Geotechnical Earthquake Engineering · → Combined Pile-Raft Foundation (CPRF) Katzenbach et al....

Geotechnical Earthquake

Engineering

by

Dr. Deepankar Choudhury Humboldt Fellow, JSPS Fellow, BOYSCAST Fellow

Professor

Department of Civil Engineering

IIT Bombay, Powai, Mumbai 400 076, India.

Email: [email protected]

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

Lecture – 43

IIT Bombay, DC 2

Module – 9

Seismic Analysis and

Design of Various

Geotechnical Structures

3

Latest News on Major

Earthquake in Iran A M7.8 earthquake occurred on the

afternoon of Tuesday, April 16, 2013

in southeastern Iran, near the Pakistan

border. Strong ground motions

extended more than 150 miles from

the epicenter, and the earthquake was

widely felt in the region. Preliminary

reports indicate dozens of fatalities

and more than 850 people injured,

with damage concentrated in the

immediate area of the earthquake. The

sparsely populated and remote region

of this earthquake has limited the

potential for broader effects from this

event

Event Time

1.2013-04-16 10:44:20 UTC

2.2013-04-16 15:14:20 UTC+04:30 at epicenter

3.2013-04-16 16:14:20 UTC+05:30 system time

Location

28.107 N 62.053 E depth=82.0km (51.0mi)

Nearby Cities

1.83km (52mi) E of Khash, Iran

2.168km (104mi) NE of Iranshahr, Iran

3.192km (119mi) SE of Zahedan, Iran

4.232km (144mi) SSW of Rudbar, Afghanistan

5.606km (377mi) NE of Muscat, Oman

Source: http://earthquake.usgs.gov

Source: http://earthquake.usgs.gov 4

Tectonic Summary (as per USGS) of M7.8

Iran Earthquake The April 16, 2013 M 7.8 earthquake east of Khash, Iran, occurred as a result of normal

faulting at an intermediate depth in the Arabian plate lithosphere, approximately 80 km

beneath the Earth's surface.

Regional tectonics are dominated by the collisions of the Arabian and India plates with

Eurasia; at the longitude of this event, the Arabian plate is converging towards the

north-northeast at a rate of approximately 37 mm/yr with respect to the Eurasian

plate. Arabian plate lithosphere is subducted beneath the Eurasian plate at the Makran

coast of Pakistan and Iran, and becomes progressively deeper to the north.

The subducted Arabian plate is known to be seismically active to depths of about 160

km. The frequency of moderate and large earthquakes within the subducted Arabian

plate is not high compared with similar events in some other subducted plates

worldwide, but several earthquakes have occurred within this slab in the region of

today's event over the past 40 years, including a magnitude 6.7 shock 50 km to the south

in 1983. In January of 2011, a M 7.2 earthquake occurred approximately 200 km to the

east, in a similar tectonic environment to the April 16 earthquake.

Source: US Geological Survey (USGS) website 5

USGS Shake Map at Iran-Pakistan

Boarder for 16.04.2013 M7.8 Earthquake

USGS Shake Map shows maximum

shaking intensity of VIII (Severe) on

the Modified Mercalli Intensity

(MMI) Scale, with potentially heavy

damage expected. USGS PAGER

estimates a population of about 2,000

were exposed to this severe (MMI

VIII) earthqauke and 377,000 to very

strong shaking (MMI VII) with

moderate to heavy damage potential.

Earthquake ruptures at depth (an

estimated 80 km) tend to present

lower ground motions in the epicentral

region than do shallower earthquakes.

Combined Pile – Raft

Foundation (CPRF)

Under Earthquake Conditions

→ Combined Pile-Raft Foundation (CPRF) Katzenbach et al. (2009)

Settlements calculated for a shallow foundation:

s > 40 cm

z = 0 - 20 m → 75 - 80 %

Messeturm · Frankfurt am Main,

Germany

Settlements:

Messeturm · Frankfurt am Main, Germany

dydxy,x,s)s(R k,raft

m

1j

k,raftj,k,pilek,tot sRsRsR

sRsRsR j,k,sj,k,bj,k,pile

Total resistance of the CPRF:

Pile resistance:

Raft resistance:

Bearing concept of a

Combined Pile-Raft Foundation (CPRF)

Katzenbach et al. (2012)

Analytical study:

9

Katzenbach et al. (1998) had suggested that designing Combined Pile-Raft

Foundations (CPRF) requires the qualified understanding of soil-structure

interaction.

