Research ArticleComputational Modelling Strategies for Nonlinear ResponsePrediction of Corroded Circular RC Bridge Piers

Mohammad M Kashani1 Laura N Lowes2 Adam J Crewe1 and Nicholas A Alexander1

1Department of Civil Engineering University of Bristol Bristol BS8 1TR UK2Department of Civil and Environmental Engineering University of Washington Seattle WA 98195-2700 USA

Correspondence should be addressed to Mohammad M Kashani mehdikashanibristolacuk

Received 30 December 2015 Accepted 19 April 2016

Academic Editor Seung-Jun Kwon

Copyright copy 2016 Mohammad M Kashani et alThis is an open access article distributed under the Creative CommonsAttributionLicense which permits unrestricted use distribution and reproduction in anymedium provided the originalwork is properly cited

A numerical model is presented that enables simulation of the nonlinear flexural response of corroded reinforced concrete (RC)components The model employs a force-based nonlinear fibre beam-column element A new phenomenological uniaxial materialmodel for corroded reinforcing steel is used This model accounts for the impact of corrosion on buckling strength postbucklingbehaviour and low-cycle fatigue degradation of vertical reinforcement under cyclic loading The basic material model is validatedthrough comparison of simulated and observed responses for uncorroded RC columnsThemodel is used to explore the impact ofcorrosion on the inelastic response of corroded RC columns

1 Introduction

A significant number of older major infrastructure artefactslocated in an aggressive environment suffer from materialaging and deterioration [1 2] In order to provide a durableand reliable solution the functionality safety and service lifeof various infrastructure artefacts should be estimated usingthe best available engineering science Therefore for exist-ing deteriorated infrastructure a rational maintenance planshould be employed in accordance with their current condi-tion Recently limited funding has implied the need for a newbridge management system that can capture all these com-plexities within a single comprehensive framework so that themaintenance strategy of bridge networks can be optimised

Among different deteriorationmechanisms the corrosionof reinforcing bars in RC structures is the most commontype of deterioration mechanisms [1 2] Moreover a hugenumber of these corroded structures are also in high seis-micity regions This has led researchers around the worldto investigate the influence of reinforcement corrosion onthe seismic performance of existing RC structures [3ndash11]Other researchers have studied the impact of reinforcementcorrosion on cyclic behaviour of corroded RC beams andcolumns experimentally [12ndash14] The experimental results

showed that corrosion will affect the failure mechanisms offlexural RC components In several cases premature bucklingof longitudinal reinforcement has been observed This is dueto the combined effect of nonuniform pitting corrosion alongthe length of longitudinal reinforcement and corrosion ofhorizontal tie reinforcement Once corroded bars buckledunder cyclic loading they fracture at lower drift demandsdue to low-cycle high amplitude fatigue degradation Theseobservations from the experimental studies suggest that thecombined effect of inelastic buckling and nonuniform pittingcorrosion results in a significant reduction in low-cyclefatigue life of corroded RC elements

Furthermore several researchers investigated the effectof corrosion on stress-strain behaviour of reinforcing bars intension [15ndash20] References [21ndash25] included a comprehen-sive experimental and computational study on the inelasticbehaviour of isolated corroded reinforcing bars including theimpact of corrosion on inelastic buckling and degradationdue to low-cycle fatigue These results are in good agreementwith the results observed by other researchers who studiedthe cyclic behaviour of RC components

Moreover in recent years several researchers have stud-ied the seismic vulnerability and fragility analysis of corrodedRC bridges [3ndash11] They have investigated the effect of

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2016 Article ID 2738265 15 pageshttpdxdoiorg10115520162738265

2 Advances in Materials Science and Engineering

reinforcement corrosion on the nonlinear behaviour andresponse of RC bridges subject to seismic loading throughnonlinear fibre-based finite element analysis [26ndash28]

However they have used very simple uniaxial materialmodels to model the impact of corrosion on the stress-strainbehaviour of reinforcing steel In most cases the corrosiondamage has only been limited to the reinforcing steel byconsidering an average reduced area andor reduced yieldstrength Furthermore the impact of corrosion on ductilityloss reduced low-cycle fatigue life and inelastic bucklingof vertical reinforcement and corrosion induced damage tocover and core confined concrete are ignored In other wordsthe extent of corrosion damage on RC bridges has beenunderestimated in previous studies

Based on the previous research by Kashani et al [23ndash25] it is evident that the impact of corrosion on inelasticbuckling cyclic behaviour and low-cycle fatigue degradationof reinforcing bars must be included in modelling corrodedRC columns As a result of earlier research by Kashani et al[23ndash25] they developed a new phenomenological model forcorroded reinforcing bars [29] and is used in this paper formodelling

Prior to the development of the material models devel-oped in [25 29] it was impossible to investigate the combinedeffect of corrosion damage inelastic buckling and low-cyclehigh amplitude fatigue degradation on nonlinear flexuralresponse of corroded RC columns Therefore there is asignificant paucity of modelling techniques and guidelines inthe literature which is addressed in this paper

The aim of this numerical exploration study provided inthis paper is to discover the impact of different corrosiondamage models on the nonlinear flexural response of cor-roded RC columnsThis paper provides comprehensivemod-elling guidelines to model the nonlinear behaviour of cor-rodedRCbridge piers including the cyclic degradation effectsup to complete collapse The results of this study highlightwhat damage mechanisms are important to be consideredin modelling nonlinear behaviour of corroded RC columnsMoreover the proposed model is able to capture multiplefailure modes of corroded RC columns simultaneously

To this end there is a need for a more detailed and accu-rate numerical model to represent the impact of corrosion on

(i) the vertical and horizontal tie reinforcement (includ-ing pitting effects buckling ductility loss and reduc-ed low-cycle fatigue life)

(ii) the cracked cover concrete (including reduced capac-ity) due to corrosion of vertical reinforcement incolumn

(iii) the confined concrete (including reduced capacityand ductility) due to corrosion of horizontal tie rein-forcement (also known as confinement reinforce-ment)

In this paper a numerical model is developed that enablessimulation of the nonlinear flexural response of RCcomponents with corroded reinforcement The modelemploys a force-based nonlinear fibre beam-column elementusing OpenSees The uniaxial material model for corroded

reinforcing steel that is developed in [29] is used This modelsimulates the stress-strain behaviour of reinforcing steel withthe effect of inelastic buckling and low-cycle high amplitudefatigue degradation under cyclic loading The basic bucklingmodel of reinforcing steel is validated through comparisonof simulated and observed experimental responses of RCcolumns with uncorroded reinforcement [25]

The cover concrete strength is adjusted to account forcorrosion induced cracking of the cover concrete whilethe strength and ductility of the core confined concreteare adjusted to account for corrosion induced damage tohorizontal tie reinforcementThemodel is used to explore theimpact of corrosion on the nonlinear response of RC columnsunder monotonic and cyclic loading

The analysis results show that the proposed model in thispaper is able to simulate multiple failure modes of corrodedcolumns simultaneously Therefore it is evident that theoutcome of this research has made a significant improvementto the existing numerical models This model provides anopen source computational platform for seismic vulnerabilityassessment (including fragility analysis) of corroded RCbridges

2 The Proposed Nonlinear FibreBeam-Column Element Model

The force-based nonlinear fibre beam-column element withGauss-Lobatto integration scheme (available in OpenSees) isused here (Figure 1(a)) To avoid any localisation effects [3031] due to the softening behaviour of vertical reinforcementin the postbuckling region the column is modelled using twoforce-based elements The first element has three integrationpoints and the second element has five integration pointsThelength of the first element is taken to be 6119871eff where 119871eff isthe calculated buckling length of the vertical reinforcement(Figure 1(a)) which is discussed in Section 4 This allowscontrol of the position of the first integration point which isset equal to the buckling length of the vertical reinforcementthat is used to define the material model of the reinforcingbars It should be noted that the new uniaxial materialmodel developed by [29] is used here to model the stress-strain behaviour of the vertical reinforcing bars This modelaccounts for the combined impact of geometrical nonlin-earity due to inelastic buckling and material nonlinearity aswell as low-cycle high amplitude fatigue degradation andcorrosion damage in a single-material model Further detailsare available in Sections 51 and 52

To model the slippage of the vertical reinforcement at thecolumn-foundation interface a zero-length section elementis used at the base The detailed discussion and validation ofthe proposed modelling methodology are available in [25]Therefore only the relevant uniaxial material models to beused in the fibre section are discussed here Figure 1(b)also shows the fibre section assigned to the proposed beam-column element The relevant sections discussing the mate-rial models are also noted in Figure 1(b)

The implementation of the corrosion damagemodels thatare developed by [21ndash25 29] into the OpenSees abstract

Advances in Materials Science and Engineering 3

Zero-lengthsection element

Element 13 integration points

Element 25 integration points

1

2

3

4

Col

umn

heig

ht (L

)

Bar-slipsection

Element section

L2 = L minus L1

L1 = 6Leff

(a)

(ii) Unconfined cover concrete modelmdashSection 54

(iii) Reinforcing steel model including inelastic buckling and damage modelsmdashSections 51and 52

(iv) Buckling length calculationmdashSection 4

(i) Confined concrete modelmdashSection 53

Pitting corrosionmodels are discussed in Section 3

(b)

Figure 1 Proposed finite element model (a) force-based nonlinear beam-column arrangement (b) fibre section

Section force deformationnD materialUniaxial material

Material

Fibre section (2D 3D)SteelConcreteBar-slip

Corroded steel with buckling

Corrosion damaged confined concrete

Corrosion damaged cover concrete

Modified steel02 for bar-slip

Damage model

FatigueMax strain Pitting corrosion model

Figure 2 Implementation of the corrosion models within the OpenSees abstract classes

classes is shown in Figure 2 The calculation of bucklinglength of the corroded vertical reinforcement uniaxial mate-rial models and corrosion damage models is discussed inSections 3ndash5

3 Influence of Corrosion on GeometricalProperties of Corroded Bars

The chloride induced corrosion results in irregular loss ofcross section of reinforcing steel known as pitting corrosion

Several researchers studied the impact of nonuniform corro-sion on cross section loss of reinforcing bars [23 32 33] In[23] a 3D optical measurement of corroded bars was con-ducted to explore the spatial variability of the corrosion pat-tern As a result Kashani et al developed a set of probabilisticdistribution models to predict the geometrical properties ofcorroded bars They found that the geometrical propertiesof corroded bars can be modelled using a lognormal dis-tribution In this study the mean values of the lognormaldistribution models are used to account for the effect ofpitting corrosion on the geometrical properties of corroded

4 Advances in Materials Science and Engineering

Corrodedreinforcement

FracturingPlastic hinge regionzone

Buckling ofcorroded reinforcement

Idealised beam on springbuckling model

Corrosion induced damage

to the column section

Corrosion induced crackin cover concrete

Kt

s

F

Lef

f=

ns

Figure 3 Schematic overview of corrosion induced damage to RC column

bars In this study the proposed models that developed in[23] are used to model the impact of pitting corrosion ongeometrical properties of corroded bars

4 Calculation of the BucklingLength considering the Stiffness ofTie Reinforcement

The detailed discussion and validation of the Dhakal-Maekawa buckling model are available in [25 34] The samemethodology is used here for calculation of the bucklinglength of corroded vertical reinforcement

Figure 3 shows a schematic overview of the extent ofcorrosion damage on a hypothetical RC columnThe damageat section level shown in Figure 3 is based on the observedexperimental tests by [35 36] The corrosion of verticalreinforcement results in longitudinal cracks at the surface ofthe columnparallel to vertical reinforcementThiswill reducethe cross-sectional area and flexural rigidity of the verticalreinforcement which are very important in buckling Corro-sion of horizontal tie reinforcement reduces the volumetricratio of confinement reinforcement which is very importantin providing confinement for core concrete Furthermorethis will result in splitting the core and cover concrete bycreation of horizontal cracks around the perimeter of thecolumn sectionMoreover horizontal ties restrain the verticalbars against buckling and corrosion results in a reduction in

stiffness of these ties Therefore these parameters need to beconsidered in calculation of the buckling length

To account for the effect of corrosion on Dhakal-Maekawa equations the flexural rigidity of the vertical rein-forcement (119864119868) and stiffness of horizontal tie reinforcement(119870119905) are adjusted This is discussed in Sections 41 and 42

41 Influence of Corrosion on Flexural Rigidity of CorrodedBars Thebuckling of reinforcing bars is an inelastic bucklingphenomenon and therefore the elastic flexural rigidity 119864

119904119868

is no longer valid [37] Reference [34] suggested an averageflexural rigidity in which it has been validated against anextensive set of experimental data for uncorroded columnsThis has beenmodified for corroded reinforcement (1198641198681015840) anddefined as

1198641198681015840=1198641199041198681015840

min2

radic1205901015840

119910

400

(1)

where 119864119904and 1205901015840119910are the elastic modulus and yield strength of

the corroded vertical reinforcement inMPa respectively and1198681015840

min is the secondmoment of area of corroded reinforcementThe detailed calculation of 1198681015840min is available in [23]

Corrosion of reinforcing bars affects the second momentof area and yield strength of reinforcement but does nothave any influence on the elastic modulus The yield strength

Advances in Materials Science and Engineering 5

0 10 20 30 40 50 600

025

05

075

1

125

15

Tension envelopemdashuncorroded reinforcementTension envelopemdashcorroded reinforcement

120578=120590120590

y

120585 = 120576120576y

(a)

minus40 minus35 minus30 minus25 minus20 minus15 minus10 minus5 0minus12

minus1

minus08

minus06

minus04

minus02

0

Buckling envelopemdashuncorroded reinforcementBuckling envelopemdashcorroded reinforcement

120578=120590120590

y

120585 = 120576120576y

(b)

Figure 4 Implemented tension and compression envelopes of corroded bars in OpenSees (20 mass loss)

can be modified based on the following empirical equationsuggested by [16]

1205901015840

119910= 120590119910(1 minus 0005120595) (2)

where 120595 is the percentage mass loss of the reinforcement

42 Influence of Corrosion on Stiffness of Tie ReinforcementIn this study the stiffness of the horizontal ties of spiralreinforcement is computed using the following empiricalequation suggested by [38]

119870119905=

4119864sp1198601015840

sp

radic(1199042 + 1198892119888)

(3)

where 119864sp is the elastic modulus 1198601015840sp is the cross-sectionalarea of corroded spiral reinforcement 119904 is the spiral pitch and119889119888is the core diameterThe focus of this paper is on circular columns However

in the case of rectangular section the axial stiffness of tiereinforcement can be computed using

119870119905=119864st1198601015840

st119897119905

(4)

where 119864st is the elastic modulus of tie reinforcement 1198601015840st isthe cross-sectional area of corroded tie reinforcement and 119897

119905

is the length of the rectangular tie reinforcement

5 Description of Uniaxial Material Modelsincluding Corrosion Damage

51 Reinforcing Steel Model Tension and CompressionEnvelopes The uniaxial material model developed by [29] isused to model the reinforcing steel This advanced materialmodel combines the material nonlinearity with geometricalnonlinearity due to inelastic buckling into a single-materialmodel The impact of geometrical nonlinearity on cyclicbehaviour of reinforcing bars is also considered Moreover

the cyclic degradation due to low-cycle fatigue and the impactof corrosion on the tension and compression envelopes(including the postbuckling behaviour) are included Furtherdiscussion about the model development is available in [29]To implement the buckling model in OpenSees the uniaxialHystereticmodel available in OpenSees is modified and used(the detailed discussion is available in [25]) Figure 4 showsour proposed tension and compression envelope curves ofcorroded bars implemented in OpenSees

52 Reinforcing Steel Model Cyclic Response and Low-CycleFatigue Degradation As explained in Section 51 the Hys-teretic material model in OpenSees is modified to define thereinforcing steel model The cyclic response of the Hystereticmodel is defined by two pinch parameters (pinch 119909 andpinch 119910) The pinching effect in the cyclic response ofreinforcing bars is affected by the stiffness of the horizontal tiereinforcementThe optimumvalues of pinch parameters havebeen obtained by a comprehensive parametric study reportedin [25] (the calibrated values are pinch 119909 = 04 and pinch119910 = 06)

