kuliah 3 stressa 29 08 2007 - centre for petroleum studies ... · program studi teknik geologi...

Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian

Institut Teknologi Bandung

Stress-1 BS/03/02 Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian


Stress-2 BS/03/02

Stress (σ)• Stress (σ) = F/A dimana A=luas permukaan• Unit stress yang umum adalah pascal (KPa, MPa, GPa), bar atau dalam

skala luas seperti psi (pound per square inch) dan kg/cm2

• Stress untuk batuan didalam bumi: σ = ρgh (lithostatic stress)• Stress pada suatu titik dapat dibagi menjadi normal (σn) dan shear (σs)

stress komponen• Stress dapat bersifat compressive (+) dan tensile (-) • Shear stress dalam system kopel akan positive bila searah jarum jam dan

negative bila berlawanan arah jarum jam• Stress 2D disuatu titik digambarkan sebagai stress ellipse• Stress 3D disuatu titik digambarkan sebagai stress ellipsoid• Principles stress : σ1> σ 2> σ 3

• Koordinat sumbu utama stress (x1,x2,x3) adalah sejajar dengan stress utama



Stress-3 BS/03/02

StressStress StrainStrain



Stress-4 BS/03/02

STRESS vs. STRAINSTRESS vs. STRAIN



Stress-5 BS/03/02

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



Stress-6 BS/03/02

Limitation of The Concept of StressLimitation of The Concept of Stressin Structural Geologyin Structural Geology



Stress-7 BS/03/02 Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian


Stress-8 BS/03/02

TECTONICS AND STRUCTURAL GEOLOGY

• Study of rock Deformation as Response to Forces and Stresses

• Involving Motion of Rigid Body

FACTOR CONTROLING DEFORMATION• SCALE FACTOR

• RHEOLOGY

• TIME FACTOR

Deformation = Translation + Rotation + Dilation + Distortion

• DESCRIPTIVE ANALYSIS

• KINEMATIC ANALYSIS

• DYNAMIC ANALYSIS



Stress-9 BS/03/02

TECTONICS AND STRUCTURAL GEOLOGY

NEW CONCEPTS IN TECTONIC AND STRUCTURAL GEOLOGY

• LINKED FAULT AND FOLD SYSTEMS1. Geometric2. Kinematic3. Dynamic

• PROGRESSIVE DEFORMATION

• SCALE INDEPENDENCE IN BRITTLE DEFORMATION

• STRUCTURAL INHERITANCE



Stress-10 BS/03/02

Twiss and Moores, 1992



Stress-11 BS/03/02

SCALE FACTOR

STRUCTURAL GEOLOGY DATAFOLLOW FRACTAL RELATIONSHIP

Plates

Aerial Photograph

Km-Scale Fold

m-Scale Fold



Stress-12 BS/03/02

Geologic Cross-Sectionand

Seismic Section

5 Km

10Km



Stress-13 BS/03/02

(Modified from Means, 1976)

Deformation of rock in various scale



Stress-14 BS/03/02

EVOLUTION OF STRUCTURE

Single Particle Particles

• Force history• Movement history



Stress-15 BS/03/02

DESCRIPTIVE ANALYSIS

• CONTACTS

• PRIMARY STRUCTURES

• SECONDARY STRUCTURES

THREE TYPES OF STRUCTURES



Stress-16 BS/03/02

RHEOLOGY

• BRITTLE • DUCTILE



Stress-17 BS/03/02

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)



Stress-18 BS/03/02

Force Equilibrium

(A) Balance

(B) Torque

(C) Static Equilibrium

(D) Dynamic Equilibrium

(Davis and Reynolds, 1996)



Stress-19 BS/03/02

STRESS

Stress defined as force per unit area:

σ = F/AA = area, Stress units = Psi, Newton (N),

Pascal (Pa) or bar (105 Pa)

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



Stress-20 BS/03/02

Z

WV

W

RV



Stress-21 BS/03/02

STRESS

• Stress at a point in 2D • Types of stress

Stre

ss (σ

)

Norm

al S

tress

(σn)

Shear Stress (σs )

Normal stress (σN)

(+) Compressive (-) TensileShear stress (σS)

(+) (-)



Stress-22 BS/03/02

STRESS on PLANE

• Coordinate System



Stress-23 BS/03/02

Stress Ellipsoid

a) Triaxial stress

b) Principal planes ofthe ellipsoid

(Modified from Means, 1976)



Stress-24 BS/03/02

Arbitrary coordinate axes and planes

C. General stress components

B. Principal stress components

X

Principal coordinate axes and planes

Z

X1

σ1

Σ

(lft)xx

(lft)x

σ

(top)zzσ

dx

σ (bot)zz

dz

σ(top)zx

σ(rt)xz

Σ(bot)z

σ(rt)xx

σ(bot)zx

(lft)xzσ

Σ(rt)x

X3

σ3

Σ(top)z

A. Stress elipse

Σz σ1

σ3 ΣxThe State of

Two-Dimensional Stress at Point

(Twiss and Moores, 1992)

Principal Stress:σ1 > σ3

Σx, Σz = Surface Stress



Stress-25 BS/03/02

B. Principal stress components

σ1

z

x

σ3

x1

x3

y

yx2

x

x

y

z

σ2

x

σzy

σxy σyyσyz

σyx

σxx

σzx

σzz

σxz

z

y

Arbitrarycoordinate planes

A. Stress elipsoid

C. General stress components

z

Principalcoordinate planes

The State of 3-Dimensional Stress at Point Principal Stress:

