walls-seismic analysis_Lec-35.pdf

7/23/2019 walls-seismic analysis_Lec-35.pdf

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Geotechnical Earthquake

Engineeringby

Dr. Deepankar ChoudhuryHumbo ldt Fel low, JSPS Fel low, BOYSCAST Fel lowProfessor

Department of Civil Engineering

IIT Bombay, Powai, Mumbai 400 076, India.Email: [email protected]

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

Lecture35


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IIT Bombay, DC 2

Module

9

Seismic Analysis andDesign of Various

Geotechnical Structures


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IIT Bombay, DC 3

Seismic Design of

Retaining Wall


4/27

Earth Pressures on Retaining Walls

D. Choudhury, IIT Bombay, India 4

Earth pressures-

at rest earth pressure

active earth pressure

passive earth pressure

Earth pressure conditions


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Failure of Retaining Walls


Failure of gravity retaining wall

(Source:http://www.geofffox.com) (Source: http://www.parmeleegeology.com/)

Retaining walls may fail during an earthquake, if they are not

designed to resist additionaldestabilizing earthquake forces.


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Seismic Analysis and Design of Retaining Walls

Seismicanalysis/design of retaining walls mainly consists of

Determining magnitude of additional destabilizing forces that act

during an earthquake

Determining seismic active and passiveearth pressures due to all

destabilizing forces (static + seismic)

Design section based on above parameters using

1. Force based approach

2. Displacement based approach for performance based

design



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Pseudo-static Method

7

Theoretical background of seismic coefficient lies in the

application ofDAlembertsprinciple of mechanics.

Example of elementary seismicslope stability analysis

(Towahata, 2008)

DAlemberts principle ofmechanics

Towhata, I., (2008), Geotechnical Earthquake Engineering, Springer,

Tokyo, Japan.


8/27D. Choudhury, IIT Bombay, India

Conventional Seismic Design of Retaining Walls

Pseudo-Static Approach Proposed by Mononobe-Okabe (1929)

Questions: Value of khand kvto be used for design?Soil amplification?

Variation of seismic acceleration with depth and time?

Effect of dynamic soil properties? etc.


9/27D. Choudhury, IIT Bombay, India

Available Literature

Mononobe-Okabe (1926, 1929)

Madhav and Kameswara Rao (1969)Richards and Elms (1979)

Saran and Prakash (1979)

Prakash (1981)

Nadim and Whitman (1983)

Steedman and Zeng (1990)Ebeling and Morrison (1992)

Das (1993)

Kramer (1996)

Kumar (2002)

Choudhury and Subba Rao (2005)Choudhury and Nimbalkar (2006)

And many others..

D. Choudhury, IIT Bombay, India


10/27


Richards and Elms (1979) proposed a method for seismic design of

gravity retaining walls which is based on permanent

wall

displacements. (Displacement based approach)

10

2 3

max max

40.087pem

y

v ad

a

Displacement should be calculated by

following formula, and should be checked

against allowable displacement.

where, vmax is the peak ground velocity, amax

is the peak ground acceleration, ay is the

yield acceleration for the wall-backfill system.

Seismic forces on gravity

retaining wall

Richards and Elms (1979)

Richards, R. Jr., and Elms, D. G. (1979). Seismic behavior of gravity retaining walls. Journal of

Geotechnical Engineering, ASCE, 105: 4, 449-469.


11/27


Choudhury and Subba Rao (2002) gave design charts for the

estimation of seismic passive earth pressure coefficient for negative

wall friction case. (Canadian Geotech. Journal , 2002)

11

The application of this case is for anchor uplift

capacity.

Design charts are given for calculation of various

parameters like kpd, which can be used to

compute seismic passive resistance, which is

given by,2

pd pcd pqd pd

1 1P = 2cHK +qHK H K

2 cos

where Ppd is seismic passive resistance,Kpd, Kpqd, and Kpcd are the seismic

passive earth pressure coefficients.

