Seismic Analysis of Some
Geotechnical Problems –
Pseudo-dynamic Approach
Dr. Priyanka Ghosh
Assistant Professor
Dept. of Civil Engineering
Indian Institute of Technology, Kanpur
INDIA
Organisation
 Introduction to Pseudo-dynamic Approach and Upper Bound
Limit Analysis
 Seismic Bearing Capacity of Strip Footing using Upper Bound
Limit Analysis
 Seismic Vertical Uplift Capacity of Horizontal Strip Anchors
using Upper Bound Limit Analysis
 Seismic Active Earth Pressure Behind Non-vertical Retaining
Wall using Limit Equilibrium Method
 Seismic Active Earth Pressure on Walls with Bilinear Backface
using Limit Equilibrium Method
 Seismic Passive Earth Pressure Behind Non-vertical Retaining
Wall using Limit Equilibrium Method
 Conclusions
Introduction to
Pseudo-dynamic Approach and
Upper Bound Limit Analysis
Pseudo-dynamic Approach
Pseudo-static Approach Pseudo-dynamic Approach
The dynamic loading
The
time
and
phase
induced by earthquake is
difference due to finite
considered as time
primary and shear wave
independent, which
velocity can be considered
ultimately assumes that
the magnitude and phase
of acceleration is uniform
throughout the soil mass
Generally does not consider Considers the amplification of
the
amplification
of
excitation
vibration which takes
place towards the ground
surface
For a Sinusoidal Base Shaking, the Acceleration
at any Depth z below the Ground Surface and
Time t
Mass of the Shaded Element m(z) and Total Weight of the
Failure Wedge W
Total Horizontal Seismic Inertia Force Qh(t)
Where, l = wavelength of the shear wave = TVs
Total Vertical Seismic Inertia Force Qv(t)
Where, h = wavelength of the primary wave = TVp
Upper Bound Limit Analysis
Theorem: If a compatible mechanism of plastic deformation
 v
p*
,
ij
p*
, is
i
assumed, which satisfies the condition
v
p*
=
i
0 on the
displacement boundary Su; then the loads Ti, Fi determined by
equating the rate at which the external forces do work to the
rate of internal dissipation of energy will be either higher or
equal to the actual limit load.
Equation
p*
p*
p*



   ij dV   Ti v i dS   Fi v i dV
p*
ij
V
S
V
v displacement rate
 pij* = plastic strain rate compatible with
p*
=
i
displacement rate
 = stress tensor associated with plastic strain
p*
ij
rate
Ti = external force on the surface S
Fi = body forces in a body of volume V
Seismic Bearing Capacity of Strip
Footing using Upper Bound
Limit Analysis
Acta Geotechnica (Springer Pub.), 2008, Vol. 3, No. 2, pp 115-123.
b
Pu
xPu
A
Footing
a
B
b
Qv1
Qv2
U21
Qh1
z
Qh2
f
W1
f
ah = faahg
D
f
W2
z
U1
U2
z
dz
dz
C
Vs, Vp
ah = ahg
(a)
U2
U21
(a  b)
U1
(b)
Collapse mechanism and velocity
hodograph
Acta Geotechnica (Springer Pub.), 2008, Vol. 3, No. 2, pp 115-123.
Variation of NE with ah and av for different values of f with H/l = 0.3,
H/h = 0.16 for (a) fa = 1.0, (b) fa = 1.2
Acta Geotechnica (Springer Pub.), 2008, Vol. 3, No. 2, pp 115-123.
40
fafa= =
1.01.0
fafa= =
1.21.2
faf= =
1.41.4
a
faf= =
1.61.6
a
30
faf= =
1.81.8
a
faf= =
2.02.0
a
NE
20
10
0
0
0.1
0.2
ah
0.3
Effect of soil amplification on NE for different values of ah with
f = 30o, av = 0.5ah, H/l = 0.3, H/h = 0.16
Acta Geotechnica (Springer Pub.), 2008, Vol. 3, No. 2, pp 115-123.
0.4
Comparison of NE with fa = 1.0, av = 0.0, H/l = 0.3 and
H/h = 0.16 for (a) f = 30o, (b) f = 40o
Acta Geotechnica (Springer Pub.), 2008, Vol. 3, No. 2, pp 115-123.
