Chapter 8

Elastic Behavior

In this chapter we describe how the elastic properties of rock are measured in the laboratory and provide tables of representative values for different rock types. However, the need to understand the resistance of rocks to deformation goes well beyond the accumulation of numbers in handbooks. To analyze a geological structure one must choose the appropriate boundary- or initial-value problem to serve as a mechanical model, and one must postulate a particular mechanical behavior. That is, one must say exactly what the relationship is between the stress acting within a material and the strain or rate of deformation. These relationships are called constitutive equations. For example, Hytch et al. (2003), studying the displacement field around an edge dislocation in silicon as revealed by electron microscopy (see above), postulated an anisotropic linear elastic constitutive law and calculated model displacements, ux and uy, that are remarkably similar to those observed in the laboratory experiment.

Exercises

Concepts from Chapter 8

These exercises explore concepts from Chapter 8 including intuitive notions of elastic behavior, computation of elastic strains given a stress state, the elastic solution for the edge dislocation, interpretation of laboratory rock mechanical data on elastic properties, and classic boundary value problems illustrating elastic heterogeneity and anisotropy.

Mechanics of dike intrusion at Ship Rock

This exercise explores models of rock deformation during the emplacement of dikes in the magma plumbing systems of volcanoes. Dikes provide conduits for flow of magma through the brittle parts of Earth's crust, and they feed fissure eruptions on many volcanoes. Mechanical models enable on to deduce the elastic properties of rock at the kilometer scale from measurements in the field of dike thickness and length.