Showing papers on "Fracture (geology) published in 1996"
TL;DR: In this article, the authors derived the cubic law of the Navier-Stokes equations for flow between smooth, parallel plates and showed that the effective hydraulic aperture is less than the mean aperture, by a factor that depends on the ratio of the mean value of the aperture to its standard deviation.
Abstract: The flow of a single-phase fluid through a rough-walled rock fracture is discussed within the context of fluid mechanics. The derivation of the ‘cubic law’ is given as the solution to the Navier-Stokes equations for flow between smooth, parallel plates - the only fracture geometry that is amenable to exact treatment. The various geometric and kinematic conditions that are necessary in order for the Navier-Stokes equations to be replaced by the more tractable lubrication or Hele-Shaw equations are studied and quantified. In general, this requires a sufficiently low flow rate, and some restrictions on the spatial rate of change of the aperture profile. Various analytical and numerical results are reviewed pertaining to the problem of relating the effective hydraulic aperture to the statistics of the aperture distribution. These studies all lead to the conclusion that the effective hydraulic aperture is less than the mean aperture, by a factor that depends on the ratio of the mean value of the aperture to its standard deviation. The tortuosity effect caused by regions where the rock walls are in contact with each other is studied using the Hele-Shaw equations, leading to a simple correction factor that depends on the area fraction occupied by the contact regions. Finally, the predicted hydraulic apertures are compared to measured values for eight data sets from the literature for which aperture and conductivity data were available on the same fracture. It is found that reasonably accurate predictions of hydraulic conductivity can be made based solely on the first two moments of the aperture distribution function, and the proportion of contact area.
1,003 citations
TL;DR: In this article, a quasi-automatic simulation of propagation of arbitrary cracks in two-dimensional, linear elastic finite element models is presented, where an underlying winged-edge data structure enables automatic local modifications of the mesh along the propagation path without loss of any unaffected structural information.
421 citations
TL;DR: In this article, the effect of the replacement of mineral coarse aggregate by rubber tire aggregate is investigated, and the authors found that the incorporation of these rubber tire chips in concrete exhibited a reduction in compressive and flexural strengths, the reduction in compression strength was approximately twice the reduction of flexural strength.
Abstract: The effect of the replacement of mineral coarse aggregate by rubber tire aggregate is investigated in this paper. Four different volume contents of rubber tire chips were used: 25, 50, 75 and 100%. The incorporation of these rubber tire chips in concrete exhibited a reduction in compressive and flexural strengths, the reduction in compressive strength was approximately twice the reduction of the flexural strength. The specimens which contained rubber tire aggregate exhibited ductile failure and underwent significant displacement before fracture. The toughness of flexural specimens was evaluated for plain and rubber tire concrete specimens. The test revealed that high toughness was displayed by specimens containing rubber tire chips as compared to control specimens.
376 citations
Patent•
23 Dec 1996TL;DR: In this paper, the authors proposed a method to fracture underground formations by placing a hydrajetting tool having at least one fluid jet forming nozzle in the well bore adjacent the formation to be fractured and jetting fluid through the nozzle against the formation.
Abstract: Methods of fracturing subterranean formations are provided. The methods basically comprise positioning a hydrajetting tool having at least one fluid jet forming nozzle in the well bore adjacent the formation to be fractured and jetting fluid through the nozzle against the formation at a pressure sufficient to form a fracture in the formation.
250 citations
TL;DR: In this paper, the concept of equivalent crack concept is defined, in passing from a damage zone to a fracture problem and conversely, the damage zone is determined which is equivalent to a crack.
247 citations
TL;DR: In this paper, a two-dimensional fracture network model is described, which attempts to address the problems of both reservoir creation and circulation using rock mass characterization and in situ stress data as the primary inputs with a view to encapsulating our present understanding of how such systems work.
