1. Geology 3120 - Failure Models
Powerpoint notes are available online at:

2. Outline Virtual rock deformation experiment
Influence of pore fluid pressure
Andersonian faulting
Byerlee’s law
Other failure models

3. Virtual Rock Deformation Experiment
Run
s1 (MPa)
s3 (Mpa)
Failure (Q) 1
250
150
none 2 50
+37° 3
490
190 4
690
310 s1 s3 +Q

4. Run 1: s1= 250 MPa; s3=150 MPa; no fracture

5. Run 1: s1= 250 MPa; s3=150 MPa; no fracture

6. Run 2: s1= 250 MPa; s3= 50 MPa; 37° fracture

7. Run 2: s1= 250 MPa; s3=150 MPa; no fracture
74°

8. Run 3: s1= 490 MPa; s3=190 MPa; 37° fracture

9. Run 3: s1= 490 MPa; s3=190 MPa; 37° fracture
74°

10. Run 4: s1= 690 MPa; s3=310 MPa; 37° fracture

11. Run 4: s1= 690 MPa; s3=310 MPa; 37° fracture
74°

12. Determining the Failure Envelope
sc = 0.29sn + 60 MPa f
f = 16
tan f = 0.29
s0 = 60 MPa
sc = 0.29sn + 60 MPa

13. Predicting Failure
Run 5: s3= 250 MPa; at what s1 fracture occur?

14. Run 5: s3= 200 MPa; at what s1 fracture occur?
Predicting Failure
74°
Run 5: s3= 200 MPa; at what s1 fracture occur?

15. Influence of Pore Fluid Pressure
Effective Stress
Applied Stress pf
Pore fluid pressure decreases normal stresses by the fluid pressure amount.
Rock can then fail under the Mohr-Coulomb Law.

16. Principal Stresses s2 - intermediate principal stress
s1 - greatest principal stress
s2 - intermediate principal stress
s3 - minimum principal stress
Principal stress directions are mutually perpendicular to each other

17. Conjugate Faults
Most simply - two fault planes that intersect to form a straight line
Perhaps more typical - two fault surfaces that intersect to form a line
Acute angle - < 90° angle
Obtuse angle - > 90° angle
Acute
Obtuse

18. Assumptions for Andersonian Faultingsn sc
Y = mX + b (
Coulomb brittle failure - no pre-existing faults
f = Q
Most rocks have f = 30° so Q = ±30°

19. Assumptions for Andersonian Faulting
Normal stress (s1 , s2, s3)
Zero shear stress
No shear stress exists at the Earth’s surface
One principal stress must act normal to the surface
s1 , s2, or s3 must be perpendicular to the surface

20. Rules of Thumb for Stresses
s1 bisects the acute angle
s2 is parallel to the intersection of conjugate faults
s3 bisects the obtuse angle

21. Normal Fault

22. Strike-slip Fault

23. Thrust Fault

24. Normal faulting South North
Find the conjugate faults and determine the orientations of principal stresses.

25. Normal faulting
South North

26. Normal faulting
South North s1 s3 s2 s1

27. Determining Sense of Slip

28. Determining Sense of Slip

29. Determining Sense of Slip

30. Determining Sense of Slip

31. Determining Sense of Slip

32. Determining Sense of Slip

33. Byerlee’s Law of Rock Frictionss
mf = sn
mf = coefficient of sliding friction

34. Byerlee verses Mohr-Coulomb Failure
For a given differential stress, brittle failure will occur by frictional sliding on pre-existing fractures (if they exist) prior to Coulomb failure

35. Failure Models

36. References
Slides 21, 22, 24, 39, 40
Davis. G. H. and S. J. Reynolds, Structural Geology of Rocks and Regions, 2nd ed., John Wiley & Sons, New York, 776 p., 1996.
Slide 41
Twiss, R. J. and E. M. Moores, Structural Geology, W. H. Freeman & Co., New York, 532 p., 1992.