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9.1: Stress and Strain - Geosciences

9.1: Stress and Strain - Geosciences


Stress is the force exerted per unit area and strain is the physical change that results in response to that force. When the applied stress is greater than the internal strength of rock, strain results in the form of deformation of the rock caused by the stress. Strain in rocks can be represented as a change in rock volume and/or rock shape, as well as fracturing the rock. There are three types of stress: tensional, compressional, and shear [1]. Tensional stress involves forces pulling in opposite directions, which results in strain that stretches and thins rock. Compressional stress involves forces pushing together, and the compressional strain shows up as rock folding and thickening. Shear stress involves transverse forces; the strain shows up as opposing blocks or regions of the material moving past each other.

Table showing types of stress and resulting strain:

Type of StressAssociated Plate Boundary type (see Ch. 2)Resulting StrainAssociated fault and offset types
TensionaldivergentStretching and thinningNormal
CompressionalconvergentShortening and thickeningReverse
SheartransformTearingStrike-slip

Video showing types and classification of faults:


10.1 Stress and Strain

Figure 10.1.1: Depiction of the stress applied to rocks within the crust. The stress can be broken down into three components. Assuming that we’re looking down in this case, the green arrows represent north-south stress, the red arrows represent east-west stress, and the blue arrows (the one underneath is not visible) represent up-down stress. On the left, all of the stress components are the same. On the right, the north-south stress is least and the up-down stress is greatest.

Rocks are subject to stress —mostly related to plate tectonics but also to the weight of overlying rocks—and their response to that stress is strain ( deformation ). In regions close to where plates are converging stress is typically compressional —the rocks are being squeezed. Where plates are diverging the stress is tensional —rocks are being pulled apart. At transform plate boundaries, where plates are moving side by side there is sideways or shear stress —meaning that there are forces in opposite directions parallel to a plane. Rocks have highly varying strain responses to stress because of their different compositions and physical properties, and because temperature is a big factor and rock temperatures within the crust can vary greatly.

We can describe the stress applied to a rock by breaking it down into three dimensions—all at right angles to one-another (Figure 10.1.1). If the rock is subject only to the pressure of burial, the stresses in all three directions will likely be the same. If it is subject to both burial and tectonic forces, the pressures will be different in different directions.

Figure 10.1.2: The varying types of response of geological materials to stress. The straight dashed parts are elastic strain and the curved parts are plastic strain. In each case the X marks where the material fractures. A, the strongest material, deforms relatively little and breaks at a high stress level. B, strong but brittle, shows no plastic deformation and breaks after relatively little elastic deformation. C, the most deformable, breaks only after significant elastic and plastic strain. The three deformation diagrams on the right show A and C before breaking and B after breaking.

Rock can respond to stress in three ways: it can deform elastically, it can deform plastically, and it can break or fracture. Elastic strain is reversible if the stress is removed, the rock will return to its original shape just like a rubber band that is stretched and released. Plastic strain is not reversible. As already noted, different rocks at different temperatures will behave in different ways to stress. Higher temperatures lead to more plastic behaviour. Some rocks or sediments are also more plastic when they are wet. Another factor is the rate at which the stress is applied. If the stress is applied quickly (for example, because of an extraterrestrial impact or an earthquake), there will be an increased tendency for the rock to fracture. Some different types of strain response are illustrated in Figure 10.1.2.

The outcomes of placing rock under stress are highly variable, but they include fracturing, tilting and folding, stretching and squeezing, and faulting. A fracture is a simple break that does not involve significant movement of the rock on either side. Fracturing is particularly common in volcanic rock, which shrinks as it cools. The basalt columns in Figure 10.1.3a are a good example of fracture. Beds are sometimes tilted by tectonic forces, as shown in Figure 10.1.3b, or folded.

Figure 10.1.3: Rock structures caused by various types of strain within rocks that have been stressed.

