ABSTRACT In this study, the displacement discontinuity formulation is used to solve the problem o... more ABSTRACT In this study, the displacement discontinuity formulation is used to solve the problem of interaction between hydraulic fractures (HF) and natural fractures (NF). Furthermore, a numerical program (2DFPM) is developed to study the mechanical activation of a NF because of the propagation of the HF. The accuracy of the numerical method is enhanced using the higher-order displacement variation along the HF and the special crack tip element near its ends. The maximum tangential stress criterion is implemented to predict the HF propagation path, and the stages of hydraulic fracturing tip approaching, coalescence and fluid penetration along the NF are modeled. The tangential stress around the NF with different contact modes (bonded, sliding and opening) is calculated by coupling the finite difference and boundary element methods. The location of secondary tensile fracture that re-initiates along the opposite side of NF is determined, and the key parameters that have great influence on interaction process are discussed. The results show that position, distance and inclination of the HF relative to the pre-existing discontinuity have a strong influence on the HF propagation path.
Artificial cracks are required for heat exchanging surface and/or flow paths in the hot dry rock ... more Artificial cracks are required for heat exchanging surface and/or flow paths in the hot dry rock reservoirs. Fracture mechanics is the only methodology that has been found effective in evaluating the size of artificial cracks, the surface area of the heat exchanger. In this study, fracture mechanics with boundary element method based on the displacement discontinuity formulation is presented to solve general problems of interaction between artificial hydro-fractures and discontinuities that are in the reservoir. The numerical results are in good agreement with the results brought in the literature. The comparison of numerical method with exact solution shows a good performance of the method in the case of interacting cracks too.
Numerical methods such as boundary element and finite element methods are widely used for the str... more Numerical methods such as boundary element and finite element methods are widely used for the stress analysis in solid mechanics. This study presents boundary element method based on the displacement discontinuity formulation to solve general problems of interaction between hydraulic fracturing and discontinuities. The crack tip element and a higher order boundary displacement collocation technique are used to study the hydraulic fracture propagation and its interaction with the pre-existing cracks and discontinuities in an elastic rock mass. The maximum tangential stress criterion (or -criterion) and the strain energy density criterion (SED) are used to obtain the fracture path and the results of both criteria are compared with each other. The comparison of numerical method with the results brought in the literature shows a good performance of the method in the case of interacting cracks.
Bulletin of Engineering Geology and the Environment
The earth’s crustal stress determination is a crucial item in civil, petroleum, and mining engine... more The earth’s crustal stress determination is a crucial item in civil, petroleum, and mining engineering and also in energy development fields. The hydraulic fracturing (HF) is one of the standard methods for estimating in situ stress, which is often analyzed with classical approach for stress estimations. The classical approach neglects the presence of pre-existing cracks in rock mass; however, the hydraulic fracturing is a phenomenon of fracture propagation in which the fracture mechanics approach is more appropriate to consider more complex items in stress estimations. In this study, the in situ stress tests are conducted in Azad Pumped Storage Power Plant (Azad PSPP) in the west of Iran and then the classical approach and four available analytical fracture mechanics methods are applied to determine the in situ stresses. Moreover, numerical modeling based on the displacement discontinuity method (DDM) is used to model hydraulic fracturing process and the results are compared with analytical methods. A comprehensive analysis on the length of pre-existing crack is done as an influential parameter on stress magnitudes. The results indicate that the magnitudes of in situ stresses calculated by the fracture mechanics approach are often greater than the stress magnitudes calculated by the classical approach. Also, the effect of crack inclination angle and pre-existing crack length on the magnitudes of σH is studied. In addition, the distribution of fluid pressure along the cracks and its influence on the stress intensity factor in the crack tip are analyzed, and consequently, the estimation of in situ stress is investigated.
