Integral bridges : a fundamental approach to the time-temperature loading problem

153 Pages·1990·2.07 MB·English

by  G. England, N. Teang, D. Bush

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Integral bridges
A fundamental approach to the time–temperature
loading problem
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Integral bridges
A fundamental approach to the time–temperature
loading problem
George L. England
PhD,DSc(Eng),CEng,FICE,FINucE,MASCE,MASME
Professor,ImperialCollegeofScience,TechnologyandMedicine,London,UK
Neil C. M. Tsang
PhD,DIC,BEng,CEng,MIStructE,MASCE
Lecturer,UniversityofStrathclyde,Glasgow,UK
(formerlyImperialCollegeofScience,TechnologyandMedicine,London,UK)
David I. Bush
PhD,BSc,CEng,MICE
PrincipalTechnicalAdvisor,HighwaysAgency,UK
ThomasTelford
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Published by Thomas Telford Publishing, Thomas Telford Ltd,1 Heron Quay, London E14 4JD
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First published 2000
A catalogue record for this book is available from the British Library
ISBN: 978 07277 3541 6
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Foreword
Deterioration of concrete bridges has proved a serious problem for the UK bridge stock where water
carrying de-icing salts has penetrated through the deck joints. The consequence is that costly and
disruptive maintenance becomes necessary.
Recognizingthatdesigningoutjointswouldoffermajorbenefitstodurability,theHighwaysAgency
publishedAdviceNoteBA42in1996topromotetheuseofintegralbridgeconstruction,i.e.jointless
bridges. This supported requirements that all bridges less then 60 m span should be of integral
construction.
With this type of construction the interaction at the fill/abutment interface, resulting from thermal
expansionandcontraction,isanimportantdesignconsideration.Toimproveadviceofferedtodesigners
andachievethefullpotentialofintegralconstructiontheHighwaysAgencyembarkedonatwopronged
research programme. This has involved developing a better understanding of the fundamental
mechanismswithinanabutmentbackfillsubjectedtodailyandseasonalbridgetemperaturevariationsas
well as monitoring the performance of three integral bridges throughout their construction and early
lives.Whentheworkiscompletedinearly2000thefindingswillbeusedtoreviseBA42,thusmeeting
the needs of designers.
TheHighwaysAgencyisalwayskeentodisseminateitsresearchtothewidestpossibleaudience.This
book presents the full findings of the first part of the research programme on integral bridges. It is
presentedintwopartstofocusseparatelyonthedifferentneedsofdesignersandresearchers.Iamsureit
willbeofgreatinteresttoallinvolvedinbridgedesign,andhopeitwillstimulatefurtherdevelopment
and innovation in this important form of construction.
John A. Kerman
Chief Highways Engineer
Highways Agency
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Preface
Theconceptofthe‘integralbridge’,i.e.withoutanymovementjoints,wasintroducedintotheUKby
Hamblymorethantenyearsago.Althoughtwomajorreports(CardandCarder,1993;Springmanetal.,
1996) have been published by the Transport Research Laboratory, regarding the temperature-induced
soil–structureinteractionproblem,theHighwaysAgencydesignstandardBA42/96isstillregardedas
beingtooconservative.Thisisbecauseofalackofunderstandingofthefundamentalmechanismswhich
are responsible for the build-up of lateral earth pressure on the abutments and the deformation–
settlement of the backfill soil. This book presents the findings of research commissioned by the
Highways Agency to examine these issues.
The book is in two parts:
• Integral bridge: Part 1 (Chapters 1–7 and Appendix 1). This part covers the concepts, findings,
conclusions and recommendations for the soil–structure interaction problem. This part will be of
particular interest to practising engineers and integral bridge designers. Detailed results of model
tests and numerical simulations are reported.
• Granularsoil:Part2(Chapters8–12andAppendix2).Inthispartfundamentalmechanicsareused
todescribethebehaviourofgranularsoilsubjectedtocyclicloading.Adescriptionisgivenofthe
numericalsoilmodelandthemodelretainingwalldevelopedwithinthisresearchproject.Thispart
will be of more interest to researchers and those keen to understand the fundamental logic of the
interaction problem.
