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Structural > Week 8 > Flashcards

Week 8 Flashcards

1
Q

Forming the Mohr Circle

A
  1. Equation of a circle with centre (p,0)
    (x-p)^2 + y^2 = r^2

x = p + rcosα

y = rsinα

σn = (σ1+σ3)/2 + (σ1-σ3)/2 cos2θ = x

σs = ‎τ = sin2θ(σ1+σ3)/2= y

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2
Q

Using the Mohr Circle diagram

A

Plane makes an angle at ‎θ between σ1 and σ3

Draw 2θ from σn = work out σn and τ for any given plane (can also use the equations)

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3
Q

Value of σs for planes // to σ1 and σ3

A

=0

Plot on σn axis

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4
Q

In a triaxial experiment…

A

σ1 = vertical

σ3 = horizontal

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5
Q

What value of 2θ for τmax?

A

90

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6
Q

What planes plot onto the Mohr circle?

A

All other planes containing the σ2 axis

Non zero τ

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7
Q

Diameter of the Mohr circle =

A

differential stress

= σ1-σ3

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8
Q

Centre of the Mohr circle =

A

mean stress

= (σ1+σ3)/2

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9
Q

Radius of the Mohr circle =

A

τmax

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10
Q

Fractures =

A

planar displacement in displacement and mechanical properties, minerals broken = loss of cohesion

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11
Q

Shear fractures =

A

faults

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12
Q

Extension/tensile fractures =

A

joints/fissures/veins/dykes

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13
Q

What happens if pore fluid pressure > σ1 in tensile/mode I fractures?

A

Liquefaction

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14
Q

Shear fractures, facts

A 
Conjugate pairs
Opposed dipping
Same displacement type
Acute angle ~60'
Active same time = mutually cross-cutting
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15
Q

Andersonian Faults

A

Assume horizontal Earth’s surface

τ=0
= principal stress plane so an axis must be perpendicular

σ1 bisects acute angle

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16
Q

Typical dip of faults (acute angle) in different Andersonian faults

A
  1. Reverse/thrust = 30’
  2. Normal = 60’
  3. Strike-slip = 90’
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17
Q

Stereonets; Where do the fault planes intersect?

A

At σ2

- principal stress axis in common

18
Q

Stereonets; What is the pole to the σ1σ3 plane?

A

σ2

19
Q

Stereonets; Which principal stress axis is 90’ from slickenline fibres?

A

σ2

20
Q

Stereonets; Which principal stress axis bisects the angle between the fault planes?

A

σ1

21
Q

Stereonets; Which principal stress axis do you get to if you count 90’ from σ1?

A

σ3

22
Q

Stereonets; Which principal stress axis is ~vertical tells you the type of fault (lithostatic = perpendicular to the Earth’s surface due to g)…

A

σ1 = normal fault

σ2 = strike-slip fault

σ3 = thrust fault

23
Q

Stereonets; What does the orientation of the slickenline tell you?

A

Where the fault planes intersect the σ1σ3 plane

24
Q

φ =

A

angle of internal friction

= TOTAL angle between τmax planes and the fault planes (add up)

Controlled by characteristic ratio of σn:τf

25
Q

How can you find τmax from σ1 or σ3?

A

Count 45’ from

26
Q

Triaxial compressional test

A

σ3 = confining pressure = depth

Initial hydrostatic state (σ1=σ2=σ3)

Compressional stresses loaded = σ1

27
Q

Triaxial compressional test; ultimate strength =

A

Differential stress at failure = σ1-σ3

28
Q

Triaxial compressional test; shearing resistance =

A

shear stress at failure = radius = τmax

29
Q

Triaxial compressional test; what happens when you increase confining pressure?

A

Increase ultimate strength (i.e. rock strength)

I.E STRENGTH OF BRITTLE CRUST INCREASES WITH DEPTH, ITS ABSOLUTE STRENGTH IS DUE TO LITHOLOGY

30
Q

Triaxial compressional test; envelope of failure

A

Can draw Mohr circles

θ values ~constant = envelope of failure

  • stable
  • critical
  • unstable
    Planes within orientation have τ > that required to fail rock
31
Q

Coulomb-Naiver failure criterion

A

τf = f(σn)

τf = S+μσn
y = c + mx
τf = shearing resistance
S = cohesion of solid/initial shear strength
μ = coefficient of internal friction (tanφ)
σn = σn on plane at failure

Stress state that leads to brittle failure in compressional conditions

When shear stress = shearing resistance = FRACTURE

32
Q

Coulomb-Naiver; Typical values of φ

A

30-40’

Irrespective of rock type

33
Q

Coulomb-Naiver; Typical values of μ

A

0.58-0.85

Irrespective of rock type

34
Q

Coulomb-Naiver; Typical values of θ

A

50-60’

Irrespective of rock type

35
Q

Coulomb-Navier; what is S?

A

Cohesion

= τf on a surface where σn = 0

36
Q

Coulomb-Navier; where does tensile strength occur?

A

Where failure envelope intersects normal stress axis (σn = -ve)

37
Q

Reality check with Mohr failure envelopes

A
  1. Envelope generally flattens towards higher differential stresses/confining pressures (approaching ductile regime)
  2. Assumes materials are isotropic i.e. S and miu don’t vary in different orientations

KEY CONTROL: orientation of anisotropy relative to principal stresses

38
Q

Von Mises criterion

A

Failure at higher differential stresses/confining pressures occurs at constant τ and different stress on planes sub// to τmax planes

39
Q

Plate motion-related stresses

A

Slab pull

Ridge push

Basal drag

Collisional resistance

40
Q

Plate motion-related second order stresses

A

Sediment loading

Glacial loading/unloading

Areas of thin crust + mantle upwelling

Ocean-continent transitions

Orogenic belts

Large weak faults

Structural (17 decks)

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