Download 1 Rheology: How Rocks Behave

Geol 345 (Spring 2014) Lecture 3 Rheology: How Rocks Behave Ch. 6: p.97-­‐103 1. Context for Crustal Deformation: Our analysis of deformation in structural geology is typically restricted to the outer 20-­‐30 km of the Earth. What happens deeper is generally in the realm of tectonics. However, we must be aware of deeper processes as they may contribute to deformation near the surface. The Earth’s interior thus: • CRUST low density; igneous rocks (granitic to basaltic); sediments/sed. rocks; metamorphic equivalents; Na, K, Ca alumino-­‐silicates 100 km thick (oceans) LITHOSPHERE 200-­‐300 km (continents) conduction
Forms the tectonic plates • MANTLE LITHOSPHERIC MANTLE ASTHENOSPHERE Mantle: Mg, Fe silicates and oxides MESOSPHERE -­‐ solid-­‐state convection conduction • OUTER CORE liquid -­‐ undergoes convection • INNER CORE solid (Fe, Ni) 2. Earth Interior Context for Deformation: The Earth’s interior is a giant heat engine, through radioactive decay, latent heat of crystallization, and tidal heating. The thermal gradient is ~25°C/km in the lithosphere, but is less deeper down. Heat flow drives internal convection in the liquid outer core and solid mantle. Conduction of heat occurs through the lithosphere, plus magmatic heat loss and asthenospheric upwelling at mid-­‐ocean ridges. Plate boundaries and motions strongly correlate to the mantle convection system. 3. Earth Interior Context for Deformation: The Earth has 7 major tectonic plates and several minor ones. They are approximated as undergoing rigid body motion with most deformation occurring in 10s-­‐100s km wide belts at their boundaries. The style of deformation varies with the type of plate boundary: divergent, convergent, and transform. 4. Age of Oceanic Crust: The oldest oceanic crust is <200 m.y. (last 4% of Earth history) so the ancient deformation history of the planet is only recorded in continental rocks (up to 3.96 Ga). 5. Divergent Plate Boundaries: Divergent plate boundaries include the mid-­‐ocean ridge spreading system and rift zones. Extension is the dominant process, causing new lithosphere to be created at some critical threshold of thinning. The dominant features are normal faults, dikes, and volcanic rocks. 6. Convergent Plate Boundaries: Convergent plate boundaries include subduction zones and fold-­‐and-­‐thrust belts. Contraction is the dominant process. The dominant features are thrust faults, folds, linear mountain belts, volcanism, plutonism, and metamorphism. 1 Geol 345 (Spring 2014) Lecture 3 7. Transform Plate Boundaries: Transform plate boundaries include transform faults (often between spreading ridge segments) and transcurrent faults (within continental lithosphere). Lateral sliding is the dominant process. The dominant features are strike-­‐slip faults. 8. Rheology: Rheology is the science of deformation and flow of matter. It is derived from the Greek rheo, which means “to flow.” We typically associate the word “flow” with fluids; however, rheology also has to do with the deformation of solids, like rocks. We can thus think of “flow” as the movement of particles during deformation. But how does this “flow” differ for different types of deformation? Let us examine a number of materials and think about how the process of deformation differs between them, why this may be, and if these materials would always behave in this manner. 9. Rheology Perception Exercise: Now that you’ve had the chance to poke at them, how would you describe the behavior of these different materials as they start to deform? Play dough ______________________________________ Pluto putty ______________________________________ Ketchup ______________________________________ Oil ______________________________________ Erasers ______________________________________ Popsicle sticks ______________________________________ Ice ______________________________________ Rock salt ______________________________________ Sandstone ______________________________________ Can you think of reasons why the behavior of these materials may be different under different circumstances? __________________________________________________________________________________ 10. Controls on Rheology: The important effect of temperature and pressure on rheology explains why rocks tend to flow plastically or viscously in the middle and lower crust. Ductile deformation is where rocks deform by solid-­‐state flow, causing them to warp and bend (at the scale of observation), perhaps with concurrent recrystallization (mineralogical and chemical changes). In the shallow crust, rocks tend to be elastic, but may eventually fracture. We are then in the realm of rock mechanics, not rheology. Brittle deformation is when rocks are physically broken by the forces imparted upon them. [Fig. 6.1. Ice in glaciers can flow viscously at Earth’s surface temperatures, but can also behave elastically and eventually fracture in a brittle manner] 2 Geol 345 (Spring 