In this lecture we start out with a lesson in mechanical engineering, then apply that knowledge to the study of the mechanical properties of the Earth.

Stress and Strain

• Stress: A force acting on a surface. Generally, the stress is measured as force per unit area of the surface. E.G. the stress applied to the inside of a car tire might be 60 pounds per square inch. Strictly speaking, stress and pressure are the same thing, but in common usage, "stress" is applied to a wider variety.

• Kinds of stress:
• Uniform: The force acts equally in all directions. Also called confining stress or confining pressure. This is the kind of stress that a submarine would experience during a dive.
• Differential: Stress that acts with different magnitudes in different directions. E.G. The weight of your body applies a differential stress to the soles of your feet. Engineers generally speak of three types:
• Tension: A force acting perpendicular to and away from a surface. E.G. when you pull on a refrigerator magnet in order to open the refrigerator door, a tensile stress is being applied to the magnet and door.
• Compression: A force acting perpendicular to and towards a surface. E.G. when you step on the bathroom scale, your body applies a compressive stress to the scale platform.
• Shear: A force acting parallel to a surface. E.G. when one pushes on the top of a deck of cards to pull them into a line, the deck is being sheared.
• Strain:

The change in a solid's shape caused by the application of a stress. Depending on the solid, a given stress might cause a great or small strain.

• Kinds of deformation - Review: We discussed this briefly with regard to earthquakes.

• Elastic deformation: Generally, when a solid is strained, it will return to its original shape when the stress is removed. This is because its chemical bonds, although stretched, have not broken, as in the illustration above. Beyond that point, however, the change in shape becomes permanent.
• Ductile deformation: (A.k.a. "plastic" deformation) A solid that is strained past its zone of elastic deformation retains its new shape. This is because it has been strained to where chemical bonds have begun to break. In the Earth, we see ductile deformation manifested as folds.
• Brittle deformation: Break enough chemical bonds, and the entire object breaks. In the Earth, we see breaks manifested as faults. The actual breakage event, of course, is manifested as an earthquake.

• Measurements of Stiffness: Young's modulus is the ratio of stress to strain. It is a measure of stiffness. (It's usually measured using tensile stress.) A stiffer solid like steel has a high Young's modulus, whereas a less stiff one like lead has a lower Young's modulus.

• Measurements of strength:
• Yield strength: The amount of stress required to cause a solid to deform ductilely.
• Tensile strength: The amount of stress required to cause a solid to break.
NOTE! Stiffness and strength are two different things. A steel bar and a biscuit are both stiff but they aren't both strong. Nylon and steel are both strong but they aren't both stiff. Materials that are both stiff and weak are said to be brittle.

More on Young's modulus.
Structural Geology: The study of stress and strain in rocks and the rock structures that result from them.

Basic descriptive terminology: Structural geologists are preoccupied with the orientation of things in space. To describe the orientations of lines and planes, three terms are used.

• For Lines:
• Bearing: (Some people say trend)The angle between the line and north.
• Plunge: The smallest angle between the line and horizontal.
• For Planes:
• Strike: Unless it is perfectly horizontal, the intersection of any plane with the horizontal forms a line. That line's bearing is its strike.
• Dip: The smallest angle between the plane and horizontal.

Fractures: Fractures are simply cracks, the traces of brittle deformation of rocks.

• Joints: Fractures along which no relative movement has occurred. Joints usually occur because of tension. We see them when:
• Ingeous rocks cool and contract to form columnar jointing.
• Rocks that formed at great depth are decompressed by the removal of overlying rocks. (Indeed, exploding rocks are a common hazard in deep mineshafts, where the rock of the minesaft wall is suddenly decompressed on one side by the excavation of the mine.)

• Faults: Fractures along which movement has occurred.

• Fault block names: A fault separates adjacent rock into two blocks. Unless the fault is exactly vertical, we distinguish two kinds of blocks. To make this easy, imagine that you are actually stading on the fault plane, as miners sometimes do:
• Footwall block: The block on which you are standing.

