Distal radial fractures are a heterogeneous group of fractures that occur at the distal radius and are the dominant fracture type at the wrist. One of the most common approaches to describe the mechanical response of the discontinuity is the characterization of an interface law, i.e., a constitutive law [Dieterich, 1979; Ruina, 1983; Marone, 1998]. In order to estimate the width of the power law distribution, we used the two points slope technique. The deformation mechanisms involve both grain rotation and grain fracturing. [52] As addressed in recent works on sandstones, these effects could result from the gouge fracturing process which occurs during the shear deformation. [27] Evidence of cataclastic flow is observed within the highly comminuted zones, i.e., gouge zone as shown in Figure 8 (σ3 = 80 MPa). For samples deformed after the failure, Mair et al. [21] For the friction criterion, no significant difference was found between the frictional angles calculated for maximum and minimum shear strengths. Figure 5 shows how a biotite grain is crossed by an horizontal intergranular crack that connects two vertical cracks. Differences between Sets 1 and 3 can be accounted for by quartz deposition resisting fracture reopening to a greater extent for Set 1 during repeated, episodic growth, where crack-seal texture is present in fracture-spanning quartz. We did neither observed any effect of the confining pressure on the gouge thickness. Fractures of the femur are common orthopaedic emergencies presenting to emergency departments (ED). After opening, unconsolidated material, i.e., gouge powder, is blown out with an air flow and a brush. Fractures were classified by the Robinson classification. We address the influence of the confining pressure (normal stress) and of the shear displacement on both the roughness and the gouge properties. An example is given in Figure 7 (σ3 = 40 MPa). [41] Grain‐size distributions are given as the volume histogram of 20 diameter bins that are equally log‐spaced between 2 μm and 2 mm. Accordingly, fracture surfaces appear flat at large scales. As ζ describes the smoothness of the surface, these results can be summarized as follows: when sheared the rupture surfaces become rougher at low confining pressure and smoother at high confining pressure. 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). Properties of Rocks, Computational The macroscopic deviatoric stress σ1 − σ3 decreases contemporary to an intense acoustic activity. 1b). Unfortunately, we were not able to sample all surfaces along the perpendicular direction because of the limited width of the biggest fracture surface developed in the samples. The main difference between w2(d) and w∞(d) is that the former is related to the second order moment of the height distribution whereas w∞ is related to the infinite moment of the distribution. Probability density distributions of the grain size for tests with (square) or without (circle) shearing after the macrorupture for the different confining pressures, σ, Thin section optical photomicrograph (cross‐polarized light) showing the process of erosion of the transition zone during the shearing. Specific feature of this version of LA is that Weibull distribution is not used for description of distribution function of fracture probability. Set 1 has power-law scaling, unbounded heights, random spacing and crack-seal quartz. [2000] observed that the mean grain size of gouge in‐filling the fracture decreases with increased normal stress. σ. [2001] for a review). hydrographique de la zone d’étude. The different aspects of damage: cracks, rupture surface, gouge, that result from the deformation process, can be observed either at the field scale (natural faults) or at the laboratory sample scale [e.g., Keller et al., 1997; Wibberley et al., 2000]. As the shear bands are composed by highly comminuted material, this is in agreement with our observation of increasing proportion of small particles as the deformation progresses. The Fourier spectrum estimate was proposed by [Schmittbuhl et al., 1995a] as the most reliable. In the application of our results, we rely mostly on the two latter techniques. Estimates of these parameters are given in Table 1. We present the mechanical behavior of the samples, the microstructures of the shear bands, and statistical properties of both the fracture surface roughness and of gouge granulometry. 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. Working off-campus? The shear band deformation involves both gouge and roughness evolution during the shearing. The limit between the gouge and the cracked material is not distinct but rather continuous. (bottom) One profile from the same surface but in the perpendicular direction. It has been observed in previous works [Menendez et al., 1996; Mair et al., 2002; Besuelle, 2001] that shear band localization within the gouge are more developed for high normal stress than for low normal stress. Objects, Solid Surface Because of geometrical effects, the shearing of a rough surface induces dilatancy [Barton and Choubey, 1977]. (1896-1977), Chinese Journal of Geophysics (2000-2018), International [25] Clear evidence of a local mode II is visible in Figure 6 which shows the offset of a biotite mineral (σ3 = 80 MPa). Table 8. Core