Crack Aperture Research Articles

Anisotropy of elastic wave velocities in deformed shales: Part 1 — Experimental results

Elastic wave velocity measurements in the laboratory are used to assess the evolution of the microstructure of shales under triaxial stresses, which are representative of in situ conditions. Microstructural parameters such as crack aperture are of primary importance when permeability is a concern. The purpose of these experiments is to understand the micromechanical behavior of the Callovo-Oxfordian shale in response to external perturbations. The available experimental setup allows for the continuous, simultaneous measurement of five independent elastic wave velocities and two directions of strain (axial and circumferential), performed on the same cylindrical rock sample during deformation in an axisymmetric triaxial cell. The main results are (1) identification of the complete tensor of elastic moduli of the transversely isotropic shales using elastic wave velocity measurements, (2) assessment of the evolution of these moduli under triaxial loading, and (3) assessment of the evolution of the elastic anisotropy under loading in terms of Thomsen’s parameters. This last outcome allows us to use the anisotropy of the elastic properties of this rock as an indicator of the evolution of its microstructure. In particular, [Formula: see text] in the dry case decreases from 0.5 (ambient pressure) toward 0.37 [Formula: see text], while [Formula: see text] and [Formula: see text] are almost insensitive to pressure. In the wet case, [Formula: see text] decreases from 0.3 (ambient pressure) toward 0.2 [Formula: see text]. Deviatoric stresses have a strong effect on [Formula: see text], [Formula: see text], and [Formula: see text] variations. In this case, [Formula: see text] drops (both for the dry and wet conditions) when failure is approached.

Mineral distribution within polymineralic veins in the Sanbagawa belt, Japan: implications for mass transfer during vein formation

Pelitic schists of the Sanbagawa metamorphic belt contain several types of polymineralic veins that formed during the late stages of exhumation. The vein mineral assemblages are quartz + albite + K-feldspar + chlorite ± calcite (Type I, II) and quartz + albite + calcite (Type III). Type I and II veins contain quartz and albite with stretched-crystal and elongate-blocky textures, respectively. The mineral species within Type I veins vary with compositional bands within the host rocks. Type III veins are characterized by euhedral to subhedral quartz grains with concentric zoning and a homogeneous distribution along the vein length. The vein textures vary depending on the crack aperture during multiple crack-seal events: <0.08 mm for Type I, and 0.5–10 mm for Type III. Type II veins show intermediate features between Type I and III veins in terms of mineral distribution (weak dependence on the host rock composition) and apparent crack aperture (less than 1–15 mm). These observations suggest a transition in the dominant transport mechanism of vein components with increasing crack aperture, from diffusion from host rocks to fluid advection along cracks.

Single Idealized Cracks: A Tool for Understanding Fractured Glass Block Leaching

AbstractWithin the scope of the long term behaviour of the R7T7 glass, which is the French nuclear glass, leaching and its coupling with transport mechanisms is studied. Experiments carried out on a SON 68 glass (inactive R7T7 type glass) model cracks in static basic conditions show a strong coupling between solution transport and glass leaching, depending on crack aperture. Moreover, gravity driven convective transport was evidenced for vertical model cracks, whereas only molecular diffusion was detected for horizontal model cracks under the same alteration conditions. In addition, an original device was developed to study the influence of temperature gradients on alteration kinetics as a convective driving force. These experiments show conclusively that thermally- or gravity-induced convective flow must be taken into account, even if such convective effects have not been established experimentally in neutral condition, which is more realistic condition for geological storage. A modeling, based on a porous geochemical software (HYTEC) accounting for both chemistry and transport, has been successfully applied to describe alteration within simple silicate glass cracks. It will be extended to study SON 68 glass model cracks, and more complex fracture networks.

