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US
Army
Corps
ofEngineers
EngineerResearchand
Development
Center
Earthquake
Engineering
Research
Program
Seismic
Analysis
of
Cantilever
Retaining
Walls,Phase
RussellA.
Green
and
Robert
M .
Ebeling eptember
2002
heel
section
Time(sec)
30 35 40
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fo r
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release;
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s
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Theontents
of
thiseportre
ot
o
e
se dor
dvertising,
publication,rromotionalurposes.itationoftrade
ames
does
no tconstitutean
official
endorsement
orapproval
of
theus e
of
such
commercialproducts.
The
indingsof
this
report
ar e
no tto
be
construed
as
an
official
Departmentof
th e
Army
position,
unless
sodesignated
by
other
authorized
documents.
PRINTED
O N
RECYCLED
PAPER
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EarthquakeEngineering RDC/ITL TR-02-3
Research
Program
eptember
2002
Seismic
Analysis
ofCantilever
Retaining
Walls,
PhaseI
by Russell A.Green
Department
of
Civil
and
Environmental
Engineering
University
of
Michigan
Ann Arbor,
M l
8109-2125
RobertM .
Ebeling
Information
Technology
Laboratory
U.S.
Army
EngineerResearchandDevelopmentCenter
3909
Halls
Ferry
Road
Vicksburg,
M S9180-6199
Finalreport
Approvedforp u b l i c r e l e a s e ;d i s t r i b u t i o n
is
u n l i m i t e d
P r e p a r e d
for
U.S.
ArmyCorps
of
Engineers
Washington,
DC0314-1000
U n d e r
Work
Unit387-9456h
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Contents
Preface j
1Introduction
1.1ntroduction
1.2Background
1.3
esearch
Objective
1.4
Researchintoth e
Seismic
Response
of
a
Cantilever RetainingWall
1.5OrganizationofReport
1.6
uture
Work
2Selection
of
Design
Ground
Motion
2 .1
election
Criteria
2.1.1
ea lversussynthetic
earthquakemotion
2.1.2Representativemagnitude
and
site-to-source
distance
2.1.3
ite
characteristics
ofmotion
2 .2is tofCandidate
Motions 0
2 .3
haracteristics
of
Ground
Motion
Selected
0
2 .4rocessing ofth e
Selected
GroundMotion
2
3Numerical
Analysis
ofCantilever RetainingWall
4
3.1
verview
ofFLAC 4
3.2
Retaining
Wall
Model
6
3.3
Numerical
Model
Parameters
9
3.3.1
ohr-Coulomb
model 9
3.3.2
tructuralelements 1
3.3.3
nterface
elements
2
3.3.4
Dimensions
of
finite
difference
zones
6
3.3.5
amping
8
3.4
ummary
9
4FLACData Reduction DiscussionofResults
0
4.1
ata Reduction
0
4.1.1
etermination
of
forces
assuming
constant-stress
distribution
1
ill
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4.1.2Determination
offerees
assuming
linearly
varying
stress
distribution
2
4.1.3ncrementaldynamicforces
0
4.1.4Reactionheight
offorces
4
4.2resentationandDiscussionofReduced
Data5
4.2.1
otal
resultant
forces
and
points
of
action
5
4.2.2Ratiooftotal
resultant
forces
and
points
ofaction
2
4.2.3
ncremental
resultantforces
and
points
ofaction
2
4.2.4ermanent
relative
displacementof th e
wall5
4.2.5 eformed
grid
ofth e
wall-soil
system,post
shaking
7
4.3
onclusions
9
References
1
Appendix A: tatic
Design
ofth e
Cantilever
Retaining
Walll
Appendix
B:Notation,
Sign
Convention,andEarth
Pressure
Expressions
l
Appendix
C:
isplacement-Controlled
Design
Procedure
l
Appendix
D:
pecifying
Ground
Motions
in
FLAC
l
Appendix
E:
Notation
l
SF298
ListofFigures
Figure
1-1.
TypicalCorps
cantileverwall,
includingstructuraland
driving
wedges
Figure
1-2.
Earth
retaining
structures
typicalofCorpsprojects
Figure1-3.
Loads
acting
onth estructuralwedge
ofacantilever
retaining
wall
Figure2-1.
Acceleration
time-history
and
5
percent
damped
pseudo-
accelerationspectrum,
scaledto
l-gpga
1
Figure2-2 .
Husid
plotofSG3351
used
fo r
determining
duration
of
strong
shaking 1
Figure
2-3.
Selected
ground
motion
(a )
recorded
motion
SG335 l and
(b )
th e
processedmotionused
as
input
into
th ebase
of
th eFLAC
model
3
Figure3-1.
Basicexplicit
calculation
cycle
used
in
FLAC
5
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Figure
3-2.
Numerical
models
used
in
th e
dynamic
analysis
of th e
cantileverretaining
wall
7
Figure3-3.
Retainingwall-soil
system
modeled
in
FLAC
8
Figure
3-4.
Deformed
finite
difference
grid,
magnified
75
times
9
Figure
3-5.
Subdivision
of th e
cantilever wall
into
five
segments,
eachhaving
constant
material
properties
1
Figure
3-6.
Approach to
circumventing
th e
limitation
in
FLAC
of
no t
allowing
interface
elements
to
be
used
at
branching
intersections
of
structural
elements 3
Figure
3-7.
Schematic
of th e
FLACinterfaceelement4
Figure
3-8.
Comparison
of th e
Gomez,
Filz,and Ebeling(2000a,b)
hyperbolic-type
interface
elementmodel
and
th e
approximate-fitelastoplastic
model5
Figure
3-9.
Interface
element
numbering
7
Figure
4-1.
Assumed
constantstress
distribution
acrosselements,
at
timet j ,
used to
computeth e
forces
actingonth e
stem
and heel
section
in
th e
firstapproach
1
Figure
4-3. Horizontal
accelerationa
h
,
and
corresponding
dimensionless
horizontalinertial coefficient
k
h
,
ofapoint
in th ebackfill
portionof th e
structural
wedge
6
Figure
4-4.
Time-histories
of
P,
Y/H
and
YP
fo r
th e
stem
and
heel
sections
7
Figure
4-5.omparisonoflateralearthpressure
coefficients
computed
using
th e
Mononobe-Okabe
active
and passive
expressions
Wood
expressionand
FLAC
8
Figure
4-6.
Stress
distributions
and
total
resultant
forceson
th e
stem
and heel
sections
at
times
corresponding to
th eth e
following:
(a )maximum
value
fo r
P
slem
and
(b )th e
maximum
values
fo r
P
h ee l
,
(YP)
slem
,
and {YP)
he e
,
1
Figure
4-7.
Time-histories
of
P
stem
I
P
heel
,
Y
stem
I
Y
heel
,
and
(YP)
slem
lYP)
he e l
3
Figure
4-8.
Time-histories
ofAP
and
AY-AP
fo r
th e
stem
and heel
sections 4
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Jstemi
Figure
4-9.
Stress
distributions,
static
andincrementaldynamic
resultantforces
on
th e
stem
and
heel
sections
at
times
corresponding to
th e
following:
(a )
maximum
value
fo r
P
slem
,
andb)
the
maximum
values
fo r
P
he e
u(Y-P\
and(7-P)w 6
Figure
4-10.
Comparisonof
th epermanentrelative
displacements
predictedbyaNewmarkslidingblock-typeanalysisand
byFLAC
7
Figure4-11.
Results
fromth eNewmark
sliding
block-type
analysis
of
th estructuralwedge
8
Figure
4-12.
Deformed
gridof
th e
wall-soilsystem,postshaking,
magnificationx10 9
Figure
4-13.
Shaketabletests
performed
onscalemodelsof
retaining
wall
0
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Preface
The
study
documented
herein
was
undertaken
as
part
ofWork
Unit 387-
9456h,
"Seismic
Design
of
Can tilever Retaining
Walls ,"
funded
by
th e
Head-
quarters,
U.S.
Army
Corps
ofEngineers(HQUSACE)
CivilWorks
Earthquake
Engineering Research Program
(EQEN)under
th e
purviewof
th e
Geotechnical
and
Structures
Laboratory
(GSL),
Vicksburg,
M S,
U.S.
