Lecture # 10

*STRUCTURAL GEOLOGY

What is Structural Geology??• Study of the architecture and geometry of the

Earth’s crust and processes which have shaped it

• Analysis of changes in shape of rock bodies (strain)

produced by tectonic forces (stress)Stress Strain

• Study of rock Deformation as Response to Forces and Stresses

• Involving Motion of Rigid Body

Structural AnalysisStructural analysis generally involves three tasks:

1. Descriptive Analysis: physical and geometrical description of rock structures (e.g. folds, faults etc)

2. Kinematic Analysis: evaluation of the displacement andchange in shape, orientation and size that rocks undergo as a result of deformation (strain)

3. Dynamic Analysis: reconstruct forces and stresses which resulting rock deformation and failure (stress)

(Modified from Means, 1976) in Sapiee. B., 2005

Deformation of rock in various scale

EVOLUTION OF STRUCTURE

Single Particle Particles

• Force history• Movement history

Factors involve:

• SCALE FACTOR (mm to km)

• RHEOLOGY (flow of matter)

• TIME FACTOR (Geologic Time Scale)

Why Important?

Geologic Cross-Sectionand

Seismic Section

5 Km

DESCRIPTIVE ANALYSIS (Fold, Fault)• CONTACTS

• PRIMARY STRUCTURES

• SECONDARY

STRUCTURES

Primary structures are features of rocks that form at or shortly after the time of formation of the rock itself.

They are important:i. to determine to original facing

direction of strata; ii. can be used as strainmarkers in

deformed rocks; iii. some primary features (fossils)

are useful in age determination;iv. interpret the environmet

conditions under which the rock was formed;

v. recognize primary features and distinguish them from later tectonic features.

Bedding• Graded beds• Ripple marks• Crossbeds• Sole marks• Channel structures• Mud cracks• Fossils (tracks, imprints, body fossils)• Impact features (raindrop imprints, volcanic bombs etc)• De-watering (flame) structures• Soft-sediment deformation• Reduction spotsIgneous structures• Columnar jointing• Flow surface features (rubble layers, ropey texture, baked horizons)• Pillow basalts

Primary Structure

• Secondary rock structures are imposed on rocks by events (such as compression or stretching) experienced by rocks after their original formational.

• The structures are most easily observed if the rocks have obvious primary structures, such as layering formed by successive episodes of deposition.

• Primary depositional layering is almost always horizontal: it parallels the general configuration of surface on which deposition takes place, such as a floodplain or the floor of a lake or ocean. In consequence, when layers are found that are not horizontal, the geologist assumes that some force has been exerted upon them that has destroyed their original horizontality.

Secondary Structure

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)

• F= m x a , gravitational acceleration: 9.8 m/sec2 •vector quantity: orientation and size. •can be applied to any plane. •normal and shear components on a plane can be resolved from an oblique force (see diagram to the right). •shear component promotes slip on the plane and the normal component inhibits slip on a plane, and the ratio of the two at which slip occurs describes the 'friction' on the plane. Pressure within a geologic context:•describes multitude of forces at a point within a fluid. •limit of F/area as area goes to 0 •fluids can not withstand a shear stress for a significant period of time, therefore if static non-flowing, all force vectors equal in size, and all must be normal vectors acting perpendicular to any given plane. Hence can be described by one number. •this is a special simple stress state - hydrostatic stress state. •geologic pressures: pore fluid pressures, magmatic pressures, 'rock pressure' = nondeviatoric component. •related strain? change in volume, no distortion (unless material is anisotropic with respect to mechanical properties).

Force Equilibrium

(A) Balance

(B) Torque

(C) Static Equilibrium

(D) Dynamic Equilibrium

(Davis and Reynolds, 1996)

STRESSStress defined as force per unit

area:

s = F/A

A = area,

Stress units = Psi, Newton (N),

Pascal (Pa) or bar (105 Pa)

Stress is force/area (hitting with a hammer)

Importance of area: Think of difference between standing on water bed in high heels or sneakers

Stress Three kinds of stress can be applied to rocks: tensional, compressive, and shear.

