Showing papers on "Fracture (geology) published in 1999"

Growth Factor Regulation of Fracture Repair

Abstract: FRACTURE REPAIR CAN BE considered as a biologically optimal process resulting in the restoration of injured skeletal tissue to a state of normal structure and function. Although the process leads to healing in the vast majority of cases, a small but significant proportion of fractures result in delayed union or persistent nonunion. Surgical interventions have been directed toward enhancing the fracture repair process, normalizing the rate of healing, and decreasing the likelihood of nonunion. During fracture repair, a number of growth factors, cytokines, and their cognate receptors are present at elevated levels in and around the fracture site. Many of these proteins are normally expressed in skeletal tissue, and others are released from associated inflammatory cells at the site of injury. The induction of these proteins is regulated both spatially and temporally, suggesting that they play an active role in promoting fracture repair. The following review will summarize the current literature on the roles of the major cytokines and growth factors involved in fracture repair. In addition, the signaling cascades induced by these molecules will be discussed. While many cytokine and growth factor signaling events have not been specifically examined in the context of fracture repair, a large body of literature on signal transduction has emanated from studies on these molecules in embryonic bone development. Given the conserved nature of these molecules and their signaling cascades from Drosophila to humans, and the similarities between the fracture repair process and embryonic bone development, it seems highly probable that these downstream signaling events are conserved in fracture repair. Fracture repair can be envisioned as involving five distinguishable processes, including the immediate response to injury, intramembranous bone formation, chondrogenesis, endochondral bone formation leading to the reestablishment of load bearing function, and bone remodeling. While these processes may be discussed individually, it should be recognized that the first four occur simultaneously during fracture repair and are likely to influence one another. Extensive remodeling of the newly formed bone follows these four concurrent processes and facilitates the reestablishment of the full biomechanical integrity of the bone. A number of investigators have commented on the similarities between the repair process and embryonic bone formation and indeed a number of specific events characteristic of embryonic bone formation are reiterated in fracture repair. This is especially evident as one begins to examine the specifics of local factors regulating fracture repair, specifically those involved in the events of endochondral bone formation. The immediate response to injury from the fracture trauma is the initiating event of the fracture repair process. Fracture trauma involves not only an interruption of skeletal integrity but also a disruption of the normal vascular structures and nutrient flow at the fracture site. This leads to reduce oxygen tension, disruption of the marrow architecture, and results in the infiltration of inflammatory cells, macrophages, and degranulating platelets during formation of a hematoma. While it is likely that the mechanical stresses, changes in oxygen tension, and loss of vascular nutrients at the fracture site may signal some aspects of the healing process, the dominant initiators of fracture repair are most likely the numerous cytokines and growth factors released into the fracture site. To date the majority of research on fracture repair has focused on the actions of a relatively limited number of cytokines including interleukin-1 (IL-1), interleukin-6 (IL-6), tumor necrosis factor alpha, and macrophage colony-stimulating factor as well as the local growth factors fibroblast growth factor (FGF), platelet-derived growth factor (PDGF), transforming growth factor-beta (TGF-b), and the bone morphogenetic proteins (BMPs)-2, -3, -4, and -7. It is interesting to note that the majority of the factors mentioned have well described roles in the formation and patterning of the embryonic skeleton or in the homeostatic

Variations in fracture system geometry and their implications for fluid flow in fractures hydrocarbon reservoirs

Abstract: Studies assembling high quality datasets of fracture systems (joints and faults) from four reservoir analogues are described. These comprise limestones (Ireland), sandstones (Norway and Saudi Arabia) and chalk (Denmark). These are used with existing information from the literature to review the major controls and scaling behaviour of fracture systems expected in reservoir rocks. Lithological layering was found to be important and two end-member fracture systems have been identified. In "stratabound" systems, fractures are confined to single layers, sizes are scale restricted, and spacing is regular. In "non-stratabound systems", fractures show a wide range of sizes (often power-law), are spatially clustered and vertically persistent. In nature, variations between and combinations of these systems exist. These end-member systems have contrasting implications for fluid flow, including the scale of fracture that controls flow and the existence of a representative elementary volume, and thus on appropriate modelling approaches.

