Showing papers on "Fracture (geology) published in 1993"

A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media

Abstract: A one-dimensional dual-porosity model has been developed for the purpose of studying variably saturated water flow and solute transport in structured soils or fractured rocks. The model involves two overlaying continua at the macroscopic level: a macropore or fracture pore system and a less permeable matrix pore system. Water in both pore systems is assumed to be mobile. Variably saturated water flow in the matrix as well as in the fracture pore system is described with the Richards' equation, and solute transport is described with the convection-dispersion equation. Transfer of water and solutes between the two pore regions is simulated by means of first-order rate equations. The mass transfer term for solute transport includes both convective and diffusive components. The formulation leads to two coupled systems of nonlinear partial differential equations which were solved numerically using the Galerkin finite element method. Simulation results demonstrate the complicated nature of solute leaching in structured, unsaturated porous media during transient water flow. Sensitivity studies show the importance of having accurate estimates of the hydraulic conductivity near the surface of soil aggregates or rock matrix blocks. The proposed model is capable of simulating preferential flow situations using parameters which can be related to physical and chemical properties of the medium.

Effect of electric field on fracture of piezoelectric ceramics

Abstract: Closed form solutions for all three modes of fracture for an infinite piezoelectric medium containing a center crack subjected to a combined mechanical and electrical loading were obtained. The explicit mechanical and electrical fields near the crack tip were derived, from which the strain energy release rate and the total potential energy release rate were obtained by using the crack closure integral. The suitability in using the stress intensity factor, the total energy release rate, or the mechanical strain energy release rate as the fracture criterion was discussed.

The mechanics of cemented carbonate sands

Abstract: The behaviour of artificially cemented carbonate sand was investigated in triaxial tests at confining pressures of up to 9 MPa. The results show that an important effect of cementing is a reduction in specific volume resulting from the increase in fines content This influences both the stress-strain behaviour and the peak strength at strains beyond those required to fracture the cement bonding. Comparisons between the behaviour of cemented and uncemented soils should, therefore, be carried out on samples with the same gradings. For cemented samples it is possible to identify a yield curve outside the state boundary surface of the uncemented soil. A framework for the behaviour has been defined which depends on the relative magnitudes of the confining pressure and cement bond strength. The behaviour of a natural cal-carenite agreed well with this framework which is also likely to be applicable to other cemented soils. Le comportement d'un sable carbonate artificiellement cimente a ete etudie a l'aide d'essa...

Tensile fracture of rock at high confining pressure: implications for dike propagation

Abstract: Field observations indicate that zones of inelastic deformation produced at the tips of propagating dikes can be much larger than those produced at the tips of tensile cracks in laboratory experiments. This is in direct conflict with the concept that fracture toughness and fracture energy are rock properties, independent of crack size and loading configuration. A Barenblatt model that treats fracture resistance as an internal cohesive stress acting at the crack tip is used to investigate the effect of confining pressure on rock tensile failure. When the confining pressure exceeds the cohesive strength of the rock, as it does at depths greater than several hundred meters, Linear Elastic Fracture Mechanics is inapplicable and the near-tip stress field of a propagating crack is determined by the crack size and loading configuration as well as by rock properties. As inelastic deformation depends upon the near-tip stress field, it follows that fracture energy may also depend upon crack size and loading configuration. For a propagating dike, the near-tip stress field is dominated by the large suction acting within a small (∼several meter) cavity at the tip generated by viscous flow of magma within the dike. Perturbations to the ambient stress are on the order of the cavity suction and act over regions on the order of the cavity length. The tip cavity pressure may be maintained by exsolution of magmatic volatiles or by influx of host rock pore fluids; inelastic deformation is enhanced by the latter. For a tip cavity pressure maintained by influx of pore fluids, the pore pressure exceeds the least compressive stress off the dike plane, even while it equals the least compressive stress at the dike tip. This can lead to tensile failure off the dike plane and the formation of observed dike-parallel joints. Shear stresses scale with the cavity suction and may produce shear failure off the dike plane; such deformation is generally enhanced if the dike is intruded perpendicular to the least compressive stress. For sills intruded parallel to bedding, shear failure in the form of bedding plane slip can lead to the observed blunting and fingering of the intrusion front. Because the tip cavity grows with dike size, the energy consumed by rock fracture also increases with dike size and is potentially as significant for large dikes as for small dikes, a view not adopted by existing fluid mechanical models of dike propagation.

