modern technique for earthquake resistantdesign

8/11/2019 modern technique for earthquake resistantdesign

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Modern Techniques for EarthquakeResistant Design of Retaining Structures

by

Dr. Deepankar Choudhury

Assistant Professor, Department of Civil Engineering,

Indian Institute of Technology (IIT) Bombay,

Powai, Mumbai 400 076, India.

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

Deepankar Choudhury, IIT Bombay

Why this Topic?


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Devastating effect of earthquake on retaining wall

September, 1999 Ji Ji, Taiwan EarthquakeSeptember, 1999 Ji Ji, Taiwan Earthquake


Preamble and Background

o Design of retaining walls under seismic condition is very important inearthquake prone areas to reduce the devastating effect of

earthquake.

o Evaluation of earth pressure under seismic condition is important.

o Estimation of passive pressure under both static and seismic

conditions are very important for the design of retaining walls,anchors, foundations etc.

o Research on static passive earth pressure is plenty whereas thesame under seismic condition is still lacking.


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Pseudo-static methodLimit Equilibrium method [Mononobe-Okabe (1926, 1929), Kapila andMaini (1962), Arya and Gupta (1966), Prakash and Saran (1966),

Madhav and Kameswara Rao (1969), Ebeling and Morrison (1992),

Morrison and Ebeling (1995), Choudhury et al. (2002), Subba Rao and

Choudhury (2005), Choudhury and Singh (2006)]

Limit Analysis [Soubra (2000)]

Method of Characteristics [Kumar and Chitikela (2002)]

Pseudo-dynamic methodSteedman and Zeng (1990), Choudhury and Nimbalkar (2005, 2006)

Force-Based Analysis

Displacement-Based AnalysisRichards and Elms (1979), Prakash (1981), Nadim and Whitman (1983), Sherif

and Fang (1984), Rathje and Bray (1999), Choudhury and Nimbalkar (2006)


Pseudo Static Analysis

Mononobe-Okabe (1926, 1929)

Failure surface and the forces considered by Mononobe-Okabe


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Mononobe-Okabe

2

ae,pe v ae,pe

1P H (1-k ) K

2=

2

ae,pe 20.5

2

cos ( - )K

sin ( ) sin ( - )cos cos cos ( ) 1 -

cos ( ) cos ( - )

i

i

= +

+ +

m

m

=

v

h1-

k-1

ktan

Seismic Passive Earth Resistance

+

+=

sin

-k1

ktansin

sin2

1

2

k1

ktan

2

1

24

v

h1-

1-

v

h1-

Subba Rao, K. S. and Choudhury, D. (2005), Seismic passive earth pressures in soils,

Journal of Geotechnical and Geoenvironmental Engineering, ASCE, USA, 131(1): pp. 131-135.

Failure surface and forces by Subba Rao and Choudhury (2005)


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Typical Design Charts

Seismic Passive Earth Pressure Distribution

Choudhury, D., Subba Rao, K. S. and Ghosh, S. (2002), Passive earth pressures distribution under seismic condition,

15th International Conference of Engineering Mechanics Division (EM2002), ASCE, Columbia University, NY, in CD.

Analytical model proposed by Choudhury et al. (2002)


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Typical Results


Design As Per Seismic Code

Using pseudo-static approach to evaluate stability of retaining walls.

Compute seismic earth pressure using Mononobe-Okabe equations.

Dynamic increment of earth pressure will act at mid height of the wall.

Effect of dry, partially submerged and saturated backfill is considered.

Range of permissible displacement is not specified.

Soil amplification has not considered.

IS 1893: 1984, Part 3 (Bridges and Retaining Walls)


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13Deepankar Choudhury, IIT Bombay

Based on modified pseudo-static analysis.

Compute seismic earth pressure using Richards and Elms (1979) model.

Permissible displacement for sliding and rocking movement of the

wall are considered.

Included non-linear behaviour in base soil and backfill.

The point of application of the dynamic earth pressure increment

is at mid-height of the wall.

Soil amplification is considered.

