# Mohr Circles

This is a partially developed activity description. It is included in the collection because it contains ideas useful for teaching even though it is incomplete.

#### Summary

In this lab, students will practice making and interpreting Mohr circles for given stress states. Students have been introduced to the concept of Mohr circles in lecture and have derived these equations through a force-balance setup. The lab is a mixture of plotting these circles and interpreting experimental data.

## Learning Goals

The goal is for students to know how to interpret Mohr circle diagrams, how they can be used to determine strength relationships, how to determine whether failure will occur, the difference between Mohr-Coulomb failure and Byerlee's law (frictional sliding), and how pore pressure affects failure.

## Context for Use

The Structural Geology course is a required course for our majors. It is composed of mostly juniors and seniors, but there is often a sophomore or two. It typically has between 12-20 students. Lab is once a week and meets for 3 hours. Some labs are completed in these three hours, some take longer. For this specific lab, only a few finish the lab in 3 hours and most finish it on their own time. Labs are due at the beginning of lab the following week.

## Description and Teaching Materials

The lab is self-contained, with the exception of the equations for normal stress, shear stress, and the Mohr circle, which were derived in class. Also, it is helpful, but not necessary, to have graph paper. The images and graphs are provided, and come from original literature, or are from the Marshak and Mitra lab book "Basic Methods of Structural Geology."

## Teaching Notes and Tips

The lab is self-contained and no additional parts are needed, with the exception of graph paper. For plotting the circles, a compass is very helpful. Students usually need more explanation of what the experiments looked like than what is provided in the text. I go over this in lecture, but they never seem to remember it. The interpretation for combining Byerlee's law and Mohr-Coulomb failure usually requires more explanation. The pore pressure question can be solved numerically, but many try to do it graphically and have to be encouraged to do it numerically. We usually discuss the implications of pore-pressure and earthquake waves as a class. These discussions carry over into lecture where we begin to discuss the disposal of waste fluids at the Rocky Mountain Arsenal and from there we go into hydraulic fracturing.

## Assessment

Points are assessed for each question and the value of each question is indicated in the text.