Stress Flashcards
Describe the concept of stress
Used to describe the physical state of a material body on which forces are applied, considers surface forces
What are the two kinds of forces?
Body forces, surface forces
Describe body forces
Act at a distance on all the volume elements of a rock, e.g. gravity, EM forces
Magnitude is directly proportional to mass or volume
Describe surface forces
Either arise directly from the action of one body on another across the surface between them or indirectly from the action of one body part of a body on another part across an imaginary internal surface
Magnitude is directly proportional to the surface area over which it acts
What governs the response of an object to a force?
The intensity of the force
Define traction
Force intensity at a point on a surface of specified orientation
Force intensity = force / area over which the force acts, measured in N/m^2 or Pascal
Define state of stress (σ)
Force intensity on surfaces of all possible orientations
Define vector
The traction acting on a surface within a loaded body, can be obtained by adding components acting normal and parallel to the surface
Describe positive traction
Compressive with an anticlockwise sense of shear, this is the Mohr circle convention
How can traction be used to define a strain ellipse?
In 2d, the tails of the traction vectors (traction acting on planes of all possible orientations)
What four numbers define state of stress?
Two normal stresses (σn=σxx,σyy) and two shear stresses (τ=σxy,σyx)
These can be written as a 2x2 matrix
When are shear stresses positive?
If the shear sense on the sides of the square that cut the negative coordinate axes are in a postive direction
This is the tensor convention (can also be used on the cube in 3d)
σxy = σyx
Describe mechanical equilibrium
σxy = - σyx
Describe principal stresses (σ1 and σ2)
When the normal stresses are parallel to the coordinate axes and shear stresses are zero
σ1 ≥ σ2
Describe the use of the Mohr circle representation of stress
To calculate the stresses on a plane of any orientation
Define stress in 3d
Stresses acting on any three mutually perpendicular surfaces
What are the three forces applied to a stress ellipsoid?
Fx (σxx,σyx,σzx) Fy (σyy,σxy,σzy), Fz (σzz, σxz,σyz)
Can be written as 3x3 matrix
Difference between normal stresses and shear stresses
Normal stresses are diagonal terms and shear stresses are off-diagonal terms
Why is stress a tensor quantity?
The individual components are defined in a coordinate frame with a particular orientation, is rotated then the values of the components change
The changed values can be calculated from the known original values using a transformation equation
What are the only non-zero terms in the stress matrix when the coordinate frame is aligned so the shear stresses are zero?
The three normal stresses, these are the three principal stresses; σ1, σ2, σ3
What are the two matrices that any stress tensor can be split into?
Mean stress and deviatoric stress
Describe mean stress
Causes or arises from dilation (volume change)
Describe deviatoric stress
Causes or arises form distortion (shape change)
Describe mean stress in the lithosphere
Usually similar in magnitude to confining pressure (controlled by burial depth and density of the overlying rock column)
Greater than deviatoric stress
When does the strain ellipsoid become a sphere?
When there is no deviatoric stress
This is isostatic/hydrostatic/lithostatic stress
What affects normal stresses by not shear stresses?
Pore fluid pressure
How does pore fluid pressure effect a Mohr diagram?
Shifts the Mohr circle to the left without changing the diameter
Give five reasons for the importance of knowing the state of stress in the Earth
Construction, borehole stability, controlled fracture of rocks for oil/gas production, predicting hazards, understanding plate tectonics
Describe borehole breakouts
Zones of failure in the wall of the borehole that give it an irregular elongate shape
Describe overcoring
A strain reducing method to reduce borehole breakouts
Describe hydrofracking
A way of establishing the orientation and magnitude of the principal stress
Fluid is pumped into packers in boreholes, an extension fracture forms at a critical pressure, fluid pressure reduces just enough to keep the crack open
How are the orientation and relative magnitude of earthquakes estimated?
Using earthquaeke first motion studies and fault plane and slip vector orientation measurements (e.g from stylolites, vein systems, conjugate fractures)
How can principal stress orientations be estimated?
Using orientation of mechanical twins and of deformation lamellae
What does an increase in the principal stress magnitude result in?
Increased incidence of calcite twinning and dislocation density and decreased subgrain diameter and dynamically recrystallised grain size
What are the orientations of principal stresses at the Earth’s surface and why?
One vertical (σv) and two horizontal
One is vertical because air and water cannot sustain a shear stress
Give the formula for the vertical stress at the Earth’s surface
σv = ρrock g z
ρrock=avg density of rock column
g=acceleration due to gravity
z=depth
Describe the stress during burial with no lateral strain (uniaxial strain)
Horizontal stress is expected to be one third to one half of the vertical stress
Describe isostatic readjustment
The raising or lowering of the lithosphere based on whether it is getting thicker by sedimentation of thinner by erosion
What is the result of isostatic readjustment?
Locally horizontal stress is greater on the thinner section of the lithosphere because they are being applied over a smaller area
What causes deviations from states of stress?
Tectonic processes
Split into three regimes (Andersonian classification) based on which of the principal stresses is verticle
Where do plates bend and what does this bending result in?
Results is stresses
Occurs at subduction zones, in response to surface loading, and in reponse to movement across latitudes.
Can occur locally adjacent to other structures, e.g. faults, folds, diapiric intrusions
Give five microscale example of high stresses can be induced in rocks
Changes in temperature and pressure, lattice defects, crystallisation of a melt, metamorphic reactions
How are microscale stresses stored in the rock?
As residual stresses that may be relieved during uplift and erosion by fracturing
What is stress at given depth often approximated as?
Strength of the rocks at that depth
What factors are considered for strength vs depth plots?
Strain-rate, geothermal gradient, lithological stratification
What three models are used for the strength at depth of the continental lithosphere?
Jelly sandwich, creme brulee, banana split
Describe the jelly sandwich model of strength at depth of the continental lithosphere
Weak lower crust between strong upper durst and upper mantle
Thought to apply to cooler geothermal gradients and hydrated lower crust
Describe the creme brulee model of strength at depth of the continental lithosphere
Strong crust and weak mantle
Thought to apple to higher geothermal gradients and dehydrated lower crust
Describe the banana split model of strength at depth of the continental lithosphere
Applied to long established major fault zones that extend to great depth
What determins the cause of a mechanical process?
Boundary conditions (the conditions that are externally imposed on a body)
Describe what happens when stresses are imposed and maintain on the boundaries
Stress is the cause of the deformation and strain is the response to it
Describe what happens when boundaries are required to move by prescribed amount or rate
Strain is the cause of the process and stresses develop in reponse to it
For example, the uniaxial reference state
