Journal of Engineering Geology

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./files/site1/files/1.pdfExtended Abstract
(Paper pages157-174)
Introduction
Considering the fact that the estimation of mode  fracture toughness by testing is time-consuming and expensive. It might be associated with certain practical difficulties. Therefore, many researchers have attempted to propose experimental relationships in order to capture these problems. Gunsallus et al. (1984) and Bhagat (1985) experimentally found that mode  fracture toughness is related to tensile strength. Whittaker et al. (1992) have also proposed a number of relationships between mode I fracture toughness, tensile strength, point load index, uniaxial compressive strength and the velocity of sound waves. Bearman (1999) obtained an experimental relationship between mode I fracture toughness and point load index, while Brown et al. (1997) presented an experimental relationship between this parameter and density. Up to now no significant research effort has been made in this field in Iran, only Ayatollahi and Fatehi addressed rock fracture toughness. Although, Ayatollahi has not presented any experimental relationships. In the present research the three-point bending test was used on a cylindrical specimen containing a straight crack in order to determine the mode  fracture toughness, and the Brazilian test was employed to determine tensile strength.
Materials and Methods
The tests were carried out on six types of rocks, namely gray sandstone,
tuff, lithic tuff, travertine, andesite, and limestone. Sandstone, travertine, and limestone are sedimentary rocks, while andesite is an extrusive igneous rock, and tuff and lithic tuff are pyroclastic rocks (pyroclastic rocks resulting from volcanic eruptions that harden by sedimentation). Therefore, the studied rocks have different origins. In order to carry out the Brazilian and the three-point bending test, cores were prepared from these blocks. In order to perform the three-point bending test, specimens with diameter of 73 mm with a thickness of 30 mm were used. The samples were cut in two semicircular by a cutting machine, and a notch with length of 15 mm is created by a diamond saw.  Notch is vertical in the center of the semicircular samples.
The Brazilian test was performed on disc shaped specimens. In order to perform the Brazilian test, specimens with diameter of 51 mm and thick of 25 mm were used. The specimens are carefully placed under the curved jaws of the machine and then loaded until fracture.
Results and Discussion
A summary of the Brazilian and the three-point bending test results are presented in Table 1. The average value of test result pertaining to each rock is reported in Table 1.
Table 1. Summary of the Brazilian and the three-point bending test results

Specimen	Tensile Strength (MPa)	Fracture Toughness (MPa√m)
Limestone	3.74	1.23
Sandstone	7.14	1.63
Tuff	16.36	2.17
Lithic Tuff	4.34	1.01
Andesite	13.25	1.86
Travertine	8.27	1.14

In this study, it was attempted to propose an experimental relationship between mode I fracture toughness and the tensile strength of the rock.
In order to determine the relationship between the tensile strength and the fracture toughness, the tensile strength vs. fracture toughness diagram was plotted in Excel to obtain Eq. 1 and the coefficient of determination (R²) (Figure 1).

The coefficient of determination (R²) in Eq. 1 shows that almost 80 percent of the mode I fracture toughness variations can be estimated using the linear relationship (Eq. 1). The relationship is applicable for determining the mode I fracture toughness resulting from the three-point bending test on semicircular specimens containing a straight crack.

In the following, the results of this study are compared to those reported by Whittacker (1992) and Zhang (2002).
In order to examine the accuracy of the presented relationships, the Root Mean Square Error (RMSE) measure was used which is computed from Eq. 2. In the best case, RMSE is zero. 

In the relationships,   represents the fracture toughness obtained from testing while  is the fracture toughness estimated using the relationships.
Comparison of the obtained results indicate that the proposed relationship has the capability of precise estimation of the mode I fracture toughness of rocks.
Conclusion
Given the many difficulties associated with the direct estimation of fracture toughness, indirect estimation methods have been proposed. One of such methods is the estimation of mode I fracture toughness using tensile strength. A linear relationship with a coefficient of determination of 0.7977 was proposed. The accuracy of this relationship has been verified by comparing its results to those from previous studies.

