Structural Geology Exam 1

synformational

formation occurred at the same time as deposition, ie cross-bedding

penecontemporaneous

formation occurred after deposition but before rock consolidates, ie slumps and debris flows

postformational

formation occurred after consolidation, ie faults

primary sedimentary structures

layering in sedimentary rocks formed during deposition. examples include cross-bedding, graded bedding, surface markings, and disrupted bedding

contact

a surface between two geological objects

depositional contacts

sediment is deposited over preexisting rock

fault contacts

units are juxtaposed by a fracture on which sliding has occurred

intrusive contacts

one rock body cuts across another

conformable contacts

boundary between adjacent beds is roughly parallel and doesn’t present large gaps in time

unconformable contacts

significant gap in time between geologic bodies, caused when sedimentation is interrupted or previous sediments are eroded

compaction

increase in density and decrease in porosity due to increasing weight and pressure of overlying sediments

styolites

thin, wavy, folded structures formed by the dissolution and reprecipitation of minerals. form in a line perpendicular to forces acting on it, often found in limestone

salt structures

doesn’t compress well, forms domes through hyalokinesis

igneous intrusions

often bear important ore, includes laccoliths (very shallow sills), dikes, plutons, stocks (many dikes coming from same area)

impact structures

formed by collision with a meteor, high pressure increases heat and causes partial melting, like the Maria basalts on the moon

Newtonian vs. continuum mechanics

Newtonian

• based on assumption of discrete particles and small-scale rigid bodies

• uses a coordinate system

• stress and deformation described as point-wise forces

continuum

• physical properties are continuous functions represented by tensors

• stress and deformation are fields

• what is happening to the entire system?

body vs surface forces

body force acts on every particle of the system (eg gravity) where surface force act on the outside of a body, relying on contact (eg normal force of a rock on air)

stress σ

force per unit area, measured in Pa (m)/(l)(t)²

• 1 Pa = 1 kg/ms²

• 1 bar = 1 atm = 10^5 Pa

normal stress component (σ)

component of stress vector perpendicular to surface, compressive

shear stress component (τ)

component of stress along/tangential to surface

rank zero tensors

3⁰ = 1 component. scalar, like pressure, temperature, time

rank one tensors

3¹ = 3 components. vectors like force, velocity, acceleration

rank two tensors

3² = 9 components. expressed by a matrix, eg stress

isotropic/mean stress

σm = (σ1+ σ2+ σ3)/3

causes volume change

lithostatic pressure calculation

P(pressure) = ρ(density)x g(gravity) x h(depth)

triaxial stress

σ1 > σ2 > σ3

biaxial stress

σ1 > σ2 σ3=0

uniaxial stress

compression: σ1 > 0 σ2 = σ3 = 0

tension: σ1= σ2 = 0 σ3 < 0

deviatoric stress

the distortional component of stress, changes shape

σdev = σtotal - σm

calculating normal stress

σ n=1/2(σ1+ σ3 )+1/2(σ1 - σ3 )cos2θ

calculating shear stress

σs= ½(σ1 - σ3 )sin2θ

homogenous strain

components of a body that were similar in form and orientation before strain remain similar

• parallel lines remain parallel

• straight lines remain straight

• circles become ellipses

finite strain

final state, may be reached by any number of pathways

incremental strain

represents steps to final state

coaxial (pure) strain

stress is along material axes

noncoaxial (simple) strain

stress is along non-material axes (shear plane)

mechanical contrast

different responses to stress in heterogenous materials

principal axes

lines that remain perpendicular before and after strain

• major, intermediate, and minor axes of strain ellipsoid

• axes x > y > z

passive strain markers

elements with no mechanical contrast, deform in a manner indistinguishable to that of the body

active strain markers

elements with mechanical contrast, eg. conglomerate clasts in a shale matrix

longitudinal strain

(l_f - l_o)/ l_o

_{change in length along a line. stretch is positive, compression is negative}

shear strain

γ = tan Ψ

where Ψ is change in angle between two initially perpendicular lines

volumetric strain

Δ = (V-Vo )/Vo

change in volume, compression is negative, expansion is positive

toughness

measures ability of a material to absorb energy in plastic range/before fracture

strain rate

ė = e/t =δl/l₀ t

where δ is ??, t is time in seconds

unit is t^-1

Typical strain rate for geologic processes 10^-12/s to 10^-15/s

shear strain rate

in fault study. γ =2ė

primary/transient range of creep curve

strain rate decreases with time after initial acceleration

secondary/steady state range of creep curve

strain accumulation is linear with time

tertiary/accelerated range of creep curve

strain rate increases with time, leads to failure

elastic behavior

reversible behavior, dictated by crystalline structure

eg. seismic waves, analog—rubber band

Hooke’s Law

expression of elasticity, σ = E ∙ e

where E is elasticity/Young’s modulus

Poisson’s ratio

ratio between elongation perpendicular to compressive stress and parallel to stress. v = = e_{perpendicular}/e_parallel ranges from 0 - 0.5

0 = fully compressible, stores lots of potential energy

0.5 = incompressible, maintain constant volume

natural rocks are usually 0.25 - 0.35

viscous behavior

permanent and non-reversible strain. σ= η ∙ ė

where η is viscosity constant

viscosity constant of air

10^-5 Pa(s)

viscosity constant of water

10^-3 Pa(s)

viscosity constant of lava

10 to 10⁴ Pa(s)

viscosity constant of sandstone

10¹⁸ Pa(s)

viscosity constant of asthenosphere

10²⁰ Pa(s)

role of confining pressure

increasing confining pressure increases strain accumulation before failure, increases viscosity and ability to flow, suppresses fracturing

role of temperature

at low temperatures, materials break but most strain before failure is recoverable (elastic)

at high temperatures, materials deform rapidly and the elastic portion of strain decreases

role of pore fluid pressure

“wet” rocks hold onto OH-, weakening structure. fluids facilitate magma formation.