Joint pattern development: Effects of subcritical crack growth and mechanical crack interaction

Abstract: Fracture networks are examined in the light of subcritical crack growth theory. Examples of equilibrium crack geometries are generated using a fracture mechanics model that explicitly tracks the propagation of multiple fractures. It is determined that propagation velocity as modeled using a subcritical fracture growth law exerts a controlling influence on fracture length distributions and spacing. Velocity is modeled as proportional to the n-th power of the mode I stress intensity. Numerous, closely spaced, similar length fractures result for n=1, with many en echelon arrays forming due to fracture interaction. Increasing the value of n results in the growth of fewer fractures that are more widely spaced. Fractures tend to cluster in narrow zones, with limited fracture growth in the intervening areas. The spacing between zones is controlled by the stress shielding effects of longer fractures on shorter ones. The amount of time required for fracture pattern development is also influenced by the subcritical velocity exponent, n. At low n, patterns take seconds to minutes to develop, while patterns generated at higher n can require hundreds of years or more.

Bone-healing patterns affected by loading, fracture fragment stability, fracture type, and fracture site compression.

Abstract: The major factors determining the mechanical milieu of a healing fracture are the rigidity of the selected fixation device, the fracture configuration, the accuracy of fracture reduction, and the amount and type of stresses occurring at the bone ends dictated by functional activity and loading at the fracture gap. Of the effects of these factors on fracture healing and remodeling in the canine tibia under unilateral external fixation, the two most significant factors in promoting periosteal callus formation were the amount of physiologic loading as dictated by the body weight and the presence of a significant fracture gap. Uniform axial loading and motion, performed at two or four weeks, did not increase callus formation but did reduce the existing fracture gap. The time-related diminution of periosteal callus (external remodeling) was related to the progress of cortical healing. Cortical reconstruction was fast in stable transverse fractures and delayed in unstable oblique fractures. Motion with loading tended to promote external callus maturation in secondary bone healing. Intracortical new bone formation and porosity were related to the healing pattern and not to the loading magnitude. Endosteal new bone formation showed a strong correlation with the presence of a fracture gap. In terms of torsional strength and energy absorption at failure, the fractures healing through a combination of primary and secondary bone union mechanisms showed the mechanical strength of the healing bone closest to intact bone.

Seismic Anisotropy of Fractured Rocks

Abstract: A simple method for including the effects of geolog­ ically realistic fractures on the seismic propagation through fractured rocks can be obtained by writing the effective compliance tensor of the fractured rock as the sum of the compliance tensor of the unfractured background rock and the compliance tensors for each set of parallel fractures or aligned fractures. The compliance tensor of each fracture set is derivable from a second rank fracture compliance tensor. For a rotationally symmetric set of fractures, the fracture compliance tensor depends on only two fracture com­ pliances, one controlling fracture compliance normal, the other, tangential, to the plane of the fractures. The

Unique method of hydraulic fracturing

Abstract: An improved method for hydraulically fracturing a formation or reservoir where a thermo-setting gellable mixture is utilized. This thermo-setting mixture is foamed either at the surface or in situ under fracturing pressures and conditions. The mixture and carrier fluid is of a composition such that the foamed mixture has a viscosity of sufficient magnitude to cause a created fracture to grow while the foamed mixture is kept under fracturing pressure and conditions. Once a fracture of a desired size and length has been generated, the resin is ignited and thermally set thus forming a porous hardened solid within the fracture thereby holding the fracture open. Once combustion is finished, no spent fracturing fluids or load fluids remain to be recovered. This porous solid props the fracture open thereby increasing the conductivity of the formation or reservoir and fluid flow therefrom.

