Week 7 Flashcards
F=
ma
Newton’s 3rd law
equal and opposite reactions
Interactions BETWEEN bodies
Is strain internal or external
Internal
What is the internal distribution of forces within an object?
Stress
Body stress =
Force/unit vol
= act upon and proportional to mass
e.g. gravity
Surface stress =
“stresses on a surface”
Force/unit area
= act across real/imagined surfaces and can vary within
What surfaces do geological bodies interact along?
Plate boundaries
Faults
Bedding planes
Joints
σ =
F/A
Units = N/m2 = Pa
F = vector therefore σ = vector
i.e. has magnitude/orientation
1MPa =
10 bars
100 MPa =
1kbar
What happens to σ when you increase A?
A = “size of area of action”
Decreases σ
Resolving σ
σn = normal stress = σcos^2θ
- perpendicular to surface
σs = shear stress = σsin2θ/2
- // to surface
θ =
angle between stress vector and surface of action
How do σn, σs, Fn and Fs vary as θ varies from 0-90?
σn decreases, Fn decreases
σs peaks at 45’, Fs increases
Planes at 45’
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’
Stress ellipsoid
σ1 >= σ2 >=σ3
All normal stresses Principal stresses Principal planes of stress Perpendicular σs = 0
Stress tensor components
x,y,z reference system
σ2,1
Stress in the ‘2’ plane (perpendicular to that axis) acting in the ‘1’ direction
Hydrostatic stress
When σ1 = σ2 = σ3
SPHERE
Isotropic
σn = σ1 = σ2 = σ3 σs = 0
Only volume changes
Mean stress
Isotropic
σm = (σ1+σ2+σ3)/3
Measuring the departure of the stress state from a hydrostatic state
DEVIATORIC STRESS
- shape changes (distortions)
σ1-σm
σ2-σm
σ3-σm
Differential stress
σ1-σ3
Used for fracturing behaviour
Stresses on planes; orientation of σ2
Assumed // to plane
Stresses on planes; σn =
(σ1+σ3)/2 + cosθ(σ1-σ3)/2
Stresses on planes; σs =
sin2θ(σ1-σ3)/2
Stresses on planes; what do the equations for σn and σs lead to
A pair of planes at σs max at 45’ to σ1 and σ3, intersecting // to σ2
Types of fracture
- MODE II
- MODE II/III
Require a tensile σ3 (-ve)
Mode II/III fractures
SHEAR fractures, form at an angle to σ1
= faults
Mode I fractures
TENSILE fractures
// to σ1σ2 plane, open // to σ3
= joints/veins/dykes
Tensile σ3
-ve
Rare within Earth (σn is normally compressive, +ve)
Effective tension arises where over pressurised fluid is injected along fractures to a pressure > σ3
What does a mean tectonic transport direction of 100’ to 280’ mean?
Top-to-the-west overthursting
POINT MAXIMUM
When points represent:
a) lines
b) poles to planes
a) linear preferred orientation
b) planar preferred orientation
GREAT CIRCLE GIRDLE DISTRIBUTION
When points represent:
a) lines
b) poles to planes
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))
GIRDLES MAY SHOW POINT MAXIMA
When points represent:
a) lines
b) poles to planes
a) some lines also have linear preferred orientation
b) some planes also have planar preferred orientation (=fold limbs)
Why do all natural datasets display spread?
Inaccurate measuremnets
Natural irregularity of structures
Dispersion of data due to later deformations
Curvilinear/curviplanar geometries
Sheath fold
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
Where are the maximum and minimum normal stresses found?
On surfaces at 0 and 90 degrees to the imposed stress/force
Where are the maximum and minimum values of shear stress found?
Max = on planes at 45’ to the imposed stress/force
Min = at 0 and 90’
