Kashani, MM, Lowes, LN, Crewe, AJ, & Alexander, NA

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Kashani, M. M., Lowes, L. N., Crewe, A. J., & Alexander, N. A. (2016).

Computational Modelling Strategies for Nonlinear Response
Prediction of Corroded Circular RC Bridge Piers. Advances in
Materials Science and Engineering, 2016, [2738265].
https://doi.org/10.1155/2016/2738265
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Advances in Materials Science and Engineering
Volume 2016, Article ID 2738265, 15 pages
http://dx.doi.org/10.1155/2016/2738265
Research Article
Computational Modelling Strategies for Nonlinear Response
Prediction of Corroded Circular RC Bridge Piers
MohammadM.Kashani,1LauraN.Lowes,2AdamJ.Crewe,1andNicholasA.Alexander1
1DepartmentofCivilEngineering,UniversityofBristol,BristolBS81TR,UK
2DepartmentofCivilandEnvironmentalEngineering,UniversityofWashington,Seattle,WA98195-2700,USA
CorrespondenceshouldbeaddressedtoMohammadM.Kashani;[email protected]
Received30December2015;Accepted19April2016
AcademicEditor:Seung-JunKwon
Copyright©2016MohammadM.Kashanietal.ThisisanopenaccessarticledistributedundertheCreativeCommonsAttribution
License,whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.
Anumericalmodelispresentedthatenablessimulationofthenonlinearflexuralresponseofcorrodedreinforcedconcrete(RC)
components.Themodelemploysaforce-basednonlinearfibrebeam-columnelement.Anewphenomenologicaluniaxialmaterial
modelforcorrodedreinforcingsteelisused.Thismodelaccountsfortheimpactofcorrosiononbucklingstrength,postbuckling
behaviour,andlow-cyclefatiguedegradationofverticalreinforcementundercyclicloading.Thebasicmaterialmodelisvalidated
throughcomparisonofsimulatedandobservedresponsesforuncorrodedRCcolumns.Themodelisusedtoexploretheimpactof
corrosionontheinelasticresponseofcorrodedRCcolumns.
1.Introduction showed that corrosion will affect the failure mechanisms of
flexuralRCcomponents.Inseveralcases,prematurebuckling
Asignificantnumberofoldermajorinfrastructureartefacts, oflongitudinalreinforcementhasbeenobserved.Thisisdue
located in an aggressive environment, suffer from material tothecombinedeffectofnonuniformpittingcorrosionalong
aginganddeterioration[1,2].Inordertoprovideadurable the length of longitudinal reinforcement and corrosion of
andreliablesolution,thefunctionality,safety,andservicelife horizontal tie reinforcement. Once corroded bars buckled
ofvariousinfrastructureartefactsshouldbeestimatedusing under cyclic loading, they fracture at lower drift demands
the best available engineering science. Therefore, for exist- due to low-cycle high amplitude fatigue degradation. These
ingdeterioratedinfrastructure,arationalmaintenanceplan observationsfromtheexperimentalstudiessuggestthatthe
shouldbeemployedinaccordancewiththeircurrentcondi- combinedeffectofinelasticbucklingandnonuniformpitting
tion.Recently,limitedfundinghasimpliedtheneedforanew corrosion results in a significant reduction in low-cycle
bridge management system that can capture all these com- fatiguelifeofcorrodedRCelements.
plexitieswithinasinglecomprehensiveframeworksothatthe Furthermore, several researchers investigated the effect
maintenancestrategyofbridgenetworkscanbeoptimised. ofcorrosiononstress-strainbehaviourofreinforcingbarsin
Amongdifferentdeteriorationmechanismsthecorrosion tension [15–20]. References [21–25] included a comprehen-
of reinforcing bars in RC structures is the most common sive experimental and computational study on the inelastic
type of deterioration mechanisms [1, 2]. Moreover, a huge behaviourofisolatedcorrodedreinforcingbars,includingthe
number of these corroded structures are also in high seis- impact of corrosion on inelastic buckling and degradation
micity regions. This has led researchers around the world duetolow-cyclefatigue.Theseresultsareingoodagreement
to investigate the influence of reinforcement corrosion on with the results observed by other researchers who studied
the seismic performance of existing RC structures [3–11]. thecyclicbehaviourofRCcomponents.
