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Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004

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Hydraulic Fracturing

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Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004

Paper Number: ARMA-04-502

Abstract

ABSTRACT: In order to evaluate the growth of fractures for cuttings re-injection, a solid transport model is included in a solidfluid coupled hydraulic fracturing simulator. The fracture geometry is a critical factor affecting the safety of the re-injection operation, and solid particle flow in the fractures is known to have a dominant effect on the fracture propagation. To improve the accuracy of the simulation, the finite element method (FEM) is introduced for modeling the particle motion in the fracture fluid. In the model, opening of the fracture, interaction between multiple particles, and change in viscosity by the solid concentration are taken into account. Numerical examples shown here reveal that the fracture geometry is highly dependent on the concentration of the solid due to the change of gravity and slurry viscosity. The injected solid concentration is one of the few controllable parameters, thus the results suggest the feasibility of geometry control. INTRODUCTION Hydraulic fracturing technique is widely used in the petroleum industry for stimulating wells. Another application of the technology is drill cuttings reinjection, in which huge fractures are created in formations around wellbores to contain the slurrified solid waste produced by the drillings [1]. The major concern of cuttings re-injection is a breakthrough of fracture into adjacent formations and surfaces. If a fracture propagates into usable aquifers, petroleum reservoirs, or the surface or seabed, it can cause the grave environmental pollution and operational risk. Although this operation requires careful design of the fracture growth, there are few controllable factors, and those that are controllable are also restricted by operation margins. A numerical study using a solid transport model in the fracture shows that the solid concentration of the injected cuttings slurry influences the fracture growth significantly through the leak-off character of the formation [2]. The authors have developed another numerical simulator of hydraulic fracturing, in which the true three-dimensional geometry and interaction of multiple fractures are considered [3]. The solid transport model is added to the fully coupled model of fluid flow in the fracture and opening of the fracture in an elastic medium. For the cuttings slurry problem, we need an accurate solution for the case of a high concentration of solid particles. In this paper, we demonstrate a solid transport model that considers the effect of the fracture wall and in the interaction of multiple particles. Furthermore, some numerical results for different concentrations of injected solids are shown to exhibit the effect of this parameter on the final geometry of the fracture. The slurry viscosity and vertical pressure gradient can be manipulated by varying the solid concentration in the slurry, so the fracture growth is controllable by this parameter. NUMERICAL MODELING A fully coupled model of a hydraulic fracturing simulator is developed for the design of well stimulation in complicated stress state and well and fracture geometries [3]. The coupled solution of the fluid pressure and fracture opening is computed using the displacement discontinuity (DD) methodfor solid, and the finite element method (FEM) for Newtonian or non-Newtonian fluid.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004

Paper Number: ARMA-04-483

Abstract

ABSTRACT: In laboratory tests, the onset of dilation occurs at stress levels far below the peak strength but yielding of the laboratory specimen is not synonymous with the onset of dilation, and is seldom measured or reported in traditional laboratory testing. In field tests, the on-set of dilation is often associated with stress-induced extension fracturing. The displacements associated with these stress-induced fractures, cannot be replicated using traditional constitutive modelling and associated or non-associated flow rules. In this paper a methodology is developed for modeling dilation using the Particle Flow Code ( PFC ) that captures many of the observations reported in conventional laboratory test results. The findings from this research show that clumped-particle geometry provides the best agreement with laboratory test results for both tensile and compressive loading paths. 1 INTRODUCTION Experience with underground excavations at depth indicates that one of the most significant phenomena observed in brittle rocks is extensile fracturing. This fracturing occurs as a result of tangential stress concentrations. Direct observation of brittle rock failure around underground openings reveals that this extensile fracturing exhibits significant dilation (Fig. 1). A detailed description of the spalling process observed around a circular test tunnel was given by Martin et al. [1] and Lajtai [3] showed that in laboratory samples the brittle failure process resulted in the opening of fractures. In materials such as metals and clays, yielding can occur without significant volume change. However, in brittle rocks on the boundary of underground openings overstressing results in the development of micro- and macro-cracks. In the mining industry, the process is often referred to as 'spalling' or 'dog-earing'. In the petroleum industry, the problem is often cast as 'well-bore breakouts'. One of the early descriptions in civil engineering was given by Terzaghi [2] and referred to as 'popping rock'. Modeling of this process has always been challenging and has received a lot of attention in the mining, nuclear waste and petroleum industries since the 1950's. With the advent of modern computers, both continuum mechanics and traditional fracture mechanics approaches have been used to model this fracturing process [3-6]. The use of continuum mechanics to (available in full paper) Fig. 1: Dilation associated with stress-induced fracturing observed in a 600-mm-diameter borehole. simulate a fracturing process that results in an open rough fracture, as described by Lajtai [3] and shown in Fig. 2, is extremely problematic as the displacement field across the fracture in a continuum must be continuous. But if the fracture is open, this requirement cannot be satisfied. In traditional fracture mechanics, the fracture has zero width, again suggesting that this approach is not applicable for representing a process that results in open fractures. In all these approaches specific flow rules are required to capture the displacement field. In continuum mechanics an associated or non-associated flow rule is assumed. For the fracture mechanics approach the control of the fracture growth is related to the fracture toughness ( KIC ) [4, 6-8]. In both approaches there are fundamental shortcomings.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004