When a body of rock is compressed in one direction it is typically extended (or stretched) in another. This is an important concept because some geological structures only form under compressional stress, while others only form under tensional stress. Most of the rock in Figure 10.1.3c is limestone, which is relatively weak and easily deformed when heated. The dark rock is chert, which is relatively stronger and remains brittle. As the limestone stretched (parallel to the hammer handle) the brittle chert was forced to break into fragments to accommodate the change in shape of the body of rock. Figure 10.1.3d shows another type of brittle structure called a fault . Like fractures, faults result from brittle breaking of a rock unit. The key difference is that the bodies of rock on either side of the fault have been displaced relative to each other by the faulting.

Media Attributions

describes the force per unit area that acts on a rock unit to change its shape or volume

the deformation of rock that is subjected to stress

In geology, deformation refers to folding (ductile bending) or faulting and fracturing (brittle breaking) of rocks in response to stress.

stress that tends to squeeze something together

stress that tends to pull something apart

the stress placed on a body of rock or sediment adjacent to a fault

the deformed rock returns to its original shape and size when the deforming stress is removed

The deformed rock cannot return to an un-deformed state once the deforming stress is removed. Irreversible strain.

A break within a body of rock in which the rock on either side is not displaced.


1000 m of the NGB (Figure 1c). We like to emphasize that this stress difference is not the differential stress, which is defined as S1-S3 and can never be negative. The labelling in Figure 1c is often used by drilling engineers as a proxy for differential stress, as there is no better data available.

500 m above. While the transition may take place within a narrower range at increased numerical resolution, this result nevertheless shows that the topology of the diapir affects the size of the depth interval above the diapir in which changes of the stress field can be expected.

22.5 MPa/km have been modelled (Figure 9). This results from the decrease of the horizontal stresses in this part of the model (Figure 7). At distance from the salt diapir, lower stress gradients are encountered, also in case of the flat salt layer with

18.5 MPa/km (Model A-02). In the sub- and suprasalt section, the modelled SV-Shmin gradients are higher than the data actually measured (Figure 1c). The average suprasalt gradient in the NGB is

7.1 MPa/km and the subsalt gradient is

11.4 MPa/km our results suggest a gradient of

20 MPa/km in the subsalt. The vertical stress in the model is essentially the weight of the overburden, therefore, this discrepancy can be explained by an underestimation of the horizontal stress magnitudes in the model. To overcome this discrepancy, lower SV-Shmin gradients would be obtained by applying higher shortening rates or by applying shortening over a longer period in order to increase horizontal stresses. However, geodetic observations do not provide evidence for higher shortening rates than about 1 mm/a as Central Europe is considered as a region of very low deformation rates. Observed rates with respect to an Eurasia Plate fixed reference system are in the range of measurement errors. This, however, does not exclude that accrued shortening in the past is still stored in the subsurface. As the aim of this study is the analysis of the conditions controlling mechanical decoupling we did not pursue this aspect further by considering the increase of the amount of shortening.


Stress-Strain Testing

A typical stress-strain testing apparatus is shown in the figure above, along with a diagram of the testing apparatus, and the typical geometry of a tensile test specimen. During a tensile test, the sample is slowly pulled while the resulting change in length and the applied force are recorded. Using the original length and surface area a stress-strain diagram can be generated.

To Read

Now that I have introduced stress, please go to your e-textbook and read the first two sections (pages 65 to 70 in Chapter 4 of Materials for Today's World, Custom Edition for Penn State University) of this lesson's reading. When finished with the reading proceed to the next web page.


Strain

As we’ve just learned, the earth’s crust is constantly subjected to forces that push, pull, or twist it. These forces are called stress. In response to stress, the rocks of the earth undergo strain, also known as deformation.

