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Tectonics and Lithosphere Dynamics > (1.1) Stress, Strain, Strength and Heat > Flashcards

(1.1) Stress, Strain, Strength and Heat Flashcards

1
Q

Define “stress”

A

Quantification of how much a substance is being pushed

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2
Q

Define “strain”

A

Deformation caused by the stress: i.e. change in dimensions: length, angle, area, volume, etc.

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3
Q

What are the units of stress?

A

Force per Unit Area (Nm-2 or Pa)

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4
Q

What is the equation for Weight?

A

Weight = Mass x Gravity

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5
Q

What is the equation for Mass?

A

Mass = Density x Volume

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6
Q

What is the equation for Volume?

A

Width x Height x Depth

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7
Q

How would you go about determining the pressure at a water depth of 100m?

A 
P = ρgh where ρ = Mass/Volume, which in the case of water is 1000kg/m3
P = 1000 kg m-3 * 9.8 m s-2 * 100 m = 980000 Pa
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8
Q

What is the equation for Pressure?

A

Pressure = Density x Gravity x Height

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9
Q

Define “normal stress”

A

Stress which is applied perpendicular to the surface

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10
Q

What is meant by σxx

A

Stress upon face x (first subscript) in the direction of x (second subscript)

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11
Q

How many normal stresses are there?

A

Three, σxx, σyy and σzz

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12
Q

What is positive stress?

A

Compressive stress

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13
Q

How is pressure transmitted in a fluid?

A

In all directions regardless of orientation

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14
Q

What is the equation for pressure in a fluid?

A

P = σxx = σyy = σzz OR P = 1/3 (σxx+σyy+σzz)

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15
Q

In a hydrostatic (lithostatic) state, pressure is given by what?

A

The weight of the overburden (P = ρgh for constant density)

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16
Q

Define “shear stress”

A

Stress which is parallel to the sides

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17
Q

How many shear stresses are there?

A

Six, σxy, σyx, σzy, σyz, σzx and σxz

Only three are required unless the solid rotates (σyx = σxy)

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18
Q

Define “deviatoric stress”

A

Total stress, minus contributions from gravity, hence leaving only tectonic forces

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19
Q

Define “effective stress”

A

Lithostatic pressure at depth, with effect of pore fluid pressure subtracted

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20
Q

What are the four ways in which stress data can be measured/estimated?

A
  1. Earthquake Focal Mechanisms
  2. Well Bore Breakouts/Drilling Induced Fractures
  3. In-Situ Stress Measurements
  4. Young Geological Data (Fault Slip Analysis/Volc. Vent Alignments
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21
Q

Give three examples of “In-situ stress measurements”

A
  1. Over-coring
  2. Hydraulic Fracturing
  3. Borehole Slotter
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22
Q

What are the units of strain?

A

Per unit dimension

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23
Q

How does strain have an effect on stress?

A

Strain can cause new stresses to build up

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24
Q

Where is strain a particularly useful quantification?

A

Plate boundaries, where we can see deformation

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25
Q

How do you define normal strain?

A

Change in length as a fraction of the original length

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26
Q

How do you define volumetric strain?

A

Change in volume as a fraction of the original volume (Dilation) - Measured in terms of the three planes

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27
Q

How do you quantify volumetric strain (the equation)

A

D (dilation) = Σxx + Σyy + Σzz
If there was a compression of 1% in x, 2% in y and 0% in z:
Σxx = 0.01, Σyy = 0.02, Σzz = 0
D = 0.01 + 0.02 + 0 = 0.03

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28
Q

How do you define shear strain?

A

Changes of angles in between lines which were originally at right angles

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29
Q

What is an acute angle?

A

An angle which is less than 90 degrees

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30
Q

What are the two mathematical conventions in quantifying shear strain?

A
  1. Measured in radians

2. Shear strain is positive if the angle is made acute from a right angle

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31
Q

Calculate the shear strain for an angle which has been sheared from 90 degrees to 80 degrees

A

Half the change in angle * Pi / 180 =

5 * Pi / 180 = 0.087

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32
Q

Calculate the shear strain for an angle which has been sheared from 90 degrees to 40 degrees

A

Half the change in angle * Pi / 180 =

25 * Pi / 180 = 0.44

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33
Q

What are the directions of the principle axes of stress in a extensional plate setting?

A

σ1 is in the vertical, σ3 is in the horizontal (the direction of extension)

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34
Q

What are the directions of the principle axes of stress in a convergent plate setting?

A

σ1 is in the horizontal in the direction of convergence, σ3 is in the vertical

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35
Q

What are the directions of the principle axes of stress in a conservative plate setting?

A

σ1 and σ3 are both in the horizontal, yet not parallel to the fault

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36
Q

What is the strain rate (in s-1) for a mountain range which is 500km wide, shortening by 1cm/yr?

A

Strain = 1cm/500km = 0.01m/500000m
31556900 seconds in a year
= 6.34 x10-16 s-1

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37
Q

What is “campaign GPS”?

