Rock Mechanics
Vahab Sarfarazi; Hadi Haeri; Mohammad Fatehi Marji; Gholamreza Saeedi; Amir Namdarmanesh
Abstract
In this paper, the effect of variations in the number and area of the rock bridges on the non-persistent discontinuities is investigated. In this regard, blocks containing rock bridges and joints with dimensions of 15 cm * 15 cm * 15 cm are prepared from plaster. The available rock bridges that have ...
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In this paper, the effect of variations in the number and area of the rock bridges on the non-persistent discontinuities is investigated. In this regard, blocks containing rock bridges and joints with dimensions of 15 cm * 15 cm * 15 cm are prepared from plaster. The available rock bridges that have occupied 0.2, 0.4, and 0.6 of the shear surface show latitudinal extension along the shear surface. There are variations in the number and extension of the rock bridges in the fixed area. For each of the samples, tests are performed on three blocks of the same material, by putting it under various direct normal stresses. Normal stresses were 3.33, 5.55, 7.77 kg/cm2. Also the obtained shear strength by laboratory tests was compared with the outputs of Jenning's criterion and Guo and Qi's criterion to determine the accuracy of these criteria for predicting the shear strength of non-persistent joints. The results show that the tensile crack started in the rock bridge under normal stress of 3.33 kg/cm2. Mixed-mode tensile shear cracks were propagated in the rock bridge under a normal stress of 5.55 kg/cm2, while a pure shear crack developed in the rock bridge under a normal stress of 7.77 kg/cm2. With the increase of normal stress, the number of microfractures increased. The variance in the number of rock bridges in the fixed area of the rock bridge does not affect the friction angle along the shear surface. Furthermore, the cohesion along the shear surface shows a small decrease with the increasing number of rock bridges. Also by the increase in the area of rock bridges, the friction angle along the shear surface remains constant, while at the same time, there is an almost linear increase in cohesion. Guo and Qi's criterion predicts the shear strength of the non-persistent joint exactly close to the shear strength of the physical samples.
Mohammadhossein Dehghani Firoozabadi; Mohammad Fatehi Marji; Abolfazl Abdollahipour; Alireza Yarahamdi Bafghi; Yousef Mirzaeian
Abstract
The presence of pores and cracks in porous and fractured rocks is mostly accompanied by fluid flow. Poroelasticity can be used for the accurate modeling of many rock structures in the petroleum industry. The approach of the stress to the value of the fracture stress and the effect of pore pressure on ...
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The presence of pores and cracks in porous and fractured rocks is mostly accompanied by fluid flow. Poroelasticity can be used for the accurate modeling of many rock structures in the petroleum industry. The approach of the stress to the value of the fracture stress and the effect of pore pressure on the deformation of rock are among the effects of fluid on the mechanical behavior of the medium. Due to the deformation-diffusion property of porous media, governing equations, strain-displacement, and stress-strain relationships can be changed to each other. In this study, constitutive equations and relationships necessary to investigate the behavior and reaction of rock in a porous environment are stated. Independent and time-dependent differential equations for an impulse and point fluid source are used to obtain the fundamental solutions. Influence functions are obtained by using the shape functions in the formulation of the fundamental solutions and integrating them. To check the validity and correctness of provided formulation, several examples are mentioned. In the first two examples, numerical application and analytical solution are used at different times and in undrained and drained conditions. In times 0 (undrained response of medium) and 4500 seconds (drained response of medium), there is good coordination and agreement between the numerical and analytical results. In the third example, using the numerical application, a crack propagation path in the wellbore wall is obtained, which is naturally in the direction of maximum horizontal stress.
Enayatallah Emami Meybodi; Syed Khaliq Hussain; Mohammad Fatehi Marji
Abstract
In this research work, X-ray diffraction (XRD) tests and petrographic studies are performed to analyze the mineral composition and lamination in the shale rock specimens. Afterward, point load (PL) and uniaxial compressive strength (UCS) tests are carried out on the anisotropic laminated shale rock. ...
