Pseudo static passive response of retaining wall supporting c-φ backfill
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This document discusses the importance of passive resistance in the design of retaining walls supporting c-φ backfill, particularly under seismic conditions. It critiques traditional analytical methods that assume linear failure surfaces, arguing that non-linear analysis provides more accurate predictions of earth pressures. The study derives an analytical expression for the passive earth pressure coefficient through a pseudo-static approach and presents results from a detailed parametric study.
![IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163
__________________________________________________________________________________________
Volume: 02 Issue: 03 | Mar-2013, Available @ http://www.ijret.org 256
)}tan)(tan(tan)1(
))1(tan(...........)(tan({tan)(
cos
sin)(
))1(cos(
sin)(
)tan(tan)(
2
1
)cos()cos(
11
2
1
1
1
2
111
cn
n
c
i
c
kRP
Rr
a
R
h
(1)
0V
;
cos
cos)(
cos
cos)(
)1)(tan(tan)(
2
1
)sin()sin(
1
1
1
2
111
a
v
cc
k
RP
(2)
Solving these equations (1 and 2), we get,
)sin(
}]sin()tan(tantan)1(
))1(tan(.................
............){(tan(
)1(
tan2
(
cos
)cos(
cos
cos
)}cos()sin(tan(
)tan)[{(tan1()(
2
1
1
1
1
1
1
11
1
2
1
s
R
R
v
ss
v
P
Nn
n
k
MN
k
P
(3)
Where,
v
h
k
k
1
tan (4)
In the present study Ns and Ms Values have been introduced
for the analysis of slices, where
Ns = (H /ΔH)Nc (5)
Ms = (H /ΔH)Mc (6)
Where,
Nc = (2c / γH) (7)
Mc = (2ca / γH) (8)
Applying the same procedure for 2nd
slice, we get,
)sin(
)}]sin(
)))tan((tan
))tan)(tan(tan)2(
))1(tan(.............................
)2{(tan(
)1(
tan2
(
cos
)cos(
)cos(
cos
))}cos(
)sin(tan(
))tan((tan3)[{1()(
2
1
1
1
1
1
1
1
1
1
1
1
2
2
R
R
Rs
R
R
R
v
Rs
r
s
R
R
Rv
P
N
n
n
k
MN
k
P
(9)
Similarly, for nth
slice, we get,
0H
;
))})1(tan()(tan(
)tan))1()(tan(1(
])(tan(tan{[
)(
cos
sin)(
))1(cos(
))1(sin()(
)})1(tan({tan)()
2
1
(
))1(cos()cos(
1
1
1
1
2
1
1
1
2
1
R
R
n
im
r
a
R
R
hr
Rnn
nc
nn
m
c
n
nc
knn
nRP
(10)
0V
;
cos
cos)(
))1(cos(
))1(cos()(
)1))()1(
tan((tan)()
2
1
(
))1(sin()sin(
1
1
1
2
1
a
R
R
vR
Rnn
c
n
nc
kn
n
nRP
(11)](https://image.slidesharecdn.com/pseudo-staticpassiveresponseofretainingwallsupportingc-backfill-140801012137-phpapp02/85/Pseudo-static-passive-response-of-retaining-wall-supporting-c-backfill-3-320.jpg)
![IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163
__________________________________________________________________________________________
Volume: 02 Issue: 03 | Mar-2013, Available @ http://www.ijret.org 257
))1(sin(
))1(sin(
))))1(tan((tan
))tan
))1()(tan(1(
)1(
tan2
cos
))1(cos(
))1(cos(
cos
))1(cos(
))1(sin(tan(
)))1(tan()(tan12(
)1()(
2
1
1
1
1
1
1
1
1
1
2
R
R
Rs
R
v
Rs
R
s
R
R
R
v
nP
n
n
nN
nn
K
nM
n
N
n
n
nn
K
P
(12)
Thus, Total passive resistance of the backfill can be stated as,
Pp = Pp1+Pp2+Pp3+………+Ppn (13)
Now the generalized equation for ith
slice can be sorted out as
follows,
0H
;
))})1(tan(
)(tan(
))tan))1((tan(
)1(tan)(
)(tan(tan{
)(
cos
sin)(
))1(cos(
))1(sin()(
)})1(tan({tan)()
2
1
(
))1(cos()cos(
1
1
1
1
2
1
1
1
2
1
R
R
n
im
r
a
R
R
hr
Rii
i
c
i
iin
m
c
i
ic
kii
iRP
(14)
0V
;
cos
cos)(
))1(cos(
))1(cos()(
)1))()1(
tan((tan)()
2
1
(
))1(sin()sin(
1
1
1
2
1
a
R
R
vR
Rii
c
i
ic
ki
i
iRP
(15)
Solving the above equations (14 and 15), the generalized
equations for ith
slice can be formulated as follows:
))1(sin(
))1(sin(
))})1(tan(
(tan{
))}tan))1(
)(tan(1(
tan)(
)])tan({[
)1(
tan2
cos
))1(cos(
))1(cos(
cos
)))1(cos(
))1(sin(tan(
)))1(
tan()(tan12(
)1()(
2
1
1
1
1
1
1
1
1
1
1
1
2
R
R
R
s
R
n
im
R
v
Rs
r
s
R
R
R
v
iP
i
i
i
N
i
i
in
m
k
iM
i
N
i
i
i
i
k
P
(16)
The condition to use Eqn. 16 is at, i = n, we have to take,
0)tan( 1 rm (17)
From all the above equations, the passive earth pressure
coefficient can be simplified as,
2
2
1
H
P
k
n
i
pi
p
(18)](https://image.slidesharecdn.com/pseudo-staticpassiveresponseofretainingwallsupportingc-backfill-140801012137-phpapp02/85/Pseudo-static-passive-response-of-retaining-wall-supporting-c-backfill-4-320.jpg)
![IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163
__________________________________________________________________________________________
Volume: 02 Issue: 03 | Mar-2013, Available @ http://www.ijret.org 265
efficient (Kp) increases due to the increase in wall friction
angle (δ), soil friction angle (Φ), cohesion (c) and adhesion
(ca); at the same time the value of Kp decreases with the
increase in wall inclinations (α), wall height (H), and seismic
accelerations (kh, kv). The inclination of the failure surface
with vertical increases with the decrease in wall inclination
(α), wall friction angle (δ), soil friction angle (Φ) and height of
retaining wall (H). Whereas, the inclination of the failure
surface with vertical decreases with the increase in wall
inclination(α), soil friction angle (Φ), cohesion (c),
adhesion(ca) and wall friction angle (δ). The generation of
sagging nature of rupture surface (in passive condition) is
showing curvilinear response in the determination passive
earth pressure coefficient acting on the retaining walls.