Abstract: Hot dry rock geothermal energy extraction experiments in artificial reservoirs created by hydraulic stimulation in naturally fractured crystalline rocks have been undertaken in several countries over the last 20 years. The experiments have had mixed results in terms of fluid recovery, system impedance, and heat extraction. Numerical models have not yet delivered a generally agreed understanding of the processes and sensitivities involved in reservoir creation and circulation. In this paper a two-dimensional fracture network model is described, which attempts to address the problems of both reservoir creation and circulation using rock mass characterization and in situ stress data as the primary inputs with a view to encapsulating our present understanding of how such systems work. The model is a prototype for a three-dimensional version currently under development and is intended mainly for engineering sensitivity studies. The basis of the model lies in approximations of fracture mechanical behavior drawn from the rock mechanics literature, a very simplified analysis of the operative physical processes, and mapping of the connectivity of fracture networks to a fine resolution regular grid. Taken together, these permit the approximate resolution of what is normally a supercomputer problem on a personal computer. The model is applied to field data gathered at Fenton Hill, New Mexico; Hijiori, Yamagata Prefecture, Japan; and Rosemanowes, Cornwall, England.
196 citations
TL;DR: In this article, a numerical scheme to simulate full crack propagation is proposed which makes use of interface laws relating interlaminar stresses to displacement discontinuities along the plane of crack propagation, and the relation between interface laws and mixed-mode failure loci in terms of critical energies is discussed and clarified.
Abstract: A study of mixed-mode crack propagation in bending-based interlaminar fracture specimens is here presented. A numerical scheme to simulate full crack propagation is proposed which makes use of interface laws relating interlaminar stresses to displacement discontinuities along the plane of crack propagation. The relation between interface laws and mixed-mode failure loci in terms of critical energies is discussed and clarified. Numerical simulations are presented and compared with analytical and experimental results.
196 citations
TL;DR: In this article, a European round robin was set up to investigate the relative merits of five different fracture toughness testing methods, and the single edge notch bend bend bend saw cut (SENB-S) method seemed to deliver the most reproducible results, both within and between laboratories.
Abstract: The brittle behaviour of ceramic materials makes imperative the development of accurate and reproducible methods of measuring their resistance to fracture. To this end, a European round robin was set up to investigate the relative merits of five different methods of fracture toughness testing. Of these the single edge notch bend — saw cut (SENB-S) method seemed to deliver the most reproducible results, both within and between laboratories. However, it has been observed empirically that if notches are cut too thick, the values of fracture toughness determined are systematically too high. An explanation and a theoretically based relationship to describe this behaviour are presented. It is suggested that this effect results from the interaction of the stress field around the notch tip and defects related to the microstructure or machining damage. Measured data from a number of materials seem to correlate well with the theory. It is shown that if correct values of fracture toughness are to be determined with the SENB-S method, the notch width must be of the order of the size of the relevant microstructural or machining-induced defects (e.g. large pores and weak grain boundaries).
193 citations
TL;DR: In this paper, a simple method is proposed to enhance the ductility of beam-to-column connections by trimming the beam flanges slightly, which can improve the overall ductility.
Abstract: The strength and ductility of steel frames depend strongly on the behavior of their beam-to-column connections. The fracture of beam-to-column connections of steel buildings in the Northridge Earthquake generated concern about the reliability of current design and construction technology on steel connections. There is an urgent need to find a reliable method to retrofit these connections and to use it for the design of new buildings. A simple method is proposed here to enhance the ductility of beam-to-column connections. On trimming the beam flanges slightly, the ductility of the connection can be improved greatly. Experimental study of the newly designed connections under cyclic load shows that the ultimate strengths are almost unaltered, whereas the stiffness is decreased only slightly. However, the plastic rotational capacity can be increased several times. Moreover, the fracture proneness of connections due to welding sensitivity and stress concentration from abrupt geometry alternation can be minimiz...
193 citations
TL;DR: In this article, a 3D non-llinear finite element analysis was employed to conduct an extensive parametric evaluation of crack front stress triaxiality for deep notch SE(B) and C(T) specimens and shallow notch SE (B) specimens, with and without side grooves.