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In this research work, X-ray diffraction (XRD) tests and petrographic studies are performed to analyze the mineral composition and lamination in the shale rock specimens. Afterward, point load (PL) and uniaxial compressive strength (UCS) tests are carried out on the anisotropic laminated shale rock. Based on the macro-mechanical properties of these tests, the discrete element method implemented in a two-dimensional particle flow code (PFC2D) is adjusted to numerically simulate the shale rock specimens. The aim of this work is to validate the numerical models by failure process, stress-strain curves, and peak failure strengths of the shale samples. Therefore, point load test is used for assessing the pattern failure mechanism, and uniaxial compressive strength test is performed for obtaining the stress-strain curves and peak strength failure points in the laboratory shale rock samples. Validation of peak strengths criteria provides the best results; the determination coefficient values for lab and numerical modeling with (R2 = 0.99). Several numerical models are prepared for estimating the mechanical behavior of shale rocks in PFC2D. The smooth joint model (SJM) is used for preparing the consistent and appropriate constitutive models for simulating the mechanical behavior of laminated shale. It is concluded that SJM provides more reasonable results for laminated shale rock that can be used for several petroleum engineering projects, especially in the central geological zone of Iran.
Vahab Sarfarazi; Hadi Haeri; Fereshteh Bagheri; Erfan Zarrin ghalam; Mohammad Fatehi Marji
Abstract
The tensile strengths of geomaterials such as rocks, ceramics, concretes, gypsum, and mortars are obtained based on the direct and indirect tensile strength tests. In this research work, the Brazilian tensile strength tests are used to study the effects of length and inclination angle of T-shaped non-persistent ...
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The tensile strengths of geomaterials such as rocks, ceramics, concretes, gypsum, and mortars are obtained based on the direct and indirect tensile strength tests. In this research work, the Brazilian tensile strength tests are used to study the effects of length and inclination angle of T-shaped non-persistent joints on the mechanical and tensile behaviors of the geomaterial specimens prepared from concrete. These specimens have a thickness of 40 mm and a diameter of 100 mm, and are prepared in the laboratory. Two T-shaped non-persistent joints are made within each Brazilian disc specimen. The Brazilian disc specimens with T-shaped non-persistent joints are tested experimentally in the laboratory under axial compression. Then these tests are simulated in the two-dimensional particle flow code (PFC2D) considering various notch lengths of 6, 4, 3, 2, and 1 cm. However, different notch inclination angles of 0, 30, 60, 90, 120, and 150 degrees are also considered. In this research work, 12 specimens with different configurations are provided for the experimental tests, and 18 PFC2D models are made for the numerical studies of these tests. The loading rate is 0.016 mm/s. The results obtained from these experiments and their simulated models are compared, and it is concluded that the mechanical behavior and failure process of these geomaterial specimens are mainly governed by the inclination angles and lengths of the T-shape non-persistent joints presented in the samples. The fracture mechanism and failure behavior of the specimens are governed by the discontinuities, and the number of induced cracks when the joint inclination angles and joint lengths are increased. For larger joints when the inclination angle of the T-shaped non-persistent joint is around 60 degrees, the tensile strength is minimum but as it is closed to 90 degrees, the compressive strengths are maximum. However, an increase in the notch length increase the overall tensile strength of the specimens. The strength of samples decreases by increasing the joint length. The strain at the failure point decreases by increasing the joint length. It is also observed that the strength and failure process of the two sets of specimens and the corresponding numerical simulations are consistence.
Jinwei Fu; Mohammad Reza Safaei; Hadi Haeri; Vahab Sarfarazi; Mohammad Fatehi Marji; Leige Xu; Ali Arefnia
Abstract
In this work, the mechanical behavior of strata deformation due to drilling and surface loading is investigated using a 3D physical model. For this purpose, a scaled-down physical model is first designed. Then the tunnel drilling and support system are built. The subsidence experiments performed due ...
