deformation at failure increases with increasing confining pressure. Therefore, specimens at higher confining pressures behave in a more ductile manner than those at lower confining pressures. The specimens undergo a large deformation at the initial stage of loading. This behavior is similar to that shown by Almeida et al. [24]. Moreover, the load-displacement behavior is different from the ‘elastic’ behavior observed for the samples tested at ambient conditions (σ₃=0). Also the load did not drop to zero after the specimen had failed. This behavior is attributed to the presence of some confinement produced by the lateral screws and the glue at the base, which held the two broken pieces together even after failure and maintained a small apparent residual value.

Mode-I fracture toughness was calculated using (1) and (3) with β=0°, for tests with different confining pressures. Fig. 7 represents the variation of mode-I fracture toughness with confining pressure. The fracture toughness increases from an average value of 0.42 MPa m^1/2 for the 98-mm specimens tested under ambient conditions to 1.57 MPa m^1/2 for those tested under a confining pressure of 28 MPa (4000 psi), representing an increase of 274%. The fracture toughness value increases about 3.73 times. A straight line best fits the data with a coefficient of determination (R²) of 0.99, and has the following form:

For the effect of specimen size on mode-I fracture toughness under confining pressure, the results for both ambient and confined conditions are shown in Fig. 8. Increasing the confining pressure from 0 to 28 MPa (4000 psi) increased the fracture toughness of the 84 mm disk from 0.35 to 1.19 MPa m^1/2, representing a 245% increase. The corresponding values for the 98-mm disks were 0.42 to 1.57, a 274% increase.

As a comparison, Schmidt and Huddle [6] conducted fracture toughness testing of Indiana limestone under mode-I conditions using a single edge notched beam in direct tension. They found a significant increase in the fracture toughness value with increasing confining pressure. Abou-Sayed [2] and Muller [7] reported a similar trend of fracture toughness variation with confining pressure. Several other studies on quarried rocks have showed a significant increase in mode-I fracture toughness with an increase in the confining pressure. The measured data shows a considerable scatter, but an increase which is roughly linear with the confining pressure has been observed [25]. Recently, Vasarhelyi [8] studied the fracture toughness behavior of an anisotropic gneiss using a single edge cracked beam under three point bend configuration and reported similar conclusions. Fig. 9 shows a comparison of the mode-I fracture toughness of various rocks as a function of confining pressure.

It is believed that rock behaves in a more ductile manner under triaxial loading at high confining pressure than at low or no confining pressure conditions. Increased fracture toughness at high confining pressures has been attributed to the relatively increased amount of energy required to create new surfaces in ductile materials. Moreover, confining pressure, a hydrostatic pressure applied to the entire specimen excluding the sealed notch, makes the entire specimen under hydrostatic compression. The hydrostatic compression produces an initial negative stress intensity factor at the crack tip (crack closing), causing an increase in the fracture toughness value when the load is applied. This effect increases with increasing confining pressure. Furthermore, an increase in confining pressure reduces the size of the FPZ.

4.1.2. Mixed-mode (I–II)

Typical load-deformation curves are shown in Fig. 10 for specimens tested in mixed-mode (I–II) under a confining pressure of 28 MPa (4000 psi). At the initial stage of testing, all the samples underwent a large deformation without any significant increase in the load.

Mixed-mode (I–II) fracture toughness results for the 98-mm disks were calculated using (1), (2), (3) and (4) then plotted in Fig. 11 for confining pressures of 0 and 28 MPa (4000 psi). For σ₃=28 MPa, the pure mode-I fracture toughness (K_IC) was 1.57 MPa m^1/2, and the pure the mode-II fracture toughness (K_IIC) was found to be 2.18 MPa m^1/2, which was achieved at a crack inclination angle of about 29°. For σ₃=0 MPa, K_IC=0.42 MPa m^1/2 and K_IIC=0.92 MPa m^1/2. The pure mode-I and mode-II fracture toughness for confined specimens increased by an amount of 274% and 137%, respectively, over those obtained under ambient conditions. This means that mode-I fracture toughness is more affected by the confining pressure than the mode-II component. The ratio of pure mode-II to pure mode-I (K_IIC/K_IC) was 1.39 for the confined specimens, compared to a value of 2.19 for the unconfined specimens; representing a 37% reduction.