Paper Number: ARMA-04-479

Abstract

ABSTRACT: This paper presents a three-dimensional, geometric-mechanical, hierarchical, stochastic model of natural rock fracture systems. In the model, fracture systems are generated through superposition of hierarchically related sets, created via stochastic methods that reflect inherent relationships between fracture system geometry and underlying geologic mechanisms. The model employs Poisson plane and line processes as well as random spatial rotation and translation to represent fracture orientations, intensity, and relations to major geologic structures. The model is implemented in the computer program GEOFRAC, which incorporates algorithms for representation of fracture systems in different geologic settings, including folds, faults, and central structures. Application of the model to the Permian reservoir in the Yates field in Texas includes geomechanical analysis of fracture evolution, development of case-specific algorithms for fracture intensity modeling based on rock properties, and numerical simulations of fracture sets related to regional depositional trends and reservoir anticlinal structure. 1. INTRODUCTION Natural rock fracture systems are three-dimensional (3D) networks of multiple interconnected fractures that evolve under time-and-space-variant geologic stresses. Since field sampling methods of fractures are typically one-dimensional (logs, cores) or two-dimensional (outcrop maps), there is usually great uncertainty about the 3D fracture system geometry. A 3D model [1], which continues a long tradition in 3D fracture system modeling at the Massachusetts Institute of Technology [2, 3, 4, 5], accounts for that uncertainty through geology-based mathematical and numerical algorithms. The geometric-mechanical model explores the inherent relations between the 3D geometry of fracture systems and the underlying geologic mechanisms. Poisson plane and line processes [6, 7] and random spatial rotation and translation represent orientations and intensity within a fracture set. The UNIX-based C++ code GEOFRAC implements the 3D stochastic model and incorporates routines for generation of fracture systems via superposition of hierarchically related fracture sets in different geologic settings. This paper presents the fundamentals of the 3D model, and its application to the fracture system in the petroleum reservoir of the Yates field in Texas. 2. FRACTURE SET MODELING A Poisson plane network; Subdivision of planes into fractured and intact areas through Poisson line tessellation and random marking of polygons; Random 3D translation and/or rotation of fractured polygons. In the 3D model, fractures are convex polygons that are randomly generated as members of fracture sets through three stochastic processes (Figure 1): A fracture set is generated in a modeling volume enclosed by representative surfaces, e.g. bedding planes, structural boundaries, datum planes, and the ground surface. The three stochastic processes reproduce fracture orientations and intensity as they vary within a fracture set, as follows. 2.1. Modeling of stress field orientation: primary stochastic process The primary stochastic process (Figure 1a): a homogeneous, anisotropic, Poisson plane network [2, 6], represents stress field orientation. The mean orientation of a fracture set is specified in polar coordinates (azimuth, T, and latitude, F) in a global frame of reference (OXYZ), the axes of which coincide with relevant global directions (Figure 2).

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-495

Abstract

ABSTRACT: Adequate determination of the propped fracture geometry is critical for Frac Pack hydraulic fracture designs and analyses. Unfortunately the fracture geometry is difficult to determine in complex reservoirs, primarily because of the difficulty to determine the post tip screenout (TSO) fracture geometry. Two-dimensional analysis or even more sophisticated computer simulations typically only model the fracture process up to the onset of TSO, and do not calculate the fracture geometry beyond the onset of TSO. This paper presents results of three-dimensional hydraulic fracturing simulator calculations of the fracture geometry beyond the onset of TSO, and as TSO followed by fracture re-growth occurs. Comparative analyses of the three-dimensional simulations indicate that fracture lengths can be substantially underestimated if the three-dimensional analysis is not considered. This leads to an incorrect and non-conservative estimate of the propped fracture geometry-both in length and in width. 1. INTRODUCTION During the past decade, hydraulic fracturing that creates the onset of fracture tip screenout (referred to as "TSO") has been recognized as an effective technology to enhance formation conductivity in high permeability reservoirs. Modeling the TSO mechanism is complex, and generally two-dimensional and even pseudo three-dimensional models do not represent these fracturing features adequately. These analyses calculate fracturing only up to the onset of TSO and then assume that the fracture length is fixed; i.e. no further fracture growth occurs. They assume that proppant packing occurs (the fracture width increases) without further fracture growth, until all proppant is injected and pumping stops. In many cases this is likely not an adequate assumption. For example, Bai et. al. (2003) using a three-dimensional fracturing simulator (Clifton, 1989) presented numerical results showing that fracture propagation can continue after the initiation of the first TSO. This understanding is very important, and allows improving the assessment of Frac Pack propped fracture efficiency. As background, it is noted that before the Frac Pack treatment is initiated, a fracture calibration test is usually conducted by injecting a quantity of proppant-free fracturing fluid. This is done primarily to estimate the formation leakoff coefficient. Based on the calibration fracture results (and using an estimate of other required properties), the initial pad (without proppant) volume and slurry schedule to be used are then generated, usually using a two-dimensional or a pseudo three-dimensional computer simulator. The time between the calibration fracture and the Frac Pack treatment is usually hours to a day, and no time is allowed between the clear fluid pad injection and the fluid-proppant slurry injection. Since the two-dimensional or pseudo three-dimensional modeling used in the Frac Pack design does not generally estimate beyond the onset of TSO, actual fracturing mechanics may not be adequately represented. This paper uses a fully three-dimensional simulator to calculate fracture growth beyond the onset of TSO and continuing as TSO occurs, and then as re-growth occurs which is often followed by another TSO and again fracture re-growth (Bai, et. al. 2003). The paper shows that the fracture geometry is often significantly underestimated without considering the complete fracture mechanics.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-471

Abstract

ABSTRACT: Poro-mechanical, thermal, and chemical processes can play a significant role when developing enhanced geothermal systems. These processes occur on various time scales and the significance of their interaction varies with the problem of interest. Of particular importance is the thermo-mechanical coupling during injection operations (time scale of months/years). In fact, the phenomena of the variation of injectivity with injection water temperature and reservoir seismicity can be attributed to thermal stresses. In this paper a three-dimensional integral equation formulation is presented for calculating thermally induced stresses associated with cooling of a fracture in a geothermal reservoir. The procedure is then implemented in a computer program and is used to treat the problem of injection into an infinite fracture. The thermally induced stresses are calculated using actual field data for an injection experiment. The resulting calculations are found to be consistent with those based on a semi-analytical solution as well as field observations. 1. INTRODUCTION Thermally-induced stresses significantly contribute to seismicity in petroleum and geothermal fields [1, 2]. The variation of injectivity with injection water temperature and reservoir seismicity in geothermal fields have been attributed to thermally-induced stresses. It has been has found that half the earthquakes in The Geysers field seem to be associated with cold water injection [2]. The mechanism by which seismicity occurs is well understood namely, shear slip on natural fractures resulting from a reduction in effective stress acting across the fracture. The magnitude of the thermal stresses associated with advective cooling has been estimated analytically [3] using an axisymmetric model of injection into a planar reservoir and a 1D heat flow in the rock mass. It has been shown that one- and two-dimensional heat flow models underestimate heat transfer to the fluid from the crack [4]. Thus, rock cooling and the associated thermal stresses should be studied using three-dimensional heat transfer and stress models. This requires coupling a 3D heat flow model to a 3D elasticity model. A reason for ignoring the three-dimensional nature of heat conduction in the reservoir is the difficulty in treating the infinite geothermal reservoir geometry by numerical discretization. However, it has been demonstrated [4] that by using 3D Green's function for heat conduction and the integral equation formulation the need for discretizing the 3D reservoir is completely eliminated. In this paper we present a 3D integral equation formulation for calculating thermally induced stresses associated with cooling of a planar fracture in an infinite reservoir. A brief presentation of the fluid flow/heat transfer model is also provided for the sake of completeness. Additional details regarding the heat transfer modeling can be found in [4]. 2. FLUID FLOW & HEAT TRANSFER A schematic view of heat extraction from a fracture or a fracture zone in rock is illustrated in Figure 1. With only a few exceptions such as the finite element solution by [5-7] and the boundary element model in [8], the heat conduction in the reservoir is typically modeled as one-dimensional heat flow perpendicular to the fracture surface [9-11].

