Evaluation of the stiffness tensor of a fractured medium with harmonic experiments

A fractured medium behaves as an anisotropic medium when the wavelength is much larger than the distance between fractures. These are modeled as boundary discontinuities in the displacement and particle velocity. When the set of fractures is plane, the theory predicts that the equivalent medium is transversely isotropic and viscoelastic (TIV). We present a novel procedure to determine the complex and frequency-dependent stiffness components. The methodology amounts to perform numerical compressibility and shear harmonic tests on a representative sample of the medium. These tests are described by a collection of elliptic boundary-value problems formulated in the space-frequency domain, which are solved with a Galerkin finite-element procedure. The examples illustrate the implementation of the tests to determine the set of stiffnesses and the associated phase velocities and quality factors.