 

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Rock anisotropy plays an important role in engineering behavior of rocks. Slates are anisotropic rocks which have long been used for gable roof, floor tiles, borrow materials, and other purposes. The slates studied in this research are calcareous and have a porphyro-lepidoblastic texture. To determine the role of the anisotropy on the tensile strength and fracture pattern, two variables including ψ (the core axis angle to foliation) and β (the angle between the axis of loading and foliation) in the Brazilian tests were used. The angles were selected at 15^° intervals. Thus, for both ψ and β, seven angles of 0˚, 15˚, 30˚, 45˚, 60˚, 75˚, and 90˚ were selected (i.e., there are 43 possible modes). In order to name and examine the failure pattern, 11 models were proposed. The average value of the failure strength for the three stations varies from 3.21 MPa to 20.94 MPa. Based on the obtained results, there is a direct relation between the average tensile strength and density. A comparison between Brazilian test data under dry and saturation conditions shows that the saturated Brazilian tensile strength is 30.8% less than the dry Brazilian tensile strength. Moreover, the changes in fracture length with the changes in ψ and β indicate an inverse relation. Eventually, the average of tensile strength (σt) and strength anisotropy index (Ia) demonstrates that the influence of orientation angle (ψ) is much larger than that of foliation-loading angle (β).
 

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Introduction
Determination of in situ stress-direction and magnitude are prerequisite for any oil well drilling and oil field development such as hydraulic fracturing. One of the simplest and most widely used methods is called borehole breakout analysis. Breakouts are compression fractures made in the direction of minimum horizontal in situ stress (Sh), if drilling mud pressure be lower than optimum mud pressure. Some borehole imaging logs such as FMI, FMS and UBI are appropriate tools for wellbore fracture detection. These fractures are distinguished in the logs as dark and symmetrical points (or lines) on both sides of the well and are used as an indicator for in situ stress studies. The size and shape of these fractures are strongly depend on the magnitude of the in situ stress. Therefore, many researchers suggested that by analyzing the geometric shape of the borehole breakout is an appropriate technique for estimation of in situ stress components. .... ./files/site1/files/0Extended_Abstract7.pdf
 

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In cases such as explosion, fire, deep drilling and geothermal energy extraction, rocks are exposed to high temperatures influencing the rock toughness. Thus, the aim of this study is to investigate the effect of temperature on the fracture toughness of the rocks. In this study, the effect of temperature on the mode I fracture toughness is investigated. To this end, three-point bending tests were performed on semicircular specimens of four types of natural rocks including sandstone, limestone, tuff, andesite, and a series of concrete specimens to determine the fracture toughness. The specimens were first heated to 100, 200, 300, 500 and 700 °C. After reaching the desired temperatures, the specimens were cooled. A series of tests was performed on the specimens at ambient temperature (25 °C). The heating rate in the electric furnace was 15 °C/min in accordance with the temperature rise in fires. Petrographic studies and X-ray diffraction analysis (XRD) were performed to identify the composition of the rocks. Furthermore, the effective porosity and the weight loss of heated specimens were determined to study the behavior of rocks. Comparison of the test results indicated the higher impact of temperature on the fracture toughness of fine-grained rocks. In addition, the fracture toughness decreased by increasing the effective porosity and decreasing the weight loss. According to the results, the mode I fracture toughness of sandstone, tuff, limestone, andesite and concrete specimens underwent a heating-cooling cycle up to 700 ^°C respectively decreased 45, 17, 44 and 9.5 and 37 percent compared with that of unheated specimens.
 

