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In this paper, the embedded discontinuity approach is applied in finite element modeling of rock in compression and tension. For this end, a rate-dependent constitutive model based on (strong) embedded displacement discontinuity model is developed to describe the mode I, mode II and mixed mode fracture of rock. The constitutive model describes the bulk material as linear elastic until reaching the elastic limit. Beyond the elastic limit, the rate-dependent exponential softening law governs the evolution of the displacement jump. Rock heterogeneity is incorporated in the present approach by random description of the mineral texture of rock. Moreover, initial microcrack population always present in natural rocks is accounted for as randomly-oriented embedded discontinuities. In the numerical examples, the model properties are extensively studied in uniaxial compression. The effect of loading rate and confining pressure is also tested in the 2D (plane strain) numerical simulations. These simulations demonstrate that the model captures the salient features of rock in confined compression and uniaxial tension. The developed method has the computational efficiency of continuum plasticity models. However, it also has the advantage, over these models, of accounting for the orientation of introduced microcracks. This feature is crucial with respect to the fracture behavior of rock in compression as shown in this paper. [ABSTRACT FROM AUTHOR]

Overhanging rock instability is a serious geological problem in mountainous regions. The initiation and propagation of a controlling crack are the fundamental causes of overhanging rock failure. In the view of fracture mechanics, the instability of toppling overhanging rock can be equivalent to the effect of pure shear and pure bending moment. This paper analyzes the evolution of displacement-load curves and failure modes of overhanging rock models at different crack lengths, crack angles, and load distances based on fracture tests of the toppling overhanging rock model. Maximum circumferential stress theory is used as the fracture criterion of mixed mode I-II fractures to calculate the stress intensity factor (SIF) of the crack tip and the theoretical failure load of the overhanging rock model. The fracture mode mechanism is analyzed by the calculated SIF. We use the extended finite element method to simulate the crack propagation path and analyze the change process from equivalent stresses of the numerical model using propagation steps. Comparisons between the physical tests, theoretical calculations, and numerical simulations verify the rationality of the experimental results. [ABSTRACT FROM AUTHOR]

Grouting plays a crucial role in dam safety. Due to the concealment of grouting activities, complexity of fracture distribution in rock masses and rheological properties of cement grout, it is difficult to analyze the effects of grouting. In this paper, a computational fluid dynamics (CFD) simulation approach of dam foundation grouting based on a 3D fracture network model is proposed. In this approach, the 3D fracture network model, which is based on an improved bootstrap sampling method and established by VisualGeo software, can provide a reliable and accurate geometric model for CFD simulation of dam foundation grouting. Based on the model, a CFD simulation is performed, in which the Papanastasiou regularized model is used to express the grout rheological properties, and the volume of fluid technique is utilized to capture the grout fronts. Two sets of tests are performed to verify the effectiveness of the Papanastasiou regularized model. When applying the CFD simulation approach for dam foundation grouting, three technical issues can be solved: (1) collapsing potential of the fracture samples, (2) inconsistencies in the geometric model in actual fractures under complex geological conditions, and (3) inappropriate method of characterizing the rheological properties of cement grout. The applicability of the proposed approach is demonstrated by an illustrative case study—a hydropower station dam foundation in southwestern China. [ABSTRACT FROM AUTHOR]

Fracture network modelling plays an important role in many application areas in which the behaviour of a rock mass is of interest. These areas include mining, civil, petroleum, water and environmental engineering and geothermal systems modelling. The aim is to model the fractured rock to assess fluid flow or the stability of rock blocks. One important step in fracture network modelling is to estimate the number of fractures and the properties of individual fractures such as their size and orientation. Due to the lack of data and the complexity of the problem, there are significant uncertainties associated with fracture network modelling in practice. Our primary interest is the modelling of fracture networks in geothermal systems and, in this paper, we propose a general stochastic approach to fracture network modelling for this application. We focus on using the seismic point cloud detected during the fracture stimulation of a hot dry rock reservoir to create an enhanced geothermal system; these seismic points are the conditioning data in the modelling process. The seismic points can be used to estimate the geographical extent of the reservoir, the amount of fracturing and the detailed geometries of fractures within the reservoir. The objective is to determine a fracture model from the conditioning data by minimizing the sum of the distances of the points from the fitted fracture model. Fractures are represented as line segments connecting two points in two-dimensional applications or as ellipses in three-dimensional (3D) cases. The novelty of our model is twofold: (1) it comprises a comprehensive fracture modification scheme based on simulated annealing and (2) it introduces new spatial approaches, a goodness-of-fit measure for the fitted fracture model, a measure for fracture similarity and a clustering technique for proposing a locally optimal solution for fracture parameters. We use a simulated dataset to demonstrate the application of the proposed approach followed by a real 3D case study of the Habanero reservoir in the Cooper Basin, Australia. [ABSTRACT FROM AUTHOR]

