Fracture roughness and gouge distribution of a granite shear band
Jean Schmittbuhl2002, Journal of Geophysical Research
Sign up for access to the world's latest research
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Abstract
1] Localization of deformation during fracture mechanical tests leads to the development of shear bands. We performed triaxial tests using Sidobre granite at four different confining pressures (from 20 to 80 MPa). We compared two sets of tests: one set was stopped immediately after the formation of the shear band; a second one included additional shear deformation. From the analysis of thin sections of these laboratory samples, we characterize the typical microstructures in the shear band (mode I and II cracks, Riedel cracks, cataclastic flow). Statistical properties of rupture surface roughness and gouge grain size reveals scaling invariance. Using a mechanical profiler, the fracture roughness is measured along parallel profiles and shown to be correctly described over up to 3 orders of magnitude by self-affine geometry with a roughness exponent close to z = 0.80. This property is very similar to tensile crack even if local processes are different. The influence of the slip is observed. Fracture surfaces are rougher along the slip direction (z = 0.74) than perpendicular to it (z* = 0.80). The confining pressure is shown to have a weak effect on the fracture roughness. It smoothes the surface: slight increase of the roughness exponent. Gouge particles extracted from the shear band present a power law distribution with an exponent ranging from 1.44 to 1.91. This exponent appears to increase with the shearing displacement and the confining pressure. When a significant shear of the band is combined with a high confining pressure (i.e., impeded dilation of the band), the hallmark of fragmentation is observed for the particle distribution and related to a smoothing of the band boundary.
Related papers
Fracture process zone in granite: a microstructural analysis
International Journal of Earth Sciences, 2001
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
Microfracturing, damage, and failure of brittle granites
Journal of Geophysical Research, 2004
The evolution of stress-induced damage and the eventual brittle failure are experimentally analyzed for Mount Scott granite of Oklahoma. We quantify the damage intensity in two methods and directly compare model predictions and actual damage. The 14 samples of the medium grain-size granite were loaded triaxially at dry conditions, room temperature and under 41MPa confining pressure. Microfractures were mapped in five samples and the majority of them (80%) belong to two groups: tensile microfractures trending subparallel to loading axis, and shear microfractures trending 10º-40º off the loading axis. The tensile microfractures dominate the low stress stage and they remain intragranular with stress increase. The relative density of shear microfractures increases with increasing stresses, and they formed elongated, intergranular zones of coalescing microfractures. We compared two independent values of damage intensity: (1) the macroscopic experimentally measured reduction of the deformation modulus, and (2) the expected reduction of this modulus calculated with several damage models for the density of the mapped microfractures. Our fracture densities data fits best the model of non-interacting cracks of Kachanov (1992).
Shear fracture energy of Westerly granite from post-failure behavior
Journal of Geophysical Research, 1982
Fracturing characteristics of two granites
Rock mechanics, 1975
Fracturing Characteristics o[ Two Granites. Thin sections of two granites with different grain sizes and similar compositions were bonded to plexiglas slides and observed by optical microscopy as the samples were loaded in compression or tension. It was concluded that Griffith Cracks could be one of many weakness planes and were dependent on grain size, recrystallization, and other properties of the granite. Most fractures were intergranular in tension and intragranular in compression. Bruchmerhmale zweier Granite. Diinnschliffe zweier Granite mit verschiedener Korngr6f~e aber ~ihnlicher Zusammensetzung wurden auf Plexiglasbl~ittchen geklebt und unter dem Mikroskop beobachtet, w/ihrend die Proben Druck-und Zugspannungen ausgesetzt wurden. Es wurde erkannt, daf~ Griffith-Spalten eine der vielen Schw~icheebenen sein k6nnren und von Korngr6f~e, Rekristallisation und anderen Eigenschaften der Granite abh~ingen. Die meisten Risse waren intergranular bei Zugspannungen und intragranular bei Druckspannungen. Indices de deux granites. Des coupes minces de deux granites de grain diff6rent mais de composition semblable ont dt4 collies sur du plexiglas et 6tudi6es au microscope polarisant pendant que les 6chantillons ont fits mis sous compression ou tension. La conclusion est que les fissures de Griffith pourraient reprdsenter un des nombreux plans de faiblesse et d4pendent du grain, de la recristallisation et d'autres propri&~s du granite. La plupart des fractures sont intergranulaires sous tension et intragranulaires sous compression.
