Showing papers on "Fracture (geology) published in 1994"

Applications of percolation theory

Abstract: Connectivity as the Essential Physics of Disordered Systems Elements of Percolation Theory Characterization of Porous Media Earthquakes, and Fracture and Fault in Patterns in Heterogeneous Rock Single-Phase Flow in Reservoir Rock Hydrodynamic Dispersion and Groundwater Flow in Rock Two-Phase Flow in Porous Media Transport, Reaction, and Deposition in Evolving Porous Media Fractal Diffusion and Reaction Kinetics Vibrations and Density of States of Disordered Materials Structural, Mechanical, and Rheological Properties of Branched Polymers and Gels Morphological and Transport Properties of Composite Media Hopping Conductivity of Semiconductors Percolation in Biological Systems.

Interface Model Applied to Fracture of Masonry Structures

Abstract: The failure of unreinforced masonry structures subjected to lateral loads is dominated, to a large extent, by the fracture of mortar joints as well as the cracking and crushing of masonry units. This can be simulated by means of a finite element approach in which the mortar joints are modeled with interface elements and the masonry units are modeled with smeared crack elements. To this end, a dilatant interface constitutive model capable of simulating the initiation and propagation of interface fracture under combined normal and shear stresses in both tension-shear and compression-shear regions, and capable of simulating the experimentally observed dilatancy was developed in this study. The performance of the interface model in representing the behavior of masonry mortar joints is evaluated with the available experimental results. Furthermore, the failure of unreinforced concrete masonry panels is analyzed with the aforementioned approach. It is concluded that the numerical model is capable of predicting the response of a masonry assemblage based on the response of its basic constituents.

The crack tip region in hydraulic fracturing

Abstract: We present analytical tip region solutions for fracture width and pressure when a power law fluid drives a plane strain fracture in an impermeable linear elastic solid. Our main result is an intermediate asymptotic solution in which the tip region stress is dominated by a singularity which is particular to the hydraulic fracturing problem. Moreover this singularity is weaker than the inverse square root singularity of linear elastic fracture mechanics. We also show how the solution for a semi-infinite crack may be exploited to obtain a useful approximation for the finite case.

Dynamic faulting under rate-dependent friction

Abstract: We discuss the effects of rate-dependent friction on the propagation of seismic rupture on active faults. Several physicists using Burridge and Knopoff's box and spring model of faulting have proposed that fault complexity may arise from the spontaneous development of a self-similar stress distribution on the fault plane. If this model proves to be correct, it has important consequences for the origin of the complexity of seismic sources. In order to test these ideas on a more realistic earthquake model, we developed a new boundary integral equation method for studying rupture propagation along an antiplane fault in the presence of nonlinear rate-dependent friction. We study rupture dynamics of models with single and twin asperities. In our models, asperities are places on the fault with a higher value of prestress. Othewise all fault parameters are homogeneous. We show that for models with such asperities, a slip velocity weakening friction leads to the propagation of supersonic healing phases and to the spontaneous arrest of fracture if the prestress outside the asperities is low enough. For models with asperities, we can also observe narrow slip velocity pulses, qualitatively similar to the so-called Heaton pulses observed in some earthquake accelerograms. We also observe a complex distribution of stress after the rupture that depends on details of the initial distribution of asperities and on the details of the friction law.

Diffusive Disappearance of Immiscible‐Phase Organic Liquids in Fractured Geologic Media

Abstract: In a new conceptual model for immiscible-phase organic liquids in fractured porous media that specifically includes the effect of molecular diffusion on the persistence of organic liquid in fractures, dissolved contaminant mass from the liquid in fractures is lost by diffusion from the fractures into the porous matrix between the fractures. Theoretical calculations for one-dimensional diffusive fluxes from single, parallel-plate fractures using parameter values typical of fractured porous geologic media establishes the concept of immiscible-phase disappearance time, which is the time required for a given volume of immiscible liquid in a specified aperture to disappear following its arrival in the fracture. Nonlithified surficial clayey deposits with matrix porosities ranging from 25 to 70% are extensive across many regions of North America and Europe, and at shallow depth, typically have fractures with apertures in the range of 1 to 100 microns. The common chlorinated solvents such as dichloromethane (DCM), trichloroethene (TCE), and tetrachloroethene (PCE) are expected to completely disappear in these deposits within a few days to weeks. For fractured sedimentary rocks with much lower matrix porosities (5–15%), disappearance times for these solvents are generally less than several years for fracture apertures ranging from 10 to 200 microns typical for shales, siltstones, sandstones, and carbonate rocks. This is sufficient time for the immiscible phase of chlorinated solvent contamination to have disappeared at many industrial sites. This conceptual model has important implications with respect to ground-water monitoring, diagnosis of the nature and degree of contamination, and expectations for ground-water remediation at many contaminated sites. Proposed methods for enhancing immiscible-phase mass removal using hydraulic manipulation, surfactants, or alcohols will be futile where the immiscible phase has disappeared into the clay or rock matrix, and reverse diffusion and desorption will control clean-up time frames. Therefore, prospects for permanent restoration of many DNAPL and LNAPL sites in fractured porous media are more limited than previously thought.