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-459

Abstract

Abstract. Hydraulic fracturing is the most dominant method of in-situ stress measurement at great depths. It is based on the fundamental concept that the extension fluid pressure is relatively constant inside the hydraulic fracture and slightly greater than the least in-situ principal stress. The various methods of in-situ stress measurement are all based on this same principle. These include measurement of fracture re-opening pressure and various techniques of shut-in pressure analysis. Experiment data from actual field measurements indicate that, contrary to general belief, the fluid pressure drops rapidly and significantly along the fracture length. The cause of the pressure drop is the rapid tapering of the fracture width along its length that consequently creates a large frictional pressure drop during fluid flow, as well as roughnesses on fracture faces due to formation inhomogeneieties. This large pressure drop, coupled with formation physical and mechanical anisotropies, promotes creation of numerous secondary branches along the tip of the fracture, as well as shear failure of the formation along existing planes of weakness. The net effect is a very complex network of tensile and shear fractures that extend randomly around and inside the fractured domain, and further complicate the fluid flow inside the fracture. After the fracturing treatment, fracture closure occurs slowly, and incompletely (hysteresis), often without a distinguishing signature on pressure fall-off data. The paper concludes that the least in-situ principal stress as measured by hydraulic fracturing is always higher than its actual value, with the difference being highly dependant on the formation mechanical and physical anisotropy, as well as the manner by which the experiments are performed. This has a domino effect on the other principal stress measurements based on fracture breakdown pressure. It proposes replacing the constant pressure assumption with a parabolic distribution. This would mean that the least in-situ principal stress is equal to 2/3 of the fracture re-opening pressure. The paper also discusses the conditions for the applicability of shut-in data for stress measurement. Introduction The appeal of hydraulic fracturing for in-situ stress measurements comes from its operational simplicity and ease of interpretation. As first introduced and developed by Kehle 1 , Fairhurst 2 , Haimson and Fairhurs 3 , von Shoenfeldt 4 and Roegiers 5 , the technique consists of creating a hydraulic fracture inside a borehole by injecting a fluid inside it. The plane of the fracture is shown to be perpendicular to the direction of the least compressive in-situ principal stress, s 1 (s 3 > s 2 > s 1 ). The shut-in pressure provides the magnitude of s1, while the breakdown pressure is related to the formation mechanical properties, its tensile stress and the second principal stress which lies in the plane perpendicular to the wellbore. The literature contains a vast collection of papers by many authors who have since studied, analyzed and contributed to the details of testing as well as the interpretation of the fracturing data. As the use of the technique became more widespread within the industry, more refined processes were developed to address various abnormalities observed during its use. These abnormalities included the following.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-491

Abstract

ABSTRACT: This paper deals with the shear-induced dilatation mechanism when a plane-strain fluid-driven fracture propagates on a plane of weakness, subjected to shear and compressive stresses. The fracture surfaces are in contact and their sliding over each other gives rise to normal opening because shear across rough surface generates opening dilation. The analysis assumes an incompressible Newtonian fluid with zero viscosity which is injected into the fracture in an impermeable elastic medium. On the basis of the plane strain elasticity, the resulting slip, crack length and net shear stress, which is defined as the difference between the applied shear stress and the friction stress based on the Coulomb law, are calculated. A slip-weakening friction law is implemented to account for crack surface roughness changes with shear displacement. Using a slip-weakening law means no stress singularity exists at the shear crack tip for propagation along the plane of weakness. The governing equations are derived for equilibrium cracks and a scaling is proposed to simplify those equations. Numerical results based on a Chebyshev polynomial expansion show that the size of slipping region can grow under negative net shear stresses as a result of the slip-weakening mechanism which helps explain the success of hydraulic fracturing in promoting shear fracturing along planes of weakness. A critical length for shear fracture initiation exists as a result of use of a slip-weakening friction law and the removal of stress singularity. Similar to dislocation cores, expenditure of energy is required for crack nucleation from this critical size. For stable shear crack growth, the net shear stress should follow a critical curve obtained numerically. If the net shear stress is larger than its critical value, the shear crack will propagate unstably, otherwise it will be arrested as lack of driving forces. In addition, since the net shear stress is bounded, there is another critical length for the onset of unstable crack growth. 1. INTRODUCTION Shear dilatation is recognized as a mechanism that can enhance permeability of fluid-driven shear fractures. In contrast to the conventional tensile or opening mode fractures in which the fracture is kept open by an internal pressure that exceeds the minimum stress, the coupling between fluid pressure and conductivity in a shear fracture is via shear displacement or slippage. The fluid pressure in the fracture acts to reduce the effective normal stress acting across it which promotes shear of the fracture. The shear displacement changes the conductivity by causing shear-induced dilation. The shear dilation mechanism has been exploited to stimulate hot dry rock reservoirs and gas reservoirs (Pine and Batchelor[1], Vychytil and Horii[2], Mayerhofer et al.[3]). In addition, microseismicity generated by shearing is commonly observed during conventional hydraulic fracture treatments[4]. Recently, hydraulic fracturing has been applied to caving inducement and preconditioning rock masses for mining by block caving methods (van As and Jeffrey[5]). The preconditioning is aimed at modifying the rock mass strength and the size of rock fragments formed during later caving.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-481