ArmyEngineer Research
and D evelopmentCenter (ERDC). echnical
Director for this
researcharea was
Dr.
Mary
EllenHynes,
GSL.The
HQUSACE
Program
Monitor
fo r
this
work
wasMs.AnjanaChudgar .Theprincipal
investigator (PI)
fo r
this
studywas
Dr.RobertM.
Ebeling,
Computer-Aided
EngineeringDivision(CAED),Infor-
mation
Technology
Laboratory
(ITL),
Vicksburg,
M S,
ERDC,
and
Program
Manager wasMr.
Donald
E.Yule,GSL.The
work
was
performed
at
University
of
Michigan,
Ann Arbor,
andat
ITL.
The
effort
at
th e
University
of
Michigan
wasfunded
through
response
to
th e
ERDC
Broad Agency
Announcement
FY01,
BAA#
ITL-1,
"A Research
Investigation
of
Dynamic
Earth
Loadson
Cantilever
Retaining
Walls
as
a
Function
of th e
Wall
Geometry,
Backfill
Characteristics,
and
Numerical
Modeling
Technique."
This
research
was
performedand thereportpreparedby
Dr.
Russell
A.
Green
of
th e
Department
of
Civiland
Environmental Engineering,
University
of
Michigan,and byDr.Ebeling
under
th e
direct
supervision
of
Mr.H.Wayne
Jones,
CAED,
and
Dr.
Jeffery
P.
Holland,
Director,
ITL.
Th e
work was
performedduring
th e
periodDecember
2001
toAugust2002
by
Dr.
Greenand
Dr.
Ebeling.hi s
report
summarizes
th e
results
of th e
firstphase
ofa
research
investigationexamining
th e
seismic
loadsinduced
on
th e
stem
ofacantilever
retaining
wall. hisinvestigationmarksth e
first
use
of th e
computer
program
FLAC
(FastLagrangian Analysis
of
Continua)
fo ranalyzing th e
dynamic
response
ofa
Corps
earth retaining
structure,
with
th e
emphasis
of
th e
investigation
being
on
th edetails
ofnumerical
modeling
with
FLAC,aswellas
th eresultsof th eanalyses.
urther
analyses
are
required
to
confirm
the
identified
trends
in
th eresultsof th e
analyses
and
to
formulate
design
recommendations
fo r
Corps
earthretaining
structures.Duringth e
course
ofthis
research
investigation,
th eauthors
had
numerous
discussions
with
other FLAC
users.
Of
particular
note
were
th e
lengthy
conversationswith M r.
Guney
Olgun,
Virginia
Polytechnic
and
State
University,Blacksburg,whichwere
instrumental
in
completing Phase
1
of
this
research
investigation. thers
who
provided
valuable
insight
intoth e
workings
of
FLAC
were
Mr.
NasonMcCullough
and
Dr.
Stephen
Dickenson,
Oregon
State
University,
Corvallis;Dr.N.
Deng
and Dr.
Farhang
Ostadan,
BechtelCorporation,
San
Francisco,
CA;Mr.
Michael
R.Lewis,
Bechtel
V I I
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Savannah
River,
Inc.,Aiken,SC;
Dr.
Peter
Byrneand
Dr.
Mike
Beaty,
University
of
British
Columbia,Vancouver;
andDr.
Marte
Gutierrez,Virginia
Tech.
At
th e
time
of
publication
of this
report,
Dr.
JamesR.
Houston
wasDirector,
ERDC,
and
COL
John
W .
Morris
III,
EN,
was
Commander
and
Executive
Director.
The
contents
of
this
report
a reno ttobeusedfora dvertising,publication,
or
promotional
purposes.
itation
of
tradenam esdoes no tconstitute an
official
endorsementor approval
ofth e
us e
ofsuchcommercial products.
VIII
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1
Introduction
1 .1
Introduction
This
report presents theresults
of th e
first
phase
ofaresearch
investigation
intoth eseismic
responseof
earth
retaining
structures
and th e
extension
of th e
displacement
controlled
design
procedure,
asapplied
to
th e
global
stability
assessment
ofCorpsretaining
structures,
toissuespertaining totheirinternal
stability.It
is
intended
toprovide
detailed
information
leading
torefinementof
th eEbelingand
Morrison
(1992)
simplified
seismicengineering
procedure
fo r
Corps
retaining
structures.Specificitems
addressed
in this
Phase
1
report
deal
with
th eseismicloadsactingon
th e
stem
portion
of
cantilever retaining
walls.A
typical
Corps
cantilever retaining
wall
is
shown
in Figure
1-1.
t
is
envisioned
that
this
information will
be
used
in
th e
development
ofarefined
engineering
procedure
of
th e
stem
and
base
reinforced
concrete
cantilever
wall
structural
members
fo rseismic
structural
design.
structural
wedge
stem
XXX
XXX
driving
wedge
base
-fA- i
heel
Figure
1-1.
ypicalCorpscanti lever wall,includingstructuralan ddrivingwedges
Chapter
1
Introduction
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1 .2 Background
Formal
considerationof
th e
permanent
seismic
wall
displacement
in
th e
seismic
design
process
fo rCorps-type
retaining
structures
is
given
in
Ebelingand
Morrison
(1992).
he
key
aspect
of
this
engineering
approachisthat
simplified
procedures
fo r
computing
th e
seismically
induced
earth
loads
on
retaining
structures
are
dependent
upon
th eamountof
permanent
wall
displacement
that
is
expected
to
occur
fo r
each
specified
design
earthquake.
The
Corps
uses
tw o
design
earthquakes
as
stipulated
inEngineerRegulation(ER)1110-2-1806
(Headquarters,
U.S.ArmyCorpsof
Engineers
(HQUSACE)
1995):th e
Operational
Basis
Earthquake
(OBE)
1
and th e
Maximum
Design
Earthquake
(MDE).
he
retaining
wall
would
be
analyzed
fo r
each
designcase.
he
load
factors
used
in
th e
design
ofreinforced
concrete
hydraulic
structures
are
different
fo r
each
ofthesetw oloadcases.
The
Ebeling
and
Morrison
simplified
engineering
procedures
for Corps
retaining
structures,as
described
in
their1992report,aregearedtowardhand
calculations.
owever,
research
efforts
are
currently
underway
at
th e
U.S.
Army
EngineerResearchand Development
Center (ERDC)to
computerize
these
engineeringprocedures
and to
make
possibleth eus e
ofaccelerationtime-
histories
in
these
design/analysis
processes
when
time-histories
are
made
availableon
Corpsprojects.nth e
Ebelingand
Morrison
simplified
seismic
analysis
procedure
tw olimit
statesare
established
fo r
th e
backfill;
th e
first
corresponds
to
walls
retaining
yielding
backfill,
while
th e
second
corresponds
to
walls
retaining nonyieldingbackfill.Examplesof
Corps
retaining
wallsthat
typically
exhibit
these
tw o
conditions
in
seismic
evaluations
areshownin
Fig-
ur e1-2.
n
this
figure
F
v
and F'
H
ar e
th e
vertical
and
horizontal
components,
respectively,
of
th e
resultant
forceof
th e
stresses
acting
on
imaginary
sections
A-A
and B-B,
and
Tand
N'
are
th e
shear
and
normalreaction
forces,respectively,
on
th e
bases
of
th e
walls.
It
isnotuncommonfo rretaining
walls
of th etypeshowninFigurel -2a ,i.e.,
soil-founded
cantilever retainingwalls,
to
have
sufficient
wall
movement
away
fromth ebackfill
during
aseismic
event
to
mobilize
th eshear
strength
within
th e
backfill,
resultinginactive
earth
pressures
actingon th estructuralwedge(a s
delineated
from
th e
driving
wedgebyimaginary
section
A-A
extending
vertically
from
th e
heel
of
th e
wallup
through
the
backfill).igure
l-2bshows
awall
exemplifying
th esecond
category,
walls
retaining
a
nony ielding
backfill.