Rtotal,k = ΣRpile,k, j + RRaft, k

Total resistance of the CPRF:

Pile resistance: sRsRsR jksjkbjkpile ,,,,,,

Raft resistance:

dydxyxssR kraft ,,)(,

αCPRF is set between 0.45-0.55

s =

(Katzenbach et al. 1998).

, ,

1

,

( )

( )

m

pile k j

j

CPRF

tot k

R s

R s

CPRF coefficient:

10

Three dimensional view of pile group and pile-raft model in ABAQUS

(Eslami et al. 2011)

Dynamic loading response:

11

Comparison of acceleration and bending moment response of under

sinusoidal accelerations


Input acceleration – 1 m/sec2

Input frequency – 1 Hz

36% decrease in

piled raft model

54 %

decrease in

piled raft

model

Seismic loading response:

• El- centro acceleration time history was chosen.

• Input acceleration and displacement- 4.21m/sec2 and 37.4 cm.

12

Acceleration response

34% reduction


piled raft pile group

9%

reduction

Horizontal displacement response under El- centro seismic

loading

Piled raft pile group

(Eslami et al. 2011) 13

Case Study

Combined Pile – Raft

Foundation (CPRF)

under Earthquake

Conditions

Case study of pile-raft foundation during 2011 Tohoku earthquake

Yamashita et al. (2011):

Building located at JAPAN PROTON ACCELERATOR RESEARCH COMPLEX (JPARC).

15

Pile raft foundation

371 PHC piles

Diameter – 0.6m to 0.8m

Earthquake occurred – 44

month after the end of

construction.

Epicenter -270 km from

the site

Ground acceleration –

3.24 m/s2 and 2.77 m/s2 for

the horizontal and vertical

directions .

Yamashita et al. (2011)

Ratio of load carried by pile Pile P1 Pile P2

Decreased from 0.85

to 0.82 after the

earthquake

Decreased from 0.67

to 0.57 after the

earthquake

(Yamashita et al. 2012) 16

IIT Bombay, DC 17

Seismic Design of

Ground Anchors

See, Rangari, S. M. (2013), PhD Thesis, IIT Bombay, Mumbai, India.

18

• To mitigate the effect of earthquake Ground Anchors can be used for structures

subjected to uplift / pullout loads.

• Estimation of Uplift Capacity of Ground Anchor is an application of passive earth

pressure theory.

• Problem is more complex under seismic conditions.

INTRODUCTION

19

The total reaction R1 and R3 on

the failure surfaces are computed

by integrating Kötter’s equation;

•W is the weight of failure

soil block,

• Pp d1 and Pp d3 are the

seismic passive

resistances,

• is soil friction angle,

• B is width and H is depth

of anchor

•Qh and Qv are total

seismic horizontal and

vertical inertial forces

respectively.

•Simple Planar failure surface. Hence the

Kötter’s (1903) equation reduces to,

sinp s

Horizontal Strip Shallow Anchor under Seismic Conditions

20

Typical Design Charts (Results) for Seismic Uplift Capacity

Factor of Horizontal Shallow Anchors

a. Using Pseudo-Static approach b. Using Pseudo-Dynamic approach Rangari, S.M., Choudhury, D., Dewaikar, D.M. (2013) in Geotechnical and Geological

Engineering , Springer, Vol. 31(2), pp. 569-580.

21

Comparison of ultimate seismic uplift capacity factor (F E = Pud/ B2) for various

values of kh and kv= 0.5 kh for = 30 , = 4 with H/ =0.3 and H/ =0.16.

kh Ghosh (2009)

Pseudo-

dynamic

Kumar

(2001)

Pseudo-

static

Choudhury and

Subba Rao

(2004)

Pseudo-static

Present study

Pseudo-

static

Pseudo-

dynamic

0.0

13.27

13.27

12.89

13.01

13.01

0.1

12.59

12.48

12.44

12.12

12.08

0.2

11.90

11.71

11.96

11.25

11.29

0.3

11.14

10.90

11.53

10.39

10.61

0.4

10.21

9.81

11.01

9.56

10.05

Comparison of Results

Rangari, S.M., Choudhury, D., Dewaikar, D.M. (2013) in Geotechnical and Geological

Engineering , Springer, Vol. 31(2), pp. 569-580.