A

Periodical GPS mapping

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38
Q

How is strain rate mapped?

A

GPS field data with time

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39
Q

Why do strain rates vary between Geological, Seismic and GPS techniques?

A

Rate doesn’t change between GPS/Geological timescales, but does over EQ timescales

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40
Q

How do faults accomodate strain?

A

Slippage both during and between earthquakes

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41
Q

How does intra-plate strain occur?

A

Strength of tectonics transfers strain to the interior

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42
Q

What is the tectonic situation of the Capricorn Plate?

A

Intra-plate strain - Faulting and folding acts as rigid plate does, yet not at a plate boundary

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43
Q

What is the North American example of intra-plate strain?

A

New Madrid Zone

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44
Q

Aside from tectonic buildup, what other process can cause intra-plate strain?

A

Glacial rebound

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45
Q

What is the recent seismic history of the New Madrid Fault Zone (Reference)?

A

3 7-8 Mw EQ’s - 1811 to 1812 (Murray et al. ?)

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46
Q

What was the original cause of the New Madrid Fault Zone (Reference)?

A

600ma igneous intrusion - reactivation again 80-60ma

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47
Q

What is the cause of the fault reactivation at the New Madrid Fault Zone?

A

Deglaciation

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48
Q

What is the technical tectonic definition of “strength”?

A

Ability to withstand pressure without rupture

49
Q

What is the technical tectonic definition of “elasticity”?

A

Strain is proportional to stress - recoverable

50
Q

What is the technical tectonic definition of “brittle”?

A

Fails during elastic deformation, e.g. faults

51
Q

What is “Young’s Modulus”?

A

A modulus of elasticity, the measure of the stiffness of a material - proportionality between strength and strain

52
Q

What is “plastic deformation”?

A

Non-linear deformation onset after elastic limits dependant on stress

53
Q

What is the “yield strength” of a material?

A

The point at which a material stops behaving elastically and plastic deformation begins

54
Q

What kind of materials fail during plastic deformation?

A

Ductile materials

55
Q

Give an example of a ductile material

A

Steel

56
Q

What happens to earth during plastic deformation?

A

Folding/flow at shear zones

57
Q

What is the technical tectonic definition of “creep”?

A

Slow migration of atomic scale defects in crystal lattices

58
Q

What is creep dependant on? (4)

A

Composition, Temperature, Applied stress, Strain rates

59
Q

What is diffusion creep?

A

Defect is a missing atom in the lattice

60
Q

What is dislocation creep?

A

Larger scale distortions of the lattice

61
Q

At temperatures __% of MP, rocks have essentially no strength

A

> 85%

62
Q

Explain a traditional yield stress envelope

A

Deviatoric (Tectonic) Stress on X axis, depth on Y axis - Brittle strength increases linearly due to pressure with depth - at certain point ductile strength takes over due to sensitivity to temp - decreases with depth.
The area inside this plot is the envelope, where the area gives lithospheric strength and does not fail inside

63
Q

Explain ductile strength in a traditional yield stress envelope setting

A

Plastic deformation - Failure by creep

64
Q

Explain brittle strength in a traditional yield stress envelope setting

A

Elastic deformation - Failure by faulting

65
Q

What is the name of the depth where the lithosphere is strongest?

A

Brittle-ductile transistion

66
Q

What is the typical depth where the lithosphere is the strongest?

A

~17km depth

67
Q

What is the typical maximum pressure the lithosphere can undergo without failure? (At the Brittle-Ductile transition)

A

500 M Pa

68
Q

What does the brittle-ductile transition mean in terms of earthquakes?

A

Large earthquakes at this depth due to the energy required for storage

69
Q

Rocks can take ___ (more/less) compressional stress than the equivalent in extensional

A

More

70
Q

What mineral is closest composition to the bulk composition of the oceanic crust and mantle?

A

Olivine

71
Q

What is included in the lithosphere?

A

Crust and mantle up until strength envelope subsides

72
Q

What is the typical temperature at the base of the lithosphere?

A

~1330 Celsius

73
Q

According to models, what depths do oceanic EQ’s occur down to?

A

The 600 - 800 Celsius isotherm

74
Q

Flexural modelling suggests that the oceanic lithosphere is elastic down to ___ to ___ celsius isotherm

A

300 to 600

75
Q

What is the typical thickness of the continental crust?

A

35-40km deep

76
Q

Upper parts of continental crust have a rheology like ___, lower parts like ___.

A

Quartz, Feldspar

77
Q

Below the crust, the layer of cooled mantle has a similar rheology to ___.

A

Olivine

78
Q

What does the strength envelope look like from the surface to depths of ~80km?

A

Individual envelopes at various depths - Quartz strength envelope to ~20km, Feldspar picks up to ~30km, then Olivine below

79
Q

What does the strength envelope of the lithosphere mean in terms of overall strength of the lithosphere?

A

Both strong and weak layers in close proximity

80
Q

What process significantly lowers the brittle-ductile strength in the lithosphere, and how does it work?

