Stress

Question 1

Describe the concept of stress

Answer 1

Used to describe the physical state of a material body on which forces are applied, considers surface forces

Question 2

What are the two kinds of forces?

Answer 2

Body forces, surface forces

Question 3

Describe body forces

Answer 3

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

Question 4

Describe surface forces

Answer 4

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

Question 5

What governs the response of an object to a force?

Answer 5

The intensity of the force

Question 6

Define traction

Answer 6

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

Question 7

Define state of stress (σ)

Answer 7

Force intensity on surfaces of all possible orientations

Question 8

Define vector

Answer 8

The traction acting on a surface within a loaded body, can be obtained by adding components acting normal and parallel to the surface

Question 9

Describe positive traction

Answer 9

Compressive with an anticlockwise sense of shear, this is the Mohr circle convention

Question 10

How can traction be used to define a strain ellipse?

Answer 10

In 2d, the tails of the traction vectors (traction acting on planes of all possible orientations)

Question 11

What four numbers define state of stress?

Answer 11

Two normal stresses (σn=σxx,σyy) and two shear stresses (τ=σxy,σyx)
These can be written as a 2x2 matrix

Question 12

When are shear stresses positive?

Answer 12

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

Question 13

Describe mechanical equilibrium

Answer 13

σxy = - σyx

Question 14

Describe principal stresses (σ1 and σ2)

Answer 14

When the normal stresses are parallel to the coordinate axes and shear stresses are zero
σ1 ≥ σ2

Question 15

Describe the use of the Mohr circle representation of stress

Answer 15

To calculate the stresses on a plane of any orientation

Question 16

Define stress in 3d

Answer 16

Stresses acting on any three mutually perpendicular surfaces

Question 17

What are the three forces applied to a stress ellipsoid?

Answer 17

Fx (σxx,σyx,σzx) Fy (σyy,σxy,σzy), Fz (σzz, σxz,σyz)
Can be written as 3x3 matrix

Question 18

Difference between normal stresses and shear stresses

Answer 18

Normal stresses are diagonal terms and shear stresses are off-diagonal terms

Question 19

Why is stress a tensor quantity?

Answer 19

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

Question 20

What are the only non-zero terms in the stress matrix when the coordinate frame is aligned so the shear stresses are zero?

Answer 20

The three normal stresses, these are the three principal stresses; σ1, σ2, σ3

Question 21

What are the two matrices that any stress tensor can be split into?

Answer 21

Mean stress and deviatoric stress

Question 22

Describe mean stress

Answer 22

Causes or arises from dilation (volume change)

Question 23

Describe deviatoric stress

Answer 23

Causes or arises form distortion (shape change)

Question 24

Describe mean stress in the lithosphere

Answer 24

Usually similar in magnitude to confining pressure (controlled by burial depth and density of the overlying rock column)
Greater than deviatoric stress

Question 25

When does the strain ellipsoid become a sphere?

Answer 25

When there is no deviatoric stress
This is isostatic/hydrostatic/lithostatic stress

Question 26

What affects normal stresses by not shear stresses?

Answer 26

Pore fluid pressure

Question 27

How does pore fluid pressure effect a Mohr diagram?

Answer 27

Shifts the Mohr circle to the left without changing the diameter

Question 28

Give five reasons for the importance of knowing the state of stress in the Earth

Answer 28

Construction, borehole stability, controlled fracture of rocks for oil/gas production, predicting hazards, understanding plate tectonics

Question 29

Describe borehole breakouts

Answer 29

Zones of failure in the wall of the borehole that give it an irregular elongate shape

Question 30

Describe overcoring

Answer 30

A strain reducing method to reduce borehole breakouts

Question 31

Describe hydrofracking

Answer 31

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

Question 32

How are the orientation and relative magnitude of earthquakes estimated?

Answer 32

Using earthquaeke first motion studies and fault plane and slip vector orientation measurements (e.g from stylolites, vein systems, conjugate fractures)

Question 33

How can principal stress orientations be estimated?

Answer 33

Using orientation of mechanical twins and of deformation lamellae

Question 34

What does an increase in the principal stress magnitude result in?

Answer 34

Increased incidence of calcite twinning and dislocation density and decreased subgrain diameter and dynamically recrystallised grain size

Question 35

What are the orientations of principal stresses at the Earth’s surface and why?

Answer 35

One vertical (σv) and two horizontal
One is vertical because air and water cannot sustain a shear stress

Question 36

Give the formula for the vertical stress at the Earth’s surface

Answer 36

σv = ρrock g z
ρrock=avg density of rock column
g=acceleration due to gravity
z=depth

Question 37

Describe the stress during burial with no lateral strain (uniaxial strain)

Answer 37

Horizontal stress is expected to be one third to one half of the vertical stress

Question 38

Describe isostatic readjustment

Answer 38

The raising or lowering of the lithosphere based on whether it is getting thicker by sedimentation of thinner by erosion

Question 39

What is the result of isostatic readjustment?

Answer 39

Locally horizontal stress is greater on the thinner section of the lithosphere because they are being applied over a smaller area

Question 40

What causes deviations from states of stress?

Answer 40

Tectonic processes
Split into three regimes (Andersonian classification) based on which of the principal stresses is verticle

Question 41

Where do plates bend and what does this bending result in?

Answer 41

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

Question 42

Give five microscale example of high stresses can be induced in rocks

Answer 42

Changes in temperature and pressure, lattice defects, crystallisation of a melt, metamorphic reactions

Question 43

How are microscale stresses stored in the rock?

Answer 43

As residual stresses that may be relieved during uplift and erosion by fracturing

Question 44

What is stress at given depth often approximated as?

Answer 44

Strength of the rocks at that depth

Question 45

What factors are considered for strength vs depth plots?

Answer 45

Strain-rate, geothermal gradient, lithological stratification

Question 46

What three models are used for the strength at depth of the continental lithosphere?

Answer 46

Jelly sandwich, creme brulee, banana split

Question 47

Describe the jelly sandwich model of strength at depth of the continental lithosphere

Answer 47

Weak lower crust between strong upper durst and upper mantle
Thought to apply to cooler geothermal gradients and hydrated lower crust

Question 48

Describe the creme brulee model of strength at depth of the continental lithosphere

Answer 48

Strong crust and weak mantle
Thought to apple to higher geothermal gradients and dehydrated lower crust

Question 49

Describe the banana split model of strength at depth of the continental lithosphere

Answer 49

Applied to long established major fault zones that extend to great depth

Question 50

What determins the cause of a mechanical process?

Answer 50

Boundary conditions (the conditions that are externally imposed on a body)

Question 51

Describe what happens when stresses are imposed and maintain on the boundaries

Answer 51

Stress is the cause of the deformation and strain is the response to it

Question 52

Describe what happens when boundaries are required to move by prescribed amount or rate

Answer 52

Strain is the cause of the process and stresses develop in reponse to it
For example, the uniaxial reference state