22

For a plane failure surface, Kötter’s equation (1903), takes the following form

where,

p = uniform pressure on failure

plane

= unit weight of soil

s = represents the distance of failure plane

as measured from ground surface

The total reaction R1 and R3 on the failure surfaces are computed by integrating

Kotter’s equation;

sinp s

Inclined Strip Shallow Anchor under Seismic Conditions

Rangari, S.M., Choudhury, D., Dewaikar, D.M. (2012) in Disaster Advances, Vol. 5(4), pp. 9-16.

23

For Design, qudnet can is expressed as,

Net seismic uplift capacity factor ( F d) can be obtained as;

where, embedment ratio, and Kp d is net seismic passive earth pressure

coefficient.

Critical angle of failure planes:

The trial value of α1 and α3 are obtained such that the values of Ppγd1 and Ppγd3

should be same obtained from failure wedges CDF and ABE respectively.

B

H

udnet dq 0.5 BF

2 2 2

d P d

v h

F tan 0.25 tan K cos tan tan

2 1 k sin k cos

Inclined Strip Shallow Anchor under Seismic Conditions


24

Typical Design Charts (Results) for Seismic Uplift Capacity

Factor of Obliquely loaded Inclined Shallow Anchors


25

COMPARISION OF RESULTS

Comparison of net SEISMIC uplift capacity factor (F d) with results from

literature for =30 , with = 30 and ε =3.

kh Choudhury and Subba Rao

(2005)

Present study

kv=0.0kh kv=0.5kh kv=1.0kh kv=0.0kh kv=0.5kh kv=1.0kh

0.0 5.85 5.85 5.85 6.28 6.28 6.28

0.1 5.48 5.32 5.16 6.27 5.95 5.61

0.2 5.39 4.76 4.43 6.25 5.62 5.05

0.3 5.28 4.31 3.53 6.13 5.2 4.41

0.4 4.99 3.69 -- 5.94 4.73 --


Deepankar Choudhury, IIT Bombay, India

Seismic Behaviour of

Municipal Solid Waste

(MSW) Landfill

Savoikar, P (2009) , PhD Thesis, IIT Bombay, Mumbai, India.

Deepankar Choudhury, IIT Bombay, India

Components of Municipal Solid Waste (MSW) Landfill

See Kavazanjian et al. (1998) in Proc. of US NCEE, Seattle.

Dynamic Properties of Municipal Solid Waste Material

Choudhury, D. and Savoikar, P (2009) in Waste Management, Elsevier, Vol 29, pp. 924-933

Typical

variation of

unit weight of

municipal

solid waste

(MSW)

material used

in landfill with

depth



Typical

variation of

shear wave

velocity of

municipal

solid waste

(MSW)

landfill with

depth



Typical

variation of

damping ratio

of municipal

solid waste

(MSW)

landfill

material with

cyclic shear

strain



Typical

variation of

normalized

shear modulus

of municipal

solid waste

(MSW)

landfill

material with

cyclic shear

strain

Seismic Ground Response Analysis of MSW Landfills

Equivalent-linear analysis of MSW landfill sections during earthquake motions

using DEEPSOIL

Choudhury, D. and Savoikar, P (2009) in Engineering Geology, Elsevier, Vol. 107, pp. 98-110.

Typical Results by Choudhury and Savoikar (2009)

Variation of MHA with depth for 40m high

landfill on type (ii) foundation

Variation of spectral amplification with

frequency for 40m high landfill.


Typical Results by Choudhury and Savoikar (2009)

Effect of various types of foundations and

landfill combinations on MHA

Influence of landfill stiffness on MHA


-100

-80

-60

-40

-20

0

20

40

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Foundation soil

Landfill base

Maximum horizontal acceleration (g)

Landfill height - 20m

Base acceleration: 0.834g

Foundation: Type

Type (i): Rock

Type (ii): Sand underlain by rock

Type (iii):Soft clay and sand underlain by rock

Type (iv):Stiff clay, soft clay, sand underlain

by rock

Type (v): Sand, silty clay,very stiff clay, hard clay

and dense sand underlain by rock

Ele

vati

on

(m

)

-60

-40

-20

0

20

40

60

80

0.00 0.05 0.10

Ele

vati

on

(m

)

Maximum horizontal acceleration (g)

Foundation soil

Landfill base

Variable stiffness

Constant stiffness

Landfill stiffness Landfill height: 60m

Foundation : Type (ii) - Sand underlain

by rock

Base acceleration: 0.067g

Comparison between DEEPSOIL and FLAC3D Results

of Ground Response Analysis for MSW Landfill

Variation of MHA with depth

Variation of Normalized Stress with depth

Savoikar, P and Choudhury, D. (2010) in Proc. of 6ICEG, New Delhi, Vol. 2, pp. 1325-1330.