Interpretation Assistance. Thin section dimensions were 40 × 80 mm for the core axis parallel ones and 40 × 40 mm for the perpendicular ones. Set 1 macro and microfracture-opening-displacement sizes are well described by a power law with slope −0.8. [62] We thanks S. Roux for helpful comments, A. M. Boullier for her help in thin section observation, and D. Hantz and Y. Orengo for technical support. Physics, Solar [20] Despite the similarity between terms and denomination, equations (1) and (2) reflect two different phenomena (see Savage et al. The five techniques show a set of curves that is very consistent with a power law behavior over at least 2 orders of magnitude. We assume that a first surface with a roughness exponent ζ1 is sheared and a new surface is generated. Figure 1. Abstract. [1995a] and Simonsen et al. The sound velocity is 4800 m/s. Here a marker allows an estimate of the shear displacement: 0.2 mm. [37] As mentioned previously, sensitivity to the confining pressure during the test is weak. Particle size is obtained from the square root of the area. The Fourier spectrum is the spectrum of the modulus square of the Fourier transform. On the other hand, the friction criterion describes the strength of a sheared surface. Very few analyses of the scaling properties of artificial shear fractures are reported in the literature. Stress, strain and AE activity are sampled every second. Acoustic activity continuously increases and reaches its maximum as the stress peak is reached. Dilatancy in the fracture of cristalline rocks, Broad bandwith study of the topography of natural rock surface, A microcrack model for the deformation and failure of brittle rock, Fractal surfaces: Measurement and application in earth sciences, Modeling of rock friction, 1, Experimental results and constitutive equations, Fractal Geometry: Mathemathical Foundations and Applications, Shear‐stress intensity factors for a planar crack with slightly curved front, Penetration of a quasi‐statically slipping crack into a seismogenic zone of heterogeneous fracture‐resistance, Appolonian packing and fractal shape of grains improving geomechanical properties in engineering geology, Fractal structure of spacial distribution of microfracturing in rock, Friction and degradation of rock joint surface under shear loads, The effect of shear load on frictional healing in simulated fault gouge, Shear fracture pattern and microstructural evolution in transpressional fault zones from field and laboratory studies, Pertinence du formalisme des transitions de phase pour aborder la mecanique des objets geologiques, Precursory AE patterns leading to rock fracture, in Proceedings of the Vth Conference on Acoustic Emission/Microseismic Activity in Geologic Structures and Materials, Quasi‐static fault growth and shear fracture energy in granite, Sequential growth of deformation bands in the laboratory, Influence of confining pressure on the mechanical and structural evolution of laboratory deformation bands, Experimental measurements of the roughness of brittle cracks, Fractal character of fracture surfaces of metals, Laboratory‐derived friction laws and their application to seismic faulting, Particle‐size distributions and microstructures within simulated fault gouge, Characterization of long‐range correlations in complex distributions and profiles, Micromechanics of brittle faulting and cataclastic flow in Berea Sandstone, The role of intragranular fracturing on grain size reduction in feldspar during mylonitization, Sliding behavior and deformation textures of heated illite gouge, Topography of natural and artificial fractures in granite rocks: Implications for studies of rock friction and fluid migration, Nucleation and growth of faults in brittle rocks, Slip instability and state variables friction laws, Technicale note: On the fractal character of rock surfaces, Field measurements of the roughness of fault surfaces, Slow crack propagation and slip correlations, The Mechanics of Earthquakes and Faulting, On the initiation of shear faults during brittle compressive failure: A new mechanism, Using wavelet transforms for hurst exponent determination, Physics of friction and strain rate localization in synthetic fault gouge, Fractal approach of structuring by fragmentation, Fractals and Chaos in Geology and Geophysics, Fractal analysis of fractures during brittle to ductile changes, Wear processes during frictionnal sliding of rocks: A theoretical and experimental study, Fracturing of ice under compression creep as revealed by a multifractal analysis, Micromechanics of shear rupture and the control of normal stress, An index for describing the anisotropy of joint surfaces, Joint profiles and their roughness parameters, Journal of Geophysical Research: Solid Earth. State variables attempt to account for interfacial processes like healing, asperity strain or roughness history. The corresponding displacement along the rupture surface was estimated to ∼2 mm, taking into account the shortening of the sample after the failure and the angle between the rupture surface and the core axis (near 30°). Accordingly, it has to be defined as a transition zone. Because of the logarithmic binning, the exponents for cumulative and density distribution are equal [Lahaie, 2000]. σ, Thin