The Uniaxial Fatigue model is wrapped to the steelmaterial model to model the low-cycle fatigue degradationof corroded vertical reinforcement The low-cycle fatiguematerial constants are modified to account for the impactof corrosion on the low-cycle fatigue life of corroded barsbased on the model developed by [29] Figure 5 shows anexample cyclic response of the implemented Hysteretic +Fatigue model for the uncorroded and corroded reinforcingsteel Further detailed discussion about modelling combinedfatigue and buckling of reinforcing bars inside RC columns isavailable in [29]

53 Corrosion Damaged Confined Concrete Model The com-pressive behaviour of confined concrete is a function ofvolumetric ratio yield strength and fracture strain of thehorizontal tie reinforcement (ie spiral hoop and transversereinforcement) [39 40] Since tie reinforcement is the nearestto the surface being exposed to chloride attack they may

6 Advances in Materials Science and Engineering

minus30 minus20 minus10 0 10 20 30minus15

minus1

minus05

0

05

1

15

Cyclic response including fatiguemdashuncorrodedCyclic response including fatiguemdashcorroded

120578=120590120590

y

120585 = 120576120576y

Figure 5 Cyclic response of the Hysteretic + Fatigue model inOpenSees (20 mass loss)

start corroding prior to the corrosion initiation of verticalreinforcement As a result the volumetric ratio of tie rein-forcement is decreased due to cross section loss There isalso a reduced yield strength and fracture strain due to thepitting effect Therefore the internal confinement pressureof the core concrete can result in premature fracture of tiereinforcement

To date there has not been any experimental study toquantify and model the effect of corrosion on the nonlinearbehaviour of confined concrete under monotonic compres-sion and cyclic loading Further research is required to under-stand and model the extent of corrosion damage on confinedconcrete behaviour However a simplified methodology isused in this research tomodify the confined concretematerialmodel (which is a function of the percentage mass loss inhorizontal tie reinforcement) to account for the effect ofcorrosion damage

In this study the uniaxial Concrete04 material modelavailable in OpenSees is used to model the concrete ThePopovics curve [41] is used for the compression envelope andthe Karsan-Jirsa model [42] is used to determine the slopeof the curve for unloading and reloading in compressionFor tensile loading an exponential curve is used to definethe envelope to the stress-strain curve Further details areavailable in [43]

The parameters proposed by [40] are used to modelthe effect of confinement on concrete in compression Themaximum compressive stress of the concrete (120590cc) and thestrain at the maximum compressive strain (120576cc) can becalculated using the equations developed in [40]

The maximum crushing strain of the confined concreteis defined by the fracture of the first horizontal tiespiralreinforcement Here the model proposed by [44] is used topredict the concrete crushing strain as defined in

120576cc = 0004 + 14 (120588sc120590119910tie120576119906tie

120590119888

) (5)

where 120576119906tie is the fracture strain of the tiespiral reinforce-

ment 120588sc is the volumetric ratio of spiral reinforcement and120590119910tie is the yield stress of spiral reinforcement

minus20 minus18 minus16 minus14 minus12 minus10 minus8 minus6 minus4 minus2 0minus15

minus125

minus1

minus075

minus05

minus025

0

Original confined concrete modelCorrosion damaged confined concrete

120574=120590120590

c

120595 = 120576120576c0

Figure 6 Corrosion damaged confined concrete model (20 massloss)

It is clear that the confined concrete model is a functionof yield strength volumetric ratio and fracture strain ofthe confinementtie reinforcement Therefore the previouslydefined equations for reinforcing steel can be used to modifythe cross-sectional area yield strength and fracture strain oftie reinforcement as a function of the percentage mass lossAccordingly these modified values can be used to accountfor the impact of corrosion on confined concrete model(Figure 6)

54 Corrosion Damaged Cracked Cover Concrete ModelOnce corrosion initiates the corrosion products accumulatearound the reinforcement Given the volume of the corrosionproducts is bigger than the original reinforcing steel it gener-ates a radial pressureexpansion on the concrete surroundingthe reinforcement This behaviour is like a thick cylinderunder internal pressure that eventually results in fracture ofthe cover concrete [45ndash47] The cracking of cover concreteresults in loss of compressive strength and crushing strainof the concrete in the compressive zone of RC sectionsTherefore consideration needs to be given to model theinfluence of this cracking on the response of cover concretein compression

The response of cracked concrete in compression isdescribed in detail by [48] which is known as compressionfield theory (CFT) Based onCFT the compressive strength ofcracked concrete in compression depends on the magnitudeof the average tensile strain in the transverse direction whichcauses longitudinal microcracks Reference [49] employedthis method in nonlinear finite element analysis of corrosiondamaged RC beams with modified constitutive model forthe cracked cover concrete as a function of percentagemass loss and validated this against experimental resultsTherefore the equations suggested by [49] are employedto model the compression response of crack cover con-crete Figure 7(a) shows the compression envelope and Fig-ure 7(b) shows the tension envelope of the uniaxial materialmodel for corrosion damaged unconfined cover concreteused in the fibre model Further details are available in[49]

Advances in Materials Science and Engineering 7

minus25 minus2 minus15 minus1 minus05 0minus1

minus075

minus05

minus025

0

Original unconfined concrete modelCorrosion induced crack unconfined concrete

120595 = 120576120576c0

120574=120590120590

c

(a)

0 1 2 3 4 5 6 70

005

01

015

02

Original concrete tension envelopeCorrosion induced cracked concrete

120574=120590120590

c

120595 = 120576120576ct

(b)

Figure 7 Corrosion damaged cracked cover concrete model for 20 mass loss (a) compression (b) tension

55 Bond-Slip Model and Zero-Length Element In seismicdesign of RC structures and bridges plastic hinges are formedat the columnbeam ends This will induce a substantialstrain penetration along the longitudinal bars into the jointthat eventually results in slippage of longitudinal bars Thisphenomenon has been observed by other researchers exper-imentally [50] Reference [51] adopted a bar-slip model forthe end slip of longitudinal reinforcement in beam-columnjoints This model has been employed by [25] to model thecyclic behaviour of RC columns and is validated against UW-PEER experimental RC column database [52]

Corrosion affects the reinforcing steel near the surface ofthe concrete due to diffusion of chloride ions from the surfaceandor carbonation of cover concrete In bridge piers thevertical reinforcement bars are anchored to the foundationwell below the foundation surface Therefore the verticalreinforcement does not corrode at this depth and the bar-slipbehaviour of bars at the anchorage zone remains the same asin the uncorroded column This has been observed by otherresearchers experimentally [12ndash14]

It should be pointed out that corrosion does affect thebond strength of corroded vertical reinforcement abovethe foundation level (internal bond-slip within the columnitself) However based on the observed experimental resultsthe reduced bond strength does not govern the failure ofcolumns References [12ndash14] reported that the failure ofcorroded columns and beams under cyclic loading is mainlygovern by fracture of bars in tension due to low-cycle fatigueand buckling of bars and crushing of confined concrete incompression

Reference [53] conducted a comprehensive detailed non-linear finite element analysis of corroded RC beams andvalidated them against experimental results They havereported that reduced bond strength only changes the crackpattern and affects the serviceability of corroded beamsTheyconcluded that reduced bond strength does not affect theultimate capacity of corroded beams Therefore bond-slip ofcorroded vertical bars within the element is not considered inthis research

The detailed discussion and implementation of the zero-length section in modelling the cyclic behaviour of RCcolumns is available in [25]

6 Impact of Corrosion Damage on NonlinearResponse of RC Bridges Piers

In this section the impact of different corrosion damagescenarios on the inelastic response of RC bridge piers isexplored A comparative study on two hypothetical corrodedRC columns with different buckling lengths of vertical barsis conducted The columns are taken from the UW-PEERexperimental RC column database [52] These columns areused to validate and calibrate the basic numerical model forthe uncorroded columns [25]

To investigate the impact of corrosion on drift capacityand strength loss of RC columns a series of nonlinearpushover analyses with varied corrosion levels are conductedTo explore the impact of cyclic degradation nonlinear cyclicanalyses using the load history that was used in the exper-iment are conducted In order to investigate the impact ofdifferent modelling techniques and damage mechanism foreach analysis type three scenarios are considered

(a) Vertical and horizontal tie reinforcement are cor-roded but cover and core concrete are not affected bycorrosion

(b) Vertical and horizontal tie reinforcement are cor-roded and the cover concrete is cracked due tocorrosion but the core concrete is not affected

(c) Vertical and horizontal tie reinforcement are cor-roded the cover concrete is cracked and the coreconcrete is affected due to corrosion of confiningtiereinforcement

These scenarios will highlight the importance of each damagecomponent that needs to be considered in modelling nonlin-ear response of corroded RC columns

8 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008

minus300minus200minus100

0100200300

ExperimentFibre model

Drift ratio

Late

ral f

orce

(kN

)

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

ExperimentFibre model

Drift ratio

Late

ral f

orce

(kN

)

(b)

Figure 8 Comparison of experimental results and calibrated numerical model of uncorroded columns (a) Lehmanrsquos column 415 (b) Moyerand Kowalskyrsquos column 1

Lehmanrsquos column 415 and Moyer and Kowalskyrsquos column1 [50 54] are considered in this study The geometricaldetails material properties and detailed experimental resultsof these columns are available in [50 54] Figure 8 showsa comparison of the numerical model and experimentalresponses of these columns It should be noted that Lehmanrsquoscolumn 415 has 119871eff119889 = 10 and Moyer and Kowalskyrsquoscolumn 1 has 119871eff119889 = 4 The detailed discussion of thenumerical model validation is available in [25] It shouldbe noted that the maximum drift capacity in this paperis considered as the point where the force-displacementresponse of the column starts softening and losing strengthIt is found that the maximum drift capacity of both columnsat uncorroded state is about 6

The buckling lengths of corroded vertical reinforcementare calculated using the methodology described in Section 4The corrosion of horizontal ties is considered in the bucklinglength calculation As discussed previously (Section 4) thebuckling length of the vertical bars is a function of thetie reinforcementrsquos stiffness and the vertical reinforcementrsquosflexural rigidity Corrosion results in a reduction in flexuralrigidity of vertical barsTherefore the required stiffness fromtie reinforcement to restrain vertical bars against bucklingis reduced However corrosion also reduces the stiffness ofthe tie reinforcement For example in Moyer and Kowalskyrsquoscolumn the vertical reinforcement buckled between two tiesIn this case it was found that corrosion did not affect thebuckling length

In Lehmanrsquos column 415 the vertical reinforcementbuckled over five ties However once the corrosion levelexceeds 10 the buckling length reduced and the verticalreinforcement buckled over four ties It should be notedthat although the buckling length is reduced 119871eff119889

1015840 is notnecessarily reduced where 119871eff is the buckling length and 1198891015840is the diameter of the corroded vertical reinforcement Thisis because corrosion also reduces the diameter of verticalbars This change in buckling length is related to the relativecorrosion level and stiffness between the vertical and tiereinforcement

In practice the horizontal tie reinforcement is closer thanthe main vertical reinforcement to the surface of concreteTherefore it might start corroding earlier than verticalreinforcementThis phenomenonmight have an effect on thebuckling length and confined concrete behaviour Howeverthere has not been any research to date to explore thecorrelation between the corrosion levels of the horizontaltie and vertical reinforcement This is an area for futureresearch and therefore in this research in the absence of anyexperimentalfield data the same corrosion is considered forboth vertical and tie reinforcement

It should be noted that the calculation of the time tocorrosion initiation and time-dependent corrosion propaga-tion is out of the scope of this paper There are mathematicalmodels available in the literature that enable an estimationof the time to corrosion initiation and propagation basedon the environmental conditions [55 56] The corrosion ratecan also be measured on site by electrical equipment whichcan then be turned into a mass loss ratio using Faradayrsquoslaw of electrolysis [57] Given that the focus of this paperis on the impact of different mass loss ratios on the seismicperformance of RC columns the corrosion level is modelledby percentage mass loss throughout this paper

61 Scenario (a) Column Nonlinear Behaviour When Cor-rosion Is Assumed Present in Vertical and Horizontal TieReinforcement Only In this scenario it is assumed that thecorrosion damage is only limited to the steel reinforcement(vertical and horizontal tie reinforcement) that is cover con-crete is uncracked and corrosion of confining reinforcementdoes not affect the confined concrete behaviour Here thesteel model described in Section 51 is used which includesthe impact of corrosion on the buckling and postbucklingbehaviour in compression and strength and ductility loss intension

Figure 9 shows the results of monotonic pushover anal-yses Figure 9(a) shows that the failure mode of Lehmanrsquoscolumn 415 is by vertical bar buckling and core confined

Advances in Materials Science and Engineering 9

0 001 002 003 004 005 006 007 0080

50100150200250300350

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

Drift ratio

Late

ral f

orce

(kN

)

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

Drift ratio

Late

ral f

orce

(kN

)

(b)

Figure 9 Pushover analyses considering corrosion induced damage in reinforcing steel (a) Lehmanrsquos column 415 (b) Moyer and Kowalskyrsquoscolumn 1

concrete crushing up to 10 mass loss However as the cor-rosion level increases beyond 10mass loss the failure modechanges from vertical bar bucking and concrete crushing incompression to fracture of the vertical bars in tension

Figure 9(b) shows that Moyer and Kowalskyrsquos column1 has also failed in bar buckling and concrete crushing incompression However because 119871eff119889 = 4 the strength lossis not as significant as that of Lehmanrsquos column 415 with119871eff119889 = 10 under monotonic loading The corrosion levelup to 20 mass loss changes Moyer and Kowalskyrsquos column1 behaviour The failure initiates with bar buckling andconcrete crushing in compression and followed by fracture ofthe vertical reinforcement in tension With corrosion levelsgreater than 20 mass loss failure is by premature fractureof the vertical bars in tension At this point a cascade of barfracture can be seen in the graphs up to complete collapse ofthe columns

Figures 10(a) and 10(b) show Lehmanrsquos column 415 with10 and 20 mass losses under cyclic loading respectivelyComparing the monotonic and cyclic responses (the samecyclic load protocol as the experiment) shows that low-cyclefatigue has a significant impact on the column responseThe monotonic analysis showed that 10 mass loss did notresult in vertical bar fracture in tension and the failure wasgoverned by bar buckling and concrete crushing However incyclic analysis the failuremode is combined bar buckling andconcrete crushing in compression (failure initiation) followedby bar fracture in tension due to low-cycle fatigue

Here we have a system that does not technically fail incrushing and buckling but survives a little longer until thenext cycle when the vertical reinforcement fails in tensionIt was found that a mass loss ratio greater than 10 has asignificant impact on the nonlinear response of the corrodedcolumn due to reduced low-cycle fatigue life Figure 10(b)shows that at 20 mass loss resulted in bar fracture at 005drift ratio in pushover analysis but it resulted in bar fractureat 003 drift ratio under cyclic loading due to low-cycle fatiguefailure

Figures 10(c) and 10(d) show a similar result for Moyerand Kowalskyrsquos column 1 Overall Moyer and Kowalskyrsquoscolumn 1 has slightly less pinched cyclic responseThis is dueto the influence of the buckling length of the vertical bars andits cyclic degradation due to buckling [25]

62 Scenario (b) Column Nonlinear Behaviour When Corro-sion Is Assumed Present in Vertical and Horizontal Tie Rein-forcement and Cover Concrete Is Cracked In this scenarioit is assumed that the reinforcing steel (vertical and tie) iscorroded and the cover concrete is cracked due to corrosionof vertical reinforcementThe results of the pushover analysesare shown in Figure 11 The results in this case are almostidentical to the previous case (Section 61) where the damagein cover concrete was not considered Therefore in canbe concluded that whether or not we seek to model thecorrosion induced cracking of cover concrete it does not havea significant impact on the nonlinear response of corrodedcolumns Further discussion and comparison of this scenariowith other damage scenarios are available in Section 63

