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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

Approved

fo r

public

release;

distribution

s

unlimited.

0

o


2/104

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


3/104

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


4/104

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


5/104

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

I V


6/104

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


7/104

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

V I


8/104

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


9/104

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


10/104

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


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


11/104

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


12/104

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


13/104

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


14/104

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


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


15/104

Can tilever Retaining

Wall

structuralwedge

U

=


16/104

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


17/104

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


18/104

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


19/104

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


20/104

I

o

o

o

Ja)

-c)

e)

Stem

i

*V\fWw

-vi '

iii-'V

-1

30

40

K

0

conditions

- 1

CZ

onditions

10

20

30

40

\j$dmw(i b

^

-{YIH)

S I

_ i

0

1 0

20 30 40

150 1

e

o;

)

.&

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:

'

-^.


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

~--


48/104

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


49/104

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


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


51/104

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


52/104

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 *~-

& * *.


53/104

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


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


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 ' : -

:*

:

:

::

'::::


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


64/104

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


65/104

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


66/104

Stem

2 :

< e

I |

l |

l |

lj

>|

|


67/104

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


68/104

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


69/104

=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

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