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Introduction
Rock masses have an enormous geometrical discontinuities such as void, notch, crack and flaw. These geometrical discontinuities which play as stress concentrator, cause to reduce the load bearing capacity of rock masses. In rock masses, the crack is the most important geometrical discontinuity assessed frequently by civil, mechanical and mining engineers and researcher. The fracture mechanics which is a branch of mechanical engineering science, has been often used for investigating the cracked rock samples. The fracture toughness is one of the important parameters in the fracture mechanics which describes the resistance of materials against the crack growth. On the other hand, since orientation of cracks relative to the loading directions can be arbitrary, brittle fracture in rocks may happen due to a combination of two major fracture modes, i.e. crack opening mode (mode I) and crack sliding mode without any opening or closing the crack flanks (mode II). In order to obtain the fracture toughness of rocks, several test configurations under pure mode I have been proposed. One of the parameters that has the influence on the fracture toughness of rocks and other materials is the thickness of test sample. Previous experimental results showed that the fracture toughness of rocks increases by increasing the specimen thickness until a specific thickness. After that, the fracture toughness decreases for thicker samples until plane strain condition occurs. Then, the fracture toughness becomes a fixed value when the thickness of sample varies.
The all preceding studies have been dealt with considering the effect of specimen thickness on fracture toughness focusing only the mode I fracture toughness and there is few research concerning the thickness effect on the mode II fracture toughness of rocks. Therefore, the aim of this paper is to investigate experimentally the effect of specimen thickness on the mode II fracture toughness.
Material and methods
To investigate the thickness effect on the mode II fracture toughness of rocks, several fracture tests were conducted on the semi-circular bend (SCB) specimens. The SCB specimen is a semi-disk of radius R and thickness t including an edge crack of length a loaded under three-point bending. When the crack is along the applied load and the bottom supports are symmetric relative to vertical crack, the SCB sample is under pure mode I loading. One of the methods for achieving the mixed mode loading in SCB sample is the asymmetry distances of bottom supports from the vertical crack located at the middle of bottom edge (see Figure 1). The pure mode II in this type of SCB sample is attained at a specific distances, i.e. at specific values of S₁ and S₂. These values of supporting distance can be obtained from finite element analysis.

Figure 1. The schematic of SCB sample.
The fracture tests were done both on pure mode I and pure mode II, for the sake of comprehensiveness. Therefore, 32 SCB samples with 4 different thicknesses and 4 repetition for each specimen size were tested for both pure mode I and pure mode II. The specimens were cut from Ghorveh marble sheets with different thicknesses by water jet machine. Then, the specimens were cracked artificially by a high speed rotary diamond saw blade. The specimen dimensions and loading conditions are presented in Table 1. Finally, the cracked SCB samples were tested by using a 300 kN ball-screw universal test machine. Table 1 also gives the average of four fracture loads (P_f) obtained for each thickness of specimen.
Table 1. The specimen dimensions and loading conditions.

	S.D.  (N)	Pf  (N)	S2 (mm)	S1 (mm)	a (mm)	t (mm)	R (mm)
Pure mode I	150	3220	57	57	28.5	15	95
Pure mode II	350	4726	11	57
Pure mode I	360	6711	57	57	28.5	25	95
Pure mode II	882	9445	11	57
Pure mode I	1450	20285	57	57	28.5	50	95
Pure mode II	4179	25441	11	57
Pure mode I	4672	31810	57	57	28.5	80	95
Pure mode II	4686	36848	11	57

Results and discussion
The mode I and mode II fracture toughness (K_Ic and K_IIc) can be calculated for SCB samples from following equations:
(1)
(2)
where P_f is fracture load, R and t are the radius and thickness of SCB sample, respectively K_I^* and K_II^* are geometry factors which depend on geometrical ratios a/R, S₁/R and S₂/R and independent of specimen dimensions and magnitude of applied load. These dimensionless parameters are often obtained from finite element analysis. For tested SCB samples, the values of K_I^* and K_II^* were extracted from previous studies as shown in Table 2. Substituting the fracture loads and specimen dimensions from Table 1 and the values of K_I^* and K_II^* given in Table 2 into Eqs. (1) and (2), the mode I and mode II fracture toughness were calculated as listed in Table 2. Figure 2 also shows the variations of mode I and mode II fracture toughness with respect to specimen thickness. As seen from this figure, the fracture toughness for both pure modes increases for thicker samples until a specific thickness. After that, the values of K_Ic and K_IIc decrease by increasing the specimen thickness. For plane strain condition in which the thickness of specimen is relatively large, the values of K_Ic and K_IIc are nearly constant.
 
 
Table 2. The dimensionless parameters K_I^* and K_II^* for tested SCB samples and their corresponding fracture toughness.