2014) Lecture 3 11. Continuum Mechanics: We use the assumptions of continuum mechanics, whereby we treat rocks as if they are homogeneous and free of defects (microfractures, mineral grain boundaries, pore spaces) and thus have identical physical properties throughout. The rock is also considered to be isotropic (deformation properties are independent of direction). [Figure: Example of progressive viscous deformation of a glacier in a laboratory experiment] 12. Constitutive Relations: Rheology implies that deformation follows explicit laws and is thus quantifiable (i.e., predictable) in response to inherent physical properties and imparted forces. There are explicit equations that describe the manner in which deformation will proceed under certain conditions. These are the constitutive equations or constitutive laws. 13. Stress and Strain: Although we will return in detail to the concepts of stress and strain later in the course, simple definitions are needed at this stage to understand rheology. Stress (σ) is the ratio of force divided by area. In other words, it is the cause of deformation. The unit of stress is 2
the Pascal, Pa (i.e., Newtons / m ). Strain (e or ε) is the measurable change in shape or volume of a deformed material. It is the end result of an applied stress. Strain has no units. Strain may be fast or slow, so we can talk about the strain rate (ė), which has -­‐1
units of per seconds (s ). 14. Elasticity: An elastic material is one that deforms by stretching the bonds between atoms as forces are applied, but it returns to its original shape when the force is removed. In other words, the strain is recoverable. In a linear sense (1D), strain can be thought of as change in length divided by the original length: e = (L – Lo) / Lo or ΔL/Lo where e stands for extension (which is considered a positive value of strain). Multiply e by 100 to get the percentage of strain. We can also consider the volumetric strain: ΔV/Vo. 15. Linear Elasticity: A linear elastic material is one that deforms in direct relation to the force applied (like a spring). Double the force equates to double the extension. In terms of stress, linear elastic materials show a linear relationship between the stress applied and the amount of strain (whether extension or contraction). The constant of proportionality is E, the Young’s modulus (also called the stiffness). σ = E e [Fig. 6.2. Elasticity demonstrated as (a) a mechanical analog (a spring); (b) on a stress vs. strain graph; and (c) on a strain history curve] 3 Geol 345 (Spring 2014) Lecture 3 16. Linear Elasticity: Linear elastic behavior can also be illustrated in terms of a linear relationship between shear stress (σs or τ) and shear strain (γ): σs = G γ where G (sometimes called µ) is a linear proportionality constant called the shear modulus (also called the rigidity). [Fig. 6.7. Shearing of a medium by a principal stress, σ1, produces a shear stress, σs, and a shear strain, γ = tan Θ] 17. Linear Elasticity: This linear relationship is called Hooke’s Law. Hence, σ = E e is a type of constitutive relationship. As strain is unitless, E must have units of stress and is usually measured in GPa (gigapascals). Most geologic materials (rocks) have values of E of the order of 10s of GPa and undergo elastic strains of a few %. [Fig. 6.3. Linear elastic behavior in 1D. The slope of the σ vs. e graph defines the Young’s modulus, E. Right: values of E for natural materials (Table 6.1)] 18. Nonlinear Elasticity: Although rocks at shallow depths tend to behave in an elastic manner up until the point of brittle failure, not all rocks are linear elastic (although many are). Some rocks have variable values of E depending on σ and e, but deform and recover the same way, and are called perfect elastic. If the recovery process is different to the deformation process, the rock is elastic with hysteresis. [Fig. 6.4. Linear elastic behavior of some geologic materials] [Fig. 6.5. Three styles of elastic behavior] 19. The Poisson Effect: We test the elasticity of rocks by compressing them between hydraulic pistons. If rocks were incompressible, any shortening along one direction would need to be balanced out by extension in the orthogonal directions. But rocks are compressible. Some of the shortening is taken up by a volume change in the rock, and the rest by an equal amount of extension in the two directions perpendicular to the shortening (this is the Poisson effect). [Fig. 6.6. Experiments showing that contraction of a rock in the z-­‐direction results in extension in the x-­‐ and y-­‐
directions. (a) Unconfined in the lateral directions. (b) Confined in the lateral directions] 20. Poisson’s Ratio: The ratio between the x-­‐ or y-­‐axis extension and the z-­‐axis contraction is called the Poisson’s ratio, ν (unitless). ν = -­‐ex /ez = -­‐ey /ez Most rocks have a value of ν in the range 0.2 -­‐ 0.33. So they extend outwards by about one-­‐quarter of the amount they are contracted. [Table 6.1] 4