Shear behaviour of fractured rock as a function of size and shear displacement
Geomechanics and Geoengineering, 2014
This paper presents laboratory results regarding the shear behaviour of an artificial tensile fracture generated in granite. We used a direct shear rig to test fractures of different sizes (from 100 mm to 200 mm) under various shear displacements up to 20 mm and cyclic shear stresses with constant normal stress of 10 MPa. To determine the evolution of surface damage and aperture during shear, cyclic loading was performed at designated shear displacements. These changes in the surfaces topography were measured with a laser profilometer 'non-contact surface profile measurement system'. In addition, changes were also measured directly by using pressure-sensitive film.
Fragmentation of Mansurov granite under quasi-static compression.PDF
The fragmentation statistics was studied in the quasi-static compression experiments conducted on prismatic specimens of Mansurov granite. The statistical analysis showed that the cumulative fragment mass distribution for granite specimens is well described by a power law function, but the fragment number-sieve size distribution deviates from the power law in the range of are equal to about 1 mm. In order to explain this fact, we investigated the structure of fractured material (Computed Tomography and microstructures study in thin sections). A sharp increase the number of grains in the range of size from to 0.5 mm to 1 mm and a change in the fragment shape (from splinter to oval) allow us to suppose that there is an addition fracture mechanism associated with disintegration of feldspar and amphiboles grains.
Dynamic fragmentation of granite for impact energies of 6–28J
Engineering Fracture Mechanics, 2012
The dynamic fragmentation of granite at impact energies of 6-28 J is examined in this paper. Results indicate that more dense materials, or those with a higher quartz content, produce less fractured mass, and have larger dominant fragment sizes and smaller aspect ratios in their fragment probability distributions. Values of the peaks in fragment size distributions are in agreement with theoretical predictions. Examination of the fracture surfaces reveals information concerning transgranular cracking, crack bifurcation mechanisms and evidence of comminution of sub-micron K-feldspar and plagioclase fragments. Fractal dimensions of the cumulative distribution of fragment sizes were '2, indicating that comminution was a dominant fragmentation mechanism in these tests. Peaks in the probability distributions of sub-micron fragments on fracture surfaces reveal a limit of coherent fragments of approximately 0.60 lm for plagioclase and K-feldspar. The smallest fragments found on the surfaces were approximately 0.30 lm and this is considered to be the comminution limit for these materials.
Micromechanical model for the rate dependence of the fracture toughness anisotropy of Barre granite
International Journal of Rock Mechanics and Mining Sciences, 2013
Laboratory measurements of mode-I fracture toughness of Barre granite under a wide range of loading rates were carried out with an MTS machine and a split Hopkinson pressure bar (SHPB) system using the notched semi-circular bend (NSCB) specimen. The fracture toughness anisotropy was found to decrease with the increase of the loading rate. A micromechanics model is utilized in this work to understand this experimental observation, invoking crack-microcrack interactions. Two micromechanics models are constructed based on the microstructural investigation of Barre granite samples using the thin-section method. In both models, the rock material is assumed to be homogenous and isotropic. The main crack (i.e., the pre-crack in the NSCB specimen) and the closest microcracks are included in the numerical analysis. Numerical results show that stress shielding occurs in the model where the two microcracks form an acute angel with the main crack and the nominal fracture toughness is bigger than the intrinsic one, while stress amplification occurs in the model where the microcrack is collinear to the main crack and the nominal fracture toughness is smaller than the intrinsic one. Assuming that the intrinsic fracture toughness of the rock material has the usual loading rate dependency, we are able to reproduce the decreasing trend of the fracture toughness anisotropy as observed from experiments.
Simulating fracture and friction of Aue granite under confined asymmetric compressive test using clumped particle model
International Journal of Rock Mechanics and Mining Sciences, 2012
Clumped particle model (CPM) Confined asymmetric test (CAT) Discrete element method (DEM) Fracture propagation path Friction behavior of rock Gutenberg-Richter b-value a b s t r a c t Fracture and friction behaviors of Aue granite (Erzgebirge, Germany) under confined asymmetric load are simulated using a clumped particle model. In contrast to conventional circular bonded particle assemblies, clumped particle models consist of groups of neighboring individual particles tied together to mimic unbreakable larger grains of irregular shape (clumps). An optimized clumped model is used for all calculations, which is calibrated by the strength and deformation data from laboratory data of uniaxial and triaxial compression. At a first order approximation, the simulated fracture paths obtained from the clumped particle model match the observed fracture paths from laboratory experiments at various confinements. Under low confinement (o 5 MPa), the fracture initiates in mode I from the edge of the asymmetric loading platen and propagates toward the unloaded portion of the granite. In this scenario, tensile cracks dominate in the fracture process zone. Under higher confining pressures (10 and 40 MPa), after nucleus of mode I fracture an inclined rupture path develops and propagates towards the loaded portion of model. Temporal change of the numerically computed Gutenberg-Richter b-values shows low b-values in the fracturing regime and higher b-values during stick-slip and frictional sliding post-failure regime, which are in accordance with the laboratory findings.
