Page 11 - Applied Petroleum Geomechanics

CHAPTER 1

Stresses and strains

Contents

1.1 Stresses 2
1.1.1 Normal and shear stresses 2
1.1.2 Stress components 3
1.1.3 Stresses in an inclined plane 3
1.1.4 Principal stresses 5
1.1.5 Effective stresses 5
1.1.6 In situ stresses, far-field and near-field stresses 7
1.2 Mohr’s circle representation of stresses 8
1.2.1 Mohr’s circles for two-dimensional stresses 8
1.2.2 Mohr’s circles for three-dimensional stresses 9
1.3 Strains 10
1.4 Stressestrain relations in isotropic rocks 12
1.4.1 Stressestrain relations for different rocks 12
1.4.2 Isotropic dry rocks 13
1.4.3 Isotropic thermal rocks 15
1.4.4 Plane stress and plane strain in isotropic thermal rocks 17
1.4.4.1 Plane stress state 17
1.4.4.2 Plane strain state 17
1.4.5 Isotropic porous rocks 19
1.5 Stressestrain relations in anisotropic elastic rocks 19
1.5.1 Orthotropic elastic rocks 22
1.5.2 Transversely isotropic elastic rocks 23
References 26

Abstract
Basic rock mechanics concepts are introduced, including stresses and strains, normal
and shear stresses, total and effective stresses, displacement and deformation, and
normal and shear strains. The 2-D and 3-D Mohr circle representations of stresses are
described, which can be used to interpret mechanical behaviors of rocks under
stresses and depletion. Stressestrain governing equations are given for both elastic
and poroelastic rocks with thermal effects. Rock anisotropic behaviors are investigated,
and the constitutive equations for transversely isotropic and orthotropic rocks are
presented. Considerations of anisotropy and poroelasticity play a very important role
in understanding mechanical behaviors of rocks, particularly in shale oil and gas for-
mations in which anisotropy and pore pressure are dominant characteristics. In situ
stress equations accounting for anisotropy effects are also derived.

Applied Petroleum Geomechanics
ISBN 978-0-12-814814-3 Copyright © 2019 Elsevier Inc.
https://doi.org/10.1016/B978-0-12-814814-3.00001-0 All rights reserved. 1