Fracture Propagation

This paper deals with inhomogeneous shearing deformation of an in"nite rubber-like slab under a temperature di!erence across its thickness. The deformation is analyzed within the context of "nite thermoelasticity with entropic origin for the stress. The isothermal strain energy functions of Mooney and of Yeoh are generalized by incorporating them into the thermoelastic model. The energy balance equation, which is decoupled from the linear momentum balance equations, is solved for the temperature "eld using the Fourier's law of heat conduction. The derived linear temperature "eld and the equations of the thermoelastic model are inserted into the linear momentum balance equations, thus yielding an ordinary di!erential equation for the shear strain. The shear strain, the degree of inhomogeneity in the shear strain, the stress "eld, and the principal stresses are then determined using a "nite di!erence method. The Mooney slab undergoes markedly greater shear strain near the colder boundary, thus exhibiting a boundary layer-like structure at higher temperature di!erences across the thickness. However, the Yeoh slab exhibits a relatively smaller variation of the shear strain even at the highest temperature di!erence. This di!erence in the behavior of the two slabs is attributed to the shear sti!ening of the Yeoh slab, which counteracts the formation of a boundary layer-like structure. Both slabs experience constant shear stresses across the thickness, whereas they experience much greater normal stress di!erences varying across the thickness. The values of the major principal stress turn out to be close to those of the "rst normal stress di!erence. The presence of a large normal stress di!erence compared with a relatively smaller shear stress in the slabs creates the possibility for Mode I type fracture propagation. (E. Bilgili). these materials when subjected to temperature gradients and "nite deformations. Rubber-like materials show non-linear stress}strain behavior, exhibit large deformation even under small loads, and have material parameters dependent on temperature . The coupling between the deformation and temperature increases the complexity of the non-linear equations that arise in "nite deformation of rubber-like materials.

Calving of icebergs is an important component of mass loss from the polar ice sheets and glaciers in many parts of the world. Calving rates can increase dramatically in response to increases in velocity and/or retreat of the glacier margin, with important implications for sea level change. Despite their importance, calving and related dynamic processes are poorly represented in the current generation of ice sheet models. This is largely because understanding the 'calving problem' involves several other long-standing problems in glaciology, combined with the difficulties and dangers of field data collection. In this paper, we systematically review different aspects of the calving problem, and outline a new framework for representing calving processes in ice sheet models. We define a hierarchy of calving processes, to distinguish those that exert a fundamental control on the position of the ice margin from more localised processes responsible for individual calving events. The first-order control on calving is the strain rate arising from spatial variations in velocity (particularly sliding speed), which determines the location and depth of surface crevasses. Superimposed on this first-order process are second-order processes that can further erode the ice margin. These include: fracture propagation in response to local stress imbalances in the immediate vicinity of the glacier front; undercutting of the glacier terminus by melting at or below the waterline; and bending at the junction between grounded and buoyant parts of an ice tongue. Calving of projecting, submerged 'ice feet' can be regarded as a third-order process, because it is paced by first- or second-order calving above the waterline. First-order calving can be represented in glacier models using a calving criterion based on crevasse depth, which is a function of longitudinal strain rate. Modelling changes in terminus position and calving rates thus reduces to the problem of determining the ice geometry and velocity distribution. Realistic solutions to the problem of modelling ice flow therefore depend critically on an appropriate choice of sliding law. Models that assume that basal velocities are controlled by basal drag can replicate much of the observed behaviour of calving glaciers with grounded termini, but an important limitation is that they cannot be used to model floating glacier termini or ice shelves. Alternative sliding laws that parameterise drag from the glacier margins provide more flexible and robust ways of representing calving in ice sheet models. Such models can explain a remarkable range of observed phenomena within a simple, unifying framework, including: downglacier increases in velocity and strain rates where basal and/or lateral drag diminishes; flow acceleration in response to thinning through time; the tendency for glaciers to stabilise at 'pinning points' in relatively shallow water or fjord narrowings; the constraints on ice shelf stability; and the contrasts in calving rates between tidewater and freshwater calving glaciers. Many unresolved issues remain, however, including the role played by the removal of backstress in the acceleration of retreating calving glaciers, and the controls on melting at and below the waterline.

Hydraulic fracture propagation is greatly influenced by mode-II fracture toughness since this is one of the factors which determine whether a fracture diverts. Direct measurement of rock fracture toughness is constrained by high cost, limited number of available cores and long turn around time. Therefore, to overcome these constrains, it is necessary to develop an effective mode-II fracture toughness test which can be used in a prediction analysis for deep rock formations. Consequently, a mode-II fracture toughness test system was designed for rocks using the straight-notched Brazilian disc (SNBD) test methodology. In the experiment, this system was used to test 20 rock samples from the WG oilfield. This enabled a fracture toughness prediction model to be established, based on an analysis of the test data. H341 acoustic, density and gamma-ray logging data were used to predict horizontal stresses and rock tensile strength. When combined with the mode-II fracture toughness prediction model, continuous values were predicted, which were successfully confirmed by field fracturing practices. It was confirmed, therefore, that this successful method met the need of providing continuous fracture toughness data during field fracturing operations.

1] Snow avalanches are a major natural hazard, endangering human life and infrastructure in mountainous areas throughout the world. In many countries with seasonally snow-covered mountains, avalanche-forecasting services reliably warn the public by issuing occurrence probabilities for a certain region. However, at present, a single avalanche event cannot be predicted in time and space. Much about the release process remains unknown, mainly because of the highly variable, layered character of the snowpack, a highly porous material that exists close to its melting point. The complex interaction between terrain, snowpack, and meteorological conditions leading to avalanche release is commonly described as avalanche formation. It is relevant to hazard mapping and essential to short-term forecasting, which involves weighting many contributory factors. Alternatively, the release process can be studied and modeled. This approach relies heavily on snow mechanics and snow properties, including texture. While the effect of meteorological conditions or changes on the deformational behavior of snow is known in qualitative or semiquantitative manner, the knowledge of the quantitative relation between snow texture and mechanical proper-ties is limited, but promising developments are under way. Fracture mechanical models have been applied to explain the fracture propagation, and micromechanical models including the two competing processes (damage and sintering) have been applied to explain snow failure. There are knowledge gaps between the sequence of processes that lead to the release of the snow slab: snow deformation and failure, damage accumulation, fracture initiation, and fracture propagation. Simultaneously, the spatial variability that affects damage, fracture initiation, and fracture propagation has to be considered. This review focuses on dry snow slab avalanches and shows that dealing with a highly porous media close to its melting point and processes covering several orders of scale, from the size of a bond between snow grains to the size of a mountain slope, will continue to be very challenging.

This paper presents milestones in the history of Fracture Mechanics (F.M.) as a tool for knowing and understanding future developments in the field. It concerns in particular lapideous materials as rocks and unreinforced concrete, which have been investigated and tested less than metals. This chapter in the science of mechanics begins with the 'energetic' approach of Alan Arnold GRIFFITH (1920) about fracture propagation and continues later on with cohesive models (A.HILLERBORG, 1976). The Griffith approach represents a new concept based on a material's discontinuity, rather than continuity, before fracture. This way allows us to understand the size effect (pointed out by R.H. LEICESTER in 1973) and snap back phenomena in brittle structural collapses.

In this study, various types of drop-weight tear test (DWTT) were conducted on a high-toughness line-pipe steel in order to analyze abnormal fracture appearance occurring in the region impacted by a hammer. A pressed notch or a chevron notch was introduced into DWTT specimens, some of which had a back slot designed to decrease the inverse fracture area. After the DWTT, percent shear area, area of inverse fracture surface, and hardness and work hardening exponent of the hammer-impacted region were measured. The results indicated that the shear area of the pressed-notch DWTT specimens was larger than that of chevron-notch DWTT specimens. In the hammer-impacted region of all the DWTT specimens, abnormal inverse fracture having a cleavage fracture mode appeared, and its fracture area was correlated well with hardness and work hardening exponent measured by an indentation test. The formation of this inverse cleavage fracture raised the fracture propagation transition temperature (FPTT) by decreasing the shear area measured in accordance of the API 5L3 specification, which was confirmed by relating to the Charpy impact test data of pre-strained steel specimens. Thus, it was desirable to exclude the inverse fracture formed in the hammer-impacted region when calculating percent shear area of DWTT because compressive pre-strain induced by work hardening did not exist in actual applications of line-pipe steels.

Hydraulic fracturing is a key technology for the development of unconventional resources such as shale gas. Due to the existence of numerous bedding planes, shale reservoirs can be considered typical anisotropic materials. In anisotropic shale reservoirs, the complex hydraulic fracture network (HFN) formed by the interaction of hydraulic fracture (HF) and bedding plane (BP) is the key to fracturing treatment. In this paper, considering the anisotropic angle, stress state and injection rate, a series of hydraulic fracturing experiments were conducted to investigate the effect of anisotropic characteristics of shale reservoirs on HFN formation. The results showed that the breakdown pressure increased first and then decreased when the anisotropic angle changed at 0 •-90 • , while the circumferential displacement had the opposite trend with a small difference. When θ = 0 • , fracturing efficiency of shale specimens was much higher than that under other operating conditions. When θ ≤ 15 • , the bedding-plane mode is ubiquitous in all shale reservoirs. While θ ranged from 30 •-45 • , a comprehensive propagation pattern of bedding-plane and crossing is presented. When θ ≥ 60 • , the HFN pattern changes from comprehensive mode to crossing mode. The propagation pattern obtained from physical experiments were verified by theoretical analysis. The closure proportion of the circumferential displacement was the highest when the propagation pattern was the bedding-plane mode (θ ≤ 15 •), following by crossing. The closure proportion was minimum only when the bedding-plane and crossing mode were simultaneously presented in the HFN. The results can provide some basic data for the design in hydraulic fracturing of tight oil/gas reservoirs.

This paper analyses the problem of a hydraulically driven fracture, propagating in an impermeable, linear elastic medium. The fracture is driven by injection of an incompressible, viscous fluid with power-law rheology and behaviour index n50: The opening of the fracture and the internal fluid pressure are related through the elastic singular integral equation, and the flow of fluid inside the crack is modelled using the lubrication theory. Under the additional assumptions of negligible toughness and no lag between the fluid front and the crack tip, the problem is reduced to self-similar form. A solution that describes the crack length evolution, the fracture opening, the net fluid pressure and the fluid flow rate inside the crack is presented. This self-similar solution is obtained by expanding the fracture opening in a series of Gegenbauer polynomials, with the series coefficients calculated using a numerical minimization procedure. The influence of the fluid index n in the crack propagation is also analysed.