The overall scope and objectives of the investigation are given in Chapter 1. Chapter 2 provides
additionalinformationonbridgetemperatureasrequiredforthedesignofintegralbridgesincomparison
with that required in designing traditional bridges with movement joints. The mechanics of the soil–
structure interaction are described briefly in Chapter 3 in order to help the reader interpret the
experimentalandnumericalresultsgiveninChapters4and5.Anoveltheoreticalmethodtoevaluatethe
settlementofanintegralabutmentfoundationispresentedinChapter6;therigidabutmentandflexible
sheetpilecantileverwallareconsideredhere.RecommendationsforupgradingthedesignstandardBA
42/96 are made in Chapter 7.
Chapter 8 describes the general behaviour of drained granular soil and then focuses on the specific
cyclicloadingfeatureswhicharerelevanttotheintegralbridge.A90°jumpchangeofprincipalstress
direction, strain ratcheting and the properties of a shakedown state are all described in detail. Each of
thesefeaturesplaysanimportantroleinthemechanicsoftheinteractionproblem.Thenewsoilmodel
for handling cyclic stress and cyclic strain loading is introduced in Chapter 9. The model is validated
against a range of control test data in Chapter 10, and then used as a component of the retaining wall
analysis in Chapter 11. The retaining wall apparatus is shown in Chapter 12.
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Acknowledgements
The authors are extremely indebted to Dr T. Dunstan and the technical staff at University College
London (UCL) for their significant contributions to this work. Material data were obtained by
Dr Bolouri-Bazaz using a Biaxial Tester developed at UCL, and the cyclic escalation of abutment
stresseswasobservedinamodelretainingwallapparatusconstructedbyMrJ.FordatUCL.Thanksgo
alsotoMsK.RegierforherassistanceintheinitialsettingupoftheretainingwallmodelandtoDrR.
Wan of the University of Calgary for his helpful discussions during the creation of the numerical
modelling procedures. Finally, the author acknowledges the Highways Agency for funding the work
under Contract HA3/33.
Coverphotograph:integralbridgeovertheM1–A1LinkRoad(CourtesyofYorkshireLinkLimited).
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Executive summary
Objectives
• Tounderstandthetemperature-inducedcyclicsoil–structureinteractionmechanismsgoverningthe
performance of integral bridges at the serviceability limit state. Particular attention is given to the
build-up of lateral backfill soil pressure on the bridge abutments.
• To identify possible inadequacies in the current design advice note BA 42/96.
• To improve the knowledge base from which future designs will benefit.
Project
Theintegralbridgeabutmentwallinvestigatedinthisprojectisofthestiffwalltypewithapinnedbase.
Repeating temperature changes of the bridge create longitudinal movements in the bridge deck and
rotationoftherigidabutmentwallaboutitsbase.Themagnitudeofthewallrotationsisgovernedbythe
bridgelength,thetypeofdeckconstructionandchangesinbridgetemperature(i.e.dailyandseasonal
temperature fluctuations). The escalation of lateral soil pressure behind the bridge abutments is then
related to the wall rotations. The research project includes:
• an experimental programme for soil elements (Leighton Buzzard sand) tested under both cyclic
stress and cyclic strain imposition, for a range of soil parameters;
• theformulationofanewconstitutivesoilmodel,forthepredictionofcyclicstress–strainbehaviour
in particular;
• theresultsfromaseriesofseven1in12scalemodelretainingwallexperiments(tosimulatetypical
seasonal wall movements in concrete bridges having lengths of 60, 120 and 160 m);
• a series of numerical simulations (50 cases in total) for a 7 m high abutment wall; and
• a comparative study relating bridge behaviour during seasonal temperature cycles only to bridge
behaviour for the combined effect of daily and seasonal temperature changes.
Thesoilmodel,whichisoftheincrementaltype,hasbeendevelopedspecificallyforthepredictionof
soilbehaviourunderplanestrainloading.Ithasbeenvalidatedagainstacomprehensiverangeofsoiltest
data obtained under both monotonic and cyclic loading. The model was then incorporated in a
semi-empiricalretainingwallanalysisforthemodellingofa7 mhighstiffabutmentwall.Bridgelengths
of 40–160 m were considered together with a range of typical UK daily and seasonal temperature
fluctuations. Computer predictions using the retaining wall analysis have been compared with
experimental results from the model retaining wall.