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In this work, the mechanical behavior of strata deformation due to drilling and surface loading is investigated using a 3D physical model. For this purpose, a scaled-down physical model is first designed. Then the tunnel drilling and support system are built. The subsidence experiments performed due to tunnel excavation and loading in a very dense and loose soil are performed. Soil is clayey sand (SC), and the percentages of its components are as sand (S = 1. 41%), gravel (G = 25%), and clay (C = 9.33%). Unstable tunnel support experiments are also carried out using physical simulation. Finally, deformations of soil surface and subsidence of strata are observed and recorded. In the tunnel with segmental support, 18.75% more load is applied than in the unsupported tunnel, and the total subsidence of the strata is reduced by 36.2%. The area of the deformed inner layers is decreased by 74.2%, and the length of the affected area in the largest layer is decreased by 48%. The depth of the cavity created at the surface is 46.66% less.
Mohammadhosein Dehghani Firoozabadi; Mohammad Fatehi Marji; Abolfazl Abdollahipour; Alireza Yarahamdi Bafghi; Yousef Mirzaeian
Abstract
In this work, an effective methodology is introduced for simulation of the crack propagation in linear poroelastic media. The presence of pores and saturated cracks that can be accompanied by fluid flow makes the use of poroelastic media inevitable. In this work, involvement of the time parameter in ...
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In this work, an effective methodology is introduced for simulation of the crack propagation in linear poroelastic media. The presence of pores and saturated cracks that can be accompanied by fluid flow makes the use of poroelastic media inevitable. In this work, involvement of the time parameter in crack propagation is of particular importance. The order of doing the work is such that first, derives the fundamental solutions of a poroelastic higher order displacement discontinuity method (PHODDM). Then will be provided a numerical formulation and implementation for PHODDM in a code named linear element poroelastic DDM (LEP-DDM). Analytical solutions use different times to check the correctness and validity of the proposed solution and the newly developed code. The numerical results show a good agreement and coordination with the analytical results in time zero and 5000 seconds . The code is able to pursue crack-propagation in time and space. This topic is introduced and shown in an example.
M. Davood Yavari; H. Haeri; V. Sarfarazi; M. Fatehi Marji; H. A. Lazemi
Abstract
The propagation mechanism of cracks emanating from two holes within the concrete specimens is studied by considering the effects of different lateral compressive stresses. The experimental part of this research work is carried out on some specially prepared pre-cracked specimens with two neighbouring ...
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The propagation mechanism of cracks emanating from two holes within the concrete specimens is studied by considering the effects of different lateral compressive stresses. The experimental part of this research work is carried out on some specially prepared pre-cracked specimens with two neighbouring holes under only a uniaxial compression in the laboratory. The numerical modeling part is performed under both the uniaxial compresion and the lateral confinment by the 2D particle flow code (PFC2D). It is shown that the lateral confinement may change the path of crack propagation in a specimen compared to that of the uniaxially-loaded one. Various senarios of the mixed mode radial crack propagation around the holes are obtained, and both the wing (induced tensile) cracks and secondary (shear) cracks are produced and propagated in various paths due to a change in the confining pressure. The fracturing pattern changes from a single tensile crack to that of the several shear bands by increasing the confining pressure. Also the number of shear cracks is increased by increasing the lateral confinement.On the other hand, as the confining pressure increases, the wing cracks start their growth from the walls and reach the center of the cracks under high confinements.
R. Alizadeh; M. Fatehi Marji; A. Abdollahipour; M. Pourghasemi Sagand
Abstract
In this work, an effective methodology is introduced for modeling the fatigue crack propagation in linear elastic brittle media. The displacement discontinuity method is used to accomplish the analysis, and the boundaries are discretized with quadratic elements in order to predict the stress intensity ...