0

10

20

30

40

50

0.0 0.5 1.0 1.5 2.0

Landfill base

7 3 8 4 62

1

FLAC3D

analysis resultsDEEPSOIL analysis results

40 m high landfill resting on type (i) foundation: rock

Ele

vati

on

(m

)

Maximum horizontal acceleration, (g)

1Kobe Eq. (0.8334g)

5Kobe Eq. (0.8334g)

2Loma Prieta Eq. (0.2778g) 6Loma Prieta Eq. (0.2778g)

3

Loma Prieta Eq. (0.067g) 7Loma Prieta Eq. (0.067g)

4Miyagi Oki Eq. (0.2265g) 8Miyagi Oki Eq. (0.2265g)

5

0

10

20

30

40

50

0 2 4 6 8 10

Landfill base

40 m high landfill resting on type (i) foundation: rockFLAC

3D analysis resultsDEEPSOIL analysis results

1Kobe Eq. (0.834g)

5Kobe Eq. (0.834g)

2Loma Prieta Eq. (0.278g)




4 Miyagi Oki Eq. (0.2265g)

8Miyagi Oki Eq. (0.2265g)

Ele

vat

ion

(m

)

Normalized stresses (Shear stress/Effective vertical stress)

1243 5687

Seismic Stability of Municipal Solid Waste (MSW) Landfill


Forces acting on Hill

type MSW Landfill on

Sloping Base

2

2132121

121

23211

2

sin.sin.cos.1

tan.cos.sin..

tan.tan.cos.1

WWWWWkWWk

WWk

WWWk

FShv

h

v



Variation of Factor of Safety

with (L/H)

And

Yield Acceleration is

computed as,

0 2 4 6 8 100.8

1.0

1.2

1.4 = 50; S

1= S

2= 3;

15

Facto

r o

f sa

fety

, FS

L/H

kh = 0.2, k

v = 0

kh = 0.2, k

v = 0.5k

h

kh = 0.2, k

v = k

h

321

2

121

231

2

21

sintan.sin.cos.

tan.cos.sintan.cos.

1tan

WWWWW

WWW

k

k

v

h

)tan.1/(tan xky

hv kkx /



Comparison between results obtained using pseudo-static and

pseudo-dynamic approaches

0.1 0.2 0.30.5

1.0

1.5

2.0

2.5

kv =0

kv =0.5k

h

kv = k

h

Facto

r o

f safe

ty, F

S

Horizontal seismic acceleration coefficient, kh

kv =0

kv =0.5k

h

kv = k

h

Pseudo-dynamic method

S1= S

2= 2;

sw

s; ; 1 = sw ;

2 =

1

S1= S

2= 2;

sw

1 = sw ;

2 =

1

Pseudo-static method

0 2 4 6 8 100.0

0.1

0.2

0.3

0.4

0.5

Yie

ld a

ccele

rati

on

co

eff

icie

nt,

ky

L/H

S1= S

2= 2;

sw

1 = sw ;

2 =

1

Pseudo-static methodPseudo-dynamic method

kv = 0

kv = 0.5k

h

kv = k

h

S1= S

2= 2;

sw

s; ; 1

= sw ;2

=1

kv = 0

kv = 0.5k

h

kv = k

h


Savoikar, P and Choudhury, D. (2010) in Waste Management, & Research Vol 28, 1096-1113

Forces acting on Side-Hill type MSW Landfill under Translational

mode of failure



Typical Results of Factor of Safety using Pseudo-

Static and Pseudo-Dynamic Approaches

Effect of fill amplification

on factor of safety



Effect of (B/H) on Factor of Safety and Yield Acceleration using

Pseudo-Static and Pseudo-Dynamic Approaches

Seismic Stability of Expanded Municipal Solid Waste

(MSW) Landfill

Choudhury, D. and Savoikar, P. (2011) in Waste Management, & Research Vol 29, 135-145

