# 2 strain lec8

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### 2 strain lec8

1. 1. Determining strike and dip from geologic maps (revisited) 75 m
2. 2. This is a satellite photo of a What is it? (Quiz)plunging anticline ("A" shape)and syncline ("V" shape) pair.Which direction is theanticline plunging (to top or tobottom of figure)?Which direction is the synclineplunging toward?What is the name for thesefold shapes?Are the apparent thicknessesof the beds less than orgreater than the truethicknesses of the beds?
3. 3. (D&R 51-97)1. Definitions and strain quantities2. Mohr circle strain diagram3. Pure shear vs. simple shear4. Strain rate
4. 4. What is strain?Strain is dilation (change in size) and/ordistortion (change in shape).The Goal of strain analysis is to explain howevery line in a body changes in length and angleduring deformation.How is this attempted?
5. 5. Homogeneous deformation: systematic and uniform. Test: straight lines in the body before deformation arestraight after deformation. Circles get deformed into ellipses.We will assume that deformation is homogeneous!Heterogeneous deformation: irregular and non-uniform. Amess to work with, mathematically.
6. 6. Some important quantities for describing strainExtension (e): (Lf-Lo)/Lo, where Lf is the final lengthof a line and Lo is the initial length of a lineStretch (S): Lf/Lo, where 0 = severe shortening, 1 =no shortening, and infinity = severe stretchingQuadratic elongation (λ): = (1+e)2 = (Lf/Lo)2 = S2
7. 7. Example of calculating extension (51.5 - 33)/33 = .56 = extensionmultiply by 100 to give you 56% extension A similar exercise can be performed for calculating %shortening in a thrust belt
8. 8. So far- we have only talked about changes in lengths of lines- what about angles?Angular shear (ψ, psi): degree to which 2 initiallyperpendicular lines are deflected from 90 degrees Shear strain (γ, gamma): = tan (ψ)
9. 9. Finite vs. Instantaneous strainWhat does finite mean? It is total strain, the finalresult of deformation that we see as geologistsInstantaneous or infinitesimal strain describes atiny increment of deformationAs will become apparent when studying howfabrics form in rocks, the orientation of finitestrain may be very different than that ofinstantaneous strain
10. 10. The "Magic" ofhomogeneous strain
11. 11. Strain ellipse and ellipsoid for homogeneous deformation:Shows how circular reference object is deformed 3-D2-D Vs=4/3πr3 Ve=4/3πabc
12. 12. Calculating strainIf the stretch values in the principal finitestretching directions are known, it is possible todetermine the stretch and shear strain for anyline of any orientation in the strained body.fundamental strain equationsγ/λ (for any line of orientation θ d from S1) = 1/2(1/λ 3-1/λ 1)sin2θ d
13. 13. Strain can be calculated graphically in the MohrStrain Circle:γ/λ = 1/2(1/λ 3-1/λ 1)sin2θ d λ1 = 1/λ 1 λ3 =1/λ 3
14. 14. Some more definitionsPlane strain: S1 is compensated by S3 so thatthere is no change in S2- and no change in volume!Noncoaxial strain: finite principal stretching axesdo not remain fixed in orientation during deformationCoaxial strain: Finite principal stretching directionshave the same orientation before and afterdeformation
15. 15. 2 end-member types of plane strainSimple shear: Rock issheared like a deck of cards.A square becomes aparallelogram. **The finitestretching axes rotate duringdeformation. Distortion bysimple shear is the mostimportant process in shapingshear-zone structures!
16. 16. Pure shear: Rock isshortened in one direction andextended in the perpendiculardirection. A square becomesa rectangle. **The finitestretching axes do not rotate.
17. 17. A better feeling for simple shearlines in circle brachiopod
18. 18. A better feeling for pure shearlines in circle brachiopod
19. 19. Strain Ratestrain rate = extension (e) divided by time (t) = e/tThe rate at which a rock is strained has importantimplications for the manner in which it deforms. "Lab" Strain RatesDuring 1 hour experiment, an initially 2.297 cm-longsample is shortened to 2.28 cm. What is the averagestrain rate during this experiment?
20. 20. "Natural" Strain Rates Basin and Range extension: present-day width = 600 km initial width = 300 km Extension occurred over ~20 m.y. What was the strain rate? How much does it differ from laboratory experiments? What are the implications?
21. 21. Next Lecture: Stress! Read D&R 98-122
22. 22. Important terminology/concepts dilation distortion homogeneous vs. heterogeneous deformation extension- definition and calculation of stretchstrain ellipse and ellipsoid- principle stretch directions finite strain vs. instantaneous strain Mohr strain diagram plane strain noncoaxial vs. coaxial strain simple shear pure shear strain rate- definition and calculation of