One of the most common geological hazards in mining and civil projects is the occurrence of insta... more One of the most common geological hazards in mining and civil projects is the occurrence of instability in the rock slopes. Rock slope behavior is mainly influenced by the presence of discontinuities in the rock masses. Therefore, the determination of shear strength parameters for these weak surfaces is of particular importance. There are various shear strength criteria for estimating the shear strength of discontinuities, which among them the Barton–Bandis criterion (B‒B criterion) and Mohr–Coulomb criterion (M‒C criterion) are the most widely used. Accurate estimation of shear strength properties does not only depend on the correct procedure of tests, but it requires an accurate and detailed explanation of test results. The uncertainty in the measured shear strength leads to many problems in the analyzing and designing of rock slopes. Therefore, to reduce the uncertainty and increase the accuracy of rock slopes analyzing, it is better to use probability methods. The probability distribution function can be assigned for each input parameter of the failure criterion. In this research, the results of the direct shear tests related to Azad pumped storage power plant project have been considered to estimate the shear strength properties of rock discontinuities. The results are divided into three groups based on the magnitude of the joint roughness coefficient (JRC). Shear strength for each group is estimated depending on the two most well-known criteria i.e., the B‒B criterion and the M‒C criterion. Further, the probability distribution functions (PDF) for each shear strength parameter are determined by @RISK software. Besides, the results of the empirical B‒B criterion are compared with the results of the direct shear tests for the three groups of rock joints. The confidence intervals associated with both criteria are estimated and compared together. The results showed that the overlapping of the confidence interval of the M‒C criterion with the confidence interval of B‒B criterion increases with increasing JRC of rock joint. The results show the B‒B criterion covers data of the direct shear test almost at low normal stress levels for different JRC groups too.
Abstract It is common for the fractured zone around dynamic faults to contain tensile cracks. The... more Abstract It is common for the fractured zone around dynamic faults to contain tensile cracks. The effect of Poisson's ratio (ν) on the creation of these cracks was investigated in this study as a function of the dynamic minimum strain energy density criterion (MSED-Criterion). In addition, the effect of rupture speed (c), friction coefficient (f), fault inclination angle (β) and confining stress (Ko) were taken into account. The MSED-Criterion permits the study of the creation of tensile cracks in brittle and ductile shear zones. It was found that by increasing Poisson's ratio, the rock behavior transfers gradually from brittle to ductile and as a consequence, the branching angle and fracture toughness increase. Whenever the rock mass tends towards ductile behavior, the possibility of creating tensile branches decreases. Ductile shear zones can sustain stresses greater than brittle zones before tensile branches are formed around dynamic faults. The branching angle of tensile cracks is directly proportional to (ν, c, β, f and Ko) and it varies between approximately 77° and 115°. These cracks are formed in the extensional side of a dynamic fault and they tend to grow towards the maximum far-field stress. The results of this study can be used in the field of earth science and earthquakes to identify the formation of tensile branches around dynamic shear ruptures and they were explained depending on experimental results and field observations of other studies.
International Journal of Rock Mechanics and Mining Sciences
Abstract Conventional or single stage triaxial compression experiments for obtaining failure enve... more Abstract Conventional or single stage triaxial compression experiments for obtaining failure envelope of rocks require several specimens to be tested under different confining pressures. As a replacement, multistage triaxial tests using one specimen have been employed in experimental rock mechanics for situations where preparing several specimens is difficult or expensive. The results obtained by the multistage triaxial test may deviate from those obtained by the single stage. However it is believed that using multistage triaxial test can decrease the cost and time and the obtained results are still reliable due to less variability in the rock properties. Several methods have been proposed for conducting multistage triaxial test including ISRM suggested method and a modified version of the ISRM method proposed by Crawford and Wylie. The results of this study demonstrate that both multistage methods give reasonable results. However, the modified method provides closer results to the single stage, because the specimen is subjected to less damage. As the number of the loading stages rises, both ISRM and the modified version provide lower strength parameters comparing to the single stage.
