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Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
Stress-1 BS/03/02 Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
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
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
Stress-3 BS/03/02
StressStress StrainStrain
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
Stress-4 BS/03/02
STRESS vs. STRAINSTRESS vs. STRAIN
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
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
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
Stress-6 BS/03/02
Limitation of The Concept of StressLimitation of The Concept of Stressin Structural Geologyin Structural Geology
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
Stress-7 BS/03/02 Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
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
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
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
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
Stress-10 BS/03/02
Twiss and Moores, 1992
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
Stress-11 BS/03/02
SCALE FACTOR
STRUCTURAL GEOLOGY DATAFOLLOW FRACTAL RELATIONSHIP
Plates
Aerial Photograph
Km-Scale Fold
m-Scale Fold
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
Stress-12 BS/03/02
Geologic Cross-Sectionand
Seismic Section
5 Km
10Km
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
Stress-13 BS/03/02
(Modified from Means, 1976)
Deformation of rock in various scale
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
Stress-14 BS/03/02
EVOLUTION OF STRUCTURE
Single Particle Particles
• Force history• Movement history
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
Stress-15 BS/03/02
DESCRIPTIVE ANALYSIS
• CONTACTS
• PRIMARY STRUCTURES
• SECONDARY STRUCTURES
THREE TYPES OF STRUCTURES
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
Stress-16 BS/03/02
RHEOLOGY
• BRITTLE • DUCTILE
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
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)
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
Stress-18 BS/03/02
Force Equilibrium
(A) Balance
(B) Torque
(C) Static Equilibrium
(D) Dynamic Equilibrium
(Davis and Reynolds, 1996)
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
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)
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
Stress-20 BS/03/02
Z
WV
W
RV
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
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)
(+) (-)
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
Stress-22 BS/03/02
STRESS on PLANE
• Coordinate System
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
Stress-23 BS/03/02
Stress Ellipsoid
a) Triaxial stress
b) Principal planes ofthe ellipsoid
(Modified from Means, 1976)
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
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
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
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
(Twiss and Moores, 1992)
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
Stress-26 BS/03/02
Geologic Sign Convention of Stress Tensor
(Twiss and Moores, 1992)
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
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
(Twiss and Moores, 1992)
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
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
(Twiss and Moores, 1992)
Mohr Diagram 2-D
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
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
(Twiss and Moores, 1992)
Mohr Diagram 2-D
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
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
(Twiss and Moores, 1992)
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
Stress-31 BS/03/02
Mohr Diagram 3-D
(Twiss and Moores, 1992)
Geometry of a three-dimensionalStress on a Mohr diagram
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
Stress-32 BS/03/02
Mohr Diagram 3-D
Maximum Shear Stress
(Twiss and Moores, 1992)
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
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
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
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)
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
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
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
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
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
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
Program Studi Teknik GeologiFakultas Ilmu dan Teknologi Kebumian
Institut Teknologi Bandung
Stress-38 BS/03/02