slide1 n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Tectonics I PowerPoint Presentation
Download Presentation
Tectonics I

Loading in 2 Seconds...

play fullscreen
1 / 40

Tectonics I - PowerPoint PPT Presentation


  • 144 Views
  • Uploaded on

Tectonics I. Tectonics I Vocabulary of stress and strain Elastic, ductile and viscous deformation Mohr ’ s circle and yield stresses Failure, friction and faults Brittle to ductile transition Anderson theory and f ault types around the solar system Tectonics II

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Tectonics I' - china


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide2

Tectonics I

    • Vocabulary of stress and strain
    • Elastic, ductile and viscous deformation
    • Mohr’s circle and yield stresses
    • Failure, friction and faults
    • Brittle to ductile transition
    • Anderson theory and fault types around the solar system
  • Tectonics II
    • Generating tectonic stresses on planets
    • Slope failure and landslides
    • Viscoelastic behavior and the Maxwell time
    • Non-brittle deformation, folds and boudinage etc…
slide3

Compositional vs. mechanical terms

    • Crust, mantle, core are compositionally different
      • Earth has two types of crust
    • Lithosphere, Asthenosphere, Mesosphere, Outer Core and Inner Core are mechanically different
      • Earth’s lithosphere is divided into plates…
slide4

How is the lithosphere defined?

    • Behaves elastically over geologic time
    • Warm rocks flow viscously
      • Most of the mantle flows over geologic time
    • Cold rocks behave elastically
      • Crust and upper mantle
  • Rocks start to flow at half their melting temperature
    • Thermal conductivity of rock is ~3.3 W/m/K
    • At what depth is T=Tm/2

Melosh, 2011

slide5
Relative movement of blocks of crustal material

Mars –

Extension and compression

Earth –

Pretty much everything

Moon & Mercury –

Wrinkle Ridges

Europa – Extension and strike-slip

Enceladus - Extension

slide6

The same thing that supports topography allows tectonics to occur

    • Materials have strength
    • Consider a cylindrical mountain, width w and height h
    • How long would strength-less topography last?

w

Weight of the mountain

h

F=ma for material in the hemisphere

v

Conserve volume

Solution for h:

i.e. mountains 10km across would collapse in ~13s

slide7

Response of materials to stress (σ) – elastic deformation

L

ΔL

ΔL

L

Linear (normal) strain (ε) = ΔL/L

Shear Strain (ε) = ΔL/L

G is shear modulus (rigidity)

E is Young’s modulus

Volumetric strain = ΔV/V

K is the bulk modulus

slide8

Stress is a 2nd order tensor

    • Combining this quantity with a vector describing the orientation of a plane gives the traction (a vector) acting on that plane

i describes the orientation of a plane of interest

j describes the component of the traction on that plane

These components are arranged in a 3x3 matrix

Are normal stresses, causing normal strain

(Pressure is )

Are shear stresses, causing shear strain

We’re only interested in deformation, not rigid body rotation so:

slide9

The components of the tensor depend on the coordinate system used…

  • There is at least one special coordinate system where the components of the stress tensor are only non-zero on the diagonal i.e. there are NO shear stresses on planes perpendicular to these coordinate axes

Shear stresses in one coordinate system can appear as normal stresses in another

=

These are principle stresses that act parallel to the principle axes

The tractions on these planes have only one component – the normal component

Pressure again:

Where:

slide10

Principle stresses produce strains in those directions

    • Principle strains – all longitudinal
  • Stretching a material in one direction usually means it wants to contract in orthogonal directions
    • Quantified with Poisson’s ratio
    • This property of real materials means shear stain is always present
  • Extensional strain of σ1/E in one direction implies orthogonal compression of –ν σ1/E
    • Where ν is Poisson’s ratio
    • Range 0.0-0.5

Linear strain (ε) = ΔL/L

E is Young’s modulus

ΔL

L

Where λ is the Lamé parameter

G is the shear modulus

or

slide11

Groups of two of the previous parameters describe the elastic response of a homogenous isotropic solid

    • Conversions between parameters are straightforward
slide13

Materials fail under too much stress

    • Elastic response up to the yield stress
    • Brittle or ductile failure after that
  • Material usually fails because of shear stresses first
    • Wait! I thought there were no shear stresses when using principle axis…
    • How big is the shear stress?