Efecto del tamaño de probeta y orientación en la resistencia a la tracción y a la tenacidad a la fractura

In this work, an experimental research was conducted to determine size and orientation effects on tension and toughness properties through CTOD-R curves, using standard and miniature specimens taken from a structural steel plate. Compliance function estimation for the miniature size samples through load-displacement curves was considered. Experimental and statistical results showed that size and orientation affect tension and toughness properties. The miniature tension test specimens showed strength values slightly greater than the standard ones but with less ductility. Miniature specimen CTOD-R curves showed sensibility to load changes and measurement method of crack aperture and crack length. Inconsistency in fracture toughness for specimen orientation longitudinal circumferential (LC) regarding size effect was also observed. Short orientations showed less strength and toughness than the other directions.

Coupled modeling of damage growth and permeability variation in brittle rocks

This paper presents a coupled model for anisotropic damage and permeability evolution by using a micro–macro approach. The damage state is represented by a second order tensor. The evolution of damage is determined from a crack propagation criterion. The free enthalpy function of cracked material is obtained by using micromechanical considerations. It is assumed that cracks exhibit normal aperture which is coupled with the crack growth due to asperities of crack faces. By using Darcy’s law for macroscopic fluid flow and assuming laminar flow in microcracks, the overall permeability of the RVE is obtained by a volume averaging procedure taking into account crack aperture in each orientation.

Source mechanism of Vulcanian degassing at Popocatépetl Volcano, Mexico, determined from waveform inversions of very long period signals

The source mechanism of very long period (VLP) signals accompanying volcanic degassing bursts at Popocatépetl is analyzed in the 15–70 s band by minimizing the residual error between data and synthetics calculated for a point source embedded in a homogeneous medium. The waveforms of two eruptions (23 April and 23 May 2000) representative of mild Vulcanian activity are well reproduced by our inversion, which takes into account volcano topography. The source centroid is positioned 1500 m below the western perimeter of the summit crater, and the modeled source is composed of a shallow dipping crack (sill with easterly dip of 10°) intersecting a steeply dipping crack (northeast striking dike dipping 83° northwest), whose surface extension bisects the vent. Both cracks undergo a similar sequence of inflation, deflation, and reinflation, reflecting a cycle of pressurization, depressurization, and repressurization within a time interval of 3–5 min. The largest moment release occurs in the sill, showing a maximum volume change of 500–1000 m3, pressure drop of 3–5 MPa, and amplitude of recovered pressure equal to 1.2 times the amplitude of the pressure drop. In contrast, the maximum volume change in the dike is less (200–300 m3), with a corresponding pressure drop of 1–2 MPa and pressure recovery equal to the pressure drop. Accompanying these volumetric sources are single‐force components with magnitudes of 108 N, consistent with melt advection in response to pressure transients. The source time histories of the volumetric components of the source indicate that significant mass movement starts within the sill and triggers a mass movement response in the dike within a few seconds. Such source behavior is consistent with the opening of a pathway for escape of pent‐up gases from slow pressurization of the sill driven by magma crystallization. The opening of this pathway and associated rapid evacuation of volcanic gases induces the pressure drop. Pressure recovery in the magma filling the sill is driven by diffusion of gases from the resulting supersaturated melt into bubbles. Assuming a penny‐shaped crack at ambient pressure of 40 MPa, the observed pressure and volume variations can be modeled with the following attributes: crack radius (100 m), crack aperture (5 m), bubble number density (1010–1012 m−3), initial bubble radius (10−6 m), final bubble radius (∼10−5 m), and net decrease of gas concentration in the melt (0.01 wt %).

Explicit equations for leak rates through narrow cracks

Explicit equations to describe the leak rate of a single phase fluid through a narrow crack under a low pressure gradient have been developed and are presented. Four distinct flow regimes, which change with crack opening displacement, have been previously identified and are the basis of this model. The fluid flow is governed by the pressure gradient and the tortuosity of the crack, which is particularly important when the opening displacement is small. The equations have been developed by considering the pressure forces created when the fluid flows down an idealized zig-zag channel. The nature of the flow, and hence the governing equations, change as the crack aperture increases. The power of this approach is clearly seen when the flow rates predicted using this model are compared both to the flow rates obtained from computational fluid dynamics analysis and those found by experimentation. The agreement between these sets of data is good, showing that the major effects governing the flow rate have been identified and then accounted for.