63 Scenario (c) Column Seismic Behaviour When Cor-rosion Is Assumed Present in Vertical and Horizontal TieReinforcement and Both Cover and Confined Concrete AreDamaged In this scenario it is assumed that the reinforc-ing steel (vertical and tie) is corroded cover concrete iscracked and the core confined concrete is affected by thecorrosion of horizontal tie reinforcement (as described inSection 53) Figure 12(a) shows the results of monotonicpushover analyses of Lehmanrsquos column 415 The results showthat the failure mechanism of this column for up to 10mass loss is bar buckling and core confined concrete crushingin compression However for corrosion levels beyond 10the failure mode changes This is a loss of drift capacitywhich starts with bar buckling and concrete crushing incompression and it is followed by bar fracture in tensionThese analyses demonstrate the importance of modelling the

10 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

Drift ratio

Late

ral f

orce

(kN

)

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

Drift ratio

Late

ral f

orce

(kN

)

(b)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

(c)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

(d)

Figure 10 Cyclic analyses considering corrosion induced damage in reinforcing steel (a) and (b) Lehmanrsquos column 415 (c) and (d) Moyerand Kowalskyrsquos column 1

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(b)

Figure 11 Pushover analyses considering corrosion induced damage in reinforcing steel and cracked cover concrete (a) Lehmanrsquos column415 (b) Moyer and Kowalskyrsquos column 1

Advances in Materials Science and Engineering 11

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(b)

Figure 12 Pushover analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a)Lehmanrsquos column 415 (b) Moyer and Kowalskyrsquos column 1

influence of corrosion on the confined concrete (throughloss of confining tie reinforcement) This corrosion damageon the confined concrete results in a rapid reduction instrength and ductility of the corroded columns compared tothe previous cases where confined concrete was considered tobe undamaged

Figure 12(b) shows the results of pushover analyses ofMoyer andKowalskyrsquos column 1 In this case the failuremodewas mainly bar buckling and concrete crushing followed byfracture of bars in tension for up to 20 mass loss Howevercorrosion levels beyond 20 mass loss have changed thefailure mode to premature fracture of bars in tension Thisdifference between the behaviour of the two columns is due tothe buckling behaviour of the vertical bars Given that Moyerand Kowalskyrsquos column 1 has much smaller buckling lengththe strength degradation in compression is much smallerthan Lehmanrsquos column 415 Therefore corrosion has more asignificant impact in terms of ductility loss of bars in tensionwhereas in Lehmanrsquos column 415 failure initiates with severebar buckling and concrete crushing then it is followed byfracture of vertical bars in tension

Figure 13 shows the results of cyclic analysis It showsthe cyclic analyses of Lehmanrsquos column 415 and Moyer andKowalskyrsquos column 1 with 10 and 20 mass loss togetherwith the corresponding pushover envelopes Figure 13 showsthat the extent of corrosion damage under cyclic loadingis more severe than monotonic loading The results ofmonotonic analysis showed that considering the ductility lossof corroded bars in tension and confinement reinforcementin compression has a big impact on bar buckling andfracture of reinforcement However cyclic analysis resultsshow that considering cyclic degradation due to low-cyclefatigue is crucial to have a realistic evaluation of the seismicperformance of existing corroded columns

For example in Figures 13(a) and 13(b) the failure ofLehmanrsquos column 415 was governed by bar buckling andconcrete crushing for a corrosion level up to 10 undermonotonic loadingHowever the same corrosion level results

in a much more severe drift capacity loss under cyclicloading due to a reduced low-cycle fatigue life Similarly inFigures 13(c) and 13(d) the failure of Moyer and Kowalskyrsquoscolumn was governed by concrete crushing in compressionfollowed by bar fracture in tension However low-cyclefatigue degradation due to cyclic loading results in prematurefracture of bars and subsequently severe loss of drift capacity

7 Comparison of the NonlinearResponses of Corroded Columns Computedin Different Scenarios

In order to clearly demonstrate the significance of corrosionmodels on the inelastic response of RC columns a com-parison between the computed responses of two columnswith different scenarios has been made The responses ofcolumns with 20 mass loss in monotonic pushover andcyclic analyses are compared and shown in Figure 14

Figure 14 shows the monotonic pushover and cyclicresponses of Lehmanrsquos column 415 andMoyer and Kowalskyrsquoscolumn 1 with 20 mass losses and different corrosiondamage models Figures 14(a) and 14(b) show that if thecorrosion induced damage to confined concrete is ignoredthe predicted failure mode is likely to be the fracture of barsin tension due to their reduced ductility However if thecorrosion induced damage to confined concrete is addedFigure 14(a) shows that the failure mode of Lehmanrsquos column415 will change to concrete crushing and buckling of thevertical bars in compression

Figure 14(b) shows that the failure mode of Moyer andKowalskyrsquos column 1 initiates with concrete crushing andbuckling of bars in compression and then it is followedby fracture of bars in tension This difference in failuremechanism is due to the differences in confinement level thebuckling length of the vertical bars the ratio of longitudinalreinforcement and the axial force ratio on the columnThere-fore in order to predict the nonlinear response accurately adetailed finite element model is required

12 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(d)

Figure 13 Cyclic analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a) and(b) Lehmanrsquos column 415 (c) and (d) Moyer and Kowalskyrsquos column 1

It is found that the failure mode under cyclic loading ismainly governed by the fracture of horizontal bars in tensiondue to reduced low-cycle fatigue life (Figures 14(c) and 14(d))This is a very important finding as it suggests that nonlinearquasistatic pushover analysis on its own is not adequate forperformance assessment of existing corroded bridge piers

With reference to Figure 14 it is evident that consideringthe impact of the corrosion damage on core confined con-crete and low-cycle fatigue degradation is crucial Thereforethey need to be considered when modelling the nonlinearbehaviour of corrosion damaged RC bridge piers underseismic loading This finding is in good agreement with theobserved experimental results by other researchers [12ndash1458]

A series of experimental studies were conducted in [12]on the cyclic behaviour of large-scale corroded cantilever RCbeams Ou et al found that as the level of corrosion increasesthe flexural failure initiates with premature buckling oflongitudinal bars This conclusion is in good agreement withthe numerical results discussed in this paper In another study[13] a series of experimental studies were conducted on cyclicbehaviour of corroded RC columns with varied axial forceMa et al have reported that once the corrosion level increases

beyond about 14 rapid strength and ductility reductionand cyclic degradation in hysteretic loops are seen due toreduced low-cycle fatigue life and premature buckling ofvertical reinforcement This conclusion is in good agreementwith the predicted failure modes using the numerical modelpresented in this paper

The detailed finite element model developed in thispaper can accurately model the nonlinear behaviour ofcorrodedRCcolumns subject to cyclic loading up to completecollapse There is a need to extend the PEER-UW columndatabase to include corroded RC columns so that furthercalibrationvalidation of the material model parameters canbe performed However the modelling technique developedin this paper is able to simulate the multiple failure modesof corroded RC columns simultaneously It represents thecurrent state of the art and as such they provide a novel com-putational framework for the seismic response prediction ofcorroded RC bridges

8 Conclusions

A series of pushover and cyclic analyses on two hypotheticalcorroded RC columns are conducted and these are used

Advances in Materials Science and Engineering 13

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(d)

Figure 14 Comparison of the computed responses of columns with different deterioration models (a) and (c) Lehmanrsquos column 415 undermonotonic and cyclic loading (b) and (d) Moyer and Kowalskyrsquos column 1 under monotonic and cyclic loading

to explore the performance of the proposed computationalframework The impact of corrosion on (i) the verticalreinforcing steel (ii) the tieconfinement (iii) the cover(unconfined) concrete and (iv) the core (confined) concreteis represented through new material models The proposednew steel material model accounts for (i) inelastic nonlinearbuckling of the vertical reinforcement (ii) the corrosion lossof area (iii) the nonuniform corrosion pitting and (iv) low-cycle high amplitude fatigueThenew cover concretematerialmodel includes the influence of internal pressure due tothe build-up of corrosion products (using compression fieldtheory) The new core concrete model includes the influenceof corrosion induced loss of confining reinforcement

The main outcomes of this study can be summarised asfollows

(1) Corrosion has a more significant impact on theductility loss (drift capacity) of RC columns than thestrength loss (plastic moment capacity)

(2) The numerical model developed in this paper is ableto predict the nonlinear flexural response of corrodedRC columns up to complete collapse Results showwhich depends on a cyclic load history that flexuralfailure can be initiated by the buckling of vertical bars

and crushing of core concrete which is then followedby fracture of bars in tension In cases where thebuckling of bars is not an issue or the buckling lengthis too short (119871eff119889

1015840le 5) the failure is governed by the

fracture of the vertical bars in tension due to low-cyclehigh amplitude fatigue

(3) The analyses results show that for the seismic perfor-mance and evaluation of existing corroded bridgesmonotonic pushover analysis is not sufficient Thecyclic degradation due to low-cycle high amplitudefatigue has a significant influence on the response ofcorroded RC columns

(4) The results of this study show that it is inadequate toassume that corrosion only affects the main verticalreinforcement in the column It was found that theconfined concrete with corroded confinement rein-forcement starts crushing much faster than uncor-roded undamaged concrete This changes the failuremode and results in premature buckling of the ver-tical reinforcement This change in the failure modecannot be predicted if the damage in core confinedconcrete due to corrosion of tie reinforcement isignored This is in good agreement with observed

14 Advances in Materials Science and Engineering

experimental results reported by other researchers[12ndash14]

(5) The modelling technique developed in this paper hassignificantly improved the earlier models and canbe used by other researchers in the future researchfor seismic vulnerability and fragility analysis ofcorroded RC bridges

Disclosure

Any findings opinions and recommendations provided inthis paper are only based on the authorsrsquo view

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This research is conducted in collaboration with the Univer-sity of Bristol and the University of Washington while thefirst author was on sabbatical leave in the US The fundingprovided by the World Wide University Network throughthe Research Mobility Program to the first author was muchappreciated The authors would like to thank Professor MarcO Eberhard and Professor John F Stanton for providingvaluable guidance during the course of this research

References

[1] S Hida F I S Ibrahim H A Capers et al ldquoAssuringbridge safety and serviceability in Europerdquo Tech Rep FHWA-PL-10-014 Office of International Programs Federal HighwayAdministration US Department of Transportation AmericanAssociation of State Highway and Transportation Officials2010

[2] ASCE Failure to Act The Economic Impact of Current Invest-ment Trends in Surface Transportation Infrastructure EconomicDevelopment Research Group Inc ASCE 2011

[3] D-E Choe P Gardoni D Rosowsky and T Haukaas ldquoProb-abilistic capacity models and seismic fragility estimates forRC columns subject to corrosionrdquo Reliability Engineering andSystem Safety vol 93 no 3 pp 383ndash393 2008

[4] L Berto R Vitaliani A Saetta and P Simioni ldquoSeismicassessment of existing RC structures affected by degradationphenomenardquo Structural Safety vol 31 no 4 pp 284ndash297 2009

[5] J Ghosh and J E Padgett ldquoAging considerations in the devel-opment of time-dependent seismic fragility curvesrdquo Journal ofStructural Engineering vol 136 no 12 pp 1497ndash1511 2010

[6] A Alipour B Shafei and M Shinozuka ldquoPerformance evalu-ation of deteriorating highway bridges located in high seismicareasrdquo Journal of Bridge Engineering vol 16 no 5 pp 597ndash6112011

[7] F Biondini E Camnasio and A Palermo ldquoLifetime seismicperformance of concrete bridges exposed to corrosionrdquo Struc-ture and Infrastructure Engineering vol 10 no 7 pp 880ndash9002014

[8] M Akiyama D M Frangopol and H Matsuzaki ldquoLife-cyclereliability of RC bridge piers under seismic and airborne chlo-ride hazardsrdquo Earthquake Engineering and Structural Dynamicsvol 40 no 15 pp 1671ndash1687 2011

[9] F Biondini A Palermo and G Toniolo ldquoSeismic performanceof concrete structures exposed to corrosion case studies of low-rise precast buildingsrdquo Structure and Infrastructure Engineeringvol 7 no 1-2 pp 109ndash119 2011

[10] C K Chiu F J Tu and F P Hsiao ldquoLifetime seismic perfor-mance assessment for chloride-corroded reinforced concretebuildingsrdquo Structure and Infrastructure Engineering vol 11 no3 pp 345ndash362 2015

[11] M Sanchez-Silva G-A Klutke and D V Rosowsky ldquoLife-cycleperformance of structures subject to multiple deteriorationmechanismsrdquo Structural Safety vol 33 no 3 pp 206ndash217 2011

[12] Y-C Ou L-L Tsai and H-H Chen ldquoCyclic performance oflarge-scale corroded reinforced concrete beamsrdquo EarthquakeEngineering and StructuralDynamics vol 41 no 4 pp 593ndash6042012

[13] Y Ma Y Che and J Gong ldquoBehavior of corrosion damagedcircular reinforced concrete columns under cyclic loadingrdquoConstruction and Building Materials vol 29 pp 548ndash556 2012

[14] A Meda S Mostosi Z Rinaldi and P Riva ldquoExperimentalevaluation of the corrosion influence on the cyclic behaviour ofRC columnsrdquo Engineering Structures vol 76 pp 112ndash123 2014

[15] A A Almusallam ldquoEffect of degree of corrosion on theproperties of reinforcing steel barsrdquo Construction and BuildingMaterials vol 15 no 8 pp 361ndash368 2001

[16] Y G Du L A Clark and A H C Chan ldquoResidual capacity ofcorroded reinforcing barsrdquoMagazine of Concrete Research vol57 no 3 pp 135ndash147 2005

[17] Y G Du L A Clarkt and A H C Chan ldquoEffect of corrosionon ductility of reinforcing barsrdquoMagazine of Concrete Researchvol 57 no 7 pp 407ndash419 2005

[18] J Cairns G A Plizzari Y Du D W Law and C FranzonildquoMechanical properties of corrosion-damaged reinforcementrdquoACI Materials Journal vol 102 no 4 pp 256ndash264 2005

[19] C A ApostolopoulosM P Papadopoulos and S G PantelakisldquoTensile behavior of corroded reinforcing steel bars BSt 500srdquoConstruction and Building Materials vol 20 no 9 pp 782ndash7892006

[20] C A Apostolopoulos ldquoMechanical behavior of corroded rein-forcing steel bars S500s tempcore under low cycle fatiguerdquoConstruction andBuildingMaterials vol 21 no 7 pp 1447ndash14562007

[21] M M Kashani A J Crewe and N A Alexander ldquoNonlinearstress-strain behaviour of corrosion-damaged reinforcing barsincluding inelastic bucklingrdquo Engineering Structures vol 48 pp417ndash429 2013

[22] M M Kashani A J Crewe and N A Alexander ldquoNonlinearcyclic response of corrosion-damaged reinforcing bars with theeffect of bucklingrdquo Construction and Building Materials vol 41pp 388ndash400 2013

[23] M M Kashani A J Crewe and N A Alexander ldquoUse of a 3Doptical measurement technique for stochastic corrosion patternanalysis of reinforcing bars subjected to accelerated corrosionrdquoCorrosion Science vol 73 pp 208ndash221 2013

[24] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoFinite element investigation of the influence of corrosionpattern on inelastic buckling and cyclic response of corrodedreinforcing barsrdquo Engineering Structures vol 75 pp 113ndash1252014

Advances in Materials Science and Engineering 15

[25] M M Kashani Seismic performance of corroded rc bridge piersdevelopment of a multi-mechanical nonlinear fibre beam-columnmodel [PhD thesis] University of Bristol Bristol UK 2014

[26] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part I Formula-tionrdquo Earthquake Engineering and Structural Dynamics vol 25no 7 pp 711ndash725 1996

[27] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part II Applica-tionsrdquoEarthquake Engineering and Structural Dynamics vol 25no 7 pp 727ndash742 1996

[28] The Open System for Earthquake Engineering Simulation(OpenSees) Pacific Earthquake Engineering Research CentreUniversity of California Berkeley Berkeley Calif USA 2011