For
a
massive
concretegravity
lockwall
foundedon
competent
rock
withhigh
base
interface
and
rock
foundation
shear
strengths
(including
high-
strength
rock
joints,if
present,
within
th e
foundation),
it
isno t
uncommon to
find
that
th e
typical
response
of
th e
wall
during
seismic
shaking
is
the
lockwall
rockingupon
its
base.
For
this
case,
wall
movements
in
sliding
ar e
typically
no t
sufficient
to
mobilize
th e
shear
strength
in
th ebackfill.
1
For
convenience,symbols
and
unusualabbreviations
are
listed
and
definedin
the
Notation
(Appendix
E).
Chapter1
Introduction
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a)
b)
Imaginary
A
Section
Flood
Channel
s o i l
fj ,*
77777777777777Z7Z*
///SS^A
rock
Imaginary
B
Section
soil
L o c k
Stop
Chamber
fe fefe
^Mculverlfe*
* *
a
92?bysy/j
B
rock
Figure
1-2.
Earthretaining
structures
typical
ofCorpsprojects:
(a )
soil-founded,
canti lever
f loodwall
retainingearthenbackfill;
(b )
rock-founded,
massive
concrete
lock
wallretainingearthenbackfill
Yielding
backfills
assumethattheshear strengthof th e
backfill
isfully
mobilized(a sa
resultof
the
wall
moving
awayfromth e
backfill
during
earth-
quake
shaking),
and th eus eof
seismically
induced
active
earth
pressure
relation-
ships(e.g.,
Mononobe-Okabe)
isappropriate.A
calculation procedure
first
proposedby
Richards
and
Elms
(1979)
fo r
walls
retaining"dry"
backfills
(i.e.,no
water table)
is
used
fo rthis
limit
state.
beling
and Morrison
(1992)
proposed
engineering
calculation
procedures
fo r
"wet"
sites
(i.e.,sites
with p artially
sub-
mergedbackfills
and for
pools
ofstanding waterin
th e
chamberorchannel)
and
developed
a
procedureto
compute
th e
resultantactive
earthpressure
force
acting
on
th e
structural
wedgeusing
th e
Mononobe-Okaberelationship.
(Most
Corps
sites
are
"wet"
sincethe
Corpsusually
dealswithhydraulicstructures.)
The
simplifiedEbeling
and Morrisonengineeringprocedure
recommendsthat
a
Richards
and Elmstype
displacement-controlledapproach
beappliedtoth e
earth
retaining
structure,
as
described
in
Section6 .3ofEbeling
and
Morrison
(1992)
for Corps
retaining
structures.
It
iscritical
to
th e
calculations
that
partial
sub-
mergence
of
th e
backfill
and
astandingpool
ofwaterin
th e
chamber(o r
channel)
are
explicitlyconsideredin th e
analysis,as
givenbytheEbelingand Morrison
simplified
computationalprocedure.
Equations
developed
by
Ebeling
and Morri-
so ntoaccount
fo r
partial
submergence
of th e
backfill
in th eMononobe-Okabe
resultant
active
earthpressure
force
computation
is
given
in
Chapter
4
of
their
report.Aprocedure
fo r
assigning
th e
corresponding
earth
pressure
distribution
was
developedby
Ebeling
and Morrison
fo r
a
partially
submerged
backfill
andis
describedusingFigures
7.8,7.9,
and
7.10
of
their
report.
Key
to
th ecategorizationofwalls
retaining
yielding
backfills
in
th eEbeling
and Morrison
simplified
engineering
procedure
fo r
Corps
retaining
structures
is
Chapter
1
Introduction
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th e
assessment
byth e
design
engineer
of
th e
minimum
seismicallyinduced
wall
displacements
to
allow
for th e
full
mobilization
of
th e
shear
resistanceof
the
backfill
and,
thus,
th e
appropriate
us e
of
the
Mononobe-Okabe
active
earth
pressure
relationship
in
th ecomputations.
Ebelingand Morrison
made
a
careful
assessment
of
th e
instrumented dynamic
earth
pressure
experimentsavailablein
th e
technical
literature
prior
to
their
publication
in
1992.
he
results
of
this
assessmentare
described
inChapter
2
ofEbelingand
Morrison
(1992). beling
and
Morrison
concluded
that
th eminimum
wall
displacement
criteria developed
by
Clough
and
Duncan
(1991)
fo r
th e
development
of"active"
static
earth
pressure
are
also
reasonable
guidance
fo r
th e
development
of
seismically
induced
active
earth
pressure.
hi s
guidance
fo r
engineered
backfills
isgiven
in
Table1
of
Ebeling
and
Morrison
(1992).
inimum
permanent
seismicallyinducedwall
displacements
awayfromth ebackfillare
expressed
in
this
tableasa
fraction
of
th e
height
ofbackfill
being
retained
byth e
wall.
The
value
for
thisratioisalso
a
function
ofthe
relative
densityof th e
engineeredbackfill.
Thus,prior
to
acceptingapermanentseismic
walldisplacementpredictionmade
following the
simplified
displacement-controlled
approach
fo rCorps
retaining
structures
(Section
6 .3of
Ebeling
and
Morrison
1992),
th e
design
engineer
is
to
check
if
hi s
computed
permanent
seismic
wall
displacement
value
meetsor
exceedsth e
minimum
displacement
value
fo r
activeearth
pressure
given
in
Table
1of
Ebeling
and
Morrison
(1992).This
ensures
thatth eus eof
active
earth
pressures
in
th e
computation
procedure
isappropriate.
In
th e
second
category
of
walls
retaining
nonyielding back fills
(Figure
l -2b),
Ebeling
and
Morrison
recommend
th e
us e
of
at-rest
type,earth
pressure
relationship
in
th e
simplifiedhand
calculations.
Wood's
(1973)
procedure
is
used
to
computeth eincrementalpseudo-staticseismic
loading,whichissuperimposed
on
th e
static,
at-rest
distributionofearthpressures.
Wood's
is
an
expedientbut
conservative
computational
procedure
(Ebelingand Morrison(1992),Chapter5).
(A
procedureto
account
fo rw et
sites
with
partiallysubmergedbackfills
and
fo r
pools
of
standing water
in
th e
chamber
or
channel
was
developed
by
Ebeling
and
Morrison
(1992)
and
outlined
in
Chapter
8oftheir
report.)
It
is
Ebeling's
experiencewithth e
type
lockwallsshown
in
Figurel-2bof
dimensions
thatare
typical
fo r
Corps
locksthat
seismicallyinduced
sliding
is
an
issue
only
with
large
groundmotion
design
events
and/or when
a
weak
rock joint
orapoorlock-to-
foundation
interfaceispresent.
After
careful
deliberation,
Ebeling
and
Morrison
in
consultation
withWhit-
man
1
and
Finn
2
judgedth e
simplified
engineering
procedure
fo rwalls
retaining
nonyielding
backfills
applicable
to
walls
in
which
th e
wallmovements
are
small,
less
than
one-fourth
to
one-half
of th e
Table
(Ebeling
and
Morrison
1992)
activedisplacement values.Recallthat th e
Ebeling
and
Morrison
engineering
procedure
is
centered
on
th e
us e
of
on e
of
only
tw o
simplified
hand-
computational
procedures
.
1
Dr.
Robert
V.
Whitman,
1992,
Professor Emeritus,
Massachusetts
Institute
of
Technology,
Boston.
2
Dr.W.
D.
Liam
Finn,
1992,
Professor Emeritus,Universityof BritishColumbia,
Vancouver.
Chapter
Introduction
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Rotational
response
of
th e
wall
(compared
to
sliding)
is
beyond
th e
scope
of
th e
EbelingandMorrison
(1992)
simplified
engineeringprocedures
fo rCorps
retainingstructures.
This
1992
pioneeringeffortfo r
th e
Corps
dealt
only
with
th e
slidingmode
ofpermanentdisplacementduring
seismic
design
events.
