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Rocks in the Earth’s crust contain cracks in variable amounts and on variable scales. Depending on the in situ stress level, cracks are always distributed in a common normal direction (so-called aligned cracks). In this study, we focus on the velocity and anisotropy of perfectly aligned cracks (parallel cracks). The theoretical model is introduced to calculate the elastic properties of cracked rocks based on solid matrix properties, crack parameters, and fluid properties. The theoretical results using high- and low-frequency limits and intermediate frequency for velocities and anisotropy are compared with experimental data measured in the laboratory, where rocks are saturated with water and air. We used four synthetic rocks with different crack densities (0.0, 0.0243, 0.0486, and 0.0729) in this study. The comparison shows that the results for high, low, and intermediate frequencies provide good predictions of the shear velocities and anisotropy for saturated cracked rocks. Quantitatively, the results of the P-wave velocity and anisotropy for intermediate frequency fit the measured data better than that for the high- and low-frequency limits. Compared with water saturation, dry cracks with high compliance have a strong influence on the total compliance of rock. The water saturation results in high P-velocities and a low P-anisotropy, while dry cracks induce much lower P-velocities and a high P-anisotropy. The shear wave anisotropy is fluid-independent, theoretical results fit the measured data well in both water saturation and the dry case. [ABSTRACT FROM AUTHOR]

Abstract: From the analysis of a multi-component seismic data from vertical seismic profiling (VSP) for frequency-dependent anisotropy, we find that shear-wave anisotropy as inferred from measured time delays between split shear-waves decreases systematically as frequency increases. Whilst in general, the polarizations of the fast split shear-waves remain constant for deep receivers, we notice systematic rotation (up to 20°) of polarizations with frequency for shallow receivers. The variation of time delays with frequency has been successfully interpreted and modelled using a multi-scale rock physics model incorporating one aligned fracture set in a porous medium with randomly distributed micro-cracks. However, this model fails to explain the frequency-dependent shear-wave polarizations. It is speculated that if aligned micro-cracks and aligned fractures are in different directions (i.e. the conjugate angle is not zero), low frequency would indicate the direction of fractures and high frequency would give the orientation of micro-cracks. This speculation, however, has not been satisfactorily proven. In this study, we extend the previous model to allow multiple fracture sets inserted into background porous media. We then derive analytic expressions of polarization of shear-waves at normal incidence, and present a systematic study of shear-wave propagation in media with multi-sets of fractures. Our study demonstrates that the shear-wave polarizations will vary with frequency and the variation depends on the azimuths and angle of incidence relative to the orientations and crack densities of individual sets, and thus may help to explain the observed dependence of shear-wave polarization on frequency. [Copyright &y& Elsevier]

• The two effects of the aspect ratio studied via an effective-medium theory. • The initiation of the graphene thermal networks relies solely on the aspect ratio. • The graphene interfacial thermal resistance is highly related to the aspect ratio. • There exists an exponential law for the second aspect-ratio effect. • The second effect cannot be neglected while the aspect ratio is below 0.01. The extremely low thickness-to-length ratio (aspect ratio) of graphene nanofillers has long been considered beneficial to the overall thermal conductivity of graphene-polymer nanocomposites as it creates large surface area and extra channels for phonon transport. From time to time, however, a lower aspect ratio of the nanofillers did not yield a higher thermal conductivity as expected. To explain such phenomena, we explored the dual role played by the aspect ratio of graphene nanofillers in the effective thermal conductivity via an effective-medium approximation based on Maxwell's far-field matching with consideration of imperfect graphene interfaces. On one hand, we found that the initiation of the graphene thermal networks relies solely on the aspect ratio. A lower aspect ratio tends to boost the establishment of the thermal channels. On the other, we discovered a persistent exponential law that relates the graphene interfacial thermal coefficient to the aspect ratio regardless of the matrix material. A lower aspect ratio causes a higher interfacial thermal resistance, thus a possible lower effective thermal conductivity. These two effects are competing against each other in the framework of this theory. The origin of the second effect was discussed and the effect cannot be neglected with an aspect ratio below 0.01. This dual-role theory was confirmed by a large number of experimental observations. [ABSTRACT FROM AUTHOR]

The topologically polarized isostatic lattices discovered by Kane and Lubensky (2014, Nat. Phys. 10, 39–45) challenged the standard effective medium theories used in the modeling of many truss-based materials and metamaterials. As a matter of fact, these exhibit Parity (P) asymmetric distributions of zero modes that induce a P-asymmetric elastic behavior, both of which cannot be reproduced within Cauchy elasticity. Here, we propose a new effective medium theory baptized "microtwist elasticity" capable of rendering polarization effects on a macroscopic scale. The theory is valid for trusses on the brink of a polarized-unpolarized phase transition in which case they necessarily exhibit more periodic zero modes than they have dimensions. By mapping each periodic zero mode to a macroscopic degree of freedom, the microtwist theory ends up being a kinematically enriched theory. Microtwist elasticity is constructed thanks to leading order two-scale asymptotics and its constitutive and balance equations are derived for a fairly generic isostatic truss: the Kagome lattice. Various numerical and analytical calculations, of the shape and distribution of zero modes, of dispersion diagrams and of polarization effects, systematically show the quality of the proposed effective medium theory. [ABSTRACT FROM AUTHOR]

The absence of direct measurement of physical properties on the rock cuttings necessitates the use of theoretical approaches. One of the most promising is the use of methods of effective medium theory. In this work we apply the generalized singular approximation of effective medium theory to solve this problem. We construct a parametric mathematical model of effective physical properties of a composite material made from rock cuttings to link the effective properties of the composite material with its compositional and microstructure parameters. The list of unknown parameters includes those characterizing the elastic and thermal properties of rocks. We develop a technique for manufacturing the composite samples that are compacted mixtures of fine-grained wax and rock cuttings. We propose a method to restore the velocities of elastic waves (compressional and shear) and thermal conductivity of rocks from experimental data on the respective physical properties of composites based on the constructed model. This method is tested on fifteen composite samples made from four rocks of different types (two sandstones, quartz glass and white marble). The theoretical values characterizing the elastic and thermal properties of rocks are compared with respective experimental data obtained in independent experiments performed for these rocks. The average difference in the elastic wave velocities and thermal conductivity does not exceed 10%, whereas the maximum difference in the respective properties varies from 14 to 23%. [ABSTRACT FROM AUTHOR]