geologi-struktur-4

7/21/2019 GEOLOGI-STRUKTUR-4

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FORCES AND VECTORS

Force is any action which alters, or tends to alter

Newton II law of motion : F = M a

Unit force : kgm/s2

= newton (N) or dyne = gram cm/s2

; N = 105

dynes

BASIC CONCEPTS

(a). Force: vector quantity with magnitude and direction

(b). Resolving by the parallelogram of forces

Modified Price and Cosgrove (1990)

Two Types of Force

Body Forces (i.e. gravitational force)

Contact Forces (i.e. loading)


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Force Equilibrium

(A) Balance

(B) Torque

(C) Static Equilibrium

(D) Dynamic Equilibrium

(Davis and Reynolds, 1996)

STRESS

Stress defined as force per unit area:

s = F/A

A = area, Stress units = Psi, Newton (N),

Pascal (Pa) or bar (105 Pa)

(Davis and Reynolds, 1996)(Twiss and Moores, 1992)


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STRESS

Stress at a point in 2D

Types of stress

Stress

(

)

Normal stress (sN)

(+) Compressive (-) Tensile

Shear stress (sS)

(+) (-)

STRESS on PLANE

Coordinate System


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Stress Ellipsoid

a) Triaxial stress

b) Principal planes of

the ellipsoid

(Modified from Means, 1976)

Arbitrary coordinateaxes and planes

C. General stress components

B. Principal stress components

X

Principal coordinateaxes and planes

Z

X1

s

(lft)xx

(lft)x

s

(top)zz

s

dx

s (bot)zz

dz

s(top)zx

s(rt)xz

(bot)z

s(rt)xx

s(bot)zx

(lft)xz

s

(rt)x

X3

s3

(top)z

A. Stress elipse

z s

s3

xThe State of

Two-Dimensional

Stress at Point

(Twiss and Moores, 1992)

Principal Stress:

s1> s3

x, z = Surface Stress


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B. Principal stress components

s

z

x

s3

x1

x3

y

yx2

x

x

y

z

s

x

szy

sxy syysyz

syx

sxx

szx

szz

sxz

z

y

Arbitrarycoordinate planes

A. Stress elipsoid

C. General stress components

z

Principalcoordinate planes

The State of3-Dimensional

Stress at Point Principal Stress:

s1> s

> s

3

Stress Tensor Notation

s11 s12 s13

s = s21 s22 s23s31 s32 s33

s12 = s21, s13 = s31, s23 = s32


Geologic Sign

Convention of

Stress Tensor



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sn

r

n

(p ) sn(p)

ss

2

2

s s 32

s s 3

sn

sn,(p)

s

(p)s s

s s 3 cos

2

s s 3 sin

ss

x3

(p)ss

(p )sns3

s

Plane P

x

s3

Mohr Diagram 2-D

A. Physical Diagram A. Mohr Diagram


x3

n'

p

(p')

p'

nx1

sn,(p')

ss

sn

s s

ssn

s3

(p)sn,(p)s s

A. Physical Diagram B. Mohr Diagram


Mohr Diagram 2-D


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s s xx' xz

sxx

s s zz' zx

2

s s xx zz

s s xx zz

ss

s snsxz

)

s

s3

szz

szx

z

s3

x3

x1

x

sxz

)

A. Physical Diagram B. Mohr Diagram


Mohr Diagram 2-D

n-

Planes of maximum

shear stress

Clockwise

shear stress

x3

x

ss ss

Counterclockwise

shear stress

' = +45

s

x3s3

sn

+

ssx

= +45

ss3 sn

ss max

Clockwise

'

ss maxCounter clockwise

s3

B. Mohr DiagramA. Physical Diagram

Planes of maximum shear stress

Mohr Diagram 2-D



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Mohr Diagram 3-D


Geometry of a three-dimensional

Stress on a Mohr diagram

Mohr Diagram 3-D

Maximum Shear Stress



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Stress Ellipsoid

FUNDAMENTAL STRESS EQUATIONS

Principal Stress:

s1> s

> s

3

All stress axes are mutually perpendicular Shear stress are zero in the direction of

principal stress

s1 + s3 s1s3sN = cos 22 2

ss = Sin 2s1s3

2

+

Mohr diagram is a graphical representative of state of stress Mean stress is hydrostatic component which tends to produce dilation Deviatoric stress is non hydrostatic which tends to produce distortion

Differential stress, if greater is potential for distortion

(Davis and Reynolds, 1996)


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1. Gaya yang bekerja tergantung besarnya material yang terkena gaya

tersebut (grafitasi)

2. Stress adalah Sataun gaya persatuan luas

3. Stress pada suatu titik dapat terbagi dua yaitu :

Stress Normal

Stress Geser

4. Asumsi Struktur Geologi pada suatu titik bersifat isotropic dan

homogen.

5. Vektor Stress pada 3D merupakan stres ellipsoid yang memiliki tiga

arah orthogonal stres dan tiga bidang utama.

6. Prinsip stress s1>s2>s3

7. Diagram Mohr adalah grafik yang menerangkan Stress pada suatu

batuan

STRESS

STRESS vs. STRAIN


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Relationship Between Stress and Strain

Evaluate Using Experiment of Rock

Deformation Rheology of The Rocks Using Triaxial Deformation Apparatus Measuring Shortening Measuring Strain Rate Strength and Ductility

2 3 4 61

C

Strain (in %)

DifferentialStress(inMPa)

ReptureStrength

400

5

100

200

300Yield

Strength

UltimateStrength

Yield StrengthAfter StrainHardening

D

A

EB

Stress Strain Diagram

A. Onset plastic deformation

B. Removal axial load

C. Permanently strained

D. Plastic deformation

E. Rupture


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0 2 4 6 8 10 12 14 16

Diffe

rentialStress,

MPa

Strain, percent

300

200

100

70

20

Crown Point Limestone

40

140130

60

80

5 10 15

2000

1500

1000

0Strain (in %)

800C

700C

500C

300C

500Differen

tialStress(inMPa)

25C

Effects of Temperature and Differential Stress

(Modified from Park, 1989)

Deformation and Material

A. Elastic strain

B. Viscous strain

C. Viscoelastic strain

D. Elastoviscous

E. Plastic strain

Hookes Law: e = s/E, E = Modulus Young or elasticity

Newtonian :s

=h

e

h

viscosity, e = strain-rate


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(Modified from Park, 1989)

Effect increasing stress to strain-rate

Stress Strain


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Limitation of The Concept of Stress in Structural Geology

No quantitative relationship between

stress and permanent strain

Paleostress determination contain

errors

No implication equation relating

stress to strain rate that causes the

deformation

geologi-struktur-4

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