Chapter 4 Rock Mechanics Strain Strain By comparing

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 (l 1) minus the length of the original line (l 0). ε = (l 1 - l 0)/l 0 = Δl/l

Linear Strain ► Stretch - also called engineer’s stretch - is simply the length of the deformed line divided by the original length. S = l 1/l = l + ε

Linear Strain ► Quadratic stretch. Elongation - The square of the λ = (l 1/10)2 = (1 + ε)2 = S 2

Linear Strain Elongation? ε = (l 1 - l 0)/l 0 = (5 -3)/3 = 0. 67 Stretch? S = l 1/l = 5/3 = 1. 67 Quadratic elongation? λ = (l 1/10)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 = (V 1 - V 0)/V 0 = δV/V 0

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+ε 1)/(1+ ε 2) Ryz= (1+ε 2)/(1+ ε 3)

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