ABSTRACT In this study, the displacement discontinuity formulation is used to solve the problem o... more ABSTRACT In this study, the displacement discontinuity formulation is used to solve the problem of interaction between hydraulic fractures (HF) and natural fractures (NF). Furthermore, a numerical program (2DFPM) is developed to study the mechanical activation of a NF because of the propagation of the HF. The accuracy of the numerical method is enhanced using the higher-order displacement variation along the HF and the special crack tip element near its ends. The maximum tangential stress criterion is implemented to predict the HF propagation path, and the stages of hydraulic fracturing tip approaching, coalescence and fluid penetration along the NF are modeled. The tangential stress around the NF with different contact modes (bonded, sliding and opening) is calculated by coupling the finite difference and boundary element methods. The location of secondary tensile fracture that re-initiates along the opposite side of NF is determined, and the key parameters that have great influence on interaction process are discussed. The results show that position, distance and inclination of the HF relative to the pre-existing discontinuity have a strong influence on the HF propagation path.
Artificial cracks are required for heat exchanging surface and/or flow paths in the hot dry rock ... more Artificial cracks are required for heat exchanging surface and/or flow paths in the hot dry rock reservoirs. Fracture mechanics is the only methodology that has been found effective in evaluating the size of artificial cracks, the surface area of the heat exchanger. In this study, fracture mechanics with boundary element method based on the displacement discontinuity formulation is presented to solve general problems of interaction between artificial hydro-fractures and discontinuities that are in the reservoir. The numerical results are in good agreement with the results brought in the literature. The comparison of numerical method with exact solution shows a good performance of the method in the case of interacting cracks too.
Numerical methods such as boundary element and finite element methods are widely used for the str... more Numerical methods such as boundary element and finite element methods are widely used for the stress analysis in solid mechanics. This study presents boundary element method based on the displacement discontinuity formulation to solve general problems of interaction between hydraulic fracturing and discontinuities. The crack tip element and a higher order boundary displacement collocation technique are used to study the hydraulic fracture propagation and its interaction with the pre-existing cracks and discontinuities in an elastic rock mass. The maximum tangential stress criterion (or -criterion) and the strain energy density criterion (SED) are used to obtain the fracture path and the results of both criteria are compared with each other. The comparison of numerical method with the results brought in the literature shows a good performance of the method in the case of interacting cracks.
Bulletin of Engineering Geology and the Environment
The earth’s crustal stress determination is a crucial item in civil, petroleum, and mining engine... more The earth’s crustal stress determination is a crucial item in civil, petroleum, and mining engineering and also in energy development fields. The hydraulic fracturing (HF) is one of the standard methods for estimating in situ stress, which is often analyzed with classical approach for stress estimations. The classical approach neglects the presence of pre-existing cracks in rock mass; however, the hydraulic fracturing is a phenomenon of fracture propagation in which the fracture mechanics approach is more appropriate to consider more complex items in stress estimations. In this study, the in situ stress tests are conducted in Azad Pumped Storage Power Plant (Azad PSPP) in the west of Iran and then the classical approach and four available analytical fracture mechanics methods are applied to determine the in situ stresses. Moreover, numerical modeling based on the displacement discontinuity method (DDM) is used to model hydraulic fracturing process and the results are compared with analytical methods. A comprehensive analysis on the length of pre-existing crack is done as an influential parameter on stress magnitudes. The results indicate that the magnitudes of in situ stresses calculated by the fracture mechanics approach are often greater than the stress magnitudes calculated by the classical approach. Also, the effect of crack inclination angle and pre-existing crack length on the magnitudes of σH is studied. In addition, the distribution of fluid pressure along the cracks and its influence on the stress intensity factor in the crack tip are analyzed, and consequently, the estimation of in situ stress is investigated.
