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KAUST-IAMCS Workshop on Modeling and Simulation of Wave Propagation and Applications

Juan Santos, Purdue University, University of Buenos Aires (Argentina), and National University of La Plata (Argentina)
Harmonic Experiments to Model Fracture Induced Anisotropy: A Finite Element Approach


Fractures are common in the Earth's crust due to different factors, for instance, tectonic stresses and natural or artificial hydraulic fracturing caused by a pressurized fluid.

A dense set of fractures behaves as an effective long-wavelength anisotropic medium. Long-wavelength equivalent means that the predominant wavelength is much longer than the fracture spacing.

These fractures are modeled as boundary discontinuities in the displacement and particle velocity, i.e., the fractures are represented as a set of internal boundaries in our domain.

There exists an analytical solution - with five stiffness components - for equi-spaced plane fractures and homogeneous background medium. The theory (Schoenberg's 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 consists in performing 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.

This methodology can be applied to more general cases such as non-homogeneous backgrounds, unequal fracture distances, etc., for which there are no analytical solutions.