(1.1) Stress, Strain, Strength and Heat Flashcards
Define “stress”
Quantification of how much a substance is being pushed
Define “strain”
Deformation caused by the stress: i.e. change in dimensions: length, angle, area, volume, etc.
What are the units of stress?
Force per Unit Area (Nm-2 or Pa)
What is the equation for Weight?
Weight = Mass x Gravity
What is the equation for Mass?
Mass = Density x Volume
What is the equation for Volume?
Width x Height x Depth
How would you go about determining the pressure at a water depth of 100m?
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
What is the equation for Pressure?
Pressure = Density x Gravity x Height
Define “normal stress”
Stress which is applied perpendicular to the surface
What is meant by σxx
Stress upon face x (first subscript) in the direction of x (second subscript)
How many normal stresses are there?
Three, σxx, σyy and σzz
What is positive stress?
Compressive stress
How is pressure transmitted in a fluid?
In all directions regardless of orientation
What is the equation for pressure in a fluid?
P = σxx = σyy = σzz OR P = 1/3 (σxx+σyy+σzz)
In a hydrostatic (lithostatic) state, pressure is given by what?
The weight of the overburden (P = ρgh for constant density)
Define “shear stress”
Stress which is parallel to the sides
How many shear stresses are there?
Six, σxy, σyx, σzy, σyz, σzx and σxz
Only three are required unless the solid rotates (σyx = σxy)
Define “deviatoric stress”
Total stress, minus contributions from gravity, hence leaving only tectonic forces
Define “effective stress”
Lithostatic pressure at depth, with effect of pore fluid pressure subtracted
What are the four ways in which stress data can be measured/estimated?
- Earthquake Focal Mechanisms
- Well Bore Breakouts/Drilling Induced Fractures
- In-Situ Stress Measurements
- Young Geological Data (Fault Slip Analysis/Volc. Vent Alignments
Give three examples of “In-situ stress measurements”
- Over-coring
- Hydraulic Fracturing
- Borehole Slotter
What are the units of strain?
Per unit dimension
How does strain have an effect on stress?
Strain can cause new stresses to build up
Where is strain a particularly useful quantification?
Plate boundaries, where we can see deformation
How do you define normal strain?
Change in length as a fraction of the original length
How do you define volumetric strain?
Change in volume as a fraction of the original volume (Dilation) - Measured in terms of the three planes
How do you quantify volumetric strain (the equation)
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
How do you define shear strain?
Changes of angles in between lines which were originally at right angles
What is an acute angle?
An angle which is less than 90 degrees
What are the two mathematical conventions in quantifying shear strain?
- Measured in radians
2. Shear strain is positive if the angle is made acute from a right angle
Calculate the shear strain for an angle which has been sheared from 90 degrees to 80 degrees
Half the change in angle * Pi / 180 =
5 * Pi / 180 = 0.087
Calculate the shear strain for an angle which has been sheared from 90 degrees to 40 degrees
Half the change in angle * Pi / 180 =
25 * Pi / 180 = 0.44
What are the directions of the principle axes of stress in a extensional plate setting?
σ1 is in the vertical, σ3 is in the horizontal (the direction of extension)
What are the directions of the principle axes of stress in a convergent plate setting?
σ1 is in the horizontal in the direction of convergence, σ3 is in the vertical
What are the directions of the principle axes of stress in a conservative plate setting?
σ1 and σ3 are both in the horizontal, yet not parallel to the fault
What is the strain rate (in s-1) for a mountain range which is 500km wide, shortening by 1cm/yr?
Strain = 1cm/500km = 0.01m/500000m
31556900 seconds in a year
= 6.34 x10-16 s-1
What is “campaign GPS”?
Periodical GPS mapping
How is strain rate mapped?
GPS field data with time
Why do strain rates vary between Geological, Seismic and GPS techniques?
Rate doesn’t change between GPS/Geological timescales, but does over EQ timescales
How do faults accomodate strain?
Slippage both during and between earthquakes
How does intra-plate strain occur?