Strain is any change in volume or shape.There are four general types of stress. One type of stress is uniform, which means the force applies equally on all sides of a body of rock. The other three types of stress, tension, compression and shear, are non-uniform, or directed, stresses.All rocks in the earth experience a uniform stress at all times. This uniform stress is called lithostatic pressure and it comes from the weight of rock above a given point in the earth. Lithostatic pressure is also called hydrostatic pressure. (Included in lithostatic pressure are the weight of the atmosphere and, if beneath an ocean or lake, the weight of the column of water above that point in the earth. However, compared to the pressure caused by the weight of rocks above, the amount of pressure due to the weight of water and air above a rock is negligible, except at the earth’s surface.) The only way for lithostatic pressure on a rock to change is for the rock’s depth within the earth to change.Because lithostatic pressure is a uniform stress, a change in lithostatic pressure does not cause fracturing and slippage along faults. Nevertheless, it may be the cause of certain types of earthquakes. In subducting tectonic plates, the increased pressure of greater depth within the earth may cause the minerals in the plate to metamorphose spontaneously into a new set of denser minerals that are stable at the higher pressure. This is thought to be the likely cause of certain types of deep earthquakes in subduction zones, including the deepest earthquakes ever recorded.

Rocks are also subjected to the three types of directed (non-uniform) stress – tension, compression, and shear.

  • Tension is a directed (non-uniform) stress that pulls rock apart in opposite directions. The tensional (also called extensional) forces pull away from each other.
  • Compression is a directed (non-uniform) stress that pushes rocks together. The compressional forces push towards each other.
  • Shear is a directed (non-uniform) stress that pushes one side of a body of rock in one direction, and the opposite side of the body of rock in the opposite direction. The shear forces are pushing in opposite ways.

In response to stress, rock may undergo three different types of strain – elastic strain, ductile strain, or fracture.

  • Elastic strain is reversible. Rock that has undergone only elastic strain will go back to its original shape if the stress is released.
  • Ductile strain is irreversible. A rock that has undergone ductile strain will remain deformed even if the stress stops. Another term for ductile strain is plastic deformation.
  • Fracture is also called rupture. A rock that has ruptured has abruptly broken into distinct pieces. If the pieces are offset—shifted in opposite directions from each other—the fracture is a fault.

Ductile and Brittle Strain

Earth’s rocks are composed of a variety of minerals and exist in a variety of conditions. In different situations, rocks may act either as ductile materials that are able to undergo an extensive amount of ductile strain in response to stress, or as brittle materials, which will only undergo a little or no ductile strain before they fracture. The factors that determine whether a rock is ductile or brittle include:

  • Composition—Some minerals, such as quartz, tend to be brittle and are thus more likely to break under stress. Other minerals, such as calcite, clay, and mica, tend to be ductile and can undergo much plastic deformation. In addition, the presence of water in rock tends to make it more ductile and less brittle.
  • Temperature—Rocks become softer (more ductile) at higher temperature. Rocks at mantle and core temperatures are ductile and will not fracture under the stresses that occur deep within the earth. The crust, and to some extent the lithosphere, are cold enough to fracture if the stress is high enough.
  • Lithostatic pressure—The deeper in the earth a rock is, the higher the lithostatic pressure it is subjected to. High lithostatic pressure reduces the possibility of fracture because the high pressure closes fractures before they can form or spread. The high lithostatic pressures of the earth’s sub-lithospheric mantle and solid inner core, along with the high temperatures, are why there are no earthquakes deep in the earth.
  • Strain rate—The faster a rock is being strained, the greater its chance of fracturing. Even brittle rocks and minerals, such as quartz, or a layer of cold basalt at the earth’s surface, can undergo ductile deformation if the strain rate is slow enough.

Most earthquakes occur in the earth’s crust. A smaller number of earthquakes occur in the uppermost mantle (to about 700 km deep) where subduction is taking place. Rocks in the deeper parts of the earth do not undergo fracturing and do not produce earthquakes because the temperatures and pressures there are high enough to make all strain ductile. No earthquakes originate from below the the earth’s upper mantle.