Different failure modes during fracture shearing have been introduced including dilation, sliding, asperity cut-off and degradation. Several laboratory studies have reported the complexity of these failure modes during shear tests performed under either constant normal load (CNL) or constant normal stiffness (CNS) conditions. This paper is concerned with the mechanical behaviour of synthetic fractures during direct shear tests using a modified shear cell and related numerical simulation studies. The modifications made to an existing true triaxial stress cell (TTSC) in order to use it for performing shear tests under CNL conditions are presented. The large loading capacity and the use of accurate hydraulic pumps capable of applying a constant shear velocity are the main elements of this cell. Synthetic mortar specimens with different fracture surface geometries are tested to study the failure modes, including fracture sliding, asperity degradation, and to understand failure during shearing. A bonded particle model of the direct shear test with the PFC2D particle flow code is used to mimic the tests performed. The results of a number of tests are presented and compared with PFC2D simulations. The satisfactory results obtained both qualitatively and quantitatively are discussed. [ABSTRACT FROM AUTHOR]

Different failure modes during fracture shearing have been introduced including normal dilation or sliding, asperity cut-off and degradation. Attempts have been made to study these mechanisms using analytical, experimental and numerical methods. However, the majority of the existing models simplify the problem, which leads to unrealistic results. With this in mind, the aim of this paper is to simulate the mechanical behaviour of synthetic and rock fracture profiles during direct shear tests by using the two-dimensional particle flow computer code PFC2D. Correlations between the simulated peak shear strength and the fracture roughness parameter D recently proposed by Rasouli and Harrison () are developed. Shear test simulations are carried out with PFC2D and the effects of the geometrical features as well as the model micro-properties on the fracture shear behaviour are studied. The shear strength and asperity degradation processes of synthetic profiles including triangular, sinusoidal and randomly generated profiles are analysed. Different failure modes including asperity sliding, cut-off, and asperity degradation are explicitly observed and compared with the available models. The D parameter is applied to the analysis of synthetic and rock fracture profiles. Accordingly, correlations are developed between D and the peak shear strength obtained from simulations and by using analytical solutions. The results are shown to be in good agreement with the basic understanding of rock fracture shear behaviour and asperity contact degradation. [ABSTRACT FROM AUTHOR]

Numerical simulation and field monitoring are conducted in this study to investigate rock deformation and failure behaviors during excavation of underground cavern group under high in situ stresses in Jinping I Hydropower Station. According to the numerical simulation, large deformation and damage in the surrounding rock mass result in anchorage cable overlimit. The traditional elastoplastic model only considers plastic yielding in rock mass and does not consider the evolution of damage in rock mass, i.e., initiation, propagation and coalescence of cracks. It is found from the numerical results that the damage behaviors of rock masses subjected to high in situ stresses are characterized by the formation of multi-fractured zones, i.e., the zonal disintegration. Theoretical basis, general rules and reinforcement method for zonal disintegration of the surrounding rock masses under high in situ stresses are proposed. The proposed methods are applied to strengthen support measures for construction of Jinping I Hydropower Station. [ABSTRACT FROM AUTHOR]

