Structure lecture - Mohr games

Lecture index: Mohr stress space. / Mohr - Coulomb failure criteria. / Energy partitioning during faulting. /

Readings:

Key terms and concepts:


Mohr stress space

Demonstration by coincidence:

This diagram defines the position of the plane using option b above.

Applet to plot Mohr diagrams given basic input.

Stress plots on Mohr diagram are useful to develop visual intuition with regard to stress states in Mohr space through the following rules.

A brief introduction into 3-D Mohr space.


Mohr - Coulomb failure criteria

Now we can explore how mapping stress states in Mohr space can help understand faulting. Remember that there is a relationship between the shear and normal tractions on a plane and frictional strength. Stronger planes require higher the shear tractions to slip, and higher normal tractions require higher shear traction to slip. For many surfaces a simple linear relationship exists, which is known as the failure envelope:

critical shear stress for slip = a strength intercept + the normal traction multiplied by a strength factor.

Given a straight line relationship the strength factor is equal to tan (Ø) where Ø describes the angle from horizontal of the straight line relationship. For many geologic materials Ø is around 30 degrees. Given that both shear stress and normal stress are the crucial variables it is possible to plot this envelope on the Mohr diagram. It is also useful to know that some materials can have non-linear failure envelopes.


This is a image of a triaxial testing apparatus which can measure the brittle strength of rock material under triaxial stress conditions. A rock sample is put in side the cylinder, and piston provides a maximum principal stress while a confining fluid under pressure provides a confining principal stress (S2-S3). the source of the image is: http://quake.wr.usgs.gov/research/physics/lab/images/fig04.jpg

You can then add the linear slip criteria (the shear and normal tractions along a plane that will cause failure) into the Mohr diagram in form of failure envelope. If shear stress associated with the stress state intersects or exceeds those associated with the envelope then failure, slip will occur.

Diagram below is of three stress states, one where failure will not occur, one were shear failure is imminent, and one where tensile failure is imminent. Failure envelopes are not always linear. Note that in this diagram, the lower failure envelope associated with negative shear stresses is not shown, but it should be there.

This is a link to an Excel sheet where you can plot up to 4 stress states along with both a failure envelope and a tensile cutoff. It also indicates if slip along a shear plane should occur.

For pristine failure: given an intact homogenous rock or where layering is close to principal stress plane (e.g. flat lying strata often are in this position) slip can occur on a newly formed plane (and not follow a pre-existing weakness. For this situation the following is the case:

Modeling different failure histories (loading paths):

For slip on pre-existing anistropy:

Different failure envelope geometries:

Tensile cutoff:

Kink bands - on the down side of the failure envelope.

Limitation of Mohr diagrams.


Energy partitioning during faulting

It is useful to discuss faulting from an energy perspective. It can give insight into why certain fault geometries may be more common. It is useful in modeling structural evolution. It links seismicity and faulting.

Basic physics:

Slip on a fault, seismic perspective:

Faulting, a long term (structural) perspective:

Much potential in this line of research!



Discussion question: Describe a specific geologic situation that would minimize the amount of energy required for faulting. Describe a specific geologic situation that would maximize the amount of energy?


Some references for energetics of faulting:


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.