introduction to geotechnical earthquake engineering … · module – 1 introduction to...

Module – 1

Introduction to Geotechnical

Earthquake Engineering

by

Dr. Deepankar Choudhury

Professor

Department of Civil Engineering

IIT Bombay, Powai, Mumbai 400 076, India.

Email: [email protected]

URL: http://www.civil.iitb.ac.in/~dc/

Lecture - 4

D. Choudhury, IIT Bombay, India

Fig. Location, year and number of fatalities (in parenthesis)

for earthquakes in India during 1800 – 2001

(Modified

after

Bilham and

Gaur, 2000)


Earthquake Distribution during 1800 to 2007, reference USGS


Seismic Zonation Map of India as per IS 1893: 2002, Part 1

Zone PGA

II 0.10g

III 0.20g

IV 0.25g

V 0.40g


Module – 2

Basics of Vibration

Theory

20


Reference:

NPTEL Video Course on

Soil Dynamics

Module – 2

by Prof. Deepankar Choudhury,

IIT Bombay, Powai, Mumbai, India.

21

Dynamic loads :

1. Earthquake load,

2. Wind load,

3. Moving load,

4. Guide way unevenness,

5. Machine induced load,

6. Blast load,

7. Impact load etc.

Vibration


Degrees of Freedom (DOF) o No of independent co-ordinates (displacements) required to define the

displaced position of all the masses relative to their all the position is

defined as degrees of freedom.

o Generally in Dynamics, mass property dictates the DOF whereas in

Statics , the stiffness property dictates the DOF

Examples

ln ( ) 4.141 0.868 1.09ln[ 0.0606exp(0.7 )]PHA g M R M


26

Simple Vibrating System (SDOF system)

Mass-Spring-Damper (MSD) System

m Kinetic Energy

k Potential Energy

c Dissipation

D’Allembart’s principle

For any object in motion, the externally applied forces, inertial force and

forces of resistance form a system of forces in equilibrium.

ln ( ) 4.141 0.868 1.09ln[ 0.0606exp(0.7 )]PHA g M R M


27

Linear Model for Equation of Motion

Governing Equation of Motion

Units MLT

system

FLT system SI unit

m M F/LT-2 kg

k MT-2 F/L N/m

c MT-1 F/LT-1 N-s/m

2

2. . . ( )d u du

m c k u p tdt dt

( )mu cu ku p t


28

Type of vibrations

Vibration

Free Vibration

[p(t) = 0)]

Forced Vibration

[p(t) = 0)]

Undampe

d (c = 0)

Damped

(c = 0)

Undampe

d (c = 0)

Damped

(c = 0)

Periodic Aperiodic

Transient (t tf) Steady state (t )


29

SDOF system

Free Vibration

1. Undamped Free Vibration

ln ( ) 4.141 0.868 1.09ln[ 0.0606exp(0.7 )]PHA g M R M

The structure is disturbed from its

static equilibrium and then vibrates

without any applied forces.

The equation of motion is:

The solution is: n nu(t) A cos( t) Bsin( t)

n k m (rad/s) natural circular frequency

A and B are determined by the initial conditions


30

ln ( ) 4.141 0.868 1.09ln[ 0.0606exp(0.7 )]PHA g M R M

t 0 o o

t 0 o o n

u u u A

u u u B

which can be written as nu(t) Csin( t )

2 2 o n oo o n

u uC u (u ) cos sin

C C

natural period n

n

2T (s)

πnatural frequency n

n

n

1f (Hz)

T 2π


31

Equation of motion: Earthquake excitation

ln ( ) 4.141 0.868 1.09ln[ 0.0606exp(0.7 )]PHA g M R M

S

D

t

I

f ku

f cu

f mu

0tmu cu ku


33 Prof. Deepankar Choudhury, Department of Civil Engineering, IIT Bombay, Mumbai, India

Forced Vibration: Response to Step Excitation

Now,

0 0

f(t) ( )

= 1, t>t

= 0, t<t

= 1/2, t=t

of motion

( )

(0) ,

(0)

a

a

a

a

u t t

Equation

mx cx kx Fu t

Initial conditions x x x x


Response to Step Excitation

(0) (0) 0x x

2 0

0

2

0

2

2

( )

= ( cos sin )

Using the initial conditions,

( ) 1 cos sin1

n

n

n n

t

D D

n

t

D D

Fx x x

m

x t CF PI

Fe A t B t

m

Fx t e t t

k


Forced Vibration due to Arbitrary excitation (Duhamel’s Integral)

0

0

0 0

0 00

( ) ( ) . ( - ) ( - ). ( )

, ( ) ( ). ( )

( )

= ( cos sin ) ( ). ( )

conditions, (0) , (0)

( )= ( cos

i

s n

n

n

t

t

t

D D

t nD D

d

dx t f d h t h t f d

So x t h t f d

x t CF PI

e A t B t h t f d

Initial x x x x

x xx t e x t

0

0

) ( ). ( )

1, ( ) .sin

, (0) 0, (0) 0

( ) ( ). ( ) Duhamel's Integral

n

t

t

D

d

t

t h t f d

where h t e tm

If x x

x t h t f d


Example Problem

1


For the system shown in Figure, mention (with reasoning) the

number of degrees of freedom for the system for a small

oscillation. Derive the governing equation of motion (from first

principle). Consider, mass of the linkage AB and other

connectors are negligible. Calculate the natural frequency and

natural period of vibration for the system if k1 = k2 = 90 N/m

and m1 = m2 = 10 kg. And c1 = c2 = 6 N-s/m. Estimate the

damped frequency, damped period, damping ratio of the

system.

2

IIT Bombay, DC 22

Module – 3

Engineering Seismology

IIT Bombay, DC 23

Seismology is the branch of Geophysics concerned

with the study and analysis of Earthquakes and the

science of energy propagation through the Earth's

crust.

Engineering Seismology is concerned with the

solution of engineering problems connected with the

Earthquakes. Seismology is extremely important

because:

•Study of earthquakes gives us important clues

about the earth’s interior

•Understanding earthquakes allows us to minimize

the damage and loss of life

What is Earthquake ?

• An earthquake is the result of a sudden release of energy in the Earth's

crust that creates seismic waves. Earthquake is also known as a quake,

tremor or temblor.

IIT Bombay, DC 25

What is an Earthquake?

An earthquake is the vibration of Earth

produced by the rapid release of accumulated

energy in elastically strained rocks

Energy released radiates in all directions from its

source, the focus

Energy propagates in the form of seismic waves

Sensitive instruments around the world record

the event

Focus and Epicenter of Earthquake

IIT Bombay, DC 27

What causes an Earthquake?

Movement of Tectonic Plates

Earth is divided into sections called Tectonic

plates that float on the fluid-like interior of the

Earth. Earthquakes are usually caused by

sudden movement of earth plates

Rupture of rocks along a fault

Faults are localized areas of weakness in the

surface of the Earth,sometimes the plate

boundary itself

Why an earthquake occurs?

• The earth's crust (the outer layer of the planet) is made up of several

pieces, called plates.

• The plates under the oceans are called oceanic plates and the rest

are continental plates

Earthquakes usually

occur where two plates

are running into each

other or sliding past

each other.

An image of the world's plates and their boundaries.

IIT Bombay, DC 29

Where do Earthquakes occur?

Plate boundaries

Faults

IIT Bombay, DC 30

Release of Accumulated energy

IIT Bombay, DC 31

The point within Earth

where faulting begins is

the focus, or hypocenter

The point directly above

the focus on the surface

is the epicenter

The Focus and Epicenter of an Earthquake

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