[29] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoPhenomenological hysteretic model for corroded reinforcingbars including inelastic buckling and low-cycle fatigue degrada-tionrdquo Computers and Structures vol 156 article 5393 pp 58ndash712015

[30] J Coleman and E Spacone ldquoLocalization issues in force-basedframe elementsrdquo Journal of Structural Engineering vol 127 no11 pp 1257ndash1265 2001

[31] J S Pugh Numerical simulation of walls and seismic designrecommendations for walled buildings [PhD thesis] Universityof Washington Seattle Wash USA 2012

[32] D V Val and R E Melchers ldquoReliability of deteriorating RCslab bridgesrdquo Journal of Structural Engineering vol 123 no 12pp 1638ndash1644 1997

[33] M S Darmawan and M G Stewart ldquoEffect of pitting corro-sion on capacity of prestressing wiresrdquo Magazine of ConcreteResearch vol 59 no 2 pp 131ndash139 2007

[34] R P Dhakal and K Maekawa ldquoReinforcement stability andfracture of cover concrete in reinforced concrete membersrdquoJournal of Structural Engineering vol 128 no 10 pp 1253ndash12622002

[35] C Lee J F Bonacci M D A Thomas et al ldquoAcceleratedcorrosion and repair of reinforced concrete columns usingcarbon fibre reinforced polymer sheetsrdquo Canadian Journal ofCivil Engineering vol 27 no 5 pp 941ndash948 2000

[36] W Aquino Long-term performance of seismically rehabilitatedcorrosion-damaged columns [PhD thesis] University of Illinoisat Urbana-Champaign Champaign Ill USA 2002

[37] S Timoshenko and J Gere Theory of Elastic StabilityMacGraw-Hill New York NY USA 1963

[38] S J Pantazopoulou ldquoDetailing for reinforcement stability in RCmembersrdquo Journal of Structural Engineering vol 124 no 6 pp623ndash632 1998

[39] J B Mander M J N Priestley and R Park ldquoObserved stress-strain behavior of confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1827ndash1849 1988

[40] J B Mander M J Priestley and R Park ldquoTheoretical stress-strain model for confined concreterdquo Journal of Structural Engi-neering (United States) vol 114 no 8 pp 1804ndash1826 1988

[41] S Popovics ldquoAnumerical approach to the complete stress-straincurve of concreterdquo Cement and Concrete Research vol 3 no 5pp 583ndash599 1973

[42] I D Karsan and J O Jirsa ldquoBehavior of concrete undercompressive loadingrdquo Journal of Structural Division vol 95article ST12 1969

[43] M P Berry andMO Eberhard ldquoPerformancemodeling strate-gies for modern reinforced concrete bridge columnsrdquo PEER

Research Report University of California Berkeley BerkeleyCalif USA 2006

[44] B D Scott R Park and M J N Priestley ldquoStress-strainbehavior of concrete confined by overlapping hoops at low andhigh strain ratesrdquo Journal of the American Concrete Institute vol79 no 1 pp 13ndash27 1982

[45] A S Al-Harthy M G Stewart and J Mullard ldquoConcrete covercracking caused by steel reinforcement corrosionrdquoMagazine ofConcrete Research vol 63 no 9 pp 655ndash667 2011

[46] T Vidal A Castel and R Francois ldquoAnalyzing crack width topredict corrosion in reinforced concreterdquo Cement and ConcreteResearch vol 34 no 1 pp 165ndash174 2004

[47] F J Molina C Alonso and C Andrade ldquoCover cracking as afunction of rebar corrosion part 2-numerical modelrdquoMaterialsand Structures vol 26 no 9 pp 532ndash548 1993

[48] F J Vecchio and M P Collins ldquoThe modified compression-field theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[49] D Coronelli and P Gambarova ldquoStructural assessment ofcorroded reinforced concrete beams modeling guidelinesrdquoJournal of Structural Engineering vol 130 no 8 pp 1214ndash12242004

[50] D E Lehman and J P Moehle ldquoSeismic performance of well-confined concrete columnsrdquo PEER Research Report Universityof California at Berkeley 2000

[51] L N Lowes and A Altoontash ldquoModeling reinforced-concretebeam-column joints subjected to cyclic loadingrdquo Journal ofStructural Engineering vol 129 no 12 pp 1686ndash1697 2003

[52] M Berry M Parrish and M Eberhard ldquoPerformance databaseUserrsquos manualrdquo in Pacific Earthquake Engineering ResearchCentre 2004 University of California at Berkeley 2004httpwwwcewashingtonedusimpeera1

[53] A N Kallias and M Imran Rafiq ldquoFinite element investigationof the structural response of corroded RC beamsrdquo EngineeringStructures vol 32 no 9 pp 2984ndash2994 2010

[54] M J Moyer and M J Kowalsky ldquoInfluence of tension strain onbuckling of reinforcement in concrete columnsrdquo ACI StructuralJournal vol 100 no 1 pp 75ndash85 2003

[55] K A T Vu andM G Stewart ldquoStructural reliability of concretebridges including improved chloride-induced corrosion mod-elsrdquo Structural Safety vol 22 no 4 pp 313ndash333 2000

[56] D V Val ldquoFactors affecting life-cycle cost analysis of RCstructures in chloride contaminated environmentsrdquo Journal ofInfrastructure Systems vol 13 no 2 pp 135ndash143 2007

[57] J P BroomfieldCorrosion of Steel in Concrete Taylor amp FrancisLondon UK 2nd edition 2007

[58] M M Kashani P Alagheband R Khan and S Davis ldquoImpactof corrosion on low-cycle fatigue degradation of reinforcingbars with the effect of inelastic bucklingrdquo International Journalof Fatigue vol 77 pp 174ndash185 2015

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

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MetallurgyJournal of

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BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

2 Advances in Materials Science and Engineering

reinforcement corrosion on the nonlinear behaviour andresponse of RC bridges subject to seismic loading throughnonlinear fibre-based finite element analysis [26ndash28]

However they have used very simple uniaxial materialmodels to model the impact of corrosion on the stress-strainbehaviour of reinforcing steel In most cases the corrosiondamage has only been limited to the reinforcing steel byconsidering an average reduced area andor reduced yieldstrength Furthermore the impact of corrosion on ductilityloss reduced low-cycle fatigue life and inelastic bucklingof vertical reinforcement and corrosion induced damage tocover and core confined concrete are ignored In other wordsthe extent of corrosion damage on RC bridges has beenunderestimated in previous studies

Based on the previous research by Kashani et al [23ndash25] it is evident that the impact of corrosion on inelasticbuckling cyclic behaviour and low-cycle fatigue degradationof reinforcing bars must be included in modelling corrodedRC columns As a result of earlier research by Kashani et al[23ndash25] they developed a new phenomenological model forcorroded reinforcing bars [29] and is used in this paper formodelling

Prior to the development of the material models devel-oped in [25 29] it was impossible to investigate the combinedeffect of corrosion damage inelastic buckling and low-cyclehigh amplitude fatigue degradation on nonlinear flexuralresponse of corroded RC columns Therefore there is asignificant paucity of modelling techniques and guidelines inthe literature which is addressed in this paper

The aim of this numerical exploration study provided inthis paper is to discover the impact of different corrosiondamage models on the nonlinear flexural response of cor-roded RC columnsThis paper provides comprehensivemod-elling guidelines to model the nonlinear behaviour of cor-rodedRCbridge piers including the cyclic degradation effectsup to complete collapse The results of this study highlightwhat damage mechanisms are important to be consideredin modelling nonlinear behaviour of corroded RC columnsMoreover the proposed model is able to capture multiplefailure modes of corroded RC columns simultaneously

To this end there is a need for a more detailed and accu-rate numerical model to represent the impact of corrosion on

(i) the vertical and horizontal tie reinforcement (includ-ing pitting effects buckling ductility loss and reduc-ed low-cycle fatigue life)

(ii) the cracked cover concrete (including reduced capac-ity) due to corrosion of vertical reinforcement incolumn

(iii) the confined concrete (including reduced capacityand ductility) due to corrosion of horizontal tie rein-forcement (also known as confinement reinforce-ment)

In this paper a numerical model is developed that enablessimulation of the nonlinear flexural response of RCcomponents with corroded reinforcement The modelemploys a force-based nonlinear fibre beam-column elementusing OpenSees The uniaxial material model for corroded

reinforcing steel that is developed in [29] is used This modelsimulates the stress-strain behaviour of reinforcing steel withthe effect of inelastic buckling and low-cycle high amplitudefatigue degradation under cyclic loading The basic bucklingmodel of reinforcing steel is validated through comparisonof simulated and observed experimental responses of RCcolumns with uncorroded reinforcement [25]

The cover concrete strength is adjusted to account forcorrosion induced cracking of the cover concrete whilethe strength and ductility of the core confined concreteare adjusted to account for corrosion induced damage tohorizontal tie reinforcementThemodel is used to explore theimpact of corrosion on the nonlinear response of RC columnsunder monotonic and cyclic loading

The analysis results show that the proposed model in thispaper is able to simulate multiple failure modes of corrodedcolumns simultaneously Therefore it is evident that theoutcome of this research has made a significant improvementto the existing numerical models This model provides anopen source computational platform for seismic vulnerabilityassessment (including fragility analysis) of corroded RCbridges

2 The Proposed Nonlinear FibreBeam-Column Element Model

The force-based nonlinear fibre beam-column element withGauss-Lobatto integration scheme (available in OpenSees) isused here (Figure 1(a)) To avoid any localisation effects [3031] due to the softening behaviour of vertical reinforcementin the postbuckling region the column is modelled using twoforce-based elements The first element has three integrationpoints and the second element has five integration pointsThelength of the first element is taken to be 6119871eff where 119871eff isthe calculated buckling length of the vertical reinforcement(Figure 1(a)) which is discussed in Section 4 This allowscontrol of the position of the first integration point which isset equal to the buckling length of the vertical reinforcementthat is used to define the material model of the reinforcingbars It should be noted that the new uniaxial materialmodel developed by [29] is used here to model the stress-strain behaviour of the vertical reinforcing bars This modelaccounts for the combined impact of geometrical nonlin-earity due to inelastic buckling and material nonlinearity aswell as low-cycle high amplitude fatigue degradation andcorrosion damage in a single-material model Further detailsare available in Sections 51 and 52

To model the slippage of the vertical reinforcement at thecolumn-foundation interface a zero-length section elementis used at the base The detailed discussion and validation ofthe proposed modelling methodology are available in [25]Therefore only the relevant uniaxial material models to beused in the fibre section are discussed here Figure 1(b)also shows the fibre section assigned to the proposed beam-column element The relevant sections discussing the mate-rial models are also noted in Figure 1(b)

The implementation of the corrosion damagemodels thatare developed by [21ndash25 29] into the OpenSees abstract

Advances in Materials Science and Engineering 3

Zero-lengthsection element

Element 13 integration points

Element 25 integration points

1

2

3

4

Col

umn

heig

ht (L

)

Bar-slipsection

Element section

L2 = L minus L1

L1 = 6Leff

(a)

(ii) Unconfined cover concrete modelmdashSection 54

(iii) Reinforcing steel model including inelastic buckling and damage modelsmdashSections 51and 52

(iv) Buckling length calculationmdashSection 4

(i) Confined concrete modelmdashSection 53

Pitting corrosionmodels are discussed in Section 3

(b)

Figure 1 Proposed finite element model (a) force-based nonlinear beam-column arrangement (b) fibre section

Section force deformationnD materialUniaxial material

Material

Fibre section (2D 3D)SteelConcreteBar-slip

Corroded steel with buckling

Corrosion damaged confined concrete

Corrosion damaged cover concrete

Modified steel02 for bar-slip

Damage model

FatigueMax strain Pitting corrosion model

Figure 2 Implementation of the corrosion models within the OpenSees abstract classes

classes is shown in Figure 2 The calculation of bucklinglength of the corroded vertical reinforcement uniaxial mate-rial models and corrosion damage models is discussed inSections 3ndash5

3 Influence of Corrosion on GeometricalProperties of Corroded Bars

The chloride induced corrosion results in irregular loss ofcross section of reinforcing steel known as pitting corrosion

Several researchers studied the impact of nonuniform corro-sion on cross section loss of reinforcing bars [23 32 33] In[23] a 3D optical measurement of corroded bars was con-ducted to explore the spatial variability of the corrosion pat-tern As a result Kashani et al developed a set of probabilisticdistribution models to predict the geometrical properties ofcorroded bars They found that the geometrical propertiesof corroded bars can be modelled using a lognormal dis-tribution In this study the mean values of the lognormaldistribution models are used to account for the effect ofpitting corrosion on the geometrical properties of corroded

4 Advances in Materials Science and Engineering

Corrodedreinforcement

FracturingPlastic hinge regionzone

Buckling ofcorroded reinforcement

Idealised beam on springbuckling model

Corrosion induced damage

to the column section

Corrosion induced crackin cover concrete

Kt

s

F

Lef

f=

ns

Figure 3 Schematic overview of corrosion induced damage to RC column

bars In this study the proposed models that developed in[23] are used to model the impact of pitting corrosion ongeometrical properties of corroded bars

4 Calculation of the BucklingLength considering the Stiffness ofTie Reinforcement

The detailed discussion and validation of the Dhakal-Maekawa buckling model are available in [25 34] The samemethodology is used here for calculation of the bucklinglength of corroded vertical reinforcement

Figure 3 shows a schematic overview of the extent ofcorrosion damage on a hypothetical RC columnThe damageat section level shown in Figure 3 is based on the observedexperimental tests by [35 36] The corrosion of verticalreinforcement results in longitudinal cracks at the surface ofthe columnparallel to vertical reinforcementThiswill reducethe cross-sectional area and flexural rigidity of the verticalreinforcement which are very important in buckling Corro-sion of horizontal tie reinforcement reduces the volumetricratio of confinement reinforcement which is very importantin providing confinement for core concrete Furthermorethis will result in splitting the core and cover concrete bycreation of horizontal cracks around the perimeter of thecolumn sectionMoreover horizontal ties restrain the verticalbars against buckling and corrosion results in a reduction in

stiffness of these ties Therefore these parameters need to beconsidered in calculation of the buckling length

To account for the effect of corrosion on Dhakal-Maekawa equations the flexural rigidity of the vertical rein-forcement (119864119868) and stiffness of horizontal tie reinforcement(119870119905) are adjusted This is discussed in Sections 41 and 42

41 Influence of Corrosion on Flexural Rigidity of CorrodedBars Thebuckling of reinforcing bars is an inelastic bucklingphenomenon and therefore the elastic flexural rigidity 119864

119904119868

is no longer valid [37] Reference [34] suggested an averageflexural rigidity in which it has been validated against anextensive set of experimental data for uncorroded columnsThis has beenmodified for corroded reinforcement (1198641198681015840) anddefined as

1198641198681015840=1198641199041198681015840

min2

radic1205901015840

119910

400

(1)

where 119864119904and 1205901015840119910are the elastic modulus and yield strength of

the corroded vertical reinforcement inMPa respectively and1198681015840

min is the secondmoment of area of corroded reinforcementThe detailed calculation of 1198681015840min is available in [23]

Corrosion of reinforcing bars affects the second momentof area and yield strength of reinforcement but does nothave any influence on the elastic modulus The yield strength

Advances in Materials Science and Engineering 5

0 10 20 30 40 50 600

025

05

075

1

125

15

Tension envelopemdashuncorroded reinforcementTension envelopemdashcorroded reinforcement

120578=120590120590

y

120585 = 120576120576y

(a)

minus40 minus35 minus30 minus25 minus20 minus15 minus10 minus5 0minus12

minus1

minus08

minus06

minus04

minus02

0

Buckling envelopemdashuncorroded reinforcementBuckling envelopemdashcorroded reinforcement

120578=120590120590

y

120585 = 120576120576y

(b)

Figure 4 Implemented tension and compression envelopes of corroded bars in OpenSees (20 mass loss)

can be modified based on the following empirical equationsuggested by [16]