	KIIc (MPa.√m)	KIc (MPa.√m)	KII*	KI*	t	R
Pure mode I	0.0	1.125	0.0	0.644	15	95
Pure mode II	0.897	0.0	0.35	0.0
Pure mode I	0.0	1.411	0.0	0.644	25	95
Pure mode II	1.075	0.0	0.35	0.0
Pure mode I	0.0	2.126	0.0	0.644	50	95
Pure mode II	1.448	0.0	0.35	0.0
Pure mode I	0.0	2.083	0.0	0.644	80	95
Pure mode II	1.311	0.0	0.35	0.0

The other point assessed in the present study is the dependency of fracture path on specimen thickness in mode II loading. It was shown that the fracture trajectory becomes more curvilinearly when the thickness of specimen increases.

Figure 2. The variations of K_Ic and K_IIc versus the specimen thickness.
Conclusion
The effect of specimen thickness on the mode I and mode II fracture toughness of rock was investigated experimentally using the SCB specimens. The experimental results showed that the fracture toughness for both pure modes increases when the thickness of specimen increases until a specific thickness. After that, the values of K_Ic and K_IIc decrease by increasing the specimen thickness. For plane strain condition in which the thickness of specimen is relatively large, the values of K_Ic and K_IIc are nearly constant. Also, it is shown the crack grows more curvilinearly for thicker SCB samples../files/site1/files/142/1.pdf
 

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Introduction
CO₂ injection in deep geological formations, such as depleted oil and gas reservoirs, in addition to the environmental benefits, is one of the effective method for enhanced oil recovery (EOR) as tertiary EOR. Presence of reservoirs with a pressure drop which require injection of gas in the southwest of Iran and having the technical and environmental effects of CO₂ injection have created a huge potential for CO₂ injection to EOR in this region. In the first step, to perform CO₂-EOR, the geomechanical assessment is needed to find out pore pressure, in-situ stress magnitudes and orientations and fractures and faults conditions. In this paper, the initial in-situ pore pressure is predicted using modified Eaton method for 47 wells in the length of the study field and calibrated using repeat formation test and mud pressure data. In-situ stress was obtained by the poroelastic method for 47 wells in the length of the study field and calibrated using leak off test and extended leak off test. Then, the orientation of in-situ stresses is obtained based on image logs. Hydraulical and mechanical activities of fractures and faults were performed by critically-stressed-fault hypothesis
Material and Methods
In this paper, the initial pore pressure is calculated using modified Eaton method and other corrections that are proposed by Azadpour et al. (2015). The estimated initial pore pressure is validated using mud weight pressure (Pmw) and repeat formation tester (RFT) data. In-situ stresses are composed of three orthogonal principal stresses, vertical stress (S_V), maximum horizontal stress (S_H), and minimum horizontal stress (S_h) with specific magnitude and orientations. The magnitude of S_V is calculated by integration of rock densities from the surface to the depth of interest. The poroelastic horizontal strain model is used to determine the magnitudes of the S_H and S_h. Then, the estimated minimum horizontal stress from poroelastic horizontal strain model is validated against direct measurements of LOT and XLOT tests. The orientation of breakouts was determined based on compressively stressed zones observed in the UBI log and using Caliper and Bit Size (BS) logs. The hole elongates perpendicular to the S_H and breakouts develop at the azimuth of S_h. Fractures and faults reactivation analyses are very important, they can potentially propagate upwards into the lower caprock and further through the upper caprock due to CO₂ injection. Fractures and faults identification were performed based on image logs. Based on performed seismic interpretations by NISOC (National Iranian South Oil Company), 15 faults have been detected in the field. Fractures and faults conductivity and activity in the current stress filed affect on fluid flow and mechanical stability or instability of the CO₂ injection site. Critically stressed fault hypothesis, introduced by Barton et al. (1995), states that in a formation with fractures and faults at different angles to the current stress field, the conductivity of fluids through their apertures are controlled by the interplay of principal stress orientations and fracture or fault directions. Hence, conductive and critically stressed fractures and faults in the current stress field were evaluated using critically stressed fault hypothesis. Fractures and faults are plotted in normalized 3D Mohr diagrams (normalized by the vertical stress), therefore conductive and critically stressed fractures and faults were determined.
Results and discussions
The maximum distribution of initial pore pressure was 20-25 MPa in the field and the average of initial pore pressure was 25 MPa in the field. Unlike the World Stress Map, the stress regime is normal in the reservoir. Because the Kazeroon fault and Dezful Embayment act as a strike-slip tensional basin, resulting in the subsidence of Dezful compared with other regions. The frequency distribution of calculated in-situ stress in 47 studied wells in the length of the field has been presented. The maximum frequency distribution of S_V, S_H and S_h were between 60-70, 50-60 and 30-40 MPa, respectively. A large amount of fracturing is observed in 20-25 m below the caprock. Based on the continuity of their low amplitude traces on the acoustic amplitude image of UBI, fractures are classified into 4 classes: discontinuous-open, continuous-open, possible-open and closed fractures. OBMI and UBI image logs processing were performed in 7 wells. As can be seen from the image log, and caliper analysis the most dominant strike of S_H around the well is 27^◦ and S_h strike is 117◦. These have two dominant orientation, some faults are along the strike of the Zagros fold-thrust belt (NW-SE) and the others are perpendicular to the Zagros fold-thrust belt strike (NE-SW).
Based on the normalized 3D Mohr diagrams it is clear that the fractures and faults that are oriented to the S_H will be the most permeable, because the faults and fractures experience the least amount of stresses in the direction of S_H and they have minimum resistance to flow in this direction, therefore will have relatively high permeability. Also, results showed the faults number 15, 6, 10 and 2 will be the most dangerous faults during CO₂ injection.
 
