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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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Deepankar Choudhury, IIT Bombay
Devastating effect of earthquake on retaining wall
September, 1999 Ji Ji, Taiwan EarthquakeSeptember, 1999 Ji Ji, Taiwan Earthquake
Deepankar Choudhury, IIT Bombay
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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Deepankar Choudhury, IIT Bombay
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)
Deepankar Choudhury, IIT Bombay
Pseudo Static Analysis
Mononobe-Okabe (1926, 1929)
Failure surface and the forces considered by Mononobe-Okabe
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Deepankar Choudhury, IIT Bombay
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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Deepankar Choudhury, IIT Bombay
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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Deepankar Choudhury, IIT Bombay
Typical Results
Deepankar Choudhury, IIT Bombay
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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Deepankar Choudhury, IIT Bombay
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
Choudhury and Nimbalkar (2006)
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
Deepankar Choudhury, IIT Bombay
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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Deepankar Choudhury, IIT Bombay
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 and Nimbalkar (2005)
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
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, = / 2, H /= 0.3, H/ = 0.16
z/H
ppe/H
kh=0.0
kh=0.1
kh=0.2
kh=0.3
Deepankar Choudhury, IIT Bombay
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).
Deepankar Choudhury, IIT Bombay
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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Typical Variation of Soil thrust factor FT,
Wall inertia factor FI and Combined dynamic factor Fw
Choudhury and Nimbalkar (2006)
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
Choudhury and Nimbalkar (2006)
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
Deepankar Choudhury, IIT Bombay
* 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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Deepankar Choudhury, IIT Bombay
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
Deepankar Choudhury, IIT Bombay