Itis
recognized
that the
Corps
ha s
some
retaining
structures
that
are
more
susceptible
to
rotation-induced
(permanent)
displacement
during
seismicevents
than to
(permanent)
sliding
displacement.
o
address
this
issue,Ebelingis
currently
conducting researchatERDC
leadingtoth e
development
ofa
simplified
engi-
neeringdesignprocedurefo r
th e
analysisofretainingstructuresthat
are
con-
strained torotate
about
th e
to e
of
th e
wall
during
seismicdesignevents
(Ebeling
and White,
in preparation).
1 .3
Research
Objective
TheEbelingand
Morrison
(1992)
simplified
seismic
engineering
procedures
fo rCorpsretainingstructuresdidno t
address
issuespertaining
to
th estructural
design
of
cantilever retaining
walls.The
objective
of
th e
research
described
in
this
reportis
to
fill
this
knowledge
ga p
and
determine the
magnitude
and
distribu-
tion
of
th eseismic
loads
acting
on ca ntilever retaining wa lls
fo r
use
in
th e
design
of
th estem
and
base
reinforced
concrete
cantilever
wallstructuralmembers.
1 .4
Research
into
the
Seismic
Response
of
a
CantileverRetainingWall
Theseismicloadsactingon th e
structural
wedgeofa
cantilever
retaining
wall
are
illustrated
in
Figure1-3.
he
structural
wedgeconsistsof th e
concrete
wall
and
th e
backfill
aboveth e
base
of
th e
wall
(i.e.,th ebackfillto
th e
leftofa
vertical
section through
th e
heel
of
th e
cantilever
wall).
he
resultant
force
of
th estatic
and dynamic
stresses
actingon theverticalsection
through th eheel
(i.e.,
heel
section)is
designated
as
P
AE
,
w,and thenormal
and
shearbase
reactions
are N'
and
T,
respectively. eismically
induced
active
earth
pressures
on
th eheelsection,
PAE,
heel
,areused
to
evaluate
th e
global
stabilityof th e
structural
wedge
of
aca ntilever retaining
wall,
presuming
thereis
sufficient
wall
movement
away
from
the
backfill to
fully
mobilize
th e
shear resistance
of th e
retained
soil.he
relative
slendernessof
th e
stemportion
of
a
cantilever wall
requiresstructuraldesign
consideration.nFigure
1-3
th e
seismicallyinduced
shear and
bending moments
on asectionof th e
stem
are
designated
ass
and m ,
respectively. heresultantforce
ofth estaticand
dynamic
stressesactingon
th e
stem
of th e
wall
shown
in
Figure
1-3is
designated
asP
Ef
stem
.
he A
isno t
included
in
the
subscript
because
th e
structural
design
load
is
no t
necessarily
associatedwithactive
earth pressures.
A
dr ysite(i.e.,no
water
table)
will
be
analyzed
in
this
first
ofaseriesof
analyses
ofcantilever
retaining
wallsusing
FLAC
(FastLagrangian Analysisof
Continua).
hi sallowsth e
researchers
to
gaina
full
understanding
of th e
dynamic
behaviorofth esimplercaseofa
cantilever
wall
retaining
dr y
backfill
Chapter
1
Introduction
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Can tilever Retaining
Wall
structuralwedge
U
=
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1 .5 Organization
of
Report
The
organizationofth ereportfollowsth e
sequenceinwhich th e
work was
performed.
hapter
2
outlinesth e
process
ofselecting th eground
motions
(e.g.,
acceleration
time-histories)
used
in th e
FLAC
analyses.
Chapter3
gives
abrief
overview
of
th e
numerical
algorithms
in
FLACand
outlines
how
th e
various
numerical
model
parameters
were
determined. hapter
4
describes
th e
data
reductionand
interpretationof th e
FLAC
results,
followed
by
th e
References.
Appendix
A
provides
detailed
calculationof
th e
geometry
and
structural
design
fo rstatic
loadingof
th e
wall
analyzeddynamically.Appendix
B
reviewsth e
sign
convention
and
notation
used
in
this
report
and
also
presents
th e
Mononobe-
Okabe
earthpressure
equations
(e.g.,
Ebelingand Morrison
1992,
Chapter
4).
AppendixCisa
brief
overview
of th e
displacement-controlled
procedure
fo r
global
stability
of
retaining walls.inally,
Appendix D
summarizes
a
parameter
study
performed
to
determine
how best
to
specify
ground
motions
in
FLAC.
1 .6
uture
Work
This
report
presentsth eresults
of
th e
first phase
ofan
ongoing
research
investigation.
Additional
FLAC
analyses
ar e
planned
to
determine
if
th e
observed trendspresented
in
Chapter
4
of thisreportare
limitedto
th e
wall
geometry
and
soil
conditions
analyzed,or
whether they
are
generaltrendsthat
are
applicableto
other
wall
geometries
and soil
conditions.
Additionally,
th e
same
wallsanalyzedusingFLAC
willbe
analyzed using th ecomputer program
FLUSH.LUSHsolvesth e
equations
ofmotionsin
th e
frequency
domain
and
usesth e
equivalent
linear
algorithm to
accountfo r
soilnonlinearity. he
advantages
of
FLUSH
arethatitisfreely
downloadable
fromth e
Internet
and ha s
considerably
faster run
times
than
FLAC.However,
th e
major disadvantage
of
FLUSH
is
that
it
does
no t
allow
for permanent
displacement
of
th e
wall.
LUSH
accounts
fo r
th e
nonlinear response
ofsoils
during
earthquakeshaking through
adjustments
of th esoil(shear)
stiffness
and
damping
parameters
(a sa
function
of
shear
strain)
that
developin
each element
of
th efinite
element mesh.
he
FLAC
and FLUSH
resultswillbecompared.
Chapter
1 Introduction
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2
Selection
of
Design
Ground
Motion
2.1
Selection
Criteria
The
selection
ofan
earthquake
acceleration
time-historyfor us e
in
the
numerical
analyses
was
guided
by
th e
following
criteria:
a.real
earthquakemotion
was
desired,no t
a
synthetic
motion.
b.he
earthquake
magnitude
and
site-to-sourcedistancecorresponding to
th e
motion
should
be
representative
of
design
ground
motions.
c.
he
motion
should
have
been
recorded
onrockorstiff
soil.
These
criteriawereused
to
assemblealistof
candidate
acceleration
time-
histories,
while
additional
criteria,discussed
in
Section2.3,wereused
to
select
on e
time-history
from
the
candidate
list.
Because
the
response
ofa
soil-structure
system
in
a
linear
dynamic
analysis
isgoverned
primarily
by
th e
spectralcontent
of
th e
time-history
and
because
it
is
possible
to
obtain
a
very
close
fi t
to
th e
designspectrum
using
spectrum-matching
methods,
it
is
sufficient to
have
a
single
time-historyfo reachcomponent
of
motion
fo reach
design
earthquake.
However,
because
th enonlinearresponseofa
soil-structure
system
may
be
strongly
affected
byth e
time-domain
character of
th e
time-histories
even
if
the
spectraofdifferent time-histories
ar e
nearlyidentical,atleastfive
time-histories
(for
each
component
ofmotion)should
be
usedfo reach
design
earthquake
(Engineering
Circular
(EC)
1110-2-6051
(HQUSACE
2000)) .
More
time-
histories
are
required
fo rnonlineardynamic
analyses
than
fo rlinearanalyses
because
th edynamic
response
ofanonlinearstructure
may
be
importantlyinflu-
enced
byth etime
domain
character
of
th e
time-history
(e.g.,
shape,
sequence,
and
number
ofpulses),inaddition
to
th e
response
spectrum
characteristics.
However,
for
th e
first
phase
of thisresearchinvestigation,onlyon e
time-history
was
selected
fo r
us e
in
th edynamicanalyses.
2.1 .1
Real
versus
synthetic
earthquake
motion
Because
th e
numericalanalyses
performed
in
th e
first
phase
of thisresearch
investigation
involve
permanent
displacement
ofthewall
andplastic
deforma-
tions
in
th e
soil
(i.e.,nonlinearity),
it
was
decided
that
areal
motion
shouldbe
Chapter2 Selection
of DesignGroundMotion
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used.he
rationale
fo r
thisdecisionwasto
avoid potentialproblems
ofdevelop-
in gasynthetic
motion that
appropriatelyincorporates
all
th efactors
that may
influenceth e
dynamic
response
of
a
nonlinearsystem.