NOTATIONS
Φ = Soil friction angle.
δ = Wall friction angle.
α = Wall inclination angle with the vertical.
Pp = Passive earth pressure.
kh = Horizontal seismic co-efficient.
kv = Vertical seismic co-efficient.
R = Soil reaction force.
γ = unit weight of soil.
Kp = Passive earth pressure coefficient
c = cohesion
ca = adhesion
REFERENCES:
[1]. Azad, A, Shahab Yasrobi, S, Pak, A. (2008), “Active
Pressure Distribution History Behind Rigid Retaining
Walls”, Soil Dynamics and Earthquake Engineering 28
(2008) 365-375.
[2]. Choudhury, D and Nimbalkar, S, (2005), “Seismic Passive
Resistance by Pseudo-dynamic Method”, Geotechnique;
55(9): 699-702.
[3]. Coulomb, C.A. (1776), “Essai Sur Une Application Des
Maximis et Minimis a Queques problems Des Statique
Relatifsa1‟Architecture”, Nem. Div. Sav.Acad,
Sci.Vol.7.
[4]. Ghanbari, A and Ahmadabadi, M. (2010), “Pseudo-
Dynamic Active Earth Pressure Analysis of Inclined
Retaining Walls Using Horizontal Slices Method”,
Transaction A: Civil Engineering Vol. 17, No. 2, pp.
118-130© Sharif University of Technology.
[5]. Ghosh, S. and Sengupta, S. (2012),“ Formulation of
Passive resistance on non vertical retaining wall
backfilled with c-Φ”, Civil and Environmental Research
ISSN 2224-5790 (Print) ISSN 2225-0514 (Online), Vol
2, No.1, 2012.
[6]. Ghosh, S. and Sharma, R. P. (2012), “Pseudo-Dynamic
Evaluation of Passive Response on the Back of A
Retaining Wall Supporting c-Φ Backfill”, Geomechanics
and Geoengineering: An International Journal, Vol. 7,
No. 2, June 2012, 115–121.
[7]. Kumar J, Subba Rao K. S, (1997), “Passive Pressure
determination by method of Slices”, Int J Num Anal
Method Geomech USA 21:337-345.
[8]. Kumar, J. (2001), “Seismic Passive Earth Pressure
Coefficients for Sands”, Can. Geotech. J., Ottawa, 38,
pp: 876-881.
[9]. Mononobe, N. and Matsuo, H. (1929), “On the
Determination of Earth Pressure During Earthquakes”
Proc. of the World Engineering Congress, Tokyo, 9, pp.
179-87.
[10]. Okabe, S. (1926), “General Theory of Earth Pressure”, J.
Japan Soc. Civil Eng., 12(1).
[11]. Rankine, W. J. M. (1857), “On the Stability of Loose
Earth”, Phil. Tras. Royal Society (London).
[12]. Shukla, S. K and Habibi, D. (2011), “Dynamic Passive
Pressure from c-Ф Soil Backfills”, Soil Dynamics and
Earthquake Engineering 31 (2011) 845-848.
[13]. Subbarao, K. S, and Choudhury, D. (2005), “Seismic
Passive Earth Pressure in Soils”, Journal of Geotechnical
and Geoenvironmental Engineering, ASCE 2005; 131(1);
131 -5.
[14]. Terzaghi, K, (1943), “Theoretical Soil Mechanics”: John
Wiley & Sons, New York, 510 p.
BIOGRAPHIES:
Sima Ghosh presently working as an Assistant Professor at
NIT Agartala, INDIA is a consistent Gold
medalist in BE (Civil) from Tripura
Engineering College (now NIT Agartala) in
1994 and M. Tech in Geotechnical
Engineering from IIT, Roorkee in 2001. She
has completed her PhD in Geotechnical
Engineering in 2012 and became the very first person to attain
the PhD Degree since the inception of PhD courses at NIT
Agatala. She has a wide range of publications in worldwide
International and National Journals including ASCE,
SPRINGER, ELSEVIER, TAYLOR & FRANCIS, EJGE, IGJ
etc. Her present research works include seismic response of
retaining walls, earthquake engineering, seismic bearing
capacity and microzonation.
Sumen Deb is a final year M. Tech student of Geotechnical
Engineering at NIT Agartala doing thesis
work on Seismic response of retaining wall
and waterfront retaining walls. Apart from
this, he is an Engineer (Civil) serving under
Rural Development Department of
Government of Tripura, INDIA for the last
10 (ten) years.](https://image.slidesharecdn.com/pseudo-staticpassiveresponseofretainingwallsupportingc-backfill-140801012137-phpapp02/85/Pseudo-static-passive-response-of-retaining-wall-supporting-c-backfill-12-320.jpg)
Pseudo static passive response of retaining wall supporting c-φ backfill
- 1. IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163 __________________________________________________________________________________________ Volume: 02 Issue: 03 | Mar-2013, Available @ http://www.ijret.org 254 PSEUDO-STATIC PASSIVE RESPONSE OF RETAINING WALL SUPPORTING c-Φ BACKFILL Sima Ghosh1 and Sumen Deb2 1 Assistant Professor, 2 PG student, Civil Engineering Department, National Institute of Technology Agartala, Tripura, India, sima.civil@nita.ac.in, d_sumen@yahoo.co.in Abstract Passive resistance is a significantly important factor for successful design and performance of various structures like anchors, bulkheads, retaining walls etc. Several analytical methods have been introduced time to time to predict the passive resistance for retaining walls supporting soil as the backfill. Most of these methods for the analysis are based on linear failure criterion. Whereas; experimental investigations, theoretical