Abstract

ABSTRACT ABSTRACT: The paper presents a theory for determining the in-situ stress state from multiple fracturing data and induced fractures from image logs. A solution can be obtained with a minimum of three data sets. However, using an inversion technique, a solution can be o btained with any number of data sets, as the solution is over determined. The magnitude of the stresses is mainly determined from the fracturing data. Fracture information from image logs is mainly used to determine the geographic direction of the principal in-situ stress. In the paper, plots of the Effective Fracture Pressure Ratio, the Fracture Angle and the Fracture Trace Angle gives a good overview how these three quantities behave, as a function of the borehole inclination and azimuth. This knowledge has advantages in planning new oil wells. The mathematical technique is to describe the general fracture equations in terms of effective stress ratios, resulting in a fracture criterion, which is independent of the borehole fracture angle. The data are leak-off data from oil wells. They are recorded in wells with different inclinations and azimuths, a requirement for a robust inversion. However, there is a non -uniqueness problem in fracturing modelling as the position on the wall where the fracture initiate, is usually not known. By using image logs, this uniqueness can be removed. The fracture trace on the image log is also helpful in finding the directions of the in-situ stresses, whether horizontal/vertical or inclined. The model presented in this paper gives opportunity to use the information of the fracture position and direction directly in the in-situ stress calculations. INTRODUCTION The application of rock mechanics in the petroleum industry has increased in later years. Due to the increasing complexity of petroleum wells, borehole stability issues have become challenges that have to be handled. Borehole collapse is one class of problems, whereas circulation losses due to unexpected fracturing accounts for significant additional expenditures. In general, drilling cannot proceed before mud losses are healed. It has become clear that assessment of the in-situ stress state is very fundamental for all modelling work of borehole stability. Data used for stress modelling includes: Leak-Off Tests at each casing shoe (usually 3 in each well) pore pressure and overburden pre ssure, and lithology. In vertical exploration wells we may also deduce the minimum horizontal stress direction from borehole breakouts. Aadnøy [1] developed an inversion technique in 1990. Since directional wells have different orientations (inclinations and azimuths), independent fracturing equations were derived. These were organized as an over determined system of equations and the in-situ stress state were solved in an inversion routine. In addition to determining the magnitude of the two horizontal stresses, it determines the direction of the stress field. Okabe et. al. [2] developed an inversion technique for data taken in the same borehole. Djurhuus and Aadnøy [3] presented a general solution to the problem and showed that the linearized version produces good solutions to the in-situ stresses and their directions.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-468

Abstract

ABSTRACT: Understanding and modeling near-surface hydraulic fracture growth is of interest because fracturing is being used to induce caving near mine openings and for remediation work at shallow environmental waste or spill sites. Thus motivated, near-surface hydraulic fracturing experiments were performed in Polymethylmethacrylate (PMMA). The fractures were driven under conditions such that the internal fluid pressure may be assumed uniform, that is, propagation was in the so-called toughness-dominated regime. As the fractures extend they interact with the free surface and grow towards it, producing a bowl-shaped fracture that eventually daylights at the surface. Injection pressure, fluid injection rate, fracture radius, and surface displacement were monitored during each test. Additionally, an experimental technique that is based on the Beer-Lambert law of light absorption was developed which enables measurement of the full-field opening of hydraulic fractures in transparent materials. The experimental results for opening and radius compare within 10% of published numerical results - which ignore the fracture curving effect - for a toughness-dominated hydraulic fracture. There is greater than 30% difference between the data and published model results for the injection pressure, and reasons for this discrepancy are discussed. Tests were performed with between zero and 12 MPa of radially-directed confining stress. Examination of the shape of the resulting fractures suggests that the radius of the fracture when it daylights is three times the initial depth when radial confinement is zero. The fracture shape data together with scaling considerations suggest a simple empirical relationship whereby the daylighting fracture radius increases with the magnitude of the radial confinement. The findings of this study, in addition to providing guidelines applicable to field design of near-surface fractures, also clearly expose the successes and areas for improvement associated with recent modeling efforts. The paper concludes with a discussion of ongoing research directed at developing a more complete mechanistic model of near-surface hydraulic fracture growth. 1. INTRODUCTION Hydraulic fracturing in near-surface conditions, that is, where the fracture radius is on the same order as the depth of the fracture, has found a number of industrial and scientific applications. Nearly one century ago, hydraulic fractures were used to induce horizontal sheeting in granite quarrying operations [1,2]. More recently, hydraulic fractures have been used in mining operations to induce caving [3] and/or precondition rock masses for caving [4]. Hydraulic fractures have also been used to stimulate contaminant recovery and to form barriers to contaminant transport in environmental remediation projects [5,6,7]. Furthermore, it is thought that hydraulic fracture is an important mechanism in a number of near-surface geophysical processes [1,8]. In all of these cases, the behavior of the fracture is heavily influenced by the nearby free surface. Hence, these fractures exhibit some unique characteristics. Among these features is the tendency of the fracture to curve, thus forming a bowl shape (Fig. 1a). Another feature is the increase in fracture compliance as the radius increases with respect to the depth. Quantitative understanding of these sorts of features is imperative to near-surface hydraulic fracture analysis and design. This has motivated some recent contributions.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-482

Abstract

ABSTRACT: Research has been undertaken through sponsorship of the Workplace Safety and Insurance Board of Ontario (WSIB) to characterize the support capabilities of conventional and innovative spray-on lining materials for mitigating dynamic failure effects created by simulated rockbursts. A variety of conventional spray support media (shotcrete and fibrecre te linings) and innovative polymer-type spray-on lining materials (TSL's) were subjected to the effects of blasting shock by near surface crater blasting to simulate rockburst influence. In similar fashion, rockbolt and bolt-and-mesh support networks were additionally tested to provide baseline comparison of support media capability to resist simulated rockburst damage. The capacity of various types of surface support agents to mitigate rock damage induced by rockbursting was assessed based upon completion of large-scale field detonation trials. Blast effects and site conditions were observed seismically and photographically to provide detailed information concerning rock heave, surface fracturing, ejected fragment motion and support media survivability characteristics. The relative effectiveness of a wide range of area support methods for suppressing dynamic rock ejection and both rock and support media damage was assessed. Results of the study have validated that the majority of thin, spray-on lining products currently available for mining use may be equally as effective, and often better, than conventional support materials for mitigating rockburst damage in highly stressed mine environments. 1. INTRODUCTION The need to supply effective area ground support is urgent when it is realized that one third of all fatal accidents, and a large proportion of serious injury incidents, which occur in hard rock mines in Ontario result from falls of ground and rockbursts [1]. Because future mining development will take place at greater depth, the incidence of stress-induced rock falls is also projected to increase. One way in which injury reduction may occur might be through use of rapidly deployable thin spray-on linings, commonly designated TSL's. Several research efforts that focus upon TSL support use have been undertaken under the sponsorship of the Workplace Safety and Insurance Board of Ontario (WSIB). Appropriate quality control and physical testing procedures for characterizing spray-on support materials, able to meet the highest possible regulatory and industry standards possible, were recommended through the initial phase of this research program. In a subsequent phase, large scale blasting trials were undertaken to test the effectiveness of some types of TSL's for mitigating dynamic rock ejection hazards that would occur in simulated rockburst events. 2. STANDARDIZED ACCEPTANCE CRITERIA A range of polymer or like products exist or are being developed that may generate significant area support for rock. The extent of support claims that have been made for such materials is, however, poorly substantiated due to the relative infancy of use of such products in commercial support application. Industry efforts for material testing, due to lack of resources or inability to test materials in uniform fashion, are unable to yield comprehensive, quantifiable and comparable material evaluations for all candidate materials available.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-506