Landfill model used for sliding stability analysis of MSW landfill

for under the berm failure using pseudo-static approach

Seismic Stability of Expanded Municipal Solid Waste

(MSW) Landfill

Choudhury, D. and Savoikar, P. (2011) in Waste Management, & Research Vol 29, 135-145

Variation of factor of safety and yield acceleration

with back slope of berm

1V:5H 1V:4H 1V:3H1V:2.5H1V:2H1V:1.75H1V:1.5H1V:1.25H1.00

1.05

1.10

1.15

1.20

1.25

Pseudo-dynamic method Pseudo-static method

Hb= 10.0 m; Hb= 10.0 m

Hb= 7.5m; Hb= 7.5 m

Hb= 5.0 m; Hb= 5.0m

Av

era

ge f

acto

r o

f sa

fety

, FS

avg

Back slope of the berm

1V:5H 1V:4H 1V:3H 1V:2.5H 1V:2H1V:1.75H1V:1.5H1V:1.25H0.06

0.08

0.10

0.12

0.14

Pseudo-dynamic method Pseudo-static method

Hb= 5.0 m ; Hb= 5.0 m

Hb= 7.5 m; Hb= 7.5m

Hb= 10.0m ; Hb= 10 m

Av

era

ge y

ield

accele

rati

on

co

eff

icie

nt,

k y

,avg

Back slope of the berm

IIT Bombay, DC 44

End of

Module – 9

Deepankar Choudhury, IIT Bombay, Mumbai, India

* Former PhD Scholars: All my former 10 Ph.D. scholars

who completed Ph.D. at IIT Bombay, mainly, (i) Dr. Sanjay S.

Nimbalkar, (ii) Dr. Syed Mohd. Ahmad, (iii) Dr. Purnanand P.

Savoikar, (iv) Dr. V. S. Phanikanth, (v) Dr. Sumedh Y. Mhaske

(vi) Dr. Jaykumar C. Shukla and (vii) Dr. Sunil M. Rangari

who directly worked under by Main Supervision.

* Current PhD Scholars: All my on-going Ph.D. scholars who

are working at IIT Bombay, namely, (a) Mr. Amey D.

Katdare, (b) Mr. Ranjan Kumar, (c) Ms. Sarika Desai, (d) Ms.

Nisha Naik, (e) Ms. P. Shylamoni, (f) Mr. Kaustav Chatterjee

and (g) Ms. Reshma Raskar Phule, who are directly working

under my Main Supervision.

Acknowledgements

D. Choudhury, IIT Bombay, India

Doctoral Theses (Completed)

@ Geotechnical Earthquake Engg. Lab, IIT Bombay

Dr. Sanjay S Nimbalkar (2007) Seismic analyses of retaining walls by

pseudo-dynamic method – Research Fellow at University of

Wollongong, Australia. (Supervised jointly with Prof. J.N. Mandal)

Dr. Syed Mohd Ahmad (2009) Seismic analyses and design of

waterfront retaining structures using pseudo-static and pseudo-

dynamic approaches – Lecturer at University of Manchester, U.K.

(Supervised alone)

Dr. Purnanand Savoikar (2009) Seismic behaviour of municipal solid

waste landfills – Head, Civil Engg. Dept., Govt. Polytech.,

Bicholim, Goa, India. (Supervised jointly with Prof. J.N.Mandal

who was Co-Supervisor)




Dr. Vivek B. Deshmukh (2010) Some studies on uplift capacity of pile anchors

and horizontal plate anchors – Associate Professor, Dept. of Structural

Engg., VJTI, Mumbai, India. (Supervised jointly with Prof. D.M.Dewaikar

who was Main Supervisor)

Dr. Vedula S. Phanikanth (2011) Ground response analysis and behaviour of

single pile in liquefied soils during earthquake – Scientist – G, Bhabha

Atomic Research Centre, Mumbai, India. (Supervised jointly with Dr.

G.R.Reddy of BARC who was External Co-Supervisor)

Dr. Raghu Nandan M. E. (2011) Effect on cyclic response and liquefaction

resistance due to desaturation of sand – Asst. Professor, Monash Univ.