Otherresearchershavestudiedtheimpactofreinforcement Moreover,inrecentyears,severalresearchershavestud-
corrosion on cyclic behaviour of corroded RC beams and iedtheseismicvulnerabilityandfragilityanalysisofcorroded
columns experimentally [12–14]. The experimental results RC bridges [3–11]. They have investigated the effect of
2 AdvancesinMaterialsScienceandEngineering
reinforcement corrosion on the nonlinear behaviour and reinforcingsteelthatisdevelopedin[29]isused.Thismodel
response of RC bridges subject to seismic loading through simulatesthestress-strainbehaviourofreinforcingsteelwith
nonlinearfibre-basedfiniteelementanalysis[26–28]. theeffectofinelasticbucklingandlow-cyclehighamplitude
However, they have used very simple uniaxial material fatiguedegradationundercyclicloading.Thebasicbuckling
modelstomodeltheimpactofcorrosiononthestress-strain model of reinforcing steel is validated through comparison
behaviour of reinforcing steel. In most cases the corrosion of simulated and observed experimental responses of RC
damage has only been limited to the reinforcing steel by columnswithuncorrodedreinforcement[25].
considering an average reduced area and/or reduced yield The cover concrete strength is adjusted to account for
strength. Furthermore the impact of corrosion on ductility corrosion induced cracking of the cover concrete while
loss, reduced low-cycle fatigue life and inelastic buckling the strength and ductility of the core confined concrete
ofverticalreinforcement,andcorrosioninduceddamageto are adjusted to account for corrosion induced damage to
coverandcoreconfinedconcreteareignored.Inotherwords, horizontaltiereinforcement.Themodelisusedtoexplorethe
the extent of corrosion damage on RC bridges has been impactofcorrosiononthenonlinearresponseofRCcolumns
underestimatedinpreviousstudies. undermonotonicandcyclicloading.
Based on the previous research by Kashani et al. [23– Theanalysisresultsshowthattheproposedmodelinthis
25] it is evident that the impact of corrosion on inelastic paperisabletosimulatemultiplefailuremodesofcorroded
buckling,cyclicbehaviour,andlow-cyclefatiguedegradation columns simultaneously. Therefore, it is evident that the
ofreinforcingbarsmustbeincludedinmodellingcorroded outcomeofthisresearchhasmadeasignificantimprovement
RCcolumns.AsaresultofearlierresearchbyKashanietal. to the existing numerical models. This model provides an
[23–25],theydevelopedanewphenomenologicalmodelfor opensourcecomputationalplatformforseismicvulnerability
corrodedreinforcingbars[29]andisusedinthispaperfor assessment (including fragility analysis) of corroded RC
modelling. bridges.
Prior to the development of the material models devel-
opedin[25,29],itwasimpossibletoinvestigatethecombined
effectofcorrosiondamage,inelasticbuckling,andlow-cycle 2.TheProposedNonlinearFibre
high amplitude fatigue degradation on nonlinear flexural Beam-ColumnElementModel
response of corroded RC columns. Therefore, there is a
significantpaucityofmodellingtechniquesandguidelinesin Theforce-basednonlinearfibrebeam-columnelementwith
theliteraturewhichisaddressedinthispaper. Gauss-Lobattointegrationscheme(availableinOpenSees)is
Theaimofthisnumericalexplorationstudyprovidedin usedhere(Figure1(a)).Toavoidanylocalisationeffects[30,
this paper is to discover the impact of different corrosion 31]duetothesofteningbehaviourofverticalreinforcement
damage models on the nonlinear flexural response of cor- inthepostbucklingregionthecolumnismodelledusingtwo
rodedRCcolumns.Thispaperprovidescomprehensivemod- force-basedelements.Thefirstelementhasthreeintegration
elling guidelines to model the nonlinear behaviour of cor- pointsandthesecondelementhasfiveintegrationpoints.The
rodedRCbridgepiersincludingthecyclicdegradationeffects lengthofthefirstelementistakentobe6𝐿eff,where𝐿eff is
up to complete collapse. The results of this study highlight the calculated buckling length of the vertical reinforcement
what damage mechanisms are important to be considered (Figure 1(a)) which is discussed in Section 4. This allows
inmodellingnonlinearbehaviourofcorrodedRCcolumns. controlofthepositionofthefirstintegrationpointwhichis
Moreover, the proposed model is able to capture multiple setequaltothebucklinglengthoftheverticalreinforcement
failuremodesofcorrodedRCcolumnssimultaneously. that is used to define the material model of the reinforcing
Tothisend,thereisaneedforamoredetailedandaccu- bars. It should be noted that the new uniaxial material
ratenumericalmodeltorepresenttheimpactofcorrosionon model developed by [29] is used here to model the stress-
strainbehaviouroftheverticalreinforcingbars.Thismodel
(i)theverticalandhorizontaltiereinforcement(includ-
accounts for the combined impact of geometrical nonlin-
ingpittingeffects,buckling,ductilityloss,andreduc-
earityduetoinelasticbucklingandmaterialnonlinearityas
edlow-cyclefatiguelife);
well as low-cycle high amplitude fatigue degradation and
(ii)thecrackedcoverconcrete(includingreducedcapac- corrosiondamageinasingle-materialmodel.Furtherdetails
ity) due to corrosion of vertical reinforcement in areavailableinSections5.1and5.2.
column; Tomodeltheslippageoftheverticalreinforcementatthe
column-foundationinterface,azero-lengthsectionelement
(iii)the confined concrete (including reduced capacity
isusedatthebase.Thedetaileddiscussionandvalidationof
andductility)duetocorrosionofhorizontaltierein-
the proposed modelling methodology are available in [25].
