Term 1 - Force, stress & tensile failure

Question 1

two fundamental types of force important in structural geology

Answer 1

– BODY FORCES (force/unit volume): act upon and are proportional to mass of body; e.g. gravity
– SURFACE FORCES (a.k.a. tractions or stresses) (force/unit area): act across real or imagined surfaces & can vary within a body

Question 2

Stress

Answer 2

Geological bodies interact along surfaces, e.g. plate boundaries, faults, bedding planes, joints etc.

The stress on a surface is given by:
σ=F/A
SI units are N/m2 = Pascal (Pa)

Also use bars/kilobars – 1MPa = 10bars, 100MPa = 1 kbar
The stress on a surface is a vector quantity, i.e. it has a magnitude (size) and orientation

Like force, stress has both orientation & magnitude, but stress is also determined by the size of the area of action

Question 3

Normal & shear stresses

Answer 3

Can resolve stress on surface, , into two components
Normal stress (σn) acting perpendicular to the surface
Shear stress(σs) acting parallel to the surface
Where θ is the angle between the stress vector and the surface of action
Note that unlike for force, the relationships are complicated by the surface areas involved (A1, A2)

Question 4

How forces and stresses vary as the orientation of the surface of action varies

Answer 4

• Surfaces at 0 and 90 degrees to the imposed stress/force display maximum (0 degrees) and minimum normal stresses (90 degrees)
• Whilst planes at 45 degrees have the maximum values of shear stress

Question 5

Stress ellipsoid: stress at a point

Answer 5

• Useful concept as rocks are made of mineral grains
• If the stress is homogeneous, the magnitude of these stresses varies to define a stress ellipsoid which will always have 3 mutually axes that correspond to the maximum, minimum and intermediate normal stresses σ1 ≥ σ2 ≥ σ3
• These are the principal stresses & uniquely they act on 3 mutually perpendicular planes where the shear stress (σs)= 0 (principal planes of stress)

Question 6

A hydrostatic stress state occurs when:

Answer 6

σ1 = σ2 = σ3
• Stress ellipsoid is a sphere
• For any plane, σn = σ1 = σ2 = σ3 ; σs = 0
• Can bring about volume change (dilations)
• If σ1 > σ2 > σ3 we can define mean stress:
σm = (σ1 + σ2 + σ3)/3
• Represents hydrostatic stress (isotropic) component of a stress field

Question 7

Deviatoric stress

Answer 7

• Deviatoric stress components:
σ1 - σm
σ2 - σm
σ3 - σm
• Measure the departure of the stress state from a hydrostatic state (anisotropic component)
• Bring about shape changes (distortions)
• A related concept is differential stress (σ1- σ3) which is of fundamental importance in controlling the fracturing behaviour of rocks

Question 8

Stress and brittle fracture

Answer 8

– Mode I tensile fractures lie parallel to σ1, σ2 plane and open parallel to σ3 (joints, veins, dykes)
– Mode II/III shear fractures that form at an angle to σ1 (Faults)

Question 9

Mode I Fractures

Answer 9

Mode I (tensile fractures)
• Mode I fractures require that σ3 is EFFECTIVELY tensile (-ve)
• Tensile stresses are rare within the Earth (σn is usually compressive, +ve)
• Effective tension arises where overpressured fluid is injected along fractures to a pressure that EXCEEDS σ3
• Common Mode I fractures = Dyke &vein emplacement

Question 10

Shear stress and normal stress equation

Answer 10

Shear - (σ1-σ3)/2 * sin2θ

Normal - (σ1+σ3)/2 + (σ1-σ3)/2 * cos2θ