Rock Deformation I: Rock Deformation I
Rock Deformation: Rock Deformation Collective displacements of points in a body relative to an external reference frame
Deformation describes the transformations from some initial to some final geometry
Deformation of a rock body occurs in response to a force
Deformation …: Deformation … Deformation involves any one or a combination of the following four components:
Ways that rocks respond to stress:
Rigid Body Translation
Rigid Body Rotation
Distortion or Strain
Dilation
Deformation Components: Deformation Components The components of deformation are divided into rigid and non-rigid body deformation
With rigid body deformation the position and orientation of points in a rock body relative to an internal reference frame are not changed
With non-rigid body deformation, the position and orientation of points within a rock body are changed relative to both an internal and external reference frame
Rigid Body Rotation: Rigid Body Rotation Rotation is a rigid body deformation that changes the configuration of points relative to some external reference frame in a way best described by rotation about some axis
Spin of the body around an axis
Particles within the body do not change relative position
No translation or strain is involved
Particle lines rotate relative to an external coordinate system
Examples
Rotation of a car
Rotation of a fault block
Clockwise Rotation about the z-axis: Clockwise Rotation about the z-axis .
Rigid Body Translation: Rigid Body Translation A rigid body deformation involving movement of the body from one place to another, i.e., change in position
Particles within the body do not change relative position
No rotation or strain are involved
Particle lines do not rotate relative to an external coordinate system
Displacement vectors are straight lines
e.g., passengers in a car, movement of a fault block
During pure translation, a body of rock is displaced in such a way that all points within a body move along parallel paths relative to some external reference frame
Translation Parallel to the Y axis: Translation Parallel to the Y axis
Strain or Distortion: Strain or Distortion Distortion is a non-rigid body operation that involves the change in the spacing of points within a body of rock in such a way that the overall shape of the body is altered with or without a change in volume
Changes of points in body relative to each other
Particle lines may rotate relative to an external coordinate system
Translation and spin are both zero
Example: squeezing a paste
In rocks we deal with processes that lead to both movement and distortion
Strain or Distortion: Strain or Distortion
Dilation: Dilation Dilation is a non-rigid body operation involving a change in volume
Pure dilation:
The overall shape remains the same
Internal points of reference spread apart (+ev) or pack closer (-ev) together
Line lengths between points become uniformly longer or shorter
Dilation: Dilation
General Deformation: General Deformation During deformation one or more of the four components of deformation may be zero
If, for example, during deformation the rock body undergoes no distortion or no volume change, then deformation consists of either a rigid-body translation, a rigid-body rotation, or includes components of both translation and rotation
In contrast, if volume change, translation, and rotation are all zero, then deformation consists of a non-rigid body distortion or strain
Strain vs. Deformation: Strain vs. Deformation Though commonly confused with each other, strain is only synonymous with deformation if there has been distortion without any volume change, translation, or rotation
Strain represents only one of four possible components involved in the overall deformation of a rock body where it has been transformed from its original position, size, and shape to some new location and configuration
Strain describes the changes of points in a body relative to each other, or, in other words, the distortions a body undergoes
The reference frame for strain is thus internal
Homogeneous vs. Inhomogeneous Strain: Homogeneous vs. Inhomogeneous Strain Mathematical treatments of strain commonly assume homogeneous rather than heterogeneous distortions or strains
However, any heterogeneously strained rock body can be subdivided into small areas that exhibit the characteristics of homogeneous strain (concept of domain)
Homogeneous Strain: Homogeneous Strain Positions of points with respect to some reference point in a strained domain are a linear function of their position with respect to the same reference point before strain
The directions of the lines may change
In other words, in homogeneous deformation, originally straight lines remain straight after deformation (also called affine deformation)
Homogeneous Strain: Homogeneous Strain Homogeneous strain affects non-rigid rock bodies in a regular, uniform manner
During homogeneous strain parallel lines before strain remain parallel after strain, as a result cubes or squares are distorted into prisms and parallelograms respectively, while spheres and circles are transformed into ellipsoids and ellipses respectively
For these generalizations to hold true, the strain must be systematic and uniform across the body that has been deformed
Homogeneous Deformation: Homogeneous Deformation Originally straight lines remain straight
Originally parallel lines remain parallel
Circles (spheres) become ellipses (ellipsoids)
Homogeneous Strain: Homogeneous Strain
Homogeneous Deformation - Pure Shear: Homogeneous Deformation - Pure Shear .
Homogeneous Deformation - Simple Shear: Homogeneous Deformation - Simple Shear
Inhomogeneous Strain: Inhomogeneous Strain Heterogeneous strain affects non-rigid bodies in an irregular, non-uniform manner and is sometimes referred to as non-homogeneous or inhomogeneous strain
During heterogeneous strain, parallel lines before strain are not parallel after strain
Circles and squares or their three-dimensional counter parts, cubes and spheres, are distorted into complex forms
Heterogeneous or Inhomogeneous strain: Heterogeneous or Inhomogeneous strain Leads to distorted complex forms