forcement (also known as confinement reinforce-
Therefore, only the relevant uniaxial material models to be
ment).
used in the fibre section are discussed here. Figure 1(b)
In this paper a numerical model is developed that enables alsoshowsthefibresectionassignedtotheproposedbeam-
simulation of the nonlinear flexural response of RC columnelement.Therelevantsectionsdiscussingthemate-
components with corroded reinforcement. The model rialmodelsarealsonotedinFigure1(b).
employsaforce-basednonlinearfibrebeam-columnelement Theimplementationofthecorrosiondamagemodelsthat
using OpenSees. The uniaxial material model for corroded are developed by [21–25, 29] into the OpenSees abstract
AdvancesinMaterialsScienceandEngineering 3
4
Element 2
L) 5 integration points
ht ( L2=L−L1
Esleecmtieonnt mn heig (i) Cmoondfienl—edS eccotniocrne t5e. 3 (ii) UcSoenncctcoironenfite n5 me.4do cdoevl—er
u 3
ol
C Element 1 (iii) Reinforcing steel model
3 integration points Pitting corrosion
including inelastic
L =6L models are
Bar-slip 1 eff discussed in buckling and damage
section 2 models—Sections 5.1
Section 3
Zero-length and 5.2
section element
1 (iv) Buckling length
calculation—Section 4
(a) (b)
Figure1:Proposedfiniteelementmodel:(a)force-basednonlinearbeam-columnarrangement;(b)fibresection.
Material
Uniaxial material nD material Section force deformation
Bar-slip Concrete Steel Fibre section (2D, 3D)
Modified steel02 Corrosion damaged Corrosion damaged Corroded steel
for bar-slip cover concrete confined concrete with buckling
Damage model
Max strain Fatigue Pitting corrosion model
Figure2:ImplementationofthecorrosionmodelswithintheOpenSeesabstractclasses.
classes is shown in Figure 2. The calculation of buckling Severalresearchersstudiedtheimpactofnonuniformcorro-
lengthofthecorrodedverticalreinforcement,uniaxialmate- siononcrosssectionlossofreinforcingbars[23,32,33].In
rial models, and corrosion damage models is discussed in [23] a 3D optical measurement of corroded bars was con-
Sections3–5. ductedtoexplorethespatialvariabilityofthecorrosionpat-
tern.AsaresultKashanietal.developedasetofprobabilistic
distributionmodelstopredictthegeometricalpropertiesof
3.InfluenceofCorrosiononGeometrical corroded bars. They found that the geometrical properties
PropertiesofCorrodedBars of corroded bars can be modelled using a lognormal dis-
tribution. In this study, the mean values of the lognormal
The chloride induced corrosion results in irregular loss of distribution models are used to account for the effect of
crosssectionofreinforcingsteelknownaspittingcorrosion. pittingcorrosiononthegeometricalpropertiesofcorroded
4 AdvancesinMaterialsScienceandEngineering
Corrosion induced crack F
in cover concrete
FrazcotunreingreiCnoforrrcoedmedent Ctoo rtrhoes icoonlu imndnu sceecdt idoanmage Plastic hinge region
s
ns Kt
=
eff
L
Idealised beam on spring Buckling of
buckling model corroded reinforcement
Figure3:SchematicoverviewofcorrosioninduceddamagetoRCcolumn.
bars. In this study the proposed models that developed in stiffnessoftheseties.Therefore,theseparametersneedtobe
[23] are used to model the impact of pitting corrosion on consideredincalculationofthebucklinglength.
geometricalpropertiesofcorrodedbars. To account for the effect of corrosion on Dhakal-
Maekawaequations,theflexuralrigidityoftheverticalrein-
4.CalculationoftheBuckling forcement(𝐸𝐼)andstiffnessofhorizontaltiereinforcement
LengthconsideringtheStiffnessof (𝐾𝑡)areadjusted.ThisisdiscussedinSections4.1and4.2.
TieReinforcement
4.1. Influence of Corrosion on Flexural Rigidity of Corroded
The detailed discussion and validation of the Dhakal- Bars. Thebucklingofreinforcingbarsisaninelasticbuckling
Maekawabucklingmodelareavailablein[25,34].Thesame phenomenon and, therefore, the elastic flexural rigidity𝐸𝑠𝐼
methodology is used here for calculation of the buckling isnolongervalid[37].Reference[34]suggestedanaverage
lengthofcorrodedverticalreinforcement. flexural rigidity in which it has been validated against an
Figure 3 shows a schematic overview of the extent of extensivesetofexperimentaldataforuncorrodedcolumns.
