GEOLOGI STRUKTUR 3

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STRAIN ANALYSIS

UNDEFORMED DEFORMED

KINEMATIC ANALYSISKinematic analysis is the reconstruction of movements

cf

A. Rigid Body Translation

ba

f

a

B. Rigid Body Rotation

cf

cde

ba

cf

d

e b

E. Nonrigid Deformation by Distortion

C. Original Object

e

b

d a ba

cb

e d

f c

d

f

eD. Nonrigid Deformation by Dilation

(Davis and Reynolds, 1996)

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TYPES OF STRAIN

H

I

H

B. Inhomogeneous strain

A. Homogeneous strain

HH

l = 5 cmo

L' = 3 cm

L

l 8

Fundamental Strain Equations

Strain

R e = n

Deformed StateUndeformed State

R = 1θ θ

r = Sn

L

l = 8 cmf

L' = 4.8 cm

Extension (e) = (lf – lo)/lo

Stretch (S) = lf/lo = 1 + e

Lengthening e>0 and shortening e<0

Strain

B. Shear strain

Deformed StateUndeformed State

A. Extension and stretch

θr

θ

T

Re tans = 1/2 ψt

ψ

γ ψ = tan ψ

Shear Strain ( ) γ

Quadratic elongation (λ) = S2

λ’ = 1/λ = 1/S2

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S1

Strain Ellipsoid

S1 = Maximum Finite StretchS3 = Minimum Finite Stretch

S2

S2S3

S3

S3

S1

S1(Davis and Reynolds, 1996)

Mohr Strain Diagram

Ad

θd = +15º

S1

1 Unit

A

S1

B

γ/λ

.49

1.01.0

2 = +30ºθd

(λ γ λ', / )

C

Distorted Clay Cake

γ/λ

1.01.0

2 θd

λ −λ

2' '3 1

λ'3.0

.56

0 C

d

λ' 2.43 = λ'1 = .42 2.01.0

A

γ λ = λ −λ . 2θ

2/ ' ' SIN 3 1

d

λ'33.0

Minus

C

λ λ' + ' 2

1 3

2.01.0

λ −λ . 2θ2

' ' COS 3 1 d

0 A'λ'1

Equalsλ'

(Davis and Reynolds, 1996)

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HOMOGENOUS DEFORMATION

O

N

Simple Shear(Noncoaxial Strain)

A B

ML

Pure Shear(Coaxial Strain)

Progressive Deformation

M

S1

25% FlatteringS3

S1

S3 S1+ 22º

+ 31º S3S1 S3

30% Flattering

S3S3

S1

S1+ 45º

40% Flattering

(Davis and Reynolds, 1996)

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A. Regional scale

100 m

perpendicu larto layer ^^

S1

S2S3

S1^

^ ^ ^S2 < 1 S2 = 1 S2 >1

STRAIN HISTORY Scale Factor

100 mμ

B. Outcrop scale

10 mm

C. Hand sample scale

D.

A.

perpendicu larto layer

perpendicu larto layer

C.B.

^

^

S1^

S1^

S2^

S2^

S2S3^

S3^

S3

D. Microscope scale

E. F.

Structural development in competent layerbased on orientation of S1, S2 and S3

Strain Measurement

• Geological Map • Geologic Cross-sectionGeologic Cross section• Seismic Section• Outcrop• Thin Section

Knowing the initial objects• Shape• Size

• Orientation

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Field of Expansion

Field ofNo Strain

Strating Sizeand Shape

S3

Strain Field Diagram

Field of Compensation

Fieldof

LinearShortening

1.0 Field of Linier Strecthing

1.0

Field of Contraction

S1

Z

X

Y

A

Z

K = 1

k = χ

Special Types of Homogenous Strain

X

Z

Y

Y

X

B

^1

S2

^a =

SS

1

2^

K = 0

ConstrictionalStrain

FlatteringStrain

Plane S

train

Sim

ple

Ext

ensi

on

Simple Flattering1

Xb =

SS

2

3^

A. Axial symmetric extension (X>Y=Z) or Prolate uniaxialB. Axial symmetric shortening (X=Y>Z) or Oblate uniaxial

C. Plane strain (X>Y=1>Z) or Triaxial ellipsoid

Flinn Diagram

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Strain Measurement from Outcrop

Δ

Δ

Δ = gap

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STRESS vs. STRAIN

Relationship Between Stress and Strain

• Evaluate Using Experiment of Rock Deformation

• Rheology of The Rocks• Using Triaxial Deformation Apparatus• Measuring Shorteningg g• Measuring Strain Rate • Strength and Ductility

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C

MP

a)

Repture

400

300Yield

Strength

UltimateStrength

Yield StrengthAfter StrainHardening D

A

EB

Stress – Strain Diagram

2 3 4 61S ( %)

Diff

eren

tial S

tress

(in

M ReptureStrength

5

100

200

Strength

Strain (in %)

A. Onset plastic deformationB. Removal axial loadC. Permanently strained D. Plastic deformationE. Rupture

140130

2000

25ºC

Effects of Temperature and Differential Stress

0 2 4 6 8 10 12 14 16

Diff

eren

tial S

tress

, MPa

300

200

100

70

20

Crown Point Limestone

40

60

801500

1000

800ºC

700ºC

500ºC

300ºC

500Diff

eren

tial S

tress

(in

MP

a)

25 C

Strain, percent5 10 15 0 Strain (in %)

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Deformation and Material

A. Elastic strainB. Viscous strainC Viscoelastic strain

(Modified from Park, 1989)

C. Viscoelastic strainD. ElastoviscousE. Plastic strain

Hooke’s Law: e = σ/E, E = Modulus Young or elasticityNewtonian : σ = ηε, η = viscosity, ε = strain-rate

Effect increasing stress to strain-rate

(Modified from Park, 1989)

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Stress Strain

Limitation of The Concept of Stress in Structural Geology

• No quantitative relationship between t d t t istress and permanent strain

• Paleostress determination contain errors• No implication equation relating stress to strain rate that causes the deformation

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