Size effects on tensile fracture properties: a unified explanation based on disorder and fractality of concrete microstructure

Abstract: Tests were carried out using three independent jacks orthogonally disposed, making it possible to apply a purely tensile force, so that the secondary flexural stresses, if kept under control, constitute a degree of error comparable with the values allowed for normal testing apparatus. The method enables a stress versus strain curve to be plotted with the descending (softening) branch up to the point where the cross-section of the tensile specimen breaks away. The principal purpose is to avoid any spurious effect that might provide a fallacious explanation of the recurring size effects on apparent tensile strength and fictitious fracture energy. Once the secondary effects have been excluded, only the disorder and fractality of the concrete microstructure remain to explain such fundamental trends. In the case of tensile strength, the dimensional decrement represents self-similar weakening of the material ligament, due to pores, voids, defects, cracks, aggregates, inclusions, etc. Analogously, in the case of fracture energy, the dimensional increment represents self-similar tortuosity of the fracture surface, as well as self-similar overlapping and distribution of microcracks in the direction orthogonal to that of the forming macrocrack.

Toughness of an interface along a thin ductile layer joining elastic solids

Abstract: The contribution of plastic deformation to the effective work of fracture is computed for a crack lying along one of the interfaces of a thin ductile layer joining two elastic solids. A model is proposed for the joint whose major parameters are the layer thickness, the elastic-plastic properties of material in the layer, and the work of separation and peak separation stress of the local interface fracture process. A symmetric mode I loading of the joint is considered under conditions where the thickness of the layer and the extent of the plastic zone are small compared with the crack length. The crack growth resistance behaviour is computed, with special emphasis on the steady-state work of fracture. The role of the layer thickness in the development of the plasticity contribution to toughness is detailed. Plastic dissipation is fully realized for layers above a certain thickness, characteristic of a plastic zone dimension, and is negligible when the layer is thin relative to this dimension. Othe...

Non-skeletal Determinants of Fractures: The Potential Importance of the Mechanics of Falls

Abstract: Bones break because the forces applied to them exceed their strength. For most non-spine fractures, this force results from a fall. Falls generate at least 10 times the energy necessary to fracture the proximal femur, but only 5%-10% of falls in older white women cause fractures and only 1% cause hip fractures. The mechanics of the fall plays a very important role in whether a fracture will occur and which bone will fracture. This review postulates that orientation of the fall and location of the impact determine the type of fracture, and whether a fracture occurs depends on the energy of the fall (distance to impact and weight of the moving parts) and how much of that energy is absorbed by protective responses, the impact surface and soft tissues over the bone. Recent case-control studies support the view that the mechanics of a fall are the most important determinant of whether it will result in a hip fracture.

The impact of grain boundary character distribution on fracture in polycrystals

Abstract: The importance of structural effects on intergranular fracture is discussed in order to understand, predict and control fracture in polycrystals. The heterogeneity of fracture in a polycrystal has been found to be due to the difference in structure-dependent propensity to intergranular fracture among grain boundaries. The grain boundary character distribution (GBCD) which describes the type and frequency of grain boundaries is shown to be one of important microstructural factors affecting fracture processes and characteristics. A recent prediction of GBCD-controlled toughness and brittle-ductile transition is introduced. The importance of the connectivity of grain boundaries, the so-called grain boundary correlation number, is also discussed. Recent successful achievement of the control of intergranular brittleness is presented as an application of the result of basic research on fracture to the control of intergranular brittleness by grain boundary design and control in advanced materials.

