Week 8

Question 1

Forming the Mohr Circle

Answer 1

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

Question 2

Using the Mohr Circle diagram

Answer 2

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)

Question 3

Value of σs for planes // to σ1 and σ3

Answer 3

=0

Plot on σn axis

Question 4

In a triaxial experiment…

Answer 4

σ1 = vertical

σ3 = horizontal

Question 5

What value of 2θ for τmax?

Answer 5

90

Question 6

What planes plot onto the Mohr circle?

Answer 6

All other planes containing the σ2 axis

Non zero τ

Question 7

Diameter of the Mohr circle =

Answer 7

differential stress

= σ1-σ3

Question 8

Centre of the Mohr circle =

Answer 8

mean stress

= (σ1+σ3)/2

Question 9

Radius of the Mohr circle =

Answer 9

τmax

Question 10

Fractures =

Answer 10

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

Question 11

Shear fractures =

Answer 11

faults

Question 12

Extension/tensile fractures =

Answer 12

joints/fissures/veins/dykes

Question 13

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

Answer 13

Liquefaction

Question 14

Shear fractures, facts

Answer 14

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

Question 15

Andersonian Faults

Answer 15

Assume horizontal Earth’s surface

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

σ1 bisects acute angle

Question 16

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

Answer 16

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

Question 17

Stereonets; Where do the fault planes intersect?

Answer 17

At σ2

- principal stress axis in common

Question 18

Stereonets; What is the pole to the σ1σ3 plane?

Answer 18

σ2

Question 19

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

Answer 19

σ2

Question 20

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

Answer 20

σ1

Question 21

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

Answer 21

σ3

Question 22

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

Answer 22

σ1 = normal fault

σ2 = strike-slip fault

σ3 = thrust fault

Question 23

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

Answer 23

Where the fault planes intersect the σ1σ3 plane

Question 24

φ =

Answer 24

angle of internal friction

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

Controlled by characteristic ratio of σn:τf

Question 25

How can you find τmax from σ1 or σ3?

Answer 25

Count 45' from

Question 26

Triaxial compressional test

Answer 26

σ3 = confining pressure = depth Initial hydrostatic state (σ1=σ2=σ3) Compressional stresses loaded = σ1

Question 27

Triaxial compressional test; ultimate strength =

Answer 27

Differential stress at failure = σ1-σ3

Question 28

Triaxial compressional test; shearing resistance =

Answer 28

shear stress at failure = radius = τmax

Question 29

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

Answer 29

Increase ultimate strength (i.e. rock strength) I.E STRENGTH OF BRITTLE CRUST INCREASES WITH DEPTH, ITS ABSOLUTE STRENGTH IS DUE TO LITHOLOGY

Question 30

Triaxial compressional test; envelope of failure

Answer 30

Can draw Mohr circles θ values ~constant = envelope of failure - stable - critical - unstable Planes within orientation have τ > that required to fail rock

Question 31

Coulomb-Naiver failure criterion

Answer 31

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

Question 32

Coulomb-Naiver; Typical values of φ

Answer 32

30-40' Irrespective of rock type

Question 33

Coulomb-Naiver; Typical values of μ

Answer 33

0.58-0.85 Irrespective of rock type

Question 34

Coulomb-Naiver; Typical values of θ

Answer 34

50-60' Irrespective of rock type

Question 35

Coulomb-Navier; what is S?

Answer 35

Cohesion = τf on a surface where σn = 0

Question 36

Coulomb-Navier; where does tensile strength occur?

Answer 36

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

Question 37

Reality check with Mohr failure envelopes

Answer 37

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

Question 38

Von Mises criterion

Answer 38

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

Question 39

Plate motion-related stresses

Answer 39

Slab pull Ridge push Basal drag Collisional resistance

Question 40

Plate motion-related second order stresses

Answer 40

Sediment loading Glacial loading/unloading Areas of thin crust + mantle upwelling Ocean-continent transitions Orogenic belts Large weak faults