Kinematic analysis and strain
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Kinematic analysis and strain . (Chapter 2, also page 25). Geologic structures are formed by material movement in all scales Kinematic analysis attempts to reconstruct the stages of progressive movement of geological structures

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Kinematic analysis and strain

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Kinematic analysis and strain

Kinematic analysis and strain

(Chapter 2, also page 25)


Kinematic analysis and strain

  • Geologic structures are formed by material movement in all scales

  • Kinematic analysis attempts to reconstruct the stages of progressive movement of geological structures

  • Geological structures do not have built-in stress gauges (no point worrying about the stresses causing the movement)


Kinematic analysis and strain

Total displacement field (page 39) can be divided into:

  • Bulk translation (Displacement of the center of mass)

  • General deformation

    General deformation can be further divided into:

    • Rigid rotation (about a point in the mass)

    • Pure strain (or deformation)

      Pure strain can have two components:

      • Dilation (change in size)

      • Distortion (change in shape)


Strain page 51 61

Strain (page 51-61)

  • Strain =dilation and /or distortion

  • Can be homogeneous or heterogeneous

    Homogeneous strain:

    • Straight lines remain straight

    • Parallel lines remain parallel

    • Can be described mathematically

      Heterogeneous strain can be divided into zones of homogeneous strain for analysis


Strain ellipse or ellipsoid page 54

Strain ellipse (or ellipsoid) page 54

  • Under homogeneous strain, a circle (or sphere) deforms to a perfect ellipse (or ellipsoid)

  • A convenient way of looking at strain

  • Forms when an undeformed circle (or sphere) is homogeneously deformed


Stretch and extension pages 55 68

Stretch and extension pages 55-68

  • Stretch (S) =

  • Extension (e) = = S-1

  • Quadratic elongation (λ) = S2 =(1+e)2


Kinematic analysis and strain

Strain Can be

  • Instantaneous (each increment of deformation. More on this later)

  • Finite (the final deformed shape after adding up all the instantaneous strain)

    Line with maximum finite stretch after deformation = The long axis of the finite strain ellipse

    Line with minimum finite stretch (maximum shortening) after deformation = The short axis of the finite strain ellipse (page 66)


Kinematic analysis and strain

Angular shear (ψ) (pages 61-63) = Measures change in angles between lines

  • Find two lines that were initially perpendicular to each other

  • Measure the angle between them after deformation

  • Subtract that angle from 90° (departure from its perpendicular position)

    Sign of ψ indicates which direction the line has rotated (page 61)

    Shear strain γ = tan ψ (page 64)


Fundamental properties of homogeneous strain in 2 d page 70

Fundamental properties of homogeneous strain in 2-D (page 70)

The finite (or principal) strain axes are mutually perpendicular (directions of zero angular shear)

Principal strain axes = Directions of maximum and minimum stretch = Directions of zero shear strain

The strain ellipse Always contain:

  • two lines that do not change length (stretch=0)

  • two directions with maximum shear strain

    Stretch and shear strain values change systematically


Kinematic analysis and strain

In reality, strain is ALWAYS three dimensional (S1>S2>S3, pages 78-79)

When S1xS2xS3≠1, Strain is accompanied by change in overall volume (pages 81-83)

Important: Ramsay’s strain field diagram (page 83, Fig. 2.58)

Special case scenario: Plane strain

When S1>S2=1>S3 (No finite strain along intermediate strain axis)

Implies no volume change


Kinematic analysis and strain

Plane strain can be expressed in 2-D

Two end member cases (pages 84-85)

  • Pure shear

  • Simple shear

    Pure shear

  • Principal strain axes do not rotate in space (no external rotation)

  • Lines within the strain ellipse rotate with respect to the principal strain axes (internal rotation present)

  • This is an example of coaxial strain (pages 83-84), not synonymous with it


  • Kinematic analysis and strain

    Simple shear

    • Principal strain axes rotate in space (external rotation present)

    • All lines except ONE rotate with respect to the principal strain axes (internal rotation present)

    • This is an example of noncoaxial strain (pages 83-84), not synonymous with it

      General shear (a combination of pure and simple shear) is also noncoaxial


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