Fractography: Observing, Measuring and Interpreting Fracture Surface Topography

Abstract: 1. Introduction to the concepts used in the observation, measurement and interpretation of fracture surface topography 2. Observing, describing and measuring fracture surface topography: some basics using Ketton stone as an example 3. Tilting cracks 4. River line patterns 5. Mirror, mist and hackle: surface roughness, crack velocity and dynamic stress intensity 6. Cleavage of crystalline solids 7. Fracture at interfaces 8. Aspects of ductile fracture 9. Crack dynamic effects 10. Applications of fractography Appendix.

Determination of double-K criterion for crack propagation in quasi-brittle fracture, Part II: Analytical evaluating and practical measuring methods for three-point bending notched beams

Abstract: In this paper, an attempt is made to determine the double-K fracture parameters K Ic ini and K Ic un using three-point bending notched beams. First, based on the knowledge from extensive investigations which showed that the nonlinearity of P-CMOD curve is mainly associated with crack propagation, a linear asymptotic superposition assumption is proposed. Then, the critical effective crack length a is analytically evaluated by inserting the secant compliance c into the formula of LEFM. Furthermore, an analytical result of a fictitious crack with cohesive force in an infinite strip model was obtained. The double-K fracture parameters K Ic ini and K Ic un as well the critical crack tip opening displacement CTODc were analytically determined. The experimental evidence showed that the double-K fracture parameters K Ic ini and K Ic un are size-independent and can be considered as the fracture parameters to describe cracking initiation and unstable fracture in concrete structures. The testing method required to determine K Ic ini and K Ic un is quite simple, without unloading and reloading procedures. So, for performing this test, a closed-loop testing system is not necessary.

Fractures and Fracture Networks

Abstract: Preface. 1. Introduction. 2. Analysis and generation of random objects. 3. Transport and mechanical properties. 4. A single fracture: generation, characterization. 5. Geometry of fracture networks. 6. Elementary transports in single fractures. 7. Elementary transport in fracture networks. Part A: Bond networks. Part B: Networks of three-dimensional discrete fractures. Part C: Fractured porous media. 8. Coupled processes in a single fracture. Index.

Scale Dependency of Hydraulic Conductivity in Heterogeneous Media

Abstract: Various types of sediments and rocks were analyzed for the relationship between hydraulic conductivity (K) and scale of measurement No variations of K with scale were observed for homogeneous media such as quartz-arenites (quartz sandstones). However, hydraulic conductivity increased with scale of measurement in heterogeneous media. The scaling behavior can be described with the equation K = c (V)m, where c is a parameter characteristic of the geological medium that relates to geological variables such as average pore size and pore interconnectivity in porous media, and probably fracture opening and fracture interconnectivity in fractured media. V is the volume of tested material (used as scale measure), and m is the exponent of the relationship (slope of the line on a log-log plot). The value of the exponent depends on the type or types of flow present. Porous flow media have an exponent of 0.5, multiple flow media an exponent between 0.5 and 1.0, and fracture and conduit flow controlled media an exponent of about 1.0. The more dominant fracture/conduit flow is relative to porous flow, the closer the exponent is to 1.0. K increases with scale up to a rock volume after which the aquifer approaches the properties of an equivalent homogeneous medium and K remains constant with scale. This volume (upper bound of the relationship) is related to the degree of heterogeneity in a medium. It is at a much larger scale in karstic media (if encountered at all) than in nonkarstic and more homogeneous media. Both confined and unconfined aquifers exhibit a similar scale dependence.

The element free galerkin method for dynamic propagation of arbitrary 3-d cracks

Abstract: A technique for modelling of arbitrary three-dimensional dynamically propagating cracks in elastic bodies by the Element-Free Galerkin (EFG) method with explicit time integration is described. The meshless character of this approach expedites the description of the evolving discrete model; in contrast to the finite element method no remeshing of the domain is required. The crack surface is defined by a set of triangular elements. Techniques for updating the surface description are reported. The paper concludes with several examples: a simulation of mixed-mode growth of a center crack, mode-I surface-breaking penny-shaped crack, penny-shaped crack growing under mixed-mode conditions in a cube, and a bar with centre through crack. Copyright © 1999 John Wiley & Sons, Ltd.

