Rock Mechanics - Elasticity Studies of Isotropic and Anisotropic Rock Samples

This paper presents the results of studies of the elasticity of some isotropic and anisotropic rock samples based on longitudinal- and shear-wave pulse velocity measurements. Experimental evidence from velocity measurements on isotropic steel samples is also presented to show, within error limits, that any two of the elastic constants required to completely describe the elasticity of an isotropic solid can be obtained from any two of the following four velocity measurements: longitudinal "rod,' "plate," extended medium (infinite medium equivalent), or shear wave. Measurements of three of these velocities in an approximately isotropic basaltic rock sample are used to illustrate this application to this type of rock. For the anisotropic study, a suite of Colorado oil shale samples is used. These rocks exhibited transverse isotropy. The five elastic constants required to completely specify this type of anisotropy are obtained from longitudinal- and shear-wave pulse velocity measurements made in directions parallel, perpen-dicular, and at 45° to the bedding plane. Density, velocity, and elastic modulus relationships among these shales are also given. Duvall 1 has described a method for determining the elastic constants of isotropic and, in two cases, anisotropic rock samples. This method is based on ultrasonic pulse techniques and on resonance-frequency measurements of rock samples in the shape of rods (diamond drill cores). Rock samples, however, are not always available in rod form. When this is the case, other methods can be used to study their