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  • Print publication year: 2011
  • Online publication date: June 2012

2 - Stress

Summary

Aims

Fractures form when the stress in the rock becomes so high that the rock breaks. Stress is thus of fundamental importance for understanding rock fractures. Stress has already been defined (Chapter 1). Here the focus is on those aspects of stress analysis that are most useful for understanding rock fractures. The primary aims of this chapter are to:

Explain some of the concepts from stress analysis, particularly those relevant to rock fractures.

Clarify the difference between a stress vector (traction vector) and a stress tensor and the relationship between these concepts.

Define the principal stresses and principal stress axes and planes.

Explain the stress ellipsoid.

Discuss stresses on an arbitrary plane and Mohr's circles of stress.

Define mean stress and deviatoric stress.

Indicate and explain the use of some special stress states.

Define stress fields and stress trajectories and explain their use in stress analysis.

Some basic definitions

Stress at a point is a tensor of the second rank, whereas the stress on a plane is a vector, that is, the stress vector or traction (Chapter 1). The magnitude of a stress, given as, say, 10 MPa, is a scalar. Before we discuss the concept of stress in more detail, it is necessary to recall some basic definitions that are assumed to be known. This section, of necessity, must be brief. More details on tensors, vectors, and scalars are provided in some of the books listed at the end of this chapter.

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References and suggested reading
Anderson, E. M., 1951. The Dynamics of Faulting and Dyke Formation with Applications to Britain, 2nd edn. Edinburgh: Oliver and Boyd.
Caddell, R. M., 1980. Deformation and Fracture of Solids. Upper Saddle River, NJ: Prentice-Hall.
Chou, P. C. and Pagano, N. J., 1992. Elasticity. Tensor, Dyadic, and Engineering Approaches. New York: Dover.
Cottrell, A. H., 1964. The Mechanical Properties of Matter. New York: Wiley.
Holzapfel, G. A., 2000. Nonlinear Solid Mechanics. New York: Wiley.
Jaeger, J. C., Cook, N. G. W., and Zimmerman, R. W., 2007. Fundamentals of Rock Mechanics, 4th edn. Oxford: Blackwell.
Malvern, L. E., 1969. Introduction to the Mechanics of a Continuous Medium. Upper Saddle River, NJ: Prentice-Hall.
Mase, G. E., 1970. Continuum Mechanics. New York: McGraw-Hill.
Mase, G. T. and Mase, G. E., 1999. Continuum Mechanics for Engineers, 2nd edn. London: CRC Press.
Means, W. D., 1976. Stress and Strain: Basic Concepts of Continuum Mechanics for Geologists. Berlin: Springer-Verlag.
Niklas, K. J., 1992. Plant Biomechanics. Chicago, IL: The University of Chicago Press.
Nye, J. F., 1984. Physical Properties of Crystals: Their Representation by Tensors and Matrices. Oxford: Oxford University Press.
Oertel, G., 1996. Stress and Deformation: A Handbook on Tensors in Geology. Oxford: Oxford University Press.
Saada, A. S., 2009. Elasticity Theory and Applications. London: Roundhouse.
Verhoogen, J., Turner, F. J., Weiss, L. E., Wahrhaftig, C., and Fyfe, W. S., 1970. The Earth. New York: Holt, Rinehart and Winston.