Seismic Vertical Uplift Capacity of
Horizontal Strip Anchors using
Upper Bound Limit Analysis
Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351.
Failure mechanism and associated forces
Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351.
Variation of fE with ah for different
values of fa,  and av with f = 20o,
H/l = 0.3 and H/h = 0.16
Pu
f E = 2
b
H
=
b
Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp
342-351.
10
fa = 1.0 (upper most)
1.2
1.4
1.6
1.8
2.0 (lower most)
9
fE
8
7
6
5
0.0
0.1
0.2
0.3
0.4
ah
Effect of soil amplification on f for different values of a with
f = 30o, av = 0.5ah,  = 3.0, H/l = 0.3 and H/h = 0.16
Fig. 5. Effect of soil amplification on fE for different values of E
ah with f = 30o, av = 0.5ah,  = 3.0, H/l = 0.3 andh H/h = 0.16.
Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351.
10
av/ah = 0.00 (upper most)
0.25
0.50
0.75
1.00 (lower most)
9
fE
8
7
6
5
0
0.1
0.2
ah
0.3
0.4
o, f= 0.16.
Fig. of
6. Effect
av onf fE for
different
values of ah values
with f = 30o, fof
3.0, H/lf= 0.3
and H/h
Effect
av ofon
different
ah =with
= 30
a = 1.4,
E for
a = 1.4,
 = 3.0, H/l = 0.3 and H/h = 0.16
Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351.
Geometry of the failure patterns for
different values of f with fa = 1.4,  = 3.0,
av = 0.5ah, H/l = 0.3 and H/h = 0.16
Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351.
Comparison of fE for fa = 1.0, av = 0.0,  = 3.0, H/l = 0.3 and H/h = 0.16
f
30o
40o
50o
ah
fE
Present analysis Kumar (2001) Choudhury & Subba Rao (2004)
0.0
1.577
1.577
1.071
0.1
1.571
1.566
1.057
0.2
1.553
1.544
1.028
0.3
1.520
1.499
0.986
0.0
1.839
1.839
1.543
0.1
1.835
1.832
1.457
0.2
1.821
1.815
1.386
0.3
1.798
1.786
1.286
0.0
2.192
2.192
1.986
0.1
2.189
2.187
1.828
0.2
2.179
2.174
1.657
0.3
2.163
2.155
1.514
Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351.
Seismic Active Earth Pressure
Behind Non-vertical Retaining Wall
using Limit Equilibrium Method
Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.
Failure mechanism and associated forces
Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.
0.8
0.8
q = 10o
5o
0o
-5o
-10o (lower
most)
0.7
0.6
Kae
1.0
q = 10o
5o
0o
-5o
-10o (lower
most)
0.7
0.6
Kae
0.8
0.7
Kae
0.6
0.5
0.5
0.5
0.4
0.4
q = 10o
5o
0o
-5o
-10o (lower
most)
0.9
0.4
0.3
0.3
d = 0.0
0.2
0.0
0.1
0.2
ah
0.3
d = 0.5f
0.2
0.0
0.4
0.1
0.2
ah
0.3
0.3
d=f
0.2
0.0
0.4
0.1
0.2
ah
0.3
0.4
(a)
0.8
1.0
q = 10o
5o
0o
-5o
-10o (lower
most)
0.7
0.6
Kae
1.4
q = 10o
5o
0o
-5o
-10o (lower
most)
0.8
1.0
Kae
Kae
0.6
0.5
q = 10o
5o
0o
-5o
-10o (lower
most)
1.2
0.8
0.6
0.4
0.4
0.4
0.3
d = 0.0
0.2
0.0
0.1
0.2
ah
0.3
0.4
d = 0.5f
0.2
0.0
0.1
0.2
ah
0.3
0.4
d=f
0.2
0.0
0.1
0.2
ah
0.3
(b)
Variation
of Kofaeactive
withpressure
ah for
f = 30Koae, with
av =ah0.5a
=0.5a
0.3h, and
H/h
0.16
(a)(a)fafa == 1.0,
1.0,
fa = 1.4
o, a =
Fig. 2. Variation
coefficient
for f =h,30H/l
H/l = 0.3
and=H/h
= 0.16
(b)(b)
fa = 1.4.
v
Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.
0.4
0.0
fa = 1.0
fa=1.0
0.1
fa = 1.2
fa=1.2
fa = 1.4
fa=1.4
0.2
fa = 1.6
fa=1.6
fa = 1.8
1.8
fa
0.3
0.4
z/H
0.5
0.6
0.7
0.8
0.9
1.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
pae/H
Fig. 3. Normalized
seismic
activepressure
earth pressure distribution
for different values
fa
Normalized seismic
active
earth
distribution
forofdifferent
values of fa
o
o
(f = 30 , d = 0.5f, q = 10 , ah = 0.2, av = 0.5ah, H/l = 0.3, H/h = 0.16).
(f = 30o, d = 0.5f, q = 10o, ah = 0.2, av = 0.5ah, H/l = 0.3, H/h = 0.16)
Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.
0.0
f = 20o
phi=20
f = 30o
phi=30
0.1
f = 40o
phi=40
f = 50o
phi=50
0.2
0.3
0.4
z/H
0.5
0.6
0.7
0.8
0.9
1.0
0
0.1
0.2
0.3
0.4
pae/H
0.5
0.6
0.7
0.8
Normalized seismic active earth pressure distribution for different values of f
Fig. 4. Normalized seismic active earth pressure distribution for different values of f
(d = 0.5f, q = 10o,(da= h0.5f,
= q0.2,
ah v= 0.2,
= 0.5a
H/l
= H/h
0.3,
H/h
= 10o, a
av = 0.5a
= 0.3,
= 0.16,
fa = =
1.4).0.16, fa = 1.4)
hh,, H/l
Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.
0.0
q = -15o
theta=-15
0.1
q = -10o
theta=-10
q = -5o
theta=-5
0.2
q = 0o
theta=0
theta=5
q = 5o
0.3
q = 10o
theta=10
theta=15
q = 15o
0.4
z/H
0.5
0.6
0.7
0.8
0.9
1.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
pae/H
Fig. 5. Normalized
seismic
earth pressure
distribution for different
of q
Normalized seismic
active
earthactive
pressure
distribution
forvalues
different
values of q
o, d = 0.5f, a = 0.2, a = 0.5a , H/l = 0.3, H/h = 0.16, f = 1.4)
(f
=
30
a
(f = 30o, d = 0.5f, ah = 0.2,h av = v0.5ahh , H/l = 0.3, H/h
= 0.16, fa = 1.4)
Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.
0.0
d = 0 del=0
phi=20,
f = 20o
f = 30o
0.1
d = 0.5f
phi=20,
del=0.5phi
phi=20,
d = f del=phi
0.2
phi=30, del=0
0.3
phi=30, del=0.5phi
phi=30, del=phi
0.4
z/H
0.5
0.6
0.7
0.8
0.9
1.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
pae/H
Fig. 6.seismic
Normalized seismic
active earth
pressure
distribution for different
values of f and for
d
Normalized
active
earth
pressure
distribution
different
o
(q = 10 , ah = 0.2, av = 0.5ah, H/l = 0.3, H/h = 0.16, fa = 1.4)
values of f and d
(q = 10o, ah = 0.2, av = 0.5ah, H/l = 0.3, H/h = 0.16, fa = 1.4)
Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.
Geometry of the failure patterns
for different values of ah with
fa = 1.4, q = 10o, d = 0.5f, av =
0.5ah, H/l = 0.3 and H/h = 0.16
Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.
Comparison of Kae
for av = 0.5ah,
H/l = 0.3, H/h = 0.16
and fa = 1.0
Canadian Geotechnical Journal, 2008,
Vol. 45, No. 1, pp 117-123.
Seismic Active Earth Pressure on
Walls with Bilinear Backface using
Limit Equilibrium Method
Computers and Geotechnics (Elsevier Pub.), (In press).
Kae1 =
2Pae1 ( t )
 H12
K ae 2 =
2 Pae 2 ( t )
 H2
Failure mechanism and associated forces
Computers and Geotechnics (Elsevier Pub.), (In press).
θ1 = 90 (upper most)
75
0.8
60
45
0.6
0.2
0.4
δ1 = δ2 = 0
0.2
ah
0.3
0.4
0.1
0.2
ah
0.3
0.4
Kae2
0.4
δ1 = δ2 = 0
0.8
0.2
ah
0.3
0.4
0.1
0.2
ah
0.3
0.4
1.2
0.8
0.4
0.2
0.0
δ1 = δ2 = f
2.4 θ = 120 (upper most)
2
110
2.0
100
90
1.6
θ2 = 120 (upper most)
110
1.2
100
1.0
90
0.6
0.1
0.0
0.0
1.4
0.6
0.2
0.0
0.2
δ1 = δ2 = 0.5f
Kae2
0.1
0.0
0.0
0.6
0.4
0.2
θ2 = 120 (upper most)
110
1.0
100
90
0.8
Kae2
θ1 = 90 (upper most)
75
1.0
60
45
0.8
θ1 = 90 (upper most)
75
0.8
60
45
0.6
Kae1
0.4
0.0
0.0
1.2
1.0
Kae1
Kae1
1.0
δ1 = δ2 = 0.5f
0.1
0.2
ah
0.3
0.4
0.4
0.0
0.0
δ1 = δ2 = f
0.1
0.2
ah
0.3
0.4
Variation of active pressure coefficients Kae1 and Kae2 with ah for f = 30˚, H1/H = 1/3, av = 0.5ah,
= 1.4, H/TVs = 0.3 and H/TVp = 0.16: (a) θ2 =100˚ (b) θ1 = 75˚
Computers and Geotechnics (Elsevier Pub.), (In press).
fa
Variation of Kae1 and Kae2 for different
combinations of q1 and q2 with f = 30˚,
d1 = d2 = 0.5f, H1/H = 1/3, av = 0.5ah, fa = 1.4,
H/TVs = 0.3 and H/TVp = 0.16
(a) Kae1 (b) Kae2
Computers and Geotechnics (Elsevier Pub.), (In press).
0.0
fa = 1.0
0.1
fa = 1.2
0.2
fa = 1.4
fa = 1.6
0.3
fa = 1.8
z/H
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
pae /H
Normalized pae distribution for different fa (f = 30˚, d1 = d2 = 0.5f, θ1 = 75˚,
θ2 = 100˚, H1/H =1/3, ah = 0.2, av = 0.5ah, H/TVs = 0.3 and H/TVp = 0.16)
Computers and Geotechnics (Elsevier Pub.), (In press).
0.0
f = 20
f = 30
f = 40
f = 50
0.1
0.2
0.3
z/H
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
pae /H
Normalized pae distribution for different f (d1 = d2 = 0.5f, θ1 = 75˚, θ2 = 100˚,
H1/H =1/3, fa = 1.4, ah = 0.2, av = 0.5ah, H/TVs = 0.3 and H/TVp = 0.16)
Computers and Geotechnics (Elsevier Pub.), (In press).
0.0
0.1
q1 = 60, q2 = 90
q1 = 70, q2 = 100
0.2
q = 80, q = 110
1
0.3
2
q1 = 90, q2 = 120
z/H
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0
0.1
0.2
0.3
0.4
0.5
pae /H
0.6
0.7
0.8
0.9
Normalized pae distribution for different θ1 and θ2 (f = 30o, d1 = d2 = 0.5f, H1/H =1/3,
fa = 1.4, ah = 0.2, av = 0.5ah, H/TVs = 0.3 and H/TVp = 0.16)
Computers and Geotechnics (Elsevier Pub.), (In press).
0.0
f = 20°
f = 30°
0.1
d1 = d2 = 0
d = d = 0.5f
1
0.2
2
d1 = d2 = f
0.3
z/H
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
pae /H
0.8
Normalized pae distribution for different wall friction and f (θ1 = 75˚, θ2 = 100˚,
H1/H =1/3, fa = 1.4, ah = 0.2, av = 0.5ah, H/TVs = 0.3 and H/TVp = 0.16)
Computers and Geotechnics (Elsevier Pub.), (In press).
Comparison of Kae1 and Kae2 for H1/H = 1/2, f = 36˚, d1 = d2 = 18˚,
θ1 = 75˚, θ2 = 105˚, av = 0.5ah and fa =1.0
Present analysis
H/TVs = 0.3
H/TVs = 0.4
H/TVs = 0.5
H/TVp = 0.16
H/TVp = 0.21
H/TVp = 0.27
Kae1
Kae2
Kae1
Kae2
Kae1
Kae2
Kae1
Kae2
0.0
0.147
0.260
0.147
0.260
0.147
0.260
0.147
0.260
0.1
0.201
0.318
0.199
0.312
0.196
0.305
0.204
0.307
0.2
0.266
0.385
0.262
0.371
0.256
0.354
0.273
0.355
0.3
0.344
0.462
0.337
0.437
0.328
0.409
0.353
0.403
0.4
0.435
0.551
0.426
0.514
0.416
0.471
0.447
0.453
0.5
0.544
0.655
0.535
0.601
0.524
0.538
0.556
0.504
ah
Computers and Geotechnics (Elsevier Pub.), (In press).
Greco [8]
Seismic Passive Earth Pressure
Behind Non-vertical Retaining Wall
using Limit Equilibrium Method
Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703.
Failure mechanism and associated forces
Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703.
4.0
8.0
q = -10o
-5o
0o
5o
10o (lower most)
3.5
3.0
q = -10o
-5o
0o
5o
10o (lower most)
7.0
6.0
Kpe
Kpe
25.0
5.0
15.0
Kpe
4.0
2.5
q = -10o
-5o
0o
5o
10o (lower
most)
20.0
10.0
3.0
2.0
5.0
2.0
d = 0.0
1.5
d = 0.5f
d=f
1.0
0.0
0.1
0.2
ah
0.3
0.4
0.0
0.0
0.1
0.2
ah
0.3
0.4
0.0
0.1
0.2
ah
Variation of passive pressure coefficient Kpe with ah for f = 30o,
av = 0.5ah, H/l = 0.3 and H/h = 0.16
Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703.
0.3
0.4
0.0
phi=20
f = 20o
0.1
phi=30
f = 30o
phi=40
f = 40o
0.2
phi=50
f = 50o
0.3
0.4
z/H
0.5
0.6
0.7
0.8
0.9
1.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
ppe/H
Normalized ppe distribution for different values of f
(d = 0.5f, q = 10o, ah = 0.2, av = 0.5ah, H/l = 0.3, H/h = 0.16)
Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703.
16.0
0.0
q = -15o
theta=-15
q = -10o
theta=-10
0.1
theta=-5
q = -5o
q = 0o
theta=0
0.2
q = 5o
theta=5
0.3
theta=10
q = 10o
theta=15
q = 15o
0.4
z/H
0.5
0.6
0.7
0.8
0.9
1.0
0.0
1.0
2.0
3.0
4.0
ppe/H
5.0
6.0
7.0
Normalized ppe distribution for different values of q
(f = 30o, d = 0.5f, ah = 0.2, av = 0.5ah, H/l = 0.3, H/h = 0.16)
Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703.
8.0
0.0
d=0
del=0
0.1
del=0.25phi
d = 0.25f
del=0.5phi
d = 0.5f
0.2
d = 0.75f
del=0.75phi
d=f
del=phi
0.3
0.4
z/H
0.5
0.6
0.7
0.8
0.9
1.0
0.0
1.0
2.0
3.0
4.0
ppe/H
Normalized ppe distribution for different values of d
(f = 30o, q = 10o, ah = 0.2, av = 0.5ah, H/l = 0.3, H/h = 0.16)
Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703.