Abstract

ABSTRACT: The frictional characteristics of a discontinuity are generally non-uniform and thus slip may start from a region of low shear strength (weak zone) and propagate into a region of high shear strength (strong zone). Hence failure may occur progressively before the peak strength is mobilized on the entire surface of the discontinuity. A series of biaxial tests are conducted on specimens with anisotropic frictional surfaces to explore the mechanisms of slip and rupture. The specimens used in the tests are composed of three individual prismatic blocks: two outer and one inner block, machined and bonded together. Bonding of each contact surface creates in half of the surface a low friction strength (weak zone) and in the other half a high friction strength (strong zone). The specimens are then loaded in biaxial compression in such a way that slip propagates from the weak to the strong zone. The slip process can be treated as a mode II crack propagation and the Stress Intensity Factor (KII) is computed by inversion of the stress field observed at the tip of the weak zone; this is done using near field and multi-parameter solutions. A good correlation between the methods has been found. The results show that KIIC depends on the normal stress, and slightly increases with increasing confining pressures. 1. INTRODUCTION The process of slip initiation and propagation along frictional discontinuities is an important problem in engineering where design often involves the application of compression to natural or artificial materials that have pre-existing closed discontinuities. The safety and deformation behavior of these materials often depend on the frictional characteristics of the discontinuities. Examples include rock slope stability, tunneling, or even progressive failure in stiff soil deposits. The frictional characteristics of a discontinuity however are not homogeneous, and as a consequence slip may start in regions of low shear resistance (weak) and propagate into regions of high shear resistance (strong). Hence failure may occur well before the full frictional resistance is mobilized along the entire surface of the discontinuity. If this is the case the choice of a 'uniform' or 'averaged' friction resistance along a particular discontinuity may not be appropriate and may result in an unsafe design. Extensive research has been performed to study and characterize the behavior of frictional surfaces. The well-known Coulomb formulation is still used extensively in practice. The Coulomb friction law [1], states that, along the slip plane, the maximum shear strength t is given by: (available in full a paper) where c is the cohesion, s' n is the effective stress normal to the slip plane, and µ is the coefficient of friction, also expressed as µ = tan F, where F is the friction angle. The rate and state dependency of the coefficient of friction µ has been investigated by many researchers [2-6] who have proposed a number of well established theories. These theories however assume that along the frictional surface properties are homogeneous and the coefficient of friction can be taken as constant or as an average over the slip surface.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-488

Abstract

ABSTRACT: Opening-mode fractures in siliciclastic and carbonate host rocks from different geologic settings consistently show power-law aperture-size distributions when measured along one-dimensional scanlines. Exponents (slopes) and pre-exponential coefficients (intensities) of the power laws, were compared in order to constrain the range of fracture intensities of various aperture sizes over the observation scales. The coefficients range over two orders of magnitude, from 0.1 to 62.4, and the exponents range from -0.45 to -1.36. On a compilation plot of power laws a broad wedge-shaped envelope defines the natural range of frequencies of fractures for aperture sizes from approximately 1000 to 0.01 mm. There is an inverse correlation between the coefficient and exponent for most of the data sets. Power laws having steep slopes tend to have low intensities, whereas power laws having shallow slopes tend to have higher intensities. There are, however, a few exceptions to this correlation. The reasons for the correlation and the departures from it are considered in the light of geologic and mechanical properties at the time of fracture formation for each case. The subcritical crack index, mechanical layer thickness, total strain and strain rate are all likely controls over the relative proportion of narrow to wide fractures in a population. 1. INTRODUCTION Empirical studies have shown that the aperture sizes of opening-mode fractures within a single set are self-organized into power-law distributions [1-3]. Power-law aperture-size distributions ranging over five orders of magnitude have been reported in sandstone and limestone [1] and over three orders of magnitude in dolomites [4]. The range over which power-law distributions apply is typically that observed at the field outcrop scale down to microfractures; on the order of 1 m to 1 µm. Small and large opening-mode fractures that have the same orientation may be different size fractions of the same fracture set. Power-law descriptions of fracture aperture populations take the form: F = ab -c , where F is cumulative fracture frequency, a is the coefficient, b is the fracture aperture, and c is the exponent of the power-law relationship. At any given aperture size, the intensity of fractures is defined by the pre-exponential coefficient, which governs the position of the curves on the ordinate, and the exponent, which is the slope of the curves and is negative. The exponent reflects the relative proportions of wide and narrow fractures in the population. A small exponent (shallow slope) indicates a fracture population with few narrow fractures relative to wide fractures, whereas a large exponent (steep slope) indicates a population with a large number of narrow fractures relative to wide fractures. The values of the exponent and coefficient are different for different fracture sets but the range and reasons for the variation have not been addressed previously. The aim of this contribution is to present a compilation of opening-mode fracture aperture-size data sets so that the aperture-size distributions from different rocks may be compared and the range of intensities of naturally occurring fractures of different aperture sizes may be constrained.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-561

Abstract

ABSTRACT: Rock particles flowing through an ore pass incur an enormous number of collisions until all the rock particles involved come to a rest. An ore pass has three major components including the lined or unlined walls of the ore pass, rock fragments, and the gate assembly at the bottom end of the pass. Recent statistical analysis indicated that a significant number of injuries and fatalities to miners have occurred in or near an ore pass including failure of the chute gate assembly. Due to high impact energy on the chute gate, this may be the main cause of gate assembly failure. To improve the safety of the miner working near an ore pass, it is very important to understand the collisions that take place during the travel as the energy regime of the bulk of materials, especially near the chute gate assembly. 1. Coefficient of Restitution and Collisions The most fundamental question is how a collision of rock impacting rock and rock impacting steel structures is defined and what happens after a collision takes place? In general, collisions involve two or more objects (at least one of the objects must be a moving object) impacting each other. Every earthy object, whether static or dynamic, has some form of energy stored in it. Collisions involving two or more objects can be defined as a phenomenon that results into exchanging or transferring energy. From both the definitions (general and physics), it is evident that collisions result in energy transfer between bodies and in turn depend on some more fundamental properties including masses of the objects, impact velocities, and the ambient atmosphere in which the collisions take place. The after-effects of a collision depend on other physical and mechanical properties of the objects that are involved in the collision. The amount of energy that remains in the object after the collision is totally dependent on its deformation characteristics. Some energy loss as heat and sound from the impact, but the elastic properties and strength of the objects dictate the energy stored or lost in fracturing of the object. A parameter known as Coefficient of Restitution (hereafter COR) is a measure of the energy loss in fracturing or energy loss in rebounding of the objects after an impact or collision. This paper deals with coefficient of restitution, its role in defining the mechanism of bulk solid flow, and specifically the collision of rock on the gate of an ore pass chute. When collisions involve two objects, there are two possibilities; (1) both the objects are moving and collisions occur between rock fragments on the move, and (2) one object is moving and the other one is static and collisions occur between either rock fragment and inner wall of ore pass or rock fragment and the ore chute gate. In both the cases, the law of conservation of momentum governs the collisions. For an object with mass, m, and moving with a velocity, v, the momentum is given by (available in full paper) For a collision involving two objects, the law of conservation of momentum can be written as (available in full paper)