Triaxial compression experiments under confining pressures of 16 and 35 MPa were first carried out for hollow-cylinder sandstone specimens using a rock mechanics testing system. Four hollow-cylinder sandstone specimens were compressed to various deformation positions before or after the peak strength. Then, the compressed hollow-cylinder sandstone specimens were analysed using a three-dimensional X-ray micro computed tomography (CT) scanning system. Based on the horizontal and vertical cross-sectional CT images, the internal damage behaviour of hollow-cylinder sandstone specimens was evaluated. It can be seen that the crack system of hollow-cylinder sandstone specimens with higher compressed deformation after the peak strength are more complicated than those with lower compressed deformation close to the peak strength. In the present study, the hollow-cylinder sandstone specimens with lower compressed deformation are only dominated by some internal wall fractures resulting mainly from shear cracks, whereas the hollow-cylinder sandstone specimens with higher compressed deformation are mainly dominated by two shear fractures, as well as some tensile cracks. For the same axial stress level, hollow-cylinder sandstone under a higher confining pressure has a more complicated crack system than that under a lower confining pressure. The experimental results demonstrated that the three-dimensional cracks in the hollow specimen under triaxial compression are first initiated from the internal wall due to shear slippage, and then propagate towards the top or bottom boundary of the specimen in shear fracture mode. To better explain the internal crack evolution mechanism of hollow-cylinder sandstone during the entire loading, a conceptual model of hollow-cylinder sandstone material under the action of confining pressure is proposed. At the same time, the effect of the borehole size on the internal damage behaviour of the compressed specimen after the peak strength is also discussed. The investigated conclusions are significant for predicting the instability occurring around deep well bores in petroleum engineering and for ensuring the safety of deep excavation damage zones in tunnel engineering. [ABSTRACT FROM AUTHOR]

Though obliquely incident plane wave across rock fractures has been extensively investigated by theoretical analysis, the quantitative identification of each wave emerged from fractures has not been achieved either in numerical simulation or laboratory experiment. On the other hand, there are no theoretical results describing the stress/velocity state of the rocks beside a fracture. The superposition of the multiple waves propagating in the media results in the variation of the stress/velocity state. To understand the superposition of the wave components in the adjacent rocks of a facture, based on the geometrical analysis of the wave paths, the lag times among passing waves at an arbitrary point are determined. The normalised critical distances from the fracture to the measuring locations where the corresponding harmonic waves depart from other waves for a certain duration are then derived. Discussion on the correction for an arbitrary incident wave is then carried out considering the changes of the duration of the reflected and transmitted waves. Under the guidance of the analysis, wave superposition is performed for theoretical results and separated waves are obtained from numerical model. They are demonstrated to be consistent with each other. The measurement and the data processing provide an approach for wave separation in a relatively unbounded media. In addition, based on the mechanical analysis on the wave front, an indirect wave separation method is proposed which provides a possibility for laboratory experiments of wave propagation with an arbitrary incident angle. [ABSTRACT FROM AUTHOR]

In the context of nuclear waste disposal in clay formations, laboratory and in situ simulation experiments were performed to study at reduced scale the excavation damaged zone (EDZ) around tunnels in the indurated Opalinus Clay at Mont Terri, Switzerland. In the laboratory, thick-walled hollow cylindrical specimens were subjected to a mechanical unloading mimicking a gallery excavation. In samples cored parallel to bedding, cracks sub-parallel to the bedding planes open and lead to a buckling failure in two regions that extend from the borehole in the direction normal to bedding. The behaviour is clearly anisotropic. On the other hand, in experiments performed on specimens cored perpendicular to bedding, there is no indication of failure around the hole and the response of the hollow cylinder sample is mainly isotropic. The in situ experiment at Mont Terri which consisted in the overcoring of a resin-injected borehole that follows the bedding strike of the Opalinus Clay showed a striking similarity between the induced damaged zone and the fracture pattern observed in the hollow cylinder tests on samples cored parallel to bedding and such a bedding controlled 'Excavation' Damaged Zone is as well consistent with the distinct fracture patterns observed at Mont Terri depending on the orientation of holes/galleries with respect to the bedding planes. Interestingly, the damaged zone observed in the hollow cylinder tests on samples cored parallel to bedding and in situ around URL galleries is found to develop in reverse directions in Boom Clay (Mol) and in Opalinus Clay (Mont Terri). This most probably results from different failure mechanisms, i.e. shear failure along conjugated planes in the plastic Boom Clay, but bedding plane splitting and buckling in the indurated Opalinus Clay. [ABSTRACT FROM AUTHOR]

