Abstract

In stability analysis in wells and other underground openings the most used model in practice is consider the rock as an elastic solid, through solution proposed by Kirsch in 1898. Usually in several engineering applications, the rock has been treated as a homogeneous material. However, rocks are generally composite materials, and hence inhomogeneous on a microscopic scale. This study has proposed another solution, in which the coupling of the poroelasticity and Cosserat's effects in stability of circular openings in rocks has been investigated. An analytical solution to the stress concentration factor on neighborhood of a circular opening in rocks was achieved and it applied in a simple and biaxial tensile field using two different rocks: granite and sandstone. The results demonstrate that there were reductions on stress concentration factor of up to 55% in comparison with the traditional solution of Kirsch.

1 Introduction
1.1 Cosserat's Theory

The generalized mechanics continuum proposed by Cosserat brothers in 1909 considers that the material points have all degrees of freedom of a rigid element, in fact, those points besides evolving translations and rotations as well. Consequently, the static fields appear in the relationship between couple-stress and gradient of rotation, such action introduces implicitly the dimensions and shape of the particles in constitutive relations, which allows considering effects of the microstructure in behavior of field.

In the generalized continuum description, the material particle is rigid and it has micro rotation wc3 as additional degrees of freedom to ui. This way, in such a continuum, the particle will have the degrees of freedom of a rigid body positioned in xi Figure 1.

The kinematic of the generalized continuum is defined as:

a) Macroscopic displacement: symmetric part of macro-strain (ε(ij)) and antisymmetric part of macro-rotation (Ω(ij)).

(equation)

b) Microscopic displacement: symmetric part of micro-strain (g(ij)) and antisymmetric part of micro-rotation (g[ij]):

(equation)

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