corrosiondamageonahypotheticalRCcolumn.Thedamage Thishasbeenmodifiedforcorrodedreinforcement(𝐸𝐼󸀠)and
at section level shown in Figure 3 is based on the observed definedas
experimental tests by [35, 36]. The corrosion of vertical
reinforcementresultsinlongitudinalcracksatthesurfaceof 𝐸 𝐼󸀠 𝜎󸀠
thecolumnparalleltoverticalreinforcement.Thiswillreduce 𝐸𝐼󸀠 = 𝑠 min√ 𝑦 , (1)
2 400
the cross-sectional area and flexural rigidity of the vertical
reinforcementwhichareveryimportantinbuckling.Corro-
sion of horizontal tie reinforcement reduces the volumetric where𝐸𝑠and𝜎𝑦󸀠 aretheelasticmodulusandyieldstrengthof
ratioofconfinementreinforcementwhichisveryimportant thecorrodedverticalreinforcementinMPa,respectively,and
in providing confinement for core concrete. Furthermore, 𝐼m󸀠inisthesecondmomentofareaofcorrodedreinforcement.
this will result in splitting the core and cover concrete by Thedetailedcalculationof𝐼󸀠 isavailablein[23].
min
creation of horizontal cracks around the perimeter of the Corrosionofreinforcingbarsaffectsthesecondmoment
columnsection.Moreover,horizontaltiesrestrainthevertical of area and yield strength of reinforcement but does not
barsagainstbucklingandcorrosionresultsinareductionin haveanyinfluenceontheelasticmodulus.Theyieldstrength
AdvancesinMaterialsScienceandEngineering 5
1.5 0
1.25 −0.2
1 −0.4
𝜎y 𝜎y
𝜎/ 0.75 𝜎/ −0.6
= =
𝜂 0.5 𝜂 −0.8
0.25 −1
0 −1.2
0 10 20 30 40 50 60 −40 −35 −30 −25 −20 −15 −10 −5 0
𝜉=𝜀/𝜀 𝜉=𝜀/𝜀
y y
Tension envelope—uncorroded reinforcement Buckling envelope—uncorroded reinforcement
Tension envelope—corroded reinforcement Buckling envelope—corroded reinforcement
(a) (b)
Figure4:ImplementedtensionandcompressionenvelopesofcorrodedbarsinOpenSees(20%massloss).
can be modified based on the following empirical equation thecyclicdegradationduetolow-cyclefatigueandtheimpact
suggestedby[16]: of corrosion on the tension and compression envelopes
(includingthepostbucklingbehaviour)areincluded.Further
𝜎𝑦󸀠 =𝜎𝑦(1−0.005𝜓), (2) discussionaboutthemodeldevelopmentisavailablein[29].
ToimplementthebucklingmodelinOpenSeestheuniaxial
where𝜓isthepercentagemasslossofthereinforcement. HystereticmodelavailableinOpenSeesismodifiedandused
(thedetaileddiscussionisavailablein[25]).Figure4shows
4.2. Influence of Corrosion on Stiffness of Tie Reinforcement. our proposed tension and compression envelope curves of
In this study the stiffness of the horizontal ties of spiral corrodedbarsimplementedinOpenSees.
reinforcement is computed using the following empirical
equationsuggestedby[38]:
5.2. Reinforcing Steel Model: Cyclic Response and Low-Cycle
4𝐸 𝐴󸀠 Fatigue Degradation. As explained in Section 5.1 the Hys-
𝐾 = sp sp , tereticmaterialmodelinOpenSeesismodifiedtodefinethe
𝑡 (3)
√(𝑠2+𝑑2) reinforcingsteelmodel.ThecyclicresponseoftheHysteretic
𝑐
model is defined by two pinch parameters (pinch 𝑥 and
where 𝐸sp is the elastic modulus, 𝐴󸀠sp is the cross-sectional pinch 𝑦). The pinching effect in the cyclic response of
areaofcorrodedspiralreinforcement,𝑠isthespiralpitch,and reinforcingbarsisaffectedbythestiffnessofthehorizontaltie
𝑑𝑐isthecorediameter. reinforcement.Theoptimumvaluesofpinchparametershave
beenobtainedbyacomprehensiveparametricstudyreported
Thefocusofthispaperisoncircularcolumns.However,
in [25] (the calibrated values are pinch 𝑥 = 0.4 and pinch
in the case of rectangular section, the axial stiffness of tie
𝑦=0.6).
reinforcementcanbecomputedusing
The Uniaxial Fatigue model is wrapped to the steel
𝐾 = 𝐸st𝐴󸀠st, (4) material model to model the low-cycle fatigue degradation
𝑡 𝑙 of corroded vertical reinforcement. The low-cycle fatigue
𝑡
material constants are modified to account for the impact
where𝐸st istheelasticmodulusoftiereinforcement,𝐴󸀠st is of corrosion on the low-cycle fatigue life of corroded bars
thecross-sectionalareaofcorrodedtiereinforcement,and𝑙𝑡 based on the model developed by [29]. Figure 5 shows an
isthelengthoftherectangulartiereinforcement. example cyclic response of the implemented Hysteretic +
Fatiguemodelfortheuncorrodedandcorrodedreinforcing
steel.Furtherdetaileddiscussionaboutmodellingcombined
5.DescriptionofUniaxialMaterialModels
fatigueandbucklingofreinforcingbarsinsideRCcolumnsis
includingCorrosionDamage
availablein[29].