Eurocode 8 1998

Choudhury and Nimbalkar (2006)

Seismic active earth pressure by pseudo-dynamic model

Choudhury, D. and Nimbalkar, S. (2006), Pseudo-dynamic approach of seismic active earth pressure behind retaining

wall, Geotechnical and Geological Engineering, Springer, The Netherlands, Vol. 24, No. 5, pp. 1103-1113.


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H

h0

( ) m(z)a (z, t)dzhQ t = [ ]2

2 Hcosw (sin sin )4 tan

ha w wtg

+ =

where, = TVs is the wavelength of the vertically propagatingshear wave and = t-H/Vs.

H

v

0

( ) m(z)a (z, t)dzvQ t = [ ]2

2 Hcos (sin sin )

4 tan

va tg

= +

The total (static plus dynamic) active thrust is given by,

where, = TVp, is the wavelength of the vertically propagating primarywave and = t H/Vp.

sin( ) ( )cos( ) ( )sin( )( )

cos( )

h vae

W Q t Q t P t

+ =

+

ah(z, t) = ah sin [{t (H z)/Vs}]

where = angular frequency; t = time elapsed; Vs

= shear wave velocity;

Vp = primary wave velocity

av(z, t) = av sin [{t (H z)/Vp}]

D. Choudhury, IITB Choudhury and Nimbalkar (2006)

( )

( ) ( ) ( )

( )

( )

( )

( ) ( )

1 22 2

1

2

1 sin cos sin

tan cos 2 tan cos 2 tan cos

where,

m 2 cos 2 sin 2 sin 2

m

ph S v

ae

S

s s

TVk TV k m m

H H

TVt H t H t

T TV H T TV T

K

=

+ + +

= +

+ +

( )2 cos 2 sin 2 sin 2pp p

TVt H t H t

T TV H T TV T

= +

( ) z s in ( )( )

ta n c o s ( )

c o s ( ) s in

ta n c o s ( )

s in ( ) s in

ta n c o s ( )

a e

ae

h

s

v

p

P tp t

z

k z zw t

V

k z zw t

V

= =

+

+

+

+ +

The seismic active earth pressure distribution is given by,

The seismic active earth pressure coefficient, Kae is defined as


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D. Choudhury, IITB

Typical non-linear variation of seismic active earth pressure


1.0

0.8

0.6

0.4

0.2

0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6

kv=0.5k

h, =30

0, =/2,H/=0.3, H/=0.16

z/H

pae/H

kh=0.0

kh=0.1

kh=0.2

kh=0.3


Effect of amplification factor on seismic active earth pressure

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.2

0.4

0.6

0.8

1.0

kh= 0.2, k

v= 0.0, = 33

0, = 16

0

fa=1.0

fa=1.2

fa=1.4

fa=1.8

fa=2.0K

ae

H/TVs

ah(z, t) = {1 + (H z).(fa 1)/H}ah sin [{t (H z)/Vs}]


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Comparison of proposed pseudo-dynamic methodwith existing pseudo-static method Active case

Dynamic moment increment,Z

, where M (Z, t) = p (z, t) cos (Z - z) dz3 3 ae0

M

H

0.0

0.2

0.4

0.6

0.8

1.0

0 0.05 0.1 0.15 0.2 0.25

Dynamic moment increment

z/H

Mononobe-Okabe method

Present method

Centrifuge test results

(Steedman and Zeng, 1990)

= 370, = 20

0, kh= 0.184, kv= 0, fa= 2,

G = 57 MPa, T = 1.0 s

Seismic passive earth pressure by pseudo-dynamic model


Choudhury, D. and Nimbalkar, S. (2005), Seismic passive resistance by pseudo-dynamic method, Geotechnique,

London Vol. 55 No. 9 . 699-702.


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D. Choudhury, IITB

Typical non-linear variation of seismic passive earth pressure


1.0

0.8

0.6

0.4

0.2

0.0

0 1 2 3 4 5 6

kv= 0.5k

h, = 30

0, = / 2, H /= 0.3, H/ = 0.16

z/H

ppe/H

kh=0.0

kh=0.1

kh=0.2

kh=0.3


0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.02

3

4

5

6

kh= 0.2, k

v= 0.0, = 30

0, = 16

0

fa=1.0

fa=1.2

fa=1.4

fa=1.8

fa

=2.0

Kpe

H/TVs

Effect of amplification factor on seismic passive earth pressure

ah(z, t) = {1 + (H z).(fa 1)/H}ah sin [{t (H z)/Vs}]


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Model proposed by Choudhury and Nimbalkar (2006) for

Seismic Design of Retaining Wall considering wall-soil inertia

Active earth pressure conditionChoudhury, D. and Nimbalkar, S. (2006), Seismic design of retaining wall by considering wall-soil inertia,

Canadian Geotechnical Journal (tentatively accepted).