This paper analyses the problem of a hydraulically driven fracture, propagating in an impermeable, linear elastic medium. The fracture is driven by injection of an incompressible, viscous fluid with power-law rheology and behaviour index n50: The opening of the fracture and the internal fluid pressure are related through the elastic singular integral equation, and the flow of fluid inside the crack is modelled using the lubrication theory. Under the additional assumptions of negligible toughness and no lag between the fluid front and the crack tip, the problem is reduced to self-similar form. A solution that describes the crack length evolution, the fracture opening, the net fluid pressure and the fluid flow rate inside the crack is presented. This self-similar solution is obtained by expanding the fracture opening in a series of Gegenbauer polynomials, with the series coefficients calculated using a numerical minimization procedure. The influence of the fluid index n in the crack propagation is also analysed.

The thrust of this Project was to obtain laboratory evidence for the field-proven capability of aphron drilling fluids to limit fluid invasion in permeable formations with little permanent formation damage and provide a sound scientific basis for this behavior. The results demonstrate how and to what extent aphron drilling fluids reduce whole mud loss and minimize collateral damage to high-permeability porous media. Now the industry can utilize this technology with greater confidence and, by doing so, recover hydrocarbons more economically.

Researchers and practitioners currently lack a quantitative field test that indicates the propensity of a given slab and weak layer combination to propagate weak layer fracture and failure to an extent that leads to avalanching. We report on the development of such a test and the evaluation of a prototype test method. This test allows researchers to observe propagation and arrest away from the initial weak layer failure by extending the down slope dimension of the small column stability test. Weak layer failure is initiated by cutting the weak layer with a 2 mm thick snow saw either from the upslope or down slope end of the isolated column. Depending on slab and weak layer characteristics, weak layer fracture/failure propagates from the edge of the saw and propagates either to the end of the column, to an indistinct point, or to the vicinity of a fracture through the thickness of the slab. During the winter of 2006, University of Calgary researchers performed over 600 of these tests in the Columbia Mountains of British Columbia, Canada, and the Rocky Mountains in Alberta, Canada. Results of our experiments allow for an evaluation of the relationship between isolated column length and cut length required to initiate propagation in this test. We evaluate the effect of slope angle and cut direction on test results, and propose a standard test column geometry. We relate our results to shear fracture and weak layer collapse theoretical models.

Fracture toughness of a rock/material is important in the design of rock drilling/boring equipment, rock bursting, prediction of rock drilling forces, hydraulic fracturing, wellbore stability and stability of jointed rock masses. A series of fracture toughness tests under mode-I, mode-II and mixed-mode (I±II) loading conditions were conducted on straight-edge notch Brazilian disk (SENBD) specimens in an attempt to develop an empirical failure envelope under both tension-shear and compression-shear conditions. This series of tests is the ®rst of its kind on a naturally weakly-cemented Antler sandstone. Even though there have been published data on arti®cially cemented sandstones, there are no data on mixed-mode fracture toughness of such soft formations. The SENBD specimen con®guration used herein provides consistent failure patterns and development of a failure envelope in the compression-shear zone, as well. Microscopic studies using thin sections of tested and untested specimens were carried out to study the fracture propagation at micro-level. # 1998

Hydraulic fracturing is a common tool to increase the productivity of hydrocarbon reservoirs, which suffer of decreasing hydrocarbon pressure and permeability of gas/oil-bearing sediments. We analyzed a microseismic data set from hydraulic fracture stimulation of the gas field in West Texas. The data were recorded by an array of 8 three-component geophones deployed in a nearby vertical borehole. We used

Sudden and unexpected collapses of underground cavities below the city of Naples (Italy) represent a serious safety hazard. The collapses occur due to the detachment of large blocks from the cavity roofs, walls and pillars, often a long time after the original quarry excavation has been completed. It is recognised that existing discontinuities, e.g., fractures, play an important role in the failure process by inducing local stress-concentrations and reducing the overall material strength. The larger fractures, which ultimately lead to collapse occur through interaction, propagation and coalescence of these discontinuities. This paper presents recent results of experiments carried out on natural, dry specimens of Neapolitan finegrained tuff to investigate the mechanisms involved in sample failure. A better understanding of fracture development and rock bridge behaviour is gained through a combination of AE and photographic monitoring in an experimental program considering samples with artificial pre-existing heterogeneities, which simulate the in situ discontinuities. For a range of rock bridge geometries the mechanisms and timing of different stages of the failure process are identified and characterised. The results show that, in general, a classical description of failure, for samples without artificial flaws or with only a single flaw, is followed: (1) crack closure; (2) linear stress-strain response and crack initiation with stable crack growth; (3) crack damage and unstable crack growth leading to failure. For samples with two artificial pre-existing flaws the third phase is split into two parts and failure of the sample occurs only after both the unstable propagation of external wing cracks and coalescence of the internal cracks in the bridge. In terms of the timing and duration of each phase, it is seen that phases 1 and 2 have little dependence on the flaw configuration but phase 3 seems to depend directly on this. In particular the angle in rock bridge between the inner tips of the pre-existing flaws, b, plays a key role: phase 3 is shorter for b = 120°than for b = 105°. These differences are due to the different modes of coalescence in the rock bridge. For b = 105°the total failure is preceded by bridge rotation, which appears to take longer than the simpler mode of failure for b = 120°. It has only been possible to determine the time ranges of interest using the AE signatures, whilst the photographs allow the fracture geometry evolution to be described. Additionally the frequency character of AE events is investigated and shown to have significant potential for characterisation of AE source types and thus failure processes.

