This document presents a method for formulating the seismic passive resistance of a non-vertical retaining wall backfilled with cohesive-frictional (c-Φ) soil. Equations are developed to calculate the seismic passive earth pressure coefficient (kp) based on parameters like soil friction angle, wall friction angle, cohesion, adhesion, seismic accelerations, surcharge loading, and wall geometry. A parametric study is conducted to analyze the effect of these parameters on kp. The results show that kp increases with soil friction angle, wall friction angle, cohesion, and adhesion. kp decreases as the ratio of horizontal to vertical seismic acceleration increases.
In this paper we have defined Dk
integral and proved the integration by parts formula.
Key Words and phrases: Absolutely Continuous function, Generalised absolutely continuous function,
Denjoy integration. 2000 Mathematics subject Classification: Primary 26A24 Secondary 26A21, 26A48,
44A10.
In this paper we have defined Dk
integral and proved the integration by parts formula.
Key Words and phrases: Absolutely Continuous function, Generalised absolutely continuous function,
Denjoy integration. 2000 Mathematics subject Classification: Primary 26A24 Secondary 26A21, 26A48,
44A10.
At Apex Institute, we endeavour to amalgamate the ancient values of uttermost dedication and responsibility that gave teaching a very pious and sacred status, with latest teaching methodologies so as to make the act of learning, a delectable experience. The arduous task is accomplished by a team of diligent academicians and entrepreneurs, who with the years of experience have mastered the techniques to transform even the most abstruse topics easy to comprehend.
Great emphasis is laid on the concepts and fundamentals with a smooth and systematic transition to the advanced levels of teaching. The interaction between students and teachers is always encouraged so as to provide a very healthy environment for growth and learning. During the process of training the students for IIT-JEE/Engg./Medical entrance examinations, great emphasis is laid on the fundamentals so as to excel in the CBSE examination also.
Illustrious faculty and excellent teaching techniques provide you will an infallible approach to success only at Apex Institute.
Our Mission
Generating excellence both in academic and competitive aspects thereby training the youth for most gruelling entrance level exams viz. IIT-JEE/Engg.& Medical entrance.
Our Vision
Generating excellence in academic, exploring creative areas of the dormant self, nurturing talent & aptitude & including perseverance among the students to keep themselves abreast of the latest developments in the field of competitive examinations.
Our Objectives
1. Striving for the best possible education to ambitious students aspiring to join corporate world as medical professionals.
2. Creating a comprehensive understanding of the subjects & help developing strategies to meet arduous competitions among the students to match, excel & ameliorate the competition oriented education.
This paper presents the study of the dynamics and control of an axial variable structure satellite (asymmetric platform and an axisymmetric rotor). Inertia moments of the rotor change slowly over time. The dynamics of the satellite is described by using ordinary differential equations with Serret-Andoyer canonical variables. For undisturbed motion, the stationary solutions are found, and their stability is studied. The control law is obtained for the satellite with variable structure on the basis of the stationary solutions. By means of computer numerical simulations, we have shown that the motion of the satellite controlled by founded internal torque is stable.
D. Mladenov - On Integrable Systems in CosmologySEENET-MTP
Lecture by Prof. Dr. Dimitar Mladenov (Theoretical Physics Department, Faculty of Physics, Sofia University, Bulgaria) on December 7, 2011 at the Faculty of Science and Mathematics, Nis, Serbia.
Localized Electrons with Wien2k
LDA+U, EECE, MLWF, DMFT
Elias Assmann
Vienna University of Technology, Institute for Solid State Physics
WIEN2013@PSU, Aug 14
The all-electron GW method based on WIEN2k: Implementation and applications.ABDERRAHMANE REGGAD
The all-electron GW method based on WIEN2k:
Implementation and applications.
Ricardo I. G´omez-Abal
Fritz-Haber-Institut of the Max-Planck-Society
Faradayweg 4-6, D-14195, Berlin, Germany
15th. WIEN2k-Workshop
March, 29th. 2008
APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students . We actually started to make a difference in the way students think and approach problems. We started to develop ways to enhance students IQ. We started to leave an indelible mark on the students who have undergone APEX training. That is why APEX INSTITUTE is very well known of its quality of education
Lecture by prof. dr Neven Bilic from the Ruđer Bošković Institute (Zagreb, Croatia) at the Faculty of Science and Mathematics (Niš, Serbia) on October 29, 2014.
The visit took place in the frame of the ICTP – SEENET-MTP project PRJ-09 “Cosmology and Strings”.
At Apex Institute, we endeavour to amalgamate the ancient values of uttermost dedication and responsibility that gave teaching a very pious and sacred status, with latest teaching methodologies so as to make the act of learning, a delectable experience. The arduous task is accomplished by a team of diligent academicians and entrepreneurs, who with the years of experience have mastered the techniques to transform even the most abstruse topics easy to comprehend.
Great emphasis is laid on the concepts and fundamentals with a smooth and systematic transition to the advanced levels of teaching. The interaction between students and teachers is always encouraged so as to provide a very healthy environment for growth and learning. During the process of training the students for IIT-JEE/Engg./Medical entrance examinations, great emphasis is laid on the fundamentals so as to excel in the CBSE examination also.
Illustrious faculty and excellent teaching techniques provide you will an infallible approach to success only at Apex Institute.
Our Mission
Generating excellence both in academic and competitive aspects thereby training the youth for most gruelling entrance level exams viz. IIT-JEE/Engg.& Medical entrance.
Our Vision
Generating excellence in academic, exploring creative areas of the dormant self, nurturing talent & aptitude & including perseverance among the students to keep themselves abreast of the latest developments in the field of competitive examinations.
Our Objectives
1. Striving for the best possible education to ambitious students aspiring to join corporate world as medical professionals.
2. Creating a comprehensive understanding of the subjects & help developing strategies to meet arduous competitions among the students to match, excel & ameliorate the competition oriented education.
This paper presents the study of the dynamics and control of an axial variable structure satellite (asymmetric platform and an axisymmetric rotor). Inertia moments of the rotor change slowly over time. The dynamics of the satellite is described by using ordinary differential equations with Serret-Andoyer canonical variables. For undisturbed motion, the stationary solutions are found, and their stability is studied. The control law is obtained for the satellite with variable structure on the basis of the stationary solutions. By means of computer numerical simulations, we have shown that the motion of the satellite controlled by founded internal torque is stable.
D. Mladenov - On Integrable Systems in CosmologySEENET-MTP
Lecture by Prof. Dr. Dimitar Mladenov (Theoretical Physics Department, Faculty of Physics, Sofia University, Bulgaria) on December 7, 2011 at the Faculty of Science and Mathematics, Nis, Serbia.
Localized Electrons with Wien2k
LDA+U, EECE, MLWF, DMFT
Elias Assmann
Vienna University of Technology, Institute for Solid State Physics
WIEN2013@PSU, Aug 14
The all-electron GW method based on WIEN2k: Implementation and applications.ABDERRAHMANE REGGAD
The all-electron GW method based on WIEN2k:
Implementation and applications.
Ricardo I. G´omez-Abal
Fritz-Haber-Institut of the Max-Planck-Society
Faradayweg 4-6, D-14195, Berlin, Germany
15th. WIEN2k-Workshop
March, 29th. 2008
APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students . We actually started to make a difference in the way students think and approach problems. We started to develop ways to enhance students IQ. We started to leave an indelible mark on the students who have undergone APEX training. That is why APEX INSTITUTE is very well known of its quality of education
Lecture by prof. dr Neven Bilic from the Ruđer Bošković Institute (Zagreb, Croatia) at the Faculty of Science and Mathematics (Niš, Serbia) on October 29, 2014.
The visit took place in the frame of the ICTP – SEENET-MTP project PRJ-09 “Cosmology and Strings”.
The reverse bias 1/C2 vs. V plots of Schottky barrier diodes are studied here. The
expressions for the slope and voltage intercept of Schottky diodes, as given in the
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potential, slope and voltage intercept of 1/C2 vs. V plots. The expressions for the
interface state density are derived. The simulated results are compared with those
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accuracy. Based on the model, the characteristics of 1/C2 vs. V plots are studied
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Quantum gravitational corrections to particle creation by black holesSérgio Sacani
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Periodic material-based vibration isolation for satellitesIJERA Editor
The vibration environment of a satellite is very severe during launch. Isolating the satellitevibrations during
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element model of a micro-satellite with a set of designed periodic isolators is built to show the feasibility of
vibration isolation. The periodic isolator is found to be a multi-directional isolator that provides vibration
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Periodic material-based vibration isolation for satellitesIJERA Editor
The vibration environment of a satellite is very severe during launch. Isolating the satellitevibrations during
launch will significantly enhance reliability and lifespan, and reduce the weight of satellite structure and
manufacturing cost. Guided by the recent advances in solid-state physics research, a new type of satellite
vibration isolator is proposed by usingperiodic material that is hence called periodic isolator. The periodic
isolator possesses a unique dynamic property, i.e., frequency band gaps. External vibrations with frequencies
falling in the frequency band gaps of the periodic isolator are to be isolated. Using the elastodynamics and the
Bloch-Floquet theorem, the frequency band gaps of periodic isolators are determined. A parametric study is
conducted to provide guidelines for the design of periodic isolators. Based on these analytical results, a finite
element model of a micro-satellite with a set of designed periodic isolators is built to show the feasibility of
vibration isolation. The periodic isolator is found to be a multi-directional isolator that provides vibration
isolation in the three directions.
Binping xiao superconducting surface impedance under radiofrequency fieldthinfilmsworkshop
Based on BCS theory with moving Cooper pairs, the electron states distribution at 0 K and the probability of electron occupation with finite temperature have been derived and applied to anomalous skin effect theory to obtain the surface impedance of a superconductor under radiofrequency (RF) field. We present the numerical results for Nb and compare these with representative RF field-dependent effective surface resistance measurements from a 1.5 GHz resonant structure.
nternational Journal of Engineering Research and Development is an international premier peer reviewed open access engineering and technology journal promoting the discovery, innovation, advancement and dissemination of basic and transitional knowledge in engineering, technology and related disciplines.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
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yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
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JMeter webinar - integration with InfluxDB and Grafana
11.changed....0002www.iiste.org call for paper...... to be changed.
1. Civil and Environmental Research www.iiste.org
ISSN 2224-5790 (Print) ISSN 2225-0514 (Online)
Vol 2, No.1, 2012
Formulation of Seismic Passive Resistance of Non-Vertical
Retaining Wall Backfilled with c-Φ Soil
Sima Ghosh1, Satarupa Sengupta2
1. Assistant Professor, Civil Engg. Department, National Institute of Technology, Agartala
2. M. Tech Student, Civil Engg. Department, National Institute of Technology, Agartala
PIN – 799055, Jirania, Tripura, India
* E-mail of the corresponding author: satarupas@yahoo.com
Abstract
The seismic passive earth pressure is really the most important parameter in some special cases like key analysis,
anchor analysis, foundation analysis etc. The simultaneous action of weight, surcharge, cohesion and adhesion is
also taken into consideration. A visual presentation is made by plotting graphs with the wide range of variation
Parameters like angle of internal friction (Φ), angle of wall friction (δ), wall inclination angle (α), cohesion (c),
adhesion (ca), seismic accelerations (kh, kv), surcharge loading (q), unit weight (γ), height (H) to provide the variation
of seismic passive earth pressure coefficient.
Keywords: Pseudo-static, seismic passive resistance, single wedge, c-Φ backfill, rigid retaining wall, wall
inclination.
1. Introduction
Computation of passive resistance is extremely important and the level of importance of the passive earth pressure
increases many fold under earthquake conditions due to the devastating effects of earthquake. Hence to analyze the
retaining wall under passive condition for both under the static and seismic conditions, the basic theory is very
complex and the several researchers have discussed on this topic. Initially Okabe (1926) and Mononobe and Matsuo
(1929) had proposed the theory to compute the pseudo-static lateral earth pressure on the wall, which is commonly
known as the Mononobe-Okabe method (see Kramer (1996)). Based on the classical limit equilibrium theory, this
method is a direct modification of the Coulomb wedge method where the earthquake effects are replaced by quasi-
static inertia forces, whose magnitude is computed with seismic coefficient concept. Again, by using the
approximate method based on modified shear beam model Wu and Finn (1999) developed charts for seismic thrusts
against rigid walls. Psarropoulos et al. (2005) have developed a general finite element solution for analyzing the
distribution of dynamic earth pressures on rigid and flexible walls. Davies et al. (1986), Morrison and Ebeling
(1995), Soubra (2000) and Kumar (2001) to name a few had analyzed the seismic passive earth pressure problems.
All the analyses as mentioned above are for Φ backfill. Subba Rao and Choudhury (2005) had given a solution for
seismic passive earth pressure supporting c-Φ backfill in such a way that they are getting separate critical wedge
surfaces and separate coefficients for unit weight, surcharge and cohesion. But from practical point of view, this fact
is not true, as for the simultaneous action of unit weight, surcharge and cohesion, we will get single failure surface.
Keeping this fact in mind, here an attempt is made to develop a formulation for the seismic passive resistance on the
back of a non-vertical retaining wall supporting c-Φ backfill in such a way that a single failure wedge is developed.
A planar rupture surface is considered in that analysis to extend the Mononobe-Okabe concept for c-Φ backfill.
2. Method of Analysis for Seismic Passive Resistance
A schematic diagram of seismic passive earth pressure is shown in the fig.1. Here a rigid retaining wall of height H
supporting c-Φ backfill of unit weight γ, unit cohesion c, unit adhesion ca, angle of wall friction δ, angle of soil
friction Φ, retaining wall inclination angle is shown. On the top of the backfill a surcharge load of intensity q per
unit length is acting. At any stage of earthquake (having seismic acceleration coefficients kh and kv) during passive
state of equilibrium, if the planer wedge surface BD generates an angle θ with the vertical, then the forces acting on
7
2. Civil and Environmental Research www.iiste.org
ISSN 2224-5790 (Print) ISSN 2225-0514 (Online)
Vol 2, No.1, 2012
the wedge system as shown in Fig.1, Pp and R being the force on the retaining wall and reaction offered by the
retained earth on the sliding wedge ABD at the face BD respectively.
Applying the force equilibrium conditions, ∑H = 0 and ∑V = 0,
Pp cos( ) (W Q)kh cH tan ca H tan R cos 0
(1)
Pp sin( ) (W Q)1 kv ca H cH R sin 0 (2)
Solving Eqn 1 and 2 and putting W = {γH2 (tanθ+tan)}/2, Q = qH(tanθ+tan), C = cH secθ, Ca = caHsec,
ψ = tan-1(kh/(1± v)) we get,
k
2q H
1 k v (tan tan ) cos cH sec cos
2
Pp sin
H 2 cos
ca H cos sec (3)
Replacing (γ+2q/H) by γe, Eqn 3 can be written as
(tan tan ) cos 2c cos
H 2 cos sin H 1 k cos sin
Pp e 1 k v e v
(4)
2 2c a sec cos
H 1 k sin
e v
2c 2c a
Substituting nc and mc , the above Equation reduces to
e H 1 k v e H 1 k v
eH 2
Pp 1 k v sin( ) cos nc cos cos cos mc cos cos cos
2 cos cos cos sin
(5)
eH 2
Pp 1 k v k p (6)
2
sin( ) cos nc cos cos cos mc cos cos cos
Where k p
cos cos cos sin
(7)
In Eqn.7, all the terms are constant except θ. The optimum value of kp is given by the condition dkp/dθ =0, Applying
this condition on Eqn.7, we get critical wedge angle θc as given by the following Eqn,
p q q r 2 r q2 r 2 p2
c cos 1
2 q2 r 2 (8)
Where
p sin mc cos sin (9)
8
3. Civil and Environmental Research www.iiste.org
ISSN 2224-5790 (Print) ISSN 2225-0514 (Online)
Vol 2, No.1, 2012
q sin( ) cos(2 ) sin( ) cos( ) mc cos cos
(10)
2nc cos cos cos cos
r 2 cos sin {sin( ) nc cos cos } (11)
Putting this value of θc in Eqn 7, we get the optimum value of passive earth pressure coefficient, which is
represented here as kpe. So, seismic passive resistance is given by,
eH 2
Ppe 1 k v k pe (12)
2
3. Parametric Study
From the Eqn 8 and its related Eqns 9, 10 and 11, it is seen that the coefficient for seismic passive resistance
depends on Φ, δ, ψ, , mc and nc. Coefficient ψ depends on seismic acceleration coefficient kh and kv. Cohesion
factor nc is taking care of the effect of cohesion and adhesion factor mc is taking care of the effect of adhesion. Both
nc and mc are also depend on γ, q, H and kv. All the factors Φ, δ, , kh and kv, γ, q, H, c and ca affects the magnitude
of seismic passive earth pressure coefficient. In the following sub sections, the affects of all these parameters on the
variation of seismic passive resistance coefficient are studied.
3.1. Effect of angle of internal friction of soil (Φ)
Fig.2 shows the variation of seismic passive earth pressure coefficient (k pe) with kh for different values of Φ at δ =
Φ/2, kv = kh/2, c = 10 kN/m2, ca = 8 kN/m2, q = 15 kN/m, γ = 18 kN/m3, H = 10 m. From the plot, it is seen that the
magnitude of kpe appreciably increases with increase in Φ. For example, for k h = 0.1, at Φ = 10, 20° 30°and 40°
, ,
the magnitude of kpe is 1.55, 2.21, 3.35 and 5.6 respectively. Due to increase in Φ, the resistance capacity of the
backfill increases which resembles for the fact to increase in kpe.
3.2 Effect of angle of wall friction (δ)
Fig.3 shows the variation of kpe with kh for different value of δ at Φ =30° kv = kh/2, c = 10 kN/m2, ca = 8 kN/m2, q =
,
15 kN/m, γ = 18 kN/m3, H = 10 m. From the plot, it is seen that the coefficient kpe increases due to increase in δ.
For example, at kh = 0.2, due to increase in δ from –Φ/2 to Φ/2, the coefficient kpe increases from 1.89 to 3.12.
3.3 Effect of kv/kh ratio
Fig.4 shows the variation of seismic passive earth pressure coefficient (k pe) with kh for ratio of kv/kh from 0 to 1 at Φ
=30° δ = Φ/2, c = 10 kN/m2, ca = 8 kN/m2, q = 15 kN/m, γ = 18 kN/m3, H = 10 m. From the plot, it is seen that k pe
,
decreases with increase kv/kh ratio. Increase in kv/kh ratio means increase in seismic disturbance of the backfill
material and due to that the resistance capacity of the backfill material is going to be reduced which resembles for
the fact of reduction of kpe due to increase in kv/kh ratio. Here in Fig.3, upto kh=0.2, the value of kpe is more or less
same for kv/kh ratio of 0, 1/2, 1.
3.4 Effect of cohesion (c)
From the earlier analyses [Saran and Gupta(2003); Ghosh and Saran (2007); Ghosh (2010); Ghosh and Sharma
(2010)], it is seen that there is no effect of cohesion on the magnitude of seismic passive earth pressure (k pe). But
from the present analysis, it is seen that cohesion of the soil appreciably increases the magnitude of k pe. Here, Fig.5
represents one such variation of kpe with kh for different value of c at Φ =30° δ = Φ/2, kv = kh/2, ca = 0, q = 15
,
kN/m, γ = 18 kN/m3, H = 10 m. In this plot, it is seen that for kh = 0.3, kpe = 2.37 at c = 0 increases to 3.12 at c = 20
kN/m2. Due to increase in c, intermolecular attraction of the soil particles increases which increases the resistance
capacity of the backfill soil mass and thus increases kpe.
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3.5 Effect of adhesion (ca)
Similar to the effect of cohesion, the adhesion also increases the magnitude of coefficient of seismic passive earth
pressure kpe. Fig.6 shows one such variation of kpe with kh for different value of ca at Φ =30° δ = Φ/2, kv = kh/2, c =
,
10kN/m2, q = 15 kN/m, γ = 18 kN/m3, H = 10 m. From this plot, it is seen that for kh = 0.2, kpe increases from 3.04
to 3.14 due to change in ca/c ratio from 0 to 1.
3.6 Effect of surcharge (q)
Fig.7 shows the variation of kpe with kh for different value of q at Φ =30° δ = Φ/2, kv =kh/2, c = 10 kN/m2, ca = 8
,
kN/m2, γ = 18 kN/m3, H = 10 m. From the plot, it is seen that kpe decreases marginally due to increase in q. For
example at kh =0.3, due to increase in q from 0 to 40 kN/m, the value of k pe decreases from 2.91 to 2.74.
3.7 Effect of unit weight of backfill material (γ)
Similar to the effect of q, the coefficient kpe also decreases due to increase in γ. Fig.8 shows one such variation of kpe
with kh for different value of γ at Φ =30° δ = Φ/2, kv =kh/2, c = 10 kN/m2, ca = 8 kN/m2, q = 15 kN/m, H = 10 m.
,
From this plot, it is seen that at kh = 0.3, kpe decreases from 3.11 to 2.66 due to increase in γ from 10 kN/m3 to 30
kN/m3.
3.8 Effect of height of retaining wall (H)
Height of retaining wall also appreciably reduces the coefficient of seismic passive earth pressure. Fig.9 shows the
variation of kpe with kh for different heights of retaining wall at Φ =30° δ = Φ/2, kv = kh/2, c = 10 kN/m2, ca = 8
,
kN/m2, q = 15 kN/m, γ = 18 kN/m3. In this plot, for example, at kh = 0.2, due to the reduction of height from 10 m to
2 m, the coefficient kpe increases from 3.12 to 4.03.
3.9. Effect of wall inclination ()
Fig.10 shows the variation of seismic passive earth pressure coefficient (ka) with kh for for Φ =30° kv=kh/2, δ=Φ/2,
,
q= 15 kN/m, c = 10 kN/m2, ca = 8 kN/m2, γ=18 kN/m3, H=10 m for different wall inclination angle (). From the
plot, it is seen that the effect of wall inclination angle is very a prominent factor for the determination of seismic
passive earth pressure coefficient (kpe). For example at kh=0.3 for the value of =20 to -20 ka increases from 2.83
to 10.11.
3.10. Collapse Mechanism
Critical wedge surface is the wedge surface, at which we get the optimum value of seismic passive earth pressure
coefficient. Here in this analysis, it is represented by θ c (measured with the vertical) and given by Eqn.8. Fig.11
shows the variation of θc with kh for different value of Φ at δ=Φ/2, kv = kh/2, c = 10 kN/m2, ca = 8 kN/m2, q = 15
kN/m, γ = 18 kN/m3, H = 10 m. From the plot, it is seen that due to increase in Φ, the magnitude of the inclination of
the critical wedge surface also increases.
4. Comparison of results
Very few studies are made for the determination of seismic passive resistance supporting c-Φ backfill. Mononobe
Okabe, Subba Rao and Choudhury (2005) had given a solution for the seismic passive resistance supporting c- Φ
backfill and a comparison of the present study is made with Mononobe Okabe, Subba Rao and Choudhury (2005) in
Table 1.
Table 1 shows that present study provides the value of seismic passive resistance in little higher side in comparison
to Subba Rao and Choudhury (2005). The concept of present study is the extension of Mononobe-Okabe solution for
c-Φ backfill. So, the findings of present study exactly matches Mononobe-Okabe (1929) for c = 0, ca = 0 and q= 0.
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5. Conclusion
Using the limit equilibrium method of analysis with pseudo-static approach, the seismic passive resistance
formulation on the back of a retaining wall has been developed. The basic theme of the analysis is to generate a
single failure wedge surface for the simultaneous action of unit weight, surcharge, cohesion and adhesion. A wide
range of variation of parameters like cohesion, adhesion, angle of wall friction, angle of soil friction, wall inclination
are used to note down the variation of coefficient of seismic passive earth pressure. The basis of the analyses
available at present is that the coefficient of seismic passive earth pressure does not depend on height of retaining
wall, cohesion, adhesion, surcharge loading, unit weight of the backfill material. But present analysis represents that
the coefficient for seismic passive earth pressure increases with increase in cohesion, adhesion but decreases due to
increase in unit weight of backfill material, surcharge loading and height of retaining wall. Matching with the other
available analysis, present analysis represents increase in coefficient for seismic passive earth pressure due to
increase in angle of internal friction and angle of wall friction of the backfill material and decreases due to increase
in seismic acceleration coefficients.
So, extending the Mononobe-Okabe concept for the determination of seismic passive response on the back of a non-
vertical retaining wall supporting c-Φ backfill, a formulation is developed for the simultaneous action of weight,
surcharge, cohesion and adhesion which is reasonable and easy to use.
