Showing papers on "Fracture (geology) published in 1990"

Ductile Fracture of Metals

Abstract: An account of the recent developments in research into ductile fracture in metals and alloys. Aspects covered include localized fracture at the root of notches and sharp cracks, and fracture in bulk plastic-deformation processes of the metal and metal forming type. Also discusses various theoretical

Modeling fracture flow with a stochastic discrete fracture network: calibration and validation: 1. The flow model

Abstract: A large-scale investigation of fracture flow was recently conducted in a granite uranium mine at Fanay-Augeres, France. Its aim was to develop a methodology for the investigation of possible nuclear waste repository sites in crystalline environments, and thus to determine what measurements to make and what models to use in order to predict the flow and transport properties of the medium, i.e., their average behaviors and spatial variabilities at different scales. Four types of data were collected: (1) geometry of the fracture network; (2) local hydraulic properties measured by injection tests in boreholes; (3) global hydraulic behavior from flow rate and piezometric head distribution at a 106 m3 scale; and (4) tracer tests performed at a scale of up to 40 m. A stochastic fracture network model assuming negligible matrix permeability was developed and calibrated essentially on data 1 and 2 above; this was then used to predict data 3 and 4 in an attempt to validate both the parameters and the structure of the model. In this first part, only the flow problem (data 1) is discussed.

Determination of fracture energy, process zone longth and brittleness number from size effect, with application to rock and conerete

Abstract: The dependence of the fracture energy and the effective process zone length on the specimen size as well as the craek extension from the notch is analyzed on the basis of Ba

Random particle model for fracture of aggregate or fiber composites

Abstract: A particle model for brittle aggregate composite materials such as concretes, rocks, or ceramics is presented. The model is also applicable to the behavior of unidirectionally reinforced fiber composites in the transverse plane. A method of random computer generation of the particle system meeting the prescribed particle size distribution is developed. The particles are assumed to be elastic and have only axial interactions, as in a truss. The interparticle contact layers of the matrix are described by a softening stress‐strain relation corresponding to a prescribed microscopic interparticle fracture energy. Both two‐ and three‐dimensional versions of the model are easy to program, but the latter poses, at present, forbidding demands for computer time. The model is shown to simulate realistically the spread of cracking and its localization. Furthermore, the model exhibits a size effect on: (1) The nominal strength, agreeing with the previously proposed size effect law; and (2) the slope of the post‐peak l...

Micromechanics of pressure-induced grain crushing in porous rocks

Abstract: The hydrostatic compaction behavior of a suite of porous sandstones was investigated at confining pressures up to 600 MPa and constant pore pressures ranging up to 50 MPa. These five sandstones (Boise, Kayenta, St. Peter, Berea, and Weber) were selected because of their wide range of porosity (5–35%) and grain size (60–460 μm). We tested the law of effective stress for the porosity change as a function of pressure. Except for Weber sandstone (which has the lowest porosity and smallest grain size), the hydrostat of each sandstone shows an inflection point corresponding to a critical effective pressure beyond which an accelerated, irrecoverable compaction occurs. Our microstructural observations show that brittle grain crushing initiates at this critical pressure. We also observed distributed cleavage cracking in calcite and intensive kinking in mica. The critical pressures for grain crushing in our sandstones range from 75 to 380 MPa. In general, a sandstone with higher porosity and larger grain size has a critical pressure which is lower than that of a sandstone with lower porosity and smaller grain size. We formulate a Hertzian fracture model to analyze the micromechanics of grain crushing. Assuming that the solid grains have preexisting microcracks with dimensions which scale with grain size, we derive an expression for the critical pressure which depends on the porosity, grain size, and fracture toughness of the solid matrix. The theoretical prediction is in reasonable agreement with our experimental data as well as other data from soil and rock mechanics studies for which the critical pressures range over 3 orders of magnitude.