A

Adding water - pore fluid pressure reduces the co-efficient of sliding friction in fault zones

81
Q

What feature is thought to occur at the base of the crust?

A

Fluid circulation

82
Q

What is the geothermal gradient controlled by? (2)

A

Abundance of radioactive material and flow of liquid

83
Q

In terms of hydrocarbon sourcing, why is the temperature variation in the lithosphere important to know? (2)

A

Long periods of primary heat causes organic rich rocks to evolve into source rocks
Oil and gas mature at different temperatures

84
Q

Why is the tectonic history of a particular region important to know for hydrocarbon sourcing?

A

Need to know if the particular region has been exposed to the oil/gas temperature windows

85
Q

Aside from the mantle losing heat upwards, what four other factors contribute?

A

Internal Heat Production (radioactivity)
Thermal Conductivity Variation (dependant on rock comp)
Surface Temp Variation (climate)
Heat Transfer by Fluid Flow (basin structure)

86
Q

What does “Internal Heat Production” entail?

A

Radioactive decay

87
Q

What three elements are large contributors towards internal heat production?

A

Th, U, K

88
Q

What types of rock tend to hold higher concentrations of radioactive material?

A

Granite, Shale

89
Q

What types of rock tend to hold lower concentrations of radioactive material?

A

Sandstones, Carbonates

90
Q

Temperature increase due to radioactivity is ___ at ___ depth (greater/less)

A

Greater, greater

91
Q

What three variables within a rock determine its variation in thermal conductivity?

A

Composition, porosity, pore-fluid composition

92
Q

What does a low thermal conductivity (K) mean for the geotherm?

A

High geotherm - material acts as a barrier to upwards heat flow

93
Q

What is the units for thermal conductivity (K)?

A

W m-1 K-1

94
Q

What is the thermal conductivity (K) of Shale?

A

1.2 W m-1 K-1

95
Q

What is the thermal conductivity (K) of Limestone?

A

2.5 W m-1 K-1

96
Q

What is the thermal conductivity (K) of Sandstone?

A

4.2 W m-1 K-1

97
Q

Why is the presence of Shale particularly an important in assessing the geotherm?

A

Shale has a low thermal conductivity as well as an abundance of radioactive materials, rendering the geotherm particularly steeper

98
Q

Models show that 10 degrees of cooling takes ____ years for equilibrium in the top 500 m

A

10,000yrs

99
Q

Models show that 10 degrees of cooling takes ____ years for equilibrium of geotherm at 6 km

A

> 1 m yrs

100
Q

How does water transfer heat in a basin?

A

Advection

101
Q

Why does heat flow in a basin complicate a simple geotherm?

A

Geotherm is a 1D representation, heat flow occurs in 3D

102
Q

What are the three ways to determine a detailed thermal history?

A
  1. Temperature measurements with boreholes
  2. Measurements of effects of heat on buried organic matter in rocks
  3. Measurement of heat effects on some rock-forming minerals
103
Q

What are the three methods of measuring heat effects on rock forming minerals?

A
  1. Fission tracks of Apatite
  2. U-Th Geochronology
  3. Mineral diagenisis & metamorphism
104
Q

Give an example of a measurement of effects of heat on buried organic matter

A

Vitrine Reflectance

105
Q

What is Vitrine?

A

A group of Macerals

106
Q

What is a Maceral?

A

A specific organic compound found in a vitrine - the organic equivalent to the word “mineral” in igneous/metamorphic rocks.

107
Q

How does Vitrine Reflectance work?

A

Microscope examination - macerals reflect different % of light, which increases with T & D although some scatter is retained on cooling.

108
Q

What is the problem with VR?

A

Need to be careful about recycled vitrine in measurements

109
Q

What did the Texan example of VR show?

A

That the maturity of vitrine tends to be greater near thrust fault/folding - a greater influence than sediment burial

110
Q

What are the three main minerals which incorporate fission tracks?

A

Sphene, Zircon, Apatite

111
Q

What is the main isotope to decay producing fission tracks in minerals?

A

Uranium-238

112
Q

What is the “closure” temperature for fissure tracks in Apatite?

A

110 degrees C

113
Q

What is the use of fission track analysis in terms of oil/gas exploration?

A

Can tell how long various apatite grains have been at different depths - i.e. a comparison to the oil/gas window

114
Q

What is the main disadvantage of fission track analysis?

A

Only shows the most recent event of entry to shallow depths - all other tracks are destroyed

115
Q

What does a high density of short tracks in the crystal lattice mean in fission track analysis?

A

Cooling long ago, recent reheating

116
Q

What does a low density of long tracks in the crystal lattice mean in fission track analysis?

A

Recent cooling

117
Q

What other method is a useful compliment to fission track analysis?

A

VR

118
Q

What are the uses of developing a vertical profile of fission track analysis?

A

Determines periods of erosion/transport and aids in analysis of provenience

119
Q

On a regional scale, ___ tectonic settings are typically hotter than ___ tectonic settings

A

Extensional / Convergent

Tectonics and Lithosphere Dynamics (2 decks)

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