Post on 31-Dec-2015
Determining strike and dip from geologic maps(revisited)
75 m
What is it? (Quiz)This is a satellite photo of a plunging anticline ("A" shape) and syncline ("V" shape) pair.
Which direction is the anticline plunging (to top or to bottom of figure)?
Which direction is the syncline plunging toward?
What is the name for these fold shapes?
Are the apparent thicknesses of the beds less than or greater than the true thicknesses of the beds?
(D&R 51-97)
1. Definitions and strain quantities
2. Mohr circle strain diagram
3. Pure shear vs. simple shear
4. Strain rate
What is strain?
Strain is dilation (change in size) and/or distortion (change in shape).
The Goal of strain analysis is to explain how every line in a body changes in length and angle during deformation.
How is this attempted?
Homogeneous deformation: systematic and uniform. Test: straight lines in the body before deformation are straight after deformation. Circles get deformed into ellipses.
We will assume that deformation is homogeneous!
Heterogeneous deformation: irregular and non-uniform. A mess to work with, mathematically.
Some important quantities for describing strain
Extension (e): (Lf-Lo)/Lo, where Lf is the final length of a line and Lo is the initial length of a line
Stretch (S): Lf/Lo, where 0 = severe shortening, 1 = no shortening, and infinity = severe stretching
Quadratic elongation ((1+e)2 = (Lf/Lo)2 = S2
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
So far- we have only talked about changes in lengths of lines- what about angles?
Angular shear (, psi): degree to which 2 initially perpendicular lines are deflected from 90 degrees
Shear strain (, gamma): = tan ()
What does 'finite' mean? It is total strain, the final result of deformation that we see as geologists
Instantaneous or infinitesimal strain describes a tiny increment of deformation
As will become apparent when studying how fabrics form in rocks, the orientation of finite strain may be very different than that of instantaneous strain
Finite vs. Instantaneous strain
The "Magic" of homogeneous
strain
Strain ellipse and ellipsoid for homogeneous deformation:
Shows how circular reference object is deformed
2-D3-D
Vs=4/3r3
Ve=4/3abc
Calculating strain
If the stretch values in the principal finite stretching directions are known, it is possible to determine the stretch and shear strain for any line of any orientation in the strained body.
fundamental strain equations
/(for any line of orientation d from S1) = 1/2(1/3-1/1)sin2d
Strain can be calculated graphically in the Mohr Strain Circle:
/= 1/2(1/3-1/1)sin2d'1 = 1/1 '3 = 1/3
Some more definitions
Plane strain: S1 is compensated by S3 so that there is no change in S2- and no change in volume!
Noncoaxial strain: finite principal stretching axes do not remain fixed in orientation during deformation
Coaxial strain: Finite principal stretching directions have the same orientation before and after deformation
2 end-member types of plane strain
Simple shear: Rock is sheared like a deck of cards. A square becomes a parallelogram. **The finite stretching axes rotate during deformation. Distortion by simple shear is the most important process in shaping shear-zone structures!
Pure shear: Rock is shortened in one direction and extended in the perpendicular direction. A square becomes a rectangle. **The finite stretching axes do not rotate.
A better feeling for simple shear
lines in circle brachiopod
A better feeling for pure shear
lines in circle brachiopod
Strain Ratestrain rate = extension (e) divided by time (t) = e/t
The rate at which a rock is strained has important implications for the manner in which it deforms.
"Lab" Strain Rates
During 1 hour experiment, an initially 2.297 cm-long sample is shortened to 2.28 cm. What is the average strain rate during this experiment?
"Natural" Strain Rates Basin and Range extension:present-day width = 600 kminitial 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?
Next Lecture: Stress!Read D&R 98-122
Important terminology/concepts
dilation
distortion
homogeneous vs. heterogeneous deformation
extension- definition and calculation of
stretch
strain 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