2 .1 .2
Representative
magnitude
and
site-to-source
distance
As
stated
in
Chapter
1,
th eobjectiveof
this
study
is
to
determine
th eseismic
structural
design
loads
for
th e
stem
portion
of
a
can tilever retaining
wall.
Accordingly,
th e
magnitude
Mand
site-to-source
distance
R
of th e
ground
motion
usedin
th e
numerical
analyses
should
be
representative
of
an
actual
designearthquake,
which
will
depend
on
severalfactors
including
geographic
location
and
consequences
offailure.n
an
effort
to
select
a
"representative"M
and
R
fo r
a
design
event,
th e
deaggregated hazard
of
five
citieslocated
in
th e
western
United
States(WUS)
were
examined:SanFrancisco,Oakland,
Los
Angeles,
San
Diego,
and
SaltLake
City.Deaggregation
of
th eseismic
hazard
is
atechnique
used
in
conjunction
with
probabilistic
seismic
hazard
analyses
(PSHA)
(E M
1110-2-6050
(HQUSACE
1999))
toexpress
th e
contributionofvarious Mand
R
combinationstoth e
overall
seismichazard
at
a
site. he
deaggregation resultsare
oftendescribed
in
terms
of
th e
mean
magnitude
M
and meandistanceRfo r
variousspectral
frequencies
(Frankel
et
al.
1997).
t
isno t
uncommon to
se t
th e
design
earthquake
magnitude
anddistance
equalto th evaluesof
M
and Rcorresponding toth e
fundamentalfrequency
of
th esystembeingdesigned.
Table2-1liststh e
M
and R
for
th e
peak
ground
acceleration
pga and1-hz
spectral
acceleration
for
th efiveW US
cities.
hese
ground
motions
have
aver-
age
return periods
of
about
2500
years
(i.e.,
2
percent proba bility
of
exceedance
in
50
years).ro mth edeaggregated
hazards,
representative MandR
fo r
th e
design
ground
motions
were
selected
as
7 .0and
25
km ,
respectively.
Table
2-1
Mean
Magnitudes
a
2500-year
Ground
nd Distances
fo r
Five
W US
Citiesfo rth e
l/lotion
W US
City
pga
Rpga
km
M
1h z
R
1hz
km
Sa n
Francisco,
CA
7. 8
25.0
7. 9
25.0
Oakland,
CA
7. 2
25.0
7. 3
25.4
Lo s
Angeles,CA
6. 8
25.2
7. 0
27.1
Sa n
Diego,
CA
7. 0
25.0
7. 0
25.1
Salt
LakeCity,UT
7.1
25.1
7. 3
25.1
2 .1 .3
Site
characteristics
of
motion
The
amplitude
and
frequency
content,as
well
asth e
phasingof th e
frequen-
cies,
of recorded
earthquake
motions
ar e
influenced
by
th e
source
mechanism
(i.e.,fault
type
and
rupture
process),
travelpath,andlocal
site
conditions,
among
otherfactors.
Because
th e
selected
ground
motion
ultimately
is
to
be
specified
as
abaserock
motion
in
th e
numerical
analyses,
th esiteconditionfo rth e
selected
ground
motions
is
desired
to
be
as
closeas
possible
toth ebase
rock
conditions
Chapter2 Selection
of DesignGround
Motion
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underlying th e
profileon
which
th e
cantilever
wall
is
located.hi s
avoids
addi-
tionalprocessing
ofthe
recorded
motion
to
removeth e
siteeffects
on
whichit
was
recorded
(e.g.,deconvolvingtherecord
to
base
rock).
Accordingly,
motions
recorded
on rockorstiff
soil
profiles
were
desiredfo rthisstudy.
2.2Listof
Candidate
Motions
Basedon
th e
selection
criteria,
th e
motions
listed
in
Table
2 -2were
considered
as
candidates
fo rus e
in
th enumericalanalyses.
Table
2 -2
Candidate
Motions
Earthquake
Station
Record
pga.g
Cape
Mendocino
M7.1,Ms7.1
89530Shelter CoveAirport
Closest
to
fault
rupture:3.8
km
Closest
to
surface
project ion
of
rupture:2.6km
SHL-UP
SHL000
SHL090
0.054
0.229
0.189
Duzce,Turkey
M7.1,Ms7.3
1058Lamont
Closest
to
fault rupture:
.9
km
Closest
to
surface
project ion
of rupture:.9m
1 0 5 8 - E
1 0 5 8 - N
1 0 5 8 - V
0.111
0.073
0.07
Duzce,Turkey
M7.1,Ms7.3
1061Lamont
Closest
to
fault
rupture: 5.6
km
Closest
to surface project ion
of
rupture:
15.6
km
1061-E
1061-N
1061-V
0.134
0.107
0.048
Loma
Prieta
M6.9,
Ms7.1
57383Gilroy Array #6
Closest
to fault
rupture:
9.9
km
Closest
tosurface
project ion
of rupture:9.9 km
G06-UP
G06000
G06000
0.101
0.126
0.1
LomaPrieta
M6.9,Ms7.1
47189
SAGO
South-surface
Closest to
fault
rupture:
4. 7
km
Closest to surface project ion
of
rupture:
4.1km
SG3-UP
SG3261
SG3351
0.06
0.073
0.067
Note:
s=
surfacewavemagnitudeof earthquake;M
=
momentmagnitudeofearthquake.
These
records
were
obtained
by
searching
th e
StrongMotion
Database
maintained
by
th e
Pacific
Earthquake
Engineering
Research
(PEER)
Center
(http://peer.berkelev.edu/smcat/)
.
2 .3Characteristics
of
Ground
MotionSelected
Asstated
previously,atleastfive
time-histories(foreachcomponent
of
motion)meeting th e
selection
criteriashould
be
used
in
nonlinear dynamicanaly-
ses
(E C1110-2-6051(HQUSACE
2000)) .
owever,
for th efirst
phase
ofthis
study,onlySG3351was
used,which
was
recorded
duringth e1989
LomaPrieta
earthquake
in
California.
he
basis
fo r
selecting
SG3351wasthatitwas
esti-
mated,usingCWROTATE
(Ebelingand
White,
in
preparation),
to
induce
th e
greatest
permanent
relative
displacement
of
th e
wall.
he
numerical
formulation
in
CWROTATE
is
based
on
th eNewmark
sliding
block
procedure
outlined
in
Ebelingand
Morrison
(1992),Section6.3,andis
discussed
further
in
AppendixC.
SG3351is
plottedinFigure2-1,
as
well
as
th e
corresponding
5percent
damped,pseudo-acceleration
response
spectrum,
scaled
to gpga.
dditionally,
10
Chapter 2
Selection
of
Design
Ground
Motion
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.&
90
V^Mr-^-'
C
60;
Y.P\
^
30
o
:
-
K
1
r
)
static
H
H
*-
10
0
Time(sec)
30
40
0
1.0
0.8
0.6
0.4
0.2 +
0.0
Heel
K
A
conditions
10
20
30
-+
40
i^ttet iiM M Ateftsa^ft^^y^
y''
.^r_i:
'
-^.
-
8/10/2019 Diseo Ssmico de Muros de Contencin en Voladizo
47/104
FLAC
Results
XLateral
E.P.
Coef.
for heel
section,
faaway
frombackfill
4
O
Lateral
E.P.
Coef.
for
heel
section,
k
h
towardsbackfill
X
Lateral
E.P.
Coef.for
stem,
k
h
away
from
backfill
K
P
g
~--_
oLateral
E.P.
Coef.
for
stem,
k
h
towards
backfill
" " - . . ^
1 3
O
~--
-
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FLAC
Results
X
Lateral
E.P.Coef.fo r
heelsection,
k
h
away
frombackfill
O
Lateral
E.P.
