Chapter 4 Rock Mechanics Strain

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Chapter 4Rock MechanicsStrain
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Strain

• By comparing rocks in the deformed state to the
  original undeformed state, we get a better
  understanding of tectonic structures.

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Definitions

• Deformation - The displacement field for
  tectonically driven particle motions
• Distortion - Involves a change in shape,
  rotation, and translation.
• Strain - Aspects of shape change measured in line
  length, angular relationship between lines, or
  volume.

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Deformation
Strain
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Definitions

• Homogenous Strain - Lines that are straight and
  parallel before deformation remain straight and
  parallel after deformation.
• Inhomogenous Strain - The landscape is distorted
  and lines may be broken.

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Homogenous and Inhomogenous Strain
Homogenous Strain
Inhomogenous Strain
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Definitions

• Incremental Strain - Describes the deformation
  history of the rock body.
• Usually cannot differentiate the deformation
  history.
• Finite Strain - A comparison can be made between
  the present shape and some previous shape.
• Finite strain is path independent.

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Measures of Strain

• Strain may be recognized as a change in line
  length, angles between lines, or volume.

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Linear Strain

• Elongation - The ratio of the length of the line
  in the deformed mass (l1) minus the length of the
  original line (l0). e (l1 - l0)/l0 ?l/l

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Linear Strain

• Stretch - also called engineers stretch - is
  simply the length of the deformed line divided by
  the original length. S l1/l l e

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Linear Strain

• Quadratic Elongation - The square of the
  stretch. ? (l1/10)2 (1 e)2 S2

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Linear Strain

Elongation?
e (l1 - l0)/l0 (5-3)/3 0.67
Stretch?
S l1/l 5/3 1.67
Quadratic elongation?
? (l1/10)2 (5/3)2 2.78
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Shear Strain

• Shear Strain (?) - Strain that results when parts
  of a rock body are deformed so that angles
  between originally orthogonal reference lines are
  rotated. ? tan ?

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Dilation Strain

• Dilation Strain (?) - Changes in volume
• Three possible mechanisms
• Closing voids - Negative volume change
• Dissolving by pressure solution - Negative volume
  change
• Fracturing the mass - Positive volume change
• ? (V1 - V0)/V0 dV/V0

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Dilation Strain
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Strain Ellipsoid

• Strain Ellipsoid - Graphical tool that provides a
  reference object for estimating shape change from
  an assumed initial sphere.
• Elliptical sections through these are sometimes
  printed on geologic maps to indicate geologic
  strain.
• Made of three mutually perpendicular axes x, y,
  and z, where X ? Y ? Z.

The Strain Ellipsoid usually has an inverse
relationship with the Stress Ellipsoid. X
corresponds to s3.
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Shear

• Simple Shear - Rotational homogenous shear with
  motion between layers.
• Pure Shear - Distortion by homogenous deformation
  without rotation.

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Strain Measurements

• Strain Markers - A deformed feature in the rock
  that can be measured to determine strain.
• Have to know the original shape for comparison.
• Should have the same mechanical characteristics
  as the original rock.

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Strain Markers

• Good strain markers include
• Reduction Spots
• Pebbles
• Ooids
• Fossils
• Vesicles
• Pillow Basalts
• Burrows

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Flinn Diagram

• Flinn Diagram - Most useful means of displaying
  constant-volume finite strain.
• Invented by the British structural geologist
  Derek Flinn in 1962.k (Rxy-1)/(Ryz-1)Rxy
  (1e1)/(1 e2)Ryz (1e2)/(1 e3)

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Wellmans Method

• Wellmans Method - A simple geometric technique
  for determining the orientation and shape of the
  strain ellipse.
• Requires at least ten strain markers.
• All must be on the same plane.
• Most commonly use brachiopods or trilobites.

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R Method