Geotechnical Earthquake Engineering - NPTELnptel.ac.in/courses/105101134/downloads/Lec-03.pdf · Geotechnical Earthquake Engineering by ... Dept. of Civil Engg., Indian Institute

Geotechnical Earthquake

Engineering

by

Prof. Deepankar Choudhury Professor, Dept. of Civil Engg.,

Indian Institute of Technology (IIT) Bombay

Powai, Mumbai 400076, India.

Email: [email protected]

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

Lecture – 3 1

D. Choudhury, IIT Bombay, India

Module – 1

Introduction to Geotechnical

Earthquake Engineering

2


Fukui 1948 Earthquake, Liquefaction Failure

Soil Liquefaction

Termed liquefaction, the

strength of the soil reduced,

often dramatically, to the point

where it is unable to support

structures or remain stable.

3


Nigata 1964 Earthquake, Liquefaction and Bearing Failure

Collapsed Buildings (Kawagishicho Apartments) due to Soil Liquefaction Accelerometers: At bldg. top: 184 Gal, At bldg base: 159 Gal

340 RC Buildings were damaged in Niigata City. The damage ratio of RC building is 22%.

4


Data of Kobe 1995 Earthquake

5

D. Choudhury, IIT Bombay, India 6


Sand blow in mud flats used for salt production southwest of Kandla Port, Gujarat

Sand Boil: Ground water rushing to the surface due to liquefaction

7


Principal Types of Earthquake Damage

Landslides

Can occur due to liquefaction

Can occur in non-liquefiable soil

8

D. Choudhury, IIT Bombay

Devastating effect of earthquake on slope stability

during San Fernando 1971 earthquake

Courtesy: EERC library, UC Berkeley

Earthquake Destruction: Landslides

9

Earthquake Destruction: Retaining Structure Failure

September 1999 Chi Chi Earthquake, Taiwan

10

Earthquake Destruction: Lifelines

11


Earthquakes

sometimes cause fire

due to broken gas lines,

contributing to the loss

of life and economy.

The destruction of lifelines

and utilities make

impossible for firefighters to

reach fires started and

make the situation worse

eg. 1989 Loma Prieta

1906 San Francisco

Earthquake Destruction: Fire

12


Tsunami Movement: ~800 kmph in deep water

~350 kmph in medium depth water

~50 kmph in shallow water

Tsunami

13


•Geomorphological changes are often caused by an

earthquake: e.g., movements--either vertical or horizontal--

along geological fault traces; the raising, lowering, and

tilting of the ground surface with related effects on the flow

of groundwater;

•An earthquake produces a permanent displacement across

the fault.

•Once a fault has been produced, it is a weakness within

the rock, and is the likely location for future earthquakes.

•After many earthquakes, the total displacement on a large

fault may build up to many kilometers, and the length of the

fault may propagate for hundreds of kilometers.

Geomorphological Changes

14

List of

Major

Historic

Earthqu

akes in

World

Year Location Deaths Magnitude

1556 China 5,30,000 8.0

1906 San Francisco 700 7.9

1960 S. Chile 2,230 9.5

1964 Alaska 131 9.2

1976 China 7,00,000 7.8

1985 Mexico City 9,500 8.1

1989 California 62 7.1

1995 Kobe 5,472 7.2

2001 Gujarat, India 1,00,000 7.7

2004 Sumatra 2,20,000 9.1

2005 Pakistan 1,00,000 7.6

2008 China 90,000 7.9

2010 Haiti 2,22,000 7.0

2010 Chile 50,000 8.8

2011 Japan 1,00,000 9.1 15


Table: Worldwide largest and deadliest earthquakes during 2000 to 2010 Largest Earthquakes Deadliest Earthquakes

Date

Magn

it

u

d

e

Fataliti

es Region Date Magnitude Fatalities Region

February 27,

2010 8.8 507

Offshore

Maule,

Chile

January 12, 2010 7.0 222,570 Haiti

September

29, 2009 8.1 192

Samoa Islands

region September 30, 2009 7.5 1,117

Southern

Sumatra,

Indonesi

a

May 12, 2008 7.9 87,587

Eastern

Sichuan,

China

May 12, 2008 7.9 87,587

Eastern

Sichuan,

China

September

12, 2007 8.5 25

Southern

Sumatera

,

Indonesia

August 15, 2007 8.0 514

Near the

Coast of

Central

Peru

November 15,

2006 8.3 0 Kuril Islands May 26, 2006 6.3 5,749

Java,

Indonesi

a

Choudhury, D. (2010) in Structural Longivity. 16


Share of Earthquake Disaster in 20th Century

Walling and Mohanty (2009)

17


Hough and Bilham, 2005

Earthquake Fatalities vs. Magnitude

18


End of

Module – 1

19


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


Force-displacement relation

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


Linear Elastic System (fs=ku)

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


32

Equation of motion: Earthquake excitation (Cont)

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

The motion can be replaced by the effective earthquake force.

( )effmu cu ku p t


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



a. Now, for = 0 0 ( ) (1 cos ) D

Fx t t

k

For undamped forced vibration,

Dynamic displacement = 2 x Static displacement



b. Now, for 0


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


End of

Module – 2

38

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