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STRUCTURAL GEOLOGY
Lecture 1: Course introduction
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Structural DeformationRocks deform when stresses placed upon them exceed the
rock strength
• brittle deformation (e.g. fractures)
• ductile deformation (e.g. folding)
Kink folding, Front Ranges, Canadian Rockies, Alberta
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Driving Forces
• Plate tectonics - plate convergence and ridge
spreading
• Deep burial of sediments• Forceful intrusion of magmas into the crust
• Meteorite impacts
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Evidence of Crustal Deformation
• Folding of strata
• Faulting
• Tilting of strata
• Joints and fractures
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Evidence of Crustal Deformation:
• Folding of rock strata
• Faulting
• Tilting of strata• Joints and fractures
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Evidence of Crustal Deformation:
• Folding of rock strata
• Faulting
• Tilting of strata• Joints and fractures
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Evidence of Crustal Deformation:
• Folding of rock strata
• Faulting
• Tilting of strata• Joints and fractures
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Analysis of Geologic Structures
Structural analysis generally involves three tasks:
Descriptive Analysis : physical and geometrical
description of rock structures (e.g. folds, faults etc)
Kinematic Analysis: evaluation of the displacement,
and change in shape, orientation and size that rocks
undergo as a result of deformation
Dynamic Analysis : reconstruct forces and stresses
which result in rock deformation and failure
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Scales of Structural Analysis
Microscopic - deformation structures occurring at
level of individual mineral grains
Mesoscopic - structures at hand-specimen to outcrop
scales (fractures, small faults, folds)
Megascopic - deformation affecting entire regions
(e.g. fold and thrust belts)
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STRUCTURAL GEOL
Lecture 2: Review of Fundamental Geol
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Lecture 2: Topics
• Geologic bed contacts• Primary sedimentary structures
• Primary igneous structures
• Secondary structures
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Fundamental Structu
Three fundamental types of geologic stru
• bed contacts
• primary structures - produced durin
or emplacement of rock body
• secondary structures - produced by dand other process after rock is emplac
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Bed Contacts
Boundaries which separate one rock unit f
• two types:
1. Normal conformable contacts
2. Unconformable contacts (‘unconformit
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Conformable Bed ConHorizontal contact between rock units w
deposition or erosional gaps
• no significant gaps in geologic time
Book Cliffs, central Utah
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Unconformable Conta
Erosion surfaces representing a significan
deposition (and geologic time)
• angular unconformity
• disconformity• non-conformity
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Angular Unconformity
Bedding contact which discordantly cuts a
strata
• discordance means strata are at an ang
• commonly contact is erosion surface
Old Red Sandstone, Scotland
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Formation of an Angular Unc
A. Sediments deposited B. Sequen
surface
C. Marine transgression D. Subside
deposition
sequence
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Erosional gap between rock units withou
discordance
• example: fluvial channel cutting into
sequence of horizontally bedded dep
Fluvial sandstones, Utah
Disconformity
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Sedimentary strata overlying igneous or m
rocks across a sharp contact
• example: Precambrian-Paleozoic contarepresents a erosional hiatus of about 500 m
Grand Canyon, USA
Nonconformity
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Structural Relations
The structural relations between bed contac
in determining:
1. presence of tectonic deformation/uplift
2. relative ages of rock units
• principle of original horizontality
• principle of cross-cutting
• principle of inclusion
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Principle of Original Horiz
Sedimentary rocks are deposited as essent
layers• exception is cross-bedding (e.g. delta fo
• dipping sedimentary strata implies tecto
tilting or folding of strata
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Principle of Cross-cutti
Igneous intrusions and faults are younge
rocks that they cross-cut
Mafic dike cutting across older sands
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Cross-cutting Relatio
Often several cross-cutting relationships a
• how many events in this outcrop?
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Principle of Inclusion
Fragments of a rock included within a ho
always older than the host
Granite inclusions in basalt
1
2
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Fundamental Structu
Three fundamental types of structures
• bed contacts
• primary structures
• secondary structures
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Structures acquired during deposition of s
rock unit
Stratification - horizontal bedding is mostructure in sedimentary rocks
Primary Sedimentary Str
Laminated mudstone
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Primary Sedimentary St
Cross-bedding - inclined stratification r
migration of sand ripples or dunes
Large-scale aeolian cross-beds, Uta
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Primary Sedimentary St
Ripples - undulating bedforms produced
unidirectional or oscillating (wave) curren
Symmetrical wave ripples
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Primary Sedimentary StrGraded bedding - progressive decrease i
upward in bed
• indicator of upwards direction in deposit
• common feature of turbidites
Coarse-grained turbidite
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Primary Sedimentary Stru
Mud cracks - cracks produced by dess
clays/silts during subaerial exposure
Mud-cracks on tidal flat
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Primary Sedimentary Str
Sole marks on base of sandstone b
Sole marks - erosional grooves and marks
scouring of bed by unidirectional flows
• good indicators of current flow direction
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Primary Sedimentary Str
Fossils – preserved remains of organisms,
• good strain indicators• determine strain from change in shape of
• relative change in length of lines/angle b
Uniaxial com
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Primary Igneous StrucPillow lavas - record extrusion and quenc
sea floor
• convex upper surface indicates way up
Pillows fo
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Flow stratification - layering in volcanic
produced by emplacement of successive la• stratification of ash (tephra) layers
Stratified pyroclastic flow Sequence of b
Primary Igneous Struc
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Importance of Primary Stru
1. Paleocurrents - determine paleoflow
2. Origin – mode of deposition, environm
3. Way-up - useful indicators of youngi
stratigraphic sequence
4. Dating - allow relative ages of rocks t
determined based on position, cross-c
relations and inclusions
5. Strain indicators - deformation of prstructures allows estimates of rock str
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Secondary structures - deformation struc
produced by tectonic forces and other str
Principle types:
• fractures/joints
• faults/shear zones• folds
• cleavage/foliation/lineation
Secondary structures are of primary interin structural geology
Secondary Structur
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Fractures and JointFractures – surfaces along which rocks ha
lost cohesion
Joints - fractures with little or no displacefailure surface
• indicate brittle deformation of rock
Joints in Sandstone, Arches National P
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FaultsFaults - fracture surfaces with appreciabl
of strata
• single fault plane
• fault zone - set of associated shear frac
• shear zone - zone of ductile shearing
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Shear Zones
Shear zone - zone of deformed rocks that a
strained than surrounding rocks
• common in mid- to lower levels of crust
• shear deformation can be brittle or ductil
ductile shear zone
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Fault TerminologyHanging wall block - fault block toward wh
dips
Footwall block - fault block on underside o
Fault plane – fault surface
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Fault Slip
Slip is the fault displacement described by
• direction of slip
• sense of slip
• magnitude of slip 030/00
Slip
sense
Slip d
Slip
magnitude
Displaced
marker
Left-handed s
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Fault Types
Dip-slip faults - slip is parallel to the fau
normal fault - footwall block dispaced ureverse (thrust) fault - footwall block di
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Fault TypesStrike-slip – fault slip is horizontal, parall
the fault plane
• right-handed (dextral)
• left-handed (sinistral)
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Fault TypesOblique slip – Combination of dip- and str
• dextral-normal
• dextral-reverse
• sinistral-normal
• sinistral-reverse
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Faults
What type of faults are shown here?
Normal faults
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Folds
Folds – warping of strata produced by co
deformation
• range in scale from microscopic featuregional-scale domes and basins
• indicators of compression and shorte
Plunging AntRecumbent fold in sandstones
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Fold Terminology
Hinge (Axial) plane - imaginary plane bi
Hinge line - trace of axial plane on fold cr
Plunge - angle of dip of hinge line
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Fold TerminologyAnticline - convex in direction of younges
Syncline - convex in direction of oldest be
Antiform - convex upward fold (stratigrap
Synform - concave upward fold
OLDER
ANTICLINE
YOUNGER YOUN
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Fold Terminology
Synformal Anticline - overturned anticlin
Antiformal Syncline - overturned synclin
YOUNGEST
A
SYNFO
O YOUNGEST
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Fold Terminology
Monocline - step-like bend in strata
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Foliation and Cleavag
Foliation - parallel alignment of planar fa
within a rock
Cleavage - tendency of rock to break alon
cleavage is a type of foliation
• resemble fractures but are not physical
Gniessic foliation Cleava
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STRUCTURAL GEOL
Lecture 3: Geometric analysis of geolog
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Structural AnalysiAnalysis of geologic structures involves th
steps:
1. Descriptive or geometric analysis - q
describe geometry of structures
2. Kinematic analysis - determine move
changes in shape or strain
3. Dynamic analysis - determine directio
magnitude of forces and stresses
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Geometrical Analysis: ‘GeMeasurement of the 3-dimensional orientat
geometry of geologic structures
• simplify geometry by decomposing struc
and planes (or other geometric elements)
Picasso: Girl
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Analysis of Complex StrAnalysis and modeling of complex structu
using sophisticated software
• model complex curviplanar surface, volu
• display as fence diagrams, geocellular 3
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Linear Geologic Structu
Lineation - any linear feature observed in
surface or imaginary line used in a geomete.g. a fold axis.
Lineation in gneiss Fold axial trace
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Orientation of Linear Stru
Orientation of lines specified with trend a
Trend - direction measured in degrees c
north (through 360º); also known as azimu
Plunge - angle of inclination of line (0 - 9
N
W
Trend 200 °
N
S
EW
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Examples of Linear Struc
Glacial striations on bedrock
Primary structures - flute casts, grooves, g
Secondary structures - slickenlines and gr
lineations
Sol
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Examples of Linear Struc
Secondary structures - slickenlines and gr
lineations• intersection lineations
Grooves on exposed fault plane Sl
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Orientation of Linear Str
Many linear structures are developed on p
surfaces such as bedding planes• orientation measured using the pitch ang
• angle from horizontal measured within
• a.k.a. ‘rake’ angle
Striationson fault
plane
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Planar Geologic Struc
Examples of planar geologic structures:
• bedding planes and contacts
• foliation
• joint surfaces• fault planes
• fold limbs
• fold axial planes (imaginary surface)
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Examples of Planar Struc
Bedding planes - most common planar geo
• primary depositional structure
• erosion surface
Inclined bedding plane
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Examples of Planar Struc
Foliation - cleavage planes produced by m
sedimentary rocks
• common structure in slates and phyllites
Foliated phyllite, Cascade Mountains, B
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Examples of Planar Struc
Joint planes - planar fracture surfaces cau
brittle failure rock
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Examples of Planar Stru
Fold axial plane - imaginary plane bisectin
fold
Recumbent fold, Port au Port Peninsula, N
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Orientation of Planar Stru
The attitude of a plane can be established
lines contained in the plane, provided they
Horizontal
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For convenience, two lines in a plane are
which are a horizontal line and line of stinclination
Orientation of Planar Str
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Strike - line formed by intersection of im
horizontal plane with inclined surface (0 -
Dip - inclination of the plane measured p
the strike line (0 - 90º)
Strike and Dip
D i p a
n g l e
S t r i k e
270
h o r i z o
n t a l
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Apparent dip - dip measured along line o
to strike• apparent dip will always be less than true
Orientation of Planar Stru
S t r i k e
270
h o r i z o
n t a l
Apparent dip
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Measurement of Orienta
Strike and trend are measured with a comp
Dip and plunge are measured using an inc
Brunton compass Inclinom
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Measurement of Strike DStrike is measured by placing the compass
with the outcrop face
• apply the right-hand rule to record strike
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Measurement of Dip A
Dip angle measured by placing the long ax
compass parallel with the dip direction
• dip read off the inclinometer
Inc
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Recording of StructureField data are recorded in a notebook and t
base map
• overlay mylar transparency on air photo
• record measurements on mylar using sym
numbers which reference notebook entri
sandstone
shale
limestone
22
34
18
25
20
s y n c l i n
e
05/044
12/090
N
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Structure Symbols
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STRUCTURAL GEOL
Lecture 4: Geometric Analysis II
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Lecture 4: Topics
• geologic maps
• structure contour and structure maps
• three-point problems, cross-sections
• stereonets
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Representation of Geologic S
Structural orientation data are displayed an
using various types of graphical aids• geologic maps
• structure maps
• cross-sections
• stereonets
• rose diagrams
• histograms
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Geologic MapsShows surface distribution of rock types an
• structures portrayed using symbols (strik
beds, fold axes, faults etc.)
• ‘read’ and interpret map to infer subsurfa
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Outcrop PatternsOutcrop patterns controlled by attitude (str
of beds and topographic relief
• predictable for inclined beds
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Rule of V’sOutcrop pattern of inclined bedding is predi
• beds dipping downstream V-downstream
• beds dipping upstream V-upstream
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Rule of V’s
Outcrop of vertical bed will always parallel
strike, regardless of terrain• e.g. vertical dike intruded into older strat
• vertical structures usually easy to spot on
imagery, air photos
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Rule of V’s
Inclined bedding dipping at same gradient
Parallel stream valley contours
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Outcrop Patterns
Which direction are beds dipping relative t
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Outcrop Patterns
Which direction are beds dipping relative t
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Block Models/DiagramRelations between outcrop pattern and su
are visualized using block models or di
• construct cross-sections along map edg
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Bryce 3-DBlock models now constructed using 3-D m
sofware
• slice and dice stratigraphy interactively
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Structure Contour MaMap showing the relief on a geologic surfac
• e.g. top or bottom of bedding plane, fault
• constructed from borehole data
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Structure Contour MaStructure contour lines are lines of equal e
• show elevation relative to horizontal dat
• values are often negative since subsurfa
commonly below sea level
Folded surface
(antiform)
Projection
of map
plane
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Datum SurfaceDatum is a horizontal reference surface (e.
• commonly use subsurface datum - usual
stratigraphic surface with low relief (e.g
• elevation given in metres relative to datu
“metres below datum surface” m b.d.s.)
BH-1 BH-2
Unit B - Shale
Unit A
Unit C
Datum = 0 m
Depth
100 m
BH-3
Elevation =
- 100 m b.d.s.
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Constructing Structure CoStructure contours can also be defined by f
equal elevation along a bed contact
• find intersections of contact with topo c
• draw structure contours through points o
100
90
80
8
9
Unit A
Unit B
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Planar SurfacesFor uniformly dipping plane, the structure
parallel lines
• contours equally spaced for surface of c
45
INCLINED BED WITH
CONSTANT DIP ANGLE STRU
- 10 m
- 20
- 30
- 40
- 50
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Curvi-planar SurfacesContours lines are curvilinear with variable
• e.g. folded surface, erosion surface with
• dip direction and magnitude changes acr
FOLDAXES
COMPLEXLY FOLDED
DIPPING SURFACESTRUCTURE
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Rules of Contouring
The general ‘rules’ of contouring also apply
maps:
1) contours cannot cross or bi-furcate
2) contours cannot end in the middle of the
a fault or other discontinuity
3) same contour interval must be used acroselevations must be labelled
4) elevation is specified relative to datum (e
sea level)
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Determining Dip Dip direction and angle can be determined
contour map
• measure horizontal separation X, find di
• tan = Z/X, = tan-1 (Z/X)
• e.g. = tan-1 (10 m/100 m), = 6º
100 m
Distance between
structure contours
STRUCTURE CONTOUR MAP
6º
- 20
- 30
- 40
- 50
- 10
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Three-point Problem1. Find minimum and maximum values
2. Draw line between max, min elevations
into equal distance intervals
3. Connect points of equal elevation to defi
contour
40
502030
40
4 0
5 0
3 0
2 0
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Isochore MapMap showing change in thickness of strati
• constructed from borehole data
• does not take into account dips of surfa
apparent thickness
BH-1
BH-2
Apparent
thickness
Unit A
Unit B
Unit C
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Zero ThicknessAreas where stratigraphic unit is absent (ero
deposited) are bounded by a zero contour
• zero contour useful in defining edges of ge.g. oil-bearing sandstones
0
0
0
20 30
40
20
30
33
34
N
0 500
metres
0
11
8
25 0
0
1231
45
722
25
0
0
0
0
00
0
0
0
0
0 10
0
146
20
0
0
2125
8
0
4
48
36
32
6
15
38 5
14
7
0
10
0
0
ISOPACH OF FURNACE CREEK UPPER SAND (THICKNESS IN METRES)
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Isopach MapMap showing thickness of unit taken perpe
• sometimes difficult to estimate true thic
there is lots of relief on bounding surface
• calculate using trig
αααα
BH-1
BH-2
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Structure Cross-sectioCross-section is a 2-D ‘slice’ through stratig
• Construct by projecting elevations of stru
onto profile
• Procedure called and “orthographic proje
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STRUCTURAL GEOLOGY
Lecture 5: Introduction to Stereonets
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Lecture 5: Topics
• Stereonet basics
• plotting lines and planes
• Some example problem and solutions
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The Stereonet
Lower hemisphere of a sphere projected onto a flat surface
• a type of ‘3-dimensional protractor’
• allows analysis of structural data in 3-dimensions• plot data on tracing paper overlaid on net
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Elements of a Stereonet
Great Circles - large circular arcs running north-south
• equivalent to lines of longitude on globe
Small Circles - circular arcs running from east to west
• equivalent to lines of latitude on globe
N
180
90270W
E
SSchmidt Net
Small
circle
Great
circle
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Elements of a StereonetPrimitive - the perimeter of the stereonet
• divided into 360 degrees at 2 ° increments
• perimeter indicates compass directions
N
180°
90°270°
WE
SSchmidt Net
0°Primitive
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Types of Stereonets
Two types of stereonets used geology:
1. Schmidt net
2. Wulff net
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N
180°
90°270°
WE
SSchmidt Net
0°
Schmidt (Equal Area) NetEach 2 degree polygon has an equal area
• used in structural geology because it preserves areal
proportions (important for analysis of distributions)
2° x 2° polygon
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Wulff (Equal Angle) Net
Great and small circles are real circular arcs
• preserves angular proportions but not area
• used in crystallography, not much in structural
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Plotting Lines - Trend and Plunge
Line projected onto lower hemisphere of net will appear
as as single point on net
• e.g line plunging at 50° in the direction 130° (50/130)
50°
130°
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Right-hand RuleWe will use the right-hand rule convention for all structural
measurements
• right-hand thumb points in direction of strike• fingers point in direction of dip
Bedding plane striking N-S and dipping
eastward at 45N
S
45
Measurement recorded
as 000/45
Strike direction
Dip direction
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Example
Plot the following lines on the stereonet:
50º - 270º
20º - 060º45º - 320º
N
180°
90°270°
WE
SSchmidt Net
0°
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Plotting PlanesThe intersection of a plane with the lower hemisphere of a
sphere is a great circle
• e.g. bedding plane striking 030º and dipping 60º SE
030°
60°
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ExamplePlot the following planes (use the right-hand rule):
000º - 30º E
060º - 60º SE130º - 20º SW
270º - 90º N
N
180°
90°270°
WE
SSchmidt Net
0°
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Plotting Poles to PlanesIn order to analyze relationships between planar surfaces
it is often more convenient to plot the pole to the plane
• pole is projection of a line drawn normal to the surface
of a plane
• e.g. pole to plane oriented 000º /30º
N
000°
30°
30°Pole to
plane
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Example: Plotting Poles to Planes
Plot the pole to the following plane: 040/30
N
180°
90°270°
W E
SSchmidt Net
0°
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Step 1:
1. Mark off strike direction 040º on primitive
N
180°
90°270°
W E
SSchmidt Net
0°
040°
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2. Rotate strike to north and draw great circle with dip of
30ºN
180°
90°270°
W E
SSchmidt Net
0° 040/30
Step 2:
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3. Count in 90 degrees along E-W towards centre of net
and mark location of pole
N
180°
90°270°
W E
SSchmidt Net
0° 040/30
Step 3:
90º
Pole to A
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Applications in Structural Geology
Stereonets are used to solve the following types of
problems:
1) rotations - restore dip of bed to pre-deformationattitude
2) find intersections of planes
3) plot geometry of folds
4) find displacements along faults
5) examine trends in lines and planes - e.g. presence of preferred orientations
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Rotational ProblemsOften we need to ‘undo’ the rotation and inclination of
strata cause by deformation and tectonism:
• find former attitude of beds or structures
• determine paleocurrent directions
• determine structural events where multiple phases of
deformation have taken place
• unfold folded layers
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Rotational Axes
Can perform rotations on three types of rotational axes:
HORIZONTALAXIS OF ROTATION
VERTICALAXIS OF ROTATION
INCLINEDAXIS OF ROTATION
N
180°
90°270°
W E
SSchmidt Net
0°
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Example: Restoring Dipping Beds
Rock sequence with angular unconformity
• determine the attitude of Group A prior to deposition of
Group B
• Group A (145/26), Group B (020/30)
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Step 1:
1. Visualize the problem first, then plot planes A
(145/26), B (020/30) and their polesN
180°
90°270°
W E
S
0°
Pole to B
B 020/30
A 145/26
Pole to A
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Step 2:
2. Rotate Group B to North and rotate both poles 30º to
the east
N
180°
90°270°
W E
S
0°
Pole to B
B 020/30
A 145/26
Pole to A
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Step 3:3. Rotate pole to A to W-E axis and fit a new plane to pole
• record dip of new plane (45º)
N
180°
90°270°
W E
S
0° B 020/30
A 145/26
90º45º
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Step 4:4. Rotate N back to top and find strike of restored Group A
• strike and dip of restored Group A is 156/45
N
180°
90°270°
W E
S
0° B 020/30
A 156/45
Restored
Pole to A
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Restoring Dipping Beds
Group A (145/26), Group B (020/30)
1. Plot bedding planes as great circles
2. Plot poles to planes
3. Rotate strike of upper bed to N-S axis
4. Rotate Group B to 30 horizontal along with its pole
5. Rotate Group A pole same amount along small circle
6. Plot planes to the poles
7. Find new strike and dip of restored Group A
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Intersection of Two PlanesIntersection of any two planes will produce a line in space
(provided they are not parallel)
• e.g. dike cross-cutting dipping strata
Line of intersection
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Example: Intersection ProblemA gold-bearing zone is discovered at the altered contact
between a marble bed (340/60) and dike (040/40)
• in what direction (inclination) should the mine shaft be
constructed to exploit the mineralized zone?
40
60
M A R B L E B E D
D I K E
URANIUM
ORE
N
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Step 1:1. Visualize the problem, then plot the planes for the
marble bed and dike and find their intersection point
N
180°
90°270°
W E
S
0°
DIKE
040/40
BED 340/60
INTERSECTION
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Step 2:
2. Now find the trend and plunge of the line of
intersection (rotate point onto W-E to find plunge)
N
180°
90°270°
W E
SSchmidt Net
0°
DIKE
040/40
BED 340/60
INTERSECTION
130/48
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Step 3:
Visualize your result and check that it makes sense.
• mine shaft must be constructed in the direction 130º SE at
an angle of 30º to exploit the ore body
40
60
M A R B L E B E D
D I K E
PROJECTION OF
MINE SHAFT
N
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Analysis of FoldsFolded strata can also be represented on a stereonet
• plot limbs as dipping planes
• plot trend and plunge of fold axis
• find orientation fold axial plane
N
180°
90°270°W E
S
0°
SE LIMB
045/65
NW LIMB
018/65
FOLD AXIS
38/032
FOLD LIMB
FOLD AXIAL PLANE
F O L D
A X I S
PLUNGE
TREND
HORIZONTAL
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π - DiagramsGeometry of fold analyzed by plotting poles (π -poles) to
fold limbs
• determine relative tightness of folding and fold
symmetry
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GEO3Z03
STRUCTURAL GEOLOGY
Lecture 6: Force and Stress in the Subsurface
Z
X
Y
Jzx
Fxx
Fzz
Fyy
Jzy
Jyz
Jyx
Jxz
Jxy
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Lecture Topics:
• Force
• Stress• Stress components
• Computing shear and normal stresses
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Basic DefinitionsStress - intensity of forces acting on rock body
Strain - change in size or shape of a rock
• body resulting from applied forces
• dilation = change in volume
• distortion = change in shape
DILATION
DISTORTION
DILATION AND
DISTORTION
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Force: Newton’s First Law
Force - ‘push or pull’ required to change the state of rest or
state of motion of a body
• object at rest is state of ‘static equilibrium’
• all forces are balanced
F1
F'1
F'2F2
F3
F'3
F1 + F2 + F3 = F'1 + F'2 + F'3
GF = 0
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Force: Newton’s Second Law
The acceleration of an object is directly proportional to
the net force applied to it and inversely proportional to
the objects mass
• Force = mass x acceleration: F = m·a
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Mass
Mass is the volume density of a body or amount of
material it contains per unit volume
M = D V
D = density (kgm-3)
V = volume (m3)
Weight - the force produced by gravitational
acceleration acting on a given mass
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Units of ForceDimensions of force:
F = ma = M C L/T2
F: [MLT-2]
Basic unit of force is the Newton (N):
force required to impart acceleration of 1 ms-2 to a body of
1 kilogram mass
1 N = 1 kgms-2 (SI units)
1 dyne = 1 gcms-2 (cgs units)
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Force as a Load
Force is also frequently described in terms of a load or
the contact force generated by a mass
• load is expressed as weight
e.g. person weighing 80 kg imparts a load of
80 kgms-2 or 80 N on the Earth
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Force Vectors
Force is a vector quantity having both magnitude and
direction
• obeys laws of vector addition/subtraction
M A G N I T
U D E
DIRECTION
F
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Vector Addition/Subtraction
F1 F2
10 N40 N
NET FORCE = F1 - F2 = 30 N
R30 N
Resultant vector can be found by adding and subtracting
vector quantities
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Parallelogram RuleResultant of any two vectors can be found by drawing
vectors tail to tail and finding diagonal
PF1
F2
FR is resultant vector of forces acting on point P
F2
F1
FR
P
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Vector Addition in 3-D
Any force vector FR can be resolved into 3 principal
components acting at right angles in a Cartesian co-
ordinate system
Z
X
Y
FRFx
Fy
Fz
FR = Fx + Fy + Fz
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Types of ForcesBody Forces - forces which act on the entire mass of a
body, independent of forces created by surrounding
materials
• gravitational acceleration
• magnetic fields
Surface Forces - forces produced by action of one
body on another across surfaces of contact
• tectonic forces transmitted across a fault plane
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Stress
Stress is the concentration of force per unit area:
F = FA
• stress is ‘intensity’ of the applied force
• also known as ‘traction’
• also a vector quantity
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Units of StressStress in Earth Science is usually measured in pascals:
• 1 pascal (Pa) = force of one Newton acting on an area
of one m2
• 1 Pa = 1 Nm-2 = 1 kgms-2m-2 = 1 kgs-2m-2
1 m2
F = 1 N
1 Pa = 1 N / m2
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Units of Stress
1 kilopascal (kPa) = 1000 Pa (10
3
Pa)
1 megapascal (MPa) = 106 Pa
1 gigapascal (GPa) = 109 Pa
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Stress Components
Stress acting on any surface (arbitrarily oriented plane)
can be resolved into two components:
normal stress, σ n (sigma) - stress acting normal to plane
shear stress, J (tau) - stress acting tangential to plane
J
Fn
F
J = 0
Fn
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Stress in 3-Dimensions Normal and shear tresses acting on a point can bedescribed using a 3-dimensional Cartesian coordinatesystem:
• σ xx - normal stress in x direction
• Jxy - shear stress in face normal to x acting in direction
of y axisZ
X
Y
Jzx
Fxx
Fzz
Fyy
Jzy
Jyz
Jyx
Jxz
Jxy
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Stress TensorStress Tensor - nine stress components required to
completely describe the stresses acting on a point in a body
Z
X
Y
Jzx
Fxx
Fzz
Fyy
Jzy
Jyz
Jyx
Jxz
Jxy
Jzx
Fxx
Fzz
Fyy
Jzy
JyzJyx
JxzJxyFace Normal to X:
Face Normal to Y:
Face Normal to Z:
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Stress Sign Conventions
Fn
Fn
COMPRESSIVE STRESS - POSITIVE
Fn
Fn
TENSILE STRESS - NEGATIVE
By convention compressive stress is positive and tensile
stress is negative
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Stress Sign Conventions
J
J
COUNTERCLOCKWISE SHEAR
STRESS - POSITIVE
J
CLOCKWISE SHEAR
STRESS - NEGATIVE
J
Sign of shear stresses indicated by ‘sense’ of motion
• clockwise or ‘right-handed’ shear is negative
• counterclockwise or ‘left-handed’ shear positive
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Stress Ellipsoid
The total stress field acting on stresses acting on a point
can be represented by the stress ellipsoid
F1 - greatest principal stress
F2 - intermediate principal stress direction
F3 - least principal stress
σ1
σ2
σ3
Ellipsoid
triaxial stress is general
case where σ 1 > σ 2 > σ 3
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Lithostatic Stress Problem
Calculate the normal stress placed on the crust by a granite
cube 1000 m on a side with a density of 2700 kgm-3
Density = 2700 kgm-3
1000 m
Lithostatic
stress?
1000 m
1000 m
GRANITE
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Mass of granite cube
= D x V
= 2700 kgm-3 x (1000 m)3
= 2.7 x 1012 kg
Lithostatic Stress Problem
Force at base of cube
= m x a
= 2700 kgm-3 x (1000 m)3 x 9.8 ms-2
= 2.65 x 1013 kg ms-2
= 2.65 x 1013 N
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Stress at base of cube:
σ = F / A
= 2700 kgm-3 x (1000 m)3 x 9.8 ms-2 / (1000 m x 1000 m)
= 2700 kgm-3 x 1000 m x 9.8 ms-2
= 2.65 x 107 Pa
= 26.5 MPa
Answer
The granite block exerts a force of 26.5 MPa
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The stress we have calculated is called the lithostatic stress
• the vertical stress produced by column of overlying rock
• in upper crust gradient is about 26.5 MPa/km
• mantle gradient is approx 35 MPa/km• geothermal gradient approx 30 °C per 1 km
Lithostatic Stress Gradient
1 kbar = 108 Pa
10 kbar = 1 GPa
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Note that we can also write the lithostatic stress in terms of
depth, z:
σ = F/A
= mg/A
= Vρg/A
= Azρg/A ; cancel area
= ρgz
Lithostatic Stress Gradient
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What would be the lithostatic stress at the base of the
continental crust at 40 km depth?
σ = ρgh
= 2700 kgm-3 x 9.8 ms-2 x 40,000 m
= 1.05 x 109 Pa
= 1.0 GPa
Example
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Lecture 7: Stress Analys
STRUCTURAL GEOLO
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Lecture 7: Topics
• Principal stress components
• Computing shear and normal Stresses
• Mohr circle diagrams
• Measurement of ambient stresses in c
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Stress Components
Stress acting on any surface (or arbitrarily
can be resolved into two components:
normal stress, n (sigma) - stress acting nor
shear stress, (tau) - stress acting tangenti
n
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Stress Ellipsoid
The total stress field acting on stresses acti
can be represented by the stress ellipsoid
1 - greatest principal stress
2 - intermediate principal stress direction
3 - least principal stress
triaxial stress is generalcase where σ 1 > σ 2 > σ 3
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Generally we simplify problems by dealing
within a single plane
• plane containing σ1 and σ3, σ1 and σ2 , or
2-D Stress Ellipse
σ3
σ1
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Stress States
Three stress configurations:
• Trixaxial stress
• Hydrostatic stress
• Uniaxial stress
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Triaxial Stress
Triaxial stress is general case where all thr
stresses are of a different magnitude
• σ 1 > σ 2 > σ 3
• elliposoid is ‘oblate’ (flattened)
σ3
σ2
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Hydrostatic StressAll normal stresses, including principal stre
• all stresses generated are normal stresses
stress components)
• σ 1 = σ 2 = σ 3
• all stress generated by a fluid are hydrosta
σ1
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Uniaxial Stress
Two of the three principal stresses are eq
• ellipsoid is a ‘needle’
Uniaxial stress
σ1 > 0 , σ 2 = 0, σ 3 = 0
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Calculation of Stress Comp
Calculate the normal (σn) and shear stress (
for a stress of 50 MPa inclined at 60º to the
Z
X
τ = ?
σxz = 50 MPa
60
σn = ?
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Calculation of Stress Com
σn = sin θ ·σxz
= sin 60 · 50 Mpa= 43.3 MPa
τ = cos θ · σxz
= cos 60 · 50 Mpa
= 25 MPa
Normal and shear stress components can be
solving for the lengths of the vectors
X
τ = 25 M
σ
6
σn = 43.4 MPa
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Stresses on Inclined P Normal and shear stress acting on a surfa
calculated if the principal stress compone
and angle of plane are known
σ1
θθ = 22.5
+50 MPa
Pole inclined
to plane
σ3 +10 MPa
+50 MPa
Inclined plane
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Fundamental Stress Equ
σn = (σ1 +σ3) + (σ1 - σ3) ·
22
τ = (σ1 - σ3) /2 · sin 2θ
Normal and shear stress acting on a surfac
calculated if the principal stress componen
are known
• calculate stress for plane of any orientatio
fundamental stress equations:
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ExampleFind the normal and shear stress compon
σ1 = 50 MPa σ3 = 10 MPa θ = 22.5 σ1
θθ = 22.5
+50 MPa
Pole inclined
to plane
σ3 +10 MPa
+50 MPa
Inclined plane
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σn = (50 + 10) + (50 - 10) · cos 45
22
σn = (σ1 +σ3) + (σ1 - σ3) ·cos 2θ
22
Example
Calculate the normal stress σn
• θ is angle measured anticlockwise from
σn = 30 + 20 (cos 45)
= 44 MPa
Pole inclined
to plane
σ3 +10 MPa
Inclined plane
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τ = (σ1 - σ3) ·sin 2θ
2
τ= (50 - 10) · sin 45
2
ExampleCalculate the shear stress component
• θ is angle measured anticlockwise from
τ= 20 (sin 45)
= 14 MPa
+
Pole inclined
to plane
σ3 +10 MPa
+
Inclined plane
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Alternate Approach: Mohr COtto Mohr (1835-1918) German engineermethod for solving stress components usi
graphical method
10 20 30 40 50 60
13
3+1
2
DIAMETER =3-
2θ
RADIUS =3
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Example: Mohr CircleFind the normal and shear stress componen
σ1 = 50 MPa
σ3 = 10 MPa
θ= 22.5 2
θ
σ1
θ θ = 22.
+50 MPaPole inclined
to plane
σ3 +10 MPa
+50 MPa
Inclined plane
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10 20 30 40 50 60
13
3+1
2
Example: Mohr Circle
1. Locate σ1 = 50 MPa σ3 = 10 MPa on sidraw centre point at σ3 +σ1/2
• (10+50)/2 = 30 MPa
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Example: Mohr Circle
2. Draw Mohr circle passing through σ1, σ3radius at angle 2θ = 45º
• angle always measured anticlockwise from• read off values of σn and τ
1020
30 40 50 60
13
3+1
2
DIAMETER =3-
2θ
RADIUS =3-
2τ = 14 MPa
σn = 14 MPa
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n10 20 30 40 50 60
13
τ = 0
σn = 50 MPa
Example: θ = 0º
2θ = 0
σ3 +10 MPa
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n10 20 30 40 50 60
13
τ = 20 MPa
σn = 30 MPa
Example: θ = 45º
2θ = 90
σ3 +10 MPa
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n10 20 30 40 50 60
13
τ = 0 MPa
σn = 10 MPa
Example: θ = 90º
2θ = 180
σ3 +10 MPa
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Draw Mohr circles for θ = 135º, θ = 180
Assignment
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Measurement of Earth SDirection and magnitude of stresses in the determined by measurement of strain
Methods of stress measurement:
• borehole breakouts
• over-coring
• hydrofracturing
• earthquake focal mechanism
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Stress Measurement: OveDrill small diameter hole (3-4 cm) with stcentre then drill larger hole (15-20 cm)
• measure expansion (relaxation) of rock m• change in shape in circle to ellipse
STRAINGAUGE
15-20 cm
5 cm
BEFORE
OVERCORING
AFTEROVERCORING
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Stress Measurement: HydroSeal off hole with packer and pump in wat
pressure until rock fractures
• water pressure required to cause fracture principal horizontal stress
• orientation of fractures gives direction of
INFLATABLE
PACKER
HYDROFRACTURES
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CALIPER
TOOL
BOREHOLE
BREAKOUT
Borehole BreakoutsStresses cause bulging and fracturing of b
• measure change in shape of borehole usi• gives orientation of principal horizontal
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World Stress MapOrientations of maximum contemporary prstress (σ1 ) have been compiled on world-w
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STRUCTURAL GEOL
Lecture 8: Strain
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Lecture 8: Strain
• Deformation• Strain
• Strain ellipsoid
• Measurement of strain
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Definitions
Deformation - response of rock body
stresses
• rigid body deformation
• non-rigid body deformation (strain)
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Rigid Body Deformati
Rigid body - rock body displaced with no
shape or volume
• translation
• rotation
TRANSLATIONROTA
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Example - displacement of fault blocks al
Rigid Body Deformatio
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Non-rigid Body Deform
Strain - change in size and shape body ex
during deformation
• dilation - change in volume
• distortion - change in shape
DILATION
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Homogeneous Strai
All points within deforming body unde
change in shape or volume
UNDEFORMED HOMOGENEDEFORM
ψ
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Homogeneous Strain ‘R
• Straight lines remain straight after defo
• Parallel lines remain parallel
UNDEFORMED HOMOGENEODEFORME
ψ
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Heterogeneous Strai
Changes in size and shape varies across d
UNDEFORMED HETEROGENEODEFORMED
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Heterogeneous Strain
Most deformation in nature is heterogeneo
e.g. folding - no lines remain parallel or str
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Analysis of StrainAnalysis of heterogeneous strain is a probl
• difficult to deal with mathematically
• subdivide into regions which can treated
homogeneous
HETEROGENEOUS STRAIN
LOCHOMOG
ST
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Types of Homogenous S
Two ‘end-members’ of homogeneous stra• simple shear
• pure shear
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Simple Shear
Rock body is sheared like a deck of cards
• square converted to a parallelogram
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Simple Shear: Geological
Shearing of fault blocks past one another
• lines within body undergo uniform rota
• line parallel to direction of shear remain
1 2 3
SHEARZONE
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Pure Shear
Uniform stretching extension in one direc
uniform contraction in plane perpendicula
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Pure Shear: Geological E
Uniform stretching of Earth’s crust at rift z
boundinage of rock
• uniform extension and contraction
• lines parallel to and perpendicular to prin
stretch do no rotate1 2 3
RIFTING
CRUST
ASTHENOSPHERE
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Measurement of Stra
Measure change in length and orientation
reference line or object called ‘strain ma
e.g. deformed fossils, sedimentary structu
CHANGE IN LINEORIENTATION
CHANGE IN LINELENGTH
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Strain Markers: Exam
Stretched pebble conglomerate - pebble
spheroidal
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Strain Markers: Exa
Augen gneiss - stretched feldspar and qu
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Strain Markers: Exam
Oncolites - carbonate concretions with c
spherical layers (deposited by algae; sim
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Strain ellipse - as in stress analysis we re
2-dimensions and work with strains occu plane
Strain Ellipse
S1
S3
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STRUCTURAL GEOLO
Lecture 9, 10: Strain Measurement and
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Lecture 9,10 Topics:
• Measurement of Strain
• Experimental deformation of rocks
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Extension (elongation), e - ratio of change
original length
e = (lf - lfo) / lo lo = origin
lf = final
Extension
lo = 10 cm
lf = 15 cm
e = (lf - lo) /
= 15 - 10
= 0.5 50% leng
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Stretch, S - ratio of final length to origina
S = lf / lo
= 1 + e
Stretch
S = lf / lo
= 15 / 10
= 1.5
line lengthen
S = 1.5 x 100
= 150% stre
lo = 10 cm
lf = 15 cm
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Elongation and stretch provide no inform
changes in angles between linesAngular shear, Ψ (psi) - measures deparfrom original position
Angular Shear
ψ = + 25
UNDEFORMED CLOCKWISE - POSITIVE ANTICLOCKWISE
ψ = - 25
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Shear Strain
Shear strain γ = tan Ψ
The change in orientation of lines in defo
can also be measured as a displacement
ψ
∆x
yγ =
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Quadratic Elongatio
Two other measures of strain derived fro
• used in fundamental strain equations (s
Quadratic elongation, λ
λ = (lo
/ lf )2
= S2
Reciprocal quadratic elongation, λ’
λ’ = 1 / λ = 1 / S2
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Summary of Strain Param
• Elongation, e• Stretch, S
• Angular shear, Ψ (psi)
• Shear Strain, γ • Quadratic elongation, λ
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How are Stress and Strain R
We know that stress causes strain in rockthe they related?
• How much and what type of strain occ
stress regime
• What factors affect strain - e.g. temper
lithology, confining pressures, fluid pres
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Rheology - study of the response of rock
materials to stress
• experimentally deform rock specimens
• produce deformation structures using ‘s
of strata
Rheology
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Triaxial Apparatus
Experimental apparatus for deforming sma
Pc
Pp
AX
LO
TRIAXIAL APPARATUS
Pp= PORE PRESURE
Pc = CONFINING PRESSURE
CORE
SAMPLE
COPPERJACKET
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Which parameters can be varied?
• vertical axial load
• horizontal confining stress
• pore water pressure within sample
Triaxial Test
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Axial load is vertical stress applied to sam
displacement of pistons
σ axial = Load (force) / Sample Area
= Load/ πr 2
Axial Load
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Confining pressure recreates stresses acting
original ‘burial depth’
• assume hydrostatic conditions - pressure
confine sample is equal to vertical confinin
• confining pressure is sum of lithostatic +
stresses
Pc = Pl + Ph
Pl = lithostatic stress, weight of overlying r
Ph = hydrostatic stress, weight of water occ
spaces
Confining Pressure
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Pore pressure is pressure exerted by flui
walls (recall water relatively incompress• pressure exerted within sample
• tends to counteract the confining press
Pore Water Pressur
Pw
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Vertical axial load is maximum stress σ1
• horizontal confining stress σ 2 = σ 3• specimen undergoes length-parallel sh
Axial Compression T
1
2
3
2
1
3
STRESS =
LOAD/SAMPLE AREA
1 >> 2
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Vertical axial load is minimum stress, σ 3• horizontal confining stress σ
1
= σ2
• specimen undergoes length-parallel shor
Axial Extension Tes
3
2
1
2
3
1
STRESS =
LOAD/SAMPLE AREA
1 = 2 >>
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Strain in sample is obtained by measuring
of pistons
• shortening of core described by e or S
Strain Measuremen
e = (lf-lo)/l
o
lo lf
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Strain recorded as load-displacement curve
plotter
Strain Measureme
DISPLACEMENT (mm)
L O A D
( k g )
SEATING POSITION
SAMPLE SHORTENING
SAMPLE RUPT
LOAD DISPLACEMENT CURVE
PISTON FREE TRAVEL
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Displacement or shortening is used to ob
rate, εε = e / t
• since e is dimensionless, units are s-1
Example: 2 cm long core sample compre
cm during first second of loading
e = (lf - lo) / lf = (1.98 - 2) / 2 = -0.02/2 =
ε = -0.01 s-1
Strain Rate
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Percentage strain is plotted against differen
σd = σ1 - σ3• percentage strain e = (lf - lo) / lf x 100
Stress-strain Diagram
Strain (%)
D i f f e r e n
t i a l S t r e s s ( M P a )
ELASTIC STRAIN
SPECIMEN RUPTURE
STRESS-STRAIN CURVE
ELASTIC LIMIT
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If sample is loaded then unloaded the stra
recovered - a behavior called ‘elastic def
• time lag in recovery is called “hysteresi
Elastic Deformation
Strain %
D i f f e r e n t i a l S t r e s s ( M P a
)
ELASTIC STRAIN
STRESS-STRAIN CURVE
STRAIN RECOVERY
SAMPLEUNLOADED
HYSTERESIS LOOP
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If stress is raised continually, sample wil
‘elastic limit’ and begin to deform plastic
• plastic deformation is a permanent, nonstrain
Plastic Deformation
Strain %
D i f f e r e n t
i a l S t r e s s ( M P a
)
ELASTICDEFORMATION
STRESS-STRAIN CURVE
PLASTICDEFORMAT
ELASTIC LIMIT
YIELD STRENGTH
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Brittle DeformationContinued loading will eventually cause th
fracture and rupture
• behavior is called brittle deformation
Strain (%)
D i f f e r e n
t i a l S t r e s s ( M P a
)
ELASTICDEFORMATION
STRESS-STRAIN CURVE
PLASTICDEFORMAT
ELASTIC LIMIT
FAIL
FRICTIOSLIDING
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Rock Strength
Yield strength - stress at which plastic de
Ultimate strength - maximum stress at peRupture strength - stress at which rock fr
Strain (%)
D i f f e r e n t i a l S t r e s s ( M P a )
STRESS-STRAIN CURVE
ELASTIC LIMIT
YIELD STRENGTHFAILU
ULTIMATE STRENGTHRUPTURESTRENGT
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Frictional Sliding
Further displacement after rupture occurs
sliding along fracture surfaces - “microfau
Strain (%)
D i f f e r e n t i a l S t r e s s ( M P a )
ELASTICDEFORMATION
STRESS-STRAIN CURVE
PLASTICDEFORMAT
ELASTIC LIMIT
YIELD STRENGTH
FAIL
FRICTIOSLIDING
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Rock Strength Fact
How does rock strength change with• confining pressure?
• pore water pressure?
• temperature?
• lithology?
• strain rate (time)?
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Confining PressureIncreased confining pressure results in a gr
and ability to deform plastically before fail
• rock yield strength and plasticity increase
• less elastic deformation - rock ‘stiffness’
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Confining Pressure: Exa
Marble deformed under varying confining
with differential stress applied at same rat
A. 0.1 MPaB. 3.5 MPa
C. 35 MPa
D. 100 MPa
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Pore Water PressurIncreased pore water pressure tends to of
confining pressure
• increasing Pw tends to decrease rock str
• important effect in deeply buried sedim
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Effective Stress
Effect of pore water pressure determined b
stress
Effective stress = Pconfining - P
• Pw low, high effective stress increased
ductility
• Pw high, low effective stress decreased
ductility
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TemperatureIncrease in temperature results in decrease
and increase in plasticity
• rock sample begins to
exhibit ‘viscous’ behavior
• decrease in rock stiffness, E
• geothermal gradient is 30 ºC
/km
• 25 km - 800 ºC
• 40 km - 1200 ºC
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LithologyThe strength of rock is related to its miner
composition
• dense, crystalline rocks tend have highes
• sedimentary rocks weaker
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Strength also dependent upon presence of
in rock• layering, foliations, fabrics (alignment o
• fractures
Lithology: Rock Heterog
Garnet biotite gneiss
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Strain RateExperimental data show that rock strength
function of the rate at which stress level i
• rapidly applied strain
results in higher rock
strength
• low rates of strain result
in lower rock strength
• gradual strain is called
‘creep’
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Time-dependent Strain:
Creep is slow ductile deformation produce
exposure to a low level of differential strai
• implication: rocks may ‘flow’ under low
over long time periods
Time
S t r a i n
SECONDARY
CREEP
PRIMARY
CREEP
TERTIARY
CREEP
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Time-dependent Strain:
Primary Creep - initial increase in rate of st
initially elastic followed by plastic behavio
Secondary Creep - steady rate of strain with
Tertiary Creep - accelerating rate of creep f
failure
Time
S t r a i n
SECONDARY
CREEP
PRIMARY CREEP
TERTIARYCREEP
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Rheids
S.W. Carey (1953) coined term “rheid” f
which exhibit time-dependent strain
“a substance whose temperature is below
point and whose deformation by viscous f
least three orders of magnitude greater tdeformation under the given conditions”
• ice, salt, gypsum
• rocks are act as rheids over geological t
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Models of Rock Behav
3 basic modes of strain behavior in r
• elastic
• plastic
• viscous
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Elastic Deformation: Hoo
Relationship between stress and elastic st
Hookes Law: σ = Ee where E = Youe = stra
S t r e s s ( )
Strai
IDEAL ELAST
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Young’s Modulus, E
Young’s modulus E, describes how much
applied to achieve a given amount of strain
• the higher the value of E, the ‘stiffer’ th
S t r e s s ( )
Strain (e)
Less Stiff
Stiff INCREASINGE
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Young’s Modulus, E
Young’s modulus is negative since strain
• values of E range from - 0.5 x 105 MPaMPa
e = (lf-lo)/lo
lo lf
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Poisson’s Ratio, ν νν ν
Poisson’s Ratio, ν (nu) is another elastic mdescribing degree to which core bulges as
ν = |elat / elong|
Typical values of ν
Limestone fine-grained 0.25
Limestone medium-grained 0.17
Granite 0.11Coarse sandstone 0.05
Shale 0.02
Biotite schist 0.01
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Plastic DeformatioIdeal plastic solid does not deform until cr
threshold is reached
• ideal solid will deform as long as stress
• rocks are not ‘ideal’ plastic solids
S
t r e s s ( )
Strain (e)
IDEAL PLASTIC DEFORMATION
CRITICAL THRESHOLDIDEAL PLASTIC
SOLID
ROCK SAMPLE
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Viscous DeformatioIdeal viscous substance has no yield stren
under any amount of strain
σ = εη ε = strain rate
η = viscosity (resistance to fl
S t r e s s ( )
Strain Rate (ε)
IDEAL VISCOUS DEFORMATION
= ηε
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Viscous Deformatio
Viscosity measured in poises (10 poises =
• mantle rocks 1023 poises
• basalt lava 103 poises
• corn syrup 102 poises
S t r e s s ( )
Str
IDEAL VISC
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Deformational Mechani
Rock accommodate strain through change
at granular to molecular levels
1. Microcracking
2. Dislocation glide and twinning
3. Dislocation Creep
4. Pressure solution
See text Chapter 4
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STRUCTURAL GEOL
Lectures 11, 12: Joints and Fract
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Lectures 11, 12: Topi
• Classification of joints and fractures• Joint surface features
• Origin of joints and fractures
• Fracture measurement and analysis
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Definitions
Fractures - surfaces along which rocks h
lost cohesionJoints - fractures with little or no displac
failure surface
Faults - fracture surfaces with appreciabl
JOINTS FRACTUR
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Occurrence and ScalJoints and fractures are most common geo
structure in the Earth’s crust
• occur in all rock types
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Systematic JointsJoints with approximately planar geometr
• parallel orientations and regular spacing
• characteristic of uniform regional stress
Entrada
(Jurassic-age)
Sandstone
Utah
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Systematic Joints
Joint System - two or more joint sets whi
fairly constant angles
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Conjugate Joints - two or more joint sets w
formed simultaneously
• formed under same stress conditions
Systematic Joints
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Joint Zones
Individual joints may form quasi-continuo
which extend over large regions
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Non-systematic JoinJoints with irregular or curved joint faces
• random, non systematic orientation
• often form subsidiary to systematic joints• local non-uniform stress fields
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Non-systematic Join
Exfoliation Joints - sheet-like curved joint
to topography by mechanical weathering o• non-systematic joints
• form best in igneous intrusive rocks
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Non-systematic JoinColumnar Joints - primary volcanic structu
formation of vertical fractures as lava cools
• polygonal pattern in cross-section reflectsshrinkage towards centre of column
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Columnar JointsJoints open up perpendicular to cooling c
lava flow
• propagate vertically from top and botto
flow
NUCLEUS
NUCLEUS
120
DIRECTION OF COOLAND JOINT PROPAGA
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Mud Cracks
Non-systematic joints formed by dessica
contraction of mud surface
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Differential Fracturi
Preferential fracturing of more brittle lith
sequence of rocks
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Veins
Veins are fractures filled with mineral pr
• record flow of fluids through fracture s
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Gash Fractures
Extension fractures produced by shearing
shear zone
• S- or Z-shaped ‘gashes’
• indicate sense of shearing
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Fracture Types
Can broadly classify into 2 types based on
has occurred across fracture surface
1. Extension fractures - formed by openin
perpendicular
to fracture
2. Shear fractures - formed by tearing par
to fracture surface
• 4 ‘modes’ of fractures
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Mode I: OpeningExtension fractures form by pull-apart dis
perpendicular to fracture walls• formed by tensional stresses acting on r
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Mode II: SlidingShear fractures formed by sliding displace
fracture surface
• formed under dominantly compressional
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Mode III: Scissorin
Shear fracture formed by “scissoring” mo
surface and fracture front
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Mode IV: Mixed mod
Fractures may form by combination of mod
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How are Fracture Modes Re
Stress Fields?
Mode I - net extension - ‘pull-apart’ for
Mode II and III - net compression
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Mode I: Stress Field
Formed under net tensile stress
• σ 1 - positive, parallel to fracture• σ 2 - positive, vertical
• σ 3 - negative and normal to fracture
1
1
33
2
2
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Mode II and III: StresShear fractures formed under net compre
• σ
1 - positive, 30-45
to fracture• σ 2 - positive, vertical
• σ 3 - positive, 45-60 fracture
1
33
1
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Can determine fracture mode by lookinsurfaces
• nature of displacement
• presence of plumose structures• slickensided surfaces
How are Fracture Modes I
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Mode I Fractures: Plumose S
Feather-like pattern of ridges and groov
surface
• forms only in extensional fractures (M
• rapid, near-explosive snapping apart
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Plumose Structure
Origin - site of initial rupture and propaga
fracture surface
Hackles - ridges radiating from fracture o
Ribs - arcuate ridges perpendicular to hac
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Mode II, III: Shear Fracture
Slickenlines - striations and grooves rec
frictional shear along fracture surface• indicate slip direction on shear fractu
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Origin of Fractures/Jo
1. Tectonic joints
2. Unloading joints3. Joints associated with igneous intrusi
4. Joints formed by meterorite impacts
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Tectonic JointsMode I tensile joints formed parallel to di
principal stress σ 1 and perpendicular to
• a.k.a “cross-fold” joints
Shear fractures form at 30-45 to σ 1
1
2
3
CROSSJOINTS
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Neotectonic JointGeologically young ( < Miocene-age) joints
present-day tectonic stress regimes.
• joints are fresh - no fillings
• may cut older joints or veins
• orientation of joint plane parallels maxim
stress σ 1
3
MODE I TENSILE
FRACTURE
OLDER FRACTURESETS
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Neotectonic Joints, S. ONeotectonic jointing present in Paleozoic r
• dominant joints are oriented SW-NE• mode I extensional joints
• some evidence for mode II shear fracture
σ1
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Unloading JointsTensile joints produced by cooling and co
crust as it is uplifted
• release joints tend to form along pre-ex
weakness in the crust
• form perpendicular to former σ 1 directi
• a.k.a. “strike joints”
UPLIFTED CRUSTCOOLS AND THERMALLY
CONTRACTS
RELEASEJOINTS
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Fracture AnalysisDetermine fracture mode and orientation
which formed fractures:
Measure:
1. Fracture orientation (azimuth or strike a
2. Length, geometry
3. Fracture density (spacing)4. Examine fracture surfaces
• presence of slickenlines
• plumose structures
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Orientation Analysi
Measure strike and dip of individual fract
determine preferred orientation directio
• plot on stereonet or rose diagram to eva
• rose diagram is a type of histogram
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Fracture Density: Circle In
Circle of known diameter is drawn on ou
orientation and length of fractures mea
• fracture density calculated as F = L /
is cumulative fracture length, r is radiu
CHA
CIR
r
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STRUCTURAL GEOLO
Lecture 13: Mechanics of Frac
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Lecture 13: Topics
• Experimental modeling of fractures • Failure envelopes
• Anderson’s theory of faulting
• Read chapter 5 and 6
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Modeling Fractures and
Formation of fractures and faults can be m
laboratory1. Triaxial tests
2. Shear box models
Pc
Pp
TRIAXIAL APPARATUS
Pp= PORE PRESURE
Pc = CONFINING PR
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Triaxial Test TypTensile Strength Test - confining stress (σ
and σ3 increased steadily until failure
Compressive Strength Test - σ1 increased wstress (σ2 = σ3) held constant
Tensile/Compressive Test - small confinin
increasing σ33
3
1
=
2
= 0
TENSILE TEST
1 =2
3
3
TENSILE/COMPRESSIVE TEST
2 =3
COMPRE
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What is Measured
• yield strength - values of σ1 and σ3 a
failure
• angle at which fractures form relative
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Measurement of Fracture
Angle of fracture measured relative to σ1
αααα = 30
3
3
θ = 60
-
-
+
2α = 60
2α = 60
TWO FRACTURES AT 30 DEGREES TO 1
1 =2
αααα = 30
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Failure Envelopes
Lines produced by plotting points of failu
several triaxial tests on same rock
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Tensile Strength T
Test carried out under conditions of zero c
(σ1 = σ2 = 0)
• sample fails at point where σ3 exceeds t
strength
20 40
20
40
-20
-20
-40
-40
2αααα = 180TENSILE
STRENGTH
= 30 MPa
TENSILE
STRENGTH
FAILURE
ENVELOPE
10 30
30
10
CONFINING
STRESS
= 0 MPa
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Tensile Strength Te
Mode I extension fracture forms parallel t
90
to σ3
αααα = 0
3
1 =2
3
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Tensile/Compressive T
Confining pressure maintained constant an
strength increased
• mode I extension fractures develop
20
20
-20
-10
-20
2αααα
= 180
TENSILE
STRENGTH
= 10 MPa
TENSILE
STRENGTH
FAILURE
ENVELOPE
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