This study investigates snowpack properties associated with skier-triggered dry slab avalanches, with a particular view on snowpack conditions favoring fracture propagation. This was done by analyzing a data set of over 500 snow profiles observed next to skier-triggered slabs (including remotely triggered slab avalanches and whumpfs) and on skier-tested slopes that did not release a slab avalanche. The relation of the snowpack variables with fracture initiation and fracture propagation, both of which are required for skier-triggering, was investigated. Specific snowpack characteristics, including hardness difference and difference in crystal size across the failure layer, associated with skier-triggered dry slab avalanches were identified and the frequency of skier-triggering was determined. In order to assess snowpack variables favouring fracture propagation, variables from failure layers associated with skier-triggered slabs that were not remotely triggered and relatively small were contrasted with snowpack variables from failure layers of remotely triggered slab avalanches, whumpfs and relatively large slab avalanches. The properties of the slab overlying the weak layer, as well as the layer above the weak layer, were found to affect fracture propagation. Stiffer slabs were associated with large avalanches as well as whumpfs and remotely triggered avalanches. Furthermore, a correlation analysis of snowpack variables with the size and width of the investigated slab avalanches further accentuated the importance of these slab properties with regards to fracture propagation.

Fracture is a very complicated phenomenon and its dynamics is not well described up to now by a consistent physical and/or mathematical model. In this paper we synthetically present the main experimental and theoretical results for the peeling of an adhesive tape, i.e. a viscoelastic dissipative system, viewed as a two-dimensional fracture propagation. From recent peeling experiments, using a common adhesive tape, the emergence of hierarchical structures in a broad range of time scales was observed in a definite region of the stick-slip regime, and this is one the indicators commonly used speaking of complex systems.

The previously reported ''Fe-Ti type'' garnet-peridotite is located in the northern part of the well known ultra-high pressure (UHP) area of the Western Gneiss Region (WGR) in Norway. Primary spinel stable up to only 2.0 GPa at 800 C coexists with Caledonian ultra-high pressure (4.0 GPa at 800 C) grt-cpx-opx-ol assemblages in the Svartberget garnet-peridotite. The body is cut by a conjugate set of metasomatic fractures filled dominantly with diamond-bearing garnet-phlogopite-websterite (5.5 GPa at 800 C) and garnetite. Single zircon U-Pb dating suggests metamorphic growth of zircon in the garnetite at 397.2 AE 1.2 Ma, either coinciding or predating an initial phase of leucosomes formation at 397-391 Ma. Field observations, major and trace elements, mineralchemistry, polyphase inclusions including microdiamond, coupled with 87 Sr/ 86 Sr ratios in clinopyroxene and whole rock ranging from 0.73 to 0.74, suggest that the Svartberget garnet-peridotite was infiltrated by melts/fluids from the host-rock gneiss during the Caledonian UHP event. Present observations in the WGR document a regional metamorphic gradient increasing towards the NW, and structures in the field can account for the exhumation of the (U) HP rocks from $2.5 to 3 GPa. Assuming lithostatic pressures the diamond-bearing Svartberget peridotite body must have come from a burial depth of more than 150 km. However, there is a lack of observable structures in the field to explain exhumation from extreme UHP conditions (5.5 GPa or more) to normal HP-UHP conditions (2.5-3 GPa), which are common pressures calculated from eclogites in western parts of the WGR. Because of the regional and mostly coherent metamorphic gradient across the WGR terrain, it is difficult to account for local extreme pressure excursions such as documented from within the Svartberget peridotite. We introduce here a conceptual model to explain the main features of the Svartberget body. During burial and heating, rocks surrounding the peridotite start to melt but surrounding non-molten rocks confine the space and pressure builds up. When pressure is high enough, conjugate brittle shear fractures develop in the peridotite. Melt (or supercritical fluid) that has the same pressure (5.5 GPa) as the surrounding gneiss can flow in as soon as fractures propagate into the peridotite. This supercritical fluid is now highly reactive and metasomatism takes place at UHP conditions along the fractures capturing micro inclusions of diamond while growing. Finally the lithosphere holding the overpressurised gneiss constrained breaks due to formation of large-scale fractures in the crust and decompression melting starts. Modelling using finite-element method (FEM) shows that melting of the gneiss results in pressure variations when gneiss is ten to hundred times weaker than surroundings and peridotite enclave. These pressure variations can be up to several GPa and are qualitatively similar to observations in the field.

For physical phenomena governed by the Biot model of porous-elasticity, a reciprocal relation, similar to the Betti's recoprocal theorem in elasticity, is constructed in Laplace transformed space. Integrating the reciprocal relation enables one to formulate boundary integral equations. The fundamental kernels for the integral equations are solved in closed forms for the case of isotropic material. Numerical implementation of two-dimensional problems includes finite element ideas of discretization and polynomial interpolation, and numerical inversion of a Laplace transform. Practical applications of the method are found in consolidation problems in soils which contain compressible as well as incompressible pore fluids. Also, as a numerical experiment, consolidation of partially saturated soil is simulated and interesting phenomena are observed. The currently developed boundary integral equation method (BIEM) for porous-elasticity may be viewed as an efficient and accurate alternative of existing finite element and finite difference methods. For linear consolidation problems, application of BIEM is always preferred to the other numerical methods whenever possible.