Experimental determination of interfacial toughness curves using Brazil-nut-sandwiches

Abstract: A Brazil-nut-sandwich with a crack on a substrate/interlayer interface is developed for fracture testing. The fracture loading phase is controlled by the angle of diametral compression. Interfacial fracture mechanics is summarized and adopted in reporting data. Experiments are conducted with aluminum, brass, steel and plexiglass as substrates and epoxy as interlayer. Interfacial toughness curves are measured for large range of loading phase. Effects of the roughness of the surfaces prior to bonding on the interfacial toughness are demonstrated. Failure patterns for the adhesive structure under different loading modes are observed with a scanning electron microscope. For the metal/epoxy systems, when the remote loading is predominantly mode I, cracks tend to kink out of interfaces and run within the epoxy layer, although the bulk epoxy fracture energy is much higher than the interfacial toughness. At large loading phases, abnormally high apparent toughness is measured. These observations are discussed in the light of crack path selection criteria in adhesive joints and large scale contact zone of crack faces.

Pressure Transient Analysis of Fractal Reservoirs

Abstract: The authors present a formulation for a fractal fracture network embedded into a Euclidean matrix. Single-phase flow in the fractal object is described by an appropriate modification of the diffusivity equation. The system's pressure-transient response is then analyzed in the absence of matrix participation and when both the fracture network and the matrix participate. The results obtained extend previous pressure-transient and well-testing methods to reservoirs of arbitrary (fractal) dimensions and provide a unified description for both single- and dual-porosity systems. Results may be used to identify and model naturally fractured reservoirs with multiple scales and fractal properties.

The use of quantitative computed tomography to estimate risk of fracture of the hip from falls

Abstract: We conducted an in vitro investigation of the loads and energies needed to fracture the proximal part of the femur in twelve fresh cadavera under loading conditions simulating one particular type of fall. The fracture loads ranged from 778 to 4,040 newtons and the work to fracture, from five to fifty-one joules. We also investigated the relationship between the fracture loads and several potential indices of bone strength, which were measured non-invasively at the subcapital, basic-cervical, and intertrochanteric regions with quantitative computed tomography. A very high positive correlation with the fracture load resulted from use of an intertrochanteric index--the product of the average trabecular computed-tomography number and the total cross-sectional area of the bone (R2 = 0.93, standard error of estimate = 295 newtons, and p less than 0.00001). We expect the use of this parameter to result in improved assessments of the degree of osteoporosis and of the component of risk of fracture of the hip that is associated with bone strength. However, the measured work to fracture for the isolated femur was an order of magnitude smaller than estimates of the energy available during a typical fall (about 450 joules), suggesting that energy absorbed during falling and impact, rather than bone strength, may be the dominant factors in the biomechanics of fracture of the hip.

Buoyancy-driven fluid fracture: the effects of material toughness and of low-viscosity precursors

Abstract: When buoyant fluid is released into the base of a crack in an elastic medjura the crack will propagate upwards, driven by the buoyancy of the fluid. Viscous fluid flow in such a fissure is described by the equations of lubrication theory with the pressure given by the sum of the hydrostatic pressure of the fluid and the elastic pressures exerted by the walls of the crack. The elastic pressure and the width of the crack are further coupled by an integro-differential equation derived from the theory of infinitesimal dislocations in an elastic medium. The steady buoyancy-driven propagation of a two-dimensional fluid-filled crack through an elastic medium is analysed and the governing equations for the pressure distribution and the shape of the crack are solved numerically using a collocation technique. The fluid pressure in the tip of an opening crack is shown to be very low. Accordingly, a region of relatively inviscid vapour or exsolved volatiles in the crack tip is predicted and allowed for in the formulation of the problem. The solutions show that the asymptotic width of the crack, its rate of ascent and the general features of the flow are determined primarily by the fluid mechanics; the strength of the medium and the vapour pressure in the crack tip affect only the local structure near the advancing tip of the crack. When applied to the transport of molten rock through the Earth's lithosphere by magma-fracture, this conclusion is of fundamental importance and challenges the geophysicist's usual emphasis on the controlling influence of fracture mechanics rather than that of fluid mechanics.