Choudhury, D. and Subba Rao, K. S. (2002). Seismic passive earth

resistance for negative wall friction, Canadian Geotechnical Journal, 39:5,

971981.


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Choudhury et al. (2004) presented a comprehensive review for

different methods to calculate seismic earth pressures and their

point of applications. (Current Scienc e, 2004)

12

2 2 22 cos 2 sin (cos cos )

2 cos (sin sin )d

H H th H

H t

22and

ps VV

excitation frequency, Vs and Vp are

shear and primary wave velocities

respectively, H is height of retaining wall.

Expression for the point of application of

seismic passive resistance by,

Choudhury, D., Sitharam, T. G. and Subba Rao, K. S.

(2004). Seismic design of earth retaining structures and

foundations. Current Science, India, 87:10, 1417-1425.


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Seismic Passive Resistance by Pseudo-static Method


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

Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 131:1, 131- 135.


14/27


Subba Rao and Choudhury (2005) gave design charts for

seismic passive earth resistance coefficients by using a

composite failure surface for positive wall friction angle. (Jl . of

Geotechnical and Geoenviro nm ental Engg ., ASCE, 2005)


Design charts were proposed for the

direct computation of seismic passiveearth resistance coefficients for various

input parameters.

The application of this case is for bearing

capacity of foundations.


15/27


Shukla et al. (2009) have described the derivation of an analyticalexpression for the total active force on the retaining wall for c- soil

backfill considering boththe horizontal and vertical seismic coefficients.

The seismic active earth pressure is given by,

8

21

(1 )2ae v ae aecP H k K cHK

where,sin( )

cos( )tan

cos (cos tan sin )

cae

c

K

2cos (1 tan )

tan (cos tan sin )

caec

c c

K

and

tan1

h

v

k

k

and cis critical failure plane angle, shearing

resistance of soilShukla, S. K., Gupta, S. K. and Sivakugan, N. (2009). Active earth pressure on retaining wall

for c-soil backfill under seismic loading condition.Journal of Geotechnical and

Geoenvironmental Engineering, ASCE, 135:5, 690696.


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Major limitations

Representation of the complex, transient, dynamic effectsof earthquake shaking by single constant unidirectional

pseudo-static acceleration is very crude.

Relation between K and the maximum ground acceleration is

not clear i.e. 1.9 g acceleration does not mean K = 1.9

Advantages

Simpleandstraight-forward

Noadvanced or complicated analysis is necessary. It uses limit state equilibrium analysis which is routinely

conducted by Geotechnical Engineers.



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Development of Modern Pseudo-Dynamic Approach

Soil amplification is considered.

Frequency of earthquake excitation is considered.

Time duration of earthquake is considered.Phase differences between different waves can be considered.

Amplitude of equivalent PGA can be considered.

Considers seismic body wave velocities traveling during earthquake.

Advantages

Pseudo-Dynamic Approach by

Steedman and Zeng (1991),Choudhury and Nimbalkar (2005)

Choudhury and Nimbalkar, (2005), in Geotechn ique, ICE Vol. 55(10), pp. 949-953.

ah(z, t) = {1 + (Hz).(fa1)/H}ahsin [{t(Hz)/Vs}]

av(z, t) = {1 + (Hz).(fa1)/H}avsin [{t(Hz)/Vp}]


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H

h0

( ) m(z)a (z, t)dzh

Q t 2 2 Hcosw (sin sin )4 tanha w wt

g

=

where, = TVs is the wavelength of the vertically propagating

shear 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) passive resistance is given by,

where, = TVp, is the wavelength of the vertically propagating primary

wave and = t H/Vp.

