2016 Test 1 Structural Review Material

8/17/2019 2016 Test 1 Structural Review Material

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INTRODUCTORY MATERIAL:

3 components to structural geology:

GEOMETRY: The shape of rock units and the boundaries that define them.

INEMATIC!: Movement responsible for developing a structure

Translat"on: Change in position

Rotat"on: Change in orientation

D"stort"on: Change in shape

D"lat"on: Change in size

DYNAMIC!: Relating the observed deformation to the stresses responsible

#r"mary !tructures $s% !econ&ary !tructures

Primary Structures: evelop during formation of a rock body! e.g." cross#bedding" ripple marks"

mudcracks" pillo$s %in basalt&

Secondary Structures: 'orm in rocks as a result of deformation

'as"c Eart( !tructure as "t relates to structural Geology

Strength profile of the lithosphere! ifferent

portions of the lithosphere as defined by

deformation style! important transitions

Controls on s(ape o) !trengt( #ro)"le:

Temperature

Strain Rate

Composition of Material

Understand how changing these factors changes the

shape of the Strength Profile

Un&erstan& (o* to &o +eloc"ty tr"angles )or plate mot"ons%


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!TRAIN

!tra"n: The change in size and shape e(perienced by a body during deformation

#lane !tra"n: )#imensional deformation $ith no chance in area %or volume&

,omogeneous De)ormat"on: Changes to the size and shape for each small part of a body are

geometrically similar to those for the entire body

• Straight lines in a body before deformation are straight after deformation

• Parallel lines in a body before deformation are parallel after deformation

• *ines may be rotated but the statements above $ill hold true.

L"near !tra"n: Changes in line length

l 0: +nitial length l f : 'inal *ength

!tretc(: ! - l f .l 0

E/tens"on: e - 0l f 1 l 02. l 0 e: ,(tension Be able to calculate both

Angular !tra"n: Change in angle bet$een t$o initially perpendicular lines

ψ : Shear -ngle es: Shear strain

γ - tanψ %engineering shear strain&

es - %4 tanψ %tensor shear strain&

!tra"n Ell"pse: The ellipse that results from the homogeneous deformation of a circle

Principle Strain -(es !5: *ine of ma(imum stretch

!3: *ine of minimum stretch

#lane !tra"n 06D2: S/S0! S)1 No change in volume.

Un"a/"al !tra"n: Compression: S1S)1! 23S03 ,(tension: S/! S)1S01

Tr"a/"al !tra"n: 'lattening: S4S)/! 23S03 Constriction: S/! /S)4S0/2


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T$o end members of Plane Strain:

#ure !(ear:

• Principle stretching a(es do not rotate during deformation

• Particle Paths are symmetric about the principle a(es

Also referred to as coaxial deformation

!"mple !(ear:

• Principle stretching a(es rotate during deformation

• Particle Paths are symmetric about the principle a(es

A type of non-coaxial deformation

!u7s"mple or General !(ear:

• Component of both pure and simple shear

• -lso a non#coa(ial deformation

Instantaneous !tra"n $s% 8"n"te !tra"n

+nstantaneous Strain: - tiny increment or snapshot of the strain

'inite Strain: The finial result of the deformation

Instantaneous !tra"n Ell"pse: The ellipse that forms from a circle over a tiny increment

Instantaneous stra"n a/es: ζ5 ζ6 ζ3

!tra"n #at(: strain states that through $hich a body passes during progressive deformation

!tate o) !tra"n: The deformation a body has undergone

#rogress"$e !tra"n: The non#rigid motion of a body that carries the body from its initial

undeformed state to its final deformed state.


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#ROGRE!!I+E !TRAIN

#ure !(ear

'inite principle strain a(es same orientation

as instantaneous principle strain a(es

Coa/"al &e)ormat"on

-ll material lines rotate e(cept those parallel

to pr"nc"ple stra"n a/es

*ines rotate in ad5acent 6uadrants in

opposite directions

No Net Rotat"on γ -

!"mple !(ear

'inite principle strain a(es rotate $ith

respect to instantaneous principle strain a(es

Non1coa/"al &e)ormat"on

-ll material lines rotate e(cept those parallel

to the s(ear plane

All lines rotate in the same direction

Net Rotat"on γ 9


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Pure Shear: Simple Shear:

These sho$ the orthorhombic and monoclinic symmetry of pure and simple shear respectively

+ORTICITY: the degree of net rotation $ithin a strained ob5ect %7k &

#ure !(ear: 8o net rotation of lines ; -

!"mple !(ear: -ll lines rotate same direction ; - 5

!u7s"mple !(ear: Some net rotation of lines 5 < ; <

!TRAIN RATE: The rate at $hich a rock is deformed ε 1 e(tension9time 1 e9t

enerally ;2#)9s to 2#


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!TRE!!

8orce: That $hich changes" or tends to change" body motion! a push or a pull.