The mixed-mode (I–II) fracture toughness for the 84-mm disks was calculated using (1), (2), (3) and (4), and plotted in Fig. 12. Pure mode-I (K_IC) and pure mode-II (K_IIC) values for the 84-mm diameter disks were found to be 1.19 and 1.49 MPa m^1/2, respectively. Corresponding values of 1.57 and 2.18 MPa m^1/2 were obtained for the 98-mm diameter disk specimens. The K_IIC for the 84-mm diameter disks under ambient conditions was found to be 0.75 MPa m^1/2 and K_IIC/K_IC was 2.14. The ratio of pure mode-II to pure mode-I (K_IIC/K_IC) for the 84-mm diameter disk specimens under a 28 MPa confining pressure was found to be 1.25 compared to 1.39 for the 98-mm disks.

The normalized fracture toughness at σ₃=28 MPa is shown in Fig. 13 to be related to those of the ambient conditions according to the following formula for D=98 mm:

(6)

(7)

(8)

(9)

4.2. Temperature

4.2.1. Mode-I

Fig. 14 shows some typical load-deformation curves of specimens tested for mode-I at different temperatures. It can be seen that the effect of temperature on load-deformation response is not significant up to a temperature of around 50°C. However, the specimen tested at a temperature of 116°C behaved in a more ductile manner. This is probably because the viscous nature of the material at the microscopic level under higher temperatures results in both excessive deformation and higher failure loads due to the resistance offered along the failure plane.

The mode-I fracture toughness was found by using (1) and (3), and its variation with temperature is shown in Fig. 15. A small increase in the pure mode-I (K_IC) fracture toughness value was observed, from a value of 0.42 MPa m^1/2 for ambient conditions to 0.52 MPa m^1/2 at 116°C. The fracture toughness at a typical reservoir temperature (i.e. 116°C) is 25% higher than the value obtained at ambient conditions. The variation of K_IC with temperature, T, (K_IC(T)) can have the following forms:

Similar findings have also been reported in the literature although various testing methods other than the notched Brazilian disks were used in those investigations. Meredith [26] investigated the influence of high temperature on measured fracture toughness (mode-I) using double torsion tests on Black gabbro, Westerly granite, and single crystals of synthetic quartz at a temperature range between 20°C and 400°C. His results showed that K_IC increased slightly with increasing temperature from 20°C to 100°C, while it steadily decreased with increasing temperature from 100°C to 400°C. This reduction may be mainly caused by the development of microcracks resulting from the considerable tensile stress due to differential thermal expansion between adjacent mineral grains in the rock sample. Atkinson et al. [12] obtained similar results for Westerly granite samples. Cutler and Leslie [27] evaluated the mode-I fracture toughness of various steel alloys, and found that different alloys displayed different behavior. Depending on the microstructure, fracture toughness may remain constant, increase, or decrease with increasing temperature. Whittaker et al. [9] summarized these findings, and mentioned that the fracture toughness variation with temperature is material dependent, and concluded that the fracture toughness for rocks generally increases slightly at low temperatures (20–100°C). Fig. 16 shows comparisons of mode-I fracture toughness for various rocks as a function of temperature.

4.2.2. Mixed-mode (I–II)

Typical load-displacement curves are shown in Fig. 17 for specimens tested at 116°C. It was observed that there was no significant increase in the load in the initial stage of loading and the curves were flatter in this region. The ductile behavior was thought to be the result of plastic ‘flow’ of the rock material. Once this stage of ductile deformation was over, the specimens began to develop a resistance against deformation, and the load-displacement curves became rather steeper.