Strength of tectonics transfers strain to the interior
What is the tectonic situation of the Capricorn Plate?
Intra-plate strain - Faulting and folding acts as rigid plate does, yet not at a plate boundary
What is the North American example of intra-plate strain?
New Madrid Zone
Aside from tectonic buildup, what other process can cause intra-plate strain?
Glacial rebound
What is the recent seismic history of the New Madrid Fault Zone (Reference)?
3 7-8 Mw EQ’s - 1811 to 1812 (Murray et al. ?)
What was the original cause of the New Madrid Fault Zone (Reference)?
600ma igneous intrusion - reactivation again 80-60ma
What is the cause of the fault reactivation at the New Madrid Fault Zone?
Deglaciation
What is the technical tectonic definition of “strength”?
Ability to withstand pressure without rupture
What is the technical tectonic definition of “elasticity”?
Strain is proportional to stress - recoverable
What is the technical tectonic definition of “brittle”?
Fails during elastic deformation, e.g. faults
What is “Young’s Modulus”?
A modulus of elasticity, the measure of the stiffness of a material - proportionality between strength and strain
What is “plastic deformation”?
Non-linear deformation onset after elastic limits dependant on stress
What is the “yield strength” of a material?
The point at which a material stops behaving elastically and plastic deformation begins
What kind of materials fail during plastic deformation?
Ductile materials
Give an example of a ductile material
Steel
What happens to earth during plastic deformation?
Folding/flow at shear zones
What is the technical tectonic definition of “creep”?
Slow migration of atomic scale defects in crystal lattices
What is creep dependant on? (4)
Composition, Temperature, Applied stress, Strain rates
What is diffusion creep?
Defect is a missing atom in the lattice
What is dislocation creep?
Larger scale distortions of the lattice
At temperatures __% of MP, rocks have essentially no strength
> 85%
Explain a traditional yield stress envelope
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
Explain ductile strength in a traditional yield stress envelope setting
Plastic deformation - Failure by creep
Explain brittle strength in a traditional yield stress envelope setting
Elastic deformation - Failure by faulting
What is the name of the depth where the lithosphere is strongest?
Brittle-ductile transistion
What is the typical depth where the lithosphere is the strongest?
~17km depth
What is the typical maximum pressure the lithosphere can undergo without failure? (At the Brittle-Ductile transition)
500 M Pa
What does the brittle-ductile transition mean in terms of earthquakes?
Large earthquakes at this depth due to the energy required for storage
Rocks can take ___ (more/less) compressional stress than the equivalent in extensional
More
What mineral is closest composition to the bulk composition of the oceanic crust and mantle?
Olivine
What is included in the lithosphere?
Crust and mantle up until strength envelope subsides
What is the typical temperature at the base of the lithosphere?
~1330 Celsius
According to models, what depths do oceanic EQ’s occur down to?
The 600 - 800 Celsius isotherm
Flexural modelling suggests that the oceanic lithosphere is elastic down to ___ to ___ celsius isotherm
300 to 600
What is the typical thickness of the continental crust?
35-40km deep
Upper parts of continental crust have a rheology like ___, lower parts like ___.
Quartz, Feldspar
Below the crust, the layer of cooled mantle has a similar rheology to ___.
Olivine
What does the strength envelope look like from the surface to depths of ~80km?
Individual envelopes at various depths - Quartz strength envelope to ~20km, Feldspar picks up to ~30km, then Olivine below
What does the strength envelope of the lithosphere mean in terms of overall strength of the lithosphere?
Both strong and weak layers in close proximity
What process significantly lowers the brittle-ductile strength in the lithosphere, and how does it work?
Adding water - pore fluid pressure reduces the co-efficient of sliding friction in fault zones
What feature is thought to occur at the base of the crust?