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In this work, an effective methodology is introduced for modeling the fatigue crack propagation in linear elastic brittle media. The displacement discontinuity method is used to accomplish the analysis, and the boundaries are discretized with quadratic elements in order to predict the stress intensity factors near the crack tips. This procedure is implemented through 2D linear elastic fracture mechanics. The normal and shear displacement discontinuity around the crack tip is applied to compute the mixed-mode stress intensity factors. The crack growth is incremental, and for each increment of extension, there is no need to use a re-meshing procedure. This method has benefits over the finite element method due to its simplicity in meshing. The crack growth direction is assessed using the maximum principal stress theory. In these analyses, a repetition method is used in order to estimate the correct path of crack propagation. Therefore, the different lengths of incremental growth do not affect the crack growth path analysis. The results are exhibited for several examples with different geometries to demonstrate the efficiency of the approach for analyzing the fatigue crack growth. The accuracy represents that this formulation is ideal for describing the fatigue crack growth problems under the mixed-mode conditions.
M. Davood Yavari; H. Haeri; V. Sarfarazi; M. Fatehi Marji; H. A. Lazemi
Abstract
Investigating the crack propagation mechanism is of paramount importance in analyzing the failure process of most materials. This process may be exposed during each kind of loading on the materials. In this work, the cracking mechanism in rock-like materials is studied using the numerical methods and ...
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Investigating the crack propagation mechanism is of paramount importance in analyzing the failure process of most materials. This process may be exposed during each kind of loading on the materials. In this work, the cracking mechanism in rock-like materials is studied using the numerical methods and compared with the experimental test results. However, the mechanism of crack growth in brittle materials such as rocks is influenced by different parameters. This research work focuses on the effect of the initial crack angles on the crack growth paths of these materials. Some cubic samples containing pre-existing cracks are tested in compression by considering different flaw orientations. The specimens are made of cement, water, and sand. Moreover, the mentioned process is numerically simulated using three different methods: the finite difference method for discontinuous bodies or discrete element method, the displacement discontinuity method, and the versatile finite element method. The micro-parameters for simulation are gained by the trial-and-error procedure for the discrete element method. Eventually, the crack growth paths observed in the experiments are compared with the numerically simulated models. The results obtained show that these central cracks propagate in two ways, which are dependent on their initial angle. By increasing the initial crack angle to greater than 30° (α > 30°), the wing crack path moves further away from the initial crack, and by decreasing α to smaller than 30° (α < 30°), only the shear cracks are initiated. Therefore, the validity and accuracy of the results are manifested by comparing all the corresponding results obtained by different methods. Based on these results, it can generally be concluded that the strength of the cubic (rock material) specimens increases with increase in the crack angles with respect to the applied loading direction.
V. Sarfarazi; H. Haeri; M. Fatehi Marji
Abstract
The tensile strength of the anisotropic rock-like material specimens is meastred directly in the laboratory using a new device converting the compressive loading to that of the tensile before the rock breakage. The specially prepared concrete slabs of dimensions 19 cm * 15 cm * 15 cm with a central hole ...
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The tensile strength of the anisotropic rock-like material specimens is meastred directly in the laboratory using a new device converting the compressive loading to that of the tensile before the rock breakage. The specially prepared concrete slabs of dimensions 19 cm * 15 cm * 15 cm with a central hole of 7.5 cm in diameter are tested experimentaly. The specimens are located in the compressive-to-tensile load converting device, and tested under a compressive loading rate of 0.02 MPa/s by the universal testing machine. The cubic slab samples are made in three different configurations to have the directions of 0°, 45°, and -45° with respect to the applied loading direction. In order to compare the direct tensile strength of the concrete samples with that of the indirect measuring tests, some Brazilian tests are also carried out on the concrete disc specimens prepared in the laboratory. By comparing the direct and indirect testing results of the concrete tensile strength, it can be concluded that the direct tensile strength values are somewhat lower than those of the indirect ones. The tensile strength values for the three different configurations of the concrete specimens are nearly the same.