The Cerro Aspero batholith (CAB) (440 km 2 ) is one of many discordant granites emplaced during the Middle to Late Devonian, marking the closure of igneous activity in the southern part of the Sierras Pampeanas de Co Ârdoba, Argentina. The main feature of the CAB is the conspicuous circular shape of some of its plutons and internal structures, which were developed entirely under pressures lower than 2 kb. The aim of this work is to study the processes responsible for the emplacement of these plutons. The CAB is composed of a succession of three major plutons aligned in a NNW±SSE trend that intrude mainly into mylonites corresponding to an Early Paleozoic shear zone. The emplacement of the plutons was controlled by a set of early master fractures, with magma ascent by means of fracture propagation. The space for magma was created by a combination of tectonically created cavities, internal magma-related buoyancy, and heating and thermal fracture of the host rocks. Field and structural evidence suggests that stoping mechanisms were the most effective for the ®nal emplacement of magma. Thermal fracture and stoping were favored by the thermal contrast between granite and host rock and by the magma viscosity as reduced by the presence of¯uorite. The apparent circular shape of the plutons is polygonal in detail and was developed from several linear and curviplanar segments as a result of brittle fracturing of the host rocks, as well as by changes in the stress ®eld, from vertical to horizontal, related to magma arrival at shallow crustal levels. q

1] The 'Propagation Saw Test' (PST) was designed to assess the fracture propagation propensity of weak snowpack layers in relation to snow slab avalanche release. Its predictions were tested against independent field observations of weak layer fracture initiation and slope-scale fracture propagation (e.g., avalanche release). A total of 170 tests were performed at 23 sites. Approximately 76% of tests correctly predicted the observed slope-scale fracture propagation or lack thereof; however, 20% of tests predicted that propagation would not occur at sites that had recently propagated fractures. The predictive accuracy of the dataset improves if only test columns approximately 1.0 m long are selected. Critical fracture energy release rate calculations show that the lowest values are found in snowpacks where fractures initiated but did not propagate. This suggests that physical descriptions of propagation propensity in weak snowpack layers should include a sustainability term. Citation: Gauthier, D., and B. Jamieson (2008), Fracture propagation propensity in relation to snow slab avalanche release: Validating the Propagation Saw Test, Geophys.

This paper considers the problem of plane-strain fluid-driven fracture propagating in an impermeable elastic medium under condition of large toughness or, equivalently, of low fracturing fluid viscosity. We construct an explicit solution for a fracture propagating in the toughness-dominated regime when the energy dissipated in the viscous fluid flow inside the fracture is negligibly small compared to the energy expended in fracturing the solid medium. The next order corrections in viscosity to this limiting solution are then derived, allowing the range of problem parameters corresponding to the toughness-dominated regime to be established. The first-order small viscosity (large toughness) solution is shown to provide an excellent approximation of the solution for the crack length in the wide range of the viscosity parameter. Furthermore, this solution, when combined with the first-order small-toughness solution of Garagash and Detournay [Journal of Applied Mechanics, 2005], provides a simple analytical approximation of the crack length solution in practically the entire range of viscosity (toughness). It is also shown that the established method of asymptotic expansion in small parameter is equally applicable to study other small effects (e.g., fluid inertia) on the otherwise toughness-dominated solution. A solution for the fracture evolution during shut-in (i.e., after fluid injection rate is suddenly stopped) is also obtained. This solution, which corresponds to a slowing fracture evolving towards the toughness-dominated steady state, draws attention to the possibility of substantial fracture growth after fluid injection is ceased especially under conditions when the fracture propagation during injection phase is dominated by viscous dissipation.

1] Late on the night of 26 October 2002, a dike intrusion started suddenly at Mount Etna, producing intense explosive activity and lava effusion on the southern flank. Five to six hours afterward, a long field of eruptive fractures propagated radially along the northeastern flank of the volcano, producing marked variations at the permanent tilt network. The dike propagation velocity was inferred by the associated seismicity. We modeled the temporal evolution of the continuously recorded tilt data, both during the vertical dike propagation on the high south flank on 26 October and during the radial propagation along the northeast flank, between 27 and 28 October. The reproduction of the recorded tilt signal allowed us to describe the geometry and characteristics of the two dikes in greater detail than the previous static inversion. We deduced that the eruption was characterized by an unusual composite mechanism, clearly showing a transition from a nearly pure opening mode displacement to a mechanism characterized by an equally strong normal dip-slip component and a smaller left lateral strike-slip component. In this study we demonstrate the interaction between the final segment of the dike and a preexisting structure that was reactivated in response to the intrusion. We show that tilt and its modeling represent a powerful tool to verify and constrain dike intrusions in detail.

1] We show that the low-pass filtered, peak amplitudes of initial P-and S-wave seismic signals recorded in the vicinity of an occurring earthquake source correlates with the earthquake magnitude and may be used for real-time estimation of the event size in seismic early warning applications. The earthquake size can be therefore estimated using only a couple of seconds of signal from the P-or S-wave onsets, i.e. while the rupture itself is still propagating and rupture dimension is far from complete. We argue that dynamic stress release and/or slip duration on the fault in the very early stage of seismic fracture, scales both with the observed peak amplitude and with the elastic energy available for fracture propagation. The probability that a fracture grows to a larger size should scale with the energy initially available. Citation: Zollo, A., M. Lancieri, and S. Nielsen (2006), Earthquake magnitude estimation from peak amplitudes of very early seismic signals on strong motion records, Geophys. Res. Lett., 33, L23312,

