geotechnical earthquake engineering · 2017. 8. 4. · h h t hh ht 2 2 s and p v v ω excitation...

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 – 35

IIT Bombay, DC 2

Module – 9

Seismic Analysis and

Design of Various

Geotechnical Structures

IIT Bombay, DC 3

Seismic Design of

Retaining Wall

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

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 additional destabilizing earthquake forces.

Seismic Analysis and Design of Retaining Walls

Seismic analysis/design of retaining walls mainly consists of

› Determining magnitude of additional destabilizing forces that act during an earthquake

› Determining seismic active and passive earth 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


Pseudo-static Method

7

Theoretical background of seismic coefficient lies in the

application of D´Alembert´s principle of mechanics.

Example of elementary seismic

slope stability analysis

(Towahata, 2008)

D’Alembert’s principle of

mechanics

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

Tokyo, Japan.

D. Choudhury, IIT Bombay, India

Conventional Seismic Design of Retaining Walls

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

Questions: Value of kh and kv to be used for design?

Soil amplification?

Variation of seismic acceleration with depth and time?

Effect of dynamic soil properties? etc.


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…………..



• 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.


• 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 kpγd, which can be used to

compute seismic passive resistance, which is

given by, 2

pd pcd pqd pγd

1 1P = 2cHK +qHK γH K

2 cosδ

where Ppd is seismic passive resistance,

Kpγd, 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,

971–981.


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

different methods to calculate seismic earth pressures and their

point of applications. (Current Science, 2004)

12

2 2 22 cos 2 sin (cos cos )

2 cos (sin sin )d

H H th H

H t

22 and

psVV

ω 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.

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.


• 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 Geoenvironmental Engg., ASCE, 2005)


• Design charts were proposed for the

direct computation of seismic passive

earth resistance coefficients for various

input parameters.

• The application of this case is for bearing

capacity of foundations.


• Shukla et al. (2009) have described the derivation of an analytical

expression for the total active force on the retaining wall for c-ϕ soil backfill considering both the horizontal and vertical seismic coefficients.

• The seismic active earth pressure is given by,

8

21 (1 )2

ae 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 αc is critical failure plane angle, ϕ shearing

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

for c-ϕ soil backfill under seismic loading condition. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 135:5, 690‒696.


Major limitations

› Representation of the complex, transient, dynamic effects of 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

› Simple and straight-forward

› No advanced or complicated analysis is necessary.

› It uses limit state equilibrium analysis which is routinely

conducted by Geotechnical Engineers.


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), in Geotechnique, ICE Vol. 55(10), pp. 949-953.

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

av(z, t) = {1 + (H – z).(fa – 1)/H}av sin [{t – (H – z)/Vp}]

H

h0

( ) m(z)a (z, t)dz hQ t 2

2 Hcosw (sin sin )4 tan

ha w wtg

=

where, = TVs is the wavelength of the vertically propagating

shear wave and = t-H/Vs.

H

v

0

( ) m(z)a (z, t)dz vQ 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) = ah sin [{t – (H – z)/Vs}]

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

Vp = primary wave velocity

sin( ) cos( ) sin( )

cos( )

h vpe

W Q QP

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

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

( ) sin( )( )

tan cos( )

cos( ) sin

tan cos( )

sin( ) sin

tan cos( )

pe

pe

h

s

v

p

dP t zp t

dz

k z zt

V

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.

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, = , 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.

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=1.0

fa=1.2

fa=1.4

fa=1.8

fa=2.0

Kp

e

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}]

Nimbalkar and Choudhury (2008)

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


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


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) in

Geotechnique


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.


H

h0

( ) m(z)a (z, t)dz hQ t 2

2 Hcosw (sin sin )4 tan

ha w wtg

=

where, = TVs is the wavelength of the vertically propagating

shear wave and = t-H/Vs.

H

v

0

( ) m(z)a (z, t)dz vQ 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 primary

wave and = t – H/Vp.

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

cos( )

h vae

W Q t Q tP 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}] and

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 km 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 sin( )( )

tan cos( )

cos( ) sin

tan cos( )

sin( ) sin

tan cos( )

aeae

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

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 Engineering,

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

Effect of soil amplification on

seismic active earth pressure

Nimbalkar and Choudhury (2008),

in Journal of Earthquake and Tsunami, 2(1), 33-52.

D. Choudhury, IIT Bombay

geotechnical earthquake engineering · 2017. 8. 4. · h h t hh ht 2 2 s and p v v ω excitation...

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