1205901015840

119910= 120590119910(1 minus 0005120595) (2)

where 120595 is the percentage mass loss of the reinforcement

42 Influence of Corrosion on Stiffness of Tie ReinforcementIn this study the stiffness of the horizontal ties of spiralreinforcement is computed using the following empiricalequation suggested by [38]

119870119905=

4119864sp1198601015840

sp

radic(1199042 + 1198892119888)

(3)

where 119864sp is the elastic modulus 1198601015840sp is the cross-sectionalarea of corroded spiral reinforcement 119904 is the spiral pitch and119889119888is the core diameterThe focus of this paper is on circular columns However

in the case of rectangular section the axial stiffness of tiereinforcement can be computed using

119870119905=119864st1198601015840

st119897119905

(4)

where 119864st is the elastic modulus of tie reinforcement 1198601015840st isthe cross-sectional area of corroded tie reinforcement and 119897

119905

is the length of the rectangular tie reinforcement

5 Description of Uniaxial Material Modelsincluding Corrosion Damage

51 Reinforcing Steel Model Tension and CompressionEnvelopes The uniaxial material model developed by [29] isused to model the reinforcing steel This advanced materialmodel combines the material nonlinearity with geometricalnonlinearity due to inelastic buckling into a single-materialmodel The impact of geometrical nonlinearity on cyclicbehaviour of reinforcing bars is also considered Moreover

the cyclic degradation due to low-cycle fatigue and the impactof corrosion on the tension and compression envelopes(including the postbuckling behaviour) are included Furtherdiscussion about the model development is available in [29]To implement the buckling model in OpenSees the uniaxialHystereticmodel available in OpenSees is modified and used(the detailed discussion is available in [25]) Figure 4 showsour proposed tension and compression envelope curves ofcorroded bars implemented in OpenSees

52 Reinforcing Steel Model Cyclic Response and Low-CycleFatigue Degradation As explained in Section 51 the Hys-teretic material model in OpenSees is modified to define thereinforcing steel model The cyclic response of the Hystereticmodel is defined by two pinch parameters (pinch 119909 andpinch 119910) The pinching effect in the cyclic response ofreinforcing bars is affected by the stiffness of the horizontal tiereinforcementThe optimumvalues of pinch parameters havebeen obtained by a comprehensive parametric study reportedin [25] (the calibrated values are pinch 119909 = 04 and pinch119910 = 06)

The Uniaxial Fatigue model is wrapped to the steelmaterial model to model the low-cycle fatigue degradationof corroded vertical reinforcement The low-cycle fatiguematerial constants are modified to account for the impactof corrosion on the low-cycle fatigue life of corroded barsbased on the model developed by [29] Figure 5 shows anexample cyclic response of the implemented Hysteretic +Fatigue model for the uncorroded and corroded reinforcingsteel Further detailed discussion about modelling combinedfatigue and buckling of reinforcing bars inside RC columns isavailable in [29]

53 Corrosion Damaged Confined Concrete Model The com-pressive behaviour of confined concrete is a function ofvolumetric ratio yield strength and fracture strain of thehorizontal tie reinforcement (ie spiral hoop and transversereinforcement) [39 40] Since tie reinforcement is the nearestto the surface being exposed to chloride attack they may

6 Advances in Materials Science and Engineering

minus30 minus20 minus10 0 10 20 30minus15

minus1

minus05

0

05

1

15

Cyclic response including fatiguemdashuncorrodedCyclic response including fatiguemdashcorroded

120578=120590120590

y

120585 = 120576120576y

Figure 5 Cyclic response of the Hysteretic + Fatigue model inOpenSees (20 mass loss)

start corroding prior to the corrosion initiation of verticalreinforcement As a result the volumetric ratio of tie rein-forcement is decreased due to cross section loss There isalso a reduced yield strength and fracture strain due to thepitting effect Therefore the internal confinement pressureof the core concrete can result in premature fracture of tiereinforcement

To date there has not been any experimental study toquantify and model the effect of corrosion on the nonlinearbehaviour of confined concrete under monotonic compres-sion and cyclic loading Further research is required to under-stand and model the extent of corrosion damage on confinedconcrete behaviour However a simplified methodology isused in this research tomodify the confined concretematerialmodel (which is a function of the percentage mass loss inhorizontal tie reinforcement) to account for the effect ofcorrosion damage

In this study the uniaxial Concrete04 material modelavailable in OpenSees is used to model the concrete ThePopovics curve [41] is used for the compression envelope andthe Karsan-Jirsa model [42] is used to determine the slopeof the curve for unloading and reloading in compressionFor tensile loading an exponential curve is used to definethe envelope to the stress-strain curve Further details areavailable in [43]

The parameters proposed by [40] are used to modelthe effect of confinement on concrete in compression Themaximum compressive stress of the concrete (120590cc) and thestrain at the maximum compressive strain (120576cc) can becalculated using the equations developed in [40]

The maximum crushing strain of the confined concreteis defined by the fracture of the first horizontal tiespiralreinforcement Here the model proposed by [44] is used topredict the concrete crushing strain as defined in

120576cc = 0004 + 14 (120588sc120590119910tie120576119906tie

120590119888

) (5)

where 120576119906tie is the fracture strain of the tiespiral reinforce-

ment 120588sc is the volumetric ratio of spiral reinforcement and120590119910tie is the yield stress of spiral reinforcement

minus20 minus18 minus16 minus14 minus12 minus10 minus8 minus6 minus4 minus2 0minus15

minus125

minus1

minus075

minus05

minus025

0

Original confined concrete modelCorrosion damaged confined concrete

120574=120590120590

c

120595 = 120576120576c0

Figure 6 Corrosion damaged confined concrete model (20 massloss)

It is clear that the confined concrete model is a functionof yield strength volumetric ratio and fracture strain ofthe confinementtie reinforcement Therefore the previouslydefined equations for reinforcing steel can be used to modifythe cross-sectional area yield strength and fracture strain oftie reinforcement as a function of the percentage mass lossAccordingly these modified values can be used to accountfor the impact of corrosion on confined concrete model(Figure 6)

54 Corrosion Damaged Cracked Cover Concrete ModelOnce corrosion initiates the corrosion products accumulatearound the reinforcement Given the volume of the corrosionproducts is bigger than the original reinforcing steel it gener-ates a radial pressureexpansion on the concrete surroundingthe reinforcement This behaviour is like a thick cylinderunder internal pressure that eventually results in fracture ofthe cover concrete [45ndash47] The cracking of cover concreteresults in loss of compressive strength and crushing strainof the concrete in the compressive zone of RC sectionsTherefore consideration needs to be given to model theinfluence of this cracking on the response of cover concretein compression

The response of cracked concrete in compression isdescribed in detail by [48] which is known as compressionfield theory (CFT) Based onCFT the compressive strength ofcracked concrete in compression depends on the magnitudeof the average tensile strain in the transverse direction whichcauses longitudinal microcracks Reference [49] employedthis method in nonlinear finite element analysis of corrosiondamaged RC beams with modified constitutive model forthe cracked cover concrete as a function of percentagemass loss and validated this against experimental resultsTherefore the equations suggested by [49] are employedto model the compression response of crack cover con-crete Figure 7(a) shows the compression envelope and Fig-ure 7(b) shows the tension envelope of the uniaxial materialmodel for corrosion damaged unconfined cover concreteused in the fibre model Further details are available in[49]

Advances in Materials Science and Engineering 7

minus25 minus2 minus15 minus1 minus05 0minus1

minus075

minus05

minus025

0

Original unconfined concrete modelCorrosion induced crack unconfined concrete

120595 = 120576120576c0

120574=120590120590

c

(a)

0 1 2 3 4 5 6 70

005

01

015

02

Original concrete tension envelopeCorrosion induced cracked concrete

120574=120590120590

c

120595 = 120576120576ct

(b)

Figure 7 Corrosion damaged cracked cover concrete model for 20 mass loss (a) compression (b) tension

55 Bond-Slip Model and Zero-Length Element In seismicdesign of RC structures and bridges plastic hinges are formedat the columnbeam ends This will induce a substantialstrain penetration along the longitudinal bars into the jointthat eventually results in slippage of longitudinal bars Thisphenomenon has been observed by other researchers exper-imentally [50] Reference [51] adopted a bar-slip model forthe end slip of longitudinal reinforcement in beam-columnjoints This model has been employed by [25] to model thecyclic behaviour of RC columns and is validated against UW-PEER experimental RC column database [52]

Corrosion affects the reinforcing steel near the surface ofthe concrete due to diffusion of chloride ions from the surfaceandor carbonation of cover concrete In bridge piers thevertical reinforcement bars are anchored to the foundationwell below the foundation surface Therefore the verticalreinforcement does not corrode at this depth and the bar-slipbehaviour of bars at the anchorage zone remains the same asin the uncorroded column This has been observed by otherresearchers experimentally [12ndash14]

It should be pointed out that corrosion does affect thebond strength of corroded vertical reinforcement abovethe foundation level (internal bond-slip within the columnitself) However based on the observed experimental resultsthe reduced bond strength does not govern the failure ofcolumns References [12ndash14] reported that the failure ofcorroded columns and beams under cyclic loading is mainlygovern by fracture of bars in tension due to low-cycle fatigueand buckling of bars and crushing of confined concrete incompression

Reference [53] conducted a comprehensive detailed non-linear finite element analysis of corroded RC beams andvalidated them against experimental results They havereported that reduced bond strength only changes the crackpattern and affects the serviceability of corroded beamsTheyconcluded that reduced bond strength does not affect theultimate capacity of corroded beams Therefore bond-slip ofcorroded vertical bars within the element is not considered inthis research

The detailed discussion and implementation of the zero-length section in modelling the cyclic behaviour of RCcolumns is available in [25]

6 Impact of Corrosion Damage on NonlinearResponse of RC Bridges Piers

In this section the impact of different corrosion damagescenarios on the inelastic response of RC bridge piers isexplored A comparative study on two hypothetical corrodedRC columns with different buckling lengths of vertical barsis conducted The columns are taken from the UW-PEERexperimental RC column database [52] These columns areused to validate and calibrate the basic numerical model forthe uncorroded columns [25]

To investigate the impact of corrosion on drift capacityand strength loss of RC columns a series of nonlinearpushover analyses with varied corrosion levels are conductedTo explore the impact of cyclic degradation nonlinear cyclicanalyses using the load history that was used in the exper-iment are conducted In order to investigate the impact ofdifferent modelling techniques and damage mechanism foreach analysis type three scenarios are considered

(a) Vertical and horizontal tie reinforcement are cor-roded but cover and core concrete are not affected bycorrosion

(b) Vertical and horizontal tie reinforcement are cor-roded and the cover concrete is cracked due tocorrosion but the core concrete is not affected

(c) Vertical and horizontal tie reinforcement are cor-roded the cover concrete is cracked and the coreconcrete is affected due to corrosion of confiningtiereinforcement

These scenarios will highlight the importance of each damagecomponent that needs to be considered in modelling nonlin-ear response of corroded RC columns

8 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008

minus300minus200minus100

0100200300

ExperimentFibre model

Drift ratio

Late

ral f

orce

(kN

)

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

ExperimentFibre model

Drift ratio

Late

ral f

orce

(kN

)

(b)

Figure 8 Comparison of experimental results and calibrated numerical model of uncorroded columns (a) Lehmanrsquos column 415 (b) Moyerand Kowalskyrsquos column 1

Lehmanrsquos column 415 and Moyer and Kowalskyrsquos column1 [50 54] are considered in this study The geometricaldetails material properties and detailed experimental resultsof these columns are available in [50 54] Figure 8 showsa comparison of the numerical model and experimentalresponses of these columns It should be noted that Lehmanrsquoscolumn 415 has 119871eff119889 = 10 and Moyer and Kowalskyrsquoscolumn 1 has 119871eff119889 = 4 The detailed discussion of thenumerical model validation is available in [25] It shouldbe noted that the maximum drift capacity in this paperis considered as the point where the force-displacementresponse of the column starts softening and losing strengthIt is found that the maximum drift capacity of both columnsat uncorroded state is about 6

The buckling lengths of corroded vertical reinforcementare calculated using the methodology described in Section 4The corrosion of horizontal ties is considered in the bucklinglength calculation As discussed previously (Section 4) thebuckling length of the vertical bars is a function of thetie reinforcementrsquos stiffness and the vertical reinforcementrsquosflexural rigidity Corrosion results in a reduction in flexuralrigidity of vertical barsTherefore the required stiffness fromtie reinforcement to restrain vertical bars against bucklingis reduced However corrosion also reduces the stiffness ofthe tie reinforcement For example in Moyer and Kowalskyrsquoscolumn the vertical reinforcement buckled between two tiesIn this case it was found that corrosion did not affect thebuckling length

In Lehmanrsquos column 415 the vertical reinforcementbuckled over five ties However once the corrosion levelexceeds 10 the buckling length reduced and the verticalreinforcement buckled over four ties It should be notedthat although the buckling length is reduced 119871eff119889

1015840 is notnecessarily reduced where 119871eff is the buckling length and 1198891015840is the diameter of the corroded vertical reinforcement Thisis because corrosion also reduces the diameter of verticalbars This change in buckling length is related to the relativecorrosion level and stiffness between the vertical and tiereinforcement

In practice the horizontal tie reinforcement is closer thanthe main vertical reinforcement to the surface of concreteTherefore it might start corroding earlier than verticalreinforcementThis phenomenonmight have an effect on thebuckling length and confined concrete behaviour Howeverthere has not been any research to date to explore thecorrelation between the corrosion levels of the horizontaltie and vertical reinforcement This is an area for futureresearch and therefore in this research in the absence of anyexperimentalfield data the same corrosion is considered forboth vertical and tie reinforcement

It should be noted that the calculation of the time tocorrosion initiation and time-dependent corrosion propaga-tion is out of the scope of this paper There are mathematicalmodels available in the literature that enable an estimationof the time to corrosion initiation and propagation basedon the environmental conditions [55 56] The corrosion ratecan also be measured on site by electrical equipment whichcan then be turned into a mass loss ratio using Faradayrsquoslaw of electrolysis [57] Given that the focus of this paperis on the impact of different mass loss ratios on the seismicperformance of RC columns the corrosion level is modelledby percentage mass loss throughout this paper

61 Scenario (a) Column Nonlinear Behaviour When Cor-rosion Is Assumed Present in Vertical and Horizontal TieReinforcement Only In this scenario it is assumed that thecorrosion damage is only limited to the steel reinforcement(vertical and horizontal tie reinforcement) that is cover con-crete is uncracked and corrosion of confining reinforcementdoes not affect the confined concrete behaviour Here thesteel model described in Section 51 is used which includesthe impact of corrosion on the buckling and postbucklingbehaviour in compression and strength and ductility loss intension

Figure 9 shows the results of monotonic pushover anal-yses Figure 9(a) shows that the failure mode of Lehmanrsquoscolumn 415 is by vertical bar buckling and core confined

Advances in Materials Science and Engineering 9

0 001 002 003 004 005 006 007 0080

50100150200250300350

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

Drift ratio

Late

ral f

orce

(kN

)

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

Drift ratio

Late

ral f

orce

(kN

)

(b)

Figure 9 Pushover analyses considering corrosion induced damage in reinforcing steel (a) Lehmanrsquos column 415 (b) Moyer and Kowalskyrsquoscolumn 1

concrete crushing up to 10 mass loss However as the cor-rosion level increases beyond 10mass loss the failure modechanges from vertical bar bucking and concrete crushing incompression to fracture of the vertical bars in tension

Figure 9(b) shows that Moyer and Kowalskyrsquos column1 has also failed in bar buckling and concrete crushing incompression However because 119871eff119889 = 4 the strength lossis not as significant as that of Lehmanrsquos column 415 with119871eff119889 = 10 under monotonic loading The corrosion levelup to 20 mass loss changes Moyer and Kowalskyrsquos column1 behaviour The failure initiates with bar buckling andconcrete crushing in compression and followed by fracture ofthe vertical reinforcement in tension With corrosion levelsgreater than 20 mass loss failure is by premature fractureof the vertical bars in tension At this point a cascade of barfracture can be seen in the graphs up to complete collapse ofthe columns