Abstract: Specimen size and geometry effects on cleavage fracture of ferritic steels tested in the ductile-to-brittle transition region remain an important technological impediment in industrial applications of fracture mechanics and in the on-going development of consensus fracture testing standards. This investigation employs 3-D nonllinear finite element analyses to conduct an extensive parametric evaluation of crack front stress triaxiality for deep notch SE(B) and C(T) specimens and shallow notch SE(B) specimens, with and without side grooves. Crack front conditions are characterized in terms of J-Q trajectories and the constraint model for cleavage fracture toughness proposed previously by Dodds and Anderson. An extension of the toughness scaling model suggested here combines a revised ‘in-plane’ constraint correction with an explicit thickness correction derived from extreme value statistics. The 3-D analyses provide ‘effective’ thicknesses for use in the statistical correction which reflect the interaction of material flow properties and specimen aspect ratios, a/W and W/B, on the varying levels of stress triaxiality over the crack front. The 3-D computational results imply that a significantly less strict size/deformation limit, relative to the limit indicated by previous plane-strain computations, is needed to maintain small-scale yielding conditions at fracture by a stress-controlled, cleavage mechanism in deep notch SE(B) and C(T) speciments. Moreover, the analyses indicate that side grooves (20 percent) should have essentially no net effect on measured toughness values of such specimens. Additional new results made available from the 3-D analyses also include revised η-plastic factors for use in experimental studies to convert measured work quantities to thickness average and maximum (local) J-values over the crack front. To estimate CTOD values, new m-factors are included for use in the expression 131-1.
175 citations
TL;DR: In this paper, the authors report the results of an experiment simulating a well-contained underground nuclear explosion, undertaken to test the ability of natural gas-transport processes to move highly dilute and rapidly decaying radionuclides to the surface.
Abstract: UNDERGROUND nuclear explosions produce trace amounts of distinctive but ephemeral radionuclide gases. In the context of monitoring a comprehensive test ban treaty, the detection of these gases within the territory of a signatory, during a challenge inspection1–5, may indicate the occurrence of a clandestine nuclear event. Here we report the results of an experiment simulating a well-contained underground nuclear explosion, undertaken to test the ability of natural gas-transport processes to move highly dilute and rapidly decaying radionuclides to the surface. We find that trace gases are transported to the surface within periods of weeks to a year, by flow along faults and fractures driven by barometric pressure variations. Both our observations and related simulations exhibit a chromatographic behaviour, with gases of higher atomic mass and lower diffusivity reaching the surface more rapidly. For a 1-kilotonne nuclear test under conditions identical to those of our experiment, we predict that short-lived 133Xe and 37Ar would be detectable, respectively, about 50 and 80 days after the detonation. Our results indicate that radionuclide sampling along natural faults and fractures, as a forensic tool, can be an extremely sensitive way to detect nearby underground nuclear explosions that do not fracture the surface.
TL;DR: In this paper, the size effect on the nominal strength of fiber composite laminates has been investigated and it has been shown that there is a significant effect on nominal strength on fiber composite notches.
Abstract: Measurements of the size effect on the nominal strength of notched specimens of fiber composite laminates are reported. Tests were conducted on graphite/epoxy crossply and quasi-isotropic laminates. The specimens were rectangular strips of widths 6.4, 12.7, 25.4 and 50.8 mm (0.25, 0.50, 1.00 and 2.00 in.) geometrically similar in two dimensions. The gage lengths were 25, 51, 102 and 203 mm (1.0, 2.0, 4.0 and 8.0 in.). One set of specimens had double-edge notches and a [0/92{sub 2}]{sub s} crossply layup, and another set had a single-sided edge notch and a [0/{+-}45/90]{sub s} quasi-isotropic layup. It has been found that there is a significant size effect on the nominal strength. It approximately agrees with the size effect law proposed by Bazant, according to which the curve of the logarithm of the nominal strength versus the logarithm of size represents a smooth transition from a horizontal asymptote, corresponding to the strength criterion (plastic limit analysis), to an inclined asymptote of {minus}0.5 slope, corresponding to linear elastic fracture mechanics. Optimum fits of the test results to identify the material fracture characteristics, particularly the fracture energy and the effective length of the fracture process zone. Finally, the R-curves are also identified on themore » basis of the maximum load data. The results show that in design situations with notches or large initial traction-free cracks the size effect on the nominal strength of fiber composite laminates must be taken into account.« less
TL;DR: In this paper, the authors present a survey of current understanding of the interrelationships among the hydraulic, mechanical, seismic and geometrical properties of single natural factures, including fracture specific stiffness, which is the key link in interrelating the physical properties of a fracture.