Coef.fo r
heelsection,
k
h
towards
backfill
X
Lateral
E.P.Coef.
for
stem,
k
h
away
from backfill
O
LateralE.P.Coef.
for stem,
k
h
towards
backfill
0.0
0.4
away
from towards
backfill backfill 0.2
0. 2
I**
I
Probable
upper
bound
Mononobe
-
Okabe
(Active)
0. 4
Maximum
P.,
\heg
0.0
towards
away
from
"0-2
backfill
backfill
-0.4
Time(sec)
3 5 ST
Maximum:
P
he e h
(Y-P)
stem
,
(Y-P)
he e
,
b.
nlargementofrange
ofFLAC
computed
values
Figure
4-5.
Concluded)
d.he
largest
K
hed
occurs
when
k
h
<
0
(i.e.,when k
h
is
directed
towardth e
backfill).
e.
he
computed
K
values
show
a
general
scatter aroundthe
curve
fo r
th e
Mononobe-Okabe
dynamic
active
earth
pressure
curve.
The
shape
of th e
Mononobe-Okabe
active
and
passive
dynamic
earth
pressure
curves
warrantdiscussion.As
k
h
increases,K
AE
increases,while
K
PE
decreases.
or
th e
conditions
examined
(i.e.,
horizontal
backfill,verticalwall,
zero
interface
friction
between
the
structural
and
driving
wedges,k
v
= 0) ,K
AE
and
Chapter4 FLACData
Reduction
Discussion
of
Results
39
-
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KpE
reach the
samelimiting
value.
he
limiting
K
value
occurswhen
the
angles
of
th e
active
andpassivefailureplanes(whichareassumed
to
be
planar
in
th e
Mononobe-Okabe
formulation)
become
horizontal;
refer to
Appendix
Bfo r
expressions
fo ranglesofth e
failure
planes.
For
comparison
purposes,the
earth
pressure
coefficient
fo r
nonyielding
backfillsis
also
plotted
in
Figure
4-5. wallretaininganonyielding
backfill
does
no t
develop
thelimiting
dynamic
active
orpassiveearthpressures
because
sufficientwallmovements
dono toccur to
mobilizeth e
full
shear
strengthofth e
backfill,
suchasisth e
case
with
massive
concrete
gravity
retainingwalls
foundedon
firm
rock.Wood
(1973)
developeda
procedure,
which
was
simplified
in
Ebelingand
Morrison
(1992),
Section5.2,to
determine
th elateral
dynamic
earthpressures
on
structures
with
nonyielding
backfills.
he
following
expression
is
from
Ebeling
and
Morrison
(1992),
Equation
6 8:
F
s r
=y-k
h
4-9)
where
F
sr
lateralseismicforce
component
yunit
weight
of th esoil
Bytreating F
sr
asth e
dynamicincrementalforce,th e
equivalent
earth
pressure
coefficient
was
computed
by
substituting
F
sr
into
Equation
4-8fo r
P
and
adding
K
0
to
th e
result. he
resulting
curve,shownin
Figure
4-5,
will
likely
be
a
conservative
upper bound
of
the
earth
pressures
that
will
occur
on
the
heel
sectionofa
cantilever
wall.
owever,
amore
probable
upper
boundisthat
formedby
a
line
drawnfromK
0
pressurefo r
fa=0and
th e
intersection
ofK
A
E
and
Kp
E
attheir
limiting
values. urther FLAC
analyses
will
be
performed
to
verify
this
hypothesized
upperbound.
Similar
to
the
trends
in P
slem
andP h e e i ,
YI H
fo r
th estemand heelsections(i.e.,
YI H
hee
i
and
YI H
slem
,
respectively)
also
show
increasing
trendsas
th e
shaking
progresses,
with
YI H
slem
having
greater
cyclic
fluctuation
than
Y I H h e e i -Of
particularnoteis
that
YI H
slem
is
ou t
ofphase
withboth
fa
and P
slem
,
while
Y I H h e e i
is
ou tofphase
with fa ,
but
in
phase
with
P
h ee
i .
sa
result
ofth e
phasing,{Y-P)h
ec
i
ha s
considerably
larger
cyclic
fluctuations
and
peak
value
than
(Y-P)
slem
.
The
magnitudes
of
Y
slem
and
Y
hee
i
are
directlyrelatedtothedistribution
of
stresses
along th estemand heel
sections,respectively.he
stress
distributions,
resultant
forces,
and
deformedshapeofth e
cantileverwallcorresponding to
maximum
values
of
P
slem
,
P
he
e i ,
(Y-P)
slem
,
and
(YP)
he
e i
are
shown
in
Figure
4-6,
wherethemaximum
values
fo r
P h e e i ,{Y-P)
sl e
m ,
and {Y-P)h
ee
ial l
occur
at th esame
instant
in
time. hemaximum
value
of
P
slem
occurs
while
fa >
0
(i.e.,fa
is
40
hapter4 FLAC
Data
Reduction
Discussion
of Results
-
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50/104
4-
CO
5
& >
2 5
20
-
15
-
5 -
^X,
X
:
-5
a)
Maximum
P
a
[X
H
1500
psf
12.5
kips
1
ftdispl
Maximum:P
he e
,, (YP)
slem
,
(YP)
he e
,
Distance
(ft)
Figure
4-6.
Stressdistributionsand
total
resultant
forcesonthestemandheel
sect ionsat
t imes
corresponding
to the following:(a )maximumvalue
fo r
P
stem
an d
(b )the
maximum
values
fo rP
heeh
{YP)
stem
an d
(YP)
heet
(T o
convert
feet tometers,
multiplyby0.3048;toconvertpsf to
pascals,multiply
by
47.88;toconvert
kips
tonewtons,multiply
by
4,448)
Chapter
4
FLAC
Data
Reduction
Discussion
of
Results
41
-
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directed
away
from th e
backfill);
refer
to
th ek / ,time-history
in
Figure
4-5b. he
relatively
triangular-shaped
stress
distributions
onth e
stemand
heel
sections
shown
in
Figure4-6aare
characteristicof those
occurring
at
th e
peaks
in
th e
h
time-history.he
pointsofaction
of
th e
resultant
forces
on
stemand
heel
sectionsare
approximately
equaltothose
prior
to
the
startof
th e
shaking.
The
maximumvaluesof P h e e i ,
(Y-P)
stem
,and{Y-P)
he e
,
occur
whilek
h
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0.4
0.2
jf
0.0
-0.2
-0.4
1.5
* 3
1.0
s
0.5
0.0
1.4
tu
1
1.2
1.0
0.8
0.6
* 5
1.5
- :
1.0
1
3
0. 5
0.0
::b)
c)
10
0
0
1
)
Stem
Heel
MjHJ\fiW *~-
& * *.
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Stern Heel
Time(sec)
Time
(sec)
Figure
4-8.
ime-histories
of
A P
an d
A
YAP fo r
thestem
an d
heel
sections
(T o
convert
kips
to
newtons,
multiplyby 4,448;toconvert
kip-feet
tonewton-meters,
multiplyby
1,355.8)
The
validity
of these
expressions
islimitedto
specific
valuesof
$,
6 ,
8,
and
(the
refer
to
AppendixB
for d efinitions
of these
variables).
or e
general
expressions
for AP
and
A7,whichare
likelymore
applicable to
most
Corps
projects,
ar e
given
in
Ebeling
and
Morrison
(1992),
Section
4.2.2.
Settingk
h
equal
to
th e
maximum
peak
value
(i.e.,k
h
=
0.32),
A P
Se e
d a n d
w h i t m a n ,
AJ
' s e e d a n d
w h i t m a n ,and
(AY-AP)
Se e
d a n d
w h i t m a nwere
computed
using
Equations
4-10a,
b,
and c;
and AP s e e d
a n d
w h i t m a n
and (AY-AP)
Se
e d a n d
w h i t m a n
are
presentedinFigure
4-8.
As
maybe
observed
in
Figure
4-8c,
A P s e e d a n d
w h i t m a n
is
veryclose
to
th e
maximum
value
ofA P
slem
from
th e
FLAC
results.
owever,
this
maybe
coincidental
given
that
A P
stem
does
no t
coincide
withth e
maximum
peak
in
th ek
n
time-history.