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Integral bridges: a fundamental approach to the time–temperature problem
Conclusions
• CyclicloadingofLeightonBuzzardsandsampleshasconfirmedtheexistenceofstrainratcheting
behaviourduringcyclicstressloading,andthestresschangesassociatedwithcyclicstrainloading
leading to a shakedown state.
• Thenewnumericalsoilmodelsuccessfullycaptures:themajorfeaturesassociatedwithmonotonic
loading;thestrainratchetingbehaviourresultingfromconstant-amplitudefluctuatingstressloading;
and the stress ratio drifting towards the shakedown state (hydrostatic stress state) during the
imposition of constant-amplitude fluctuating strains.
• Parametric studies from both the numerical simulations and the model retaining wall tests have
identifiedthesignificantrolesplayedbyeachofthedailyandseasonaltemperaturefluctuationsof
the bridge deck.
– Stress changes escalate quickly to span the hydrostatic stress state (K= 1) and settle to peak
stressratios(duringpassivewallmovements)correspondingtoK»1.2fora60 mbridgeovera
service life of 120 years.
– Soildisplacementscontinuetochange,andaflowmechanismhasbeenidentifiedwhichleads
to:settlementadjacenttothewall(110 mmin120 yearsfora60 mbridge);flowawayfromthe
wallat depth;andpossibleheave(5 mmin 120 yearsfor60 mbridge)ofthe freesurfaceat a
horizontal distance from the wall, equal to approximately one wall height. This behaviour
coincides with general but slow densification of the backfill material.
– Long-term soil stresses on the abutment wall are little affected by the initial density of the
backfill material or by the season (summer, winter, etc.) during which the structure enters
service. However, the early performance is influenced by both parameters. The initial rate of
stress escalation is higher for bridges completed in winter.
– Forbridgesthatareupto60 mlong,long-termsettlementisonlyslightlyaffectedbytheinitial
position of the abutment wall at the completion of construction.
– The significance of daily wall movements (approximately one-quarter to one-tenth of the
seasonalmovements)istoinducemoresoildensificationanddeformation.Incomparisonwith
values for seasonal movements alone, the inclusion of daily wall movements increased the
settlement adjacent to the wall by 100% and the heave away from the wall by 150%.
– Dailywallmovementsencouragethesoilstressestoremainclosertohydrostaticvaluesinitially
andlatertobecomesimilartothoseforseasonalcyclesalone,afteradditionalsoildensification
has occurred.
• Soil behaviour under cyclic loading cannot be predicted with confidence from monotonic stress–
straindata,asdescribedinthedesigndocumentBA42.However,studiesherehaveshownthatfora
suitablechoiceofK theempiricalapproachcontainedinBA42canprovideusefulestimatesforthe
p
magnitudeofstressescalationactingontheabutmentsofintegralbridges.Thereisunfortunatelyno
rationalwayofchoosingK fordifferenttypesofgranularmaterialwithoutreferencetoexperimental
p
testing. Further studies should also indicate whether or not monotonic data can be employed to
estimate the peak stress ratios for the worst-case serviceability limit.
• InitspresentformtheinformationcontainedinBA42providesaconservativedesignloadingfor
integralbridgeabutmentsforbridgesupto60 mlong.However,itdoesnotprovideanyinformation
forthedeterminationofsoildeformation(inparticular,heaving),ortheconsequentchangestothe
lateral earth pressures on the wing walls. Unsafe wing wall design could thus result.
• Finally, although it is recommended that the form of the calculation for lateral earth pressure as
proposed in BA 42 should be maintained, a new formula for the evaluation ofK*is proposed.
