1. The Mechanics of the crust
How do rocks deform in the crust ?
Mechanisms
Bearing strength
Must consider: Brittle crust
Ductile crust

2. The Brittle and the Ductile regime

3. Brittle : Fault Breccia

4. cataclastic intermediate between brittle and ductile Fault Gouge =>

5. Ductile : Mylonite

6. Triaxial experiment allow to impose various confining (blue) and deviatoric (red – blue) normal stresses

7. The regime stress-strain curves evolves when the confining pressure increases

8. The effect of increasing confining pressure
Confining stress

9. Two distinct types of plasticity
Strain Hardening Plasticity
At depth :
Strain Hardening Plasticity :
can accommodate
permanent strain without
losing the ability to resist load
At The surface :
Strain Softening Plasticity:
its ability to resist load
decreases with permanent
strain
Strain Softening Plasticity

10. The mode of failure evolves when increasing the confining pressure
Cataclastic
Brittle

11. IMPORTANT The loss of resistance of the upper crust
While the lower crust is still resistant
Is responsible for the the earthquakes instability :
For a given applied force the displacement should be infinite
Infinite displacement in the upper crust
upper crust
force

12. Confining Pressure Effects
The effect of increasing confining pressure

13. Responsible for the faults close to the surface
The Brittle regime
Responsible for the faults close to the surface

14. Common Observation : Conjugate Shear Fractures
Conjugate fractures
Are pair of fault which
Slip at the same time
They have opposite
shear senses

15. On rock experiments conjugates fault are also observed in the lab.

16. Mechanical Explanation of conjugates faults

17. Byerlee’s Law rule for rock friction deduced from triaxial experiment (t-s : mohr space)
NOT STABLE
STABLE s

18. Impossible Stress State
Any stress state whose circle lies outside the envelope is an unstable stress state, and is not physically possible
Before stress reaches this state, the sample would have failed

19. Failure Envelope
The Shaded stable Area is bounded by the failure envelope in black

20. Stable Stress State
Any stress state lying within the envelope is stable

21. Defining Stress State
Stress state tangent to the envelope defines the failure state
A fault forms…

22. Coulomb Criterion The failure enveloppe is linear
The further away from the origin the circle center is, the larger is the radius of the circle
The bigger is the maximum compression

23. Coulomb’s Criterion t = σs = C + μ σn
C is a constant that specifies the shear stress necessary to cause failure if the normal stress is zero (order 10 Mpa)
The two fractures occur at an angle fº, and correspond to the tangency points of the circle representing the stress state at failure with the Coulomb failure envelope

24. Byerlee’s Law rule for rock friction deduced from triaxial experiment (t-s : mohr space)
For σn < 200 MPa,
For 200MPa < σn < 5000MPa
where:
t = shear stress (MPa)
sn = normal stress (MPa)

25. Possibles Applications : Thrust are usualy diping under 30°
Continental deformation

26. The dip angle can serve to define the friction associated with the earthquake
Exercice what
is the friction angle
Here
subduction zone

27. Exercice : Conjugates faults
Plot on a stereonet the conjugates faults
Fa) Strike : 25°E, dip : 35°E
Fb) Strike : 30°W, dip : 15°W
Measure the angle between the fault planes
Deduce the internal friction angle and the principal directions of compression and extension

28. Normal Faults close to the surface
Here the two normal
Faults are conjugate
Faults they typically
form an angle of 60°

29. Conjugates Fault and Stress
Conjugate shear fractures develop at about  = 30 degrees from the maximum compressional stress : 1
1 bisects the acute angle of about 60o between the two fractures
The minimum compressional stress 3 bisects the obtuse angle between the two fractures

30. Conjugates Faults and the Principal Stresses
Reverse faults are more likely to form if 3 is vertical and constant (at a standard state), while horizontal, compressive 1 and 2 increase in value compared to the standard state
Normal faults form if 1 is vertical and constant, while horizontal 3 and 2 decrease in value, or if horizontal 3 is tensile
Strike-slip faults form if 2 is vertical and constant, while horizontal 1 and 2 increase and decreases in value, respectively
NEAR the
SURFACE

32. Brace-Goetze strength profiles
Brittle
Ductile
After Kohlstedt et al., 1995

35. Brittle ductile transitions
Low temperature brittle – ductile transition
brittle faulting to cataclastic flow
High temperature brittle - ductile transition
cataclasis to intracrystalline plastic flow and/or diffusion creep

36. Frictional Sliding
Frictional force does not depend on the shape of the object
Both objects, of the same mass, have the same sliding force, despite having different areas of contact

37. Amonton’s Law
Frictional resistance to sliding  normal stress component across the surface
First “published” account this empirical law of friction was made by the French physicist Guillaume Amonton in 1699, although Leonardo da Vinci’s notes indicate he knew of the result about 200 years earlier
If normal stress increases, the asperities are pushed more deeply into the opposing surface, and increasing resistance to sliding
Amonton reference:
Da Vinci reference:

38. Fracture Surface
Fracture surface, showing voids and asperities (Figure 6.23a, text)
As another, also bumpy, surface tries to slide over the first surface, their asperities interact, causing friction
Images:

39. Real Area of Contact
The bumps mean that only a small part of the surfaces are actually in contact
Dark areas are real area of contact (RAC) (Figure 6.23c, text)

40. Surface Anchors
The forces normal to these surfaces will be concentrated on the small areas in contact
Asperities cumulatively act as small anchors, retarding any slippage along the surface (Figure 6.23b, text)

41. Criteria for Frictional Sliding
Before the initiation of frictional sliding, enough shear must be present to overcome friction
We can define a criterion for frictional sliding to represent the necessary shear
Experimental work has shown that, independent of rock type, the following criterion holds
σs/σn = constant

42. Movement of Stress Along σ3 Axis
When represented on a Mohr diagram, the Mohr circle moves to the left along the normal stress axis
Figure 6.27 in text

43. Pore Pressure and Shear Fracturing
Pore pressure also plays a role on shear fracturing
Since pore pressure counteracts the confining pressure, we can rewrite the equation for shear stress to take pore pressure into account:
σs = c + μ(σn - Pf)