Continuum and micromechanics treatment of constraint in fracture

Abstract: Two complementary methodologies are described to quantify the effects of crack-tip stress triaxiality (constraint) on the macroscopic measures of elastic-plastic fracture toughness J and Crack-Tip Opening Displacement (CTOD). In the continuum mechanics methodology, two parameters J and Q suffice to characterize the full range of near-tip environments at the onset of fracture. J sets the size scale of the zone of high stresses and large deformations while Q scales the near-tip stress level relative to a high triaxiality reference stress state. The material's fracture resistance is characterized by a toughness locus Jc(Q) which defines the sequence of J-Q values at fracture determined by experiment from high constraint conditions (Q∼0) to low constraint conditions (Q<0). A micromechanics methodology is described which predicts the toughness locus using crack-tip stress fields and critical J-values from a few fracture toughness tests. A robust micromechanics model for cleavage fracture has evolved from the observations of a strong, spatial self-similarity of crack-tip principal stresses under increased loading and across different fracture specimens. We explore the fundamental concepts of the J-Q description of crack-tip fields, the fracture toughness locus and micromechanics approaches to predict the variability of macroscopic fracture toughness with constraint under elastic-plastic conditions. Computational results are presented for a surface cracked plate containing a 6:1 semielliptical, a=t/4 flaw subjected to remote uniaxial and biaxial tension. Crack-tip stress fields consistent with the J-Q theory are demonstrated to exist at each location along the crack front. The micromechanics model employs the J-Q description of crack-front stresses to interpret fracture toughness values measured on laboratory specimens for fracture assessment of the surface cracked plate.

Relating the occurrence of crevasses to surface strain rates

Abstract: The presence of crevasses on the surface of ice masses indicates that a fracture criterion has been met. Understanding how crevasses form will provide information about the stress and strain-rate fields in the ice. This study derives a relationship between measurements of strain rate and observations of crevassing on the surface of ice masses. A literature search yielded 17 polar and alpine locations where strain rates had been measured and crevassing recorded. By plotting strain rates (converted to stresses using a creep law) using axes representing the surface-parallel principal stresses, failure envelopes were derived by enclosing measurements where surface crevassing was absent. The derived failure envelopes were found to conform well to theoretical ones predicted by the Coulomb and the maximum octahedral shear stress (von Mises) theories of failure. The derived failure envelopes were scaled by the tensile strength, which was found to vary from 90 to 320 kPa. There was no systematic variation of tensile strength with either temperature at 10 m depth or the method used to locate the crevasses. The observed variation in tensile strength could result from variations in ice properties (e.g. crystal size, impurity content or density) or could be related to uncertainty in the constitutive relation. Creep flow and fracture share a very similar temperature dependence, suggesting similar crystal-scale processes are responsible for both. The observed relationship will provide a supplementary tool with which to verify and test models of ice dynamics against remotely sensed imagery. The study also indicates that a temperature rise of a few degrees throughout the ice column will not result directly in any increase in calving rates from the large Antarctic ice shelves such as the Filchner–Ronne or Ross Ice Shelves.

Ultrasonic imaging and acoustic emission monitoring of thermally induced microcracks in Lac du Bonnet granite

Abstract: Concurrent ultrasonic tomography and acoustic emission monitoring were employed to study thermally induced microfracturing in an unconfined, 15-cm cube of Lac du Bonnet granite from Atomic Energy of Canada Limited's Underground Research Laboratory. An electrical resistance cartridge heater, placed in a central vertical borehole, was used to cycle the sample to progressively higher peak temperatures between 75°C and 175°C. Tomography data were collected, at room temperature, before and after each thermal cycle. Acoustic emission monitoring proceeded during both heating and cooling phases of each thermal cycle. Microfractures opened above 80°C and eventually coalesced into a macroscopic fracture plane. The macroscopic fracture originated at the outer edges of the sample and then extended inward, parallel to the fast velocity direction, and eventually intersected the borehole. Both acoustic emission locations and slowness difference tomography clearly delineated the fracture plane. We attribute the development of the macroscopic fracture to a thermal gradient cracking mechanism acting upon a brittle, anisotropic medium.

Fracture toughness and fracture mechanisms of PBT/PC/IM blend

Abstract: Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) techniques were employed in the morphology and fracture mechanisms studies on a commercial polybutylene terephthalate/polycarbonate/impact modifier (PBT/PC/IM) blend. The fracture mechanisms involved at different temperatures under both impact and static loading were revealed. It was found that massive plastic deformation of the matrix material occurred after rubber particle cavitation; and it was this plastic deformation that was responsible for the drastic enhancement in fracture toughness although the widespread cavitation did absorb a considerable amount of energy as well. The major source of toughness was the same for both impact and static fracture tests, but the toughening processes became effective at a much lower temperature under static than impact conditions. The sequence of toughening events was also observed using TEM.