Soil thrust factor, aeT

a

KF

K=

( )Wall inertia factor, IE

I

Ia

C tF

C=

cos sin tan

tan

b

Ia

b

C

=

( )Combined dynamic factor, w

w T I

w

W tF F F

W= =

Proposed Design Factors for Retaining Wall

by Choudhury and Nimbalkar (2006)

cos sin tan ( ) ( ) tanwhere, ( )

tan ( ) tan

b hw vw b

IE

b ae b

Q t Q t C t

P t

+= +


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D. Choudhury, IITB

Typical Variation of Soil thrust factor FT,

Wall inertia factor FI and Combined dynamic factor Fw


0.0 0.1 0.2 0.3

0

1

2

3

4

5

6

Combined dynamic factor FW

Wall inertia factor FI

Soil thrust factor FT

kv=0.5k

h, = 30

0, = 15

0, H/TV

s= 0.3, H/TV

p= 0.16,

H/TVsw

=0.012, H/TVpw

=0.0077

FactorsF

W,FI,

FT

kh

D. Choudhury, IITB Choudhury and Nimbalkar (2006)

0.0 0.1 0.2 0.30

2

4

6

8

10

kh

FW

kv=0.5k

h, = /2, H/TV

s= 0.3, H/TV

p= 0.16,

H/TVsw

=0.012, H/TVpw

=0.0077

= 200

= 300

= 400

0.0 0.1 0.2 0.30

1

2

3

4

5

6

7

FW

kh

kv=0.5k

h, = 30

0, H/TV

s= 0.3, H/TV

p= 0.16,

H/TVsw

=0.012, H/TVpw

=0.0077

/= -0.5

/= 0.0

/= 0.5

/= 1.0

Effect of angle of internal friction () Effect of wall friction angle ()

Typical Results


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D. Choudhury, IITB

Comparison of Soil thrust factor FT, Wall inertia factor FIand Combined Dynamic Factor Fw


24.0597.4643.2236.6831.9093.5000.00

0.5

7.7533.2552.3825.0392.0212.4930.000.4

6.4003.0272.1144.6622.4641.8920.15

3.8852.0821.8663.8321.9941.9220.00

0.3

3.6812.2051.6693.6762.9281.2560.20

2.8401.8061.5723.2172.3471.3710.10

2.2951.5301.5002.8001.8341.5270.00

0.2

1.7181.3761.2482.2532.1601.0430.10

1.5881.2871.2342.0601.8121.1370.05

1.4761.2091.2211.8681.5171.2310.00

0.1

1.01.01.01.01.01.00.00

0.0

FWFIFTFWFIFT

Richards and Elms (1979)Present studykvkh


* Using limit equilibrium method and adopting both pseudo-static and

pseudo-dynamic approach for seismic forces, comprehensive results

of active and passive earth pressures are obtained for static and

seismic conditions with wide range of variation in design parameters.

active and passive earth pressure coefficients,

point of application of resultant earth force,

effects of shear and primary waves,

wall-soil inertia are considered together,

design factor Fw is proposed for wall design.

* Present solutions compare well with existing theories for static caseand very rarely available seismic cases. In most of the cases, present

study generates new solutions for the seismic cases.

Concluding Remarks


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Apart from the approximate pseudo-static approach, considering shearand primary waves through the soil-structure with variation of time

can be used to get better solution by using pseudo-dynamic approach.

* Point of application of seismic earth pressure should be computed

based on some logical analysis instead of some arbitrary selection.

* IS code must be revised for design of retaining wall under seismic

conditions.

Concluding Remarks (contd.)

Hope to build STABLE Earthquake Resistant

Retaining Structures in Soil


modern technique for earthquake resistantdesign

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