Strain hardening

Special case of plastic flow

Strain Softening

Ductile (distributed) failure

Brittle failure

slide14

How much shear stress is there?

    • Depends on orientation relative to the principle stresses
    • In two dimensions…
    • Normal and shear stresses form

a Mohr circle

Maximum shear stress:

On a plane orientated at 45° to the principle axis

Depends on difference in max/min principle stresses

Unaffected (mostly) by the intermediate principle stress

slide15

(Tresca criterion)

  • Consider differential stress
    • Failure when:
    • Failure when:
  • Increase confining pressure
    • Increases yield stress
    • Promotes ductile failure

(Von Mises criterion)

  • Increase temperature
    • Decrease yield stress
    • Promotes ductile failure
slide16

Low confining pressure

    • Weaker rock with brittle faulting
  • High confining pressure (+ high temperatures)
    • Stronger rock with ductile deformation
slide17

What sets this yield strength?

  • Mineral crystals are strong, but rocks are packed with microfractures
  • Crack are long and thin
    • Approximated as ellipses
    • a >> b
    • Effective stress concentrators
    • Larger cracks are easier to grow

σ

b

a

σ

slide18

Failure envelopes

    • When shear stress exceeds a critical value then failure occurs
    • Critical shear stress increases with increasing pressure
    • Rocks have finite strength even with no confining pressure
    • Coulomb failure envelope
      • Yo is rock cohesion (20-50 MPa)
      • fF is the coefficient of internal friction (~0.6)

What about fractured rock?

Cohesion = 0

Tensile strength =0

Byerlee’s Law:

Melosh, 2011

slide19

Why do faults stick and slip?

  • Basically because the coefficients of static and dynamic friction are different
  • Stick-slip faults store energy to release as Earthquakes
    • Shear-strain increases with time as:
    • Stress on the fault is:
      • G is the shear modulus
      • σfd (dynamic friction) left over from previous break
      • Fault can handle stresses up to σfs before it breaks (Static friction)
    • Breaks after time:
    • Fault locks when stress falls to σfd (dynamic friction)
    • If σfd < σfs then you get stick-slip behavior
slide20

Brittle to ductile transition

    • Confining pressure increases with Depth (rocks get stronger)
    • Temperature increases with depth and promotes rock flow
    • Upper 100m – Griffith cracks
    • P~0.1-1 Kbars, z < 8-15km, shear fractures
    • P~10 kbar, z < 30-40km distributed deformation (ductile)
    • This transition sets the depth of faults

Melosh, 2011

Golembek

slide21

Back to Mohr circles…

  • Coulomb failure criterion is a straight line
    • Intercept is cohesive strength
    • Slope = angle of internal friction
    • Tan(slope) = fs
  • In geologic settings
    • Coefficient of internal friction ~0.6
    • Angle of internal friction ~30°
  • Angle of intersection gives fault orientation
  • So θ is ~60°
  • θ is the angle between the fault plane and the minimum principle stress,
slide22

Anderson theory of faulting

    • All faults explained with shear stresses
    • No shear stresses on a free surface means that one principle stress axis is perpendicular to it.
    • Three principle stresses
      • σ1 > σ2 > σ3
      • σ1 bisects the acute angle (2 x 30°)
      • σ2 parallel to both shear plains
      • σ3 bisects the obtuse angle (2 x 60°)
    • So there are only three possibilities
    • One of these principle stresses is the one that is perpendicular to the free surface.
    • Note all the forces here are compressive…. Only their strengths differ