TL;DR: In this paper, experimental results related to hydraulic fracturing of a horizontal well, specifically the nonplanar fracture geometries resulting from fracture initiation and propagation, are presented and recommendations to ensure clear communication channels between the wellbore and the fracture are given.
Abstract: This paper presents experimental results related to hydraulic fracturing of a horizontal well, specifically the nonplanar fracture geometries resulting from fracture initiation and propagation. Experiments were designed to investigate nonplanar fracture geometries. This paper discusses how these nonplanar fractures can be responsible for premature screenout and excessive treatment pressure when a horizontal well is hydraulically fractured. Reasons for unsuccessful hydraulic fracturing treatments of a horizontal well are presented and recommendations to ensure clear communication channels between the wellbore and the fracture are given.
TL;DR: In this paper, the authors examined the calculated stress fields to assess, in a classic Mohr-Coulomb context, the potential for consequent fracture and found that topographic relief can cause stresses of sufficient magnitude to break rock, creating fracture sets having a spatial distribution and orientation governed by landform shape and the regional state of stress.
Abstract: Stresses at Earth's surface are profoundly influenced by topography Simple models indicate that gravitational and regional stresses are concentrated, attenuated, even reversed within landforms Such topographically induced stresses are potentially manifest as bedrock fractures Fractures reduce rock mass strength, decrease erosional resistance, and create conduits for water By creating fractures, topographically induced stresses can alter processes of mass wasting, bedrock incision, and groundwater flow We use Savage et al's [1985] solution for stresses in symmetric ridges and valleys on an elastic half-space in plane strain to assess topographic effects on regional and gravity-induced stresses We have extended their solution to include lateral loads that vary with depth, which better approximates states of stress found in Earth's crust and allows us to examine a greater range of stress regimes We examine the calculated stress fields to assess, in a classic Mohr-Coulomb context, the potential for consequent fracture This model indicates that topographic relief can cause stresses of sufficient magnitude to break rock, creating fracture sets having a spatial distribution and orientation governed by landform shape and the regional state of stress We find that in extensional tectonic regimes, topographically induced stresses favor surface-parallel fractures through ridges and steeply dipping fractures through valleys Conversely, in compressional regimes, topographically induced stresses favor steeply dipping fractures through ridges and surface-parallel fractures through valleys Such topographic interactions with regional stresses pose consequences for interpretations of fracture orientation, for assessments of slope stability, and for processes of landscape development
TL;DR: In this article, the authors developed a framework for dynamical fracture, concentrating on the derivation of basic field equations that describe the motion of the crack tip in two space-dimensions.
Abstract: This paper develops a framework for dynamical fracture, concentrating on the derivation of basic field equations that describe the motion of the crack tip in two space-dimensions. The theory is based on the notion of configurational forces in conjunction with a mechanical version of the second law.
TL;DR: In this article, the Strombus gigas conch shell has a crossed-lamellar micro-architecture, which is layered at five distinct length scales and can be considered a form of ceramic "plywood".
Abstract: Flexural strength, crack-density evolution, work of fracture, and critical strain energy release rates were measured for wet and dry specimens of the Strombus gigas conch shell. This shell has a crossed-lamellar microarchitecture, which is layered at five distinct length scales and can be considered a form of ceramic “plywood”. The shell has a particularly high ceramic (mineral) content (99.9 wt%), yet achieves unusually good mechanical performance. Even though the strengths are modest (of the order 100 MPa), the laminated structure has a large strain to fracture, and a correspondingly large work of fracture, up to 13 kJ m−2. The large fracture resistance is correlated to the extensive microcracking that occurs along the numerous interfaces within the shell microstructure. Implications of this impressive work of fracture for design of brittle laminates are considered.
TL;DR: In this paper, the authors present a method of pressure falloff analysis which removes this ambiguity and allows an accurate determination of the magnitude of pressure dependent leakoff and the effects of fracture tip extension and recession, height recession, and transient flow in the fracture.