analysis and failed structures have indicated that the rupture surface is supposed to be nonlinear for the most practical environment. Thus, the assumption of planar sliding surface is supposed to underestimate the lateral earth pressure on the active side, which may make retaining walls unsatisfactorily designed at the passive side for support depending on earth pressures. For this reason, the nonlinear analyses were introduced in the earth pressure theories. The methodologies for nonlinear analysis under seismic loading conditions are mostly based on the assumption of log spiral failure surface. Eminent researchers have predicted the failure surface to be a combination of log spiral and straight line. In this paper an effort has been made to derive the analytical expression of passive earth pressure coefficient on the retaining wall from the c-Ф backfill subjected to both horizontal and vertical seismic coefficients. The solution has been carried out by using Horizontal Slices Method (HSM) and limit equilibrium principles to generate a non-linear failure surface. Pseudo-static approach has been used to determine the seismic passive earth pressure. Generalized equation has been developed to find the solution. Results have been prepared in tabular form considering variation of parameters. The results have duly been compared with previous studies to justify the present analysis. Detailed parametric study has been made for the variation of different parameters like angle of internal friction (Φ), angle of wall friction (δ), wall inclination angle (α), Horizontal and vertical seismic coefficients (kh and kv), cohesion (c), adhesion (ca) and height of retaining wall (H). Index Terms:- Pseudo-static, seismic passive earth pressure, c-Φ backfill, rigid retaining wall, Wall inclination, nonlinear failure surface. -----------------------------------------------------------------------***----------------------------------------------------------------------- 1. INTRODUCTION The passive resistance refers to a condition which enables the resistance of a mass of soil against the movement of the structure. The concept is very important for the stability of various structures like anchors, bulk heads and also for bearing capacity of foundation etc. In common practice, the total static passive earth pressure or force from soil backfills is calculated using the methods based on Rankine‟s (1857) or Coulomb‟s (1776) analytical expressions. But, retaining walls are exposed to the extreme unfavorable effects of earthquakes and its strong dynamic waves. The very first expressions from Okabe (1926) and Mononobe-Matsuo (1929) analysis has provided the solution for dynamic earth pressure considering the wall backfilled by Φ nature of soil. They extended Coulomb wedge (1776) theory for evaluating dynamic earth pressure by incorporating the seismic acceleration as inertia forces. Kumar and Subba Rao (1997) adopted a method of slices to predict the passive earth pressure co-efficient. Ghosh and Sengupta (2012) and Sharma and Ghosh (2012) have suggested essential solutions for c-Φ nature of backfill under seismic loading conditions. These analyses are mainly based on linear nature of failure surfaces. Terzaghi (1943) has given a solution by considering log spiral failure for the analysis of lateral earth pressure to show the nonlinearity of failure surface. The log spiral method was adopted by Kumar (2001), where the passive earth pressure co-efficient for an inclined retaining wall has been computed by taking the failure surface as a combination of a logarithmic spiral and a straight line. Subba Rao and Choudhury (2005) analyzed the seismic earth pressure in soils using the limit equilibrium method based on pseudo-static approach and considering the effects of cohesion (c) in soils. Whereas, Azad et. al. (2008) and Ghanbari and Ahmadabadi (2010) have given the solution by considering the Horizontal Slices Method with linear kind of failure surface. The passive resistance from cohesionless (Ф) backfills has been analyzed by Choudhury and Nimbalkar (2005) considering the concept of phase difference due to finite shear wave propagation using pseudo-dynamic methods. From the earlier studies, it reveals that specially, in case of passive condition, non-linear failure surface generates more acceptable solution in comparison to linear failure surface
- 2. IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163 __________________________________________________________________________________________ Volume: 02 Issue: 03 | Mar-2013, Available @ http://www.ijret.org 255 analyses. Therefore, in this study, an attempt has been made to generate a non-linear failure surface. To do this analysis, Horizontal Slice Method is used. 2. ANALYTICAL SOLUTION For the analysis, let us consider a retaining wall inclined at an angle, α with the vertical as shown in Fig.1. The wall of height, H retains a horizontal c-Φ backfill and the failure surface of the retaining wall is considered to be non-linear as shown in the figure. The failure surface makes the angles of θn with the vertical at bottom and θ1 with the vertical at the top as shown in Figure. The failure wedge is divided into „n‟ number of slices with equal thickness of ΔH as shown in Fig.2. The assumptions for various parameters related to slices have been detailed in Fig.2. The rate of change of inclination of failure surface with the vertical (θ1 to θn) has been assumed as θR = {(θ1 ~ θn)/ (n- 1)}. Free Body Diagram of retaining wall-backfill system under passive pseudo-static state of equilibrium has been elaborated in Fig.2. The forces acting on the wall has been calculated by considering the following parameters: Hi-1, Hi = Horizontal shear acting on the top and bottom of the ith slice. Wi = Weight of the failure wedge of ith slice. Vi-1, Vi = Vertical load (UDL) on top and bottom of ith slice. Φ = The angle of internal friction of soil. Pi = Passive earth pressure on ith slice. Ri = The reaction of the retained soil on ith slice. δ = The angle of wall friction. C = Cohesion acting on the failure surface. Ca = Adhesion acting on the wall surface. kh = Horizontal seismic coefficient. kv = Vertical seismic coefficient. 3. DERIVATION OF FORMULATIONS CONSIDERING PASSIVE STATE OF EQUILIBRIUM Applying the force equilibrium conditions for 1st slice from Fig.2, we can solve the equations in the following pattern: 0H ; C1 Ci Cn V1 H1 Ф δ R1P1 α W1kh W1(1±kV) ΔHθ1 Vn-1 Hn-1 Фδ Rn Pn α Wnkh Wn (1±kV) θn Vi-1 Vi Hi-1 Hi Ф RiPi α WiKh Wi(1±KV) θ1+(i-1) θR SLICE - 1 SLICE - n SLICE- i ΔH ΔHH δ Fig.2: Showing the forces acting on wedge slices during passive state of equilibrium (1<i<n) Ca1 Cai Can Ѳn α Φ R W(1±kV) Wkh Ca C δ Pp H ψ Ѳ1+ѲR Ѳ1SLICE -1 SLICE -2 LAYER -n Fig.1 Battered face retaining wall under passive pseudo-static state of equilibrium
- 3. IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163 __________________________________________________________________________________________ Volume: 02 Issue: 03 | Mar-2013, Available @ http://www.ijret.org 256 )}tan)(tan(tan)1( ))1(tan(...........)(tan({tan)( cos sin)( ))1(cos( sin)( )tan(tan)( 2 1 )cos()cos( 11 2 1 1 1 2 111 cn n c i c kRP Rr a R h (1) 0V ; cos cos)( cos cos)( )1)(tan(tan)( 2 1 )sin()sin( 1 1 1 2 111 a v cc k RP (2) Solving these equations (1 and 2), we get, )sin( }]sin()tan(tantan)1( ))1(tan(................. ............){(tan( )1( tan2 ( cos )cos( cos cos )}cos()sin(tan( )tan)[{(tan1()( 2 1 1 1 1 1 1 11 1 2 1 s R R v ss v P Nn n k MN k P (3) Where, v h k k 1 tan (4) In the present study Ns and Ms Values have been introduced for the analysis of slices, where Ns = (H /ΔH)Nc (5) Ms = (H /ΔH)Mc (6) Where, Nc = (2c / γH) (7) Mc = (2ca / γH) (8) Applying the same procedure for 2nd slice, we get, )sin( )}]sin( )))tan((tan ))tan)(tan(tan)2( ))1(tan(............................. )2{(tan( )1( tan2 ( cos )cos( )cos( cos ))}cos( )sin(tan( ))tan((tan3)[{1()( 2 1 1 1 1 1 1 1 1 1 1 1 2 2 R R Rs R R R v Rs r s R R Rv P N n n k MN k P (9) Similarly, for nth slice, we get, 0H ; ))})1(tan()(tan( )tan))1()(tan(1( ])(tan(tan{[ )( cos sin)( ))1(cos( ))1(sin()( )})1(tan({tan)() 2 1 ( ))1(cos()cos( 1 1 1 1 2 1 1 1 2 1 R R n im r a R R hr Rnn nc nn m c n nc knn nRP (10) 0V ; cos cos)( ))1(cos( ))1(cos()( )1))()1( tan((tan)() 2 1 ( ))1(sin()sin( 1 1 1 2 1 a R R vR Rnn c n nc kn n nRP (11)
- 4. IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163 __________________________________________________________________________________________ Volume: 02 Issue: 03 | Mar-2013, Available @ http://www.ijret.org 257 ))1(sin( ))1(sin( ))))1(tan((tan ))tan ))1()(tan(1( )1( tan2 cos ))1(cos( ))1(cos( cos ))1(cos( ))1(sin(tan( )))1(tan()(tan12( )1()( 2 1 1 1 1 1 1 1 1 1 2 R R Rs R v Rs R s R R R v nP n n nN nn K nM n N n n nn K P (12) Thus, Total passive resistance of the backfill can be stated as, Pp = Pp1+Pp2+Pp3+………+Ppn (13) Now the generalized equation for ith slice can be sorted out as follows, 0H ; ))})1(tan( )(tan( ))tan))1((tan( )1(tan)( )(tan(tan{ )( cos sin)( ))1(cos( ))1(sin()( )})1(tan({tan)() 2 1 ( ))1(cos()cos( 1 1 1 1 2 1 1 1 2 1 R R n im r a R R hr Rii i c i iin m c i ic kii iRP (14) 0V ; cos cos)( ))1(cos( ))1(cos()( )1))()1( tan((tan)() 2 1 ( ))1(sin()sin( 1 1 1 2 1 a R R vR Rii c i ic ki i iRP (15) Solving the above equations (14 and 15), the generalized equations for ith slice can be formulated as follows: ))1(sin( ))1(sin( ))})1(tan( (tan{ ))}tan))1( )(tan(1( tan)( )])tan({[ )1( tan2 cos ))1(cos( ))1(cos( cos )))1(cos( ))1(sin(tan( )))1( tan()(tan12( )1()( 2 1 1 1 1 1 1 1 1 1 1 1 2 R R R s R n im R v Rs r s R R R v iP i i i N i i in m k iM i N i i i i k P (16) The condition to use Eqn. 16 is at, i = n, we have to take, 0)tan( 1 rm (17) From all the above equations, the passive earth pressure coefficient can be simplified as, 2 2 1 H P k n i pi p (18)
- 5. IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163 __________________________________________________________________________________________ Volume: 02 Issue: 03 | Mar-2013, Available @ http://www.ijret.org 258 4. RESULTS AND DISCUSSIONS On optimization of kp with respect to θ1 and θn, we get the seismic passive earth pressure co-efficient which is denoted here as Kp. Lists of values obtained on optimization have been presented in tabulated form herewith (Table-1 to Table-8). Table-1: Passive earth pressure coefficients (Kp) for Nc=0.1, kh=0.1 Here, a detailed parametric study has been conducted to find the variations of seismic passive earth pressure co-efficient with a wide range of variation of parameters like angle of internal friction (Ф), angle of wall friction (δ), wall inclination angle (α), cohesion (c), adhesion (ca), seismic acceleration (kh, kv), and the height of retaining wall (H). The values have been optimized for the ith slice considering passive pseudo-static state of equilibrium. Variations of parameters considered are detailed below: Ф = 20°, 30° and 40°; δ =0, Φ/2 and Φ; α = +20°, 0° and -20°; kh = 0, 0.1 and 0.2; kv = 0, kh/2, kh; Nc = 0.1, 0.2; Mc = 0, Nc/2, Nc; H = 5m, 7.5m and 10m. Table-2: Passive earth pressure coefficients (Kp) for Nc=0.1, kh=0.1 Ф δ Mc kv=kh α=-20° α=0° α=+20° 20 0 0 2.489 1.789 1.527 Nc/2 2.571 1.838 1.551 Nc 2.651 1.886 1.588 Ф/2 0 3.48 2.008 1.765 Nc/2 3.572 2.248 1.797 Nc 3.663 2.294 1.826 Ф 0 5.350 2.806 2.060 Nc/2 5.468 2.855 2.086 Nc 5.583 2.905 2.110 30 0 0 4.432 2.661 2.050 Nc/2 4.546 2.728 2.073 Nc 4.659 2.793 2.099 Ф/2 0 9.594 4.135 2.7347 Nc/2 9.766 4.208 2.780 Nc 9.380 4.280 2.824 Ф 0 -- 7.699 3.946 Nc/2 -- 7.797 3.989 Nc -- 7.895 4.031 40 0 0 8.713 4.101 2.869 Nc/2 8.876 4.188 2.895 Nc 9.035 4.274 2.897 Ф/2 0 -- 9.814 4.653 Nc/2 -- 9.634 4.718 Nc -- 9.753 4.781 Ф 0 -- -- 10.268 Nc/2 -- -- 10.351 Nc -- -- 10.434 Ф δ Mc kv=0 kv=kh/2 α=- 20° α=0° α= +20° α= - 20° α=0° α= +20° 20 0 0 2.813 2.000 1.709 2.651 1.898 1.617 Nc/2 2.905 2.063 1.746 2.738 1.951 1.648 Nc 2.995 2.117 1.796 2.823 2.001 1.691 Ф/2 0 3.960 2.479 1.984 3.72 2.34 1.875 Nc/2 4.064 2.533 2.019 3.818 2.391 1.908 Nc 4.168 2.585 2.052 3.916 2.44 1.939 Ф 0 6.147 3.177 2.319 5.748 2.991 2.19 Nc/2 6.276 3.233 2.347 5.872 3.044 2.217 Nc 6.404 3.288 2.375 5.993 3.097 2.243 30 0 0 5.005 2.978 2.271 4.719 2.819 2.16 Nc/2 5.132 3.053 2.305 4.839 2.89 2.188 Nc 5.258 3.126 2.343 4.959 2.959 2.221 Ф/2 0 10.986 4.657 3.063 10.294 4.396 2.899 Nc/2 11.173 4.739 3.114 10.471 4.473 2.947 Nc 11.359 4.82 3.163 10.649 4.550 2.993 Ф 0 -- 8.767 4.437 -- 8.233 4.192 Nc/2 -- 8.876 4.485 -- 8.336 4.237 Nc -- 8.985 4.532 -- 8.440 4.282 40 0 0 9.846 4.582 3.164 9.280 4.342 3.032 Nc/2 10.026 4.680 3.173 9.451 4.434 3.034 Nc 10.206 4.776 3.188 9.622 4.525 3.042 Ф/2 0 -- 10.752 5.203 -- 10.135 4.928 Nc/2 -- 10.886 5.275 -- 10.260 4.996 Nc -- 11.018 5.345 --- 10.386 5.063 Ф 0 -- -- 11.607 -- -- 10.939 Nc/2 -- -- 11.647 -- -- 11.027 Nc -- -- 11.788 -- -- 11.113
- 6. IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163 __________________________________________________________________________________________ Volume: 02 Issue: 03 | Mar-2013, Available @ http://www.ijret.org 259 Table-3: Passive earth pressure coefficients (Kp) for Nc=0.1, kh=0.2 Table-4: Passive earth pressure coefficients (Kp) for Nc=0.1, kh=0.2 Ф δ Mc kv=0 kv=kh/2 α=- 20° α=0° α= +20° α= - 20° α= 0° α=20° 20 0 0 2.450 1.814 1.572 2.115 1.588 1.385 Nc/2 2.532 1.861 1.593 2.187 1.629 1.400 Nc 2.613 1.907 1.626 2.257 1.669 1.416 Ф/2 0 3.311 2.267 1.780 2.815 1.887 1.551 Nc/2 3.405 2.221 1.808 2.898 1.927 1.576 Nc 3.498 2.267 1.834 2.980 1.966 1.599 Ф 0 4.896 2.704 2.035 4.077 2.320 1.768 Nc/2 5.016 2.752 2.058 4.182 2.362 1.787 Nc 5.135 2.801 2.080 4.287 2.405 1.805 30 0 0 4.516 2.775 2.155 3.938 2.455 1.936 Nc/2 4.636 2.845 2.181 4.046 2.516 1.951 Nc 4.756 2.913 2.221 4.152 2.577 1.969 Ф/2 0 9.453 4.212 2.839 8.053 3.685 2.506 Nc/2 9.635 4.289 2.885 8.216 3.754 2.547 Nc 9.816 4.365 2.930 8.379 3.821 2.587 Ф 0 -- 7.641 4.016 -- 6.564 3.521 Nc/2 -- 7.746 4.060 -- 6.657 3.560 Nc -- 7.847 4.104 -- 6.750 3.598 40 0 0 9.062 4.346 3.047 7.923 3.863 2.783 Nc/2 9.238 4.440 3.054 8.081 3.946 2.778 Nc 9.414 4.532 3.091 8.238 4.028 2.803 Ф/2 0 -- 9.860 4.903 -- 8.62 4.352 Nc/2 -- 9.992 4.972 -- 8.735 4.412 Nc -- 10.124 5.038 -- 8.851 4.472 Ф 0 -- -- 10.615 -- -- 9.275 Nc/2 -- -- 10.704 -- -- 9.353 Nc -- -- 10.792 -- -- 9.432 Ф δ Mc kv=kh α=-20° α=0° α=+20° 20 0 0 1.774 1.426 1.200 Nc/2 1.835 1.489 1.206 Nc 1.895 1.550 1.215 Ф/2 0 2.310 1.593 1.315 Nc/2 2.380 1.627 1.337 Nc 2.450 1.659 1.357 Ф 0 3.243 1.929 1.495 Nc/2 3.334 1.965 1.510 Nc 3.424 2.000 1.524 30 0 0 3.357 2.133 1.715 Nc/2 3.451 2.186 1.723 Nc 3.544 2.239 1.732 Ф/2 0 6.623 3.156 2.172 Nc/2 6.772 3.215 2.208 Nc 6.920 3.274 2.242 Ф 0 -- 5.474 3.024 Nc/2 -- 5.557 3.058 Nc -- 5.639 3.091 40 0 0 6.776 3.379 2.490 Nc/2 6.917 3.452 2.503 Nc 7.054 3.524 2.517 Ф/2 0 -- 7.369 3.798 Nc/2 -- 7.473 3.851 Nc -- 7.576 3.903 Ф 0 -- -- 7.922 Nc/2 -- -- 7.993 Nc -- -- 8.064
- 7. IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163 __________________________________________________________________________________________ Volume: 02 Issue: 03 | Mar-2013, Available @ http://www.ijret.org 260 Table-5: Passive earth pressure coefficients (Kp) for Nc=0.2, kh=0.1 Table-6: Passive earth pressure coefficients (Kp) for Nc=0.2, kh=0.1 Ф δ Mc kv=kh α= -20° α= 0° α= +20° 20 0 0 2.651 1.886 1.588 Nc/2 2.807 1.976 1.669 Nc 2.958 2.062 1.730 Ф/2 0 3.663 2.294 1.826 Nc/2 3.843 2.385 1.880 Nc 4.019 2.472 1.929 Ф 0 5.583 2.905 2.11 Nc/2 5.81 3.000 2.157 Nc 6.034 3.094 2.200 30 0 0 4.659 2.793 2.099 Nc/2 4.879 2.919 2.179 Nc 5.096 3.040 2.274 Ф/2 0 9.38 4.280 2.824 Nc/2 10.26 4.421 2.908 Nc 10.595 4.559 2.968 Ф 0 -- 7.895 4.031 Nc/2 -- 8.086 4.114 Nc -- 8.277 4.195 40 0 0 9.035 4.274 2.897 Nc/2 9.351 4.442 2.963 Nc 9.667 4.605 3.018 Ф/2 0 -- 9.753 4.781 Nc/2 -- 9.990 4.904 Nc -- 10.228 5.023 Ф 0 -- -- 10.434 Nc/2 -- -- 10.599 Nc -- -- 10.761 Ф δ Mc kv=0 kv=kh/2 α=- 20° α= 0° α= +20° α= - 20° α= 0° α= +20° 20 0 0 2.995 2.117 1.746 2.823 2.001 1.691 Nc/2 3.171 2.219 1.876 2.989 2.097 1.773 Nc 3.340 2.316 1.942 3.149 2.189 1.836 Ф/2 0 4.168 2.585 2.052 3.916 2.44 1.939 Nc/2 4.368 2.687 2.112 4.106 2.536 1.996 Nc 4.465 2.785 2.167 4.293 2.629 2.048 Ф 0 6.404 3.288 2.375 5.993 3.097 2.243 Nc/2 6.659 3.396 2.428 6.235 3.198 2.292 Nc 6.911 3.502 2.478 6.474 3.298 2.339 30 0 0 5.258 3.126 2.343 4.959 2.959 2.221 Nc/2 5.504 3.267 2.447 5.192 3.093 2.312 Nc 5.745 3.403 2.566 5.42 3.222 2.421 Ф/2 0 11.359 4.82 3.163 10.649 4.55 2.993 Nc/2 11.733 4.977 3.256 11.003 4.699 3.082 Nc 12.104 5.132 3.346 11.35 4.846 3.167 Ф 0 -- 8.985 4.532 -- 8.440 4.282 Nc/2 -- 9.200 4.625 -- 8.646 4.370 Nc -- 9.409 4.716 -- 8.846 4.455 40 0 0 10.206 4.776 3.188 9.622 4.525 3.042 Nc/2 10.561 4.964 2.258 9.956 4.703 3.099 Nc 10.912 5.145 3.362 10.289 4.875 3.189 Ф/2 0 -- 11.018 5.345 -- 10.386 5.063 Nc/2 -- 11.282 5.483 -- 10.636 5.193 Nc -- 11.546 5.617 -- 10.887 5.32 Ф 0 -- -- 11.788 -- -- 11.113 Nc/2 -- -- 11.969 -- -- 11.285 Nc -- -- 12.15 -- -- 11.456
- 8. IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163 __________________________________________________________________________________________ Volume: 02 Issue: 03 | Mar-2013, Available @ http://www.ijret.org 261 Table-7: Passive Earth pressure coefficients (Kp) for Nc=0.2, kh=0.2 Ф δ Mc kv=0 kv=kh/2 α= -20° α= 0° α= +20° α= - 20° α= 0 α= +20° 20 0 0 2.613 1.907 1.626 2.257 1.669 1.416 Nc/2 2.770 1.995 1.701 2.395 1.745 1.468 Nc 2.923 2.080 1.757 2.529 1.817 1.530 Ф/2 0 3.498 2.267 1.834 2.980 1.966 1.599 Nc/2 3.681 2.355 1.883 3.140 2.042 1.640 Nc 3.860 2.441 1.927 3.297 2.116 1.678 Ф 0 5.135 2.801 2.080 4.287 2.405 1.805 Nc/2 5.367 2.896 2.121 4.496 2.487 1.839 Nc 5.599 2.989 2.160 4.696 2.567 1.872 30 0 0 4.756 2.913 2.099 4.152 2.577 1.969 Nc/2 4.991 3.045 2.179 4.361 2.693 2.032 Nc 5.220 3.172 2.274 4.565 2.806 2.109 Ф/2 0 9.816 4.365 2.930 8.379 3.821 2.587 Nc/2 10.3178 4.513 2.016 8.702 3.952 2.663 Nc 10.533 4.660 3.097 9.019 4.082 2.735 Ф 0 -- 7.847 4.104 -- 6.750 3.598 Nc/2 -- 8.050 4.190 -- 6.934 3.674 Nc -- 8.252 4.273 -- 7.111 3.747 40 0 0 9.414 4.532 3.091 8.238 4.028 2.803 Nc/2 9.759 4.712 3.150 8.547 4.189 2.836 Nc 10.097 4.887 3.240 8.853 4.345 2.901 Ф/2 0 -- 10.124 5.038 -- 8.851 4.472 Nc/2 -- 10.382 5.170 -- 9.082 4.588 Nc -- 10.639 5.298 -- 9.313 4.702 Ф 0 -- -- 10.792 -- -- 9.432 Nc/2 -- -- 10.967 -- -- 9.589 Nc -- -- 11.142 -- -- 9.747 Table-8: Passive Earth pressure coefficients (Kp) for Nc=0.2, kh=0.2 4.1 Effect of Wall Inclination Angle (α) Fig.3 shows the variation of passive earth pressure coefficient with respect to soil friction angle (Φ) at different wall inclination angles (α= -20°, 0°, 20°) for Nc=0.1, Mc=Nc, δ = Φ/2, kh=0.2 and kv= kh/2. From the plot, it is seen that the magnitude of seismic passive earth pressure co-efficient (Kp) decreases with the increase in wall inclination angle (α). δ Mc kv=kh α= -20° α= 0° α= +20° 20 0 0 1.895 1.426 1.215 Nc/2 2.012 1.489 1.236 Nc 2.127 1.550 1.270 Ф/2 0 2.45 1.659 1.357 Nc/2 2.588 1.723 1.392 Nc 2.722 1.786 1.423 Ф 0 3.424 2.000 1.524 Nc/2 3.605 2.069 1.552 Nc 3.780 2.137 1.578 30 0 0 3.544 2.239 1.732 Nc/2 3.727 2.34 1.772 Nc 3.906 2.438 1.824 Ф/2 0 6.920 3.274 2.242 Nc/2 7.208 3.388 2.308 Nc 7.489 3.501 2.371 Ф 0 -- 5.639 3.091 Nc/2 -- 5.804 3.155 Nc -- 5.961 3.219 40 0 0 7.054 3.524 2.517 Nc/2 7.328 3.665 2.528 Nc 7.600 3.802 2.569 Ф/2 0 -- 7.576 3.903 Nc/2 -- 7.781 4.006 Nc -- 7.980 4.105 Ф 0 -- -- 8.064 Nc/2 -- -- 8.207 Nc -- -- 8.343
- 9. IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163 __________________________________________________________________________________________ Volume: 02 Issue: 03 | Mar-2013, Available @ http://www.ijret.org 262 The increase in inclination is imposing greater amount of backfill soil, thus the passive resistance is getting reduced. For example, at Ф=20°, δ=Φ/2 and kh=0.2, kv=kh/2, Nc=0.1, Mc=Nc, the magnitude of Kp is 1.966 at α = 0° which reduces to Kp = 1.599 at α = +20°. Again, at Ф = 30°, δ = Φ /2 and kh = 0.2, kv = kh/2, Nc=0.1, Mc=Nc, the magnitude of Kp is 8.379 at α = -20° which decreases upto Kp = 3.821 at α =0°. 4.2 Effect of Wall Friction Angle (δ) Fig.4 shows the variations of passive earth pressure coefficient with respect to soil friction angle (Ф) at different Wall friction angles (δ= 0, Ф/2, Ф) for Nc=0.1, Mc=Nc, α=20°, kh=0.2, kv= kh/2. From the plot, it is seen that due to the increase in δ, passive pressure co-efficient (Kp) is increased. The friction between wall and soil is increasing the passive resistance. For example, at Ф = 30°, α =+20°, Nc=0.1, Mc=Nc, kh = 0.2 and kv = kh/2, the magnitude of Kp increases from 2.221 to 2.930 for δ = Ф/2 over δ = 0°. Again, the value is increased upto Kp = 4.104 for δ = Φ with all other conditions remaining unchanged. 4.3 Effect of Soil Friction Angle (Ф) Fig.5 shows the variations of active earth pressure coefficient (Kp) with respect to wall inclination angle (α) for different soil friction angles at Nc=0.1, Mc=Nc, kh=0.2, kv= kh/2. It is observed that the increase in the value of Ф increases the passive resistance. The reason behind is that the self resistance of soil increases for higher values of Ф. 4.4 Effect of kh and kv Fig.6 shows the variations of passive earth pressure coefficient (Kp) with respect to vertical seismic acceleration coefficient (kv) for kh=0.1, 0.2, 0.3 at Ф = 30°, δ= Ф/2, α = +20°, Nc=0.1, Mc=Nc and kv=kh/2. From the figure, it is seen that the magnitude of seismic passive earth pressure co-efficient (Kp) is decreased due to the increase in horizontal seismic acceleration (kh). Fig.7 shows the variation of passive earth pressure coefficient (Kp) with respect to soil friction angle (Ф) for different values of kh at
- 10. IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163 __________________________________________________________________________________________ Volume: 02 Issue: 03 | Mar-2013, Available @ http://www.ijret.org 263 kv=kh/2, α = +20°, δ=Ф/2, Nc=0.1 and Mc=Nc. With the increase in the value of Ф, the passive resistance increases. For example, at Ф = 30°, δ = Φ/2, α = +20°, Nc=0.2, Mc=Nc and kv = kh/2 the magnitude of Kp is decreased from 3.167 to 2.735 for kh = 0.2 over kh = 0.1. Again for, Ф =20°, the values of Kp are 1.872 and 2.048 for kh = 0.2 and kh = 0.1 respectively. Fig.8 Shows the variation of passive earth pressure coefficient (Kp) with respect to soil friction angle (Ф) for different values of kv at kh=0.2, α = 20°, δ= Ф/2 Nc=0.1and Mc=Nc. From the plot, it is seen that due to the increase in Kv, the passive pressure co-efficient (Kp) is going to be decreased. For example, at Ф = 40°, δ = Ф/2, α = +20°, Nc=0.2, Mc=Nc and kh = 0.2, the magnitude of Kp is 4.702 at kv=kh/2 which is reduced upto Kp = 4.105 for kv=kh. As the seismic acceleration increases, the disturbance in backfill soil and wall also increases, thus the passive resistance of the backfill soil reduces. 4.5 Effect of Cohesion (c) and Adhesion (ca) Fig.9 shows the variation of passive earth pressure coefficient (Kp) with respect to soil friction angle (Φ) at different values of Nc for Mc=Nc, δ = Φ/2, kh=0.2 and kv= kh/2. For the values of Mc being 0, Nc/2 and Nc at Nc=0.1, δ= Ф/2, kh=0.2, kv= kh/2 and α = +20º the value of Kp gradually increases with the increase of Nc value. Cohesion increases the intermolecular attraction, thus the passive resistance also increases. For example, at Φ =30°, Mc = Nc /2, δ= Ф/2, kh=0.2, kv= kh/2 and α = +20° the values of Kp are 2.547, and 2.663 respectively for Nc = 0.1 and 0.2. Fig. 10 shows the variation of passive earth pressure coefficient (Kp) with respect to soil friction angle (Φ) at different values of Mc for Nc=0.1, δ=Φ/2, kh=0.2 and kv= kh/2. For example, at Φ =20°, Nc = 0.2, δ= Ф/2, kh=0.2, kv= kh/2 and α = +20° the values of Kp is 2.032 for Mc=Nc/2, whereas the value increases upto 2.109 for Mc=Nc all other conditions remaining unchanged. Thus, it is observed that the increased cohesive and adhesive property of soil material enhances the seismic passive resistance of the retaining wall.