A P s e e d a n d w h i t m a nisless
than
maximum
value
ofAP/,
e
e i ,whichis
associated
witha
high
frequency
spike.
Mostnotable
of
th e
observed
trendsinFigure
4-8
isthat
th e
maximum
value
of
(AY-AP)
slem
isconsiderably
lessthanth e
maximum
value
of(AY-AP)i,eei
and (AY-AP)s
ee
d a n d
w h i t m a n -
n
regard
toth e
comparisonofthe
maximum
values
of(AY-AP)
slem
and
(AY-AP)
he e
i ,
th e
difference
is
du e
largely
to
44
Chapter
4 FLACData
Reduction
Discussion
of
Results
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8/10/2019 Diseo Ssmico de Muros de Contencin en Voladizo
54/104
th ephasingof th erespectiveA 7
and
AP
time-histories,
where
AY
slem
and
A P
areou tofphase
with
each
other,while AY
hee
i and A P
hee
are
in
phase.
stem
AnalogoustoFigure
4-6,
P
stattc
and
A P
fo rth estem
and heelsectionsare
shown
in Figure4-9
superimposedon thestress
distributions
and deformed
shape
of
th e
cantilever wall
a t
times
corresponding
to
maximum values
ofP
stem
,
P
he e
i ,
{Y-P)
stem
,
and
(Y-P)
he e
i .fparticular
note
are
heights
above
th ebaseat
which
AP
on
th e
stem
and
heel
sections
act
(i.e.,
AY
slem
and AY
heeh
respectively).
orth e
condition where
P
stem
is
maximum,
AY
stem
is
approximately
equalto
Y
static
,
which
is
about
0.3-
owever,
AY
hee
i
is
closer
to
0.5-H.or
th econditionwhen
P
hee
,
{ Y - P ) s i e m ,
and(Y-P)
he e
i
are maximum,
AY
slem
is
just
over
0.75
H
whileAY
heel
remains
at
approximately
0.5-iZ. igure
4-9
also
illustrates
th e
phasing
of
th e
variousparameters.or
th e
condition where
P
stem
is
maximum,
A P
stem
islarge,
whileAY
slem
and
A P
hed
arerelatively
small.or
th e
condition
where
P
heeb
(Y-P)
s
, e m ,
and
{Y-P)
heet
are maximum,
A P
slem
issmall,whileAY
stem
and
A P
hee
are
relatively
large.
4.2 .4Permanentrelativedisplacementofth ewall
Using
an
acceleration time-historycomputedby
FLAC
a t
approximately
middepth
of th e
backfill
and
locatednearth e
free-field
boundary
in
th e
FLAC
model,a
Newmark
sliding
block-type
analysis
wasperformedon th e
structural
wedge. hi s
analysis
was
similar
to
those
performed
using
CWROTATE
(Ebeling
and
White,
in
preparation)
with
th eSHAKE
computed time-histories,
which
are
presented
in
Appendix
C.
he
results
fromth esliding
block-type
analysiswere
compared towallmovements
computed
by
FLAC.
The
FLAC
computed
free-fieldacceleration
time-history
usedin
th e
sliding
block
analysis
is
shown
in
Figure
4-10a.
Also
shown
in
Figure
4-10a
is
th e
acceleration
time-historyof th e
structural
wedge,
as
determined by
sliding
block
analysis. elativemovementof th e
soil
and the
structural
wedge
occurs
when
th e
free-field
accelerationexceedsth e
maximum
transm issible
acceleration
(N*-g)
of
th e
structural
wedge,
where
N*-gwas
determined to
be
0 . 2 2 g
in
AppendixC.igure
4-1
lashows
anenlargementofthe region where
th e
two
acceleration time-histories
differ;
Figure
4-1 lb,
c,
and
d
show
th e
progressionof
th e
stepsused tocompute thepermanen t relativedisplacement usingaNewmark
slidingblock-typeanalysis.
igure
4-10b
showsa
comparison
of th eFLAC
computed
permanent
relative
displacement
time-history
with
that
computed
in
th esliding
blockanalysis.
he
magnitude
and
th e
occurrence
timesof th e
slips
are
very
similar
fo r
both
analyses.
However,
th e
FLAC
resultshavewhat
is
believed
to
be
a
"numerical
creep"
prior
to
approximately
7
sec
and
after
approximately
2 0sec.
hi s
numerical
creep
islikely
due to
precision
error
that
occurs
when thedisplacementexperiencedduringone time
increment is
Chapter4 FLAC
Data
Reduction
Discussion
of
Results
5
-
8/10/2019 Diseo Ssmico de Muros de Contencin en Voladizo
55/104
ZJ
a)
20
-
r
15
-
Maximum
P
slem
1 1 1 1 1
;:;:*i*& i
::
|
1500
psf
;:
':*
:
:
:
:
:
:
:
:
:
:
:
:
:
:
J
:
&
:
12.5
kips
g
jj|i:i ;:
:i;i:i;|:;|:
1
ft
displ
10 -
:
:x:
:
:::
:
:
:
::
|
:*
:
:
:
:
: :
:
:
:
:
:
li i i ^^ 'i i M
;r
5
l> .
v
-
.'
..
.
J
p ..-
-
..
I *n
.
'
L-Jk
heel,
static
,-',','.
'
',
L\r
S
(
em
;
;
;
-(HHMI
J" " '
*^
J
v
rdt
"**
5
-T T
W
'A'.
.-..-
-
J-.-.-
.
p ..
1.,
.
*
tem,
static
1
S-:::
:
:
:
:
:
:|:
:
:l* /
: i -
' s t em,
static
s tem
:;:;:;:;**;:;:
1
J* -
* A e W ,
s/arte
o
\
\
i i i i i i l i i i l i i ^
lllli
j -
^ ;;i;i;i;:;i
r
: :;:;:;: i;:;:;:
fi Sili ^
::f::;:|:::i::i;:::::::
b)
Miximum:P
hee
,, (YP)
slem
(YP)
hee
,
20
-
^
\ :\:WX:\\\:-
:
:
\:jk
AP
[::&:; :;: :;:
15
-
A T? ,:
/N
V X
f
.-.
.
..
.
t ' : -
:*
:
:
::
'::::
-
8/10/2019 Diseo Ssmico de Muros de Contencin en Voladizo
56/104
200
c
o
o
isused
in bothconcrete
designand geotechnical
engineering,
with
very
distinct
meanings).
Accordingly,
rather
than
giving
a
compiled
list
of
variable
definitions
used
in this
appendix,
variables
ar edefinedmathematically
and
illustratively
as
they
are
presented
in
th ecalculations.
Conversion
factors
fo rnon-SI
units
of
measurement used
in
this
appendix
are
given
in
Table
A-l.
2
References
cited
in
this
appendix
are
included
in
th e
References
section
at
the
end
of
the
main text.
Appendix A Static Designof
theCanti leverRetaining
Wal l 1
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A.2Stage
1:
Sizing
of
theCantilever
Retaining
Wall
As
stated
previously,
th e
first
design
stageconsistsof
sizingth e
cantilever
wall
such
that
global
stability
requirements
are
satisfied
(i.e.,
sliding,
overturn-
ing,
and
bearingcapacity),
in
general
accordance
withEM
1110-2-2502
(HQUSACE
1989).
he
structural
wedge
ofth e
proposed
wall
and
backfill
is
shown
in
Figure
A-l,
as
well
as
th e
backfillandfoundation
materialproperties.
Toassess
the
global
stability
of
th e
wall,
th e
external
forcesandcorrespond-
ingpointsofaction
acting
on
the
structuralwedgeneed
to
be
determined.
he
externalforcesincludeth e
resultant
of th e
lateral
earth
pressure
and
reactionary
forces
actingalong th e
baseofth e
wall.
However,
before
the
reactionary
forces
ca n
be
determined,th e
weights
and
centers
ofgravity
of
th e
concrete
and
soil
composingthe
structuralwedge
are
required.