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-545

Abstract

ABSTRACT: A High Energy Crushing Test (HECT) system was used to simulate the operational settings of a jaw crusher so that comparison of fracture toughness and specific comminution energy (the energy required to reduce a rock particle to a given size) could be performed. Since power consumption is a function of the crusher settings, as well as the material being crushed, the closed side set of the HECT system was varied, resulting in single particle breakage tests run at two reduction ratios, 1.5 and 3. The results of the fracture toughness and HECT system tests indicate a strong and linearly proportional relationship between fracture toughness and specific comminution energy. Additionally, fracture toughness was shown to be related to specific comminution energy more strongly than any other material property tested, including tensile strength. A model for the prediction of power consumption has been developed based on the results. At the experimental level the model has been able to predict the specific comminution energy to within 3%. At the operational level the model allows for the determination of jaw crusher power consumption based on the nature of the rock being broken and the average amount of size reduction being done on the feed material. 1. INTRODUCTION The size reduction of brittle materials is the most essential mechanical operation within the raw material processing, i.e. mining, industry. It is also an inefficient, energy intensive process that consumes billions of kilowatt-hours of electricity per year (approximately 3-5% of all electricity consumed on the national level [1, 2]. In fact only 1% of the total energy input into size reduction processes is used in fragmentation and the creation of smaller particles, with most of the energy manifesting in the form of heat and noise. How has a process so fundamental, and costly, to the mining industry remained so inefficient? In a large part because the scientific research required to lay down he theoretical foundations of particle size reduction has lagged behind the actual achievements of technology, resulting in the design and operation of crushing equipment based on standards that fail to adequately describe the entire particle breakage process [3]. Since the technology is already in place, improvements in comminution are dependent upon optimizing the application and operation of that technology. In fact, the United States National Materials Advisory Board estimated that improving the energy efficiency of comminution processes, using practical approaches, could result in energy savings of over 20 billion kilowatt-hours per year [4]. The importance of classical comminution work (Von Rittinger, Kick, and Bond) is that it indicates some relationship between the energy required to decrease the size of a particle and the resultant size of the broken particle. Bond's work in particular highlights the importance of selecting and evaluating crushing equipment, and determining power requirements, based on product size and some measure of a materials resistance to fracture. Over the last three decades more research has focused on the physics of particle fracture during the crushing process and the material characteristics related to fragmentation.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-585

Abstract

ABSTRACT: The Discontinuous Deformation Analysis (DDA) is a numerical model for the statics and dynamics of discontinuous block systems. In this paper, a three-dimensional (3D) version of DDA is briefly described and extended to allow the consideration of thermal loading. The thermal loading submatrices required for 3D DDA are derived. The extended 3D DDA is then applied to analyze the thermal-mechanical behavior of a block of fractured rock in an in situ thermal test known as the Large Block Test (LBT). The deformations of multi-point borehole extensometers (MPBXs) are calculated using 3D DDA forward analysis. The computed and measured MPBX anchor point deformations are compared in terms of their variations with time as well as their magnitudes. It can be seen that the shapes of the plots of the computed MPBX deformations with time are consistent with those of the measure ones. However, the magnitudes of the computed anchor point deformations are generally smaller than the measured ones, which may be due to accumulated round-off errors. The results show that the extended 3D DDA method can be applied to analyze coupled thermal-mechanical behavior of discontinuous rocks, with potential applications in the design of underground storage caverns and nuclear waste repositories. 1. INTRODUCTION Coupled thermal-mechanical behavior of fractured rocks is an important consideration in the design of civil engineering works, such as slopes, underground storage caverns, and nuclear waste repositories. A numerical method useful in such a consideration is the three-dimensional Discontinuous Deformation Analysis (3D DDA). The original DDA developed by Shi [1] is a twodimensional (2D) numerical model for the statics and dynamics of discontinuous block systems. With many people contributing to its development and application, 2D DDA is well developed in terms of both theory and computer coding [2-6]. However, the highly directional nature of jointed rock mass behaviour makes the application of 2D DDA to many practical problems inappropriate. While various researchers are working on 3D DDA, only some preliminary work on this subject has been published [7-9]. In this paper, 3D DDA is briefly described and extended to allow the consideration of thermal loading. The thermal loading submatrices required for 3D DDA are derived. As a validation study, the extended 3D DDA is then applied to analyze the thermal-mechanical behavior of a block of fractured rock in an in situ thermal test known as the Large Block Test (LBT). The results of a 3D DDA analysis are reported and the computed and measured deformations compared. 2. BASIC PRINCIPLES OF 3D DDA 2.1. Displacement and Deformation of a RockBlock In DDA, time steps are used to drive the computation. Large displacement and large deformation result from the accumulation of small displacements and small deformations within the individual time steps. Given that each time step satisfies the condition of infinitesimal displacement and deformation and assuming that each block has uniform stress and strain, the displacement and deformation of a block are determined by 12 independent deformation variables: (available in full paper)

