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Seismic Analysis of Seismic Analysis of
Some Some
Geotechnical Problems Geotechnical Problems
– Pseudo-dynamic – Pseudo-dynamic
Approach 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 ApproachPseudo-static Approach Pseudo-dynamic Approach
The dynamic loading induced by earthquake is considered as time independent, which ultimately assumes that the magnitude and phase of acceleration is uniform throughout the soil mass
The time and phase difference due to finite primary and shear wave velocity can be considered
Generally does not consider the amplification of vibration which takes place towards the ground surface
Considers the amplification of excitation
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, wavelength of the shear wave = TVs
Total Vertical Seismic Inertia Force Qv(t)
Where, wavelength of the primary wave = TVp
Upper Bound Limit Analysis
Theorem: If a compatible mechanism of plastic deformation
, , is assumed, which satisfies the condition = 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.
*p
ij *p
iv *p
iv
Equation
V S V
*p
ii
*p
ii
*p
ij
*p
ij dVvFdSvTdV
*p
ij
*p
iv
*p
ij
= displacement rate
= plastic strain rate compatible with
displacement rate
= stress tensor associated with plastic strain
rateTi = 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.
Footing
Pu
Pu
B
C
D
Qh1
Qv1
W1
U1
U21
U2
Qh2
Qv2
W2z
z
dzdz
z
Vs, Vp
ah = hg
ah = fahg
(a)
A
b
U2
U21
U1
(b) Collapse mechanism and velocity
hodograph Acta Geotechnica (Springer Pub.), 2008, Vol. 3, No. 2, pp 115-123.
Variation of NE with h and v for different values of with H/ = 0.3,
H/ = 0.16 for (a) fa = 1.0, (b) fa = 1.2
Acta Geotechnica (Springer Pub.), 2008, Vol. 3, No. 2, pp 115-123.
Effect of soil amplification on NE for different values of h with
= 30o, v = 0.5h, H/ = 0.3, H/ = 0.16
0
10
20
30
40
0 0.1 0.2 0.3 0.4
fa = 1.0
fa = 1.2
fa = 1.4
fa = 1.6
fa = 1.8
fa = 2.0
NE
h
fa = 1.0
fa = 1.2
fa = 1.4
fa = 1.6
fa = 1.8
fa = 2.0
Acta Geotechnica (Springer Pub.), 2008, Vol. 3, No. 2, pp 115-123.
Comparison of NE with fa = 1.0, v = 0.0, H/ = 0.3 and
H/ = 0.16 for (a) = 30o, (b) = 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 fE with h for different
values of fa, and v with = 20o,
H/ = 0.3 and H/ = 0.16
Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351.
2b
Pf u
E
b
H
5
6
7
8
9
10
0.0 0.1 0.2 0.3 0.4
Fig. 5. Effect of soil amplification on fE for different values of h with = 30o, v = 0.5h, = 3.0, H/ = 0.3 and H/ = 0.16.
fa = 1.0 (upper most) 1.2 1.4 1.6 1.8 2.0 (lower most)
fE
h
Effect of soil amplification on fE for different values of h with
= 30o, v = 0.5h, = 3.0, H/ = 0.3 and H/ = 0.16
Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351.
5
6
7
8
9
10
0 0.1 0.2 0.3 0.4
v/h = 0.00 (upper most) 0.25 0.50 0.75 1.00 (lower most)
fE
h
Fig. 6. Effect of v on fE for different values of h with = 30o, fa = 1.4, = 3.0, H/ = 0.3 and H/ = 0.16.Effect of v on fE for different values of h with = 30o, fa = 1.4,
= 3.0, H/ = 0.3 and 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 with fa = 1.4, = 3.0,
v = 0.5h, H/ = 0.3 and H/= 0.16
Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351.
h
fE
Present analysis Kumar (2001) Choudhury & Subba Rao (2004)
30o
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
40o
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
50o
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
Comparison of fE for fa = 1.0, v = 0.0, = 3.0, H/= 0.3 and H/ = 0.16
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.
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.0 0.1 0.2 0.3 0.4
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.0 0.1 0.2 0.3 0.4
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 0.1 0.2 0.3 0.4
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.0 0.1 0.2 0.3 0.4
0.2
0.4
0.6
0.8
1.0
0.0 0.1 0.2 0.3 0.4
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.0 0.1 0.2 0.3 0.4
h h h
Kae Kae Kae
= 10o
5o
0o
-5o
-10o (lower most)
= 10o
5o
0o
-5o
-10o (lower most)
= 10o
5o
0o
-5o
-10o (lower most)
= 0.0 = 0.5 =
Fig. 2. Variation of active pressure coefficient Kae with h for = 30o, v = 0.5h, H/ = 0.3 and H/ = 0.16 (a) fa = 1.0, (b) fa = 1.4.
h hh
Kae KaeKae
= 10o
5o
0o
-5o
-10o (lower most)
= 10o
5o
0o
-5o
-10o (lower most)
= 10o
5o
0o
-5o
-10o (lower most)
= 0.0 = 0.5 =
(a)
(b)
Variation of Kae with h for= 30o, v = 0.5h, H/ = 0.3 and H/= 0.16 (a) fa = 1.0, (b) fa = 1.4 Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.
0.0
0.1
0.2
0.3
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
fa=1.0
fa=1.2
fa=1.4
fa=1.6
fa = 1.8
pae/H
z/H
Fig. 3. Normalized seismic active earth pressure distribution for different values of fa ( = 30o, = 0.5, = 10o, h = 0.2, v = 0.5h, H/ = 0.3, H/ = 0.16).
fa = 1.0
fa = 1.4
fa = 1.2
fa = 1.6
fa = 1.8
Normalized seismic active earth pressure distribution for different values of fa
( = 30o, = 0.5, = 10o, h = 0.2, v = 0.5h, H/ = 0.3, H/ = 0.16) Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
phi=20
phi=30
phi=40
phi=50
= 20o
pae/H
z/H
Fig. 4. Normalized seismic active earth pressure distribution for different values of ( = 0.5, = 10o, h = 0.2, v = 0.5h, H/ = 0.3, H/ = 0.16, fa = 1.4).
= 30o
= 40o
= 50o
Normalized seismic active earth pressure distribution for different values of
( = 0.5, = 10o, h = 0.2, v = 0.5h, H/ = 0.3, H/ = 0.16, fa = 1.4) Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.
0.0
0.1
0.2
0.3
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
theta=-15
theta=-10
theta=-5
theta=0
theta=5
theta=10
theta=15
= 0o
pae/H
z/H
Fig. 5. Normalized seismic active earth pressure distribution for different values of ( = 30o, = 0.5, h = 0.2, v = 0.5h, H/ = 0.3, H/ = 0.16, fa = 1.4)
= 5o
= 10o
= 15o
= -15o
= -10o
= -5o
Normalized seismic active earth pressure distribution for different values of
( = 30o, = 0.5, h = 0.2, v = 0.5h, H/= 0.3, H/= 0.16, fa = 1.4) Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.
0.0
0.1
0.2
0.3
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 0.9
phi=20, del=0
phi=20, del=0.5phi
phi=20, del=phi
phi=30, del=0
phi=30, del=0.5phi
phi=30, del=phi
= 0
pae/H
z/H
Fig. 6. Normalized seismic active earth pressure distribution for different values of and ( = 10o, h = 0.2, v = 0.5h, H/ = 0.3, H/ = 0.16, fa = 1.4)
= 20o
= 30o
= 0.5
=
Normalized seismic active earth pressure distribution for different values of and
( = 10o, h = 0.2, v = 0.5h, H/ = 0.3, 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 h with fa
= 1.4, = 10o, = 0.5, v = 0.5h,
H/ = 0.3 and H/ = 0.16
Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.
Comparison of Kae for
v = 0.5h, H/ =
0.3, 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).
22 2
2 aeae
P tK
H
11 2
1
2 aeae
P tK
H
Computers and Geotechnics (Elsevier Pub.), (In press).
Failure mechanism and associated forces
Variation of active pressure coefficients Kae1 and Kae2 with h for = 30˚, H1/H = 1/3, v = 0.5h, fa
= 1.4, H/TVs = 0.3 and H/TVp = 0.16: (a) θ2 =100˚ (b) θ1 = 75˚
0.0 0.1 0.2 0.3 0.40.0
0.2
0.4
0.6
0.8
1.0
h
Kae
1
0.0 0.1 0.2 0.3 0.40.0
0.2
0.4
0.6
0.8
1.0
h
Kae
1
0.0 0.1 0.2 0.3 0.40.0
0.2
0.4
0.6
0.8
1.0
1.2
h
Kae
1
θ1 = 90 (upper most) 75 60 45
δ1 = δ2 = 0.5
θ1 = 90 (upper most) 75 60 45
δ1 = δ2 =
θ1 = 90 (upper most) 75 60 45
δ1 = δ2 = 0
0.0 0.1 0.2 0.3 0.40.2
0.4
0.6
0.8
1.0
h
Kae
2
0.0 0.1 0.2 0.3 0.40.2
0.4
0.6
0.8
1.0
1.2
1.4
h
Kae
2
0.0 0.1 0.2 0.3 0.40.0
0.4
0.8
1.2
1.6
2.0
2.4
h
Kae
2
θ2 = 120 (upper most) 110 100 90
δ1 = δ2 = 0 δ1 = δ2 = 0.5
θ2 = 120 (upper most) 110 100 90
δ1 = δ2 =
θ2 = 120 (upper most) 110 100 90
Computers and Geotechnics (Elsevier Pub.), (In press).
Variation of Kae1 and Kae2 for different
combinations of 1 and 2 with = 30˚,
1 = 2 = 0.5, H1/H = 1/3, v = 0.5h, fa = 1.4,
H/TVs = 0.3 and H/TVp = 0.16
(a) Kae1 (b) Kae2
Computers and Geotechnics (Elsevier Pub.), (In press).
Computers and Geotechnics (Elsevier Pub.), (In press).
Normalized pae distribution for different fa (= 30˚, 1 = 2 = 0.5, θ1 = 75˚, θ2
= 100˚, H1/H =1/3, h = 0.2, v = 0.5h, H/TVs = 0.3 and H/TVp = 0.16)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
pae
/H
z/H
fa = 1.0
fa = 1.2
fa = 1.4
fa = 1.6
fa = 1.8
Computers and Geotechnics (Elsevier Pub.), (In press).
Normalized pae distribution for different (1 = 2 = 0.5, θ1 = 75˚, θ2 = 100˚, H1/H
=1/3, fa = 1.4, h = 0.2, v = 0.5h, H/TVs = 0.3 and H/TVp = 0.16)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
pae
/H
z/H
= 20 = 30 = 40 = 50
Computers and Geotechnics (Elsevier Pub.), (In press).
Normalized pae distribution for different θ1 and θ2 ( = 30o, 1 = 2 = 0.5, H1/H =1/3,
fa = 1.4, h = 0.2, v = 0.5ah, H/TVs = 0.3 and H/TVp = 0.16)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
pae
/H
z/H
1 = 60 ,
2 = 90
1 = 70 ,
2 = 100
1 = 80 ,
2 = 110
1 = 90 ,
2 = 120
Computers and Geotechnics (Elsevier Pub.), (In press).
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
pae
/H
z/H
1 =
2 = 0
1 =
2 = 0.5
1 =
2 =
= 20° = 30°
Normalized pae distribution for different wall friction and (θ1 = 75˚, θ2 = 100˚,
H1/H =1/3, fa = 1.4, h = 0.2, v = 0.5h, H/TVs = 0.3 and H/TVp = 0.16)
Computers and Geotechnics (Elsevier Pub.), (In press).
h
Present analysis
Greco [8] 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
Comparison of Kae1 and Kae2 for H1/H = 1/2, = 36˚, 1 = 2 = 18˚,
θ1 = 75˚, θ2 = 105˚, v = 0.5h and fa =1.0
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.
