Geology 3263
Structural Geology
Homework Ch 5 – Rheology KEY
This homework is for the lecture marked “Chapter 5 Rheology” in topic
folder 5.
A. Refer to the graph on this page for questions 1-4
1. What is the depth for a confining pressure of 140 MPa?
140 MPa x 1 km/25 MPa = 5.6 km
2. What happens to the yield strength with increasing confining pressure?
Yield strength is the top differential stress along the linear (elastic) part, UP
3. What happens to the ultimate strength with increasing confining pressure?
Ultimate Strength is the top differential stress along the ductile part, UP
4. What happens to the rupture strength * with increasing confining
pressure? From about 11.5 to about 14.5 with increasing c
B. Refer to the graph on this page for questions 5 - 6
Sandstones and shales contain a significant fluid component
P*c = c – f i.e confining pressure is diminished by fluid pressure
5. What is the fluid pore pressure f for P*c = 150 MPa?
P*c = c – f , 150 MPa = 200 – 50 MPa
6. What happens to the ultimate (peak) strength (dots)
a. as effective confining pressure increases? Increases
b. as the pore pressure increases? P*c = c – f so P*c decreases
as f increases, so the lowest experiment line P*c = 0 has the
greatest pore pressure, with the lowest ultimate strength, so
ultimate strength decreases as the pore pressure increases.
C. Refer to the graph on this page for questions 7-8.
The role of Temperature.
7. If the temperature gradient is 25oC/km
what is the simulated depth of the
temperature 800 oC if the surface temperature is 25oC?
275/25 = 11 km
775/25 = 31 km
8. What happens to the
ultimate (blue bar) and decreases
yield strength (dot o) decreases
as temperature (depth) increases?
D. Refer to the graph on this page for questions 9-11.
The role of strain rate d/dt aka ’
Notice units for
l cancel
Tension (extension)
9. Look at the differential stress rupture points (furthest point
right).For the same rock (here Yule Marble) is the rupture point
stress higher under slow or fast strain rate? Fast
10. What happens to the yield strength (circles ) as the strain
rate e’ decreases? The slow experiment has lowest yield point,
and is mostly plastic
11. Example: Divergent Margin
Consider a cross section where Yule Marble was extended to 44
km from an initial length of 23 km. If the deformation took 1
d
 / t
  
million years,
dt
o
a. Calculate the strain rate. 44-23/3.1536 x 1013 sec = 6.67 x 10 -13
b. How does that compare to the experimental strain rates shown
above? This is much smaller (slower) Our experiments are too
brief.
E. Refer to the graph on this page for question 12.
12. A material is perfectly plastic if the ductile portion is nearly horizontal.
a. Which of these tests behaved closest to perfectly plastic in the ductile
region? 140 MPa
b. If the ductile portion of the curve is not approximately horizontal, it may
rise or fall after the yield point.
If it rises, more stress is needed the maintain deformation after the initial
pass through the yield point. This is called strain hardening.
If the curve declines (less stress required for the same strain) it is called
strain softening.
Label each line with strain softening or strain hardening.
140 and 130 MPa show the least strain softening.