Perphosphate viscosity breakers in well fracture fluids

Abstract: The present invention relates to: i) fracture fluid compositions for fracturing subterranean formations to enhance production of fluids from wells in which the viscosity breaker is one or more esters or amides of the perphosphate ion, and to: ii) fracturing processes using fracture fluids comprising esters or amides of the perphosphate ion.

Dependence of ceramic fracture properties on porosity

Abstract: A connected-grain model developed earlier to study the modulus of elasticity as a power-law of density was extended to study the dependence of the flexural strength of polycrystalline ceramics on porosity. Relations were derived for specific surface fracture energy, fracture toughness and flexural strength as power laws of (1 −p), wherep is porosity. Model validity was confirmed with data on α-alumina, UO2, Si3N4, and the YBa2Cu3O7−δ superconductor.

Fracture of brittle spheres under compression and impact loading. I. Elastic stress distributions

Abstract: Numerical values are derived for the elastic stress fields in spheres under conditions of quasi-static compression and free impact against plane targets. The results are relevant to the brittle fracture of spheres under compression and impact loading and allow some anomalies observed in indirect methods of tensile testing to be clarified.

Fatigue Fracture of High-Strength Concrete and Size Effect

Abstract: The results of an experimental study of fatigue fracture of geometrically similar high-strength concrete specimens of very different sizes are reported and analyzed. Three-point bend notched beams were subjected to cyclic loading. The number of cycles to failure ranged from 200 to 41,000. It was found that Paris law for the crack length increment per cycle as a function of the stress intensity factor, which was previously verified for normal concrete, is also applicable to high-strength concrete. However, for specimens of different sizes, an adjustment for the size effect needs to be introduced, of a similar type as previously introduced for normal concrete. A linear regression plot estimating the size-adjustment parameters is derived. An LEFM (linear elastic fracture mechanics)-type calculation of the deflections under cyclic loading on the basis of the size-adjusted Paris law yields correct values for the terminal phase but grossly underpredicts the initial deflections. Overall, the results underscore the importance of considering fatigue fracture growth in the case of high-strength concrete structures subjected to large, repeated loads, and taking into account the very high brittleness under fatigue loading.

Particulate fracture during deformation of a spray formed metal-matrix composite

Abstract: The mechanisms of deformation and failure in a 2618 Al alloy reinforced with 15 vol pct SiC particilates were studied and compared with those of the unreinforced alloy, processed by spray forming as well. Tensile and fracture toughness tests were carried out on naturally aged and peak-aged specimens. The broken specimens were sliced through the middle, and the geometric features of fractured and intact particulates were measured. The experimental observations led to the conclusion that failure took place by the progressive fracture of the particulates until a critical volume fraction was reached. An influence of the particulate size and aspect ratio on the probability of fracture was found, the large and elongated particulates being more prone to fail, and the fracture stress in the particulates seemed to obey the Weibull statistics. The dif- ferences in ductility found between the naturally aged and peak-aged composites were explained in terms of the number of broken particulates as a function of the applied strain. Numerical simulations of the deformation process indicated that the stresses acting on the particulates are higher in the peak-aged material, precipitating the specimen failure. Moreover, the compressive residual stresses induced on the SiC during water quenching delayed the onset of particulate breakage in the naturally aged material.

Relationship between Fracture Surface Roughness and Fracture Behavior of Cement Paste and Mortar

Abstract: Fracture surfaces of cement and mortar specimens were characterized using a confocal microscope to create three-dimensional computer-based topographic maps. The texture of the fracture surfaces was quantified using image analysis techniques to compute a roughness parameter and fractal dimension. Total porosity, pore-size distribution, compressive strength, and fracture properties of the specimens were determined and compared with the roughness parameter. Fracture properties were determined by notched-beam tests and the results were analyzed both by using conventional linear elastic fracture mechanics as well as a compliance-based approach that incorporated R-curve type of behavior. A positive correlation between fracture surface roughness and fracture toughness was demonstrated.

