SGES 3371 STRUCTURAL GEOLOGY II

1
SGES 3371STRUCTURAL GEOLOGY II
2
Week 112D Strain Analysis I
3
DEFORMATION

• Any change in shape, position or orientation of a
  body (displacements) resulting from the
  application of a differential stress
• 4 components rotation, translation (change in
  position), dilation (change in size) strain
  (distortion)
• Strain can be homogeneous or inhomogeneous
  (unequal distribution of strain)

4

• Deformation
• Rigid body deformation (rotation translation)
• Non-rigid body deformation (strain dilation)
• Difficult to determine the rotational,
  translational and dilational components of
  deformation (original position volume often
  unknown)
• If we know the original shape of a body, the
  strain can be quantified

Original
5

• Strain
• Homogeneous
• Heterogeneous

6
Homogeneous Strain

• All points within the body undergone the same
  change in shape, volume or orientation (change in
  a regular uniform manner)
• Must comply all the 3 conditions below
• Originally straight lines remain straight
• Originally parallel lines remain parallel
• Circles become ellipses in 3D spheres become
  ellipsoids
• If one or more conditions are not met ?
  heterogeneous strain
• Heterogeneous strain leads to complex distorted
  forms
• Heterogeneously strained body is more complex to
  describe, but is geologically more common
• Heterogeneously strained region is analysed by
  dividing it into smaller locally homogeneous
  region (domain)
• Homogeneity is scale dependent

7
Strain Ellipsoid

• In homogeneously strained 3D body, there are gt 3
  lines of particles (material lines) that do not
  rotate relatively to each other (gt2 in 2D)
• These material lines, which are mutually
  perpendicular are the principal strain axes of
  the strain ellipsoid
• The principal strain axes are X, Y Z, where
  XgtYgtZ

8
Coaxial Noncoaxial Strain

• All material lines except those parallel to the
  principal strain axes, rotate relative to each
  other
• Noncoaxial strain the material lines are not the
  same throughout the strain history they may
  rotate relative to the finite strain axes at each
  incremental strain (aka rotational strain)
• Coaxial strain if the material lines remain the
  principal strain axes at each incremental strain
  (aka non-rotational strain)

Noncoaxial Strain
Coaxial Strain
9
Pure Shear Simple Shear

• Internal vorticity measure of the degree of
  noncoaxiality descibe the rotation of material
  lines with respect of the principal strain axes
• If internal vorticity is zero, the strain history
  is coaxial and this is known as Pure Shear
• If the distance prependicular to the shear plane
  remains the same and lines parallel to the shear
  plane remains parrallel, it is known as Simple
  Shear (eg. shearing of a deck of card)

Noncoaxial Strain Simple Shear
Coaxial Strain Pure Shear
10
Measurement of Strain

• Longitudinal strain, elongation, e
• Volumetric strain, ?
• Angular shear, ?
• Shear strain, ? tan ?
• Stretch, s
• Quadratic elongation, ?
• Natural strain, e

11
Longitudinal strain

• Change in length divided by the original length
• Dimensionless quantity
• Expressed by elongation, e
• e (l lo)/lo or dl/lo
• l final length, lo initial length, dl
  length change
• Positive lengthening negative shortening

12
Stretch

• Change in length can also be expressed as stretch
• Stretch, s l/lo 1 e

13
Volumetric strain

• Similar to longitudinal strain but in 3D
• Also dimensionless quantity
• Express by ?
• ? (V Vo)/Vo or dV/Vo
• V final volume Vo initial volume, dV
  volume change
• Positive expansion negative contraction

14
Angular strain

• Measured by the change in angle of 2 lines that
  were initially perpendicular
• Change in angle angular shear, ?
• Shear strain, ? tan ?
• Shear strain is dimensionless

? greek letter psi
15
L-L perpendicular to W-W before
deformation Angular shear along L-L
-30 Angular shear along W-W 30
16
Shear Strain

• Shear strain can be measured as a displacement
• Shear strain, ? tan ? ?x/y

17
Strain Parameters A 6 B 3 ? 45 Sx 2
Sy 0.5 ?x 30 ?y -30