Week 7

Question 1

F=

Answer 1

ma

Question 2

Newton’s 3rd law

Answer 2

equal and opposite reactions

Interactions BETWEEN bodies

Question 3

Is strain internal or external

Answer 3

Internal

Question 4

What is the internal distribution of forces within an object?

Answer 4

Stress

Question 5

Body stress =

Answer 5

Force/unit vol

= act upon and proportional to mass

e.g. gravity

Question 6

Surface stress =

Answer 6

“stresses on a surface”

Force/unit area

= act across real/imagined surfaces and can vary within

Question 7

What surfaces do geological bodies interact along?

Answer 7

Plate boundaries

Faults

Bedding planes

Joints

Question 8

σ =

Answer 8

F/A

Units = N/m2 = Pa

F = vector therefore σ = vector
i.e. has magnitude/orientation

Question 9

1MPa =

Answer 9

10 bars

Question 10

100 MPa =

Answer 10

1kbar

Question 11

What happens to σ when you increase A?

Answer 11

A = “size of area of action”

Decreases σ

Question 12

Resolving σ

Answer 12

σn = normal stress = σcos^2θ
- perpendicular to surface

σs = shear stress = σsin2θ/2
- // to surface

Question 13

θ =

Answer 13

angle between stress vector and surface of action

Question 14

How do σn, σs, Fn and Fs vary as θ varies from 0-90?

Answer 14

σn decreases, Fn decreases

σs peaks at 45’, Fs increases

Question 15

Planes at 45’

Answer 15

EXPERIENCE THE MAX SHEAR STRESS

• will reach critical condition for failure quicker
• if shear stress is the only thing affecting the fault will be at 45’

Question 16

Stress ellipsoid

Answer 16

σ1 >= σ2 >=σ3

All normal stresses
Principal stresses
Principal planes of stress
Perpendicular
σs = 0

Question 17

Stress tensor components

Answer 17

x,y,z reference system

σ2,1

Stress in the ‘2’ plane (perpendicular to that axis) acting in the ‘1’ direction

Question 18

Hydrostatic stress

Answer 18

When σ1 = σ2 = σ3

SPHERE

Isotropic

σn = σ1 = σ2 = σ3
σs = 0

Only volume changes

Question 19

Mean stress

Answer 19

Isotropic

σm = (σ1+σ2+σ3)/3

Question 20

Measuring the departure of the stress state from a hydrostatic state

Answer 20

DEVIATORIC STRESS
- shape changes (distortions)

σ1-σm

σ2-σm

σ3-σm

Question 21

Differential stress

Answer 21

σ1-σ3

Used for fracturing behaviour

Question 22

Stresses on planes; orientation of σ2

Answer 22

Assumed // to plane

Question 23

Stresses on planes; σn =

Answer 23

(σ1+σ3)/2 + cosθ(σ1-σ3)/2

Question 24

Stresses on planes; σs =

Answer 24

sin2θ(σ1-σ3)/2

Question 25

Stresses on planes; what do the equations for σn and σs lead to

Answer 25

A pair of planes at σs max at 45’ to σ1 and σ3, intersecting // to σ2

Question 26

Types of fracture

Answer 26

1. MODE II
2. MODE II/III

Require a tensile σ3 (-ve)

Question 27

Mode II/III fractures

Answer 27

SHEAR fractures, form at an angle to σ1

= faults

Question 28

Mode I fractures

Answer 28

TENSILE fractures

// to σ1σ2 plane, open // to σ3

= joints/veins/dykes

Question 29

Tensile σ3

Answer 29

-ve

Rare within Earth (σn is normally compressive, +ve)

Effective tension arises where over pressurised fluid is injected along fractures to a pressure > σ3

Question 30

What does a mean tectonic transport direction of 100’ to 280’ mean?

Answer 30

Top-to-the-west overthursting

Question 31

POINT MAXIMUM

When points represent:

a) lines
b) poles to planes

Answer 31

a) linear preferred orientation

b) planar preferred orientation

Question 32

GREAT CIRCLE GIRDLE DISTRIBUTION

When points represent:

a) lines
b) poles to planes

Answer 32

a) planar preferred orientation (all lines lie in common plane)
b) linear preferred orientation (all planes contain a common line; beta axis (=regional fold axis))

Question 33

GIRDLES MAY SHOW POINT MAXIMA

When points represent:

a) lines
b) poles to planes

Answer 33

a) some lines also have linear preferred orientation

b) some planes also have planar preferred orientation (=fold limbs)

Question 34

Why do all natural datasets display spread?

Answer 34

Inaccurate measuremnets

Natural irregularity of structures

Dispersion of data due to later deformations

Curvilinear/curviplanar geometries

Question 35

Sheath fold

Answer 35

Initially slightly curved fold hinge line becomes accentuated by intense ductile shearing and strain

Fold hinges progressively rotated round into parallelism with mineral lineation (=X axis of finite strain)

Eye structures are common

Question 36

Where are the maximum and minimum normal stresses found?

Answer 36

On surfaces at 0 and 90 degrees to the imposed stress/force

Question 37

Where are the maximum and minimum values of shear stress found?

Answer 37

Max = on planes at 45’ to the imposed stress/force

Min = at 0 and 90’