Effect of thermal regime on growth increment and spacing of contraction joints in basaltic lava

Abstract: Columnar joints in volcanic rocks are thermal contraction cracks that bound elongate rock columns. The joints grow incrementally toward the interior of a cooling extrusion by successive formation of new segments on the joint edges. Joint spacing as measured by column diameter is often smaller in the upper portion of a lava flow and larger in the lower portion. We investigated incremental growth of columnar joints and factors controlling their spacing by measuring growth increments and spacings of joints in basaltic lava and by modeling the observations using fracture mechanics principles. The field data show that growth increment and spacing are linearly correlated and increase up to a limit with distance from the cooling surface on which the joints start. The models of incremental joint growth combine fracture mechanics with thermomechanical models of layers cooling by conduction or water-steam convection in joints. A joint propagates when tensile stress concentrated at its tip builds up during cooling and exceeds the lava's resistance to fracture. The joint arrests when its tip reaches hot ductile lava with a very high resistance to fracture. Blunting of the arrested tip by ductile flow reduces joint tip stresses and thus stabilizes the joint until further cooling restores critical stress at the tip. The models predict that the joint growth increment will increase slightly from cycle to cycle up to a limit as observed in the field. Faster solidification rates with higher thermal gradients produce smaller growth increments because the level to which a joint propagates will have migrated relatively little when the arrested joint tip cools sufficiently to restart joint growth. An analysis accounting for the mechanical interaction of joints shows that a joint extended beyond its neighbors reduces the joint tip stress of its neighbors, thereby inhibiting their growth and determining a minimum joint spacing. The predicted minimum spacing increases with growth increment in agreement with field measurements. The data and model results therefore indicate that faster solidification promotes smaller joint growth increments that, in turn, produce smaller joint spacings.

Round Robin Testing for Mode I Interlaminar Fracture Toughness of Composite Materials

Abstract: This report summarizes the results of several interlaboratory “round robin” test programs for measuring the Mode I interlaminar fracture toughness of advanced fiber-reinforced composite materials. Double cantilever beam (DCB) tests were conducted by participants in ASTM Committee D-30 on High Modulus Fibers and Their Composites and by representatives of the European Group on Fracture (EGF) and the Japanese Industrial Standards Group (JIS). DCB tests were performed on three AS4 carbon fiber-reinforced composite materials: AS4/3501-6 with a brittle epoxy matrix, AS4/BP907 with a tough epoxy matrix, and AS4/PEEK with a tough thermoplastic matrix. Difficulties encountered in manufacturing panels, as well as conducting the tests, are discussed. Critical issues that developed during the course of the testing are highlighted. Results of the round robin testing used to determine the precision of the ASTM DCB test standard are summarized.

Seismic cracking and energy dissipation in concrete gravity dams

Abstract: A finite element method for seismic fracture analysis of concrete gravity dams is presented. The proposed smeared crack analysis model is based on the non-linear fracture behaviour of concrete. The following features have been considered in the development of the model: (i) the strain softening of concrete due to microcracking; (ii) the rotation of the fracture band with the progressive evolution of microcrack damage in finite elements; (iii) the conservation of fracture energy; (iv) the strain-rate sensitivity of concrete fracture parameters; (v) the softening initiation criterion under biaxial loading conditions; (vi) the closing-reopening of cracks under cyclic loading conditions. The seismic fracture and energy response of dams and the significance of viscous damping models to take account of non-cracking structural energy dissipation mechanisms are discussed. The influences of global or local degradation of the material fracture resistance on the seismic cracking response of concrete dams were also studied. Two-dimensional seismic response analyses of Koyna Dam were performed to demonstrate the application of the proposed non-linear fracture mechanics model.

Acoustic emissions from rapidly moving cracks.

Abstract: Linear elasticity is unable to predict completely the dynamics of a rapidly moving crack without the addition of a phenomenological fracture energy. Our measurements of acoustic emission, crack velocity, and surface structure demonstrate quantitatively similar dynamical fracture behavior in two very different materials, polymethylmethacrylate and soda-lime glass. This unexpected agreement suggests that there exist universal features of the fracture energy that result from dissipation of energy in a dynamical instability.