Researchers and practitioners currently lack a quantitative field test that indicates the propensity of a given slab and weak layer combination to propagate weak layer fracture and failure to an extent that leads to avalanching. We report on the development of such a test and the evaluation of a prototype test method. This test allows researchers to observe propagation and arrest away from the initial weak layer failure by extending the down slope dimension of the small column stability test. Weak layer failure is initiated by cutting the weak layer with a 2 mm thick snow saw either from the upslope or down slope end of the isolated column. Depending on slab and weak layer characteristics, weak layer fracture/failure propagates from the edge of the saw and propagates either to the end of the column, to an indistinct point, or to the vicinity of a fracture through the thickness of the slab. During the winter of 2006, University of Calgary researchers performed over 600 of these tests in the Columbia Mountains of British Columbia, Canada, and the Rocky Mountains in Alberta, Canada. Results of our experiments allow for an evaluation of the relationship between isolated column length and cut length required to initiate propagation in this test. In addition, we evaluate the limited slope dependence and cut direction dependence of test results. We show that under certain conditions associated with nearby avalanche activity, a critical cut length emerges that is independent of slope angle; propagation under these conditions arrests only at the end of the isolated column. We discuss these results in terms of both shear fracture and weak layer collapse theoretical models.

During the winters of 2002-2003 and 2003-2004, fractures in weak snowpack layers were recorded with a portable digital high-speed camera in the Columbia Mountains of British Columbia, Canada. Fractures were photographed at 250 frames per second in 21 compression tests, four rutschblock tests, three cantilever beam tests as well as on five skier-tested slopes. Theoretical slab avalanche release models generally assume propagation of a brittle shear fracture in an incompressible weak snowpack layer. However, displacement measurements of markers placed in the snow above the weak layer indicated that slope normal displacement (due to crushing of the weak layer) was directly caused by the fracture in the weak layer and independent of slope angle, whereas the slope parallel displacement following fracture was probably dependent on slope angle. Furthermore, displacement measurements from rows of markers placed in the snow above weak layers resulted in fracture speed measurements ranging from 17 to 26 m/s, in good agreement with the only other published fracture speed measurement known to the authors: 20 m/s.

This paper presents an experimental work aimed at assessing the correlation between fracture toughness (K IC ) and fracture roughness for a series of Westerly granite specimens thermally treated up to 850°C. Mode I fracture toughness as a function of thermal treatment is determined using Cracked Chevron Notched Brazilian Disc specimens. The degree of roughness of the resultant fracture surfaces is analyzed with the aid of a high accuracy, high precision stereo-topometric measurement system. Roughness and toughness values display a negative correlation as a function of temperature. Fracture toughness decreases with increasing temperature due to the gradual opening of grain-grain boundaries in response to thermal stresses. Mode I fractures preferentially follow these weakened grain-grain boundaries, which in addition to the thermal expansion of individual grains, result in rougher failure profiles with increasing temperature. At low temperature, a distinct anisotropy in roughness was observed in all fracture surfaces with higher roughness values perpendicular to the direction of fracture propagation. However, higher treatment temperatures resulted in the homogenization of fracture roughness in all directions. These results confirm the important link among petrofabric analysis, fracture toughness, and fracture roughness in response to thermal treatment.

We describe a novel implicit level set algorithm to locate the free boundary for a propagating hydraulic fracture. A number of characteristics of the governing equations for hydraulic fractures and their coupling present considerable challenges for numerical modeling, namely: the degenerate lubrication equation; the hypersingular elastic integral equation; the indeterminate form of the velocity of the unknown fracture front, which precludes the implementation of established front evolution strategies that require an explicit velocity field; and the computationally prohibitive cost of resolving all the length scales. An implicit algorithm is also necessary for the efficient solution of the stiff evolution equations that involve fully populated matrices associated with the coupled non-local elasticity and degenerate lubrication equations. The implicit level set algorithm that we propose exploits the local tip asymptotic behavior, applicable at the computational length scale, in order to locate the free boundary. Local inversion of this tip asymptotic relation yields the boundary values for the Eikonal equation, whose solution gives the fracture front location as well as the front velocity field. The efficacy of the algorithm is tested by comparing the level set solution to analytic solutions for hydraulic fractures propagating in a number of distinct regimes. The level set algorithm is shown to resolve the free boundary problem with first order accuracy. Further it captures the field variables, such as the fracture width, with the first order accuracy that is consistent with the piecewise constant discretization that is used.

Based on the idea of taking simultaneous advantage of the effects of different types of fibers, new materials called hybrid fiber reinforced concretes have been developed by combining fibers of different geometry and material. In the present paper, the benefits in terms of concrete toughness from a combination of micro- and macrosteel fibers are evaluated under both bending and uniaxial

An investigation of U--Pb isotopic systematics in zircons from mylonitized Henderson Gneiss revealed that selected zircon fractions from the mylonite zone suffered total loss of radiogenic Pb at 460 m.y. To further investigate the relationship between Pb loss, U gain, and grain size reduction associated with increasing strain in the shear zone, we have characterized the chemistry and morphology of zircons in the mylonitic rocks, using both electron microprobe analysis and scanning electron microscopy.