Variation of passive pressure coefficient Kpe with h for = 30o,
v = 0.5h, H/ = 0.3 and H/ = 0.16
1.5
2.0
2.5
3.0
3.5
4.0
0.0 0.1 0.2 0.3 0.4
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0.0 0.1 0.2 0.3 0.4
0.0
5.0
10.0
15.0
20.0
25.0
0.0 0.1 0.2 0.3 0.4h h h
Kpe Kpe Kpe
= -10o
-5o
0o
5o
10o (lower most)
= -10o
-5o
0o
5o
10o (lower most)
= -10o
-5o
0o
5o
10o (lower most)
= 0.0 = 0.5
=
Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703.
Normalized ppe distribution for different values of
( = 0.5, = 10o, h = 0.2, v = 0.5h, H/ = 0.3, H/ = 0.16)
0.0
0.1
0.2
0.3
0.4
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 16.0
phi=20
phi=30
phi=40
phi=50
= 20o
ppe/H
z/H
= 30o
= 40o
= 50o
Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
theta=-15
theta=-10
theta=-5
theta=0
theta=5
theta=10
theta=15
= 0o
ppe/H
z/H
= 5o
= 10o
= 15o
= -5o
= -10o
= -15o
Normalized ppe distribution for different values of
( = 30o, = 0.5, h = 0.2, v = 0.5h, H/ = 0.3, H/ = 0.16)
Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 1.0 2.0 3.0 4.0 5.0
del=0
del=0.25phi
del=0.5phi
del=0.75phi
del=phi
= 0
ppe/H
z/H
= 0.25
=
= 0.5
= 0.75
Normalized ppe distribution for different values of
( = 30o, = 10o, h = 0.2, v = 0.5h, H/ = 0.3, H/ = 0.16)
Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703.
Comparison of Kpe for = 0.5 = 0o, v = 0.0, H/ = 0.3 and H/ = 0.16
h Kpe
Present analysis
Chang (1981)
Soubra (2000) Lancellotta (2007)
25o
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
30o
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
35o
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
40o
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.
h Kpe
Present analysis
Mononobe-Okabe method
Caquot and Kerisel (1948)
Zhu and Qian (2000)
20o
0
0.0 1.84 1.84 1.74 1.83
0.1 1.66 1.64 - -
0.2 1.45 1.40 - -
0.5
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 - -
30o
0
0.0 2.54 2.54 2.33 2.51
0.2 2.07 2.02 - -
0.4 1.53 1.35 - -
0.5
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 - -
Comparison of Kpe for = 0.5 = 10o, v = 0.5h, H/ = 0.3 and H/ = 0.16
Geotechnical and Geological Engg. Journal (Springer Pub.), 2007, Vol. 25, No. 6, pp 693-703.
Conclusions
The magnitude of NE 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 , a
significant increase in NE was observed at lower
value of h
Strip Footing
Acta Geotechnica (Springer Pub.), 2008, Vol. 3, No. 2, pp 115-123.
The values of fE were found to decrease extensively
with increase in both h and v, 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 h
Horizontal Strip Anchor
Computers and Geotechnics (Elsevier Pub.), 2009, Vol. 36, No. 1-2, pp 342-351.
In presence of , the active earth pressure first
decreases with increase in up to z/H = 0.3 and then
increases significantly at higher depth with increase
in for a particular value of
The seismic active earth pressure distribution was
found to be non-linear behind the wall in pseudo-
dynamic 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
Active Pressure on Cantilever Wall
Canadian Geotechnical Journal, 2008, Vol. 45, No. 1, pp 117-123.
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
h 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
Wall with Bilinear Backface
Computers and Geotechnics (Elsevier Pub.), (In press).
It was found that the magnitude of seismic passive earth pressure decreases with the increase in the values of wall inclination , horizontal and vertical earthquake acceleration coefficients
In presence of , the passive earth pressure increases with the increase in for a particular value of
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
Passive Pressure on Cantilever Wall
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 "The concern for man and his destiny must be the chief interest of all technical efforts. Never forget this among your equations and diagrams“technical efforts. Never forget this among your equations and diagrams“
-Albert Einstein.-Albert Einstein.