section optical photomicrograph showing the transition between gouge, cracks, and undamaged material (plane‐polarized light). The maximum‐minimum difference (MMD) technique consists of searching for the difference between the maximum and minimum height w∞(d) for a size of the window d. For a monofractal self‐affine set, the expected behavior is w∞(d) ∝ dζ. We have compared tests stopped immediately after the macrorupture and tests that include a supplementary shearing stage. The foundations of the Weibull theory for brittle fracture are reviewed. The apparent linear behavior of both stress and AE during the macrofailure is due to the lack of sampling points. The sample strain was deduced from the displacement, taking into account the stiffness of the loading system (shortening of the piston) and the length of the sample. [6] The mechanical behavior of rock discontinuities has been addressed using different approaches according to the morphology of the shear zone: flat or rough surfaces, and with or without in‐filling material of various thicknesses. Particle size distribution from a geometric model where particles are created from the evolution of the roughness exponent of synthetic surfaces. Constitutive laws that include state variables (e.g., gouge thickness) have been proposed to describe the gouge properties. Results imply that thermal history and diagenesis are important for fracture-size-distribution patterning. [13] Figure 1 shows a typical mechanical behavior observed during triaxial compression. Such a crack pattern is observed in the whole sample: both in the shear band and far from it in the bulk sample. Coalescence of mode I cracks exists because of the very short distance between cracks, because of the geometry of the grain boundaries, due to the presence of weak planes within grains. [53] Moreover, the power law fit of the particle size distributions is possible on a broader range for tests with shear displacement. We focus on the thickness of the shear band because of the transition zone between the bulk and gouge materials. The AE recording were performed on an AE system. Yet the opening-mode sets display contrasting fracture-aperture-size distributions, spacing patterns, and tendency to be bed bounded. Each curve is an average over the analysis of each profile of the data set. Only data sets of profiles oriented along the slip direction are reported. In order to quantify the cracks creation and propagation during the deformation, an acoustic emission (AE) transducer was applied on the outside of the cell piston which was used as a waveguide. [28] We focus here on the description of the fracture surfaces obtained after completion of the mechanical tests. From our observations, the gouge thickness ranges from 0.1 to 1 mm. Processes in Geophysics, Atmospheric The roughness exponent ζ1 is chosen as the measured roughness exponent just after failure: ζ1 = 0.8. La dernière modification de cette page a été faite le 30 décembre 2020 à 19:39. ... Distal radial fractures can be seen in any group of patients and there is a bimodal age and sex distribution: younger patients … Copyright © 2013 Elsevier Ltd. All rights reserved. [46] Figure 15 displays the effect of both the confining pressure and the shearing displacement on the e exponent. It consists of averaging the Wavelet transform Wb(a) of the profile over the translation factor b for a given scale factor a. [61] Quantitative measurement of roughness and gouge show scaling invariance. This might explain the high value of the e exponent. Figure 11 shows the analysis for each technique applied on profiles oriented along the slip direction. The different methods are very consistent and show that the roughness exponent is close to 0.75 as classically obtained for fracture surfaces [Power et al., 1987; Schmittbuhl et al., 1995b; Bouchaud, 1997; Power and Durham, 1997]. Geophysics, Marine The grain‐size distribution of the gouge has been measured by mean of a Laser Particle Size Analyzer (LPSA). [8] Evidence of the mechanical effects of in‐filling granular material on joint shearing have been obtained from laboratory tests. [17] Stage 4 is a shearing stage during which the deformation of the sample is localized along the macrofailure surface. https://doi.org/10.1016/j.jsg.2013.06.011. This deformation mode is observed exclusively within the transition zone. Warner Bros. 2021 Film Slate - New Hybrid Distribution Model. Shear cracks are not surface free processes and involve significantly higher energy release rates [Atkinson, 1991]. Our model is purely geometrical one. These are typical values for a granite. Shear deformation occurs both on the rupture surface and within the gouge layer involving friction surface erosion [e.g., Wang and Scholz, 1994] and grain fracturing [e.g., Michibayashi, 1996; Biarez and Hicher, 1997]. The fundamental of new version of LA to fracture is briefly stated. Accordingly spatial correlations are on lower scales along the slip than perpendicular to it. Fracture roughness is shown to be correctly described over up to 3 orders of magnitude by a self‐affine geometry with a roughness exponent ζ, varying from 0.7 to 0.78. Power-law aperture scaling results from growth partitioned amongst variably cemented fractures. For highly angular