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-577

Abstract

ABSTRACT: Existing borehole stability analysis tools are based on an assumed, fixed, circular borehole geometry. In a strict sense, these tools are valid only as long as the borehole remains circular. They cease to be valid and their applicability becomes limited when borehole breakouts or fractures are present at the borehole wall. Reliance on these methods can limit the ability to evaluate borehole stability and determine the safe mud weight window to the geometry or geometries on which the model being used is based-a circular borehole. When breakouts or fractures have formed, a different model is required to analyze the conditions around the borehole, to determine required mud weights, and to evaluate methods that can be employed to restabilize the borehole. The authors demonstrate this effect by analyzing and evaluating two specific borehole geometries-the circular borehole and a borehole intersected by an induced or natural fracture. Using existing borehole stability theories and basic hydraulic fracturing analysis, the authors review and evaluate various means available to alter the size of the mud weight window. Of particular interest are the two limiting cases: a circular borehole with no defects and a drilling-induced or natural fracture intersecting the borehole. Mechanisms reviewed include chemically altering the rock's mechanical properties or altering the borehole's surface characteristics, creating impermeable bridges within existing fractures, plugging existing or induced fractures with high-viscosity deformable or undeformable materials, and permanently sealing fractures with "rigid" cement. Calculations presented demonstrate the "borehole strengthening" that can be achieved by strengthening the rock matrix or by plugging an existing natural or induced fracture using materials that are deformable and do not rigidly adhere to the fracture walls (such as extremely viscous gel-like materials), materials that are not deformable (such as cement) and require time to cure, and materials that glue the fracture walls together. 1. INTRODUCTION Lost circulation during drilling operations continues to be a significant problem in the oil and gas industry. Control and remediation of lost circulation can require large expenditures and, if impossible, can result in the loss of the well. Lost-circulation problems will continue to plague the industry as it drills for oil and gas in reservoirs or fields with partially depleted sands that have to be penetrated to reach deeper productive intervals. Effective means to assess lost-circulation technologies are required. Lost circulation can occur in a number of ways. It can occur gradually through leakoff; abruptly as we penetrate into subsurface voids, rubbelized zones, and high-permeability intervals; or through the sudden initiation and continued propagation of a fracture. The remainder of this discussion focuses on the last of these lost-circulation issues-lost circulation through fracturing. Using existing borehole stability theories and basic hydraulic fracturing analysis, we review and evaluate various means available to help eliminate or remediate fracturing-related lost circulation. Of particular interest are two limiting cases: Avoidance of fracture initiation in a circular borehole with no defects ?Arresting or mitigating drilling-induced or natural fractures intersecting the borehole Mechanisms reviewed include chemically altering the rock's mechanical properties, altering the borehole's surface characteristics, creation of impermeable bridges within existing fractures, plugging existing or induced fractures with highviscosity deformable or undeformable materials, and permanently sealing fractures

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-562

Abstract

ABSTRACT: The Jackfork sandstone formation is widely distributed in the Ouachita Mountains in southeastern Oklahoma and southwestern Arkansas, USA. It has become of interest in recent years because substantial gas reserves have been found. As the formation is very tight, hydraulic fracturing stimulations are normally required. A systematic investigation of the petrophysical and geomechanical properties of the formation is needed to assure the success of future exploration and development of these reserves. This paper presents laboratory measurements of such properties. Petrophysical properties measured include porosity, permeability, bulk density, grain density, and seismic velocity; some of them were measured in both horizontal and vertical directions. Geomechanical properties determined are uniaxial tensile strength, uniaxial compressive strength, triaxial compressive strengths under three different confining pressures, Young's modulus, Poisson's ratio, cohesion, the angle of friction, and Mode-I fracture toughness. A brief comment is included for each property measured on its potential applications in future reservoir exploration and development. In addition, a detailed introduction is given on the upgrading and application of the CDISK method for Mode-I fracture toughness measurement on small samples. 1. INTRODUCTION The Jackfork sandstone formation has become of interest in recent years because substantial gas reserves have been found in it [1]. As the formation is very tight, hydraulic fracturing stimulations are normally required. Among the 15 wells initially drilled, 13 were hydraulically fractured and completed successfully; but the other two failed, partly due to the lack of proper information on the petrophysical and geomechanical properties of this formation. The work presented in this paper was designed to fulfill that task, together with the introduction of an upgraded method for measuring fracture toughness on small samples. 2. GEOLOGY OF JACKFORK FORMATION The Jackfork sandstone was named for the Jackfork Mountain in the Ouachita Mountains located in Pittsburg and Pushmataha counties, Oklahoma, USA. It is a Pennsylvania formation that extends from southeastern and central southern Oklahoma to southwestern Arkansas in the Ouachita Mountains area (Fig. 1) [2]. (available in full paper) While current gas exploration activities are all within Oklahoma, it is believed that gas reserves will also be discovered on the Arkansas side [1]. For this reason and due to the accessibility to the outcrops, samples for this work were picked from the R.D. Plant Quarry in Kirby, Arkansas. 3. PREVIOUS PETROLEUM ACTIVITIES The first discovery well in the Jackfork sandstone was drilled in 1992 in southern Latimer County, Oklahoma. Gas was first hit in the lower Jackfork sandstone at the depth of 3,612 m. The second discovery well was drilled about 5 km away. It encountered several productive intervals in the upper Jackfork sandstones. A third well was drilled 16 km away from the first one. This well confirmed the discovery of gas reserves. Sidewall sample analyses found the permeability is extremely low; and hydraulic fracturing stimulation is required [1]. 4. PETROPHYSICAL PROPERTIES 4.1. Porosity, Bulk Density and Grain Density The bulk volume of rock consists of two parts: the grain volume and the pore volume. Porosity, ø, is the percentage of pore volume within the bulk volume.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-511

Abstract

ABSTRACT: A new semi-empirical model that predicts fracture deformation under normal compressive loading is presented. The development of a simple exponential model is given first after which a modified and more general exponential model, with an additional degree of freedom in the model parameters, is presented. The simple and the modified exponential models are then compared to available fracture closure models, namely the empirical Barton-Bandis hyperbolic model, and a power-law model based on Hertzian contact theory, to determine how good they fit the results of fracture closure experiments conducted under monotonically increasing normal compressive loading. A new parameter called the half-closure stress, s½, is introduced and is used, in addition to the maximum fracture closure, ¿¿ m , in the model fitting procedures for the Barton-Bandis and the simple and generalized exponential models. The half-closure stress is shown to be related to the initial normal stiffness, K ni , used in the original Barton-Bandis model. An additional parameter, n, is used in fitting the modified exponential model to the experimental data. Of the models presented herein, the modified exponential model was found to provide the best fit to the experimental data, for the same values of s½ and ¿¿ m , over the entire range of compressive stresses. The power-law model based on Hertzian contact theory was found to be unsuitable for accurate prediction of fracture normal deformation behavior. 1. INTRODUCTION Fracture deformability resulting from normal compressive stress is of fundamental importance to the study of the hydraulic and mechanical behavior of rock discontinuities. Fracture deformation directly affects the factors that govern the hydraulic conductivity of single fractures such as aperture distribution, contact area distribution, and spatial connectivity of the apertures [1,2]. Since fracture geometry networks and fluid flow through single fractures govern the hydraulic behavior of fractured rock masses, it follows directly that deformability of single fractures due to the action of compressive stress would affect the hydraulic properties of a rock mass. It is also generally understood that the mechanical behavior of rock masses is controlled significantly by the deformation of discontinuities [3]. The most fundamental properties of the bounding surfaces of a fracture affecting fracture deformation include the rock type, weathered state and matedness of the surfaces, and the spatial and size distributions of asperities on the surfaces. The roughness of each bounding fracture surface is directly related to the size and spatial distributions of the surface asperities, whereas the aperture size and spatial distributions, and the contact area distribution are functions of the cross-correlation of the surface asperity spatial and size distributions. The mechanical strength and deformability of the asperities are functions of the rock type and weathered state of the bounding surfaces. It is also a well known experimental observation that the shear displacement of the bounding surfaces of a fracture, that governs fracture mating, drastically affects the aperture and contact area distributions, even for zero to moderate normal loads, for which the asperity spatial and size distributions of the individual surfaces are practically unchanged [4,5].