A Simple Crack Depth Estimation Method From Backscattering Response

A depth estimation method for a crack on metal surfaces has been studied and a simple estimation formula and measurement method have been proposed. This formula is based on our previous theoretical analysis that the backscattering from a crack causes periodical nulls (dips) as the frequency changes, and the first dip occurs when the depth of the crack becomes nearly one-half the incident wavelength. Dependencies of the crack's aperture and the incident angle have also been studied and considered as our depth estimation parameters. Test measurement has been made to check the validity of our estimation procedure.

Three‐dimensional liquid transport in concrete cracks

AbstractCracks in concrete are measured in 3D by microfocus X‐ray computer tomography. The tomographic images are thresholded matching a characteristic of the measured crack attenuation profile. A methodology is proposed to convert the 3D measured voxel data into a network of parallel plates. The methodology is based on the determination of the aperture map and skeleton of the void space, and the segmentation of the void space in crack segments. The segmentation and network approach allows to study crack aperture and connectivity distributions of the crack. Static invasion percolation and moving front technique are used to analyse liquid flow in cracks. One‐dimensional simulations of transport in a crack with variable crack width exemplify the retardation effect of narrow passages. In 2D, the narrow passages can be by‐passed resulting in preferential flow patterns, where coarse crack zones remain unfilled. Mesh sensitivity in the network approach is studied showing a limited influence of the mesh size on the filling patterns, caused by a change of connectivity when refining the mesh. Comparison of 3D and 2D simulations indicates that flow in 2D crack sections can strongly underestimate possible fluid penetration depths. Finally the network model is validated analysing water uptake in a fractured brick sample. Copyright © 2004 John Wiley &amp; Sons, Ltd.

Influence of cracking on the diffusion properties of cement-based materials: Part I: Influence of continuous cracks on the steady-state regime

The influence of traversing cracks on the steady-state diffusion properties of concrete was studied. The effect of both anisotropic and isotropic crack networks was first theoretically assessed using an analytical approach. To simplify the transport equations, cracks were assumed to be of uniform size and evenly distributed on a one- or two-dimensional grid. Results of the theoretical analysis were then compared to experimental data. Both series of results indicate that cracking can markedly alter the diffusion properties of the material and favor the penetration (or the leaching) of drifting species. A simple method to predict the effect of cracking on the concrete diffusivity is proposed. Predictions are made on the basis of two parameters: the crack density and the mean crack aperture. This method can provide a first estimate of the diffusion properties of severely damaged concrete elements.

Permeability changes in granite with crack growth during immersion in hot water

Permeability tests and observation of induced, as well as inherent, cracks have been carried out to quantitatively explain permeability changes in granite taking place during a weathering test in terms of micro-structure by cracks. To this end, permeability tensors were estimated from observations of crack systems using the Replica Method and of the crack apertures with a scanning electron microscope. The following conclusions were reached: the drastic increase in permeability around an immersion of 1000 d in 90°C water could not be explained by the existence of a percolation threshold because all the specimens were percolative in the sense that the traces of crack tensor were above the critical density for percolation. On the other hand, SEM observation revealed that, with immersion, crack apertures widened and their distribution spread. Permeability estimated using the third (not the first) moment of observed apertures showed the increase in measured permeability well. When evaluating the connectivity parameter λ to give a quantitative accordance between measured and estimated permeability, it had a constant value as low as 0.17, irrespective of the immersion period, in spite of the higher density of micro-cracks than the percolation threshold. It can be said that, in considering the natural three-dimensional crack system, the third moment of physical apertures plays a more important role in predicting the permeability and λ is greatly affected by the spread of crack apertures.