The mixed-mode (I–II) fracture toughness is calculated using (1), (2), (3) and (4). The mixed-mode (I–II) fracture toughness results for the specimens tested under both high temperature and ambient conditions are shown in Fig. 18. Pure mode-II (K_IIC) was 1.00 MPa m^1/2 with a 9% increase from that at ambient conditions. The ratio of K_IIC/K_IC was found to be 1.92 compared to the value 2.19 for ambient conditions. Moreover, the mode-I fracture toughness values showed more variation at the extremes of the crack inclination angles. The normalized fracture toughness at a temperature of 116°C is shown in Fig. 19 and related to the ambient condition results according to the following:

(12)

(13)

4.3. Comparing results at ambient and in situ conditions

Fig. 20 presents the load-displacement relation for SNBD specimens with β=0 under diametrical compression at three different conditions: ambient, a confining pressure of 28 MPa, and a temperature of 116°C. A comparison of these curves shows a higher fracture load for the confined case and the ductility phenomenon at high temperature and confining pressure can be clearly seen. Table 1 gives a comparison between K_IC, K_IIC and K_IIC/K_IC at ambient and in situ conditions.

The combined effect of confining pressure and temperature on K_IC is shown in Fig. 21, for D=98 mm. The 3-D plot represents a superposition of the individual effects of confining pressure and temperature. Therefore, the combined effect of in situ temperature and confining pressure on the fracture toughness in the field, K_IC(field), can be written as follows:

5. Conclusions

The study of the effect of temperature and confining pressure on the fracture toughness of rock is of practical significance; particularly in situations like hydraulic fracturing used to enhance oil and gas recovery from a reservoir, and the safe disposal/storage of radioactive waste in underground cavities. It is therefore essential to determine the fracture toughness of rocks in the temperature and confining pressure ranges of operation. Testing under such conditions requires the development of apparatus that can simulate in situ conditions.

The SNBD type was found to be the most convenient geometry to use for the determination of pure mode-I, pure mode-II, and mixed-mode (I–II) fracture toughness of rocks. This is made possible after successfully machining a straight notch inside the disk, using the combination of a drill and a wire saw to make a precise notch. The following conclusions pertain specifically to the tested limestone rock formation from Saudi Arabia.

The mode-I fracture toughness (K_IC) was found to increase substantially with increased confining pressure. This increase is almost linear in the pressure range from 0 to 28 MPa. For disks with D=98 mm, K_IC increased from 0.42 MPa m^1/2 at ambient conditions to 1.57 MPa m^1/2 at σ₃=28 MPa, i.e. an increase of 274%. On the other hand, K_IC for such disks increased only slightly to a value of 0.52 MPa m^1/2 at a temperature of 116°C, i.e. an increase of 25% only.

The mode-II fracture toughness (K_IIC) was found to increase with increased confining pressure. For 98 mm disks, K_IIC increased from 0.92 MPa m^1/2 at ambient conditions to 2.18 MPa m^1/2 at σ₃=28 MPa, i.e. an increase of 137%. On the other hand, K_IIC increased to a value of 1.00 at 116°C, i.e. an increase of 9% only. The increases of K_IIC due to confining pressure and temperature (137% and 9%, respectively), are much less than those of K_IC (274% and 25%, respectively).

The ratio of K_IIC/K_IC is equal to 2.19, 1.39, and 1.92, at ambient conditions, under a confining pressure of 28 MPa, and at a temperature of 116°C. This leads to the conclusion that the mode-II component may be the most critical mode controlling failure at high values of temperature and confining pressure.

Rock samples exhibited some ductile behavior at high temperature and confining pressure. This behavior is attributed to some changes in the microstructure of the rock material at these conditions.

Acknowledgements

The authors acknowledge the support of King Fahd University of Petroleum & Minerals for providing computing and laboratory facilities. They also would like to acknowledge the support of Saudi-ARAMCO through Research Institute, KFUPM. They are also grateful to Dr Abdulraheem, from the Petroleum Engineering Section, RI and to Mr Hasan Zakaria, from the geotechnical laboratory.

Corresponding author. Tel.: +996-3-860-2550; fax: +966-3-860-2879; email: nshayea@kfupm.edu.sa