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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