Fluid permeability of deformable fracture networks

We consider the problem of defining the fracture permeability tensor for each grid block in a rock mass from maps of natural fractures. For this purpose we implement a statistical model of cracked rock developed by M. Oda, where the permeability tensor is related to the crack geometry via a volume average of the contribution from each crack in the population. In this model, tectonic stress is implicitly coupled to fluid flow through an assumed relationship between crack aperture and normal stress across the crack. We have included three enhancements to the basic model. (1) A realistic model of crack closure under stress has been added along with the provision to apply tectonic stresses to the fracture system in any orientation. The application of compressive stress results in fracture closure, and consequently, a reduction in permeability. (2) The fracture permeability can be linearly superimposed onto an arbitrary anisotropic matrix permeability. (3) The fracture surfaces are allowed to slide under the application of shear stress, causing fractures to dilate and result in a permeability increase. Through two examples we demonstrate that significant changes in permeability magnitudes and orientations are possible when tectonic stress is applied to fracture systems.

Long-period events, the most characteristic seismicity accompanying the emplacement and extrusion of a lava dome in Galeras Volcano, Colombia, in 1991

Since its reactivation in 1988 the principal eruptions of Galeras Volcano occurred on May 4–9, 1989, July 16, 1992, and January 14, March 23, April 3, April 14 and June 7, 1993. The initial eruption was a phreatic event which clearly marked a new period of activity. A lava dome was extruded within the main crater in October 1991 and subsequently destroyed in an explosive eruption on July 16, 1992. The eruptions that followed were all vulcanian-type explosions. The seismicity accompanying the emplacement, extrusion, and destruction of the lava dome was dominated by a mix of long-period (LP) events and tremor displaying a variety of waveforms. Repetitive LP events with dominant periods in the range 0.2–1 s were observed in October and November 1991 and visually correlated with short energetic pulses of gas venting through a crack bisecting the dome surface. Each LP event was characterized by a weak precursory signal with dominant periods in the range 0.05–0.1 s lasting roughly 7 s. Using the fluid-driven crack model of Chouet (1988, 1992), we infer that two distinct cracks may have acted as sources for the LP and precursor signals. Spectral analyses of the data yield the following parameters for the LP source: crack length, 240–360 m; crack width, 130–150 m; crack aperture, 0.5–3.4 mm; crack stiffness, 100–500; sound speed of fluid, 880 m/s; and excess pressure, 0.01–0.19 MPa. Similar analyses yield the parameters of the precursor source: crack length, 20–30 m; crack width, 15–25 m; crack aperture, 2.3–8.7 mm; crack stiffness, 5–15; sound speed of fluid, 140 m/s; and excess pressure, 0.06–0.15 MPa. Combined with geologic and thermodynamic constraints obtained from field observations, these seismic parameters suggest a gas-release mechanism in which the episodic collapse of a foam layer trapped at the top of the magma column subjacent to the dome releases a slug of pressurized gas which escapes to the surface while dilating a preexisting system of cracks in the dome structure. Accordingly, the fracture observed on the crystallized dome body is the surface extension of the LP-source crack, where LP activity is induced by the rapid emission and expansion of gas flowing through this conduit. The width and aperture of the crack estimated in the model are in good agreement with the length and aperture of the fracture estimated from visual observations. The source parameters of the precursor signal are suggestive of a nozzle-like conduit connecting the LP-source crack to the underlying magma reservoir. Excitation of this conduit segment is attributed to the rapid emission and acceleration of the frothy fluid resulting from the collapse of the foam layer at the top of the reservoir. The calculated periodicity of foam collapse events is in agreement with the observed average rate of thirteen LP events per hour.

The Effect of Crack Geometry on Hydrodynamic Dispersion in Cracked Media

ABSTRACT A theoretical as well as a numerical study has been carried out with special emphasis on developing a basic understanding of how crack geometry influences hydraulic phenomena such as permeability and hydrodynamic dispersion in cracked bodies. The permeability tensor Kij is formulated in terms of length, aperture and orientation of cracks plus one more non-dimensional scalar λ depending on connectivity among cracks. By extending the Robinson's formula, a general expression for λ is given as a function of density and anisotropy of existing cracks. Dispersion tensor Dij con-sists of two different sources. The first comes from the fact that each tracer is forced to move along cracks the directions of which deviate from the mean path. The second comes from non-uniform distribution of hydraulic head throughout a cracked body. The second source has increasing importance not only when crack density is low, but also when crack arrangement is highly anisotropic. The distribution of head becomes extremely non-uniform, especially when overall hydraulic head gradient is parallel to the preferred orientation of cracks. The permeability tensor Kij is isotropic so long as the related crack tensor Nij is isotropic. Dispersion tensor Dij is anisotropic unless the fourth-rank crack tensor Nijkl is isotropic. Accordingly, any crack body characterized by an isotropic permeability tensor is not necessarily isotropic in dispersion.