In this paper, a Stable Generalized/eXtended Finite Element Method (SGFEM) is combined with mesh adap-tivity for the robust and computationally efficient simulation of mixed-mode brittle fracture propagation. Both h-refinement around the fracture front and p-enrichment of the analysis domain are used to control discretization errors. A Linear Elastic Fracture Mechanics (LEFM) model based on Grif-fith's criterion is adopted. LEFM scaling relations are used at each fracture propagation step to back calculate SIFs that meet Griffith's criterion. As a result, no iterations are necessary to find loading scaling parameters or fracture size that meet Griffith's criterion. The method is validated against several experimental data sets for mode I and mode I+II fracture propagation problems. Very good agreement between SGFEM and experimental results are observed. These include fracture path, Crack Opening Displacement (COD), and load and fracture length versus COD curves. The computational efficiency of the method is also assessed.

The way that faults transport crustal fluids is important in many fields of earth sciences such 15 as petroleum geology, geothermal research, volcanology, seismology, and hydrogeology. For 16 understanding the permeability evolution and maintenance in a fault zone, its internal 17 structure and associated local stresses and mechanical properties much be known. This 18 follows because the permeability is primarily related to fracture propagation and their linking 19 up into interconnected clusters in the fault zone. Here we show that a fault zone can be 20 regarded as an elastic inclusion with mechanical properties that differ from those of the host 21 rock. As a consequence, the fault zone develops its own local stresses which differ from the 22 associated regional stresses. The local stresses, together with fault-rock heterogeneities and 23 interfaces (discontinuities; fractures, contacts), determine fracture propagation, deflection 24 (along discontinuities/interfaces), and arrest in the fault zone and, thereby, its permeability 25 development. We provide new data on the internal structure of fault zones, in particular the 26 fracture frequency in the damage zone as a function of distance from the fault core. New 27 numerical models show that the local stress field inside a fault zone, modelled as an 28 inclusion, differ significantly from those of the host rock, both as regards the magnitude and 29 the directions of the principal stresses. Also, when the mechanical layering of the damage 30 zone, due to its variation in fracture frequency, is considered, the numerical models show 31 Manuscript Click here to view linked References 2 abrupt changes in local stresses not only between the core and the damage zone but also 32 within the damage zone itself. Abrupt changes in local stresses within the fault zone generate 33 barriers to fracture propagation and contribute to fracture arrest. Also, analytical solutions on 34 the effects of material toughnesses (critical energy release rates) of layers and their interfaces 35

A previously developed lattice model is improved and then applied to simulations of mixed-mode crack propagation in concrete. The concrete meso-structure is simulated by a three-dimensional lattice system connecting nodes which represent the centers of aggregate particles. These nodes are generated randomly according to the given grain size distribution. Only coarse aggregates are taken into account. Three-dimensional Delaunay triangulation is used to determine the lattice connections. The effective cross-section areas of connecting struts are defined by performing a three-dimensional domain tessellation partly similar to Voronoi tessellation. The deformations of each link connecting two adjacent aggregate pieces are defined in the classical manner of Zubelewicz and Bažant in which rigid body kinematics is assumed to characterize the displacement and rotation vectors at the lattice nodes. Each strut connecting adjacent particles can transmit both axial and shear forces. The adopted constitutive law simulates fracture, friction and cohesion at the meso-level. The behavior in tension and shear is made dependent on the transversal confining strain, which is computed assuming a linear displacement field within each tetrahedron of Delaunay triangulation, and neglecting the effect of the particle rotations. A mid-point explicit scheme is used to integrate the governing equations of the problems. General procedures to handle the boundary conditions and to couple the lattice mesh to the usual elastic finite element mesh are also formulated. Numerical simulations of mixed-mode fracture test data are used to demonstrate that the model is capable of accurately predicting complex crack paths and the corresponding load-deflection responses observed in experiments.

This paper presents a new technique that is able to predict ductile fracture propagation occurrences in large metallic structures, by means of an appropriate application of the finite element modelling. This technique takes account of a cohesive zone in the vicinity of the crack tip, where a nodal release technique is implemented. Two parameters, governing the process zone of the material under investigation, have to be determined: the process zone dimension (named ''D distance'') and the critical value of crack tip opening angle (CTOA). CTOA C can be determined through an experimental laboratory procedure two specimen CTOA test (TSCT) that is already known and used by researchers who study fracture propagation on pipelines [Demofonti G, et al. Step-by-step procedure for the two specimen CTOA test. ]. The second parameter required, D distance, is determined minimizing the differences of Finite Element results towards experimental data of an instrumented impact test (drop weight tear test). Some interesting improvements, concerning distinction between the initiation energy and the propagation energy accounted in TSCT procedure, are also discussed, in order to successfully extend its use to both high strength and high toughness steels.

Shear fracture propagation in rock is accompanied by localized microcracking in a process zone surrounding the fracture tip. We investigated the crack microstructures along experimentally formed shear fractures from four granite samples (uniaxial compression tests). Five transects across a macroscopic fracture were inspected optically in transmitted light. Five hundred thirty-two photomicrographs were taken from seven study areas along each transect. We determined length, width, density, and orientation of open cracks and their assignment to intra-, transgranular, or grain-boundary cracks. Crack density decreases with increasing distance to the macroscopic shear fracture and toward the fracture tip. The highest crack densities correlate with the maximum number of acoustic emissions. Most cracks enclose a small angle (0–20°) with the macroscopic shear fracture. Intragranular cracks are more abundant than transgranular and grain-boundary cracks. The number of transgranular cracks increases towards the macroscopic shear fracture, but the number of grain-boundary cracks decreases. The decrease in crack density with increasing distance to the fault is accompanied by a change from strongly preferred crack orientation in the fault core to a random crack distribution away from the fault. Fracture process zone widths range from 2.1±0.8 mm (Ag51r) to 5.6±1.9 mm (Ag18r). The ratio of process zone width to fault length is approximately 0.04–0.07. This observation agrees with observations from natural fault zones. The fracture surface energy ranges from 0.2 to 1.2 J. This corresponds to

