Structural Flashcards
Define and explain the term brittle failure, using a geological structure as an example
when the material loses cohesion due to the development of one or more fractures and material continuity is lost - i.e. it breaks. Brittle failure can be in tension or compression – faults would be a good geological example. Stress strain graphs up to failure would ideally accompany this as a diagram.
Write down the equation for the Coulomb failure criterion and define what the terms are, including units where appropriate
τ = σnµ + c, where:
τ is the shear stress at failure (N/m2);
σn is the normal stress at failure (N/m2);
µ is the coefficient of friction = tanβ where β is the internal angle;
c is the cohesion (the shear stress to fail when the normal stress is zero (N/m2)
What is the equation for the internal angle of a material?
β = 90 - 2α
What are the equations for the shear stress and normal stress at failure for a material?
τfailure = yi = rcosβ = ((σ1 - σ3)/2)cosβ = ((σ1 - σ3)/2)sin2α
σn = xi = (σ1 + σ3)/2 - ((σ1 - σ3)/2)cos2α
where:
2α = Φ;
(σ1 + σ3)/2 = k
Explain the term principal stress axes.
The principle stress axes are defined for a body with no net acceleration/rotation and for which there exists three planes with zero shear stress. Lines normal to these planes are the principle stress axes, which are orthogonal to each other, and are defined as the minimum (σ3), intermediate (σ2) and maximum (σ1) principle stresses. One typically defines the surface of the earth as a plane of zero shear stress, and one principle stress axis is typically vertical for structural problems (i.e. gravity).
Explain the term strain ellipsoid.
Strain ellipsoid diagram
The ellipsoid is a mathematical representation of strain in a deformed object with orthogonal axes representing the greatest, intermediate and least elongation of a strained body.
Theoretically the starting condition is a sphere of unit radius.
The axes of the strain ellipse are principle strain axes which represent the quadratic elongation (strain²).
Ideally one would like to know the orientation of the principle strain axes relative to the orginal co-ordinate axes defined for the unstrained sphere
Outline the main rheological properties of the lithosphere
The lithosphere is the brittle outer layer of the Earth that includes the crust and the rigid upper mantle – typically e.g. 125km thick or more. It can rupture; have
faults etc.
Outline the main rheological properties of the asthenosphere
The asthenosphere lies underneath the lithosphere and is warm enough that it can deform plastically and flow in solid-state. Convection occurs in the asthenosphere and the links to plate tectonics
Explain the role that rheology plays in buckle folding
Buckle folding occurs for layer parallel shortening when there is a difference in viscosity between adjacent layers, as well as some interlayer roughness.
Diagrams would include type 1B and type 3 folds produced in the less competent layers.
Hinge thickening and vergence in folds as the more competent layers are finally deformed and the weaker layers undergo some shear
What is meant by the term rheology?
Rheology is the study of the flow of matter or liquids – hence deformation.
What are rifts?
Rifts are areas of localised extension, with through-going active normal faults accommodating this crustal extension.
Features include grabens, horsts and hangingwall basins and normal fault arrays (expand on development and evolution of these features including the way faults link up). Diagrams showing these features are needed.
Give examples of where rifting is happening today
The rift valley(s) of eastern Africa, the red sea and the gulf of suez