σ1 > σ2 > σ3

Stress Tensor Notation

σ11 σ12 σ13

σ = σ21 σ22 σ23σ31 σ32 σ33

σ12 = σ21, σ13 = σ31, σ23 = σ32




Stress-26 BS/03/02

Geologic Sign Convention of Stress Tensor




Stress-27 BS/03/02

σn

r

n

(p) σn (p)

σ s

2

2

σ −σ 1 3

2σ +σ 1 3

σn

(σn , (p)

σ1

(p)σ )s

σ −σ 2θ1 3 cos2

σ −σ 2θ1 3 sin

σs

2θx3

(p)σ s

(p)σ n

σ3

θ

σ1

Plane P

x

σ3

Mohr Diagram 2-D

A. Physical Diagram A. Mohr Diagram




Stress-28 BS/03/02

− α

x3

n'

p

(p')θ

p'

nx1

α

−2α

(σn , (p')

σs

σn

2ασ )s

σ1

σn

σ3

(p)(σn , (p)σ )s

2θ

A. Physical Diagram B. Mohr Diagram


Mohr Diagram 2-D



Stress-29 BS/03/02

(σ σ )xx' xz

2θ

σxx

(σ σ )zz' zx

2(σ + σ )xx zz

(σ −σ )xx zz

σs

σ1σn

2σxz

(θ + 90º)

α σ1

σ3

σzz

σzx

z

σ3

θ

x3

x1

x

σxz

2 (θ + 90º)2α

A. Physical Diagram B. Mohr Diagram


Mohr Diagram 2-D



Stress-30 BS/03/02

n-

Planes of maximumshear stress

Clockwiseshear stress

x3

x1

σs σs

Counterclockwiseshear stress

θ' = +45º

σ1

x3σ3

σ1

n+

σs

x1

θ = +45º

σ1σ32θ = +90º σn

σ s max

Clockwise

2θ = −90' º

σ s max

Counter clockwise

σ3

B. Mohr DiagramA. Physical Diagram

Planes of maximum shear stress

Mohr Diagram 2-D




Stress-31 BS/03/02

Mohr Diagram 3-D


Geometry of a three-dimensionalStress on a Mohr diagram



Stress-32 BS/03/02

Mohr Diagram 3-D

Maximum Shear Stress




Stress-33 BS/03/02

Stress Ellipsoid

FUNDAMENTAL STRESS EQUATIONS

Principal Stress:σ1 > σ2 > σ3

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

σ1 + σ3 - σ1 – σ3σN = cos 2θ2 2

σs = Sin 2θσ1 – σ3

2



Stress-34 BS/03/02

• 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)



Stress-35 BS/03/02

0

0

0

0

0 0a

b

c

0

00

0 0a

a

b

0

00

0

0

a

b

b

0

00

0 0a

p 00

0 p0

0 0p

0 00

0 -a0

0 00

F. Triaxial stressD. Axial or confinedcompression

E. Axial extension or extensional stress

σn

p

σs

σn

σs

σ = σ = σ1 2 3

σ2

0

0

σ = σ2 3

σs

σnσ1σ = σ1 2

σs

σnσ3

σ1

σ3

0

σs

σnσ3 σ3σ3

0

0

σs

σn

σ2

σ1σ3

C. Uniaxial tensionA. Hydrostatic stress B. Uniaxial compression

Image of Stress



Stress-36 BS/03/02

0 00

0 -a0

0

0

a

σs

Δ 3σ

Δ 1σ

σn

σn

σ1σ3 σn

σs

σ3

0

Δ 3σ

σ − σ3 n

=0

0Δ 1σ σ − σ1 n 0

σs

σ1 σnσ3 σ2

σ3 σ1 σ3 σ1 σn

Dσ = σ − σ1 3

DσDσ Dσ

σs

σ1 σn

σ1

σ2

σ3

Eσ 2

σ −2 pf

Eσ 3 Eσ1

pf

Eσ 2

0 Eσ 3

Eσ 1

0=00

0 000

0

000 σ −3 pf

σ −1 pf

Applied

G. Pure shear stress H. Deviatoric stress (two-dimensional)

I. Differential stress (Three examples)

J. Effective stress

Effective

AppliedDeviatoric

Image of Stress



Stress-37 BS/03/02

• Body force works from distance and depends on the amount of materialsaffected (i.e. gravitational force).

• Surface force are classes as compressive or tensile according to thedistortion they produce.

• Stress is defined as force per unit area.• Stress at the point can be divided as normal and shear component

depending they direction relative to the plane.• Structural geology assumed that force at point are isotropic and

homogenous• Stress vector around a point in 3-D as stress ellipsoid which have three

orthogonal principal directions of stress and three principal planes. • Principal stress σ1>σ2>σ3

• The inequant shape of the ellipsoid has to do with forces in rock and hasnothing directly to do with distortions.

• Mohr diagram is a graphical representative of state of stress of rock

STRESS



Stress-38 BS/03/02

kuliah 3 stressa 29 08 2007 - centre for petroleum studies ... · program studi teknik geologi...

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