Abstract: The effects of natural fissure opening, or pressure dependent leakoff, on the pressure behavior observed during fracturing are significant. Previous work has suggested that this behavior can be identified from pressure diagnostic plots during pumping, or from pressure falloff analysis. However, these techniques lead to ambiguous conclusions regarding the magnitude, and even existence, of pressure dependent leakoff. This paper presents a method of pressure falloff analysis which removes this ambiguity and allows an accurate determination of the magnitude of pressure dependent leakoff. The effects of fracture tip extension and recession, height recession, and transient flow in the fracture are also identified. The effect of pressure dependent fracture compliance, which has not been previously published, is also described.
TL;DR: In this paper, the Riemann zeta function is used for the analytical and numerical solution of aggregate problems, including fracture surface area, fracture porosity, fracture permeability and shear-wave anisotropy.
TL;DR: In this article, the authors have loaded cracks in mixed mode I + III within polymethyl methacrylate (PMMA or Plexiglas) rectangular blocks resembling conceptual fracture mechanics models of mixed mode loading and have analyzed the resulting geometries.
Abstract: Mixed mode I + III loading of a fracture front results in out-of-plane propagation into echelon stepping fractures. Because a planar fracture geometry is the exception rather than the rule, and because the introduction of even a minor component of mode II or III loading is known to promote out-of-plane propagation, an understanding of mixed mode fracture growth is imperative to analyze fracture behavior. We have loaded cracks in mixed mode I + III within polymethyl methacrylate (PMMA or Plexiglas) rectangular blocks resembling conceptual fracture mechanics models of mixed mode loading and have analyzed the resulting geometries. The observed angle of twist of echelon fractures from the parent crack plane increases with the ratio KIII/KI and falls below theoretical predictions. Fracture propagation paths depend not only on the load ratio applied but also on sample geometry, loading configuration, and interaction among growing fractures. Sample geometry and loading configuration are approximately accounted for using analytical determinations of the stress intensity factors. We propose that interaction among growing fractures may contribute to the discrepancy between theoretically predicted twist angles and those observed in these and other mixed mode I + III experiments. Analysis of these experimental results has motivated the design of a new sample and loading configuration to test the propagation paths of uniformly loaded mixed mode I + III fractures.
TL;DR: In this paper, a series of displacement controlled uniaxial compression experiments were conducted to investigate the effects of specimen slenderness and friction between loading platen and specimen on the development of localized fracture zones in the specimen.
Abstract: Localization of deformations has been investigated in a series of displacement controlled uniaxial compression experiments. Of main interest are the effects of specimen slenderness and friction between loading platen and specimen. Both effects have a direct influence on the development of localized fracture zones in the specimen. The results indicate that the use of a double layer of teflon with an intermediate layer of grease yields size-independent results as far as the pre-peak stress–strain behaviour and the peak strength are concerned. However, in terms of stress and strain, a significant influence of both the specimen slenderness and the amount of boundary restraint has been observed in the post-peak regime. It is found that the post-peak curves become almost completely identical when they are plotted in terms of nominal stress and post-peak displacement. For any type of loading platen used, the post-peak relative stress-displacement curves are found to be independent of the specimen height. Furthermore, since during post-peak localization relative sliding and movements of larger parts of the specimen are observed, the definition of a unique Poisson's ratio is virtually impossible.
TL;DR: In this article, a finite element model of silicon microcantilever beams is created, and ABAQUS is used to calculate the displacements and stresses produced by an applied load force.
Abstract: Silicon microcantilever beams are fractured and characterized. The specially designed beams, etched into two wafers, are loaded to fracture in bending using a unique measurement system. A finite element model of the beams is created, and ABAQUS is used to calculate the displacements and stresses produced by an applied load force. A special testing scheme is devised to obtain certain model parameters: E〈110〉, the Young’s modulus along the length of the beam and Lforce, the position of the applied force. With these parameters defined, the model is well correlated with that of the experimental data. The fracture stress (strength) of the beam is obtained from the stress produced in the model at the fracture location by a load equivalent to the experimental fracture force. This fracture stress can be used as a design parameter for silicon micromechanical structures. Numerous beams are fractured from both the front and back sides of the wafer, and statistical fracture strength results are compiled for each of t...