Figures 10(a) and 10(b) show Lehmanrsquos column 415 with10 and 20 mass losses under cyclic loading respectivelyComparing the monotonic and cyclic responses (the samecyclic load protocol as the experiment) shows that low-cyclefatigue has a significant impact on the column responseThe monotonic analysis showed that 10 mass loss did notresult in vertical bar fracture in tension and the failure wasgoverned by bar buckling and concrete crushing However incyclic analysis the failuremode is combined bar buckling andconcrete crushing in compression (failure initiation) followedby bar fracture in tension due to low-cycle fatigue

Here we have a system that does not technically fail incrushing and buckling but survives a little longer until thenext cycle when the vertical reinforcement fails in tensionIt was found that a mass loss ratio greater than 10 has asignificant impact on the nonlinear response of the corrodedcolumn due to reduced low-cycle fatigue life Figure 10(b)shows that at 20 mass loss resulted in bar fracture at 005drift ratio in pushover analysis but it resulted in bar fractureat 003 drift ratio under cyclic loading due to low-cycle fatiguefailure

Figures 10(c) and 10(d) show a similar result for Moyerand Kowalskyrsquos column 1 Overall Moyer and Kowalskyrsquoscolumn 1 has slightly less pinched cyclic responseThis is dueto the influence of the buckling length of the vertical bars andits cyclic degradation due to buckling [25]

62 Scenario (b) Column Nonlinear Behaviour When Corro-sion Is Assumed Present in Vertical and Horizontal Tie Rein-forcement and Cover Concrete Is Cracked In this scenarioit is assumed that the reinforcing steel (vertical and tie) iscorroded and the cover concrete is cracked due to corrosionof vertical reinforcementThe results of the pushover analysesare shown in Figure 11 The results in this case are almostidentical to the previous case (Section 61) where the damagein cover concrete was not considered Therefore in canbe concluded that whether or not we seek to model thecorrosion induced cracking of cover concrete it does not havea significant impact on the nonlinear response of corrodedcolumns Further discussion and comparison of this scenariowith other damage scenarios are available in Section 63

63 Scenario (c) Column Seismic Behaviour When Cor-rosion Is Assumed Present in Vertical and Horizontal TieReinforcement and Both Cover and Confined Concrete AreDamaged In this scenario it is assumed that the reinforc-ing steel (vertical and tie) is corroded cover concrete iscracked and the core confined concrete is affected by thecorrosion of horizontal tie reinforcement (as described inSection 53) Figure 12(a) shows the results of monotonicpushover analyses of Lehmanrsquos column 415 The results showthat the failure mechanism of this column for up to 10mass loss is bar buckling and core confined concrete crushingin compression However for corrosion levels beyond 10the failure mode changes This is a loss of drift capacitywhich starts with bar buckling and concrete crushing incompression and it is followed by bar fracture in tensionThese analyses demonstrate the importance of modelling the

10 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

Drift ratio

Late

ral f

orce

(kN

)

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

Drift ratio

Late

ral f

orce

(kN

)

(b)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

(c)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

(d)

Figure 10 Cyclic analyses considering corrosion induced damage in reinforcing steel (a) and (b) Lehmanrsquos column 415 (c) and (d) Moyerand Kowalskyrsquos column 1

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(b)

Figure 11 Pushover analyses considering corrosion induced damage in reinforcing steel and cracked cover concrete (a) Lehmanrsquos column415 (b) Moyer and Kowalskyrsquos column 1

Advances in Materials Science and Engineering 11

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(b)

Figure 12 Pushover analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a)Lehmanrsquos column 415 (b) Moyer and Kowalskyrsquos column 1

influence of corrosion on the confined concrete (throughloss of confining tie reinforcement) This corrosion damageon the confined concrete results in a rapid reduction instrength and ductility of the corroded columns compared tothe previous cases where confined concrete was considered tobe undamaged

Figure 12(b) shows the results of pushover analyses ofMoyer andKowalskyrsquos column 1 In this case the failuremodewas mainly bar buckling and concrete crushing followed byfracture of bars in tension for up to 20 mass loss Howevercorrosion levels beyond 20 mass loss have changed thefailure mode to premature fracture of bars in tension Thisdifference between the behaviour of the two columns is due tothe buckling behaviour of the vertical bars Given that Moyerand Kowalskyrsquos column 1 has much smaller buckling lengththe strength degradation in compression is much smallerthan Lehmanrsquos column 415 Therefore corrosion has more asignificant impact in terms of ductility loss of bars in tensionwhereas in Lehmanrsquos column 415 failure initiates with severebar buckling and concrete crushing then it is followed byfracture of vertical bars in tension

Figure 13 shows the results of cyclic analysis It showsthe cyclic analyses of Lehmanrsquos column 415 and Moyer andKowalskyrsquos column 1 with 10 and 20 mass loss togetherwith the corresponding pushover envelopes Figure 13 showsthat the extent of corrosion damage under cyclic loadingis more severe than monotonic loading The results ofmonotonic analysis showed that considering the ductility lossof corroded bars in tension and confinement reinforcementin compression has a big impact on bar buckling andfracture of reinforcement However cyclic analysis resultsshow that considering cyclic degradation due to low-cyclefatigue is crucial to have a realistic evaluation of the seismicperformance of existing corroded columns

For example in Figures 13(a) and 13(b) the failure ofLehmanrsquos column 415 was governed by bar buckling andconcrete crushing for a corrosion level up to 10 undermonotonic loadingHowever the same corrosion level results

in a much more severe drift capacity loss under cyclicloading due to a reduced low-cycle fatigue life Similarly inFigures 13(c) and 13(d) the failure of Moyer and Kowalskyrsquoscolumn was governed by concrete crushing in compressionfollowed by bar fracture in tension However low-cyclefatigue degradation due to cyclic loading results in prematurefracture of bars and subsequently severe loss of drift capacity

7 Comparison of the NonlinearResponses of Corroded Columns Computedin Different Scenarios

In order to clearly demonstrate the significance of corrosionmodels on the inelastic response of RC columns a com-parison between the computed responses of two columnswith different scenarios has been made The responses ofcolumns with 20 mass loss in monotonic pushover andcyclic analyses are compared and shown in Figure 14

Figure 14 shows the monotonic pushover and cyclicresponses of Lehmanrsquos column 415 andMoyer and Kowalskyrsquoscolumn 1 with 20 mass losses and different corrosiondamage models Figures 14(a) and 14(b) show that if thecorrosion induced damage to confined concrete is ignoredthe predicted failure mode is likely to be the fracture of barsin tension due to their reduced ductility However if thecorrosion induced damage to confined concrete is addedFigure 14(a) shows that the failure mode of Lehmanrsquos column415 will change to concrete crushing and buckling of thevertical bars in compression

Figure 14(b) shows that the failure mode of Moyer andKowalskyrsquos column 1 initiates with concrete crushing andbuckling of bars in compression and then it is followedby fracture of bars in tension This difference in failuremechanism is due to the differences in confinement level thebuckling length of the vertical bars the ratio of longitudinalreinforcement and the axial force ratio on the columnThere-fore in order to predict the nonlinear response accurately adetailed finite element model is required

12 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(d)

Figure 13 Cyclic analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a) and(b) Lehmanrsquos column 415 (c) and (d) Moyer and Kowalskyrsquos column 1

It is found that the failure mode under cyclic loading ismainly governed by the fracture of horizontal bars in tensiondue to reduced low-cycle fatigue life (Figures 14(c) and 14(d))This is a very important finding as it suggests that nonlinearquasistatic pushover analysis on its own is not adequate forperformance assessment of existing corroded bridge piers

With reference to Figure 14 it is evident that consideringthe impact of the corrosion damage on core confined con-crete and low-cycle fatigue degradation is crucial Thereforethey need to be considered when modelling the nonlinearbehaviour of corrosion damaged RC bridge piers underseismic loading This finding is in good agreement with theobserved experimental results by other researchers [12ndash1458]

A series of experimental studies were conducted in [12]on the cyclic behaviour of large-scale corroded cantilever RCbeams Ou et al found that as the level of corrosion increasesthe flexural failure initiates with premature buckling oflongitudinal bars This conclusion is in good agreement withthe numerical results discussed in this paper In another study[13] a series of experimental studies were conducted on cyclicbehaviour of corroded RC columns with varied axial forceMa et al have reported that once the corrosion level increases

beyond about 14 rapid strength and ductility reductionand cyclic degradation in hysteretic loops are seen due toreduced low-cycle fatigue life and premature buckling ofvertical reinforcement This conclusion is in good agreementwith the predicted failure modes using the numerical modelpresented in this paper

The detailed finite element model developed in thispaper can accurately model the nonlinear behaviour ofcorrodedRCcolumns subject to cyclic loading up to completecollapse There is a need to extend the PEER-UW columndatabase to include corroded RC columns so that furthercalibrationvalidation of the material model parameters canbe performed However the modelling technique developedin this paper is able to simulate the multiple failure modesof corroded RC columns simultaneously It represents thecurrent state of the art and as such they provide a novel com-putational framework for the seismic response prediction ofcorroded RC bridges

8 Conclusions

A series of pushover and cyclic analyses on two hypotheticalcorroded RC columns are conducted and these are used

Advances in Materials Science and Engineering 13

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(d)

Figure 14 Comparison of the computed responses of columns with different deterioration models (a) and (c) Lehmanrsquos column 415 undermonotonic and cyclic loading (b) and (d) Moyer and Kowalskyrsquos column 1 under monotonic and cyclic loading

to explore the performance of the proposed computationalframework The impact of corrosion on (i) the verticalreinforcing steel (ii) the tieconfinement (iii) the cover(unconfined) concrete and (iv) the core (confined) concreteis represented through new material models The proposednew steel material model accounts for (i) inelastic nonlinearbuckling of the vertical reinforcement (ii) the corrosion lossof area (iii) the nonuniform corrosion pitting and (iv) low-cycle high amplitude fatigueThenew cover concretematerialmodel includes the influence of internal pressure due tothe build-up of corrosion products (using compression fieldtheory) The new core concrete model includes the influenceof corrosion induced loss of confining reinforcement

The main outcomes of this study can be summarised asfollows

(1) Corrosion has a more significant impact on theductility loss (drift capacity) of RC columns than thestrength loss (plastic moment capacity)

(2) The numerical model developed in this paper is ableto predict the nonlinear flexural response of corrodedRC columns up to complete collapse Results showwhich depends on a cyclic load history that flexuralfailure can be initiated by the buckling of vertical bars

and crushing of core concrete which is then followedby fracture of bars in tension In cases where thebuckling of bars is not an issue or the buckling lengthis too short (119871eff119889

1015840le 5) the failure is governed by the

fracture of the vertical bars in tension due to low-cyclehigh amplitude fatigue

(3) The analyses results show that for the seismic perfor-mance and evaluation of existing corroded bridgesmonotonic pushover analysis is not sufficient Thecyclic degradation due to low-cycle high amplitudefatigue has a significant influence on the response ofcorroded RC columns

(4) The results of this study show that it is inadequate toassume that corrosion only affects the main verticalreinforcement in the column It was found that theconfined concrete with corroded confinement rein-forcement starts crushing much faster than uncor-roded undamaged concrete This changes the failuremode and results in premature buckling of the ver-tical reinforcement This change in the failure modecannot be predicted if the damage in core confinedconcrete due to corrosion of tie reinforcement isignored This is in good agreement with observed

14 Advances in Materials Science and Engineering

experimental results reported by other researchers[12ndash14]

(5) The modelling technique developed in this paper hassignificantly improved the earlier models and canbe used by other researchers in the future researchfor seismic vulnerability and fragility analysis ofcorroded RC bridges

Disclosure

Any findings opinions and recommendations provided inthis paper are only based on the authorsrsquo view

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This research is conducted in collaboration with the Univer-sity of Bristol and the University of Washington while thefirst author was on sabbatical leave in the US The fundingprovided by the World Wide University Network throughthe Research Mobility Program to the first author was muchappreciated The authors would like to thank Professor MarcO Eberhard and Professor John F Stanton for providingvaluable guidance during the course of this research

References

[1] S Hida F I S Ibrahim H A Capers et al ldquoAssuringbridge safety and serviceability in Europerdquo Tech Rep FHWA-PL-10-014 Office of International Programs Federal HighwayAdministration US Department of Transportation AmericanAssociation of State Highway and Transportation Officials2010

[2] ASCE Failure to Act The Economic Impact of Current Invest-ment Trends in Surface Transportation Infrastructure EconomicDevelopment Research Group Inc ASCE 2011

[3] D-E Choe P Gardoni D Rosowsky and T Haukaas ldquoProb-abilistic capacity models and seismic fragility estimates forRC columns subject to corrosionrdquo Reliability Engineering andSystem Safety vol 93 no 3 pp 383ndash393 2008

[4] L Berto R Vitaliani A Saetta and P Simioni ldquoSeismicassessment of existing RC structures affected by degradationphenomenardquo Structural Safety vol 31 no 4 pp 284ndash297 2009

[5] J Ghosh and J E Padgett ldquoAging considerations in the devel-opment of time-dependent seismic fragility curvesrdquo Journal ofStructural Engineering vol 136 no 12 pp 1497ndash1511 2010

[6] A Alipour B Shafei and M Shinozuka ldquoPerformance evalu-ation of deteriorating highway bridges located in high seismicareasrdquo Journal of Bridge Engineering vol 16 no 5 pp 597ndash6112011

[7] F Biondini E Camnasio and A Palermo ldquoLifetime seismicperformance of concrete bridges exposed to corrosionrdquo Struc-ture and Infrastructure Engineering vol 10 no 7 pp 880ndash9002014

[8] M Akiyama D M Frangopol and H Matsuzaki ldquoLife-cyclereliability of RC bridge piers under seismic and airborne chlo-ride hazardsrdquo Earthquake Engineering and Structural Dynamicsvol 40 no 15 pp 1671ndash1687 2011

[9] F Biondini A Palermo and G Toniolo ldquoSeismic performanceof concrete structures exposed to corrosion case studies of low-rise precast buildingsrdquo Structure and Infrastructure Engineeringvol 7 no 1-2 pp 109ndash119 2011

[10] C K Chiu F J Tu and F P Hsiao ldquoLifetime seismic perfor-mance assessment for chloride-corroded reinforced concretebuildingsrdquo Structure and Infrastructure Engineering vol 11 no3 pp 345ndash362 2015

[11] M Sanchez-Silva G-A Klutke and D V Rosowsky ldquoLife-cycleperformance of structures subject to multiple deteriorationmechanismsrdquo Structural Safety vol 33 no 3 pp 206ndash217 2011

[12] Y-C Ou L-L Tsai and H-H Chen ldquoCyclic performance oflarge-scale corroded reinforced concrete beamsrdquo EarthquakeEngineering and StructuralDynamics vol 41 no 4 pp 593ndash6042012

[13] Y Ma Y Che and J Gong ldquoBehavior of corrosion damagedcircular reinforced concrete columns under cyclic loadingrdquoConstruction and Building Materials vol 29 pp 548ndash556 2012

[14] A Meda S Mostosi Z Rinaldi and P Riva ldquoExperimentalevaluation of the corrosion influence on the cyclic behaviour ofRC columnsrdquo Engineering Structures vol 76 pp 112ndash123 2014

[15] A A Almusallam ldquoEffect of degree of corrosion on theproperties of reinforcing steel barsrdquo Construction and BuildingMaterials vol 15 no 8 pp 361ndash368 2001

[16] Y G Du L A Clark and A H C Chan ldquoResidual capacity ofcorroded reinforcing barsrdquoMagazine of Concrete Research vol57 no 3 pp 135ndash147 2005

[17] Y G Du L A Clarkt and A H C Chan ldquoEffect of corrosionon ductility of reinforcing barsrdquoMagazine of Concrete Researchvol 57 no 7 pp 407ndash419 2005

[18] J Cairns G A Plizzari Y Du D W Law and C FranzonildquoMechanical properties of corrosion-damaged reinforcementrdquoACI Materials Journal vol 102 no 4 pp 256ndash264 2005

