On crack density, crack porosity, and the possibility to interrelate them

Kachanov, Mark; Mishakin, V. V.

doi:10.1016/j.ijengsci.2019.06.010

Cited by 18 publications

(6 citation statements)

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“…But for low aspect ratio cracks, the crack porosity parameter is irrelevant for linear elastic properties, and crack density should be used instead (Kachanov & Mishakin, 2019; Vernik, 2016). In the general case, there is no direct relation of crack density and crack porosity (Kachanov & Mishakin, 2019). In the GeoMixSelf model we constrain all the cracks to the same oblate spheroidal shape with axes ratio {1:1: ξ }, and thus, crack density ρ may be simply derived from crack porosity φ as:

ρ = 3 φ / (4 π \cdot ξ)

…”

Section: Discussionmentioning

confidence: 99%

“…Their aspect ratios, preferred orientation and volume fraction (crack porosity) are used to calculate effective bulk elastic properties. But for low aspect ratio cracks, the crack porosity parameter is irrelevant for linear elastic properties, and crack density should be used instead (Kachanov & Mishakin, 2019; Vernik, 2016). In the general case, there is no direct relation of crack density and crack porosity (Kachanov & Mishakin, 2019).…”

Section: Discussionmentioning

confidence: 99%

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Intrinsic Elastic Anisotropy of Westerly Granite Observed by Ultrasound Measurements, Microstructural Investigations, and Neutron Diffraction

et al. 2021

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Granitic rocks attract attention because of their elastic and mechanical properties. A large number of dedicated experimental studies has been initiated due to relevance of granites to development of nuclear waste storage, geothermal projects, rock mechanics, and earthquake mechanics. Quantification of elastic properties of granites is important to determine crustal seismic velocities and stress orientation. Generally, it is assumed that granitic rocks are elastically isotropic. To determine whether rock material is isotropic or anisotropic ultrasonic methods can be applied (Babuška, 1968; Bajuk et al., 1967; Barruol and Kern. 1996; Kern & Wenk, 1990). Multidirectional (up to 132 independent directions) experiments are necessary in case of lower symmetry, unknown orientation of anisotropy or simply to diminish the effect of rock heterogeneity (e.g.,

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ρ = 3 φ / (4 π \cdot ξ)

…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Intrinsic Elastic Anisotropy of Westerly Granite Observed by Ultrasound Measurements, Microstructural Investigations, and Neutron Diffraction

et al. 2021

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“…Thus, we assume that the RK15-22 gneiss may be considered crack free at a pressure of 740 MPa. It is recognized that at low crack porosities effective elastic properties of the material depend on the crack density, while crack porosity is irrelevant (Vernik, 2016;Kachanov and Mishakin, 2019). Crack porosity and crack density may be related for certain types and distributions of cracks.…”

Section: Measured Elastic Anisotropies Of Natural Samplesmentioning

confidence: 99%

Elastic anisotropies of deformed upper crustal rocks in the Alps

Keppler

Vasin

Lokajı́ček

et al. 2021

Preprint

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Abstract. The upper crust within collisional orogens is very heterogeneous both in composition and grade of deformation, leading to very variable physical properties at small scales. This yields difficulties for seismic investigations of tectonic structures at depth since local changes in elastic anisotropy cannot be detected. In this study, we show elastic anisotropies of the range of typical lithologies within deformed upper crustal rocks in the Alps. Furthermore, we aim to model average elastic anisotropies for these rocks and their changes with increasing depth due to the closure of microcracks. We therefore sampled rocks in the Adula Nappe of the central Alps, which is typical for upper crust in collisional orogens. The two major rock types found are orthogneisses and paragneisses, however, small lenses of metabasites and marbles also occur. Crystallographic preferred orientations (CPOs) and volume fractions of minerals in the samples were measured using time-of-flight neutron diffraction. Combined with single crystal elastic anisotropies these were used to model seismic properties of the rocks. The sample set shows a wide range of different seismic velocity patterns even within the same lithology, due to the heterogeneity of deformed upper crust. To approximate an average for these upper crustal units, we picked common CPO types of rock forming minerals within the gneiss samples, which represent the most common lithology. These data were used to determine an average elastic anisotropy of a typical upper crustal rock within the Alps. Average mineral volume percentages within the gneiss samples were used for the calculation. In addition, ultrasonic measurements of elastic anisotropies of the samples at increasing pressures were performed. These measurements, as well as the microcrack pattern determined in thin sections of the samples were used to model the closure of microcracks in the average sample at increasing depth. At ≈740 MPa microcracks are assumed to be closed yielding average elastic anisotropies of 4 % for the average gneiss. This value is an approximation, which can be helpful for seismic models at a lithospheric scale. At a crustal or smaller scale, however, it is an oversimplification and local lithological as well as deformational changes shown by the range of elastic anisotropies within the sample set have to be considered.

