Intrinsic elasticity of a textured transversely isotropic muscovite aggregate: Comparisons to the seismic anisotropy of schists and shales

Abstract

[1] The anisotropic properties of phyllosilicate rocks are investigated through the modeling of the pore-free ''intrinsic'' elasticity of a textured muscovite aggregate. The elastic constants were calculated for textures, as defined using orientation distribution functions (ODFs), ranging from perfectly aligned to completely random. The ODFs were described using a Gaussian distribution, the width of which is controlled by the standard deviation of the orientations of the crystal c axis with respect to the sample foliation plane under the assumption that the sample has hexagonal (transversely isotropic) symmetry. The values were obtained using the widely used Voigt-Reuss-Hill averaging techniques as well as the geometric mean average (GMA). The GMA is more physically meaningful in that it requires that the elastic constants determined in either the stiffness or the compliance domains be invertible. Comparisons between these different averages indicate that, strictly, the Voigt and Reuss values do not necessarily provide the limiting bounds as is expected for the isotropic case. Despite this, some characteristics of the elastic wave P wave anisotropy are only weakly dependent on the averaging procedure employed. The calculated elastic constants are converted to the anisotropic e, d, and g parameters in order to allow for comparison to existing measurements in the literature. However, these ''intrinsic'' results are not intended to provide a measure of the properties of phyllites per se but to provide a reference against which more sophisticated models that incorporate porosity, layering, and composition may be constructed.

Anisotropy of experimentally compressed kaolinite-illite-quartz mixtures

“…This is intermediate between an upper-bound Voigt average that provides uniform strain and a lower-bound Reuss average that provides uniform stress. In axially symmetric materials, the elastic tensor is reduced to five independent stiffness coefficients: C 11 , C 13 , C 33 , C 44 , and C 66 ͑in Voigt notation͒, listed in Table 3 ͑see also the approach in Cholach and Schmitt, 2006͒. A weighted average ͑considering volume fractions obtained from X-ray diffraction data͒ was calculated from polycrystal tensors for each mineral phase to obtain the polyphase tensor -a tensor averaging the properties of the bulk mineral content of the material. Finally, from polyphase tensors we calculated velocity surfaces V P , V S1 , and V S2 using Christoffel's equation.…”

Geophysical Properties of the Near Surface Earth: Seismic Properties

“…c See discussion in Cholach and Schmitt (2006). d Value is the Voigt-Reuss-Hill average calculated assuming hexagonal symmetry (Watt and Peselni, 1980) using the values reported in Bass (1995).…”

Bifurcation and Degradation of Geomaterials in the New Millennium

“…The dehydration or degradation of the Stern layer in clay particles can be the affecting factor for such contractile -Bradley 1987;Gonçalvès 2010). Furthermore, the clay shale features in is its intrinsic oriented fabric (Wong and Wang 1997;Hornby et al 1994;Cholach and Schmitt 2006). The anisotropic deformation behavior can be due to the intrinsic oriented fabric.…”