Ellipsoidal anisotropy in elasticity for rocks and rock masses

TL;DR

This paper explores ellipsoidal anisotropic models in elasticity, demonstrating their analytical solutions, fitting to rock data, and numerical homogenization for fractured rock masses, advancing understanding of rock behavior under stress.

Contribution

It introduces two main types of ellipsoidal elastic models and shows their effectiveness in modeling sedimentary rocks and fractured rock masses.

Findings

Ellipsoidal models fit in situ rock data well.

Analytical solutions are available for certain elasticity problems.

Numerical homogenization results support model validity.

Abstract

One of the interesting features with the ellipsoidal models of anisotropy presented in this paper is their acceptance of analytical solutions for some of the basic elasticity problems. It was shown by Pouya (2000) and Pouya and Zaoui (2006) that many closed-form solutions for basic problems involving linear isotropic materials could be extended by linear transformation to cover a variety of "ellipsoidal" materials. This paper will describe two main varieties of ellipsoidal elastic models and show how well they fit the in situ data for sedimentary rocks; numerical homogenization results for several varieties of fractured rock masses will also be provided.