5.1. Reinforcing Steel Model: Tension and Compression
Envelopes. Theuniaxialmaterialmodeldevelopedby[29]is 5.3.CorrosionDamagedConfinedConcreteModel. Thecom-
used to model the reinforcingsteel. This advanced material pressive behaviour of confined concrete is a function of
modelcombinesthematerialnonlinearitywithgeometrical volumetric ratio, yield strength, and fracture strain of the
nonlinearityduetoinelasticbucklingintoasingle-material horizontaltiereinforcement(i.e.,spiral,hoop,andtransverse
model. The impact of geometrical nonlinearity on cyclic reinforcement)[39,40].Sincetiereinforcementisthenearest
behaviour of reinforcing bars is also considered. Moreover, to the surface, being exposed to chloride attack, they may
6 AdvancesinMaterialsScienceandEngineering
1.5 0
1 −0.25
0.5 −0.5
𝜎/𝜎y 0 𝜎/𝜎c −0.75
= =
𝜂 −0.5 𝛾 −1
−1 −1.25
−1.5 −1.5
−30 −20 −10 0 10 20 30 −20 −18 −16 −14 −12 −10 −8 −6 −4 −2 0
𝜉=𝜀/𝜀y 𝜓=𝜀/𝜀c0
Cyclic response including fatigue—uncorroded Original confined concrete model
Cyclic response including fatigue—corroded Corrosion damaged confined concrete
Figure 5: Cyclic response of the Hysteretic + Fatigue model in Figure6:Corrosiondamagedconfinedconcretemodel(20%mass
OpenSees(20%massloss). loss).
start corroding prior to the corrosion initiation of vertical Itisclearthattheconfinedconcretemodelisafunction
reinforcement. As a result the volumetric ratio of tie rein- of yield strength, volumetric ratio, and fracture strain of
forcement is decreased due to cross section loss. There is theconfinement/tiereinforcement.Therefore,thepreviously
also a reduced yield strength and fracture strain due to the definedequationsforreinforcingsteelcanbeusedtomodify
pitting effect. Therefore, the internal confinement pressure thecross-sectionalarea,yieldstrength,andfracturestrainof
of the core concrete can result in premature fracture of tie tiereinforcementasafunctionofthepercentagemassloss.
reinforcement. Accordingly these modified values can be used to account
To date, there has not been any experimental study to for the impact of corrosion on confined concrete model
quantifyandmodeltheeffectofcorrosiononthenonlinear (Figure6).
behaviour of confined concrete under monotonic compres-
sionandcyclicloading.Furtherresearchisrequiredtounder-
5.4. Corrosion Damaged Cracked Cover Concrete Model.
standandmodeltheextentofcorrosiondamageonconfined
Oncecorrosioninitiatesthecorrosionproductsaccumulate
concrete behaviour. However, a simplified methodology is
aroundthereinforcement.Giventhevolumeofthecorrosion
usedinthisresearchtomodifytheconfinedconcretematerial
productsisbiggerthantheoriginalreinforcingsteel,itgener-
model (which is a function of the percentage mass loss in
atesaradialpressure/expansionontheconcretesurrounding
horizontal tie reinforcement) to account for the effect of
the reinforcement. This behaviour is like a thick cylinder
corrosiondamage.
underinternalpressurethateventuallyresultsinfractureof
In this study the uniaxial Concrete04 material model
the cover concrete [45–47]. The cracking of cover concrete
available in OpenSees is used to model the concrete. The
results in loss of compressive strength and crushing strain
Popovicscurve[41]isusedforthecompressionenvelopeand
of the concrete in the compressive zone of RC sections.
the Karsan-Jirsa model [42] is used to determine the slope
Therefore consideration needs to be given to model the
of the curve for unloading and reloading in compression.
influenceofthiscrackingontheresponseofcoverconcrete
For tensile loading, an exponential curve is used to define
incompression.
the envelope to the stress-strain curve. Further details are
The response of cracked concrete in compression is
availablein[43].
described in detail by [48] which is known as compression
The parameters proposed by [40] are used to model
fieldtheory(CFT).BasedonCFTthecompressivestrengthof
the effect of confinement on concrete in compression. The
maximum compressive stress of the concrete (𝜎cc) and the crackedconcreteincompressiondependsonthemagnitude
strain at the maximum compressive strain (𝜀cc) can be oftheaveragetensilestraininthetransversedirection,which
causes longitudinal microcracks. Reference [49] employed
calculatedusingtheequationsdevelopedin[40].
thismethodinnonlinearfiniteelementanalysisofcorrosion
The maximum crushing strain of the confined concrete
damaged RC beams with modified constitutive model for
is defined by the fracture of the first horizontal tie/spiral
the cracked cover concrete as a function of percentage
reinforcement. Here the model proposed by [44] is used to
mass loss and validated this against experimental results.