Laboratory measurement of capillary pressure‐saturation relationships in a rock fracture

Abstract: A laboratory technique has been developed to measure the hysteretic relationship between capillary pressure and fluid saturation for a rough-walled rock fracture under different states of normal stress. The technique incorporates a loading system and a uniquely designed capillary barrier to the nonwetting phase which allows for fracture closure and provides excellent hydraulic connection of the wetting phase in the fracture with external pressure control. The method is applied to a single, rough-walled fracture in limestone using oil and water as the nonwetting and wetting phase, respectively. The measured capillary pressure curves were found to be well represented by a Brooks-Corey porous media capillary pressure function. A distinct entry pressure, giving rise to initial nonwetting phase invasion, was observed in each test. It was found that the inferred aperture distributions became less skewed with increased normal load. These aperture distributions were inferred using one of three conceptual models presented for nonwetting phase invasion of a rough-walled fracture under conditions of main drainage.

Non-universal scaling of fracture length and opening displacement

Abstract: THE deformation of the Earth's brittle crust is dominated by the formation and growth of faults in response to tectonic loading. The scaling properties of such systems provide clues to the underlying mechanisms of fault propagation. For example, if fault growth were a self-similar process, described by a scaling law that applies in all locations1, this might imply a universal faulting mechanism governed by either constant fracture toughness or constant yield stress. Universal scaling laws have been proposed1–4, but their general applicability remains the subject of some debate5. In the natural environment, strict scale invariance can apply only between well-defined bounds6, and it is known that the Earth's crust has many distinct length scales—ranging from the grain size of rocks and the thickness of sedimentary layers up to the finite width of the seismogenic crust—each of which may vary from place to place. Here we report the scaling properties of two populations of tensile fractures in the Krafla fissure swarm of northeast Iceland (spanning nearly four orders of magnitude in length and five in displacement), which clearly show that the presence of such length scales dramatically alters the scaling behaviour. Despite the geological homogeneity of the region studied, our data cannot be described by a single scaling law.

Numerical simulation of fracture set formation: A fracture mechanics model consistent with experimental observations

Abstract: A physically based model for the evolution of a single set of planar, parallel fractures subject to a constant remote stress is presented. The model simulates the mechanical interaction between fractures using a recently developed approximation technique for stress analysis in elastic solids with many fractures. A comparison between experimental and numerical results shows that the model can accurately simulate the development of experimentally generated fracture sets. Once the flaw geometry is specified, only one parameter controls the geometric evolution of the fracture set. This parameter, the velocity exponent, relates fracture propagation velocity to stress concentration at the fracture tip. Monte Carlo sensitivity analyses suggest that this parameter also controls the extent to which fracture growth is concentrated within zones or clusters. Similar analyses suggest that the extent of fracture clustering is less sensitive to the flaw density.

Inverse problems in the mechanics of materials : an introduction

Abstract: Elasticity and plasticity fracture and damage conservation laws dynamic fracture inverse problems in vibrations diffraction of elastic waves diffraction of acoustic waves photothermal detection tomography microgravity identification of materials residual stresses. (Part contents).

Two-parameter fracture mechanics: Theory and applications

Abstract: A family of self-similar fields provides the two parameters required to characterize the full range of high- and low-triaxiality crack tip states. The two parameters, J and Q, have distinct roles: J sets the size scale of the process zone over which large stresses and strains develop, while Q scales the near-tip stress distribution relative to a high triaxiality reference stress state. An immediate consequence of the theory is this: it is the toughness values over a range of crack tip constraint that fully characterize the material`s fracture resistance. It is shown that Q provides a common scale for interpreting cleavage fracture and ductile tearing data thus allowing both failure modes to be incorporated in a single toughness locus. The evolution of Q, as plasticity progresses from small scale yielding to fully yielded conditions, has been quantified for several crack geometries and for a wide range of material strain hardening properties. An indicator of the robustness of the J-Q fields is introduced; Q as a field parameter and as a pointwise measure of stress level is discussed.

Particle size, volume fraction and matrix strength effects on fatigue behavior and particle fracture in 2124 aluminum-SiCp composites

Abstract: The effects of particle size, volume fraction and matrix strength on the stress-controlled axial fatigue behavior and the probability of particle fracture were evaluated for 2124 aluminum alloy reinforced with SiC particles. Average particle sizes of 2, 5, 9 and 20/~m and volume fractions of 0.10, 0.20 and 0.35 were examined for four different microstructural conditions. Tensile and yield strengths and fatigue life were substantially higher in the reinforced alloys. Strength and fatigue life increased as reinforcement particle size decreased and volume fraction loading increased. The frequency of particle fracture during crack propagation was found to be dependent on matrix strength, particle size and volume fraction and on maximum crack tip stress intensity. Particle fracture can be rationalized, phenomenologically, by the application of modified process zone models, originally derived for static fracture processes, and weakest link statistics which account for the dependence of matrix yield strength and flow behavior and particle strength on the probability of particle fracture during monotonic fracture and fatigue crack propagation.

