Strain

Strain

1. Strain Lecture #11

2. STRAIN ANALYSIS UNDEFORMED DEFORMED Strain is defined as the change in size and shape of a body resulting from the action of an applied stress field

3. KINEMATIC ANALYSIS Kinematic analysis is the reconstruction of movements (Davis and Reynolds, 1996)

4. Eastic strain if the body of rock returns to its previous shape after the stress has been removed. A good example is the slow rebound of the North American crust after having been downwarped by the great weight of the Pleistocene glaciers. Brittle strain occurs when the stress is great enough to break (fracture) the rock . Plastic strain results in a permanent change in the shape of the rock. A ductile rock is one that “flows plastically” in response to stress. Whether the strain is plastic or brittle depends on both the magnitude of the stress and how quickly the stress is applied. A great stress that is slowly applied often folds rocks into tight, convoluted patterns without breaking them. Type of Deformation

5. TYPES OF STRAIN

6. Fundamental Strain Equations Extension (e) = (l f – l o )/l o Stretch (S) = l f /l o = 1 + e Lengthening e>0 and shortening e<0 Quadratic elongation ( l ) = S 2 l ’ = 1/ l = 1/S 2

7. Strain Ellipsoid S 1 = Maximum Finite Stretch S 3 = Minimum Finite Stretch (Davis and Reynolds, 1996)

8. Mohr Strain Diagram (Davis and Reynolds, 1996)

9. HOMOGENOUS DEFORMATION

10. Progressive Deformation (Davis and Reynolds, 1996)

11. STRAIN HISTORY Structural development in competent layer based on orientation of S 1 , S 2 and S 3 Scale Factor

12. Strain Measurement Geological Map Geologic Cross-section Seismic Section Outcrop Thin Section Knowing the initial objects Shape Size Orientation

13. Strain Field Diagram

14. Special Types of Homogenous Strain A. Axial symmetric extension (X>Y=Z) or Prolate uniaxial B. Axial symmetric shortening (X=Y>Z) or Oblate uniaxial C. Plane strain (X>Y=1>Z) or Triaxial ellipsoid Flinn Diagram

15. Strain Measurement from Outcrop

16. D = gap D D

17. STRESS vs. STRAIN

18. Relationship Between Stress and Strain Evaluate Using Experiment of Rock Deformation Rheology of The Rocks Using Triaxial Deformation Apparatus Measuring Shortening Measuring Strain Rate Strength and Ductility

19. Stress – Strain Diagram Onset plastic deformation Removal axial load Permanently strained Plastic deformation Rupture

20. Effects of Temperature and Differential Stress

21. (Modified from Park, 1989) Deformation and Material Elastic strain Viscous strain Viscoelastic strain Elastoviscous Plastic strain Hooke’s Law: e = s /E, E = Modulus Young or elasticity Newtonian : s = h e, h = viscosity, e = strain-rate

22. (Modified from Park, 1989) Effect increasing stress to strain-rate

23. Stress Strain

24. Limitation of The Concept of Stress in Structural Geology No quantitative relationship between stress and permanent strain Paleostress determination contain errors No implication equation relating stress to strain rate that causes the deformation

25. Questions…