Post on 19-Apr-2018
Geotechnical Earthquake
Engineering
by
Prof. Deepankar Choudhury Professor, Dept. of Civil Engg.,
Indian Institute of Technology (IIT) Bombay
Powai, Mumbai 400076, India.
Email: dc@civil.iitb.ac.in
URL: http://www.civil.iitb.ac.in/~dc/
Lecture – 3 1
D. Choudhury, IIT Bombay, India
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
D. Choudhury, IIT Bombay, India
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
D. Choudhury, IIT Bombay, India
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
D. Choudhury, IIT Bombay, India
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
D. Choudhury, IIT Bombay, India
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
D. Choudhury, IIT Bombay, India
Tsunami Movement: ~800 kmph in deep water
~350 kmph in medium depth water
~50 kmph in shallow water
Tsunami
13
D. Choudhury, IIT Bombay, India
•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
D. Choudhury, IIT Bombay, India
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
D. Choudhury, IIT Bombay, India
Share of Earthquake Disaster in 20th Century
Walling and Mohanty (2009)
17
D. Choudhury, IIT Bombay, India
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
D. Choudhury, IIT Bombay, India
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
D. Choudhury, IIT Bombay, India
Force-displacement relation
ln ( ) 4.141 0.868 1.09ln[ 0.0606exp(0.7 )]PHA g M R M
D. Choudhury, IIT Bombay, India
Linear Elastic System (fs=ku)
ln ( ) 4.141 0.868 1.09ln[ 0.0606exp(0.7 )]PHA g M R M
D. Choudhury, IIT Bombay, India
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
D. Choudhury, IIT Bombay, India
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
D. Choudhury, IIT Bombay, India
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 )
D. Choudhury, IIT Bombay, India
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
D. Choudhury, IIT Bombay, India
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
D. Choudhury, IIT Bombay, India
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
D. Choudhury, IIT Bombay, India
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
D. Choudhury, IIT Bombay, India
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
34 Prof. Deepankar Choudhury, Department of Civil Engineering, IIT Bombay, Mumbai, India
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
35 Prof. Deepankar Choudhury, Department of Civil Engineering, IIT Bombay, Mumbai, India
Response to Step Excitation
a. Now, for = 0 0 ( ) (1 cos ) D
Fx t t
k
For undamped forced vibration,
Dynamic displacement = 2 x Static displacement
36 Prof. Deepankar Choudhury, Department of Civil Engineering, IIT Bombay, Mumbai, India
Response to Step Excitation
b. Now, for 0
37 Prof. Deepankar Choudhury, Department of Civil Engineering, IIT Bombay, Mumbai, India
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