Preamble

The theory of elasticity in Chapter 10, even the discussion of inelastic deformation, does not provide a description of the processes that led to the geological features that we see in the surface layers of the crust. We need a different theoretical approach to the deformation of materials such as crustal rocks that are granular, cool and at low pressure. What determines how or why rocks deform or break? How are the orientations of faults related to the stresses that cause them? How is crustal stress estimated? How is the safety of mines and tunnels assessed? Can laboratory observations of rock failure be extrapolated to describe earthquakes? These are questions addressed by the discipline of rock mechanics. In its modern form it is used mainly by mining engineers and the applied mathematicians who work with them. Here it is applied to tectonics.

The mathematical methodology of the subject uses the tensor notation. This is given a brief introduction in Section 10.3, in the discussion of elasticity of crystals, and is extended in this chapter. It is a convenient representation of stress patterns involving superimposed compression and shear, including rotation of reference axes, to identify principal stresses. The most obvious and useful application is to the criteria for mechanical failure.

Earthquakes are dramatic instances of failure and most of them are shallow, by which we mean that they are confined to the lithosphere, the cool surface layer of the Earth.