Dynamic Fracture in Single Crystal Silicon

Abstract: We have measured the velocity of a running crack in brittle single crystal silicon as a function of energy flow to the crack tip. The experiments are designed to permit direct comparison with molecular dynamics simulations; therefore the experiments provide an indirect but sensitive test of interatomic potentials. Performing molecular dynamics simulations of brittle crack motion at the atomic scale we find that experiments and simulations disagree showing that interatomic potentials are not yet well understood.

Fatigue and Fracture

Abstract: COMMITTEE MANDATE Concern for crack initiation and growth under cyclic loading as well as unstable crack propagation and tearing in ship and offshore structures. Due attention shall be paid to practical application and statistical description of fracture control methods in design, fabrication and service. Consideration is to be given to the suitability and uncertainty of physical models. The work shall be coordinated with that of Committee V.2.

Finite element simulation of ring expansion and fragmentation: The capturing of length and time scales through cohesive models of fracture

Abstract: The expanding ring test of Grady and Benson (1983) is taken as a convenient yet challenging validation problem for assessing the fidelity of cohesive models in situations involving ductile dynamical fracture. Attention has been restricted to 1100-0 aluminum samples. Fracture has been modelled by recourse to an irreversible cohesive law embedded into cohesive elements. The finite element model is three-dimensional and fully Lagrangian. In order to limit the extent of deformation-induced distortion, we resort to continuous adaptive remeshing. The cohesive behavior of the material is assumed to be rate independent and, consequently, all rate effects predicted by the calculations are due to inertia and the rate dependency in plastic deformation. The numerical simulations are revealed to be highly predictive of a number of observed features, including: the number of dominant and arrested necks; the fragmentation patterns; the dependence of the number of fragments and the fracture strain on the expansion speed; and the distribution of fragment sizes at fixed expansion speed.

Fracture anisotropy in silicon single crystal

Abstract: In this study the effect of crystallographic orientation on fracture toughness and the fracture path of silicon single crystal was investigated Vickers microhardness indentation was used to introduce cracks along various crystallographic orientations on the (110), (001), and (111) planes The fracture toughness variation was found to follow the symmetry of the indentation axis with no distinct correlation with the elastic constants The observations made suggest that the inclination angle of cleavage planes relative to the indent plane affects the fracture path and toughness significantly Prestraining decreased the hardness and improved the toughness without a modification of fracture path

Extent of power-law scaling for natural fractures in rock

Abstract: New data sets from natural faults and extension fractures exhibit simple power-law scaling across 3.4‐4.9 orders of magnitude, regardless of rock type or movement mode. The data show no evidence of natural gaps or scaling changes. Each data set consists of independent measurements made at different observational scales; a power-law regression to the subset of smaller fractures in each case provides an extrapolation that accurately predicts associated larger fractures. Consequently, data representing a limited range of fracture sizes may be used to characterize a much broader spectrum of fracture sizes.

Molecular-dynamics study of ductile and brittle fracture in model noncrystalline solids

Abstract: Molecular-dynamics simulations of fracture in systems akin to metallic glasses are observed to undergo embrittlement due to a small change in interatomic potential. This change in fracture toughness, however, is not accompanied by a corresponding change in flow stress. Theories of brittle fracture proposed by Freund and Hutchinson indicate that strain rate sensitivity is the controlling physical parameter in these cases. A recent theory of viscoplasticity in this class of solids by Falk and Langer further suggests that the change in strain rate sensitivity corresponds to a change in the susceptibility of local shear transformation zones to applied shear stresses. A simple model of these zones is developed in order to quantify the dependence of this sensitivity on the interparticle potential.