[19] C A ApostolopoulosM P Papadopoulos and S G PantelakisldquoTensile behavior of corroded reinforcing steel bars BSt 500srdquoConstruction and Building Materials vol 20 no 9 pp 782ndash7892006

[20] C A Apostolopoulos ldquoMechanical behavior of corroded rein-forcing steel bars S500s tempcore under low cycle fatiguerdquoConstruction andBuildingMaterials vol 21 no 7 pp 1447ndash14562007

[21] M M Kashani A J Crewe and N A Alexander ldquoNonlinearstress-strain behaviour of corrosion-damaged reinforcing barsincluding inelastic bucklingrdquo Engineering Structures vol 48 pp417ndash429 2013

[22] M M Kashani A J Crewe and N A Alexander ldquoNonlinearcyclic response of corrosion-damaged reinforcing bars with theeffect of bucklingrdquo Construction and Building Materials vol 41pp 388ndash400 2013

[23] M M Kashani A J Crewe and N A Alexander ldquoUse of a 3Doptical measurement technique for stochastic corrosion patternanalysis of reinforcing bars subjected to accelerated corrosionrdquoCorrosion Science vol 73 pp 208ndash221 2013

[24] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoFinite element investigation of the influence of corrosionpattern on inelastic buckling and cyclic response of corrodedreinforcing barsrdquo Engineering Structures vol 75 pp 113ndash1252014

Advances in Materials Science and Engineering 15

[25] M M Kashani Seismic performance of corroded rc bridge piersdevelopment of a multi-mechanical nonlinear fibre beam-columnmodel [PhD thesis] University of Bristol Bristol UK 2014

[26] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part I Formula-tionrdquo Earthquake Engineering and Structural Dynamics vol 25no 7 pp 711ndash725 1996

[27] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part II Applica-tionsrdquoEarthquake Engineering and Structural Dynamics vol 25no 7 pp 727ndash742 1996

[28] The Open System for Earthquake Engineering Simulation(OpenSees) Pacific Earthquake Engineering Research CentreUniversity of California Berkeley Berkeley Calif USA 2011

[29] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoPhenomenological hysteretic model for corroded reinforcingbars including inelastic buckling and low-cycle fatigue degrada-tionrdquo Computers and Structures vol 156 article 5393 pp 58ndash712015

[30] J Coleman and E Spacone ldquoLocalization issues in force-basedframe elementsrdquo Journal of Structural Engineering vol 127 no11 pp 1257ndash1265 2001

[31] J S Pugh Numerical simulation of walls and seismic designrecommendations for walled buildings [PhD thesis] Universityof Washington Seattle Wash USA 2012

[32] D V Val and R E Melchers ldquoReliability of deteriorating RCslab bridgesrdquo Journal of Structural Engineering vol 123 no 12pp 1638ndash1644 1997

[33] M S Darmawan and M G Stewart ldquoEffect of pitting corro-sion on capacity of prestressing wiresrdquo Magazine of ConcreteResearch vol 59 no 2 pp 131ndash139 2007

[34] R P Dhakal and K Maekawa ldquoReinforcement stability andfracture of cover concrete in reinforced concrete membersrdquoJournal of Structural Engineering vol 128 no 10 pp 1253ndash12622002

[35] C Lee J F Bonacci M D A Thomas et al ldquoAcceleratedcorrosion and repair of reinforced concrete columns usingcarbon fibre reinforced polymer sheetsrdquo Canadian Journal ofCivil Engineering vol 27 no 5 pp 941ndash948 2000

[36] W Aquino Long-term performance of seismically rehabilitatedcorrosion-damaged columns [PhD thesis] University of Illinoisat Urbana-Champaign Champaign Ill USA 2002

[37] S Timoshenko and J Gere Theory of Elastic StabilityMacGraw-Hill New York NY USA 1963

[38] S J Pantazopoulou ldquoDetailing for reinforcement stability in RCmembersrdquo Journal of Structural Engineering vol 124 no 6 pp623ndash632 1998

[39] J B Mander M J N Priestley and R Park ldquoObserved stress-strain behavior of confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1827ndash1849 1988

[40] J B Mander M J Priestley and R Park ldquoTheoretical stress-strain model for confined concreterdquo Journal of Structural Engi-neering (United States) vol 114 no 8 pp 1804ndash1826 1988

[41] S Popovics ldquoAnumerical approach to the complete stress-straincurve of concreterdquo Cement and Concrete Research vol 3 no 5pp 583ndash599 1973

[42] I D Karsan and J O Jirsa ldquoBehavior of concrete undercompressive loadingrdquo Journal of Structural Division vol 95article ST12 1969

[43] M P Berry andMO Eberhard ldquoPerformancemodeling strate-gies for modern reinforced concrete bridge columnsrdquo PEER

Research Report University of California Berkeley BerkeleyCalif USA 2006

[44] B D Scott R Park and M J N Priestley ldquoStress-strainbehavior of concrete confined by overlapping hoops at low andhigh strain ratesrdquo Journal of the American Concrete Institute vol79 no 1 pp 13ndash27 1982

[45] A S Al-Harthy M G Stewart and J Mullard ldquoConcrete covercracking caused by steel reinforcement corrosionrdquoMagazine ofConcrete Research vol 63 no 9 pp 655ndash667 2011

[46] T Vidal A Castel and R Francois ldquoAnalyzing crack width topredict corrosion in reinforced concreterdquo Cement and ConcreteResearch vol 34 no 1 pp 165ndash174 2004

[47] F J Molina C Alonso and C Andrade ldquoCover cracking as afunction of rebar corrosion part 2-numerical modelrdquoMaterialsand Structures vol 26 no 9 pp 532ndash548 1993

[48] F J Vecchio and M P Collins ldquoThe modified compression-field theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[49] D Coronelli and P Gambarova ldquoStructural assessment ofcorroded reinforced concrete beams modeling guidelinesrdquoJournal of Structural Engineering vol 130 no 8 pp 1214ndash12242004

[50] D E Lehman and J P Moehle ldquoSeismic performance of well-confined concrete columnsrdquo PEER Research Report Universityof California at Berkeley 2000

[51] L N Lowes and A Altoontash ldquoModeling reinforced-concretebeam-column joints subjected to cyclic loadingrdquo Journal ofStructural Engineering vol 129 no 12 pp 1686ndash1697 2003

[52] M Berry M Parrish and M Eberhard ldquoPerformance databaseUserrsquos manualrdquo in Pacific Earthquake Engineering ResearchCentre 2004 University of California at Berkeley 2004httpwwwcewashingtonedusimpeera1

[53] A N Kallias and M Imran Rafiq ldquoFinite element investigationof the structural response of corroded RC beamsrdquo EngineeringStructures vol 32 no 9 pp 2984ndash2994 2010

[54] M J Moyer and M J Kowalsky ldquoInfluence of tension strain onbuckling of reinforcement in concrete columnsrdquo ACI StructuralJournal vol 100 no 1 pp 75ndash85 2003

[55] K A T Vu andM G Stewart ldquoStructural reliability of concretebridges including improved chloride-induced corrosion mod-elsrdquo Structural Safety vol 22 no 4 pp 313ndash333 2000

[56] D V Val ldquoFactors affecting life-cycle cost analysis of RCstructures in chloride contaminated environmentsrdquo Journal ofInfrastructure Systems vol 13 no 2 pp 135ndash143 2007

[57] J P BroomfieldCorrosion of Steel in Concrete Taylor amp FrancisLondon UK 2nd edition 2007

[58] M M Kashani P Alagheband R Khan and S Davis ldquoImpactof corrosion on low-cycle fatigue degradation of reinforcingbars with the effect of inelastic bucklingrdquo International Journalof Fatigue vol 77 pp 174ndash185 2015

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 3

Zero-lengthsection element

Element 13 integration points

Element 25 integration points

1

2

3

4

Col

umn

heig

ht (L

)

Bar-slipsection

Element section

L2 = L minus L1

L1 = 6Leff

(a)

(ii) Unconfined cover concrete modelmdashSection 54

(iii) Reinforcing steel model including inelastic buckling and damage modelsmdashSections 51and 52

(iv) Buckling length calculationmdashSection 4

(i) Confined concrete modelmdashSection 53

Pitting corrosionmodels are discussed in Section 3

(b)

Figure 1 Proposed finite element model (a) force-based nonlinear beam-column arrangement (b) fibre section

Section force deformationnD materialUniaxial material

Material

Fibre section (2D 3D)SteelConcreteBar-slip

Corroded steel with buckling

Corrosion damaged confined concrete

Corrosion damaged cover concrete

Modified steel02 for bar-slip

Damage model

FatigueMax strain Pitting corrosion model

Figure 2 Implementation of the corrosion models within the OpenSees abstract classes

classes is shown in Figure 2 The calculation of bucklinglength of the corroded vertical reinforcement uniaxial mate-rial models and corrosion damage models is discussed inSections 3ndash5

3 Influence of Corrosion on GeometricalProperties of Corroded Bars

The chloride induced corrosion results in irregular loss ofcross section of reinforcing steel known as pitting corrosion

Several researchers studied the impact of nonuniform corro-sion on cross section loss of reinforcing bars [23 32 33] In[23] a 3D optical measurement of corroded bars was con-ducted to explore the spatial variability of the corrosion pat-tern As a result Kashani et al developed a set of probabilisticdistribution models to predict the geometrical properties ofcorroded bars They found that the geometrical propertiesof corroded bars can be modelled using a lognormal dis-tribution In this study the mean values of the lognormaldistribution models are used to account for the effect ofpitting corrosion on the geometrical properties of corroded

4 Advances in Materials Science and Engineering

Corrodedreinforcement

FracturingPlastic hinge regionzone

Buckling ofcorroded reinforcement

Idealised beam on springbuckling model

Corrosion induced damage

to the column section

Corrosion induced crackin cover concrete

Kt

s

F

Lef

f=

ns

Figure 3 Schematic overview of corrosion induced damage to RC column

bars In this study the proposed models that developed in[23] are used to model the impact of pitting corrosion ongeometrical properties of corroded bars

4 Calculation of the BucklingLength considering the Stiffness ofTie Reinforcement

The detailed discussion and validation of the Dhakal-Maekawa buckling model are available in [25 34] The samemethodology is used here for calculation of the bucklinglength of corroded vertical reinforcement

Figure 3 shows a schematic overview of the extent ofcorrosion damage on a hypothetical RC columnThe damageat section level shown in Figure 3 is based on the observedexperimental tests by [35 36] The corrosion of verticalreinforcement results in longitudinal cracks at the surface ofthe columnparallel to vertical reinforcementThiswill reducethe cross-sectional area and flexural rigidity of the verticalreinforcement which are very important in buckling Corro-sion of horizontal tie reinforcement reduces the volumetricratio of confinement reinforcement which is very importantin providing confinement for core concrete Furthermorethis will result in splitting the core and cover concrete bycreation of horizontal cracks around the perimeter of thecolumn sectionMoreover horizontal ties restrain the verticalbars against buckling and corrosion results in a reduction in

stiffness of these ties Therefore these parameters need to beconsidered in calculation of the buckling length

To account for the effect of corrosion on Dhakal-Maekawa equations the flexural rigidity of the vertical rein-forcement (119864119868) and stiffness of horizontal tie reinforcement(119870119905) are adjusted This is discussed in Sections 41 and 42

41 Influence of Corrosion on Flexural Rigidity of CorrodedBars Thebuckling of reinforcing bars is an inelastic bucklingphenomenon and therefore the elastic flexural rigidity 119864

119904119868

is no longer valid [37] Reference [34] suggested an averageflexural rigidity in which it has been validated against anextensive set of experimental data for uncorroded columnsThis has beenmodified for corroded reinforcement (1198641198681015840) anddefined as

1198641198681015840=1198641199041198681015840

min2

radic1205901015840

119910

400

(1)

where 119864119904and 1205901015840119910are the elastic modulus and yield strength of

the corroded vertical reinforcement inMPa respectively and1198681015840

min is the secondmoment of area of corroded reinforcementThe detailed calculation of 1198681015840min is available in [23]

Corrosion of reinforcing bars affects the second momentof area and yield strength of reinforcement but does nothave any influence on the elastic modulus The yield strength

Advances in Materials Science and Engineering 5

0 10 20 30 40 50 600

025

05

075

1

125

15

Tension envelopemdashuncorroded reinforcementTension envelopemdashcorroded reinforcement

120578=120590120590

y

120585 = 120576120576y

(a)

minus40 minus35 minus30 minus25 minus20 minus15 minus10 minus5 0minus12

minus1

minus08

minus06

minus04

minus02

0

Buckling envelopemdashuncorroded reinforcementBuckling envelopemdashcorroded reinforcement

120578=120590120590

y

120585 = 120576120576y

(b)

Figure 4 Implemented tension and compression envelopes of corroded bars in OpenSees (20 mass loss)

can be modified based on the following empirical equationsuggested by [16]

1205901015840

119910= 120590119910(1 minus 0005120595) (2)

where 120595 is the percentage mass loss of the reinforcement

42 Influence of Corrosion on Stiffness of Tie ReinforcementIn this study the stiffness of the horizontal ties of spiralreinforcement is computed using the following empiricalequation suggested by [38]

119870119905=

4119864sp1198601015840

sp

radic(1199042 + 1198892119888)

(3)

where 119864sp is the elastic modulus 1198601015840sp is the cross-sectionalarea of corroded spiral reinforcement 119904 is the spiral pitch and119889119888is the core diameterThe focus of this paper is on circular columns However

in the case of rectangular section the axial stiffness of tiereinforcement can be computed using

119870119905=119864st1198601015840

st119897119905

(4)

where 119864st is the elastic modulus of tie reinforcement 1198601015840st isthe cross-sectional area of corroded tie reinforcement and 119897

119905

is the length of the rectangular tie reinforcement

5 Description of Uniaxial Material Modelsincluding Corrosion Damage

51 Reinforcing Steel Model Tension and CompressionEnvelopes The uniaxial material model developed by [29] isused to model the reinforcing steel This advanced materialmodel combines the material nonlinearity with geometricalnonlinearity due to inelastic buckling into a single-materialmodel The impact of geometrical nonlinearity on cyclicbehaviour of reinforcing bars is also considered Moreover

the cyclic degradation due to low-cycle fatigue and the impactof corrosion on the tension and compression envelopes(including the postbuckling behaviour) are included Furtherdiscussion about the model development is available in [29]To implement the buckling model in OpenSees the uniaxialHystereticmodel available in OpenSees is modified and used(the detailed discussion is available in [25]) Figure 4 showsour proposed tension and compression envelope curves ofcorroded bars implemented in OpenSees

52 Reinforcing Steel Model Cyclic Response and Low-CycleFatigue Degradation As explained in Section 51 the Hys-teretic material model in OpenSees is modified to define thereinforcing steel model The cyclic response of the Hystereticmodel is defined by two pinch parameters (pinch 119909 andpinch 119910) The pinching effect in the cyclic response ofreinforcing bars is affected by the stiffness of the horizontal tiereinforcementThe optimumvalues of pinch parameters havebeen obtained by a comprehensive parametric study reportedin [25] (the calibrated values are pinch 119909 = 04 and pinch119910 = 06)

The Uniaxial Fatigue model is wrapped to the steelmaterial model to model the low-cycle fatigue degradationof corroded vertical reinforcement The low-cycle fatiguematerial constants are modified to account for the impactof corrosion on the low-cycle fatigue life of corroded barsbased on the model developed by [29] Figure 5 shows anexample cyclic response of the implemented Hysteretic +Fatigue model for the uncorroded and corroded reinforcingsteel Further detailed discussion about modelling combinedfatigue and buckling of reinforcing bars inside RC columns isavailable in [29]

53 Corrosion Damaged Confined Concrete Model The com-pressive behaviour of confined concrete is a function ofvolumetric ratio yield strength and fracture strain of thehorizontal tie reinforcement (ie spiral hoop and transversereinforcement) [39 40] Since tie reinforcement is the nearestto the surface being exposed to chloride attack they may