σ2

slide23
Before we talk about faults….
  • Fault geometry
    • Dip measures the steepness of the fault plane
    • Strike measures its orientation
slide25

Extensional Tectonics

  • Crust gets pulled apart
  • Final landscape occupies more area than initial
  • Can occur in settings of
    • Uplift (e.g. volcanic dome)
    • Edge of subsidence basins (e.g. collapsing ice sheet)

Steeply dipping

Shallowly dipping

slide26
Horst and Graben
    • Graben are down-dropped blocks of crust
    • Parallel sides
    • Fault planes typically dip at 60 degrees
    • Horst are the parallel blocks remaining between grabens
    • Width of graben gives depth of fracturing
    • On Mars fault planes intersect at depths of 0.5-5km
slide28
In reality graben fields are complex…
    • Different episodes can produce different orientations
    • Old graben can be reactivated

Lakshmi -Venus

Ceraunius Fossae - Mars

slide30

Compressional Tectonics

  • Crust gets pushed together
  • Final landscape occupies less area than initial
  • Can occur in settings of
    • Center of subsidence basins (e.g. lunar maria)
  • Overthrust – dip < 20 & large displacements
  • Blindthrust – fault has not yet broken the surface

Steeply dipping

Shallowly dipping

slide33

Right-lateral (Dextral)

Left-lateral (Sinistral)

Shear Tectonics

  • Strike Slip faults
    • Shear forces cause build up of strain
    • Displacement resisted by friction
    • Fault eventually breaks
  • Vertical Strike-slip faults = wrench faults
  • Oblique normal and thrust faults have a strike-slip component

Europa

slide34

Tectonics I

    • Vocabulary of stress and strain
    • Elastic, ductile and viscous deformation
    • Mohr’s circle and yield stresses
    • Failure, friction and faults
    • Brittle to ductile transition
    • Anderson theory and fault types around the solar system
  • Tectonics II
    • Generating tectonic stresses on planets
    • Slope failure and landslides
    • Viscoelastic behavior and the Maxwell time
    • Non-brittle deformation, folds and boudinage etc…
slide36
How to faults break?
  • Shear zone starts with formation of Riedel shears (R and R’)
    • Orientation controlled by angle of internal friction
  • Formation of P-shears
    • Mirror image of R shears
    • Links of R-shears to complete the shear zone

Revere St., San Francisco

(Hayward Fault)

slide37
Wrinkle ridges
    • Surface expression of blind thrust faults (or eroded thrust faults)
    • Associated with topographic steps
    • Upper sediments can be folded without breaking
    • Fault spacing used to constrain the brittle to ductile transition on Mars

Montesi and Zuber, 2003.

slide38

Where η is the dynamic viscosity

  • Rocks flow as well as flex
    • Stress is related to strain rate
    • Viscous deformation is irreversible
    • Motion of lattice defects, requires activation energies
    • Viscous flow is highly temperature dependant

w

h

Back to our mountain example

v

Solution for h:

Works in reverse too…

In the case of post-glacial rebound

τ ~ 5000years

w ~ 300km

Implies η ~ 1021 Pa s – pretty good

slide39
How to quantify τfs
    • Sliding block experiments
    • Increase slope until slide occurs
    • Normal stress is:
    • Shear stress is:
    • Sliding starts when:
  • Experiments show:
    • Amonton’s law – the harder you press the fault together the stronger it is
    • So fs=tan(Φ)
    • fs is about 0.85 for many geologic materials
  • In general:
    • Coulomb behavior – linear increase in strength with confining pressure
    • Co is the cohesion
    • Φ is the angle of internal friction
    • In loose granular stuff Φ is the angle of repose (~35 degrees) and Co is 0.
slide40
Effect of pore pressure
    • Reduces normal stress…
    • And cohesion term…
    • Material fails under lower stresses
    • Pore pressure – interconnected full pores
    • Density of water < rock
    • Max pore pressure is ~40% of overburden
  • Landslides on the Earth are commonly triggered by changes in pore pressure