Rock Mechanics
E. Bakhshi; V. Rasouli; A. Ghorbani; M. Fatehi Marji
Abstract
In this work, we used a grain-based numerical model based on the concept of lattice. The modelling was done to simulate the lab experiments carried out on the mortar samples. Also the analytical solutions corresponding to the viscosity-dominated regime were used to estimate the fracture length and width, ...
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In this work, we used a grain-based numerical model based on the concept of lattice. The modelling was done to simulate the lab experiments carried out on the mortar samples. Also the analytical solutions corresponding to the viscosity-dominated regime were used to estimate the fracture length and width, and the results obtained were compared with the numerical simulations. As the analytical solutions are proposed for a penny-shaped fracture with no presence of any obstacle such as natural interfaces, in this work, we presented the results of lattice simulations for hydraulic fracturing in the cement sample, similar to the lab, but with no natural fractures, and compared the results obtained with analytical solutions. The results indicated that in the case of a continuous medium, the analytical solutions may present a reasonable estimation of the fracture geometry. Also the viscosity-dominated leak-off model showed a better match between the analytical solutions and the numerical simulation results, confirmed by observing fluid loss into the sample in the lab post-experiment. In the case of assuming leak-off, the results indicated that the fracture width and length would reduce. However, it should be noted that in real cases, rock formations exhibit fractures and inhomogeneity at different scales so that the applications of the analytical solutions are limited.
A. Abdollahipour; M. Fatehi Marji; H. Soltanian; E. A. Kazemzadeh
Abstract
The permeability and coupled behavior of pore pressure and deformations play an important role in hydraulic fracturing (HF) modeling. In this work, a poroelastic displacement discontinuity method is used to study the permeability effect on the HF development in various formation permeabilities. The numerical ...
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The permeability and coupled behavior of pore pressure and deformations play an important role in hydraulic fracturing (HF) modeling. In this work, a poroelastic displacement discontinuity method is used to study the permeability effect on the HF development in various formation permeabilities. The numerical method is verified by the existing analytical and experimental data. Then the propagation of a hydraulic fracture in a formation with a range of permeabilities is studied. The time required for propagation of an HF to 10 times its initial length is used to compare the propagation velocity in the formations with different permeabilities. The results obtained show that the HF propagation can be significantly delayed by a permeability less than almost 10-9 D. Also the effect of HF spacing on the propagation path is studied. It was shown that the stress shadowing effect of HFs remained for a longer spacing than in the elastic model due to the required time for fluid leak-off in the formation. Also the propagation angles are higher in the poroelastic model predictions than the elastic model. Therefore, it is proposed to use the poroelastic model when studying multi-HF propagation in order to avoid errors caused by neglecting the pore fluid effects on the HF propagation paths.
S. E. Mirsalari; M. Fatehi Marji; J. Gholamnejad; M. Najafi
Abstract
Analysis of the stresses, displacements, and horizontal strains of the ground subsidence due to underground excavation in rocks can be accomplished by means of a hybridized higher order indirect boundary element/finite difference (BE/FD) formulation. A semi-infinite displacement discontinuity field is ...
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Analysis of the stresses, displacements, and horizontal strains of the ground subsidence due to underground excavation in rocks can be accomplished by means of a hybridized higher order indirect boundary element/finite difference (BE/FD) formulation. A semi-infinite displacement discontinuity field is discretized (numerically) using the cubic displacement discontinuity elements (i.e. each higher order element is divided into four sub-elements bearing a cubic variation in the displacement discontinuities). Then the classical finite difference formulation (i.e. the backward, central, and forward finite difference formulations) is hybridized using the boundary element formulation, enabling us to obtain the nodal tangential stresses and horizontal strains along the elements. Several example problems are solved numerically, and the results obtained are then compared with their corresponding results available in the literature. These comparisons show the effectiveness and validness of the proposed method. A classical practical problem is also used to verify the applicability of the hybridized method.
