Aims

All brittle deformation is related to stress concentration. The deformation, such as the formation of fractures, occurs because the local stresses in certain parts of the crust or rock bodies are raised above the average (nominal) stress in the surrounding parts. Understanding stress raisers and concentrations is of fundamental importance for assessing likely sites for rock-fracture initiation and propagation; in fact, the Griffith theory of fracture (Chapter 7) is partly based on the idea of stress concentrations around small elliptical flaws in brittle materials. The main aims of this chapter are to:

• Define the concepts of a stress concentration and a stress raiser.

• Provide the basic equations for calculating stress concentrations around elliptical and circular holes and cavities.

• Explain stress concentrations in terms of the atomic structure of solids.

• Provide an analogy between stress concentrations and fluid flow around obstacles.

• Use the equations for stresses around elliptical cavities to explain stress concentrations around fluid-filled reservoirs and magma chambers.

• Use the equations for stresses around circular holes to explain stress measurements using hydraulic fractures injected from drill holes.

Basic definitions

Stress concentration occurs when a part of a loaded material has properties that differ from those of the surrounding parts. The easiest way to visualise stress concentration is to consider stresses in a body with a hole or a notch. A hole is a two-dimensional cavity.