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“…The P wave modulus at the LF and HF limits of both models tend to converge to that of the planar crack model having the same mean aperture h mean (black dashed curve). Due to the absence of contact areas, the crack density (given by the number of cracks and their surface in a certain volume) controls the stiffness of the models (Kachanov & Mishakin, ). The crack density is high and equal in all our models, which means that the difference in their stiffness is controlled by the difference in the crack volumes of the models.…”

Section: Resultsmentioning

confidence: 99%

Squirt Flow in Cracks with Rough Walls

et al. 2020

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We explore the impact of roughness in crack walls on the P wave modulus dispersion and attenuation caused by squirt flow. For that, we numerically simulate oscillatory relaxation tests on models having interconnected cracks with both simple and intricate aperture distributions. Their viscoelastic responses are compared with those of models containing planar cracks but having the same hydraulic aperture as the rough wall cracks. In the absence of contact areas between crack walls, we found that three apertures affect the P wave modulus dispersion and attenuation: the arithmetic mean, minimum aperture, and hydraulic aperture. We show that the arithmetic mean of the crack apertures controls the effective P wave modulus at the low-and high-frequency limits, thus representing the mechanical aperture. The minimum aperture of the cracks tends to dominate the energy dissipation process and, consequently, the characteristic frequency. An increase in the confining pressure is emulated by uniformly reducing the crack apertures, which allows for the occurrence of contact areas. The contact area density and distribution play a dominant role in the stiffness of the model, and in this scenario, the arithmetic mean is not representative of the mechanical aperture. On the other hand, for a low percentage of minimum aperture or in the presence of contact areas, the hydraulic aperture tends to control the characteristic frequency. Analyzing the local energy dissipation, we can more specifically visualize that a different aperture controls the energy dissipation process at each frequency, which means that a frequency-dependent hydraulic aperture might describe the squirt flow process in cracks with rough walls. Key Points:• We solve the quasi-static linearised Navier-Stokes equations coupled to elasticity equations • Seismic attenuation due to squirt-flow is strongly affected by the roughness of the crack walls • The minimum and the hydraulic apertures significantly affect the energy dissipation process presented a comparison between numerical results and an analytical model for squirt flow. In general, accepted analytical models should reproduce the equations of Gassmann (1951) in the low-frequency limit (Chapman et al., 2002). The reason is that at the relaxed state for undrained boundary conditions (low-frequency limit), the time of a half period of a passing wave allows for fluid pressure to equilibrate through FPD. At the unrelaxed state (high-frequency limit), the fluid pressure has no time to equilibrate during a half period of a passing wave and the elastic properties of the saturated material are predicted by the formulation of Mavko and Jizba (1991), which assumes that no FPD occurs during the passage of the wave. At intermediate frequencies, FPD occurs inside the cracks during the passage of the wave and part of its energy is dissipated. Nevertheless, all analytical solutions assume smooth walls for the cracks despite the fact that crack walls in rocks have been observed to present complex profiles including wall roughnes...

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On crack density, crack porosity, and the possibility to interrelate them

Cited by 18 publications

References 5 publications

Intrinsic Elastic Anisotropy of Westerly Granite Observed by Ultrasound Measurements, Microstructural Investigations, and Neutron Diffraction

Intrinsic Elastic Anisotropy of Westerly Granite Observed by Ultrasound Measurements, Microstructural Investigations, and Neutron Diffraction

Elastic anisotropies of deformed upper crustal rocks in the Alps

Squirt Flow in Cracks with Rough Walls

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