SGES 3371 STRUCTURAL GEOLOGY II

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SGES 3371STRUCTURAL GEOLOGY II
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x x A y y B A 6 B 3
x x y?x y y ?x 30 ?x 0.58
x cos?x sin?y y cos?y - sin?x ? 45
x x y y x?y ?y -30 ?y -0.58
x Sxx y Syy Sx 2 Sy 0.5
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2D Strain Analysis II - Mohr Circle

• Fundamental Strain Equations
• Can be used to determine the stretch and shear
  strain of any line of any orientation in a
  strained body, provided S1 and S3, as well as the
  angle ,?d between the line and S1 are known.
• Quadratic elongation, ? (l/lo)2 S2
• Reciprocal quadratic elongation, ? 1/ ? 1/S2
  
• Ratio of shear strain to quadratic elongation (?/
  ?) is important as it describe the change in
  angle versus change in length.
• The fundamental strain equations of Ramsay can be
  written as
• ? 0.5(1/ ?3) (1/ ?1) 0.5(1/ ?3) -
  (1/ ?1) cos2?d
• ?/? 0.5(1/ ?3) - (1/ ?1) sin2?d
• where ? S2 along line L which makes an angle
  ?d with S1 ?1 greatest quadratic elongation
  S12 ?3 minimum quadratic elongation S32
• ? shear strain

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• Distortion of a circle. We can use the lines L
  and M to calculate the strain.
• Assuming the diameter of original circle 1
  unit we can measure S1, S3 and ?d. S11.55 unit,
  S3 0.65 unit, ?d26.5
• then ?1S122.4 ?3S320.42
• ? 0.5(1/ ?3) (1/ ?1) 0.5(1/ ?3) - (1/
  ?1) cos2?d
• 0.5(1/0.42)(1/2.4) 0.51/0.65
  1/2.4cos-53 0.81
• ?/? 0.5(1/ ?3) - (1/ ?1) sin2?d
  0.51/0.42 1/2.4sin-53 -0.78
• ? 1/ ? 1.2 S v? 1.1
• ? -0.78x1.2 -0.94 angular shear, ?
  arctan-0.94 -43

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• Fundamental strain equations can be represented
  graphically as a circle in the Mohr circle strain
  diagram.
• It can be defined as a circle with radius 0.5(?3
  - ?1), centred on the x-axis at a distance of
  0.5(?3 ?1) from the origin.
• The pair (?, ?/?) value and ? can be obtain for
  any line than make an angle ?d to the maximum
  finite stretch, S1.
• In the example below ?d is counter-clockwise or
  negative.

0.5(?3 ?1)
2?d
?3
?1
?
0.5(?3 - ?1)
(?, ?/?)
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• We use the values of the earlier example where
• S11.55 unit, S3 0.65 unit, ?d26.5 then
  ?1S122.4 ?3S320.42
• ?11/2.40.42 ?31/0.422.4 center of
  circle0.5(0.422.4) 1.41
• From the perimeter of the circle, ?0.82 ?/?
  -0.78
• Thus ? 1/0.82 1.2 Sv? v1.2 1.1 and ?
  -0.78x1.2 -0.94
• ? arctan-0.94 -43 measured ? angle

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• For objects such fossils that have undergone the
  same deformation, but have different angular
  relationship with S1, their (?, ?/?) will be
  plotted on the same Mohr strain circle.