M. Mohebbi; A.R. Yarahmadi Bafghi; M. Fatehi Marji; J. Gholamnejad
Abstract
Presence of joints and fractures in rocks strongly influences the behavior of the rock mass by dividing the media into smaller units. These structures intensify the potential instability besides the development of sliding and rotational movements. The assumption of discontinuum media changes the whole ...
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Presence of joints and fractures in rocks strongly influences the behavior of the rock mass by dividing the media into smaller units. These structures intensify the potential instability besides the development of sliding and rotational movements. The assumption of discontinuum media changes the whole analysis conditions in relation to the continuum analysis. Acquisition of geometrical and structural discontinuity data alongside their mechanical properties is of paramount importance in a rock mass analysis. Orientation, spacing, expansion, and other geometrical characteristics of the rock mass and their relative geometrical position to the studied projects influence the pattern and potential of failure. Therefore, inevitably, the first step involved in the analysis of rock mass is geometric data collection of the discontinuities as a crucial step before analysis. In this study, the traditional data collection methods in structural discontinuities with their disadvantages are reviewed. Then the discontinuity data collection based on digital image analysis is developed and applied in a case study to several walls of the Choghart iron ore mine. The results obtained show that this method has a very good accuracy in assessing the fine structures, and also it collects data in a much shorter time. This study, therefore, suggests that the proposed method can be used as a practical approach.
A. Abdollahipour; M. Fatehi Marji; A. R. Yarahmadi Bafghi; J. Gholamnejad
Abstract
Hydraulic fracturing (HF), as a stimulation technique in petroleum engineering, has made possible the oil production from reservoirs with very low permeability. The combination of horizontal drilling and multiple HF with various perforation angles has been widely used to stimulate oil reservoirs for ...
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Hydraulic fracturing (HF), as a stimulation technique in petroleum engineering, has made possible the oil production from reservoirs with very low permeability. The combination of horizontal drilling and multiple HF with various perforation angles has been widely used to stimulate oil reservoirs for economical productions. Despite the wide use of HF, there are still ambiguous aspects that require more investigation. Therefore, optimizing the geometry of the initial fractures using numerical methods is of high importance in a successful HF operation. Different geometrical parameters of the initial HF cracks including patterns, spacings, crack lengths, and perforation phase angles were modeled using the higher order displacement discontinuity method (HODDM) in horizontal and vertical oil wells. Several well-known issues in HF such as crack interference and crack arrest were observed in certain patterns of the HF cracks. Also the best possible arrangements of the HF cracks were determined for a better production. The results obtained were verified by the in-situ measurements existing in the literature. In addition, the best perforation phase angle in vertical wells was investigated and determined.
H. Haeri; A. R Khaloo; K. Shahriar; M. Fatehi Marji; P. Moaref vand
Abstract
In this work, the mechanism for fracture of brittle substances such as rocks under a uniform normal tension is considered. The oriented straight micro-cracks are mostly created in all the polycrystalline materials resulting from the stress concentrations. The present work focuses on the interactions ...
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In this work, the mechanism for fracture of brittle substances such as rocks under a uniform normal tension is considered. The oriented straight micro-cracks are mostly created in all the polycrystalline materials resulting from the stress concentrations. The present work focuses on the interactions of the pre-existing micro-cracks, which can grow and propagate within a rock-like specimen. The micro-crack initiation and propagation in rock-like specimens is investigated using the Fortran Code TDDCRACK2D, which is a 2D displacement discontinuity method (DDM) for crack analysis, a boundary element computer code based on the linear elastic fracture mechanics (LEFM) theory. In the present work, a higher order DDM is used to implement special crack tip elements for estimation of the stress intensity factors (SIFs) and crack initiation angles for the wing-crack problems initiated at different angles from the original micro-crack tips in an infinite specimen under a uniform tension.