We present a tightly controlled and comprehensive set of analytical data for the 250~Ma Siberian flood-basalt province. Consideration of major-and trace-element compositions, along with strontium, lead, and neodymium isotopic compositions, strongly supports earlier Russian subdivision of this magmatism into three magmatic cycles, giving rise to three assemblages of eleven basalt suites in the ascending order lvakinsky-Gudchikhinsky, Khakanchansky-Nadezhdinsky, and Morongovsky-Samoedsky. Geochemical and isotopic discontinuities of varying magnitude characterize most of the boundaries between the eleven recognized basalt suites in the Noril'sk area.

The geometry of postmortem rough fracture surfaces of porous glass ceramics made of sintered glass beads is shown experimentally to be self-affine with an exponent 0:40 0:04, remarkably lower than the ''universal'' value 0:8 frequently measured for many materials. This low value of is similar to that found for sandstone samples of similar microstructure and is also practically independent on the porosity in the range investigated (3% 26%) as well as on the bead diameter d and of the crack growth velocity. In contrast, the roughness amplitude normalized by d increases linearly with while it is still independent, within experimental error, of d and of the crack propagation velocity. An interpretation of this variation is suggested in terms of a transition from transgranular to intergranular fracture propagation with no influence, however, on the exponent .

This paper presents a numerical method, known as Hybrid Lattice Particle Modeling (HLPM), for the study of mode I crack formation and propagation in twodimensional geometry subject to a fixed-grip condition. The HLPM combines the strength of two numerical techniques, a Particle Model (PM) with a Lattice Model (LM), for the simulation of solid subject to dynamic loading, resulting in large deformation and possible fragmentation. A Lennard-Jones-type potential is employed to describe the nonlinear dynamic interaction among macroscopic-size particles. Crack initiation and propagation is investigated for materials with different Young's modulus and tensile strength. It is demonstrated that crack patterns and propagation closely match the anticipated physical behavior of ductile and brittle materials. The outcome of this

1] We analyze the nucleation and propagation of shear cracks along nonplanar, kinked, and branched fault paths corresponding to the configurations used in recent laboratory fracture studies by Rosakis (2003, 2009). The aim is to reproduce numerically those shear rupture experiments and from that provide an insight into processes which are active when a crack, initially propagating in mode II along a straight path, interacts with a bend in the fault or a branching junction. The experiments involved impact loading of thin Homalite-100 (a photoelastic polymer) plates, which had been cut along bent or branched paths and weakly glued back together everywhere except along a starter notch near the impact site. Strain gage recordings and high-speed photography of isochromatic lines provided characterization of the transient deformation fields associated with the impact and fracture propagation. We found that dynamic explicit 2-D plane-stress finite element analyses with a simple linear slip-weakening description of cohesive and frictional strength of the bonded interfaces can reproduce the qualitative rupture behavior past the bend and branch junctions in most cases and reproduce the principal features revealed by the photographs of dynamic isochromatic line patterns. The presence of a kink or branch can cause an abrupt change in rupture propagation velocity. Additionally, the finite element results allow comparison between total slip accumulated along the main and inclined fault segments. We found that slip along inclined faults can be substantially less than slip along the main fault, and the amount depends on the branch angle and kink or branch configuration. (2009), Finite element simulations of dynamic shear rupture experiments and dynamic path selection along kinked and branched faults,

The focus of this paper is on constructing the solution for a semi-infinite hydraulic crack for arbitrary toughness, which accounts for the presence of a lag of a priori unknown length between the fluid front and the crack tip. First, we formulate the governing equations for a semi-infinite fluid-driven fracture propagating steadily in an impermeable linear elastic medium. Then, since the pressure in the lag zone is known, we suggest a new inversion of the integral equation from elasticity theory to express the opening in terms of the pressure. We then calculate explicitly the contribution to the opening from the loading in the lag zone, and reformulate the problem over the fluid-filled portion of the crack. The asymptotic forms of the solution near and away from the tip are then discussed. It is shown that the solution is not only consistent with the square root singularity of linear elastic fracture mechanics, but that its asymptotic behavior at infinity is actually given by the singular solution of a semi-infinite hydraulic fracture constructed on the assumption that the fluid flows to the tip of the fracture and that the solid has zero toughness. Further, the asymptotic solution for large dimensionless toughness is derived, including the explicit dependence of the solution on the toughness. The intermediate part of the solution (in the region where the solution evolves from the near tip to the far from the tip asymptote) of the problem in the general case is obtained numerically and relevant results are discussed, including the universal relation between the fluid lag and the toughness.

Hydraulic fracturing is essential for producing gas and oil at an economic rate from low permeability sands. Most fracturing treatments use water and polymers with a gelling agent as a fracturing fluid. The water is held in the small pore spaces by capillary pressure and is not recovered when drawdown pressures are low. The un-recovered water leaves a water saturated zone around the fracture face that stops the flow of gas into the fracture. This is a particularly acute problem in low permeability formations where capillary pressures are high. Depletion (lower reservoir pressures) causes a limitation on the drawdown pressure that can be applied.