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

where = angular frequency; t = time elapsed; Vs= shear wave velocity;

Vp= primary wave velocity

sin( ) cos( ) sin( )

cos( )

h v

pe

W Q QP

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

Choudhury, D. and Nimbalkar, S. (2005), in Geotechnique, I CE London, U.K., Vol. 55, No. 10, 949-953. 8


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( ) sin( )( )

tan cos( )

cos( ) sintan cos( )

sin( ) sin

tan cos( )

pe

pe

h

s

v

p

dP t zp t

dz

k z ztV

k z zt

V

The coefficient of seismic passive resistance (Kpe) is given by,

The seismic passive earth pressure distribution is given by,

where and

Choudhury, D. and Nimbalkar, S. (2005), in Geotechnique, London, U.K ., Vol. 55, No. 10, 949-953.


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Typical non-linear variation of seismic passive earth pressure

Choudhury and Nimbalkar (2005)

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, = , H/= 0.3, H/= 0.16

z/H

ppe

/H

kh=0.0

kh=0.1

kh=0.2

kh=0.3

Choudhury, D. and Nimbalkar, S. (2005), in Geotechnique, London, U.K ., Vol. 55, No. 10, 949-953.


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0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

2

3

4

5

6

kh= 0.2, k

v= 0.0, = 30

0, = 16

0

fa=1.0f

a=1.2

fa=1.4

fa=1.8

fa=2.0

Kpe

H/TVs

Effect of amplification factor on seismic passive earth pressureah(z, t) = {1 + (H z).(fa1)/H}ahsin [{t (H z)/Vs}]

Nimbalkar and Choudhury (2008)

Nimbalkar, S. and Choudhury, D. (2008), in Jour nal of Earthquake and Tsunami , Singapore, Vol. 2(1), 33-52.


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1.0

0.8

0.6

0.4

0.2

0.0

0 1 2 3 4 5

H/= 0.3, H/= 0.16

kh= 0.2, k

v= 0.5k

h, = 30

0,= /2

ppe

/H

z/H

Mononobe-Okabe method

Present study

Comparison of proposed pseudo-dynamic method

with existing pseudo-static method Passive case


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Comparison of proposed pseudo-dynamic method

with existing pseudo-static methods Passive case

0.0 0.1 0.2 0.30

1

2

3

4

5

6

7

8

Mononobe-Okabe method

Choudhury (2004)

Present study

Kpe

kh

= 350, = /2, k

v= 0.5k

v, H/= 0.3, H/= 0.16 Choudhury and

Nimbalkar

(2005) inGeotechnique


24/27

Choudhury and Nimbalkar (2006)

Seismic Active Earth Pressure by Pseudo-Dynamic Approach

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.


25/27


H

h0

( ) m(z)a (z, t)dzh

Q t 2 2 Hcosw (sin sin )4 tanha w wt

g

=

where, = TVs is the wavelength of the vertically propagating

shear wave and = t-H/Vs.

H

v

0

( ) m(z)a (z, t)dzvQ t 2 2 Hcos (sin sin )4 tanva t

g

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

where, = TVp, is the wavelength of the vertically propagating primary

wave and = t H/Vp.

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

cos( )

h v

ae

W Q t Q t P t

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

where = angular frequency; t = time elapsed; Vs= shear wave velocity;

Vp= primary wave velocity.

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


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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 2

p

p p

TVt H t H t

T TV H T TV T

( ) z sin( )( )

tan cos( )

cos( ) sintan cos( )

sin( ) sin

tan cos( )

aeae

h

s

v

p

P tp t

z

k z zw tV

k z zw t

V

The seismic active earth pressure distribution is given by,

The seismic active earth pressure coefficient, Kaeis defined as

T i l li i ti f


27/27

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, ,H/=0.3, H/=0.16

z/H

pae/H

kh=0.0

kh=0.1

kh=0.2

kh=0.3

Choudhury and Nimbalkar (2006), in

Geotechnical and Geological Engineeri ng,

24(5), 1103-1113.

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 + (Hz).(fa1)/H}ahsin [{t(Hz)/Vs}]

Effect of soil amplification on

seismic active earth pressure

Nimbalkar and Choudhury (2008),

in Jour nal of Ear thquake and Tsunami , 2(1), 33-52.

D. Choudhury, IIT Bombay

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walls-seismic analysis_Lec-35.pdf