- 11. IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163 __________________________________________________________________________________________ Volume: 02 Issue: 03 | Mar-2013, Available @ http://www.ijret.org 264 4.6 Effect of Height (H) Fig.11 shows the variation of passive earth pressure coefficient (Kp) with respect to soil friction angle (kh) for different heights at Nc=0.1, Mc=Nc, δ = Φ/2, kh=0.2 and kv= kh/2. The comparative results have been put considering the height of wall to be 5m, 7.5m and 10m. From the figure it is observed that the value of Kp gradually decreases with increase in height of retaining wall. It is also seen that the magnitude of Kp is increased with the increase in soil friction angle (Φ) for a constant height of retaining wall. Higher retaining walls support greater amount of backfill and thus the passive resistance is supposed to decrease. 4.7 Nonlinearity of Failure Surface Fig.12 shows the comparison between failure surface of backfill for wall inclination, α = +20° at Ф = 30°, δ= Ф/2, kh=0.2 and kv= kh/2, Nc=0.1 and Mc=Nc. It is observed that the failure surface is curvilinear in nature for present analysis. The failure line is linear for Ghosh and Sengupta (2012) analysis. For example, at α =+20° for Φ =30º, δ= Φ/2, Nc=0.1, Mc=Nc and kh=0.2, kv=kh/2 the value of failure surface inclination with the vertical at bottom 63° and angle at the top is 70°, whereas; at α = -20° the value of the inclination of failure surface with vertical at bottom 74° and angle at the top is 86°. It is seen that the inclination of the failure surface with vertical reduces with the increase in the wall inclination angles when the inclination of the wall is away from the backfill. 5. COMPARISON OF RESULTS Fig.13 shows the comparison of results for variations of passive earth pressure coefficient with respect to soil friction angle (Φ) at α = +20°, δ= Ф/2, kh=0.2 and kv=kh/2, Nc=0.1 and Mc=Nc. The present values are comparable with existing earth pressure theories. Here, the graph is plotted to compare the results obtained from present study with the results of Ghosh and Sharma (2012) analysis. The comparison of the values shows that the present value of Kp is around 5-10% smaller than the values of Ghosh and Sharma (2012) analysis. CONCLUSIONS In this study, the Horizontal Slices Method of analysis with pseudo–static approach has been considered to determine the seismic passive resistance of the retaining wall with non-linear failure surface. The present study shows that the non-linearity of the failure surface is affecting the evaluation of seismic passive earth pressure. It is also noted that the nature of the failure surface changes with the change in wall inclination angle and the shape of the failure surface is sagging in nature. The detailed parametric study shows that the results are comparable to other suitable methods established earlier. The present study shows that the seismic passive earth pressure co-
- 12. IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163 __________________________________________________________________________________________ Volume: 02 Issue: 03 | Mar-2013, Available @ http://www.ijret.org 265 efficient (Kp) increases due to the increase in wall friction angle (δ), soil friction angle (Φ), cohesion (c) and adhesion (ca); at the same time the value of Kp decreases with the increase in wall inclinations (α), wall height (H), and seismic accelerations (kh, kv). The inclination of the failure surface with vertical increases with the decrease in wall inclination (α), wall friction angle (δ), soil friction angle (Φ) and height of retaining wall (H). Whereas, the inclination of the failure surface with vertical decreases with the increase in wall inclination(α), soil friction angle (Φ), cohesion (c), adhesion(ca) and wall friction angle (δ). The generation of sagging nature of rupture surface (in passive condition) is showing curvilinear response in the determination passive earth pressure coefficient acting on the retaining walls. NOTATIONS Φ = Soil friction angle. δ = Wall friction angle. α = Wall inclination angle with the vertical. Pp = Passive earth pressure. kh = Horizontal seismic co-efficient. kv = Vertical seismic co-efficient. R = Soil reaction force. γ = unit weight of soil. Kp = Passive earth pressure coefficient c = cohesion ca = adhesion REFERENCES: [1]. Azad, A, Shahab Yasrobi, S, Pak, A. (2008), “Active Pressure Distribution History Behind Rigid Retaining Walls”, Soil Dynamics and Earthquake Engineering 28 (2008) 365-375. [2]. Choudhury, D and Nimbalkar, S, (2005), “Seismic Passive Resistance by Pseudo-dynamic Method”, Geotechnique; 55(9): 699-702. [3]. Coulomb, C.A. (1776), “Essai Sur Une Application Des Maximis et Minimis a Queques problems Des Statique Relatifsa1‟Architecture”, Nem. Div. Sav.Acad, Sci.Vol.7. [4]. Ghanbari, A and Ahmadabadi, M. (2010), “Pseudo- Dynamic Active Earth Pressure Analysis of Inclined Retaining Walls Using Horizontal Slices Method”, Transaction A: Civil Engineering Vol. 17, No. 2, pp. 118-130© Sharif University of Technology. [5]. Ghosh, S. and Sengupta, S. (2012),“ Formulation of Passive resistance on non vertical retaining wall backfilled with c-Φ”, Civil and Environmental Research ISSN 2224-5790 (Print) ISSN 2225-0514 (Online), Vol 2, No.1, 2012. [6]. Ghosh, S. and Sharma, R. P. (2012), “Pseudo-Dynamic Evaluation of Passive Response on the Back of A Retaining Wall Supporting c-Φ Backfill”, Geomechanics and Geoengineering: An International Journal, Vol. 7, No. 2, June 2012, 115–121. [7]. Kumar J, Subba Rao K. S, (1997), “Passive Pressure determination by method of Slices”, Int J Num Anal Method Geomech USA 21:337-345. [8]. Kumar, J. (2001), “Seismic Passive Earth Pressure Coefficients for Sands”, Can. Geotech. J., Ottawa, 38, pp: 876-881. [9]. Mononobe, N. and Matsuo, H. (1929), “On the Determination of Earth Pressure During Earthquakes” Proc. of the World Engineering Congress, Tokyo, 9, pp. 179-87. [10]. Okabe, S. (1926), “General Theory of Earth Pressure”, J. Japan Soc. Civil Eng., 12(1). [11]. Rankine, W. J. M. (1857), “On the Stability of Loose Earth”, Phil. Tras. Royal Society (London). [12]. Shukla, S. K and Habibi, D. (2011), “Dynamic Passive Pressure from c-Ф Soil Backfills”, Soil Dynamics and Earthquake Engineering 31 (2011) 845-848. [13]. Subbarao, K. S, and Choudhury, D. (2005), “Seismic Passive Earth Pressure in Soils”, Journal of Geotechnical and Geoenvironmental Engineering, ASCE 2005; 131(1); 131 -5. [14]. Terzaghi, K, (1943), “Theoretical Soil Mechanics”: John Wiley & Sons, New York, 510 p. BIOGRAPHIES: Sima Ghosh presently working as an Assistant Professor at NIT Agartala, INDIA is a consistent Gold medalist in BE (Civil) from Tripura Engineering College (now NIT Agartala) in 1994 and M. Tech in Geotechnical Engineering from IIT, Roorkee in 2001. She has completed her PhD in Geotechnical Engineering in 2012 and became the very first person to attain the PhD Degree since the inception of PhD courses at NIT Agatala. She has a wide range of publications in worldwide International and National Journals including ASCE, SPRINGER, ELSEVIER, TAYLOR & FRANCIS, EJGE, IGJ etc. Her present research works include seismic response of retaining walls, earthquake engineering, seismic bearing capacity and microzonation. Sumen Deb is a final year M. Tech student of Geotechnical Engineering at NIT Agartala doing thesis work on Seismic response of retaining wall and waterfront retaining walls. Apart from this, he is an Engineer (Civil) serving under Rural Development Department of Government of Tripura, INDIA for the last 10 (ten) years.