Page 140 - Applied Petroleum Geomechanics
P. 140
CHAPTER 4
Basic rock fracture mechanics
Contents
4.1 Stress concentration at the crack tip 134
4.2 Linear-elastic fracture mechanics 135
4.2.1 Griffith crack theory 135
4.2.2 Stress intensity factor and fracture toughness 137
4.2.3 Three basic fracture modes 138
4.2.4 Fracture tip stresses and displacements 139
4.2.4.1 Model I fracture 139
4.2.4.2 Model II fracture 140
4.2.4.3 Model III fracture 141
4.2.5 Stresses and displacements in an inclined fracture 142
4.2.6 Plastic zone and fracture process zone at the fracture tip 145
4.2.6.1 Plastic process zone at the fracture tip 145
4.2.6.2 Fracture process zone at the fracture tip in rock 146
4.2.7 Fracture toughness of rock and its correlation to tensile strength 148
4.3 Sneddon solutions of fracture widths 150
4.3.1 2-D plane strain solution of the Griffith fracture 150
4.3.2 General solution for fracture width of the Griffith fracture 151
4.3.3 3-D solution for a penny-shaped fracture 151
4.4 Natural fractures and mechanical behaviors of discontinuities 152
4.4.1 Discontinuities and discrete fracture network 152
4.4.2 Mechanical behaviors of discontinuities 155
4.4.3 Mechanical behaviors of rock masses 159
References 160
Abstract
Stress concentration occurs owing to the presence of cracks and sharp corners,
causing rock failures; even the intact rock has a very high strength. Inglis and Griffith
theories are introduced to study the stress and displacement relationships when
fractures exist in the rock. Stress distributions around the fracture tips in three fracture
modes are introduced. The stresses and fracture intensity factors in an inclined fracture
under anisotropic far-field stresses are also discussed, which may be applicable for
inclined wellbore and hydraulic fracturing problems. Sneddon’s solutions of fracture
widths in both 2-D and 3-D conditions are discussed, which can be applied to hy-
draulic fracturing modeling and wellbore strengthening design. Fracture propagation
Applied Petroleum Geomechanics
ISBN 978-0-12-814814-3 Copyright © 2019 Elsevier Inc.
https://doi.org/10.1016/B978-0-12-814814-3.00004-6 All rights reserved. 133