• Kinds of faults: Distinguished based on the orientation of the fault plane and the sense of movement.
• Strike-slip faults: Faults in which neither block is downthrown but the sense of motion is parallel the the fault plane's strike. Transform boundaries of plates are examples of strike-slip faults.
• Dip-slip faults:
• Normal faults: Faults in which the hanging wall is downthrown (i.e. has moved down) with respect to the footwall.
• Reverse faults: High angle faults (i.e. their dip is at least 30 deg.) in which the hanging wall has moved up with respect to the footwall.
• Thrust faults: Low angle faults (i.e. their dip is at less than 30 deg.) in which the hanging wall has moved up with respect to the footwall.

In the field, faults almost never appear as in the nice clear block diagrams. Weathering and erosion immediately attack any topographic expression of faults, like in the image above. Once that happens, faults are inconspicuous and reveal their presence only indirectly. Some keys:

Folds: Folds and associated structures are the record of ductile deformation of rocks.

• Fold geometry terms: At its simplest, a fold is where a planar feature (stratum, foliation plane, etc.) is bent along an axis.
• Limb: the halves of the folded rock on either side of the bend.
• Axial plane: The plane bisecting the two limbs, representing the surface along which bending was focused.
• Axis: The intersection of the axial plane with the folded surface.
• Plunge: As with any linear feature, the angle between the axis and the horizontal.
• Kinds of folds:
• Anticline: A fold in which the limbs dip away from the axis. Anticlines, viewed end-on, resemble a capital A. Just think A for Anticline. The oldest rocks are at the axis. The youngest are farthest away.
• Syncline: A fold in which the limbs dip toward the axis. Synclines resemble a capital V or U, viewed end-on. The youngest rocks are at the axis. The oldest are farthest away.
• Monocline: A local steepening in an otherwise uniformly dipping surface.

Topographic expression of folds:

Paradoxically, structural anticlines tend to be topographically low-lying whereas the axes of synclines tend to stand up topographically. This is a result of the mechanical effects of folding on the rocks being folded.

Within any given layer, rock on convex surfaces feels tension relative to the rock on concave surfaces, especially if it is an upper surface. Rock in concave surfaces is actually being compressed relatively. Thus, rock on the upper surfaces of anticlines is being "pulled apart" whereas rock in the upper surfaces of synclines is being compressed. Weathering and erosion, therefore, attack anticlines more vigorously, and the axes of synclines are expressed topographically as ridges.

One last thing about folds: Nowhere is it written that a rock can't be folded more than once. The rock below displays two obvious generations of folding. (In fact, there are two others that are less obvious.)

Domes and basins: Occasionally rocks in a region will be uplifted or will subside relative to their surroundings. This yields:

• Domes (aka "uplifts"): Regions of local uplift in which all strata dip away from a central point such as the 50 km. wide Richat Structure pictured above. The oldest rocks are in the center and the youngest at the periphery.
• Basins: Regions of local subsidence in which all strata dip toward a central point. The youngest rocks are in the center and the oldest at the periphery.

As with folds (and for the same reasons), structural domes tend to be topographic depressions and vice versa.

Key concepts and vocabulary:

• Stress
• Strain
• Uniform stress (a.k.a. confining stress or confining pressure)
• Differential stress
• Tension
• Compression
• Shear
• Deformation
• Elastic deformation
• Ductile deformation
• Brittle deformation
• Stiffness
• Strength
• Young's modulus
• Lines and planes in space
• Bearing (a.k.a. trend)
• Plunge
• Strike
• Dip
• Fractures
• Joints
• Faults
• Hanging wall block
• Footwall block
• Fault varieties
• Dip-slip faults
• Normal fault
• Reverse fault
• Thrust fault
• Strike-slip fault
• Slickensides
• Fault breccia
• Offset of rock units
• Fold terminology
• Limb
• Axis
• Axial plane
• Plunge
• Anticline
• Syncline
• Relationship of syncline axes and topography after erosion
• Domes
• Basins