grain these assumptions may lead to an overestimate of their size. The final recorded point is the fracture strength. Hence the definition of a rupture surface separating the gouge zone from the consolidated cracked zone is not simple. Processes, Information [3] Low‐scale observations reveal that the rupture zone or shear band is made of a granular material (i.e., gouge or cataclasis), in‐filled between two rupture surfaces. This smoothing leads to a morphological simplification of the transition zone. Accordingly, estimates reported for W2 in Table 3 are somehow systematically lower than the others. Except for one surface, sampling for roughness measurements along the slip direction consists of 22,550 points and of 11,330 points for sampling perpendicular to the slip direction. As a consequence, this process does not account for the significant increase of the exponent e that is observed for high confining pressure. [49] Mode II cracks are observed exclusively within the transition zone. Cause of fracture distribution based on age group. The second‐order shear offsets are estimated to be smaller than 0.1 mm. Each domain is characterized by specific microstructures: mode I and II cracks and, gouge. The beginning of this stage is classically associated to the initiation of dilatancy which corresponds to the opening of cracks parallel to σ1 [Jaeger and Cook, 1979; Scholz, 1990; Reches and Lockner, 1994]. We used Daubechies wavelets [Press et al., 1992]. The roughness exponent ζ obtained for tests with or without shearing, have been compared for various confining pressures. From the left to the right, one may first observe a highly fractured and disordered material, i.e., the gouge (or cataclastic material). Related to Geologic Time, Mineralogy The range increase indicates that the scaling invariance extends to a larger range of scales as the deformation increases. On the contrary at higher confining pressure (60–80 MPa), the roughness exponent increases. Although extensive research for the optimal treatment of clavicle fractures has been performed, comparative studies between monotrauma and polytrauma patients are lacking. Power law scaling is found for: crack lengths, crack spatial distributions [Hirata et al., 1987; Velde et al., 1993], rupture surface roughness [Brown and Scholz, 1985; Schmittbuhl et al., 1993, 1995b; Bouchaud, 1997], and grain‐size distribution of the gouge [Sammis and Biegel, 1989; Marone and Scholz, 1989; Weiss and Gay, 1998]. Both angles were estimated to be 46° ± 2°. Schmittbuhl et al. On the contrary, tests from the series gsd40 correspond to a long slow quasi‐static shear. [32] Several tools exist to analyze self‐affine properties of rough surfaces. l= L.sin + D.cosDD The formula of the fracture frequency is: Dis the angle between the fractures and the borehole, if the borehole is vertical =p/2-DipD But in general case the formula to calculate the angle is: D D a D a = D cos D. + FIGURE 1. A transition zone exists as shown in Figure 4 from a plane perpendicular to σ1 (σ3 = 40 MPa). In Cambrian Mesón Group, NW Argentina, small faults and three opening-mode fracture sets defined by orientation and cement texture (Sets 1–3) formed sequentially in sandstone that most likely had constant mechanical properties throughout deformation. Because of this transition zone, a prediction only from thin section observations, of the morphology of the rupture surface which will appear after opening the broken sample, is not possible. When there is no evolution of the roughness exponent (ζ1 = ζ2), particles are created since the final surface is statistically independent of the initial surface but the distribution is flat. Small Bodies, Solar Systems This has been verified by microscopic observations. On the contrary, for high confining pressures, the increase of ζ indicates that the fracture surface becomes smoother as the shearing progresses. [1995a] predict that the correction should be close to +0.08. The deviatoric stress σ1 − σ3 decreases during shear and shows a decrease of the shear strength angle. Advantages of this technique are mainly the broad range of grain size that can be measured simultaneously (from 2 μm to 2 mm in diameter) and the high speed of the measurements. These results show a complex coupling between the fault gouge and fault roughness. To compare fracture distribution and treatment in monotrauma and polytrauma patients with a clavicle fracture. Planets, Magnetospheric Enter your email address below and we will send you your username, If the address matches an existing account you will receive an email with instructions to retrieve your username, Typical mechanical behavior observed for the triaxial compression test gds42 at σ, Mechanical behavior observed during triaxial compression tests (top) stopped and (bottom) continued after the macrorupture for confining pressures ranging from 20 to 80 MPa. The dotted line labels an highly deformed biotite which allows to estimate the tangential displacement to 1 mm. The thickness of these shearing bands is 0.1 mm which is significantly smaller than the gouge thickness of 1 mm. The specimens were impregnated in order to preserve their microstructure and especially to highlight fractured zones. For low confining pressure σ3, the decrease of ζ indicates