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'

Week 7 Flashcards by Elle Kinsman

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Newton’s 3rd law

equal and opposite reactions

Interactions BETWEEN bodies

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Is strain internal or external

Internal

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What is the internal distribution of forces within an object?

Stress

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Body stress =

Force/unit vol

= act upon and proportional to mass

e.g. gravity

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Surface stress =

“stresses on a surface”

Force/unit area

= act across real/imagined surfaces and can vary within

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What surfaces do geological bodies interact along?

Plate boundaries

Faults

Bedding planes

Joints

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σ =

F/A

Units = N/m2 = Pa

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

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1MPa =

10 bars

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100 MPa =

1kbar

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What happens to σ when you increase A?

A = “size of area of action”

Decreases σ

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Resolving σ

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

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

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θ =

angle between stress vector and surface of action

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

σn decreases, Fn decreases

σs peaks at 45’, Fs increases

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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’

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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

1. MODE II 2. 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'