Preferred orientations of open microcracks in granite and their relation with anisotropic elasticity
International Journal of Rock Mechanics and Mining Sciences, 2003
In order to study how to deal with open microcracks in rock, anisotropic behaviors of Oshima granite were investigated by carrying out wave velocity tests and uniaxial compression tests, together with observations of microcracks under an optical microscope equipped with a universal stage. Anisotropy in the longitudinal wave velocity V L and secant deformation modulus E 10 at 10% strength is caused by pre-existing open microcracks, not by pre-existing healed microcracks. The structural anisotropy formed by open microcracks, which is quantitatively represented by a second-rank tensor (called crack tensor), is in good agreement with the directional changes of E 10 and V L : The mechanical, as well as structural, anisotropy shows rhombic symmetry with orthogonal symmetry axes in the directions roughly normal to the rift, grain and hardway planes, which are parallel to the major joint sets in the field. Since longitudinal wave velocity changes drastically depending on the density and orientation of open microcracks in granitic rocks, it is suggested that the crack tensor can be determined from non-destructive wave velocity tests. The elastic modulus tensor theoretically formulated in terms of the second-rank crack tensor can be used, as a first-order approximation at least, to describe the anisotropic elasticity of Oshima granite induced by pre-existing open microcracks. It is of particular importance to point out that the micro-scale structure by open microcracks is geometrically similar to the macro-scale structure by joints and faults (scale independent). This finding strongly suggests that some of the conclusions related to open microcracks are applicable to deal with macro-scale cracks in rock masses.
Related papers
Rupture initiation in shear fracture of rocks: An experimental study
Journal of Geophysical Research, 1988
We used a torsional geometry to grow shear ruptures in two fine-grained rock types. The sample has a slot that is loaded to produce a strong mode 3 shear stress concentration. The onset and growth of the damage zone is detected by monitoring the elastic stiffness of the samples. We find that the samples continue to harden after the onset of fracture. This is initially accompanied by oblique tensile cracks forming at the stress concentration. The peak in supported load apparently corresponds to the onset of strain localization, with the development of cross-cutting shear fractures. We attempted to estimate the partitioning of energy dissipation between elastic and frictional components with a fracture mechanics analysis. The elastic energy increases with normal stress, but scatter in the inelastic data does not allow identification of convincing trends. The sample is too small to develop a complete transition to a shear rupture. The geometry of the fractures is used to explain the energy relations as well as other experimental observations existing heterogeneities, such as faults or cavities, which modify mental rock deformation were used, Solnhofen limestone and the stress field and dominate the initial failure development. Westerly granite. Solnhofen limestone is an ultrafine grained
Crack Evolution in Damage Stress Thresholds in Different Minerals of Granite Rock
Rock Mechanics and Rock Engineering, 2019
Crack evolution in a rock depends on the mineralogy, microstructure and fabric of specific rock type. This study aims to investigate how mineralogy and grain shape affect the microcrack initiation and propagation of granite rock, which contains plagioclase, quartz, k-feldspar, biotite and amphibole, during uniaxial compression loading. Physico-mechanical properties and microcrack features such as linear microcrack density (LMD) and microcrack type were investigated. By acoustic emission (AE) measurements, damage stress thresholds were identified. Then, crack characteristics of a fresh sample were compared with the samples that were loaded until damage threshold stresses. The results demonstrate that at an early stage of loading, pre-existing microcracks growth and LMD of intergranular crack increase. In the elastic phase, all microcracks types increase at the same rate. When the loading reaches to the strength limit of the sample, the total LMD reduced, because cracks start to coalesce and form new and large transgranular microcrack. Investigating crack propagation in mineral shows that at first, microcrack generates in biotite and at last in quartz. Plagioclase has the highest LMD and microcracks usually formed within the cleavage plane, but alteration and inclusions of tiny minerals can drastically change the LMD and orientation of microcracks. Biotite can terminate or let the microcrack to pass through the crystal based on the orientation of the microcrack plane and cleavage microcrack within the mineral. Furthermore, crystals with an aspect ratio higher than two have higher LMD. By getting close to the uniaxial compression strength, more microcracks appear close to the grain boundary which increases the circularity of the grain.