The brittle compressive fracture of ice

Abstract: The brittle compressive fracture under uniaxial loading of fresh-water, granular ice Ih has been studied. Measurements are reported of the fracture stress at temperatures from −10 to −50°C at strain rates of 10 −3 and 10 −1 s −1 for grain sizes from approximately 1 to 10 mm. Also a summary is reported of measurements by Jones et al . (unpublished) of the kinetic coefficient of friction for ice on ice at temperatures from −10 to −40°C at sliding velocities from 5 × 10 −7 m s −1 to 5 × 10 −2 ms −1 . Observations via high speed photography of internal cracking during loading are included. The strength, albeit scattered, increases with decreasing grain size, with decreasing temperature and at −10°C with decreasing strain rate. Similarly, the coefficient of friction increases with decreasing temperature and at −10°C with decreasing sliding velocity. Wing cracks were observed on some inclined cracks nucleated during loading. The results are explained in terms of the frictional crack sliding-wing crack model [as developed by Ashby and Hallam, Acta metall. 34, 497 (1986)] of compressive fracture. Finally, a simple model is presented for the transition from ductile to brittle behavior. It is based upon the competition between the building up and the relaxation of internal stresses within the vicinity of the internal cracks, and it leads to a transition strain rate which can be expressed in terms of the fracture toughness, the creep rate, the kinetic coefficient of friction and the microstructural scale of the material.

Fracture apertures from electrical borehole scans

Abstract: Three-dimensional finite-element modeling was performed to investigate the response to fractures of the Formation MicroScanner (Mark of Schlumberger), which records high-resolution electrical scans of the borehole wall. It is found that the equation W=cARmbRx0l describes, over two orders of magnitude of resistivity contrasts between borehole mud and the formation, the relationship between fracture width W (in mm), formation sensitivity Rx0, mud resistivity Rm, and the additional current flow A caused by the presence of the fracture. A is the additional current which can be injected into the formation divided by the voltage, integrated along a line perpendicular across the fracture trace. Coefficient c and exponent b are obtained numerically from forward modeling. Tool standoffs of up to 2.5 mm and fracture dips in the range from 0° to 40° were found to have an insignificant effect on the above relation. A three‐step approach to detect, trace,and quantify fractures is used. Potential fractures in Formation...

Emission of charged particles from indentation fracture of rocks

Abstract: IT has long been realized that earthquakes are often associated with various kinds of anomalous electromagnetic phenomena. These phenomena might be caused by rock failure in the Earth's crust, but the details of the mechanisms are still unknown. Here we describe an attempt to measure the emission of charged particles from rocks undergoing indentation fracture under atmospheric conditions, using a specially designed indentation system. High electron and ion emission intensities could be detected during parts of the loading cycle when cracking occurred around the indent. The emission behaviour of feldspar and quartz in granite was different from that of the hygroscopic matrix of hornblende andesite; moisture in the hornblende andesite enhanced emission appreciably. The different behaviour observed may be attributable to two different mechanisms.

Size Effect in Fracture of Ceramics and Its Use To Determine Fracture Energy and Effective Process Zone Length

Abstract: The paper shows that a previously proposed size effect law can be used to identify nonlinear fracture properties solely from measured maximum loads of geometrically similar ce­ ramic fracture specimens of sufficiently different sizes. This law represents a first-order global approximation of the de­ viations from linear elastic fracture mechanics, independent of the type of the toughening mechanism in the fracture process zone. It provides a simple and unambiguous way to determine the size- and shape-independent values of the fracture energy, the effective length of the process zone, and the effective crack-tip opening displacement. It also yields the R curve, which is geometry (shape) dependent. The prox­ imity of response to linear elastic fracture mechanics is characterized by a brittleness number, which is shape in­ dependent. [Key words: mechanical properties, fracture, R curve, energy, modeling.]

Pullout Problem: Stress versus Fracture Mechanical Approach

Abstract: The pullout of a single fiber from a brittle matrix is widely recognized as one of the basic tests to be performed to provide information about the expected behavior of a given fiber-reinforced brittle matrix composite material. Thus, it is of great importance that the pullout test be interpreted in a way that yields the true material parameters. Two approaches to the fiber/matrix debonding problem can be made: (1) The stress approach where the criterion for growth of the debonded fiber/matrix interface is expressed in terms of the interfacial stress; and (2) the fracture mechanical approach where the criterion for interfacial debonding is expressed in terms of energy equilibrium. This paper investigates these two approaches by applying both to the same model, which includes frictional stresses on the debonded interface. The debonding load-versus-crack length relationships predicted by the two approaches are compared and differences in the parametric dependency are discussed. The results predicted by the fracture mechanical approach are compared with available experimental results.