that the fracture surface becomes rougher as the shearing progress. After an imposed shear, there is a significant evolution of the geometry of the surface. [51] The power law exponent e of the grain‐size distribution can be regarded as the relative proportion of small versus large particles (a high e exponent corresponding to a high proportion of small particles). Parameters that most affect reservoir performance include fracture width, height, and spacing, as well as the number of fracture sets and their orientations. Three dimensional view of the fracture in 75 mm diameter sandstone specimen Figure 3. [11] The experiments consisted of deforming Sidobre granite samples under triaxial compression conditions, with confining pressure ranging from 20 to 80 MPa. Set 3 fractures are quartz-lined, opening-mode fractures with extensive open pore space, having a narrow (characteristic) opening-displacement size distribution; they are regularly spaced and stratabounded. The crack thickness (opening) is less than 1 μm. Power-law opening-displacement size distributions may be favored in cases where fracture growth is unequally partitioned amongst variably cemented fractures, whereas a characteristic size is favored where growth is unaffected by cementation. Petrographic thin sections were cut parallel and perpendicular to σ1. In most cases we sampled the surfaces only parallel to the presumed slip direction. [22] This section describes the local mechanisms of deformation observed in the shear bands from petrographic thin sections observed under optical microscope. Fracture distribution in the Giddings Austin Chalk is controlled by both structure and the stratigraphy of the Austin Group. Thermal history and cement accumulation influence fracture-size-distribution patterning. This clearly shows that the fracture geometry (more specifically the spatial correlations that exist along the fracture geometry) are very robust even if the mechanical load is different: (1) the influence of the confining pressure (from 20 to 80 MPa) is weak; and (2) quasi‐static or dynamical shear produces the same roughness. The total set of data corresponds to 201,120 sampling points. There is a small anisotropy along the fracture surfaces that corresponds to the stria created during the shear process. [40] After each test, the gouge material in‐filling in the rupture zone was carefully extracted for granulometry measurement. Note that the thickness of this transition zone ranges from zero (on the lower part of the photograph) to 1 mm (on the upper part of Figure 4). Vertebral fractures (VFx) occur most frequently in the mid-thoracic and thoraco-lumbar regions, which experience the highest mechanical loading along the spine. At low confining pressure (σ3 = 20 and 40 MPa), ζ is lower for tests with shear displacement. Subsequently, a more detailed comparison of the samples can be performed. We see from Figure 17 that the distribution is a power law distribution for large particles with a slope that increases with the final exponent ζ2. [38] From the measurement of the roughness along profiles perpendicular to the slip direction (i.e., samples labeled with a star in Table 3), the anisotropy of the fracture roughness can be addressed. 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. The macrofailure is near instantaneous. Except for σ3 = 40 MPa, particle size distributions for tests without imposed shear are above those for tests with a shear stage. The confining pressure was applied by means of a triaxial cell. Set 2 fractures are microscopic, mostly quartz filled and have characteristic aperture sizes, are probably not bed bounded and have either a near-random or clustered spatial distribution. The offset is close to 1 mm. [58] We propose a simple model to illustrate a possible coupling between gouge and fracture roughness. Comparisons with other granulometry measurement techniques have shown the reliability of the technique [Mair et al., 2000]. The samples were subjected to axial deformation at a constant piston displacement rate until macrofailure occurred. [35] A more quantitative comparison between methods and mechanical paths is possible by comparing the roughness exponent estimates for each profile set as listed in Table 3. The diameter and length of the samples are 40 and 100 mm, respectively. The proportion of small particles increases with the imposed postpeak shear displacement. In this case, ϕ really corresponds to the frictional strength and S0 to the apparent cohesion resulting from the imbrication of the surface at high normal stress. In Figures 2 and 3, one may observe that this test was stopped at an anomalously high stress value which suggests that the rupture zone was not fully developed. This can be considered as a consequence of the grain fragmentation during shearing. Journal of Geomagnetism and Aeronomy, Nonlinear ... Distal radial fractures can be seen in any group of patients and there is a bimodal age and sex distribution: younger patients … Such performance is closely correlated with fatigue at the electrodes, which can be induced by the fracture of the particle. Their thickness has been estimated to be of the order of 0.05–0.1 mm depending mainly on the gouge thickness.
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