Saturated flow in a single fracture: evaluation of the Reynolds Equation in measured aperture fields

Abstract: Fracture transmissivity and detailed aperture fields are measured in analog fractures specially designed to evaluate the utility of the Reynolds equation. The authors employ a light transmission technique with well-defined accuracy ({approximately}1% error) to measure aperture fields at high spatial resolution ({approximately}0.015 cm). A Hele-Shaw cell is used to confirm the approach by demonstrating agreement between experimental transmissivity, simulated transmissivity on the measured aperture field, and the parallel plate law. In the two rough-walled analog fractures considered, the discrepancy between the experimental and numerical estimates of fracture transmissivity was sufficiently large ({approximately} 22--47%) to exclude numerical and experimental errors (< 2%)as a source. They conclude that the three-dimensional character of the flow field is important for fully describing fluid flow in the two rough-walled fractures considered, and that the approach of depth averaging inherent in the formulation of the Reynolds equation is inadequate. They also explore the effects of spatial resolution, aperture measurement technique, and alternative definitions for link transmissivities in the finite-difference formulation, including some that contain corrections for tortuosity perpendicular to the mean fracture plane and Stokes flow. Various formulations for link transmissivity are shown to converge at high resolution ({approximately} 1/5 the spatial correlation length) in the smoothly varying fracture. At coarser resolutions, the solution becomes increasingly sensitive to definition of link transmissivity and measurement technique. Aperture measurements that integrate over individual grid blocks were less sensitive to measurement scale and definition of link transmissivity than point sampling techniques.

Experimental studies of water seepage and intermittent flow in unsaturated, rough‐walled fractures

Abstract: Flow visualization experiments were conducted on a transparent replica of a natural, rough-walled rock fracture from the Stripa Mine, Sweden, for inlet conditions of constant pressure and flow rate over a range of angles of inclination. The experiments demonstrated that infiltrating water proceeds through unsaturated rock fractures along nonuniform, localized preferential flow paths. Even though constant inlet conditions were maintained, pervasive unsteady or intermittent flow was also observed in these experiments, where portions of the flow channel underwent cycles of snapping and reforming. Experiments conducted on parallel plates with a sequence of apertures progressing from small to large to small reproduced intermittent flow. Measurements of the frequency of intermittent flow events and the volume of water metered between events were obtained from the fracture replica and parallel plate experiments and related to the Bond and capillary numbers to generalize the results. The frequency data from the fracture replica experiments did not follow the same trend as the data from the parallel plate experiments for similar Bond and capillary numbers, but the volume of water metered data was consistent in these experiments.

Electrostatically actuated failure of microfabricated polysilicon fracture mechanics specimens

Abstract: Polysilicon fracture mechanics specimens have been fabricated using standard microelectromechanical systems (MEMS) processing techniques, and thus have characteristic dimensions comparable with typical MEMS devices. These specimens are fully integrated with simultaneously fabricated electrostatic actuators which are capable of providing sufficient force to ensure catastrophic crack propagation from blunt notches produced using micromachining. Thus, the entire fracture experiment takes place on–chip, without any external loading source. Fracture has been initiated using both monotonic and cyclic resonance loading. A reduction in the nominal toughness under cyclic loading is attributed to subcritical growth of sharp cracks from the micromachined notches in the fracture mechanics specimens. Fatigue fracture has been observed in specimens subjected to as many as 10 9 cycles, and environmental corrosion is implicated in at least some aspects of the fatigue.