Malaysia. (Supervised jointly with Dr. A. Juneja who was Main Supervisor)

Dr. Sumedh Y. Mhaske (2011) GIS-GPS based geotechnical studies for seismic

liquefaction hazards in Mumbai city – Head and Associate Prof., Dept. of

Civil Engg., VJTI, Mumbai, India. (Supervised alone)


Dr. Ganesh S. Kame (2012) Analysis of a continuous vertical plate

anchor embedded in cohesion-less soil – Prof., Dept. of Civil Engg.,

Saraswati College of Engg., Kharghar, Mumbai, India. (Supervised

jointly with Prof. D.M.Dewaikar who was Main Supervisor)

Dr. Jaykumar C. Shukla (2013) Seismic hazard estimation and

ground response analysis for Gujarat region – Engineer at L&T

Surgent & Lundy, Surat, India. (Supervised jointly with Prof.

D.L.Shah of MS Univ. Baroda who was External Co-Supervisor)

Dr. Sunil M. Rangari (2013) Seismic uplift capacities of horizontal

and inclined strip anchors in cohesionless soil – Asst. Prof., Airoli,

Mumbai, India. (Supervised jointly with Prof. D.M.Dewaikar who

was Co-Supervisor)

7 more are continuing currently………………..




* M.Tech. Students: My Former M.Tech. students who did

M.Tech. Dissertation under my supervision at IIT Bombay,

mainly, (i) Mr. Santiram Chatterjee, (ii) Ms. Somdatta Basu,

(iii) Mr. Rajeev Kumar Bharti, (iv) Ms. Deepa Modi, (v) Mr.

Mayukh Mukhopadhayay, (vi) Mr. Manoranjan Tripathy,

(vii) Mr. Debarghya Chakraborty, (viii) Ms. Gaytree

Dandekar, (ix) Ms. K. Sangeetha, (x) Ms. Ritika Sangroya.

Also my current M.Tech. students who are doing their

M.Tech. Dissertation at IIT Bombay under my supervsion,

namely, (xi) Mr. V. Dilli Rao, (xii) Mr. A. Sarin, (xiii) R. P.

Singh and (xiv) Mr. Ashutosh Kumar.

Acknowledgements (contd…)


* My Supervisor, Teachers in India: Prof. K. S. Subba Rao,

Prof. A. Sridharan, Prof. T. G. Sitharam, Prof. G. L. S. Babu,

Prof. J. Kumar, Prof. C. S. Manohar of IISc Bangalore.

And Prof. N. N. Som, Prof. R. D. Purkayastha, Prof. S. C.

Das, Prof. P. Bhattacharyay, Prof. S. P. Mukherjee of

Jadavpur University.

* My Collaborators in India: Prof. M. R. Madhav of JNTU

(IITK), Prof. J.N. Mandal, Prof. D.M. Dewaikar, Prof.

B.V.S.Viswanadham and Prof. S. Ghosh of IITB, Prof.

Priyanka Ghosh of IITK, Dr. G. R. Reddy, Dr. K. Bhargava

and Dr. A. K. Ghosh of BARC, Dr. P. C. Basu of AERB,

Prof. D. L. Shah of MSU Baroda, Prof. P. Samui of VIT,

Prof. G. Bhattacharyay of BESU, Prof. A. M. Krishna of

IITG, Prof. C. Ghosh of NDMA.



* Collaborators from Outside-India: Prof. Jonathan D. Bray

of UC Berkeley USA, Prof. Buddhima Indraratna of

UoWollongong Australia, Prof. C. F. Leung of NUS

Singapore, Prof. R. Kitamura of Kagoshima Univ. Japan,

Prof. Rolf Katzenbach of TU Darmstadt Germany, Prof. S.

Bhattacharya of Univ. of Surrey UK.

* Significant Funding Agencies: AERB Mumbai, BRNS-DAE

Mumbai, INAE New Delhi, SERC-DST New Delhi, INSA New

Delhi, IRCC-IITB Mumbai, India.

And, Alexander von Humboldt Foundation, Bonn, Germany;

Japan Society for Promotion of Science, Tokyo, Japan;

UKIERI UK-India; Samsung C&T, Korea.



* Special Thanks to Mr. Kaustav Chatterjee and

Mr. V. Dilli Rao (my current Ph.D. and M.Tech.

student), who helped me to prepare the slides and

editing the video content of this course. Also

thanks to all NPTEL staff and colleagues at IIT

Bombay.


Contact Email: [email protected]

[email protected] D. Choudhury, IIT Bombay, India 53

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