Rheology of rocks (models for stress-strain relationships)

Alfred Wegener
"All that can be said with certainty is that the earth behaves as a solid, elastic body when acted upon by short-period forces such as seismic waves, and there is no question of plastic flow here. However, under forces applied over geological time scales, the earth must behave as a fluid: for example, this is shown by the fact that its oblateness corresponds directly to its period of rotation. But the critical point in time where elastic deformations merge into flow phenomena depends precisely on the viscosity coefficient."

The concept of rheology is needed to make sense of the earth.

Lecture index: Utility of understanding stress-strain relationships. / Five components of a constant load test in strain time space. / Three models to explain stress strain relationships. / Combination models and definition of rheid. /

Reading: Chapt. 6 in Fossen, Structural Geology

Utility of understanding stress-strain relationships

Stress-strain relationships are important because:

Five components of a constant load test in strain time space

An idealized constant load (constant stress) test result looks something like the above. Strain over time is the strain rate, and so changes in the slope of the line represents changes in strain rates. The temperature, pressure, material properties, and load amount all influence the specific shape of the curve. The curve shown here is for conditions that produce the full suite of components. Under certain conditions only limited portions of this behavior will be seen.

How can we model this behavior? First, we can divide it this history into separate components.

Three models to explain stress strain relationships

These are idealized simple mechanical models, each with their own iconic representation.

Combination models and definition of a rheid

Linking these three components in different ways produces some 'emergent' behavior.

The top row depicts three basic deformational behaviors that can be combined to build models for more complex behavior. The second row depicts models of the the spring and dashpot combined in series, and then in parallel. The lower most depiction is with the two modes above combined in series, and this model reproduces elastic, primary and secondary creep behavior as depicted and described above.

Consider the 3 time and stress constant load curves above. Note that mid-way the driving stress (the load) is removed and recoveryis possible. Which one best represents the Maxwell body, which one best represents the Kelvin body, and which Carey's rheid body?

Definition of rheidity: The units are time. The rheidity of a given material is the time at which the permanent deformation = 1000 times the recoverable deformation. At this point you can consider the last term to dominate and the material is acting like a viscous fluid for those time frames. If deformation conditions persist for this amount of time then the finite deformation can be treated as viscous.

YouTube demonstration of rheidity (time dependent behavior): http://www.youtube.com/watch?v=f2XQ97XHjVw.

Dr. John Mainstone at the University of Queensland (Australia) and the slowly dripping pitch. About one drip per decade occurs. Image source: http://en.wikipedia.org/wiki/Pitch_drop_experiment . More images and web cam at http://smp.uq.edu.au/content/pitch-drop-experiment .

For rock salt and normal crustal conditions rheidity is about 10 years. Rheidity and viscosity are very sensitive to temperature.

Link to salt flowage image and information.

Copyright Harmon D. Maher Jr., This may be used for non-profit educational purposes as long as proper attribution is given. Otherwise, please contact me. Thank you.