 

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Introduction
Hydraulic fracturing is one of the most important stimulation methods for oil and gas reservoirs with low permeability. Various factors, such as in-situ stresses, joints and natural fractures of the formation, fluid rheology, mechanical properties of the formation, injection fluid flow rate and perforation operation, effect on the pressure and hydraulic fracture geometry. Many researchers have studied hydraulic fracturing behavior of rocks since decades ago. The researches have showed that hydraulic fracturing operations increase the production of oil wells by up to 30 percent and increase gas wells by 90 percent. Currently, this operation is performed on about 60% of all drilled wells.
Material and methods
In this research, for the experimental investigation of the hydraulic fracturing, considering the reservoir condition, 39 concrete cubic samples with 100 × 100 × 100 mm dimensions and 60 concrete cylindrical samples with a diameter of 54 mm and a height of 110 mm were constructed and the effect of the sample geometry and in-situ stress field on the fracture geometry, breakdown pressure, the pattern of crack propagation and finally the cross fractures in vertical wellbores were investigated.
Results and discussion
In cubic specimens under uniaxial stress, with increasing vertical stress to 8 MPa, first the breakdown pressure has been increased by about 132% and then with increasing vertical stress to 16 MPa, the breakdown pressure has been decreased by about 69%. In cylindrical specimens under uniaxial stress, with increasing vertical stress to 12 MPa, first the breakdown pressure increased by about 113% and then with increasing vertical stress to 16 MPa, the breakdown pressure decreased by about 6%. As the vertical stress increases to a certain limit, the pores and micro-cracks inside the sample close, thus the tensile strength and breakdown pressure increase. In the following, increasing vertical stress causes more small cracks to open and reduces the tensile strength of the rock. In cubic specimens under triaxial stresses, with increasing vertical stress, the breakdown pressure has been increased. Also, in cylindrical specimens under triaxial stresses as the maximum horizontal stress increased, the breakdown pressure increased.
Conclusion
The obtained results demonstrated that increasing the uniaxial stress in the vertical wellbore in both types of studied sample geometry, first the breakdown pressure increases and then from one boundary onwards, with increasing vertical stress, the breakdown pressure decreases. In cubic specimens under triaxial stress, with increasing vertical stress, the breakdown pressure increases. Additionally, in cylindrical specimens under triaxial stresses as the maximum horizontal stress increases, the breakdown pressure increases, so that, in the 8 MPa maximum horizontal stress, the breakdown pressure increases by about 81%../files/site1/files/151/3.pdf