1. Chapter 4 Rock Mechanics Strain

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

3. 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.

4. Deformation
Strain

5. 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.

6. Homogenous and Inhomogenous Strain

7. 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.

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

9. Linear Strain
Elongation - The ratio of the length of the line in the deformed mass (l1) minus the length of the original line (l0). ε = (l1 - l0)/l0 = Δl/l

10. Linear Strain
Stretch - also called engineer’s stretch - is simply the length of the deformed line divided by the original length. S = l1/l = l + ε

11. Linear Strain
Quadratic Elongation - The square of the stretch. λ = (l1/10)2 = (1 + ε)2 = S2

12. Linear Strain Elongation? ε = (l1 - l0)/l0 = (5-3)/3 = 0.67 Stretch?
S = l1/l = 5/3 = 1.67
Quadratic elongation?
λ = (l1/10)2 = (5/3)2 = 2.78

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

14. Dilation Strain Dilation Strain (Δ) - Changes in volume
Three possible mechanisms
Closing voids - Negative volume change
Dissolving by pressure solution - Negative volume change
Fracturing the mass - Positive volume change
Δ = (V1 - V0)/V0 = δV/V0

15. Dilation Strain

16. 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 σ3.

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

18. 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.

19. Strain Markers Good strain markers include: Reduction Spots Pebbles
Ooids
Fossils
Vesicles
Pillow Basalts
Burrows

20. Flinn Diagram
Flinn Diagram - Most useful means of displaying constant-volume finite strain.
Invented by the British structural geologist Derek Flinn in k = (Rxy-1)/(Ryz-1) Rxy= (1+ε1)/(1+ ε2) Ryz= (1+ε2)/(1+ ε3)

21. Wellman’s Method
Wellman’s 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.

22. R Method