PTYS 554 Evolution of Planetary Surfaces Tectonics I

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…


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…


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


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


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


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


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:


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:


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


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

Conversions between parameters are straightforward


Typical numbers (Turcotte & Schubert)


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


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


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)


Low confining pressure Weaker rock with brittle faulting

High confining pressure (+ high temperatures) Stronger rock with ductile deformation


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


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:


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?


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


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,


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


Before we talk about faults….

Fault geometry Dip measures the steepness of the fault plane Strike measures its orientation


Largest principle (σ1) stress perpendicular to surface

Typical dips at ~60°


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


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



In reality graben fields are complex… Different episodes can produce different orientations Old graben can be reactivated

Lakshmi -VenusCeraunius Fossae - Mars


Smallest (σ3) principle stress perpendicular to surface

Typical dips of 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


Montesi and Zuber, 2003.


Intermediate (σ2) principle stress perpendicular to surface

Fault planes typically vertical


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


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…


Random extras


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)


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.


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


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


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

ygPf

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PTYS 554 Evolution of Planetary Surfaces Tectonics I