A historical review of metamorphic fluid flow

Abstract: Recognition of the importance of fluid flow in the process of metamorphism was an outgrowth of efforts by petrologists over the last 50–60 years to understand the mineralogical evolution of metamorphic rocks. Mineralogical, chemical, and isotopic data are now routinely used to identify where fluid has flowed in metamorphic terranes, to measure the amount of fluid, to constrain the direction of flow relative to temperature and pressure gradients and lithologic contacts, and to determine the age of flow. Fluid may flow through a static, interconnected network of microscopic tubes at grain corners only under special combinations of mineralogy, fluid composition, pressure, and temperature. Fluid flow typically is restricted to hydraulic fractures whose formation and maintenance require dynamic processes such as increasing temperature, active de volatilization reactions, and/or deformation. Hydraulic fracture flow is heterogeneous in both space and time. Metamorphic fluid transport may be driven by density differences between rock and fluid, by density variations in fluid generated from temperature gradients, by deformation, and by surface tension. Metamorphic fluid flow plays a significant role in heat and mass transfer in Earth's crust and in the mechanisms and rates of deformation.

Fracture toughness of compacted cohesive soils using ring test

Abstract: Testing procedures and methods of analysis for determining the fracture toughness of soils using the ring test are described and values of fracture toughness measured for 132 compacted specimens of two cohesive soils are presented. The critical mode I stress‐intensity factor, the critical J integral, and the tensile strength can be determined simultaneously from a single ring‐test specimen. The critical J integral was approximately equal to the energy‐release rate computed from the critical mode I stress‐intensity factor measured for the same specimen. A strong correlation between fracture toughness and ring‐specimen tensile strength was found. Effects of material type, water content, soil‐placement conditions, rate of loading, and specimen size have been studied, and values of fracture toughness measured by bending tests are compared to ring‐test results. Test results show that fracture toughness of cohesive soils is affected significantly by material type and water content at time of fracture. In contra...

Fracture toughness of two phase WC-Co cermets

Abstract: The present analysis is an attempt to show that fracture toughness of cermets based on WC-Co and the like can be predicted with reasonable accuracy from a simple fracture mechanics relationship. The resistance to fracture has been considered to manifest primarily from the plastic deformation of Co phase. The constrained deformation behavior of the ductile Co phase between the rigid WC grains, approximated to the behavior of ideal plastic flow of a ductile layer sandwiched between rigid platens, has been incorporated into the fracture toughness predictions. Reasonable assumptions on in situ flow and fracture behavior of Co phase have been made in such estimations. Comparison of the calculated fracture toughness values with the experimental data of a large number of WC-Co systems of varying microstructural conditions, indicates reasonable agreement.

High performance overlay for rock drilling bits

Abstract: A method to apply a high performance overlay to a metal substrate of a rock bit to render the substrate surfaces of the rock bit more resistant to erosion, corrosion and substrate cracking while performing in an earthen formation is described. The method comprises the steps of bombarding the surfaces with a thermal spray of entrained fine particles of a cermet based composition at a velocity in excess of 3,000 ft/per sec. The resultant coating of the cermet based composition has a tensile bond strength in excess of 20,000 psi that results in an increase of the strain to fracture of the rock bit surface. The hard overlay has a resistance to severe service environments of high strain and shock tolerance as well as a higher load carrying capacity.

Brittle fracture in austenitic steel

Abstract: The fracture mode of austenitic steel may feature a ductile to brittle transition (DBT), depending on alloy composition and temperature. The DBT variation can be explained in terms of the actual deformation structure evolving during cold work and the correlated internal stresses. The crucial features of microstructure causing brittle fracture are found to be the intersections of deformation twins and the total density of free dislocations. To avoid brittle fracture, the stresses of intersecting twins must be screened by dislocations. Manganese and nitrogen promote brittle fracture since they lower the stacking fault energy and thus shift the onset of twinning to low strain levels where the total dislocation density is low. Nickel additions oppose this trend. The results of the microstructural fracture model agree well with experimental results and the model is confirmed by continuum-mechanical considerations.