Application of a lattice-gas numerical algorithm to modelling water transport in fractured porous media

A 2D lattice-gas numerical algorithm was used to simulate liquid infiltration into unsaturated porous media with a parallel sided central crack. The chosen model, the interacting liquid-gas model of Appert and Zaleski, has dynamic properties leading to a phase transition and liquid and gas phases can be simulated by the model. These two phases are used to simulate biphasic flow in porous media. Fourteen numerical experiments of liquid infiltration were carried out which differed in the morphology of the microporous matrix, in the aperture of the central crack and in the amount of liquid supplied. For the same microporous matrix, the infiltration dynamics in the dual media depended upon the ratio between the amount of liquid supplied and the crack aperture. Variations in water storage over time and liquid flow regimes within the cracks are discussed.

A high-pressure technique for determining the microcrack porosities of damaged brittle materials

The microcrack porosity of a damaged brittle material is found by accurately measuring the compressibilities under a hydrostatic pressure to 200 MPa. Crack apertures are sensitive to the stress applied normal to their plane and, as a result, at low confining pressures the bulk of the strain records the response of the progressive closure of these cracks. At higher pressures when much of the microcrack porosity is closed the observed strains are nearly the same as that expected for the solid compounds within the rock. The higher pressure response may then be used to estimate the expected solid strains that are removed from those observed to leave that portion of the strain due to microcrack porosity. This procedure differs from that of other workers who either ignore the portion of the strain due to intrinsic compression or account for it indirectly by taking the derivative of the observed strain curves. The final results may be analyzed in tensor form to show possible anisotropies in microcrack orientations within a given sample. An example of the experiment on a rock sample that was damaged during removal from the earth by drilling yielded a microcrack porosity of 0.79%, which was a substantial fraction of the total porosity near 5%. At 200 MPa, the principal crack strains had magnitudes of 1.86, 2.61, and 3.39 mstrains; the orientation of this last and greatest magnitude strain differing from the vertical direction by approximately 20°. This suggests that the planes of the predominant family of microcracks within the test piece were subhorizontal. This suggests that a portion of the microcracks result from drilling-induced damage and not solely from stress relief of the sample upon removal from the earth.

Aperture of rough cracks.

We analyze the problem of the geometrical aperture between the two faces of a crack described as a self-affine surface. We consider the contact of the two surfaces after a relative rigid-body displacement (translation and/or rotation) of one side of the crack with respect to the opposite one. A number of properties are obtained analytically and illustrated by numerical simulations on generated self-affine surfaces. The results concern the scaling of the average aperture, which is shown to include a very slowly varying correction term (logarithmic with respect to the displacement); this affects severely the dependence of the measured aperture on the displacement. These results are used to analyze experimental data obtained on a granite sample and to estimate the roughness exponent from a global measurement. This estimate is shown to agree with an analysis of the roughness based on profilometry measurements.

Finite Element Study On the Closure of Thermal Microcracks In Feldspar/Quartz-Rocks-Ii. Intra-, Transgranular and Mixed Cracks