'orce is a vector: it has a magnitude and a direction

'o&y 8orces: -ct on every point $ithin a body %e.g. gravity&

!ur)ace 8orces: -ct on a specific surface in or on a body %e.g. a fault plane&

!TRE!!: The intensity of the force acting on a body

!tress can 7e 7ro;en &o*n "nto t*o components 0"n 61D= or t(ree components "n 31D2

Normal !tress 0σn2: The stress perpendicular to a plane

!(ear !tress 0σs2: The stress parallel to a plane

!"gn con$ent"ons:

Normal !tress: positive %=>?& 1 compressive

negative %=#?& 1 tensile

!(ear !tress: positive %=>?& 1 counterclock$ise

negative %=#?& 1 clock$ise

!tress trans)ormat"on e>uat"ons:

σn - σ cos6θ

σs - 0σ s"n 6θ2.6

#r"nc"ple !tress A/es

I) σ5 9 σ3 *e get t(e !tress Ell"pse

σ5: a/"s o) greatest pr"nc"pal stress

σ3: a/"s o) least pr"nc"pal stress

σ and σ0 are al$ays perpendicular and always

perpendicular to planes of no shear stress

T(e Mo(r C"rcle: - complete representation of the

stress at a point: ,ach point on the circle represents

the surface stress %both normal and shear& on a planeat a different orientation

Relat"ons "n t(e Mo(r C"rcle

D"))erent"al !tress 0σ&")) 2: σdiff = σ#σ0

diameter of Mohr circle


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Mean !tress 0σmean2: σmean = (σ>σ0&9) center of Mohr circle

De$"ator"c !tress 0σ&e$2: σdev = (σ#σ0&9) radius of Mohr circle

also maximum value of shear stress

σn - σmean ? σ&e$ cos06θ2

σs - σ&e$ s"n06θ2

Remember" for any plane σs @σdev and σ4σn4σ0

#oor )lu"& pressure results in the E))ect"$e stress

e))ect"$e stress 1 confining pressure A fluid pressure

Moves the Mohr circle to the left $ith no distortion

An&ersons T(eory o) 8ault"ng: Relation of principle stresses and ideal fault geometry.

The ,arthBs surface is a free surface %contact bet$een rock and atmosphere&" and cannot be

sub5ect to shear stress. -s the principal stress directions are directions of zero shear stress" theymust be parallel %) of them& and perpendicular % of them& to the ,arthBs surface.

Combined with an angle of failure of 30° from 1 , this gives:


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8ormal 'aults Thrust 'aults Strike#slip faults

E))ect"$e !tress: ,ffective Stress 1 Confining or -pplied Stress A 'luid Pressure


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R,EOLOGY

R(eology: The mechanical behavior of rocks

Three basic models of rheology:

ELA!TIC: Strain linearly proportional to Stress. -ll strain

recovered after stress removed.

,oo;es La*: σ - Ee e: e(tension %strain&

E 0Young@s Mo&ulus2: a measure of material stiffness

• -s differential stress is applied" strain is instantaneous.

• Strain is proportional to differential stress.

• eformation %strain& is recovered instantly once stress is

removed

#o"sson@s Rat"o 0ν2: degree to $hich a material bulges as it

shortens ν 1 elat9elong

+I!COU!: Strain rate %ε& linearly proportional to differential stress.

escribes deformation of a fluid.

σn 1 ηε or σs 1 ηγ

η 1 viscosity

• -s differential stress is applied" strain is instantaneous.

• Strain rate is proportional to differential stress.

eformation %strain& is non#recoverable

#LA!TIC: Material $ill not deform until yield stress is met or

e(ceeded.

σs @ K

Y"el& stress 0 K 2: The differential stress at $hich the rock is no longer behaving in anelastic fashion.

• Material $ill not deform until yield stress reached.

• Strain rate is impossible to determine.

• eformation %strain& is non#recoverable

Detter escription of Plastic eformation is Power aw

#OER LA: Strain rate is proportional to the stress raised to

some po$er %n&

ε = -σne(p[#E9RTF or more simply ε 1 C%σ&n


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Ot(er ey R(eolog"cal 'e(a$"ors:

• Confining Pressure increases strength

• Temperature decreases strength

• Strain Rate increases strength

!tra"n ,ar&en"ng an& !tra"n !o)ten"ng

!tra"n ,ar&en"ng: -s strain accumulates"more stress is re6uired to maintain strain

rate! t(e mater"al gets (ar&er to &e)orm!tra"n !o)ten"ng: -s strain accumulates"

less stress is re6uired to maintain strainrate! t(e mater"al gets eas"er to &e)orm


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8RACTURE!

8racture A surface along $hich rocks or minerals have lost cohesion %broken&

Granular 8lo*: eformation accommodated by rotation and frictional sliding bet$een

individual mineral grains $ithout any fracturing.

Cataclast"c 8lo*: eformation accommodated by fracturing and crushing of grains" in addition

to rotation and frictional sliding along grain contacts.

TY#E! O8 8RACTURE!

Mo&e I 0e/tens"on )racture2: relative motion of $alls of fracture is perpendicular to the fracture

$alls.

!(ear 8ractures:

Mo&e II: Relative motion of $alls of fracture is parallel to the propagation direction

Mo&e III: Relative motion of $alls of fracture is perpendicular to the propagation direction

Contract"onal 8racturesB:

Mo&e I+

o"nt: -n individual e(tension fracture $ith very little displacement normal to the fracture

surface.

De)ormat"on 'an&: Thin %mm& zone of strain localization formed by grain reorganization

and9or grain crushing. Can be zones of s(ear" compact"on" or &"lat"on.

+mportant for fluid flo$ near faults.

Coulom7 8a"lure La*: Stress re6uired to form a shear fracture in a rock. Straight lineappro(imation of the shear fracture envelope

σs =C? tanφ σn


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σsG: critical shear stress

C: cohesive strength

tanφ: coefficient of internal friction

'yerlee 8a"lure La*: Stress re6uired to get slip along a pre#e(isting fracture in a rock.

σc = tanφ∗σn

tanφ: coefficient of sliding friction

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2016 Test 1 Structural Review Material