predicttheconcretecrushingstrainasdefinedin
Therefore, the equations suggested by [49] are employed
𝜌 𝜎 𝜀
sc 𝑦tie 𝑢tie to model the compression response of crack cover con-
𝜀cc =0.004+1.4( 𝜎 ), (5) crete.Figure7(a)showsthecompressionenvelopeandFig-
𝑐
ure7(b)showsthetensionenvelopeoftheuniaxialmaterial
where 𝜀𝑢tie is the fracture strain of the tie/spiral reinforce- model for corrosion damaged unconfined cover concrete
ment,𝜌scisthevolumetricratioofspiralreinforcement,and used in the fibre model. Further details are available in
𝜎𝑦tieistheyieldstressofspiralreinforcement. [49].
AdvancesinMaterialsScienceandEngineering 7
0 0.2
−0.25 0.15
𝜎c 𝜎c
𝜎/ −0.5 𝜎/ 0.1
= =
𝛾 𝛾
−0.75 0.05
−1 0
−2.5 −2 −1.5 −1 −0.5 0 0 1 2 3 4 5 6 7
𝜓=𝜀/𝜀c0 𝜓=𝜀/𝜀ct
Original unconfined concrete model Original concrete tension envelope
Corrosion induced crack unconfined concrete Corrosion induced cracked concrete
(a) (b)
Figure7:Corrosiondamagedcrackedcoverconcretemodelfor20%massloss:(a)compression;(b)tension.
5.5. Bond-Slip Model and Zero-Length Element. In seismic Thedetaileddiscussionandimplementationofthezero-
designofRCstructuresandbridges,plastichingesareformed length section in modelling the cyclic behaviour of RC
at the column/beam ends. This will induce a substantial columnsisavailablein[25].
strainpenetrationalongthelongitudinalbarsintothejoint
that eventually results in slippage of longitudinal bars. This
6.ImpactofCorrosionDamageonNonlinear
phenomenonhasbeenobservedbyotherresearchersexper-
ResponseofRCBridgesPiers
imentally [50]. Reference [51] adopted a bar-slip model for
the end slip of longitudinal reinforcement in beam-column
In this section the impact of different corrosion damage
joints. This model has been employed by [25] to model the
scenarios on the inelastic response of RC bridge piers is
cyclicbehaviourofRCcolumnsandisvalidatedagainstUW-
explored.Acomparativestudyontwohypotheticalcorroded
PEERexperimentalRCcolumndatabase[52].
RC columns with different buckling lengths of vertical bars
Corrosionaffectsthereinforcingsteelnearthesurfaceof
is conducted. The columns are taken from the UW-PEER
theconcreteduetodiffusionofchlorideionsfromthesurface
experimental RC column database [52]. These columns are
and/or carbonation of cover concrete. In bridge piers, the
usedtovalidateandcalibratethebasicnumericalmodelfor
vertical reinforcement bars are anchored to the foundation
theuncorrodedcolumns[25].
well below the foundation surface. Therefore, the vertical
To investigate the impact of corrosion on drift capacity
reinforcementdoesnotcorrodeatthisdepthandthebar-slip
and strength loss of RC columns a series of nonlinear
behaviourofbarsattheanchoragezoneremainsthesameas
pushoveranalyseswithvariedcorrosionlevelsareconducted.
intheuncorrodedcolumn.Thishasbeenobservedbyother
Toexploretheimpactofcyclicdegradation,nonlinearcyclic
researchersexperimentally[12–14].
analyses using the load history that was used in the exper-
It should be pointed out that corrosion does affect the
iment are conducted. In order to investigate the impact of
bond strength of corroded vertical reinforcement above
different modelling techniques and damage mechanism for
the foundation level (internal bond-slip within the column
eachanalysistypethreescenariosareconsidered:
itself).However,basedontheobservedexperimentalresults,
the reduced bond strength does not govern the failure of (a)Vertical and horizontal tie reinforcement are cor-
columns. References [12–14] reported that the failure of roded,butcoverandcoreconcretearenotaffectedby
corrodedcolumnsandbeamsundercyclicloadingismainly corrosion.
governbyfractureofbarsintensionduetolow-cyclefatigue
(b)Vertical and horizontal tie reinforcement are cor-
and buckling of bars and crushing of confined concrete in
roded and the cover concrete is cracked due to
compression.
corrosion,butthecoreconcreteisnotaffected.
Reference[53]conductedacomprehensivedetailednon-
linear finite element analysis of corroded RC beams and (c)Vertical and horizontal tie reinforcement are cor-
validated them against experimental results. They have roded; the cover concrete is cracked and the core
reportedthatreducedbondstrengthonlychangesthecrack concreteisaffectedduetocorrosionofconfining/tie
patternandaffectstheserviceabilityofcorrodedbeams.They reinforcement.
concluded that reduced bond strength does not affect the
ultimatecapacityofcorrodedbeams.Therefore,bond-slipof Thesescenarioswillhighlighttheimportanceofeachdamage
corrodedverticalbarswithintheelementisnotconsideredin componentthatneedstobeconsideredinmodellingnonlin-
thisresearch. earresponseofcorrodedRCcolumns.