Backfill:
medium-dense
cohesionless
compacted
fill,
y
m
=
12 5
pcf,
=
35
Foundation:hinlayer of
compactedfilloverlying
naturaldepositof
dense
cohesionlesssoil,y
m
=
12 5
pcf,
< j>
=
40
Reinforced
concrete:
y=
150
pcf,
f
c
= 4ksi,f
y
=48 ks i
Hydraulic
factor:
1.3
1.5
ft
-B
h
=
8ft
&&;
Backfill
. ..
Toe
Base
Heel
B=13ft
Figure A-1. Structuralwedgeofproposedwall,
and
backfill
andfoundation
properties
A2
Appendix
A
StaticDesign
of
theCanti leverRetaining
Wall
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To
simplifyth edeterminationof th eweightand
center ofgravity
of
th e
structural
wedge,
itis
divided
into
subsections
havinguniformunitweights
and
simple
geometries,
as
shown in FigureA-2.Oncethe
weights
and
centers
of
gravity
ofeach
subsection
are
determined,
th e
weight
and centerofgravity
of th e
entire
structural
wedge
are
easilydetermined,as
illustrated
in
th e
accompanying
sketches.
Figure
A-2.
Backfill:
Division
ofwal l
andbackfill
into
sub-
sectionsfo retermininginternal
forcesand
centroids
of
structural
wedge
N
ft
W
s
=
125pcfx8'xl8'
=18,000lb s
Ax
toe
-W
s
= 18,000lb sx9'
=
162,000ft-lbs
00
_ J
T
ToeH-
Ax
toe
=
9
ft
-*
Appendix
A
StaticDesign
of
th eCanti leverRetaining
Wal l
A3
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Stem
2 :
< e
I |
l |
l |
lj
>|
|
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Weightofentirewall:
3
W c , i = 3900
l b s
4050
l b s
675
l b s
i= l
=
8625
l b s
Centroid
of
entire
wall:
3
W
ji
Ax
to e
,i
=
25,350
ft-lbs
+
17,212.5
ft-lbs
+
225 0
ft-lbs
i=l
=
44,812.5
ft-lbs
3
/^Wci-Axtoci
i
=
l
=
5.2
ft
from
the
to e
3
i
=
l
Ina
CTWALL
analysis
th e
retaining
wall
systemisdividedintotw oor
three
wedges:
he
structural
wedge;th edriving wedge;and th eresisting wedge,
when
present
(Pace
1994).
FigureA-lshowsth e
structural
wedge,whichisdefinedby
th e
outline
of
th e
cantileverretainingwall.
Thelateralextent
of
th estructural
wedge
is
defined
byimaginary
vertical
sections
made
through
th e
heel
of
th e
walland th eto eof th ewall.Thesoil
masscontained
within
this
regionis
also
considered part ofth e
structural
wedge.The
driving
soilwedgeonth e
retained
soilside(toth e
right
of
th e
Figure
A-l
structural
wedgeand no tshown
in this
figure)generates
earth
pressure
forcestending to
destabilizeth e
structural
wedge.
No
resisting
wedge
is
present to the
left
of th e
FigureA-lstructuralwedge
in this
case.
Thegeneralwedgemethodofanalysis(E M
1110-2-2502(HQUSACE
1989))
is
used
to
calculateth e
lateral
earth pressure
force
actingon
th e
structural
wedge.
CTWALL
(Pace1994)
performs
th e
sliding
and
overturning
stability
analyses
during
execution.
Forces
computed
during
th eCTWALLanalysisof th e
user-specified
wall
geometry
may
be
used
to
compute
th e
factor
ofsafety
against
a foundation
bearing
failure.
This
computation
is
made
external
to
the
CTWALL
execution.
A
sliding
stability
analysis
using
CTWALL
(Pace1994)followsCorps
design
criteria
(E M1110-2-2502) .A
sliding
stability
analysisisconducted
of
th e
driving
wedge,
structural
wedge,
and
resisting w edge
(when
present)
to
determine
a
common
factor of
safetyagainst
sliding
fo rth e
entire
retaining
structural
system(ofth e
three
wedges).
The
procedure
isa
limit
equilibrium
Appendix
A
StaticDesign
of
th eCanti leverRetainingWal l
5
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procedure
and
isiterative
in
nature. ritical
failureanglesfo r
th e
driving
side
and
resistingside
(when
present)
potentialplanar
slipplanesare
sought
fo ran
assumed
slidingfactorofsafetyvalue.
The
resulting
earth
forcesaresummed.f
th esu m
is
zero,
th e
system
is
in
equilibrium
and th e
criticalsliding
factor of
safety
value
ha s
been
found.
Anoverturning
stability
analysis
using
CTWALL
(Pace1994)followsCorps
designcriteria (E M1110-2-2502) .The
program
will
calculate
a
percentage
ofth e
base
in
compression
and
report
th e
location
oftheresultantofal lforces
applied
to
th e
structuralwedge. he
program
will
iterate,if
necessary,
to
find
th e
percent
of
the
baseincompression.
ension
along
th ebaseisnotallowedfo r
thesesoil-
foundedwalls.
A
linear
base
pressure
distribution
assumption
ismade
by
CTWALL(forth e
portion
ofth ebase
in
compression)
in
conjunctionwith
th e
limit
equilibrium
procedure
ofanalysis. heoverturning
analysis
checks
that
a
user-specified
wallconfigurationsatisfies
Corpsdesigncriteria.hese
criteria
are
expressedin
terms
ofbase
areain
compression
(versus
computing
th e
ratio
of
the
stabilizing mom ent
about
th e
to e
of
th e
wall
dividedby
th e
overturning
moment).
he
overturning
analysis
uses
an
approximation
fo r
at-rest
earth
pressureforcesin
the
driving
wedge
analysis
to
determine
the
earthforceth e
driving
wedge
(i.e.,
th e
retained
soil)exertson
th estructural
wedge.
Per
EM
11102-2502
(section
3-11),
th e
shear mo bilization
factor
(SMF)
isse t
equal
to
2/3.
The
SMF
and
factor
of
safety
are
inverses
of
each
other.An
SMF
of
2 /3is
equivalent to
a
factorofsafety
equal
to
1.5.
Thedetermination
ofth e
lateral
earth
forces
and
pressures
are
illustrated
in
th e
following
equationsin
simplified
hand
computations
(and
were
usedto
checkth e
CTWALL
analyses
fo rthefinalwall
configuration):
SMF
=
2 /3
=
1/1.5
ta n
( ) > '
m
o b )
=
SMF ta n
(f)
1
1.5
^
, * =
25
ta n(35)
In
accordancewithEM
1110-2-2502,
the
angle
of
friction
alongside
the
structural
wedge
defined
byth e
vertical
section through
th e
heel
ofth e
wall
is
assumed
equalto
zero
(i.e.,
8
=0). hus,
fo rth ecase
being
considered(i.e.,
homogenous
backfill),
th e
wedge
analysis
procedure
reverts
to
th e
classical
Rankineprocedure,whichis
illustrated
in
th e
following
sketches.
A6 ppendix
A Static
Design
ofthe
Canti lever
Retaining
Wall
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=ton^/'/ICO
k
h
=taif(45
'mob
2 5
=
ta n
2
(45-
2
=0.41
< * h
-Ymoist Hkh
=
125pcf-20'-0.41
=
1013.8
psf
20ft
Fh,,
1
Aytoe
=
2
Dhn
1
2
1013.8
psf-2 0'
=
10,137.5lb s
H
3
20 '
T
Aytoe
=
. 667ft
F
h
,s t a t i cx
Ay,
oe
=
10,137.5lb s 6 . 667 '
=67 ,583
ft-lbs
The
remaining,yet-to-be-determined,
forces
acting
on
th e
structural
wedge
areth e
reactionary
shear
and
normal
forces(i.e.,Tand
N,
respectively)
acting
on
th ebaseof th e
wall.igure
A-3showsa
free
body
diagram
of th e
structural
wedge
with
th e
known
and unknown
forcesidentified.
A s
illustrated
in
th e
followingequations,
th e
magnitude
ofT and
J V
are
determinedby
summing
th e
forces
in
th e
horizontal
and vertical
directions,
respectively,
while
th e
point at
whichJ V acts
isdeterminedbysumming
th e
momentsaroundth