Geometric analysis of damaged microcracking in granites
2000
Practically identical samples are tested at the same con®ning pressure and temperature but at dierent deviatoric stress levels. Thin sections are observed using an optical microscope and recorded as images in order to study the crack network evolution. The compound cracks are decomposed into elementary cracks (right segments) with constant orientation and then reassembled in order to determine crack length and cumulated crack length. The results of crack observations are discussed in the light of the mechanisms of crack evolution at microscopic level compared to the stress± strain curves. It results from our observations that mean crack length increases only moderately in comparison with maximal crack length and the number of cracks. Zhao reports similar results (cf. Zhao, Y., 1998. Crack pattern evolution and a fractal damage constitutive model for rock. Int. J. Rock. Mech. Min. Sci. 35 (3), 349±366). The evolution of microcracking can be attributed more to new crack nucleation rather than to growth of the pre-existing cracks.
Shear localization, velocity weakening behavior, and development of cataclastic foliation in experimental granite gouge
Journal of Structural Geology, 2015
Microstructural aspects of room-temperature deformation in experimental Westerly granite gouge were studied by a set of velocity stepping rotary-shear experiments at 25 MPa normal stress. The experiments were terminated at: (a) 44 mm, (b) 79 mm, and (c) 387 mm of sliding, all involving variable-amplitude fluctuations in friction. Microstructural attributes of the gouge were studied using scanning (SEM) and scanning transmission electron microscopy (STEM), image processing, and energy dispersive X-ray (EDX) analyses. The gouge was velocity weakening at sliding distances >10 mm as a core of cataclasites along a through-going shear zone developed within a mantle of less deformed gouge in all experiments. Unlike in experiment (a), the cataclasites in experiments (b) and (c) progressively developed a foliation defined by stacks of shear bands. The individual bands showed an asymmetric particle-size grading normal to shearing direction. These microstructures were subsequently disrupted and reworked by high-angle Riedel shears. While the microstructural evolution affected the effective thickness and frictional strength of the gouge, it did not affect its overall velocity dependence behavior. We suggest that the foliation resulted from competing shear localization and frictional slip hardening and that the velocity dependence of natural fault gouge depends upon compositional as well as microstructural evolution of the gouge.
Shear fracture in sandstone under plane-strain compression
Engineering Fracture Mechanics, 2006
Experiments on Berea sandstone at 5 MPa confinement were conducted to investigate shear banding under planestrain compression. Locations of acoustic emission showed propagation of a shear band during post-peak response. The eventual failure surface consisted of two distinct regions called primary and kinked fractures, with evidence of a process zone at the termination of the primary fracture. Features identified using thin-section microscopy suggested that the primary fracture was formed in shear while the kinks displayed mixed-mode qualities. A linear analysis of a closed crack demonstrated that part of the post-peak response could be explained as shear-crack growth, with Berea sandstone having a mode II fracture toughness of 3 MPa p m.