8 AdvancesinMaterialsScienceandEngineering
200
300
150
N) 200 N) 100
e (k 100 e (k 50
orc 0 orc 0
Lateral f −−210000 Lateral f−−15000
−150
−300
−200
−0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08
Drift ratio Drift ratio
Experiment Experiment
Fibre model Fibre model
(a) (b)
Figure8:Comparisonofexperimentalresultsandcalibratednumericalmodelofuncorrodedcolumns:(a)Lehman’scolumn415;(b)Moyer
andKowalsky’scolumn1.
Lehman’scolumn415andMoyerandKowalsky’scolumn Inpractice,thehorizontaltiereinforcementiscloserthan
1 [50, 54] are considered in this study. The geometrical the main vertical reinforcement to the surface of concrete.
details,materialproperties,anddetailedexperimentalresults Therefore, it might start corroding earlier than vertical
of these columns are available in [50, 54]. Figure 8 shows reinforcement.Thisphenomenonmighthaveaneffectonthe
a comparison of the numerical model and experimental bucklinglengthandconfinedconcretebehaviour.However,
responsesofthesecolumns.ItshouldbenotedthatLehman’s there has not been any research to date to explore the
column 415 has 𝐿eff/𝑑 = 10 and Moyer and Kowalsky’s correlation between the corrosion levels of the horizontal
column 1 has 𝐿eff/𝑑 = 4. The detailed discussion of the tie and vertical reinforcement. This is an area for future
numerical model validation is available in [25]. It should researchandtherefore,inthisresearch,intheabsenceofany
be noted that the maximum drift capacity in this paper experimental/fielddata,thesamecorrosionisconsideredfor
is considered as the point where the force-displacement bothverticalandtiereinforcement.
responseofthecolumnstartssofteningandlosingstrength. It should be noted that the calculation of the time to
Itisfoundthatthemaximumdriftcapacityofbothcolumns corrosioninitiationandtime-dependentcorrosionpropaga-
atuncorrodedstateisabout6%. tionisoutofthescopeofthispaper.Therearemathematical
Thebucklinglengthsofcorrodedverticalreinforcement models available in the literature that enable an estimation
arecalculatedusingthemethodologydescribedinSection4. of the time to corrosion initiation and propagation based
Thecorrosionofhorizontaltiesisconsideredinthebuckling ontheenvironmentalconditions[55,56].Thecorrosionrate
length calculation. As discussed previously (Section 4), the canalsobemeasuredonsitebyelectricalequipmentwhich
buckling length of the vertical bars is a function of the can then be turned into a mass loss ratio using Faraday’s
tie reinforcement’s stiffness and the vertical reinforcement’s law of electrolysis [57]. Given that the focus of this paper
flexuralrigidity.Corrosionresultsinareductioninflexural isontheimpactofdifferentmasslossratiosontheseismic
rigidityofverticalbars.Therefore,therequiredstiffnessfrom performanceofRCcolumns,thecorrosionlevelismodelled
tie reinforcement to restrain vertical bars against buckling bypercentagemasslossthroughoutthispaper.
is reduced. However, corrosion also reduces the stiffness of
thetiereinforcement.Forexample,inMoyerandKowalsky’s
column,theverticalreinforcementbuckledbetweentwoties. 6.1. Scenario (a): Column Nonlinear Behaviour When Cor-
In this case, it was found that corrosion did not affect the rosion Is Assumed Present in Vertical and Horizontal Tie
bucklinglength. Reinforcement Only. In this scenario, it is assumed that the
In Lehman’s column 415, the vertical reinforcement corrosiondamage is onlylimited to thesteel reinforcement
buckled over five ties. However, once the corrosion level (verticalandhorizontaltiereinforcement);thatis,covercon-
exceeds 10%, the buckling length reduced and the vertical creteisuncrackedandcorrosionofconfiningreinforcement
reinforcement buckled over four ties. It should be noted does not affect the confined concrete behaviour. Here, the
that although the buckling length is reduced, 𝐿eff/𝑑󸀠 is not steel model described in Section 5.1 is used which includes
necessarilyreduced,where𝐿eff isthebucklinglengthand𝑑󸀠 the impact of corrosion on the buckling and postbuckling
isthediameterofthecorrodedverticalreinforcement.This behaviourincompressionandstrengthandductilitylossin
is because corrosion also reduces the diameter of vertical tension.