TL;DR: In this paper, the fracture surface morphology and toughness of notched PST crystals of TiAl strongly depend on their notch orientation with respect to the lamellar boundaries and crystal orientation of γ lamellae, and the relative magnitudes of fracture toughness and microstructural characteristics of fracture surfaces for these orientations are discussed in terms of crystallography and toughening mechanisms available in PST crystals.
TL;DR: In this article, the physical basis of the Burchell fracture model for graphites is described and the model combines a fracture mechanics failure criteria and a microstructurally based description of fracture.
TL;DR: In this paper, the authors report on the mechanical characterization of thin hard films deposited on softer substrates using the micro-indentation technique together with spherically tipped indenters.
TL;DR: In this paper, the use of ductile fracture criteria in conjunction with the finite element method for predicting failures in cold bulk metal forming is described, and a general good agreement is found.
TL;DR: In this paper, the initial stage of crater formation on asteroid 243 Ida is examined, up to the cessation of fracture and the establishment of the cratering flow; at this stage we can infer final crater diameters but not profiles.
TL;DR: In this paper, the authors applied compact compression specimen (CCS) H integral technique to the characterization of the dynamic fracture toughness of PMMA under transient loading and determined the forces and displacements on the boundaries of a cracked CCS using a Kolsky apparatus.
TL;DR: In this paper, the role of plastic-frictional energy dissipation in the fracture process zone plays in the work-of-fracture method for measuring the fracture energy of concrete or other quasibrittle materials is analyzed.
Abstract: The role that plastic-frictional energy dissipation in the fracture process zone plays in the work of-fracture method for measuring the fracture energy of concrete or other quasibrittle materials is analyzed, and a possible improvement of this method is proposed. It is shown that by measuring the unloading compliance at a sufficient number of states on the post-peak descending load-deflection curve, it is possible to calculate the pure fracture energy, representing the energy dissipated by the fracture process alone. However, this value of fracture energy is pertinent only if the material model (constitutive law and fracture law) used in structural analysis takes into account separately the fracture-damage deformations and the plastic-frictional deformations. Otherwise, one must use the conventional fracture energy, which includes plastic-frictional energy dissipation. Either type of fracture energy should properly be determined by extrapolation to infinite specimen size. Further, it is shown that the unloading compliancies to be used in the calculation of the pure fracture energy can be corrected to approximately eliminate the time-dependent effects (material viscoelasticity) and reverse plasticity. Finally, it is proposed to improve the work-of-fracture method by averaging the work done by fracture over only a central portion of the ligament. However, experiments are needed to check whether the specimen size required for this improved method would not be impracticably large.
TL;DR: In this article, the average fracture spacing is estimated from an analytical solution based on observed borehole-fracture intersections and observed fracture porosity; the only data required are the dimensions of the core or imaged borehole and the total height of all sampled fractures.
Abstract: Knowledge of the spacing of fractures in reservoir rocks (i.e., the distance between parallel fractures in a subsurface joint set) can lead to a better understanding of the production characteristics of a reservoir and serve to quantify the relative degree of deformation in subsurface rocks. In this paper, I present a new method for estimating the spacing of subsurface fractures; this new method is easy to use from the standpoint of both data collection and data analysis. The average fracture spacing method can be applied with boreholes of any orientation relative to a fracture set. The method is especially powerful when it is used for the relatively common case of a borehole nearly parallel to a fracture set (e.g., vertical borehole intersecting vertical fractures). Average fracture spacing is estimated from an analytical solution based on observed borehole-fracture intersections and observed fracture porosity; the only data required are the dimensions of the core (or imaged borehole) and the total height of all sampled fractures. Because the likelihood of intersecting fractures increases when a well is deviated perpendicular to the fractures of a set, fracture reservoirs commonly are candidates for deviated boreholes. An informed decision on borehole deviation requires predicting the fracture intersection frequency as a function of both deviation magnitude and direction. A new method, based on probabilities of borehole-fracture intersections, uses spacing and height data from subsurface joint-like fractures and the borehole diameter to predict fracture intersection frequencies for all possible well deviations. Fracture intersection frequency solutions are presented with respect to a conventional geographic reference frame, thus simplifying even the most complex three-dimentional situations.