One of the most common geological hazards in mining and civil projects is the occurrence of insta... more One of the most common geological hazards in mining and civil projects is the occurrence of instability in the rock slopes. Rock slope behavior is mainly influenced by the presence of discontinuities in the rock masses. Therefore, the determination of shear strength parameters for these weak surfaces is of particular importance. There are various shear strength criteria for estimating the shear strength of discontinuities, which among them the Barton–Bandis criterion (B‒B criterion) and Mohr–Coulomb criterion (M‒C criterion) are the most widely used. Accurate estimation of shear strength properties does not only depend on the correct procedure of tests, but it requires an accurate and detailed explanation of test results. The uncertainty in the measured shear strength leads to many problems in the analyzing and designing of rock slopes. Therefore, to reduce the uncertainty and increase the accuracy of rock slopes analyzing, it is better to use probability methods. The probability distribution function can be assigned for each input parameter of the failure criterion. In this research, the results of the direct shear tests related to Azad pumped storage power plant project have been considered to estimate the shear strength properties of rock discontinuities. The results are divided into three groups based on the magnitude of the joint roughness coefficient (JRC). Shear strength for each group is estimated depending on the two most well-known criteria i.e., the B‒B criterion and the M‒C criterion. Further, the probability distribution functions (PDF) for each shear strength parameter are determined by @RISK software. Besides, the results of the empirical B‒B criterion are compared with the results of the direct shear tests for the three groups of rock joints. The confidence intervals associated with both criteria are estimated and compared together. The results showed that the overlapping of the confidence interval of the M‒C criterion with the confidence interval of B‒B criterion increases with increasing JRC of rock joint. The results show the B‒B criterion covers data of the direct shear test almost at low normal stress levels for different JRC groups too.
Abstract It is common for the fractured zone around dynamic faults to contain tensile cracks. The... more Abstract It is common for the fractured zone around dynamic faults to contain tensile cracks. The effect of Poisson's ratio (ν) on the creation of these cracks was investigated in this study as a function of the dynamic minimum strain energy density criterion (MSED-Criterion). In addition, the effect of rupture speed (c), friction coefficient (f), fault inclination angle (β) and confining stress (Ko) were taken into account. The MSED-Criterion permits the study of the creation of tensile cracks in brittle and ductile shear zones. It was found that by increasing Poisson's ratio, the rock behavior transfers gradually from brittle to ductile and as a consequence, the branching angle and fracture toughness increase. Whenever the rock mass tends towards ductile behavior, the possibility of creating tensile branches decreases. Ductile shear zones can sustain stresses greater than brittle zones before tensile branches are formed around dynamic faults. The branching angle of tensile cracks is directly proportional to (ν, c, β, f and Ko) and it varies between approximately 77° and 115°. These cracks are formed in the extensional side of a dynamic fault and they tend to grow towards the maximum far-field stress. The results of this study can be used in the field of earth science and earthquakes to identify the formation of tensile branches around dynamic shear ruptures and they were explained depending on experimental results and field observations of other studies.
International Journal of Rock Mechanics and Mining Sciences
Abstract Conventional or single stage triaxial compression experiments for obtaining failure enve... more Abstract Conventional or single stage triaxial compression experiments for obtaining failure envelope of rocks require several specimens to be tested under different confining pressures. As a replacement, multistage triaxial tests using one specimen have been employed in experimental rock mechanics for situations where preparing several specimens is difficult or expensive. The results obtained by the multistage triaxial test may deviate from those obtained by the single stage. However it is believed that using multistage triaxial test can decrease the cost and time and the obtained results are still reliable due to less variability in the rock properties. Several methods have been proposed for conducting multistage triaxial test including ISRM suggested method and a modified version of the ISRM method proposed by Crawford and Wylie. The results of this study demonstrate that both multistage methods give reasonable results. However, the modified method provides closer results to the single stage, because the specimen is subjected to less damage. As the number of the loading stages rises, both ISRM and the modified version provide lower strength parameters comparing to the single stage.
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Papers by Mahmoud Behnia