Tensional stress occurs when a rock is subjected to forces that tend to elongate it or pull it apart; a rock that has experienced tensional stress tends to be narrower and longer than its original shape, like a piece of gum or taffy that has been pulled (pulled apart)

A compressive stress on a rock is applied from opposite sides and has a tendency to shorten (compress) the rock between the opposing stresses, which may also stretch it parallel to the stress-free direction. (push together)

A shear stress results when forces from opposite directions create a shear plane in an area in which the forces run parallel to one another. The scale of shear stress can vary from a few centimeters to hundreds of meters. (moved horizontally past each other)

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

Str

ess (

s)

Norm

al Str

ess

(s n

)

Shear Stress (ss)

Normal stress (sN)

(+) Compressive (-) TensileShear stress

(sS)

(+) (-)

Sapiee. B., 2005

STRESS on PLANE

• Coordinate System

Stress Ellipsoid

a) Triaxial stress

b) Principal planes of the ellipsoid

(Modified from Means, 1976) in Sapiee. B., 2005

Arbitrary coordinate axes and planes

C. General stress components

B. Principal stress components

X

Principal coordinate axes and planes

Z

X1

(lft)xx

(lft)x

(top)zz

dx

(bot)zz

dz

(top)zx

(rt)xz

(bot)z

(rt)xx

(bot)zx

(lft)xz

(rt)x

X3

3

(top)z

A. Stress elipse

z

3 xThe State of

Two-Dimensional Stress at Point

(Twiss and Moores, 1992)

Principal Stress:

s1 > s3

Sx, Sz = Surface Stress

B. Principal stress components

z

x

3

x1

x3

y

yx2

x

x

y

z

x

zy

xy yyyz

yx

xx

zx

zz

xz

z

y

Arbitrarycoordinate planes

A. Stress elipsoid

C. General stress components

z

Principalcoordinate planes

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

s1 > s > s3

Stress Tensor Notation

s11 s12 s13

s = s21 s22 s23

s31 s32 s33

s12 = s21, s13 = s31, s23 = s32

(Twiss and Moores, 1992)

Geologic Sign Convention of Stress Tensor(Twiss and Moores, 1992)

n

r

n

(p) n (p)

s

2

2

3

2 3

n

n , (p)

(p) s

3 cos2

3 sin

s

x3

(p) s

(p) n

3

Plane P

x

3

Mohr Diagram 2-D

A. Physical Diagram A. Mohr Diagram

(Twiss and Moores, 1992)

x3

n'

p

(p')

p'

nx1

n , (p')

s

n

s

n

3

(p)n , (p) s

A. Physical Diagram B. Mohr Diagram

(Twiss and Moores, 1992)

xx' xz

xx

zz' zx

2 xx zz

xx zz

s

n

xz

º)

3

zz

zx

z

3

x3

x1

x

xz

º)

A. Physical Diagram B. Mohr Diagram

(Twiss and Moores, 1992)

n-

Planes of maximumshear stress

Clockwiseshear stress

x3

x

s s

Counterclockwiseshear stress

' = +45º

x33

n+

s

x

= +45º

3 º n

s max

Clockwise

' º

s max

Counter clockwise

3

B. Mohr DiagramA. Physical Diagram

Planes of maximum shear stress

(Twiss and Moores, 1992)

Mohr Diagram 3-D

(Twiss and Moores, 1992)

Geometry of a three-dimensionalStress on a Mohr diagram

Maximum Shear Stress

(Twiss and Moores, 1992)

Stress Ellipsoid

FUNDAMENTAL STRESS EQUATIONS

Principal Stress:s1 > s > s3

• All stress axes are mutually perpendicular• Shear stress are zero in the direction of principal stress s1 + s3 - s1 – s3

sN = cos 2q2 2

ss = Sin 2qs1 – s3

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)

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

n

p

s

n

s

3

0

0

3

s

n

s

n3

3

0

s

n3 33

0

0

s

n

3

C. Uniaxial tensionA. Hydrostatic stress B. Uniaxial compression

Image of Stress

0 00

0 -a0

0

0

a

s

3

n

n

3 n

s

3

0

3

3 n

=0

0 n 0

s

n3

3 3 n

D 3

DD D

s

n

3

E

pf

E 3 E

pf

E

0 E 3

E

0

=00

0 00

0

0

0

0

0 3 p f

pf

Applied

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

I. Differential stress (Three examples)

J. Effective stress

Effective

AppliedDeviatoric

From where does stress come?

Motions of tectonic plates on Earth’s surface

Deformation primarily occurs alongplate boundaries

Body force works from distance and depends on the amount of materials affected (i.e. gravitational force). Surface force are classes as compressive or tensile according to the distortion 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 s1>s2>s3

The inequant shape of the ellipsoid has to do with forces in rock and has nothing directly to do with distortions. Mohr diagram is a graphical representative of state of stress of rock

STRESS

Questions…