6 Advances in Materials Science and Engineering

minus30 minus20 minus10 0 10 20 30minus15

minus1

minus05

0

05

1

15

Cyclic response including fatiguemdashuncorrodedCyclic response including fatiguemdashcorroded

120578=120590120590

y

120585 = 120576120576y

Figure 5 Cyclic response of the Hysteretic + Fatigue model inOpenSees (20 mass loss)

start corroding prior to the corrosion initiation of verticalreinforcement As a result the volumetric ratio of tie rein-forcement is decreased due to cross section loss There isalso a reduced yield strength and fracture strain due to thepitting effect Therefore the internal confinement pressureof the core concrete can result in premature fracture of tiereinforcement

To date there has not been any experimental study toquantify and model the effect of corrosion on the nonlinearbehaviour of confined concrete under monotonic compres-sion and cyclic loading Further research is required to under-stand and model the extent of corrosion damage on confinedconcrete behaviour However a simplified methodology isused in this research tomodify the confined concretematerialmodel (which is a function of the percentage mass loss inhorizontal tie reinforcement) to account for the effect ofcorrosion damage

In this study the uniaxial Concrete04 material modelavailable in OpenSees is used to model the concrete ThePopovics curve [41] is used for the compression envelope andthe Karsan-Jirsa model [42] is used to determine the slopeof the curve for unloading and reloading in compressionFor tensile loading an exponential curve is used to definethe envelope to the stress-strain curve Further details areavailable in [43]

The parameters proposed by [40] are used to modelthe effect of confinement on concrete in compression Themaximum compressive stress of the concrete (120590cc) and thestrain at the maximum compressive strain (120576cc) can becalculated using the equations developed in [40]

The maximum crushing strain of the confined concreteis defined by the fracture of the first horizontal tiespiralreinforcement Here the model proposed by [44] is used topredict the concrete crushing strain as defined in

120576cc = 0004 + 14 (120588sc120590119910tie120576119906tie

120590119888

) (5)

where 120576119906tie is the fracture strain of the tiespiral reinforce-

ment 120588sc is the volumetric ratio of spiral reinforcement and120590119910tie is the yield stress of spiral reinforcement

minus20 minus18 minus16 minus14 minus12 minus10 minus8 minus6 minus4 minus2 0minus15

minus125

minus1

minus075

minus05

minus025

0

Original confined concrete modelCorrosion damaged confined concrete

120574=120590120590

c

120595 = 120576120576c0

Figure 6 Corrosion damaged confined concrete model (20 massloss)

It is clear that the confined concrete model is a functionof yield strength volumetric ratio and fracture strain ofthe confinementtie reinforcement Therefore the previouslydefined equations for reinforcing steel can be used to modifythe cross-sectional area yield strength and fracture strain oftie reinforcement as a function of the percentage mass lossAccordingly these modified values can be used to accountfor the impact of corrosion on confined concrete model(Figure 6)

54 Corrosion Damaged Cracked Cover Concrete ModelOnce corrosion initiates the corrosion products accumulatearound the reinforcement Given the volume of the corrosionproducts is bigger than the original reinforcing steel it gener-ates a radial pressureexpansion on the concrete surroundingthe reinforcement This behaviour is like a thick cylinderunder internal pressure that eventually results in fracture ofthe cover concrete [45ndash47] The cracking of cover concreteresults in loss of compressive strength and crushing strainof the concrete in the compressive zone of RC sectionsTherefore consideration needs to be given to model theinfluence of this cracking on the response of cover concretein compression

The response of cracked concrete in compression isdescribed in detail by [48] which is known as compressionfield theory (CFT) Based onCFT the compressive strength ofcracked concrete in compression depends on the magnitudeof the average tensile strain in the transverse direction whichcauses longitudinal microcracks Reference [49] employedthis method in nonlinear finite element analysis of corrosiondamaged RC beams with modified constitutive model forthe cracked cover concrete as a function of percentagemass loss and validated this against experimental resultsTherefore the equations suggested by [49] are employedto model the compression response of crack cover con-crete Figure 7(a) shows the compression envelope and Fig-ure 7(b) shows the tension envelope of the uniaxial materialmodel for corrosion damaged unconfined cover concreteused in the fibre model Further details are available in[49]

Advances in Materials Science and Engineering 7

minus25 minus2 minus15 minus1 minus05 0minus1

minus075

minus05

minus025

0

Original unconfined concrete modelCorrosion induced crack unconfined concrete

120595 = 120576120576c0

120574=120590120590

c

(a)

0 1 2 3 4 5 6 70

005

01

015

02

Original concrete tension envelopeCorrosion induced cracked concrete

120574=120590120590

c

120595 = 120576120576ct

(b)

Figure 7 Corrosion damaged cracked cover concrete model for 20 mass loss (a) compression (b) tension

55 Bond-Slip Model and Zero-Length Element In seismicdesign of RC structures and bridges plastic hinges are formedat the columnbeam ends This will induce a substantialstrain penetration along the longitudinal bars into the jointthat eventually results in slippage of longitudinal bars Thisphenomenon has been observed by other researchers exper-imentally [50] Reference [51] adopted a bar-slip model forthe end slip of longitudinal reinforcement in beam-columnjoints This model has been employed by [25] to model thecyclic behaviour of RC columns and is validated against UW-PEER experimental RC column database [52]

Corrosion affects the reinforcing steel near the surface ofthe concrete due to diffusion of chloride ions from the surfaceandor carbonation of cover concrete In bridge piers thevertical reinforcement bars are anchored to the foundationwell below the foundation surface Therefore the verticalreinforcement does not corrode at this depth and the bar-slipbehaviour of bars at the anchorage zone remains the same asin the uncorroded column This has been observed by otherresearchers experimentally [12ndash14]

It should be pointed out that corrosion does affect thebond strength of corroded vertical reinforcement abovethe foundation level (internal bond-slip within the columnitself) However based on the observed experimental resultsthe reduced bond strength does not govern the failure ofcolumns References [12ndash14] reported that the failure ofcorroded columns and beams under cyclic loading is mainlygovern by fracture of bars in tension due to low-cycle fatigueand buckling of bars and crushing of confined concrete incompression

Reference [53] conducted a comprehensive detailed non-linear finite element analysis of corroded RC beams andvalidated them against experimental results They havereported that reduced bond strength only changes the crackpattern and affects the serviceability of corroded beamsTheyconcluded that reduced bond strength does not affect theultimate capacity of corroded beams Therefore bond-slip ofcorroded vertical bars within the element is not considered inthis research

The detailed discussion and implementation of the zero-length section in modelling the cyclic behaviour of RCcolumns is available in [25]

6 Impact of Corrosion Damage on NonlinearResponse of RC Bridges Piers

In this section the impact of different corrosion damagescenarios on the inelastic response of RC bridge piers isexplored A comparative study on two hypothetical corrodedRC columns with different buckling lengths of vertical barsis conducted The columns are taken from the UW-PEERexperimental RC column database [52] These columns areused to validate and calibrate the basic numerical model forthe uncorroded columns [25]

To investigate the impact of corrosion on drift capacityand strength loss of RC columns a series of nonlinearpushover analyses with varied corrosion levels are conductedTo explore the impact of cyclic degradation nonlinear cyclicanalyses using the load history that was used in the exper-iment are conducted In order to investigate the impact ofdifferent modelling techniques and damage mechanism foreach analysis type three scenarios are considered

(a) Vertical and horizontal tie reinforcement are cor-roded but cover and core concrete are not affected bycorrosion

(b) Vertical and horizontal tie reinforcement are cor-roded and the cover concrete is cracked due tocorrosion but the core concrete is not affected

(c) Vertical and horizontal tie reinforcement are cor-roded the cover concrete is cracked and the coreconcrete is affected due to corrosion of confiningtiereinforcement

These scenarios will highlight the importance of each damagecomponent that needs to be considered in modelling nonlin-ear response of corroded RC columns

8 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008

minus300minus200minus100

0100200300

ExperimentFibre model

Drift ratio

Late

ral f

orce

(kN

)

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

ExperimentFibre model

Drift ratio

Late

ral f

orce

(kN

)

(b)

Figure 8 Comparison of experimental results and calibrated numerical model of uncorroded columns (a) Lehmanrsquos column 415 (b) Moyerand Kowalskyrsquos column 1

Lehmanrsquos column 415 and Moyer and Kowalskyrsquos column1 [50 54] are considered in this study The geometricaldetails material properties and detailed experimental resultsof these columns are available in [50 54] Figure 8 showsa comparison of the numerical model and experimentalresponses of these columns It should be noted that Lehmanrsquoscolumn 415 has 119871eff119889 = 10 and Moyer and Kowalskyrsquoscolumn 1 has 119871eff119889 = 4 The detailed discussion of thenumerical model validation is available in [25] It shouldbe noted that the maximum drift capacity in this paperis considered as the point where the force-displacementresponse of the column starts softening and losing strengthIt is found that the maximum drift capacity of both columnsat uncorroded state is about 6

The buckling lengths of corroded vertical reinforcementare calculated using the methodology described in Section 4The corrosion of horizontal ties is considered in the bucklinglength calculation As discussed previously (Section 4) thebuckling length of the vertical bars is a function of thetie reinforcementrsquos stiffness and the vertical reinforcementrsquosflexural rigidity Corrosion results in a reduction in flexuralrigidity of vertical barsTherefore the required stiffness fromtie reinforcement to restrain vertical bars against bucklingis reduced However corrosion also reduces the stiffness ofthe tie reinforcement For example in Moyer and Kowalskyrsquoscolumn the vertical reinforcement buckled between two tiesIn this case it was found that corrosion did not affect thebuckling length

In Lehmanrsquos column 415 the vertical reinforcementbuckled over five ties However once the corrosion levelexceeds 10 the buckling length reduced and the verticalreinforcement buckled over four ties It should be notedthat although the buckling length is reduced 119871eff119889

1015840 is notnecessarily reduced where 119871eff is the buckling length and 1198891015840is the diameter of the corroded vertical reinforcement Thisis because corrosion also reduces the diameter of verticalbars This change in buckling length is related to the relativecorrosion level and stiffness between the vertical and tiereinforcement

In practice the horizontal tie reinforcement is closer thanthe main vertical reinforcement to the surface of concreteTherefore it might start corroding earlier than verticalreinforcementThis phenomenonmight have an effect on thebuckling length and confined concrete behaviour Howeverthere has not been any research to date to explore thecorrelation between the corrosion levels of the horizontaltie and vertical reinforcement This is an area for futureresearch and therefore in this research in the absence of anyexperimentalfield data the same corrosion is considered forboth vertical and tie reinforcement

It should be noted that the calculation of the time tocorrosion initiation and time-dependent corrosion propaga-tion is out of the scope of this paper There are mathematicalmodels available in the literature that enable an estimationof the time to corrosion initiation and propagation basedon the environmental conditions [55 56] The corrosion ratecan also be measured on site by electrical equipment whichcan then be turned into a mass loss ratio using Faradayrsquoslaw of electrolysis [57] Given that the focus of this paperis on the impact of different mass loss ratios on the seismicperformance of RC columns the corrosion level is modelledby percentage mass loss throughout this paper

61 Scenario (a) Column Nonlinear Behaviour When Cor-rosion Is Assumed Present in Vertical and Horizontal TieReinforcement Only In this scenario it is assumed that thecorrosion damage is only limited to the steel reinforcement(vertical and horizontal tie reinforcement) that is cover con-crete is uncracked and corrosion of confining reinforcementdoes not affect the confined concrete behaviour Here thesteel model described in Section 51 is used which includesthe impact of corrosion on the buckling and postbucklingbehaviour in compression and strength and ductility loss intension

Figure 9 shows the results of monotonic pushover anal-yses Figure 9(a) shows that the failure mode of Lehmanrsquoscolumn 415 is by vertical bar buckling and core confined

Advances in Materials Science and Engineering 9

0 001 002 003 004 005 006 007 0080

50100150200250300350

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

Drift ratio

Late

ral f

orce

(kN

)

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

Drift ratio

Late

ral f

orce

(kN

)

(b)

Figure 9 Pushover analyses considering corrosion induced damage in reinforcing steel (a) Lehmanrsquos column 415 (b) Moyer and Kowalskyrsquoscolumn 1

concrete crushing up to 10 mass loss However as the cor-rosion level increases beyond 10mass loss the failure modechanges from vertical bar bucking and concrete crushing incompression to fracture of the vertical bars in tension

Figure 9(b) shows that Moyer and Kowalskyrsquos column1 has also failed in bar buckling and concrete crushing incompression However because 119871eff119889 = 4 the strength lossis not as significant as that of Lehmanrsquos column 415 with119871eff119889 = 10 under monotonic loading The corrosion levelup to 20 mass loss changes Moyer and Kowalskyrsquos column1 behaviour The failure initiates with bar buckling andconcrete crushing in compression and followed by fracture ofthe vertical reinforcement in tension With corrosion levelsgreater than 20 mass loss failure is by premature fractureof the vertical bars in tension At this point a cascade of barfracture can be seen in the graphs up to complete collapse ofthe columns

Figures 10(a) and 10(b) show Lehmanrsquos column 415 with10 and 20 mass losses under cyclic loading respectivelyComparing the monotonic and cyclic responses (the samecyclic load protocol as the experiment) shows that low-cyclefatigue has a significant impact on the column responseThe monotonic analysis showed that 10 mass loss did notresult in vertical bar fracture in tension and the failure wasgoverned by bar buckling and concrete crushing However incyclic analysis the failuremode is combined bar buckling andconcrete crushing in compression (failure initiation) followedby bar fracture in tension due to low-cycle fatigue

Here we have a system that does not technically fail incrushing and buckling but survives a little longer until thenext cycle when the vertical reinforcement fails in tensionIt was found that a mass loss ratio greater than 10 has asignificant impact on the nonlinear response of the corrodedcolumn due to reduced low-cycle fatigue life Figure 10(b)shows that at 20 mass loss resulted in bar fracture at 005drift ratio in pushover analysis but it resulted in bar fractureat 003 drift ratio under cyclic loading due to low-cycle fatiguefailure

Figures 10(c) and 10(d) show a similar result for Moyerand Kowalskyrsquos column 1 Overall Moyer and Kowalskyrsquoscolumn 1 has slightly less pinched cyclic responseThis is dueto the influence of the buckling length of the vertical bars andits cyclic degradation due to buckling [25]

62 Scenario (b) Column Nonlinear Behaviour When Corro-sion Is Assumed Present in Vertical and Horizontal Tie Rein-forcement and Cover Concrete Is Cracked In this scenarioit is assumed that the reinforcing steel (vertical and tie) iscorroded and the cover concrete is cracked due to corrosionof vertical reinforcementThe results of the pushover analysesare shown in Figure 11 The results in this case are almostidentical to the previous case (Section 61) where the damagein cover concrete was not considered Therefore in canbe concluded that whether or not we seek to model thecorrosion induced cracking of cover concrete it does not havea significant impact on the nonlinear response of corrodedcolumns Further discussion and comparison of this scenariowith other damage scenarios are available in Section 63

63 Scenario (c) Column Seismic Behaviour When Cor-rosion Is Assumed Present in Vertical and Horizontal TieReinforcement and Both Cover and Confined Concrete AreDamaged In this scenario it is assumed that the reinforc-ing steel (vertical and tie) is corroded cover concrete iscracked and the core confined concrete is affected by thecorrosion of horizontal tie reinforcement (as described inSection 53) Figure 12(a) shows the results of monotonicpushover analyses of Lehmanrsquos column 415 The results showthat the failure mechanism of this column for up to 10mass loss is bar buckling and core confined concrete crushingin compression However for corrosion levels beyond 10the failure mode changes This is a loss of drift capacitywhich starts with bar buckling and concrete crushing incompression and it is followed by bar fracture in tensionThese analyses demonstrate the importance of modelling the

10 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

Drift ratio

Late

ral f

orce

(kN

)

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

Drift ratio

Late

ral f

orce

(kN

)

(b)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

(c)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

(d)

Figure 10 Cyclic analyses considering corrosion induced damage in reinforcing steel (a) and (b) