Indian Geotechnical Conference (IGC-2010)igs/ldh/files/igc 2015 pune/THEME 9...Rizwan Khan, M. Tech...
Transcript of Indian Geotechnical Conference (IGC-2010)igs/ldh/files/igc 2015 pune/THEME 9...Rizwan Khan, M. Tech...
50
th
IGC
50th
INDIAN GEOTECHNICAL CONFERENCE
17th
– 19th
DECEMBER 2015, Pune, Maharashtra, India
Venue: College of Engineering (Estd. 1854), Pune, India
NUMERICAL STUDY ON THE BEHAVIOUR OF A RIGID RETAINING WALL
WITH RELIEF SHELVES
V. B. Chauhan1, S. M. Dasaka
2, Rizwan Khan
3
ABSTRACT
Rigid non-yielding retaining walls are made usually as gravity retaining walls. These gravity retaining
walls are bulky in size. There may be situations where high retaining walls are required to resist the
lateral earth pressure. However, massive gravity walls may not be viable due to economic and space
constraints. Also, in some cases, sufficient yielding of rigid cantilever retaining walls may not be
permitted due to site constraints, and these walls need to be designed for higher earth pressures, than the
active earth pressures. Earth pressure on a retaining wall decides the sectional dimensions of the wall, and
there have been several attempts in the literature to reduce the earth pressures on the retaining walls, by
using techniques such as using lightweight backfill, placement of compressible inclusions at the wall-
backfill interface, to name a few. A retaining wall with pressure relief shelves is one of the least explored
techniques to reduce the earth pressure on retaining walls. A few researchers previously proposed this
technique without systematic analysis and proper validation, and demonstrated that provision of relief
shelves can reduce lateral earth pressure on retaining walls. This area has never well researched to
understand the mechanical behaviour of these walls in terms of lateral earth pressure, because of its
particularity, complexity and existing variable factors. Such walls have been constructed in various parts
of the world for about a decade, but their behaviour was never well documented. Hence, the present study
is aimed at understanding the behaviour of such walls and to explore the effectiveness of these walls to
reduce earth pressure and lateral thrust and to get proper insight about the associated mechanisms
involved in the pressure reduction, if any. This work presents numerical analysis of rigid non-yielding
retaining wall retaining a dry cohesionless backfill with pressure relief shelves using FLAC3D
. A 6m high
rigid non-yielding (at-rest) retaining wall, retaining a dry cohesionless backfill, has been chosen for the
present study. Two cantilever relief shelves of thickness of 0.20m are placed at different heights of the
wall. Width of these relief shelves are varied as 0.5m, 0.6m, 0.7m and 0.8m, to conduct a parametric
study to understand the influence of width of relief shelves on the contact pressure below base slab,
surface settlement profile of backfill, deflection of relief shelves and reduction in lateral earth pressure.
Lateral earth pressure on the retaining walls studied is shown in Fig. 1. The present studies reveal that
1Ph. D. research scholar, Civil Engineering Department, IIT Bombay, Mumbai, India, [email protected]
2Associate Professor, Civil Engineering Department, IIT Bombay, Mumbai, India, [email protected]
3M. Tech student, Civil Engineering Department, IIT Bombay, Mumbai, India, [email protected]
V. B. Chauhan, S. M. Dasaka & Rizwan Khan
retaining walls with relief shelves can considerably reduce the thrust on wall in the range of 10.56-12.5%
when relief shelves are used with retaining wall, compared to that of retaining wall without relief shelf.
Deflection of relief shelves has marginally increased backfill surface settlement by 0.7-1 mm, which
might not affect the serviceability of the structure. Provision of relief shelves attributes towards a
redistribution and reduction of total contact pressure below the base slab considerably. Total contact
pressure below the base slab is reduced by around 13% for walls with relief shelves of 0.5-0.6 m with
width, thereby making these walls much safer against bearing capacity failure.
Fig. 1 Lateral earth pressure on the wall for various retaining walls
Amongst all the cases studied, relief shelves of width of 0.5m proved effective in reducing lateral earth
pressure and total contact pressure below base slab by 10.56% and 13.4%, respectively, without leading
to excessive deflection of relief shelves.
Keywords: Retaining wall, relief shelf, earth pressure, numerical modelling, FLAC 3D
50
th
IGC
50th
INDIAN GEOTECHNICAL CONFERENCE
17th
– 19th
DECEMBER 2015, Pune, Maharashtra, India
Venue: College of Engineering (Estd. 1854), Pune, India
NUMERICAL STUDY ON THE BEHAVIOUR OF A RIGID RETAINING WALL
WITH RELIEF SHELVES
V. B. Chauhan, Ph. D. student, Civil Engineering Department, IIT Bombay. [email protected]
S. M. Dasaka, Associate Professor, Civil Engineering Department, IIT Bombay. [email protected] Rizwan Khan, M. Tech student, Civil Engineering Department, IIT Bombay. [email protected]
ABSTRACT: This paper presents numerical study on a 6m high retaining wall with 2 relief shelves having varying
width of relief shelves ranging 0.5-0.8m to understand the influence of width of relief shelves on the contact
pressure below base slab, surface settlement profile of backfill, deflection of relief shelves and reduction in lateral
earth pressure. It is found that retaining walls with relief shelves can considerably reduce the lateral thrust on wall
in the range of 10.56-12.5%. Among all the cases studied, relief shelves of width of 0.5m proved effective in
reducing lateral earth pressure and total contact pressure below base slab by 10.56% and 13.4% respectively,
without leading to excessive deflection of relief shelves.
INTRODUCTION
Retaining walls are an integral part of almost all
infrastructure projects, to support vertical or near
vertical backfills. Rigid non-yielding retaining
walls are made usually as gravity retaining walls.
These gravity retaining walls are bulky in size.
There may be situations where high retaining walls
are required to resist the lateral earth pressure.
However, massive gravity walls may not be viable
due to economic and space constraints [1]. Also, in
some cases, sufficient yielding of rigid cantilever
retaining walls may not be permitted due to site
constraints, and these walls need to be designed for
higher earth pressures, than the active earth
pressures. One alternative to tackle such issues is
to reduce the lateral thrust on the wall. As far as
structural design is considered, estimation of lateral
thrust on retaining walls plays a major role
affecting the cost of project [2, 3]. So, by reducing
lateral earth pressure, sectional dimensions of
retaining wall as well as cost of project can be
reduced. There are many methods available to
reduce the lateral earth pressure, such as use of
geo-inclusion materials such as expanded
polystyrene (EPS) [4], glass-fiber insulation [5]
and cardboard [6], light weight backfill, to name a
few. One such technique, which is least explored,
is retaining wall with relief shelves. Relief shelves
are horizontal platforms, which are constructed
monolithically with the stem of wall, and extend
into the backfill at right angles, throughout the
length of the retaining wall. Number of such
shelves is constructed at regular spacing along the
height of the wall. A few researchers previously
proposed this technique without systematic
analysis and proper validation, and demonstrated
that provision of relief shelves can reduce lateral
earth pressure on retaining walls. This area has
never well researched to understand the mechanical
behaviour of these walls in terms of lateral earth
pressure [7-10], because of its particularity,
complexity and existing variable factors. Such
walls have been constructed in various parts of the
world for about a decade, but their behaviour was
never well documented. Hence, the present study is
aimed at understanding the behaviour of such walls
and to explore the effectiveness of these walls to
reduce earth pressure and lateral thrust and to get
proper insight into the associated mechanisms
involved in the pressure reduction.
LITERATURE REVIEW
Effect of provision of relief shelves was studied
and noted that extending the relief shelves beyond
V. B. Chauhan, S. M. Dasaka & Rizwan Khan
the rupture surface in soil can considerably reduce
the lateral earth pressure and increase the stability
of retaining wall [7]. It was suggested that for walls
with greater heights, more than one relief shelf
could be a viable solution (Fig. 1). In the case of
counterfort retaining walls, the relief shelves can
be provided spanning the length of counterfort.
Fig. 1. Counterfort wall with relief shelves [7]
Researchers have demonstrated the benefit of
single relief shelf on the reduction of total lateral
thrust on a cantilever wall, through stability
analysis of wedges [8]. Through small-scale
physical model tests, it was showed that the
maximum height of sand that could be retained by
wall just prior to the incipient overturning is higher
in case of walls with relief shelf than that of walls
without relief shelf [8]. A possible solution for
earth pressure reduction on retaining walls was
suggested for high retaining walls [10], as shown
in (Fig. 2). Through an analysis, it was
demonstrated that contribution of the relief shelf to
the overall stability of the retaining wall, in terms
of extra stabilizing moment. It was suggested that
the soil below the relieving shelf should not
provide any support to relief shelf to realize the
reduction in earth pressure [11]. A similar
technique, named Graviloft, which is a
combination of gravity retaining and reinforced
concrete loft, was illustrated [12]. In such walls, a
loft was provided perpendicular to non-prismatic
section of stem.
Fig. 2. Cantilever retaining wall with relief shelves
[10]
It is demonstrated that proper design and
placement of such lofts optimized the resources
leading to 40% cost saving. Graviloft technology
has been successfully implemented for guide walls,
wing walls and divides walls of maximum height
of 26m in various projects such as box culvert,
aqueduct and barrage in the state of Maharashtra,
India [12]. Such walls resulted in smaller cross
section area of stem and base slab than
conventional gravity walls.
A well-documented case study of failure of a 10-13
m high cantilever retaining wall with relief shelves
has been reported in Hyderabad, India. The above
structure had failed after few years of construction,
and cracks on the stem of retaining wall just below
one of the relief shelves were noted, as shown in
Fig. 3. The forensic studies reveal that quality of
concrete used in the wall construction was very
satisfactory, and construction defects were
completely ruled out. Though the reasons behind
the failure of the above structure are not known
yet, the authors are of the opinion that the lateral
earth pressures might have been estimated
wrongly. In spite of wide use of these walls, there
is no common consensus on the efficacy of these
walls in the lateral pressure reduction.
50
th
IGC
50th
INDIAN GEOTECHNICAL CONFERENCE
17th
– 19th
DECEMBER 2015, Pune, Maharashtra, India
Venue: College of Engineering (Estd. 1854), Pune, India
Fig. 3. Cantilever retaining wall with relief shelves
in Hyderabad, India
Moreover, no design guidelines are available on
the selection of optimum number, sectional
dimensions, and location of relief shelves, for a
given height of retaining wall. Failure of such
structures has motivated the authors to critically
examine the rigid retaining walls with relief
shelves and possible mechanism beyond lateral
pressure reduction.
NUMERICAL MODELLING OF RELIEF
SHELF WALLS
A 6 m high rigid non-yielding (at-rest) retaining
wall, retaining a dry cohesionless backfill, has been
chosen for the present study, and conventional
retaining wall without relief shelves (Fig. 4a) is
hereafter referred to as RS 0.0. Finite Difference
numerical package (FLAC 3D) is used in the study
to understand the effect of relief shelves on the
contact pressure below base slab, surface
settlement profile of backfill, deflection of relief
shelves and reduction in lateral earth pressure, two
cantilever relief shelves of same widths placed at
different heights of the wall are considered, as
shown in Fig. 4b. Sectional dimension of retaining
wall with relief shelves is shown in Fig. 4b,
wherein width of relief shelf (B) is varied as 0.5m,
0.6m, 0.7m and 0.8m.
Fig. 4. Geometry of retaining walls with and
without relief shelves (all dimensions in m)
These walls are hereafter referred to as RS 0.5, RS
0.6, RS 0.7 and RS 0.8, respectively. The thickness
of relief shelves is taken as 0.20m, throughout the
study. The length of foundation zone is kept as 30
m, which is five times the selected wall height, as
shown in Fig. 5.
Fig. 5. Numerical model of rigid retaining wall
with relief shelves
Factors of safety of retaining wall (RS 0.0) in
sliding and overturning modes of failure are
estimated as 3.95 and 4.0, respectively. To model a
plane strain problem, the length of retaining wall is
V. B. Chauhan, S. M. Dasaka & Rizwan Khan
considered as 1m. Sectional dimensions of all
retaining walls studied are shown in Fig. 4.
The mesh of numerical model of retaining is
divided into 10695 zones of uniform size. Fig. 5
shows the numerical grid considered to simulate
the rigid retaining wall. Fixed boundary condition
at bottom of foundation and roller boundary
condition at vertical ends of soil are chosen to
represent field conditions. Wall is not allowed to
move away from backfill, as it is considered as at-
rest wall.
MATERIALS AND INTERFACE
PROPERTIES
The rigid wall is modelled as elastic material.
Backfill material is modelled as a purely frictional,
elasto-plastic material following Mohr-Coulomb
failure criterion. Backfill and foundation soil
properties considered in the analysis are obtained
from [13], as shown in Table 1.
Table 1 Material properties [13]
Property Backfill Foundation Retaining
wall Bulk unit weight (kN/m
3)
16.5 17.5 24.0
Bulk Modulus
(kN/m2)
5200 5500 3.16×107
Poisson’s
Ratio
0.33 0.33 0.2
Cohesion
(kN/m2)
0 0 -
Friction angle
(Degrees)
43.5° 45.0° -
Dilation angle
(Degrees)
22.5° 22.5° -
Interface between different materials is modelled
as linear spring-slider system with interface shear
strength, defined by the Mohr-Coulomb failure
criterion. The relative interface movement is
controlled by interface normal stiffness (kn) and
shear stiffness (ks). A recommended thumb rule is
that ks and kn be set to ten times the equivalent
stiffness of the stiffest neighboring zone [14]. The
suggested maximum stiffness value is as follows:
min3
4max10 zGKkk sn
(1)
Where (∆z)min, K and G are the smallest dimension
in normal direction, bulk modulus and shear
modulus of the continuum zone adjacent to the
interface, respectively. This approach gives the
preliminary values of the interface stiffness
components, and these can be updated to avoid
intrusion to adjacent zone and to prevent excessive
computational time [15]. The interface at the base
of the wall has been assigned a value of normal
stiffness, kn= ks=1.5×109
kN/m2/m, thus preventing
penetration of wall into foundation soil. The
interface between the backfill soil and wall is
assigned a value of normal stiffness kn=1.5×109
kN/m2/m and zero shear stiffness to ascertain the
smooth interface between backfill and retaining
wall [16].
RESULTS AND DISCUSSION
The results of numerical modelling (FLAC3D
) of
earth pressure distribution on the rigid non-yielding
retaining wall without relief shelves are compared
with experimental test results [13], as shown in
Fig. 6, and it is noted from the figure that
numerical pressure distribution matches well with
that of experimental findings.
Fig. 6. Validation of numerical model used in the
present study
50
th
IGC
50th
INDIAN GEOTECHNICAL CONFERENCE
17th
– 19th
DECEMBER 2015, Pune, Maharashtra, India
Venue: College of Engineering (Estd. 1854), Pune, India
Hence, the same numerical model is extended to
study the behaviour of rigid retaining walls with
two relief shelves provided at different levels, in
terms of the lateral earth pressure distribution,
contact pressure below base slab, total lateral
thrust, backfill settlement and deflection of relief
shelves.
Selection of number of relief shelves for a given
height of retaining wall should be done in such a
way that width of relief shelves should not be very
large as well as sufficient gap should be available
between two successive relief shelves for proper
compaction of backfill during the construction.
Hence, for 6 m high retaining wall, 2 relief shelves
are chosen for the present analysis.
For a rigid non-yielding wall, contact pressure
below base slab is governed by weight of wall,
center of gravity of wall and lateral thrust of soil.
Variation of contact pressure below base slab for
all retaining walls considered in the present study
is shown in Fig. 7.
Fig. 7. Contact pressure below the base for various
retaining walls
Retaining wall with relief shelves is different in
shape compared to the conventional retaining wall
and addition of horizontal relief shelves have
increased the weight of wall and shifted the center
of gravity of such wall towards backfill. Reduction
of lateral thrust has also played a role in variation
of contact pressure at base. Total contact pressure
below the base slab for all retaining walls
considered in the study is tabulated in Table 2.
Total contact pressures below the base slab is
reduced by 13.4% and 13.7% in case of RS 0.5 and
RS 0.6 walls. However, contact pressure
distribution below the base slab of retaining wall
without relief shelves is more or less same as that
of walls with relief shelves, viz. RS 0.7 and RS 0.8.
This behaviour of contact pressure distribution
might be attributed to increased weight of wall due
to added weight of shelves, reduction of lateral
earth pressure and shifting of center of gravity of
wall. These parameters have played in such a way
that contact pressure below the base has not
changed significantly in case of RS 0.7 and RS 0.8
walls. So, it can be concluded that proper selection
of width of relief shelves can reduce total contact
pressure below the base slab significantly and
subsequently increase the factor of safety against
bearing capacity failure. Surface settlement of
backfill is a criterion of serviceability of retaining
walls. Excessive backfill settlement leads to
collapse of backfill soil and subsequently failure of
surrounding structures.
Table 2. Total contact pressure below the base slab
Wall type RS
0.0
RS
0.5
RS
0.6
RS
0.7
RS
0.8
Total
pressure
kN/m
240.9 208.5 202.8 242.9 233.2
% Change
in contact
pressure
----- -13.4 -13.7 +0.85 -3.1
Fig. 8 presents surface settlement of all retaining
walls considered in this study. Backfill settlement
near the wall is ranging between 2-5 mm and it
gradually increases up to a maximum value of 10
mm far away from the stem. Surface settlement of
retaining walls with relief shelves is higher than
that of walls without shelves by 0.7-1 mm in the
region 1.5-4 m away from face of stem. This
increased settlement of backfill is attributed to
deflection of relief shelves. Pronounced effect of
deflection of relief shelves on backfill surface
V. B. Chauhan, S. M. Dasaka & Rizwan Khan
settlement has continuously been diminished with
increasing distance from stem and achieved the
same profile, as that of walls without relief shelves
beyond 8m from stem.
Fig. 8. Surface settlement profile of backfill
Fig. 9. Vertical deflection profile of top relief shelf
Deflection profile of top and bottom relief shelves
are compared in Figs. 9 and 10, respectively, and
maximum deflection of such relief shelves is listed
in Table 3. Deflection of relief shelves were found
maximum at bottom relief shelf compared to top
relief shelf for all retaining walls with relief
shelves except RS 0.5. Deflection of relief shelves
has significantly increased, when width of relief
shelf is greater than 0.5m. This observation
highlights that for the wall under study, maximum
width of relief shelves should be restricted to 0.5m.
Large width of relief shelves are leading to
excessive deflection due to their own weight,
which may further increase due to creep.
Fig. 10. Vertical deflection profile of bottom relief
shelf
Table 3. Maximum deflection (mm) of relief
shelves for various retaining walls
Relief Shelf RS 0.5 RS 0.6 RS 0.7 RS 0.8
Top RS 3.5 7.69 10.87 14.49
Bottom RS 3.10 8.46 11.40 14.74
Distribution of earth pressure on all retaining walls
is shown in Figs. 11 and 12. Provision of two relief
shelves has made the whole retaining wall into
three small segments. From Figs. 11 and 12, it can
be observed that lateral earth pressures in top
segment of all retaining walls with relief shelves
are less than that of retaining wall without relief
shelf, but attain higher values in the middle and
lowermost segments. Earth pressure behind the
relief shelves are lower than that of retaining wall
without relief shelf at corresponding height. Earth
pressure in lower most region has attained a peak
which might be due to numerical instability arising
from the presence of three corners in wall
geometry (two at base slab and one at junction of
stem and base slab). Presence of such corners
makes interfaces complex in numerical analysis,
which is due to intersection and overlapping of two
interfaces at a point.
50
th
IGC
50th
INDIAN GEOTECHNICAL CONFERENCE
17th
– 19th
DECEMBER 2015, Pune, Maharashtra, India
Venue: College of Engineering (Estd. 1854), Pune, India
Fig. 11. Lateral earth pressure on the wall for
various retaining walls
Fig. 12. Lateral earth pressure on the wall for
various retaining walls
Table 4 Total lateral thrust and reduction in thrust
on retaining walls
Wall
type
Total thrust kN/m % Reduction
in thrust
RS 0.0 196.93 --
RS 0.5 176.12 10.56
RS 0.6 174.83 11.2
RS 0.7 174.4 11.5
RS 0.8 172.0 12.5
Total lateral thrust is calculated for all the retaining
walls considered in the present study, as shown in
Table 4.
Fig. 13. Comparison of reduction of lateral earth
pressure on wall by various methods
In the present study, a significant amount of total
lateral thrust reduction in the range of 10.56-12.5%
is obtained by provision of two relief shelves.
A comparison of lateral earth pressure distribution
obtained in the present study and the method
suggested by Bowles[10] on 6m high retaining
wall with relief shelves is presented in Fig. 13.
Percentage reduction in total thrust is found to be
66.1% when compared with method suggested by
Bowles[10], while the same for RS 0.5 has been
found to be 10.56%. However, further studies in
this direction are warranted, to get more insight
into the retaining walls with relief shelves,
especially physical model tests with earth pressure
measurements.
CONCLUSION
The study involves comprehensive finite difference
numerical analysis to assess the effectiveness of
providing relief shelves to the retaining walls. This
technique of reducing earth pressure on retaining
walls may prove economical, if properly
implemented. A 6 m high retaining wall with two
relief shelves is analyzed in this study. The effect
of width of relief shelves on backfill surface
settlement, contact pressure below base slab,
V. B. Chauhan, S. M. Dasaka & Rizwan Khan
deflection of relief shelves and earth pressure
reduction are analyzed and following conclusions
are drawn.
1. Among all the cases studied, retaining walls
with relief shelves can considerably reduce
the lateral thrust on wall in the range of
10.56-12.5%.
2. Proper selection number, location, and
dimensions of relief shelf can considerably
reduce the total contact pressure below the
base slab and making the retaining wall
much safer in bearing capacity failure
mode.
3. Among all the cases studied, relief shelves
of width of 0.5 m proved effective in
reducing lateral earth pressure and total
contact pressure below base slab by 13.4%
and 10.5% respectively, without leading to
excessive deflection of relief shelves.
4. Deflection of relief shelves increased
backfill surface settlement by 0.7-1 mm,
which might not affect the serviceability of
the structure.
REFERENCES
1. Hatami, K., Bathurst, R.J., and Pietro, P. D.
(2001), Static response of reinforced soil
retaining walls with non-uniform
reinforcement, Int. J. Geomech.,
10.1061/(ASCE)1532-3641(2001)1:4(477).
2. Goel, S. and Patra, N. R. (2008), Effect of
arching on active earth pressure for rigid
retaining walls considering translation mode,
Int. J. Geomech., 10.1061/(ASCE)1532-
3641(2008)8:2(123).
3. Soon, S. C. and Drescher, A. (2007), Nonlinear
failure criterion and passive thrust on retaining
walls, Int. J. Geomech., 10.1061/(ASCE)1532-
3641(2007)7:4(318).
4. Horvath, J. S. (1997), The compressible
inclusion function of EPS geofoam, Geotext.
Geomembr., 15 (1-3), 77-120.
5. Rehnman, S. E. and Broms, B. B. (1972),
Lateral pressures on basement walls: Results
from full scale tests, Proc., 5th
European
conference on Soil Mechanics, Madrid, vol. 1,
189-197.
6. Edgar, T. V., Puckett, J. A. and D’Spain, R. B.
(1989), Effect of geotextiles on lateral
pressures and deformation in highway
embankments, Geotext. Geomembrane, 8(4),
275-292.
7. Jumikis, A.R. (1964), Mechanics of soils, D.
Van Nostrand Company Inc, Princeton, NJ.
8. Chaudhuri, P.R., Garg, A.K., Rao, M.V.B.,
Sharma, R.N., Satija, P.D. (1973), Design of
retaining wall with relieving shelves, IRC J.
35(2), 289 - 325.
9. Banerjee, S. P. (1977), Soil behaviour and
pressure on retaining structures with relief
shelves, Indian Highways, 21-34.
10. Bowles, J.E. (1997), Foundation analysis and
design, 5th Edition, McGraw-Hill, Singapore.
11. Kurian, N.P. (2007), Design of foundation
systems, principles and practice, 3rd
Edition,
Narosa Publishing House, Delhi.
12. Balwan, R.J. and Kumbha, A. (2011), Graviloft
retaining wall: A case study, Proc., Indian
Geotechnical Conference, Kochi, India, 1068-
1070.
13. Ertugrul, O. L. and Trandafir, A.C. (2011),
Reduction of lateral earth forces acting on rigid
non-yielding retaining walls by EPS geofoam
inclusions,J. Mater. Civil Eng., 23(12), 1711-
1718.
14. FLAC3D
(5.0) (2011), Itasca Consulting Group
Inc., Minneapolis, US.
15. Bhattacharjee, A. and Muralikrishna, A.
(2011), Behaviour of gravity retaining walls
subjected to seismic excitation using FLAC
3D,Int. J. Earth Sci, Eng., 4(6), 71-74.
16. Nadim, F. and Whitman, R.V. (1983),
Seismically induced movement of retaining
walls, J. Geotech. Eng., 10.1061/(ASCE)0733-
9410(1983)109:7(915).