Announcements Next week lab:

1-3 PM Mon. and Tues. with Andrew McCarthy.

Please start on lab before class and come prepared with specific questions Cottonwood wash ex. Due on Mon. in lecture

There will be NO lecture next Wed., Oct. 2.

Please use the time to: 1) Study important terms/concepts at end of Powerpoint lectures 2) Work on practice problems (perhaps as a group in this room) 3) Fault project

Stress and the Mohr diagram (D&R, 98-122)

1. Why learn about stress? 2. What is stress?

3. Lithostatic stress 4. Important stress tractions and stress ellipse 5. Stress Mohr circle

Why study stress?

Dynamic/mechanical analysis:

Interpret the stresses that produce deformation - Tectonic stresses and processes

-

Rock deformation

Force vs. Stress

Force:

That which changes, or tends to change, body motion

Newton's first law of motion:

F=ma mass in kg; acceleration in m/s 2 1 Newton (1N) = 1kg m/s 2 Forces are vector quantities; they have magnitude and direction.

Body forces: act on every point within a body GRAVITY! F = mg Surface forces: act on a specific surface in a body

Stress:

that which tends to deform a body how is it different than force?

Deformation depends on how force is distributed!

Stress may be thought of as a description of force concentration

Stress on a plane (traction),

s

= F/A

what about units of stress?

1N/m 2 = 1 Pa 100 MPa = 1 kbar

lithostatic stress vertical force =

r

Vg =

r

L 3 g vertical stress =

r

L 3 g/L 2 =

r

gL

r

gL = (2700 kg/m 3 )(10m/s 2 )(1500m) = 40500000 Pa = 40.5 MPa = .405 kbar

a stress traction is a vector, like force normal stress (traction):

stress perpendicular to plane

shear stress (traction):

stress parallel to plane

s

3

A complete definition of

Stress =

a description of tractions at a given point on

all

possible surfaces going through the point s

1

s

1:

Principal axis of greatest compressive stress s

3:

Principal axis of least compressive stress s

3

s

1 and

s

3 always perpendicular and always perpendicular to planes of no shear stress

s

1

The

goal

of stress analysis is to determine the normal and shear stresses on any plane of any orientation, given the directions and magnitudes of the principal stresses

Analytical approach: Fundamental stress equations

s

N

s

S

 s 1  s 1  s 3  2 s 3 2  sin s 1 2   s 3 2 cos 2  

=

angle of plane from s 1 s

N

 s 1  s 3 2 2  s

S

2  s 1  s 3 2 2

Equation for a circle!

Geometric approach: Mohr Stress Diagram a plot of

s

s vs.

s

n first step:

plot s 1 and s 3 recalling that they are in directions of no shear stress; draw Mohr circle

second step:

Draw a line representing the plane at 2  , measured from s 3.

differential stress: (

s

1 -

s

3 ) diameter of circle

causes distortion

mean stress: (

s

1 +

s

3 )/2 center of circle

causes dilation

deviatoric stress: (

s

1 -

s

3 )/2 radius of circle

causes distortion

Mohr circles are useful for visualizing states of stress hydrostatic:

equal stress magnitude in all directions

pore fluid pressure:

serves to decrease confining pressure

effective stress

= confining pressure – fluid pressure

Next Lecture

Stress and Deformation

( D&R, 122-126; 226-252)

Important terminology/concepts

force vs. stress static vs. dynamic equilibrium body forces vs. contact forces lithostatic stress definition of stress greatest/least principal stress directions normal stress (traction) shear stress (traction) Mohr circle stress diagram mean stress differential stress deviatoric stress effective stress pore fluid pressure hydrostatic state of stress dynamic/mechanical analysis

Ratio of s S / s N can be used to evaluate if failure is going to occur!