SUMMARY The formation of microcracks is studied in a planar composite material using the finite element method. Intraganular (IGC), transgranular (TGC) and mixed-type cracking is modelled in a system containing angular-cornered quartz (QTZ) grains surrounded by feldspar (FSP). Physical rock properties (elastic moduli, seismic velocity) show a gradual increase with increasing confining pressure due to the closure of cracks as expected from experiments only in the case of IGC. the collapse closure of grain-boundary cracks (GBC) and the TGC is documented by a jump in the pressure-dependent rock properties. Strictly parallel aligned flaws should be replaced by preferred oriented ones or by crack populations with different closing pressures to provide a gradual closure curve. the thermal microcracks investigated can be categorized with respect to their closure process quantified in terms of crack length, aperture and aspect ratio versus confining pressure. Major crack types (GBC I, IGC and TGC) close at pressures ranging from 30 to about 70MPa after cooling the composite by 400 °C. For mixed-type cracks (GBC & IGC), the GBC closes at 30MPa before the remaining IGC starts to shorten at 50 MPa. the friction coefficient μ along the re-closed GBC-planes is responsible for whether the IGC closes totally (μ= 0.1) or degenerates into a residual pore located at the grain boundary (μ≥ 0.3). For μ≥ 0.3 significant in situ porosity of QTZ/FSP-rich rocks may be found as deep as 10 km within the crust of the earth. Lowering the friction coefficient residual porosity can disappear at shallower depths (e.g. μ= 0.1 for the mixed type crack results in a closing pressure of 50 MPa corresponding to a depth of about 2 km).

Models of quartz overgrowth and vein formation: Deformation and episodic fluid flow in an ancient subduction zone

Steady state models of overgrowth and vein formation are developed using kinetic data for quartz dissolution and precipitation and estimates of fluid advection, pore‐fluid and grain‐boundary diffusion. Application of these models to overgrowths and veins in the Kodiak accretionary complex suggests that the Kodiak Formation deformed continuously by a grain‐boundary diffusion‐limited mechanism, accompanied by episodic pore fluid diffusion of quartz from the matrix to vertical fluid‐filled fractures near the base of the accretionary wedge. These processes produced two types of syntectonic crystal textures within the Kodiak Formation: overgrowths containing displacement‐controlled fibers, and throughgoing veins composed of face‐controlled elongate blocky quartz crystals. Based on textural observations, displacement‐controlled quartz growth in overgrowths is rate‐limited by either diffusion along a cohesive interface or the rate of matrix strain. The magnitude of elongation recorded by displacement‐controlled crystal growth varies smoothly (elongation of 1 to 3) from the shallowest to the deepest structural levels of the Kodiak Formation, suggesting that the diffusional component of deformation in the accretionary wedge increases with depth. In contrast, face‐controlled quartz growth is largely restricted to Veins within the deepest level, where the cleavage is subhorizontal and deformation involves a component of simple shear, suggesting proximity to a decollement. The face‐controlled quartz veins represent mode I cracks which seal periodically and contain continuous planar solid inclusion bands, cracks which partially seal periodically and contain discontinuous solid inclusion bands, or cracks that remain open and contain euhedral quartz crystals with no solid inclusions. The initial crack aperture, inferred from spacing of inclusion bands, varies from 8 μm in crack seal features to much larger values in euhedral growth veins. Euhedral growth veins remain open throughout their development (105 to 106 years), and crack seal veins develop as a consequence of many crack‐seal events over a 103–106 year period. In both cases, textural evidence suggests that most transport of silica occurs by local pore‐fluid diffusion from matrix to vein. Wall rock inclusion bands suggest that “crack” events and “seal” events each occurred within periods of 102–104 years. A picture emerges of intermittent fluid flow upward from the decollement into a branching hierarchy of vertical fractures in the accretionary wedge during hydrofracturing events, followed by local transport and precipitation of silica causing sealing of the fractures at depth and propagation of pulses of fracture fluid upward.

Permeability of thermally cracked granite

Permeability of granite specimens heated up to 650°C were measured in the laboratory with respect to both confining and pore pressure. An unexpected behavior (permeability decrease) was found in the low temperature range (20–125°C). Permeability variations are interpreted with the help of a theoretical model of porosity. Complementary measurements of porosity and absolute surface area have also been obtained. A discussion in terms of microstructural controlling parameters concludes to a decrease of crack aperture at low temperatures (20–125°C), followed by an increase at higher temperatures (T &gt;125°C).