Stress what is it, and how do we infer it from geologic structures we observe and measure?

Stress is a force measured over a given area. As geologists we dont get to see stress, - we infer it from strain. Structural geology largely considers stress in terms of the

orientation of a particular stress state, and differences between stresses acting in one direction vs another

It is very difficult to directly measure the magnitude of stress in

the Earth.

Reading: Some of this material is derived from Chapter 4 in Fossen, the rest is from lectures Ive developed.

We can start by considering stress applied over a plane in two dimensions (which is called plane strain), important because it keeps movement contained within the plane we are viewing.

Class question: Why would we want to distinguish a normal stress from shear

stress? They are both just stresses, right? Lets start with the orientation of a particular stress relative to a

plane. How would a normal stress be oriented relative to the plane? How would a shear stress be oriented relative to the plane? How would deformation vary as normal and shear stresses changed? Would flattening or shearing of rock occur under one condition more than the other?

Rock climbers understand this intuitively. When they climb slabs of rock, how do they orient their bodies? Parallel to the rock face, or with their legs at a high angle to the rock? Experienced slab climbers keep their backside out from the rock, so their shoes are pushing against the rock surface, maximizing normal stress (and friction as well). Inexperienced climbers hug the rock, and increase the shear stress between their shoes and the rock surface (decreasing friction). At which point they usually fall off..

Stemming in a chimney also requires a good understanding of the correct application of normal stresses.

Heads up You should know basic rules for angles in trigonometry eqns Angles as they relate to sine, cosine and tangent Also (very) basic algebra, ratios, substitution No differential eqns, matrix algebra, quantum mechanics ;-0( (sorry) But if you dont like using equations, use the graphical tools well Introduce in the next lecture on Mohr Stress Diagrams (based on the equations here).

You are NOT responsible for the derivation, just remembering the equations

Lets consider normal and shear stresses Here we are placing a force on a plane of particular orientation, then resolving normal and shear stresses on that plane. (sigma = stress)

Theta is defined as the angle between the maximum stress and the plane the stresses are acting on

Lets first solve for the shear stresses acting on a plane of known orientation

Equations well need

Lets first solve for the shear stresses acting on a plane of known orientation

Lets first solve for the shear stresses acting on a plane of known orientation

So now weve solved for shear stress

Now lets solve for normal stress acting on the plane

Now lets solve for normal stress acting on the plane

Now lets solve for normal stress acting on the plane

So now weve solved for normal stress

Here then are the equationss for both normal & shear stresses

For what value is the shear stress greatest?

Calculating maximum shear stress

For what value is the shear stress greatest? (45) 2 = 90

F

A

/4

Find the dip of the plane such that shear stress, ss is Minimized and normal stress sn maximized.

A

F

Draw the plane on the block figure.

Class problem

Class Problem

A

F

Draw the plane on a block figure.

Find the dip of the plane such that shear stress is minimized and normal stress is maximized.

The relationship between stresses and

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 /4 /2

n

s

F/A = 1