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6. References
Coulomb, C. A. (1773), “Essai sur une application des regles des maximis et minimis a quelque problems de
statique relatifs 1’ architecture, Memoires d’Academie Roy. Pres. Diverssavants.7.
Davies, T.G., Richards, R. and Chen, K. H. (1986), “Passive Pressure during Seismic Loading”, J. Geotechnical
Engg., Vol.112(4), pp:479-83.
Kramer, S. L. (1996), “Geotechnical Earthquake Engineering”, Englewood Cliffs, NJ: Prentice Hall.
Kumar, J. (2001), “Seismic Passive Earth Pressure Coefficients for Sands”, Can. Geotech. J., Ottawa, 38, pp: 876-
881.
Mononobe, N. and Matsuo, H. (1929), “On the Determination of Earth Pressure during Earthquakes”, Proceedings,
World Engg. Conference, Vol. 9, 176 p.
Morrison, E.E. and Ebeling, R. M.(1995), “Limit Equilibrium Computation of Dynamic Passive Earth Pressure”,
Can. Geotechnical J, Vol.32, pp:481-87.
Okabe, S. (1926), “General Theory of Earth Pressure”, J. of the Japanese Society of Civil Engineers, Tokyo, Japan,
12(1).
Psarropoulos, P. N., Klonaris, G. and Gazetas, G. (2005), “Seismic Earth Pressures on Rigid and Flexible Retaining
Walls”, Soil Dynamics and Earthquake Engg, Vol. 25, pp:795-809.
Soubra, A. H. (2000), “Static and Seismic Passive Earth Pressure Coefficients on Rigid Retaining Structures”,
Canadian Geotech. J., Vol. 37, pp: 463-478.
Subba Rao, K. S. and Choudhury, D. (2005), “Seismic Passive Earth Pressures in Soils”, Journal of Geotechnical
and Geoenvironmental Engineering, vol.131, No.1,pp: 131-135.
Wu, G. and Finn W.D. (1999), “Seismic Lateral Earth Pressure for Design of Rigid Walls”, Canadian Geotechnical
Journal, Vol: 36, pp: 509-22.
q per unit length
A D
(W+Q)kh
ca
Pp c
δ (W+Q)(1± v)
k
H R
R
B
Fig.1. Forces acting on retaining wall – soil wedge system during passive state of equilibrium.
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Vol 2, No.1, 2012
7
6 40
5 30
20
4
10
kpe 3
2
1
0
0 0.2 0.4 0.6
kh
Fig.2.Variation of seismic passive earth pressure coefficient (kpe) with kh for kv=kh/2, δ=Φ/2, γ = 18 kN/m3, c=10
kN/m2, ca = 8 kN/m2, q = 15 kN/m, H=10 m, =20
6
0
5
/2
4 /2
3
kpe
2
1
0
0 0.1 0.2 kh 0.3 0.4 0.5
Fig.3.Variation of seismic passive earth pressure coefficient (kpe) with kh for kv=kh/2, =30, γ = 18 kN/m3, c=10
kN/m2, ca = 8 kN/m2, q = 15 kN/m, H=10 m, =20
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4
3.5
3 kv=kh/2
2.5 kv=0
kpe
2
kv=kh
1.5
1
0.5
0
0 0.2 0.4 0.6
kh
Fig.4.Variation of seismic passive earth pressure coefficient (kpe) with kh for =30, δ=Φ/2, γ = 18 kN/m3, c=10
kN/m2, ca = 8 kN/m2, q = 15 kN/m, H=10 m, =20
4
3.5
3 c=10
2.5 c=20
kpe
2 c=0
1.5
1
0.5
0
0 0.1 0.2 0.3 0.4 0.5
kh
Fig.5.Variation of seismic passive earth pressure coefficient (kpe) with kh for kv=kh/2, =30, δ=Φ/2, γ = 18 kN/m3,
ca = 0 kN/m2, q = 15 kN/m, H=10 m, =20
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Table 1: Comparison of the results obtained from the present study with Mononobe Okabe, Subba Rao and
Choudhury'2005 [Φ = 30°, δ = Φ/2, c= 0 kN/m2, ca = 0 kN/m2, q = 0 kN/m, γ = 18 kN/m3]
18
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