Rock is a heterogeneous geological material. When rock is subjected to internal hydraulic pressure and external mechanical loading, the fluid flow properties will be altered by closing, opening, or other interaction of pre-existing weaknesses or by induced new fractures. Meanwhile, the pore pressure can influence the fracture behavior on both a local and global scale. A finite element model that can consider the coupled effects of seepage, damage and stress field in heterogeneous rock is described. First, two series of numerical tests in relatively homogeneous and heterogeneous rocks were performed to investigate the influence of pore pressure magnitude and gradient on initiation and propagation of tensile fractures. Second, to examine the initiation of hydraulic fractures and their subsequent propagation, a series of numerical simulations of the behavior of two injection holes inside a saturated rock mass are carried out. The rock is subjected to different initial in situ stress ratios and to an internal injection (pore) pressure at the two injection holes. Numerically, simulated results indicate that tensile fracture is strongly influenced by both pore pressure magnitude and pore pressure gradient. In addition, the heterogeneity of rock, the initial in situ stress ratio ( K), the distance between two injection holes, and the difference of the pore pressure in the two injection holes all play important roles in the initiation and propagation of hydraulic fractures. At relatively close spacing and when the two principal stresses are of similar magnitude, the proximity of adjacent injection holes can cause fracturing to occur in a direction perpendicular to the maximum principal stress. [ABSTRACT FROM AUTHOR]

Fractured rock has often been conceptualized as a dual-continuum system for many practical applications. This study proposes a systematic approach to deal with multiphase flow in a dual-continuum system. Considering that fluid flow occurs in pore volumes (including fracture apertures), we first develop a so-called pore-space conservation equation for deformed fractured rock and then combine this equation with fluid mass balance to derive governing equations for multiphase flow associated with rock deformation. Constitutive relationships are also presented for describing stress dependence of hydraulic properties and effective mechanical parameters for bulk rock body (as a function of the corresponding parameters for fracture and matrix continua). Finally, we applied the developed approach to a CO geological sequestration problem to demonstrate the usefulness of the approach. [ABSTRACT FROM AUTHOR]

In the present study, fracture initiation and propagation from a pre-existing plane interface in a Brazilian disc is investigated using a finite-discrete element combined method. Different fracture patterns, depending on the frictional resistance of the pre-existing crack or interface, are observed from the numerical simulation. It is found that when there is no or very little frictional resistance on the surfaces of the pre-existing crack, the primary fractures (wing cracks), which are tensile in nature and are at roughly right angles to the pre-existing crack, start from the tips of the pre-existing crack. As the friction coefficient increases, the wing cracks' initiation locations deviate from the crack tips and move toward the disc center. Secondary fractures, which are also tensile in nature, initiate from the disc boundary and occur only when the length of the pre-existing crack is sufficiently long. The secondary fractures are roughly sub-parallel to the pre-existing crack. The failure load is found to be influenced by the friction coefficient of the pre-existing crack. A 38 % failure load increase can result when the friction coefficient changes from 0 to 1. A good understanding of the fracture initiation and propagation in the forms of primary and secondary fractures provides insight into explaining some fracture patterns observed underground. [ABSTRACT FROM AUTHOR]

The failure mechanism of hydraulic fractures in heterogeneous geological materials is an important topic in mining and petroleum engineering. A three-dimensional (3D) finite element model that considers the coupled effects of seepage, damage, and the stress field is introduced. This model is based on a previously developed two-dimensional (2D) version of the model (RFPA2D-Rock Failure Process Analysis). The RFPA3D-Parallel model is developed using a parallel finite element method with a message-passing interface library. The constitutive law of this model considers strength and stiffness degradation, stress-dependent permeability for the pre-peak stage, and deformation-dependent permeability for the post-peak stage. Using this model, 3D modelling of progressive failure and associated fluid flow in rock are conducted and used to investigate the hydro-mechanical response of rock samples at laboratory scale. The responses investigated are the axial stress-axial strain together with permeability evolution and fracture patterns at various stages of loading. Then, the hydraulic fracturing process inside a rock specimen is numerically simulated. Three coupled processes are considered: (1) mechanical deformation of the solid medium induced by the fluid pressure acting on the fracture surfaces and the rock skeleton, (2) fluid flow within the fracture, and (3) propagation of the fracture. The numerically simulated results show that the fractures from a vertical wellbore propagate in the maximum principal stress direction without branching, turning, and twisting in the case of a large difference in the magnitude of the far-field stresses. Otherwise, the fracture initiates in a non-preferred direction and plane then turns and twists during propagation to become aligned with the preferred direction and plane. This pattern of fracturing is common when the rock formation contains multiple layers with different material properties. In addition, local heterogeneity of the rock matrix and macro-scale stress fluctuations due to the variability of material properties can cause the branching, turning, and twisting of fractures. [ABSTRACT FROM AUTHOR]