Fracture morphology and viscous transport
International Journal of Rock Mechanics and Mining Sciences, 2008
The morphology of a fracture in a granite block is sampled using a high resolution profiler providing a 3999 Â 4000 pixel image of the roughness. We checked that a self-affine model is an accurate geometrical model of the fracture morphology on the basis of a spectral analysis. We also estimated the topothesy of the experimental surface to be l r % 2 Â 10 À7 mm and the roughness exponent to be z % 0:78. A finite difference scheme of the Stokes equation with a lubrication approximation was used to model the viscous flow through a fracture aperture defined as the gap between the experimental fracture surface and a flat plane. We finally compare our numerical results to experimental measurements of the flux through the fracture of a glycerol/water mixture (to be at sufficiently low Reynolds number where Stokes equations holds) changing the average aperture of the fracture. The comparison is successful despite a limited resolution of the experimental measurements. Interestingly we show that only long wavelengths of the fracture morphology control the fracture hydraulic conductivity. r
Stable and unstable damage evolution in rocks with implications to fracturing of granite
Geophysical Journal International, 2006
We address the relation between the rock rigidity and crack density by comparing predictions of a viscoelastic damage rheology model to laboratory data that include direct microscopic mapping of cracks. The damage rheology provides a generalization of Hookean elasticity to a non-linear continuum mechanics framework incorporating degradation and recovery of the effective elastic properties, transition from stable to unstable fracturing, and gradual accumulation of irreversible deformation. This approach is based on the assumption that the density of microcracks is uniform over a length scale much larger than the length of a typical crack, yet much smaller than the size of the entire deforming domain. For a system with a sufficiently large number of cracks, one can define a representative volume in which the crack density is uniform and introduce an intensive damage variable for this volume. We tested our viscoelastic damage rheology against sets of laboratory experiments done on Mount Scott granite. Based on fitting the entire stress-strain records the damage variable is constrained, and found to be a linear function of the crack density. An advantage of these sets experiments is that they were preformed with different loading paths and explicitly demonstrated the existence of stable and unstable fracturing regimes. We demonstrate that the viscoelastic damage rheology provides an adequate quantitative description of the brittle rock deformation and simulates both the stable and unstable damage evolution under various loading conditions. Comparison between the presented data analysis of experiments with Mount Scott granite and previous results with Westerly granite and Berea sandstone indicates that granular or porous rocks have lower seismic coupling. This implies that the portion of elastic strain released during a seismic cycle as brittle deformation depends on the lithology of the region. Hence, upper crustal regions with thick sedimentary cover, or fault zones with high degree of damage are expected to undergo a more significant inelastic deformation in the interseismic period compared to 'intact' crystalline rocks.
Geometric analysis of damaged microcracking in granites Franc ß
2000
Practically identical samples are tested at the same con®ning pressure and temperature but at dierent deviatoric stress levels. Thin sections are observed using an optical microscope and recorded as images in order to study the crack network evolution. The compound cracks are decomposed into elementary cracks (right segments) with constant orientation and then reassembled in order to determine crack length and cumulated crack length. The results of crack observations are discussed in the light of the mechanisms of crack evolution at microscopic level compared to the stress± strain curves. It results from our observations that mean crack length increases only moderately in comparison with maximal crack length and the number of cracks. Zhao reports similar results (cf. Zhao, Y., 1998. Crack pattern evolution and a fractal damage constitutive model for rock. Int. J. Rock. Mech. Min. Sci. 35 (3), 349±366). The evolution of microcracking can be attributed more to new crack nucleation ra...
5647-FRACTURING, Acoustic Emission and Numerical Simulation of Granite Under Mode II Loading
Mode II loading of drill core samples of medium-grained granite is conducted using the Punch-Through Shear (PTS-) test. Cylindrical samples with circular notches at both end surfaces are subjected to independent confining pressure and shear loading of the intact portion between the notches. This paper presents results from PTS-testing at confining pressure of 30 MPa, including the pressure dependency of Mode II fracture toughness, K IIC , the resulting fracture pattern, acoustic emission (AE) characteristics and computer simulation. At failure a shear fracture connects the upper and lower notch. Fracture evolution on the macroscopic scale is described. Analysis of AE and micro-structural observations show contribution of both tensile and shear cracks to fracture propagation. AE polarity analysis shows a shift from dominantly tensile cracking to shear cracking during increasing punch loading. This suggests that fracturing in the PTS-test involves mixed-mode fracturing. The fracture initiation and propagation is analysed using the displacement discontinuity code FRACOD 2D. The code simulates the fracture initiation and propagation and acoustic emission of the PTS-test with a fair agreement with the experimental results.
Influence of fracture geometry on shear behavior
International Journal of Rock Mechanics and Mining Sciences, 2000
Laboratory research during the past 10 years has explained many critical links between the geometrical characteristics of fractures and their hydraulic and mechanical behavior. One of the remaining research challenges is to directly link fracture geometry with shear behavior, including behavior in response to changes in normal stress and shear direction. This paper describes results from a series of shear tests performed on identical copies (replicas) of a natural granite fracture. Based on these tests, we developed a method using image processing techniques to identify and quantify damage that occurs during shearing. We ®nd that there is a strong relationship between the fracture's geometry and its mechanical behavior under shear stress and the resulting damage. Using a three-dimensional geostatistical model of the fracture surfaces, we analyze the dependence of the size and location of damage zones on the local geometry and propose an algorithm for predicting areas that are most likely to be damaged during shearing in a given direction. 7
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.