5.0
Comparison of Kpe for d = 0.5f, q = 0o, av = 0.0, H/l = 0.3 and H/h = 0.16
f
25o
30o
35o
40o
ah
Kpe
Present
analysis
Chang
(1981)
Soubra (2000)
Lancellotta (2007)
0.0
3.55
3.45
3.43
3.10
0.1
3.26
2.89
3.15
2.86
0.2
2.96
2.74
2.85
2.62
0.3
2.63
2.38
2.50
2.26
0.0
4.98
4.64
4.69
4.29
0.1
4.60
4.29
4.35
3.93
0.2
4.21
3.93
3.99
3.57
0.3
3.80
3.45
3.59
3.21
0.0
7.36
6.67
6.67
5.71
0.1
6.84
6.19
6.24
5.48
0.2
6.31
5.71
5.78
5.00
0.3
5.76
5.24
5.29
4.52
0.0
11.77
10.00
9.99
8.33
0.1
11.00
9.29
9.40
7.86
0.2
10.21
8.57
8.79
7.26
0.3
9.41
8.10
8.15
6.67
Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703.
Comparison of Kpe for d = 0.5f, q = 10o, av = 0.5ah, H/l = 0.3 and H/h = 0.16
f
d
0
20o
0.5f
f
0
30o
0.5f
f
ah
Kpe
Present
analysis
MononobeOkabe method
Caquot and
Kerisel
(1948)
Zhu and
Qian (2000)
0.0
1.84
1.84
1.74
1.83
0.1
1.66
1.64
-
-
0.2
1.45
1.40
-
-
0.0
2.27
2.27
-
2.26
0.1
2.00
1.96
-
-
0.2
1.70
1.62
-
-
0.0
2.86
2.86
2.57
2.66
0.1
2.47
2.42
-
-
0.2
2.04
1.93
-
-
0.0
2.54
2.54
2.33
2.51
0.2
2.07
2.02
-
-
0.4
1.53
1.35
-
-
0.0
3.80
3.80
-
3.73
0.2
2.96
2.85
-
-
0.4
2.00
1.70
-
-
0.0
6.45
6.45
4.98
5.20
0.2
4.79
4.58
-
-
0.4
2.96
2.43
-
-
Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703.
Conclusions
Strip Footing
 The magnitude of NE decreases with increase in soil
amplification, shear and primary wave velocities,
which can not be predicted by the existing pseudo-
static approach
 In the upper-bound solution, for higher values of f, a
significant increase in NE was observed at lower
value of ah
Acta Geotechnica (Springer Pub.), 2008, Vol. 3, No. 2, pp 115-123.
Horizontal Strip Anchor
 The values of fE were found to decrease extensively
with increase in both ah and av, and soil amplification
 In presence of horizontal and vertical earthquake
acceleration, the present values were found to be the
highest
 In presence of amplification of vibration, no
significant difference between present values and
the existing pseudo-static values was found except
for higher values of embedment ratio  and ah
Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351.
Active Pressure on Cantilever Wall
 In presence of q, the active earth pressure first
decreases with increase in d up to z/H = 0.3 and then
increases significantly at higher depth with increase
in d for a particular value of f
 The seismic active earth pressure distribution was
found to be non-linear behind the wall in pseudodynamic analysis
 The non-linearity of active earth pressure
distribution increases with the increase in seismicity,
which causes the point of application of total active
thrust to be shifted
Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.
Wall with Bilinear Backface
 It was found that the magnitude of seismic active
earth pressures for upper and lower parts of the wall
increases with an increase in the horizontal
earthquake acceleration coefficient ah and the wall
inclinations θ1 and θ2, respectively
 Unlike the pseudo-static analysis, the seismic active
earth pressure distribution was found to be
nonlinear behind the wall in pseudo-dynamic
analysis and the nonlinearity of seismic active earth
pressure distribution increases with an increase in
seismicity, which causes the point of application of
the total active thrust to be shifted
Computers and Geotechnics (Elsevier Pub.), (In press).
Passive Pressure on Cantilever Wall
 It was found that the magnitude of seismic passive
earth pressure decreases with the increase in the
values of wall inclination q, horizontal and vertical
earthquake acceleration coefficients
 In presence of q, the passive earth pressure
increases with the increase in d for a particular value
of f
 The present analysis adopted the Coulomb failure
mechanism, which generally overestimates the
passive pressure coefficient Kpe in case of a rough
retaining wall and the error generated by the
Coulomb theory increases as the wall inclination
increases in the inward direction
Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703.
"The concern for man and his destiny must be the chief interest of all
technical efforts. Never forget this among your equations and diagrams“
-Albert Einstein.