Ice triaxial deformation and fracture

Abstract: An experimental investigation into the mechanical behaviour of polycrystalline ice in triaxial compression has been conducted using conditions generally favourable to brittle fracture and microcracking. Under triaxial stresses at high strain rate, ice failure occurs by abrupt shear fracturing, generally inclined at about 45° to the maximum principal stress. At −20°C, such failure is suppressed by the imposition of a small confining pressure, allowing a transition to ductile-type flow accompanied by distributed microcracking, but at —40°C shear fracture persists under confinement of up to at least 50 MPa. For low confining pressures (< 10 MPa), brittle strength is strongly pressure-dependent; above this it is pressure-independent. Evidence is presented that suggests this may reflect a change from a fracture process influenced by friction to fracture initiated by localized yielding. Ductile yield strength is found to be little influenced by confining pressure despite the inhibition of cracking that leads to greatly contrasting observed crack densities. Flow conforms to the well-known power law for ice with Q = 69 J mol−1 and n = 4.2 over the temperature range −20° to −4-5° C Under these conditions, microcracking in ice appears to remain remarkably stable and non-interacting.

Modeling of Subsidence and Stress-Dependent Hydraulic Conductivity for Intact and Fractured Porous Media

Abstract: This study investigates the changes in deformation and stress dependent hydraulic conductivities that occur as a result of underground mining in intact and fractured porous media. The intact porous medium is assumed to be comprised of regularly packed spherical grains of uniform size. The variation in grain size or pore space due to the effect of changing intergranular stresses results in a change in rock hydraulic conductivity. A model is developed to describe the sensitivity of hydraulic conductivity to effective stresses through Hertzian contact of spherical grains. The fractured porous medium is approximated as an equivalent fracture network in which a single fracture is idealized as a planar opening having a constant equivalent thickness or aperture. Changes in fracture aperture as a result of changes in elastic deformation control the variation of hydraulic conductivity. A model is presented to illustrate the coupling between strain and hydraulic conductivity. Subsidence induced deformations that result from mining induced changes in hydraulic conductivity in both intact and fractured media. These changes are examined and compared with results from a mining case study.

Mass transfer at fracture intersections: An evaluation of mixing models

Abstract: Models of solute transport in fractured geologic media that are based on the discrete network approach require that a method be adopted for transferring mass through each fracture intersection. The two usual models for mass partitioning between the outflow branches of crossing fractures assume either stream tube routing or complete mixing. A mathematical analysis of two-dimensional, laminar flow through the intersection of two orthogonal fractures with smooth walls is carried out to examine the mixing process. Mixing ratios are expressed in terms of a local Peclet number (Pe = υr/D), where υ is an average fluid velocity within the fracture intersection, r is the radius of the fracture intersection, and D is the diffusion coefficient. As a general observation the concept of complete mixing within a fracture intersection does not properly represent the mass transfer process at any value of the Peclet number. A mixing ratio equivalent to complete mixing may be observed, but only for particular flow geometries and in a limited range of the Peclet number. Stream tube routing models provide a good approximation for Peclet numbers greater than 1; and in some cases this limit may be as low as 10−2. The actual value of the lower limit depends upon the geometry of the bounding streamline that separates the flow into the two outflow fractures, in relation to the fracture through which solute enters the intersection. There is a range in the Peclet number, of roughly 3 orders of magnitude, where the extent of mixing is dependent upon the value of Pe within the intersection.

Macroscopic fracture characteristics of random particle systems

Abstract: This paper deals with determination of macroscopic fracture characteristics of random particle systems, which represents a fundamental but little explored problem of micromechanics of quasibrittle materials. The particle locations are randomly generated and the mechanical properties are characterized by a triangular softening force-displacement diagram for the interparticle links. An efficient algorithm, which is used to repetitively solve large systems, is developed. This algorithm is based on the replacement of stiffness changes by inelastic forces applied as external loads. It makes it possible to calculate the exact displacement increments in each step without iterations and using only the elastic stiffness matrix. The size effect method is used to determine the dependence of the mean macroscopic fracture energy and the mean effective process zone size of two-dimensional particle systems on the basic microscopic characteristics such as the microscopic fracture energy, the dominant inhomogeneity spacing (particle size) and the coefficients of variation of the microstrength and the microductility. Some general trends are revealed and discussed.