Fluid circulation
What is the geothermal gradient controlled by? (2)
Abundance of radioactive material and flow of liquid
In terms of hydrocarbon sourcing, why is the temperature variation in the lithosphere important to know? (2)
Long periods of primary heat causes organic rich rocks to evolve into source rocks
Oil and gas mature at different temperatures
Why is the tectonic history of a particular region important to know for hydrocarbon sourcing?
Need to know if the particular region has been exposed to the oil/gas temperature windows
Aside from the mantle losing heat upwards, what four other factors contribute?
Internal Heat Production (radioactivity)
Thermal Conductivity Variation (dependant on rock comp)
Surface Temp Variation (climate)
Heat Transfer by Fluid Flow (basin structure)
What does “Internal Heat Production” entail?
Radioactive decay
What three elements are large contributors towards internal heat production?
Th, U, K
What types of rock tend to hold higher concentrations of radioactive material?
Granite, Shale
What types of rock tend to hold lower concentrations of radioactive material?
Sandstones, Carbonates
Temperature increase due to radioactivity is ___ at ___ depth (greater/less)
Greater, greater
What three variables within a rock determine its variation in thermal conductivity?
Composition, porosity, pore-fluid composition
What does a low thermal conductivity (K) mean for the geotherm?
High geotherm - material acts as a barrier to upwards heat flow
What is the units for thermal conductivity (K)?
W m-1 K-1
What is the thermal conductivity (K) of Shale?
1.2 W m-1 K-1
What is the thermal conductivity (K) of Limestone?
2.5 W m-1 K-1
What is the thermal conductivity (K) of Sandstone?
4.2 W m-1 K-1
Why is the presence of Shale particularly an important in assessing the geotherm?
Shale has a low thermal conductivity as well as an abundance of radioactive materials, rendering the geotherm particularly steeper
Models show that 10 degrees of cooling takes ____ years for equilibrium in the top 500 m
10,000yrs
Models show that 10 degrees of cooling takes ____ years for equilibrium of geotherm at 6 km
> 1 m yrs
How does water transfer heat in a basin?
Advection
Why does heat flow in a basin complicate a simple geotherm?
Geotherm is a 1D representation, heat flow occurs in 3D
What are the three ways to determine a detailed thermal history?
- Temperature measurements with boreholes
- Measurements of effects of heat on buried organic matter in rocks
- Measurement of heat effects on some rock-forming minerals
What are the three methods of measuring heat effects on rock forming minerals?
- Fission tracks of Apatite
- U-Th Geochronology
- Mineral diagenisis & metamorphism
Give an example of a measurement of effects of heat on buried organic matter
Vitrine Reflectance
What is Vitrine?
A group of Macerals
What is a Maceral?
A specific organic compound found in a vitrine - the organic equivalent to the word “mineral” in igneous/metamorphic rocks.
How does Vitrine Reflectance work?
Microscope examination - macerals reflect different % of light, which increases with T & D although some scatter is retained on cooling.
What is the problem with VR?
Need to be careful about recycled vitrine in measurements
What did the Texan example of VR show?
That the maturity of vitrine tends to be greater near thrust fault/folding - a greater influence than sediment burial
What are the three main minerals which incorporate fission tracks?
Sphene, Zircon, Apatite
What is the main isotope to decay producing fission tracks in minerals?
Uranium-238
What is the “closure” temperature for fissure tracks in Apatite?
110 degrees C
What is the use of fission track analysis in terms of oil/gas exploration?
Can tell how long various apatite grains have been at different depths - i.e. a comparison to the oil/gas window
What is the main disadvantage of fission track analysis?
Only shows the most recent event of entry to shallow depths - all other tracks are destroyed
What does a high density of short tracks in the crystal lattice mean in fission track analysis?
Cooling long ago, recent reheating
What does a low density of long tracks in the crystal lattice mean in fission track analysis?
Recent cooling
What other method is a useful compliment to fission track analysis?
VR
What are the uses of developing a vertical profile of fission track analysis?
Determines periods of erosion/transport and aids in analysis of provenience
On a regional scale, ___ tectonic settings are typically hotter than ___ tectonic settings
Extensional / Convergent
