Force, Traction, and Stress
In this chapter we define the relationships among forces, tractions, and stresses. Structures develop as the rocks of the earth’s crust strain and flow, and the distribution of this deformation is related to the stresses acting within the rock mass and the tractions acting on its surfaces. In the context of a deformable solid, the stress is associated with strain, whereas in the context of a flowing fluid, the stress is associated with the rate of deformation. In most natural examples the stress varies with position and time: it is a field quantity with spatial and temporal variations. For example, the frontispiece for this chapter is a photographic visualization of the distribution of shear stress in the grains of a model sandstone (Gallagher et al., 1974). An understanding of the possible variations of these fields in the earth is of fundamental importance to structural geologists.
Concepts from Chapter 6
These exercises explore concepts from Chapter 6 including the traction vector, the stress tensor, normal and shear tractions on geological surfaces (e.g. faults), principal stress magnitudes and directions, stress states within mineral grains, and the use of Kirsch's solution to study wellbore stability and hydraulic fracturing.
Stress perturbation during magma injection at Spanish Peaks
The stress field from the Kirsch solution for a cylindrical hole in an elastic body is investigated as a model for the stress perturbation around the magma chamber under West Spanish Peak, Colorado. Stress trajectories are computed and compared to patterns of radial dikes in order to estimate the magma pressure and remote horizontal principal stresses at the time of dike intrusion.
The following button links to a folder in Box where images from the text and images that are supplementary to those found in the text live.
The following button links to a folder in Box where MATLAB scripts (.m) geared for the MATLAB editor live.