The Application of Stress and Strain Principles to the Analysis of Deformed Rocks
Introduction. Knowledge of the behavior of materials, that is, their response to stress, is of great interest to our technologically-driven contemporary society. It is of particular importance to the engineering, manufacturing and scientific communities which seek to not only develop but to better understand basic properties of matter and to determine how such knowledge may be applied for societal benefit. Such benefit includes, but is by no means limited to, the development of synthetic substances which retain specified qualities under specific environmental stresses as well as the prediction of the behavior of naturally-occurring materials (such as rocks) subjected to extraordinary and long-lived environmental stresses. The latter benefit has been eagerly sought by structural geologists and seismologists attempting to decipher the strain history and mechanical behavior of ancient as well as young rocks in a full range of geological settings. Such studies are conducted for purposes which range from determining a rock's suitability as a building material to a site's suitability to support a designed structure to unraveling Earth history to earthquake prediction. Much of the knowledge of the behavior of geological materials has been an outgrowth of the joint endeavors of materials scientists and structural geologists. Working together, a systematic method by which the physical conditions to which a rock has been subjected throughout its history, as well as informed speculations about its behavior under specified future physical conditions, has been established. The following is a brief introduction to basic materials science terms and concepts which are particularly relevant to and useful to the interpretation of geological materials.
Elasticity. By definition, elasticity is the property exhibited by all materials, regardless of origin, in which the deformation they have experienced (in response to stress) is not permanent. That is, all of the strain a body of matter has acquired is fully recoverable. In other words, once the stress is removed, the body returns to its original (pre-stress) state and dimensions. Again, all materials exhibit some measure of elasticity, regardless of their state or composition. It is important to not confuse elastic behavior with the generic trade name applied to certain type latex-based materials which are commonly used in everything from waistbands in clothing to orthopaedic bandages. A material is considered to be ideally elastic as long as it conforms to Hooke's Law, that is, the amount of strain experience by a body is directly proportional to the applied stress. Each material possesses its own unique elasticity constant (referred to as either the elastic modulus, bulk modulus, or shear modulus) which expresses how hard (or how easy) it is to deform it. Not surprisingly, most rocks possess very high elasticity constants, which indicates that very large forces are required to produce even miniscule amounts of deformation. On the other hand, a rubber band possesses a very small elasticity constant, indicating that very small forces produce very large deformations.
The Yield Stress. Regardless of the type of material you are working with, it will eventually experience permanent deformation (non-recoverable strain) if the applied stresses become sufficiently great. The stress value at which a body becomes permanently deformed, broken or misshapen, is referred to as the yield (or failure) stress. Alternately, the yield stress is frequently referred to as the elastic limit. Ideally, materials which are subjected to stresses below their yield stress remain essentially elastic in their behavior. Each material possesses its own unique yield stress. Needless to say, most rocks usually possess very high yield stresses compared to other materials, both naturally-occurring and synthetic. The permanent deformation which a body has experienced as a consequence of being stressed beyond its elastic limit is generally referred to as failure.
Failure. Once a body of matter has been stressed beyond the yield stress (or elastic limit) it suffers permanent deformation or failure. This deformation may be expressed in one of three ways, that is, either through volume reduction of the body, the development of brittle fractures within and through the body or the plastic flow of material away from zones of greatest stress towards regions of lowest stress.
-Volume reduction via compaction generally occurs in rocks which possess a high porosity. That is, rocks which were formed with a considerable amount of unoccupied space between their mineral grains. Clastic sedimentary rocks are usually quite porous, although extrusive igneous rocks (particularly those with a vesicular or scoriaceous texture) may also possess a considerable measure of porosity. Soils and unconsolidated sediments always experience a measure of compaction. Rocks that deform by compaction experience a simple non-isochoric deformation which results in a net reduction in volume.
-Brittle failure is characterized by the development of a network of continuous, interwoven planar or curviplanar surfaces called fractures which completely penetrate a rock mass. Here the deformation is confined to the fracture surfaces and not internally to the rock fragments which are surrounded by them. The snapping of a piece of chalk, the chipping of a slab of concrete, or the shattering of a pane of glass all constitute brittle failure. If neighboring rock fragments in a body that has suffered brittle failure experience a relative displacement with respect to one another, the bounding surfaces are referred to as faults. Brittle deformation, and hence faulting, is generally confined to the uppermost 100 kilometers of the Earth, where ambient rock temperatures are relatively low. That part of the Earth in which deformation of rock material is primarily brittle in nature, is referred to (an defined as) the lithosphere. [The tectonic (or lithospheric) plates which constitute the outermost architectural element of the Earth are defined on the basis of the brittle way in which they deform when stressed.]
Mervyn S. Paterson
Mervyn S. Paterson is an Australian engineer best known for his application of the principles of engineering and materials science to the analysis of the structures, fabric, and behavior of rocks, particularly those generated during brittle deformation.
-Plastic failure is defined as the flow of matter in response to stress. Instead of being confined to narrow, discrete zones of separation across which rock fragments are displaced, plastic failure involves the deformation of the entire body of rock in which grains are flattened, extended, and rotated without the concurrent development of discrete through-going fault planes or fracture surfaces. Recrystallization of minerals usually always accompanies plastic failure, and this is expressed in the development of foliation and, more strikingly, the development of folds. Plastic deformation occurs at depths within the Earth where rock materials are experiencing great heat, thusly reducing their internal strength (or competence). Metamorphic rocks almost always exhibit some degree of plastic failure or flow. Plastic flow is ubiquitous to the asthenosphere, the high temperature zone which directly underlies the lithosphere from its base to depths in excess of 700 kilometers.
1. How does the study of the mechanical behavior of rocks benefit society? Cite specific
2. Define the term elasticity. Which type of materials exhibit elasticity? Can a material
exhibit unlimited elasticity? Explain.
3. Briefly explain the meaning and significance of the elastic constant.
4. Define the term plasticity. How does plasticity differ from elasticity? At what point does
elastic behavior become plastic behavior? Explain.
5. Briefly define yield stress. Explain its significance in terms of material behavior and what
sort of information about a particular material it provides.
6. Briefly define the term failure. Which sorts of features in a rock body indicate a history of
7. Briefly define and distinguish among the three basic types of permanent deformation. At
which location within the Earth do each of these types of deformation occur? Be
8. How is the Earth's lithosphere defined and characterized? How is the Earth's
asthenosphere characterized? What is the observed consequence of the lithosphere-
asthenosphere system? (THINK!)
9. Assign each of the following situations a proper deformation term: