STRUCTURAL GEOLOGY.pdf

8/19/2019 STRUCTURAL GEOLOGY.pdf

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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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• Faulting



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• Faulting



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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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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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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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Foliation - cleavage planes produced by m

sedimentary rocks

• common structure in slates and phyllites

Foliated phyllite, Cascade Mountains, B


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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

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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


140/484

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


141/484

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


142/484

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)


143/484

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


144/484

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


145/484

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


146/484

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


147/484

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


148/484

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


149/484

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


150/484

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


151/484

Units of Stress

1 kilopascal (kPa) = 1000 Pa (10

3

Pa)

1 megapascal (MPa) = 106 Pa

1 gigapascal (GPa) = 109 Pa


152/484

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


153/484

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


154/484

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:


155/484

Stress Sign Conventions

Fn

Fn

COMPRESSIVE STRESS - POSITIVE

Fn

Fn

TENSILE STRESS - NEGATIVE

By convention compressive stress is positive and tensile

stress is negative


156/484

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


157/484

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


158/484

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


159/484

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


160/484

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


161/484

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


162/484

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


163/484

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


164/484

Lecture 7: Stress Analys

STRUCTURAL GEOLO


165/484

Lecture 7: Topics

• Principal stress components

• Computing shear and normal Stresses

• Mohr circle diagrams

• Measurement of ambient stresses in c


166/484

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


167/484

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


168/484

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


169/484

Stress States

Three stress configurations:

• Trixaxial stress

• Hydrostatic stress

• Uniaxial stress


170/484

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


171/484

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


172/484

Uniaxial Stress

Two of the three principal stresses are eq

• ellipsoid is a ‘needle’

Uniaxial stress

σ1 > 0 , σ 2 = 0, σ 3 = 0


173/484

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 = ?


174/484

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


175/484


176/484

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


177/484

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:


178/484

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


179/484

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


180/484

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


181/484

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


182/484

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


183/484

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


184/484

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


185/484

n10 20 30 40 50 60

13

τ = 0

σn = 50 MPa

Example: θ = 0º

2θ = 0

σ3 +10 MPa


186/484

n10 20 30 40 50 60

13

τ = 20 MPa

σn = 30 MPa

Example: θ = 45º

2θ = 90

σ3 +10 MPa


187/484

n10 20 30 40 50 60

13

τ = 0 MPa

σn = 10 MPa

Example: θ = 90º

2θ = 180

σ3 +10 MPa


188/484

Draw Mohr circles for θ = 135º, θ = 180

Assignment


189/484

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


190/484

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


191/484

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


192/484

CALIPER

TOOL

BOREHOLE

BREAKOUT

Borehole BreakoutsStresses cause bulging and fracturing of b

• measure change in shape of borehole usi• gives orientation of principal horizontal


193/484

World Stress MapOrientations of maximum contemporary prstress (σ1 ) have been compiled on world-w


194/484

STRUCTURAL GEOL

Lecture 8: Strain


195/484

Lecture 8: Strain

• Deformation• Strain

• Strain ellipsoid

• Measurement of strain


196/484

Definitions

Deformation - response of rock body

stresses

• rigid body deformation

• non-rigid body deformation (strain)


197/484

Rigid Body Deformati

Rigid body - rock body displaced with no

shape or volume

• translation

• rotation

TRANSLATIONROTA


198/484

Example - displacement of fault blocks al

Rigid Body Deformatio


199/484

Non-rigid Body Deform

Strain - change in size and shape body ex

during deformation

• dilation - change in volume

• distortion - change in shape

DILATION


200/484

Homogeneous Strai

All points within deforming body unde

change in shape or volume

UNDEFORMED HOMOGENEDEFORM

ψ


201/484

Homogeneous Strain ‘R

• Straight lines remain straight after defo

• Parallel lines remain parallel

UNDEFORMED HOMOGENEODEFORME

ψ


202/484

Heterogeneous Strai

Changes in size and shape varies across d

UNDEFORMED HETEROGENEODEFORMED


203/484

Heterogeneous Strain

Most deformation in nature is heterogeneo

e.g. folding - no lines remain parallel or str


204/484

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


205/484

Types of Homogenous S

Two ‘end-members’ of homogeneous stra• simple shear

• pure shear


206/484

Simple Shear

Rock body is sheared like a deck of cards

• square converted to a parallelogram


207/484

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


208/484

Pure Shear

Uniform stretching extension in one direc

uniform contraction in plane perpendicula


209/484

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


210/484

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


211/484

Strain Markers: Exam

Stretched pebble conglomerate - pebble

spheroidal


212/484

Strain Markers: Exa

Augen gneiss - stretched feldspar and qu


213/484

Strain Markers: Exam

Oncolites - carbonate concretions with c

spherical layers (deposited by algae; sim


214/484


215/484

Strain ellipse - as in stress analysis we re

2-dimensions and work with strains occu plane

Strain Ellipse

S1

S3


216/484


217/484

STRUCTURAL GEOLO

Lecture 9, 10: Strain Measurement and


218/484

Lecture 9,10 Topics:

• Measurement of Strain

• Experimental deformation of rocks


219/484

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


220/484

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


221/484

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


222/484

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 =


223/484

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


224/484

Summary of Strain Param

• Elongation, e• Stretch, S

• Angular shear, Ψ (psi)

• Shear Strain, γ • Quadratic elongation, λ


225/484

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


226/484

Rheology - study of the response of rock

materials to stress

• experimentally deform rock specimens

• produce deformation structures using ‘s

of strata

Rheology


227/484

Triaxial Apparatus

Experimental apparatus for deforming sma

Pc

Pp

AX

LO

TRIAXIAL APPARATUS

Pp= PORE PRESURE

Pc = CONFINING PRESSURE

CORE

SAMPLE

COPPERJACKET


228/484


229/484

Which parameters can be varied?

• vertical axial load

• horizontal confining stress

• pore water pressure within sample

Triaxial Test


230/484

Axial load is vertical stress applied to sam

displacement of pistons

σ axial = Load (force) / Sample Area

= Load/ πr 2

Axial Load


231/484

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


232/484

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


233/484

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


234/484

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 >>


235/484

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


236/484

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


237/484

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


238/484

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


239/484

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


240/484

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


241/484

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


242/484

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


243/484

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


244/484

Rock Strength Fact

How does rock strength change with• confining pressure?

• pore water pressure?

• temperature?

• lithology?

• strain rate (time)?


245/484

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’


246/484

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


247/484

Pore Water PressurIncreased pore water pressure tends to of

confining pressure

• increasing Pw tends to decrease rock str

• important effect in deeply buried sedim


248/484

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


249/484

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


250/484

LithologyThe strength of rock is related to its miner

composition

• dense, crystalline rocks tend have highes

• sedimentary rocks weaker


251/484

Strength also dependent upon presence of

in rock• layering, foliations, fabrics (alignment o

• fractures

Lithology: Rock Heterog

Garnet biotite gneiss


252/484

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’


253/484

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


254/484

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


255/484

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


256/484

Models of Rock Behav

3 basic modes of strain behavior in r

• elastic

• plastic

• viscous


257/484

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


258/484

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


259/484

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


260/484

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


261/484

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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