bars.Thischangeinbucklinglengthisrelatedtotherelative Figure9showstheresultsofmonotonicpushoveranal-
corrosion level and stiffness between the vertical and tie yses. Figure 9(a) shows that the failure mode of Lehman’s
reinforcement. column 415 is by vertical bar buckling and core confined
AdvancesinMaterialsScienceandEngineering 9
350 200
300
N) 250 N) 150
k k
orce ( 200 orce ( 100
al f 150 al f
ater 100 ater 50
L L
50
0 0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Drift ratio Drift ratio
Control 40% mass loss Control 40% mass loss
10% mass loss Bar buckling and concrete crushing 10% mass loss Bar buckling and concrete crushing
20% mass loss Bar fracture in tension 20% mass loss Bar fracture in tension
30% mass loss 30% mass loss
(a) (b)
Figure9:Pushoveranalysesconsideringcorrosioninduceddamageinreinforcingsteel:(a)Lehman’scolumn415;(b)MoyerandKowalsky’s
column1.
concretecrushingupto10%massloss.However,asthecor- Figures 10(c) and 10(d) show a similar result for Moyer
rosionlevelincreasesbeyond10%massloss,thefailuremode and Kowalsky’s column 1. Overall, Moyer and Kowalsky’s
changesfromverticalbarbuckingandconcretecrushingin column1hasslightlylesspinchedcyclicresponse.Thisisdue
compressiontofractureoftheverticalbarsintension. totheinfluenceofthebucklinglengthoftheverticalbarsand
Figure 9(b) shows that Moyer and Kowalsky’s column itscyclicdegradationduetobuckling[25].
1 has also failed in bar buckling and concrete crushing in
compression.However,because𝐿eff/𝑑 = 4,thestrengthloss 6.2.Scenario(b):ColumnNonlinearBehaviourWhenCorro-
is not as significant as that of Lehman’s column 415 with sionIsAssumedPresentinVerticalandHorizontalTieRein-
𝐿eff/𝑑 = 10 under monotonic loading. The corrosion level forcement and Cover Concrete Is Cracked. In this scenario,
upto20%masslosschangesMoyerandKowalsky’scolumn it is assumed that the reinforcing steel (vertical and tie) is
1 behaviour. The failure initiates with bar buckling and corrodedandthecoverconcreteiscrackedduetocorrosion
concretecrushingincompressionandfollowedbyfractureof ofverticalreinforcement.Theresultsofthepushoveranalyses
the vertical reinforcement in tension. With corrosion levels are shown in Figure 11. The results in this case are almost
greater than 20% mass loss failure is by premature fracture identicaltothepreviouscase(Section6.1)wherethedamage
oftheverticalbarsintension.Atthispointacascadeofbar in cover concrete was not considered. Therefore in can
fracturecanbeseeninthegraphsuptocompletecollapseof be concluded that whether or not we seek to model the
thecolumns. corrosioninducedcrackingofcoverconcreteitdoesnothave
Figures10(a)and10(b)showLehman’scolumn415with a significant impact on the nonlinear response of corroded
10%and20%masslossesundercyclicloading,respectively. columns.Furtherdiscussionandcomparisonofthisscenario
Comparing the monotonic and cyclic responses (the same withotherdamagescenariosareavailableinSection6.3.
cyclicloadprotocolastheexperiment)showsthatlow-cycle
fatigue has a significant impact on the column response.
6.3. Scenario (c): Column Seismic Behaviour When Cor-
The monotonic analysis showed that 10% mass loss did not
rosion Is Assumed Present in Vertical and Horizontal Tie
result in vertical bar fracture in tension and the failure was
Reinforcement and Both Cover and Confined Concrete Are
governedbybarbucklingandconcretecrushing.However,in
Damaged. In this scenario, it is assumed that the reinforc-
cyclicanalysis,thefailuremodeiscombinedbarbucklingand
ing steel (vertical and tie) is corroded, cover concrete is
concretecrushingincompression(failureinitiation)followed
cracked, and the core confined concrete is affected by the
bybarfractureintensionduetolow-cyclefatigue.
corrosion of horizontal tie reinforcement (as described in
Here we have a system that does not technically fail in
Section 5.3). Figure 12(a) shows the results of monotonic
crushing and buckling but survives a little longer until the
pushoveranalysesofLehman’scolumn415.Theresultsshow
next cycle when the vertical reinforcement fails in tension.
It was found that a mass loss ratio greater than 10% has a that the failure mechanism of this column for up to 10%
significantimpactonthenonlinearresponseofthecorroded masslossisbarbucklingandcoreconfinedconcretecrushing
column due to reduced low-cycle fatigue life. Figure 10(b) in compression. However, for corrosion levels beyond 10%,
shows that at 20%mass loss resulted in bar fractureat 0.05 the failure mode changes. This is a loss of drift capacity
driftratioinpushoveranalysis,butitresultedinbarfracture which starts with bar buckling and concrete crushing in
at0.03driftratioundercyclicloadingduetolow-cyclefatigue compression and it is followed by bar fracture in tension.
failure. Theseanalysesdemonstratetheimportanceofmodellingthe