Buoyancy-driven fluid fracture : similarity solutions for the horizontal and vertical propagation of fluid-filled cracks

Abstract: Buoyancy-driven flows resulting from the introduction of fluid of one density into a crack embedded in an elastic solid of different density are analysed. Scaling arguments are used to determine the regimes in which different combinations of the buoyancy force, elastic stress, viscous pressure drop and material toughness provide the dominant pressure balance in the flow. The nonlinear equations governing the shape and rate of spread of the propagating crack are formulated for the cases of vertical propagation of buoyant fluid released into a solid of greater density and of lateral propagation of fluid released at an interface between an upper layer of lesser density and a lower layer of greater density. Similarity solutions of these equations are derived under the assumption that the volume of fluid is given by Qtα, where Q and α are constants. Both laminar and turbulent flows are considered.Fluid fracture is an important mechanism for the transport of molten rock from the region of production in the Earth's mantle to surface eruptions or near-surface emplacement. The theoretical solutions provide simple models which describe the relation between the elastic and fluid-mechanical phenomena involved in the vertical transport of melt through the Earth's lithosphere and in the lateral intrusion of melt at a neutral-buoyancy level close to the Earth's surface.

Determination of Fracture Inflow Parameters With a Borehole Fluid Conductivity Logging Method

Abstract: There is much current interest in determining the flow characteristics of fractures intersecting a well bore in order to provide data for use in estimating the hydrologic behavior of fractured rocks. Inflow rates from these fractures into the well bore are usually very low. Moreover, in most cases only a few percent of the fractures identified by core inspection and geophysical logging actually conduct water, the rest being closed, clogged, or isolated from the water flow system. A new procedure is proposed and a corresponding method of analysis developed to locate water-conducting fractures and obtain fracture inflow rates by means of a time sequence of electric conductivity logs of the borehole fluid. The physical basis of the analysis method is discussed, and the procedure is applied to an existing set of data, which shows initiation and growth of nine conductivity peaks in a 900-m section of a 1690-m borehole, corresponding to nine water-conducting fractures intersecting the borehole. By applying our analysis to these nine peaks, the flow rates and the salinity of the water from these fractures are determined. These results are used with other information to obtain transmissivities of the nine fractures, which are validated against independent hydraulic measurements by packer tests. The salinities measured in fluids from the fractures are also validated against salinity values obtained by chemical sampling of fluids from different depths of the borehole. The applicability of this technique is discussed in the context of a borehole-testing program.

On thermohydrologic conditions near high‐level nuclear wastes emplaced in partially saturated fractured tuff: 1. Simulation studies with explicit consideration of fracture effects

Abstract: We have performed modeling studies on the simultaneous transport of heat, liquid water, vapor, and air in partially saturated, fractured porous rock. Formation parameters were chosen as representative of the potential nuclear waste repository site in the Topopah Spring unit of the Yucca Mountain tuffs. The presence of fractures makes the transport problem very complex, both in terms of flow geometry and physics. The numerical simulator used for our flow calculations takes into account most of the physical effects believed to be important in multiphase fluid and heat flow. It has provisions for handling the extreme nonlinearities that arise in phase transitions, component disappearances, and capillary discontinuities at fracture faces. We model a region around an infinite linear string of nuclear waste canisters, taking into account both the discrete fractures and the porous matrix. Thermohydrologic conditions in the vicinity of the waste packages are found to depend strongly on relative permeability and capillary pressure characteristics of the fractures, which are unknown at the present time. If liquid held on the rough walls of drained fractures is assumed to be mobile, strong heat pipe effects are predicted. Under these conditions the host rock will remain in two-phase conditions right up to the emplacement hole, and formation temperatures will peak near 100°C. If it is assumed that liquid cannot move along drained fractures, the region surrounding the waste packages is predicted to dry up, and formation temperatures will rise beyond 200°C. A substantial fraction of waste heat can be removed if emplacement holes are left open and ventilated, as opposed to backfilled and sealed emplacement conditions. Comparing our model predictions with observations from in situ heater experiments reported by Zimmerman and coworkers, some intriguing similarities are noted. However, for a quantitative evaluation, additional carefully controlled laboratory and field experiments will be needed.