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-569

Abstract

ABSTRACT: NIOSH researchers have identified a pattern of fracture zone development that suggests an explanation for fracture formation around rectangular openings in underground mines. This pattern is characterized by shearing and dilation that result in either faults or in the repeated formation and propagation of en echelon fractures from sites of tension. Two computer modeling codes, Fast Lagrangian Analysis of Continua (FLAC) and Particle Flow Code (PFC), were used to model different aspects of this pattern. Use of very small elements with FLAC enabled the identification of sites of initial tension near the skin of square-cornered rectangular openings, while PFC allowed the initiation and progressive development of fractures from these sites to be followed as the fractures evolved. Such studies can lead to a greater understanding of how roof support can be better selected and installed for specific conditions in underground mines prone to roof falls and rock bursts. These studies may also lead to modifications of corner and opening shapes that could be incorporated into mine designs to produce more stable mine openings and reduce the risks of rock falls and rock bursts. 1. INTRODUCTION Mining-induced fractures are typically either hidden from view or become obscured when fractured rock around mine openings collapses or is ejected in a rock burst. Consequently, knowledge of the distribution, geometry, and extent of mining-induced fractures has been limited. However, fracture patterns that suggest mechanisms of fracture formation are occasionally seen where new crosscuts intersect old ones. The old fractures are exposed in the walls of the new opening, but well-described examples are rare in the literature. Most investigators agree that extension fractures form parallel to the direction of maximum principal stress. Recently favored explanations for how decimeter and longer (macroscale) fractures develop have mainly involved the proliferation, interaction, and coalescence of smaller fractures. Fairhurst and Cook [1] proposed that stress-induced microcracks first form an incipient cleavage parallel to the surface of a mine opening. These microcracks then grow into larger fractures as a result of the applied stress. These fractures shorten with depth, and their ends define a shape concave toward the opening that represents the limit of breakage in the case of a rock burst, roof collapse, or pillar hour-glassing. However, in a field example where thin layers were displayed at the margin of a rock burst breakout, White [2] concluded that the closely spaced fractures had not extended across the entire volume of the ejected rock, but were present only near the periphery of the breakout. Other examples that support this scenario are described in White et al.[3] Stacey [4] proposed that failure about mine openings will occur if extension strain reached a certain value, which he considered a material property. He noted that extension strain is highest near the corners of rectangular openings and suggested that failure begins at these locations. He proposed that the extent of failure is determined by how much rock around the opening exceeds the requisite extension strain. For rectangular openings, critical extension strain is deepest at the midpoint between corners and its limit duplicates the concave shape identified by Fairhurst and Cook [1] and commonly seen after roof falls and rock bursts. However, Stacey did not differentiate extension resulting from tension from Poissonresponse extension.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-553

Abstract

ABSTRACT: Linear elastic fracture mechanics is widely used to describe fracture behavior in hard rock, and fracture toughness values for many such rocks are in the literature. The main application has been in hydraulic fracturing. However, hydraulic fracturing operations are now widely performed in unconsolidated and weakly-cemented sandstones or "soft rocks." Soft rocks can have significantly different mechanical behavior than hard rocks, but typically linear elastic models are still applied in these rocks for fracture design purposes. Because of the difficulty of coring and preparing of samples, fracture toughness testing of soft sandstone samples from the subsurface is very challenging. In the study reported here, we assess the fracture mechanics behavior of weakly cemented sandstone numerically with the Discrete Element Method (DEM), in which input parameters are evaluated by comparison with selected elastic and fracture properties. The first step in the study was to carry out the assessment for well cemented Berea sandstone. Mode I fracture toughness was determined using the semi-circular specimen under three-point bending (SCB) test. Further DEM simulations were then run by progressively weakening the bond strength from the reference values determined for Berea sandstone in order to estimate the behavior of weakly-cemented sandstones. The variation of fracture toughness with particle size, notch length, and specimen size is presented and discussed. The assessments of fracture behavior in this study provide a framework of guidelines for fracture mechanics testing and characterization in weakly cemented sandstones. 1. INTRODUCTION In hard rock, Linear Elastic Fracture Mechanics (LEFM) is generally used for the analysis fracture propagation. In weakly cemented and poorly consolidated rocks, fracture propagation mechanisms may be complex, including inelastic deformation, disaggregation, and near-tip shear failure. The mechanical behavior of weakly cemented granular materials is strongly influenced by the amount or characteristic of the cement between particles, and several studies have been conducted on the effect of cement on the deformation and failure behavior of sandstones 2]. BernabÃ¨ et al. [3] created well-consolidated artificial sandpacks using sand and cement material, and measured the variations in strength, dilation and stress-strain behavior with cement content. They observed that small amounts of cement deposited at grain-to-grain contacts had a significant effect on mechanical behavior and strength. Nakagawa and Myer [4] showed that load-displacement paths for samples with constant porosity were identical for different cement saturation ratios until the grains achieved a certain level of intergranular cohesion. After the critical cohesion was achieved, deformation due to intergranular slip decreased and the deformation behavior became more rock-like than soil-like. Continuum modeling of inelastic deformation and brittle fracturing of rocks can be classified as an indirect method, where damage is represented by its effect on constitutive relations [5]. The present study employs the Discrete Element Method (DEM), which can be categorized as a direct method, where deformation is represented by explicitly introducing cracks and tracking grain motion. DEM has several advantages over continuum based numerical methods. Instead of the complex constitutive relationships that must be characterized to use continuum methods, DEM traces the motion and interactions of individual particles based on the direct application of Newtonâ??s second law. Particles interact through contacts and bonds with other particles.