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Notation
Thefollowingsymbolsareusedinthisbookingeneral.Otherspecificsymbolsnotlistedherearedefined
in the main text.
d displacement of retaining wall at the backfill surface level
E modulus of elasticity
G shear modulus of elasticity
K wall reaction ratio or Kelvin stress ratio (sK/sK in Appendix 2.2)
1 3
K* design soil stress ratio to the upper half of the abutment wall, as defined in BA 42
R principal stress ratio (s/s)
1 3
H height of wall from the toe to the backfill surface
e void ratio
e initial void ratio of soil
0
a coefficient of thermal expansion of the bridge deck
D displacement of retaining wall at local soil level, or incremental value (when used with other
symbols)
g shear strain
e axial strain
e axial strain in horizontal direction
h
e axial strain in vertical direction
vr
e axial elastic strain
e
e axial plastic strain
p
e volumetric strain
v
h dashpot viscosity
q angular rotation of the abutment wall (=d/H)
f frictional angle of granular soil at failure
f
f frictional angle of granular soil at critical state
cr
f mobilized frictional angle of soil
m
s axial stress
s axial stress in horizontal direction
h
s horizontal stress inpassivecondition
hp
s horizontal stress inactivecondition
ha
s,s axial stress in vertical direction
v vr
s i= 1, 2 and 3 for major, intermediate and minor principal stress, or i=x, y and z for stress in
i
defined directionx,yorz
s mean confining pressure in soil
c
t shear stress
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Integral bridges: a fundamental approach to the time–temperature problem
EBT effective bridge temperature
TBS transitional boundary surface
Symbols for the new numerical model in Appendix 2.2
E modulus of elasticity for the Maxwell spring (Equation A2.9)
E coefficient of modulus of elasticity for the Maxwell spring (Equation A2.9)
0
E modulus of elasticity for the Kelvin spring (Equation A2.11)
k
E coefficient of modulus of elasticity for the Kelvin spring (Equation A2.11)
k0
m power coefficient of Maxwell dashpot viscosity (Equation A2.10)
n power coefficient of modulus of elasticity for the Maxwell spring (Equations A2.9 and A2.11)
F void function (Equation A2.7)
e
K stress ratio,sK/sK,of the Kelvin element
1 3
S fabric strength in stress ratio term
f
e reference void ratio for calculating critical void ratio (Equation A2.13)
c0
e critical void ratio (Equation A2.13)
cr
e final void ratio of an incremental step
new
e initial void ratio of an incremental step
old
De incremental void ratio due to hydrostatic compaction.
c
De incrementalelasticstrain;i=1,2or3formajor,intermediateorminorprincipaldirectionsor
i,e
i =x,yorzfor stress in defined direction ofx,yorz
De incrementalplasticstrain;i=1,2or3formajor,intermediateorminorprincipaldirectionsor
i,p
i=x,yorzfor stress in defined direction ofx,yorz
De incremental volumetric strain;j= c, p or tot denotes compaction, plastic or total, respectively
v,j
h Maxwell dashpot viscosity
h coefficient of Maxwell dashpot viscosity
0
h Kelvin dashpot viscosity
k
h coefficient of Kelvin dashpot viscosity
k0
f frictional angle of granular soil at critical state
cr
a the power coefficient for the modified Rowe’s dilatancy equation (Equation A2.14)
k the gradient in a semi-log plot relating confining pressure to void ratio under hydrostatic
compaction
l thegradientinasemi-logplotrelatingconfiningpressuretocriticalvoidratio(EquationA2.13)
y fabric factor (Equation A2.16)
n,n elastic Poisson’s ratio
e
n flow Poisson’s ratio (Equation A2.15)
f
sK stress of Kelvin spring
s mean confining pressure in soil
c
s reference mean confining pressure for calculating critical state void ratio
c0
is stresslevelinastressincrement;i=0forinitialstressatthebeginningofanincrement;i=1for
j
stressafterelasticincrement;i=2forstressafterMaxwelldashpotrelaxation;i=3forstress
after adjustment by Kelvin element
Ds a stress increment;j=x,yorzfor stress in defined direction ofx,yorz
j
Dse elastic component of a stress increment;j=x,yorzfor stress in defined direction ofx,yorz
j
Dsf flow component of a stress increment;j=x,yorzfor stress in defined direction ofx,yorz
j
Dsi internal component of a stress increment;j=x,yorzfor stress in defined direction ofx,yorz
j
DsK a stress increment of Kelvin spring;j=x,yorzfor stress in defined direction ofx,yorz
j
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