Stress and Fault Types

The following correlations can be made between types of stress in the earth, and the type of fault that is likely to result:

  • Tension leads to normal faults.
  • Compression leads to reverse or thrust faults.
  • Horizontal shear leads to strike-slip faults.

Correlations between type of stress and type of fault can have exceptions. For example, zones of horizontal stress will likely have strike-slip faults as the predominant fault type. However there may be active normal and thrust faults in such zones as well, particularly where there are bends or gaps in the major strike-slip faults.

To give another example, in a region of compression stress in the crust, where sheets of rock are stacked on active thrust faults, strike-slip faults commonly connect some of the thrust faults together.


72 12.1 Stress and Strain

Rocks are subject to stress —mostly related to plate tectonics but also to the weight of overlying rocks—and their response to that stress is strain (deformation). In regions close to where plates are converging stress is typically compressive—the rocks are being squeezed. Where plates are diverging the stress is extensive—rocks are being pulled apart. At transform plate boundaries, where plates are moving side by side there is sideways or shear stress—meaning that there are forces in opposite directions parallel to a plane. Rocks have highly varying strain responses to stress because of their different compositions and physical properties, and because temperature is a big factor and rock temperatures within the crust can vary greatly.

We can describe the stress applied to a rock by breaking it down into three dimensions—all at right angles to one-another (Figure 12.2). If the rock is subject only to the pressure of burial, the stresses in all three directions will likely be the same. If it is subject to both burial and tectonic forces, the pressures will be different in different directions.

Figure 12.2 Depiction of the stress applied to rocks within the crust. The stress can be broken down into three components. Assuming that we’re looking down in this case, the green arrows represent north-south stress, the red arrows represent east-west stress, and the blue arrows (the one underneath is not visible) represent up-down stress. On the left, all of the stress components are the same. On the right, the north-south stress is least and the up-down stress is greatest. [SE]

Rock can respond to stress in three ways: it can deform elastically, it can deform plastically, and it can break or fracture. Elastic strain is reversible if the stress is removed, the rock will return to its original shape just like a rubber band that is stretched and released. Plastic strain is not reversible. As already noted, different rocks at different temperatures will behave in different ways to stress. Higher temperatures lead to more plastic behaviour. Some rocks or sediments are also more plastic when they are wet. Another factor is the rate at which the stress is applied. If the stress is applied quickly (for example, because of an extraterrestrial impact or an earthquake), there will be an increased tendency for the rock to fracture. Some different types of strain response are illustrated in Figure 12.3.

Figure 12.3 The varying types of response of geological materials to stress. The straight dashed parts are elastic strain and the curved parts are plastic strain. In each case the X marks where the material fractures. A, the strongest material, deforms relatively little and breaks at a high stress level. B, strong but brittle, shows no plastic deformation and breaks after relatively little elastic deformation. C, the most deformable, breaks only after significant elastic and plastic strain. The three deformation diagrams on the right show A and C before breaking and B after breaking. [SE]

The outcomes of placing rock under stress are highly variable, but they include fracturing, tilting and folding, stretching and squeezing, and faulting. A fracture is a simple break that does not involve significant movement of the rock on either side. Fracturing is particularly common in volcanic rock, which shrinks as it cools. The basalt columns in Figure 12.4a are a good example of fracture. Beds are sometimes tilted by tectonic forces, as shown in Figure 12.4b, or folded as shown in Figure 12.1.

Figure 12.4 Rock structures caused by various types of strain within rocks that have been stressed [all by SE]

When a body of rock is compressed in one direction it is typically extended (or stretched) in another. This is an important concept because some geological structures only form under compression, while others only form under tension. Most of the rock in Figure 12.4c is limestone, which is relatively easily deformed when heated. The dark rock is chert, which remains brittle. As the limestone stretched (parallel to the hammer handle) the brittle chert was forced to break into fragments to accommodate the change in shape of the body of rock. A fault is a rock boundary along which the rocks on either side have been displaced relative to each other (Figure 12.4d).


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