Transport of reactive tracers in rock fractures

Abstract: In this thesis, fluid flow and solute transport in heterogeneous aquifers and particularly in frac-tured rock have been investigated using Lagrangian Stochastic Advective-Reaction (LaSAR) framework. The heterogeneity of the aquifer structure or fracture configuration, as well as the various reaction/retention processes have been considered in the modelling approach. Advection and retention processes are considered to be the dominant transport processes. Monte-Carlo simulation results for transport of nonreactive tracers in 2D generic heterogeneous aquifers indicate that the travel time τ can be well approximated by a lognormal distribution up to a relative high degree of heterogeneity of the aquifers. Comparison between the Monte-Carlo simulation results and the results of first-order approximation reveals that the analytical solutions of the statistical moments of τ are valid only when the variability of the aquifer properties is small. For reactive tracers, Monte-Carlo simulations have been conducted by accounting for spatial variability of both hydraulic conductivity and one sorption parameter simultaneously. The simulation results indicate that the reaction flow path μ is a nonlinear function of distance for shorter distance, linear function for longer distance, and also that μ and τ are well correlated over the considered parameter range. The parameter β, which is purely determined by the flow condi-tions, quantifies the hydrodynamic control of retention processes for transport of tracers in frac-tures. Numerical simulations have been performed to study the statistical properties of the pa-rameter β, travel time τ and flow rate Q in a single heterogeneous fracture and in a sequence of fractures. The results of Monte-Carlo simulations indicate that the parameter β and τ are corre-lated with a power-law relationship β ∼ τm. The correlation between β and the flow rate Q have also been studied and an inverse power-law relationship β ∼ Q-m is proposed. The establishment of these relationships provides a link between the parameter β and measurable parameters τ (or Q). The LaSAR approach has been applied for prediction, evaluation and interpretation of the results of a number of tracer tests (TRUE-1, TRUE Block Scale and TRUE Block Scale Continuation) conducted by SKB at the Aspo site for tracer transport in fractures. The breakthrough curves may be predicted reasonably well, provided that the retention parameters, boundary conditions and hydraulic properties of the domain are given. The evaluation of TRUE tests indicates that the retention occurs mainly in the rim zone on site characterization time scales, while on the per-formance assessment time scale, diffusion and sorption in the unaltered rock matrix are likely to become dominant retention mechanisms.

Enhanced damage modelling for fracture and fatigue

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Quantifying diffusive mass transfer in fractured shale bedrock

Abstract: A significant limitation in defining remediation needs at contaminated sites often results from an insufficient understanding of the transport processes that control contaminant migration. The objectives of this research were to help resolve this dilemma by providing an improved understanding of contaminant transport processes in highly structured, heterogeneous subsurface environments that are complicated by fracture flow and matrix diffusion. Our approach involved a unique long-term, steady state natural gradient injection of multiple tracers with different diffusion coefficients (Br, He, Ne) into a fracture zone of a contaminated shale bedrock. The spatial and temporal distribution of the tracers was monitored for 550 days using an array of groundwater sampling wells instrumented within a fast flowing fracture regime and a slow flowing matrix regime. The tracers were transported preferentially along strike-parallel fractures, with a significant portion of the tracer plumes migrating slowly into the bedrock matrix. Movement into the matrix was controlled by concentration gradients established between preferential flow paths and the adjacent rock matrix. Observed differences in tracer mobility into the matrix were found to be a function of their free-water molecular diffusion coefficients. The multiple tracer technique confirmed that matrix diffusion was a significant process that contributed to the overall physical nonequilibrium that controlled contaminant transport in the shale bedrock. The experimental observations were consistent with numerical simulations of the multitracer breakthrough curves using a simple fracture flow model. The simulated results also demonstrated the significance of contaminant diffusion into the bedrock matrix. The multiple tracer technique and ability to monitor the fracture and matrix regimes provided the necessary experimental constraints for the accurate numerical quantification of the diffusive mass transfer process. The experimental and numerical results of the tracer study were also consistent with indigenous contaminant discharge concentrations within the fracture and matrix regimes of the field site. These findings suggest that the secondary source contribution of the bedrock matrix to the total off-site transport of contaminants is relatively large and potentially long-lived.

Fracture of Glass/Poly(vinyl butyral) (Butacite®) Laminates in Biaxial Flexure

Abstract: Glass-polymer laminates designed as safety glazing for automotive and architectural applications demonstrate a rich variety of deformation and failure modes due to the complex stress fields developed on loading and the statistical nature of glass fracture. This complexity in stress development results from the large modulus mismatch between float glass and typical polymers used in safety glazing (E glass /E polymer ≃10 3 -10 5 ). We investigate stress development and the sequence of glass-ply fracture in model two-ply glass-poly(vinyl butyral) (PVB; Butacite®) laminates during loading in biaxial flexure using a circular (upper) punch on three-point (lower) support. The experiment is analyzed using a three-dimensional finite-element model with a viscoelastic constitutive model of plasticized PVB deformation. The stress analysis shows that the maximum biaxial stress shifts location from one glass ply to the other as a function of loading rate and/or temperature and the loading-support dimensions. We identify two primary modes for the initiation of failure associated with changes in maximum stress location: (1) first crack initiated in upper, ring-loaded, glass ply (at the internal glass-polymer interface) and (2) first crack initiated in lower, supported, glass ply (outer glass surface). The sequence of glass ply fracture is seen to depend strongly on loading rate and temperature: high temperatures, relative to the polymer-glass transition temperature, and/or slow loading rates bias first cracking to the upper ply; low temperatures and/or high loading rates promote lower ply first cracking. We present a method to compute the probability of first cracking by combining the finite-element-based stress analysis with a Weibull statistical description of glass fracture. The test protocol and stress analysis presented can form the basis of a laboratory-scale test for laminates and can be readily extended to describe load-bearing capacity of laminate plates used in large-scale commercial applications.

Scale effects on the in-situ tensile strength and fracture of ice. Part II: First-year sea ice at Resolute, N.W.T.

Abstract: A set of lab- to structural-scale (0.5 < L < 80 m) in-situ full thickness (1.8 m) fracture tests were conducted on first-year sea ice at Resolute, N.W.T. using self-similar (plan view) edge-cracked square plates. With a size range of 1:160, the data is used, via size effect analyses, to evaluate the influence of scale effects on the fracture behavior of sea ice over the range 10-1 m (laboratory) to 100 m and to predict the scale effect on tensile strength up to ≈ 1000 m. Details of this large-scale sea ice fracture test program are presented in this paper. The experimental results are presented as well as the fracture modeling of the data. The influence of scale on the ice strength and fracture toughness is dramatic. The applicability of various size effect laws are investigated and criteria for LEFM test sizes are presented. For the thick first-year sea ice tested, the size-independent fracture toughness is of order 250 kPa√m, not the 115 kPa√m that is commonly used. The number of grains spanned by the associated test piece is 200, much larger than the number 15 typically quoted for regular tension-compression testing. The size-independent fracture energy is 15 J/m2, while the requisite LEFM test size for the edge-cracked square plate geometry (for loading durations of less than 600 s and an average grain size of 1.5 cm), is 3 m square. Size effect analyses of sub-ranges of the data show that unless the specimen sizes tested are themselves sufficiently large, the true nature of the scale effect is not revealed, which was a concern raised by Leicester 25 years ago. In the case of the fracture tests reported in this paper, based on the lab-scale and field-scale strength data measured between 0.1 and 3 m and using Bažant’s size effect law, it is possible to accurately predict the tensile strengths for all of the remaining tests, up to and including 80 m.

Experimental and theoretical fracture mechanics applied to Antarctic ice fracture and surface crevassing

Abstract: Recent disintegration of ice shelves on the Antarctic Peninsula has highlighted the need for a better understanding of ice shelf fracture processes generally. In this paper we present a fracture criterion, incorporating new experimental fracture data, coupled with an ice shelf flow model to predict the spatial distribution of surface crevassing on the Filchner-Ronne Ice Shelf. We have developed experiments that have enabled us to quantify, for the first time, quasi-stable crack growth in Antarctic ice core specimens using a fracture initiation toughness, Kinit, for which crack growth commences. The tests cover a full range of near-surface densities, ρ = 560–871 kg m−3 (10.9–75.7 m depth). Results indicate an apparently linear dependence of fracture toughness on porosity such that Kinit = 0.257 ρ-80.7, predicting a zero-porosity toughness of Ko = 155 kPa m1/2. We have used this data to test the applicability to crevassing of a two-dimensional fracture mechanics criterion for the propagation of a small sharp crack in a biaxial stress field. The growth of an initial flaw into a larger crevasse, which involves a purely tensile crack opening, depends on the size of the flaw, the magnitude of Kinit and the nature of the applied stress field. By incorporating the criterion into a stress map of the Filchner-Ronne Ice Shelf derived from a depth-integrated finite element model of the strain-rate field, we have been able to predict regions of potential crevassing. These agree well with satellite imagery provided an initial flaw size is assumed in the range 5–50 cm.