Fractured Core Analysis: Interpretation, Logging, and Use of Natural and Induced Fractures in Core

Abstract: The characterization of naturally fractured reservoirs should include core analyses that encompass interpretation of natural and induced fractures. Unfortunately, to date, the differentiation of induced fractures from natural ones in core has been somewhat speculative and often is based on improper techniques. Consequently, bad interpretations have been made and useful information contained in both natural and induced fractures is overlooked. This book addresses the problem of distinguishing natural fractures from induced fractures in both oriented and unoriented core. Natural fractures include any cored fracture that existed in a volume of rock prior to initiation of drilling or coring-related stresses. Induced fractures in core are those that develop during drilling, coring, and subsequent handling. Many of the procedures for distinguishing between the two are based primarily on recognition of fracture surface structures and fracture traces that differ between natural fractures and induced fractures.

Dynamic fracture initiation and propagation in 4340 steel under impact loading

Abstract: Dynamic fracture initiation and propagation in 4340 steel was investigated experimentally using the optical method of reflected caustics combined with high speed photography. A new crack propagation testing configuration consisting of a three point bend specimen loaded in a drop weight tower was used. It was found that prior to crack initiation the stress intensity factor time record calculated using the dynamic tup load and a static formula disagrees with the actual stress intensity factor measured by caustics. During crack propagation, the crack tip velocity and stress intensity factor time records varied smoothly and repeatably allowing for a straightforward interpretation of the data. The experiments show that for the particular heat treatment of 4340 steel used, the dynamic fracture propagation toughness depends on crack tip velocity through a relation that is a material property.

A Method for Estimation of the Density of Fault Displacements below the Limits of Seismic Resolution in Reservoir Formations

Abstract: The fracture density per unit volume in a reservoir formation can be measured directly from seismic data for fractures with displacements greater than the limit of seismic resolution Plots of displacement size vs cumulative number are produced from seismic interpretations digitized and processed using software developed for the analysis of fault geometries and displacements

Buoyancy-driven magma fracture: A mechanism for ascent through the lithosphere and the emplacement of diamonds

Abstract: Magma-driven fractures must be an important mechanism for the transport of magma through the crust and lithosphere. Dikes are pervasive throughout the crust and clearly play an important role in active volcanoes. A magma fracture is the only mechanism that allows sufficiently high magma velocities to prevent complete solidification during transport through cold country rock. The analysis of magma-driven fractures is complex because it involves flow in the fracture (often turbulent), the elastic deformation of the country rock surrounding the fracture, and the propagation of the fracture. For vertically propagating magma fractures, buoyancy forces may be the dominant driving mechanism. In order to simplify the analysis of this problem we neglect the elastic distortion of the country rock and the fracturing process. We consider a buoyant fluid initially in an elliptical two-dimensional cavity. The shape of the upwardly deforming cavity is shown to satisfy the nonlinear kinematic wave equation. For laminar flow the cavity initially deforms but does not move upward. At a critical time the solution near the top of the crack becomes multivalued indicating the presence of an upwardly propagating shock wave. The tail of the upwardly propagating crack closes but does not move upwards. Solutions have also been obtained for turbulent flow. Velocities of upward propagation for appropriate parameter values indicate this mechanism can explain the observed characteristics of kimberlite eruptions. Inclusion of elastic and fracture properties will determine the structure of the shock wave, that is, the crack tip, but would not effect the applicability of our solution.

Three-Dimensional Modeling of Hydraulic Fractures in Layered Media: Part I—Finite Element Formulations

Abstract: A comprehensive model represented by a set of equations governing the mechanics of planar hydraulic fracture propagation in a multi-layered reservoir is presented. A general-purpose integral formulation for the formation elasticity is developed along with a numerical scheme for mode I fracture response evaluation of an arbitrarily shaped planar pressurized crack in a layered medium. Non-Newtonian fluid flow in the hydraulically induced fracture is governed by a two-dimensional nonlinear partial differential equation. Finite element formulations for the governing equations as well as calibrative examples illustrating the computational features of the model are presented. Numerical schemes for determining the moving fracture front and coupling of the fluid flow and structural/fracture responses are also developed.