ptys 554 evolution of planetary surfaces tectonics i
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PTYS 554
Evolution of Planetary Surfaces
Tectonics ITectonics I
PYTS 554 – Tectonics I 2
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…
PYTS 554 – Tectonics I 3
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…
PYTS 554 – Tectonics I 4
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
Melosh, 2011
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
PYTS 554 – Tectonics I 5
Relative movement of blocks of crustal material
Moon & Mercury –
Wrinkle Ridges
Europa – Extension and strike-slip Enceladus - Extension
Mars –
Extension and compressionEarth –
Pretty much everything
PYTS 554 – Tectonics I 6
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?
Weight of the mountain
Conserve volume
w
h
v
F=ma for material in the hemisphere
Solution for h:
i.e. mountains 10km across would collapse in ~13s
PYTS 554 – Tectonics I 7
Response of materials to stress (σ) – elastic deformation
LΔL ΔL
Linear (normal) strain (ε) = ΔL/L Shear Strain (ε) = ΔL/L
E is Young’s modulus G is shear modulus (rigidity)
Volumetric strain = ΔV/V
K is the bulk modulus
L
PYTS 554 – Tectonics I 8
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 interestj describes the component of the traction on that planeThese 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:
PYTS 554 – Tectonics I 9
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
Where:
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:
PYTS 554 – Tectonics I 10
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
Where λ is the Lamé parameter
G is the shear modulus
or
LΔL
Linear strain (ε) = ΔL/L
E is Young’s modulus
PYTS 554 – Tectonics I 11
Groups of two of the previous parameters describe the elastic response of a homogenous isotropic solid
Conversions between parameters are straightforward
PYTS 554 – Tectonics I 12
Typical numbers (Turcotte & Schubert)
PYTS 554 – Tectonics I 13
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?
Brittle failure Ductile (distributed) failure
Strain hardening
Strain Softening
Special case of plastic flow
PYTS 554 – Tectonics I 14
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 axisDepends on difference in max/min principle stressesUnaffected (mostly) by the intermediate principle stress
PYTS 554 – Tectonics I 15
Consider differential stress Failure when:
Failure when:
Increase confining pressure Increases yield stress Promotes ductile failure
Increase temperature Decrease yield stress Promotes ductile failure
(Tresca criterion)
(Von Mises criterion)
PYTS 554 – Tectonics I 16
Low confining pressure Weaker rock with brittle faulting
High confining pressure (+ high temperatures) Stronger rock with ductile deformation
PYTS 554 – Tectonics I 17
Crack are long and thin Approximated as ellipses a >> b Effective stress concentrators
Larger cracks are easier to grow
a
b
σ
σ
What sets this yield strength? Mineral crystals are strong, but rocks are packed with microfractures
PYTS 554 – Tectonics I 18
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)
Melosh, 2011
What about fractured rock?Cohesion = 0Tensile strength =0
Byerlee’s Law:
PYTS 554 – Tectonics I 19
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
Why do faults stick and slip?
PYTS 554 – Tectonics I 20
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
PYTS 554 – Tectonics I 21
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,
PYTS 554 – Tectonics I 22
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
PYTS 554 – Tectonics I 23
Before we talk about faults….
Fault geometry Dip measures the steepness of the fault plane Strike measures its orientation
PYTS 554 – Tectonics I 24
Largest principle (σ1) stress perpendicular to surface
Typical dips at ~60°
PYTS 554 – Tectonics I 25
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)
Extensional Tectonics
Shallowly dipping
Steeply dipping
PYTS 554 – Tectonics I 26
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
PYTS 554 – Tectonics I 27
PYTS 554 – Tectonics I 28
In reality graben fields are complex… Different episodes can produce different orientations Old graben can be reactivated
Lakshmi -VenusCeraunius Fossae - Mars
PYTS 554 – Tectonics I 29
Smallest (σ3) principle stress perpendicular to surface
Typical dips of 30°
PYTS 554 – Tectonics I 30
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
Shallowly dipping
Steeply dipping
PYTS 554 – Tectonics I 31
Montesi and Zuber, 2003.
PYTS 554 – Tectonics I 32
Intermediate (σ2) principle stress perpendicular to surface
Fault planes typically vertical
PYTS 554 – Tectonics I 33
Strike Slip faults Shear forces cause build up of strain Displacement resisted by friction Fault eventually breaks
Right-lateral (Dextral)
Left-lateral (Sinistral)
Shear Tectonics
Vertical Strike-slip faults = wrench faults
Oblique normal and thrust faults have a strike-slip component
Europa
PYTS 554 – Tectonics I 34
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…
PYTS 554 – Tectonics I 35
Random extras
PYTS 554 – Tectonics I 36
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)
PYTS 554 – Tectonics I 37
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.
PYTS 554 – Tectonics I 38
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
Where η is the dynamic viscosity
w
h
v
Solution for h:
Back to our mountain example
Works in reverse too…In the case of post-glacial rebound
τ ~ 5000 yearsw ~ 300km
Implies η ~ 1021 Pa s – pretty good
PYTS 554 – Tectonics I 39
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.
Nsfs f
fsf
PYTS 554 – Tectonics I 40
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
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