Transcript Chapter 4 Rock Mechanics Strain Strain ► By comparing rocks in the deformed state to the original undeformed state, we get a better understanding of tectonic.

Chapter 4
Rock Mechanics
Strain
Strain
► By
comparing rocks in the deformed state to
the original undeformed state, we get a
better understanding of tectonic structures.
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.
Deformation
Strain
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.
Homogenous and
Inhomogenous Strain
Homogenous Strain
Inhomogenous Strain
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.
Measures of Strain
► Strain
may be recognized as a change in
line length, angles between lines, or
volume.
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
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
Linear Strain
► Quadratic
stretch.
Elongation - The square of the
λ = (l1/10)2 = (1 + ε)2 = S2
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
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
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
Dilation Strain
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.
Shear
► Simple
Shear - Rotational homogenous
shear with motion between layers.
► Pure
Shear - Distortion by homogenous
deformation without rotation.
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.
Strain Markers
► Good







strain markers include:
Reduction Spots
Pebbles
Ooids
Fossils
Vesicles
Pillow Basalts
Burrows
Flinn Diagram
► Flinn
Diagram - Most useful means of
displaying constant-volume finite strain.
► Invented by the British structural
geologist Derek Flinn in 1962.
k = (Rxy-1)/(Ryz-1)
Rxy= (1+ε1)/(1+ ε2)
Ryz= (1+ε2)/(1+ ε3)
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.
R Method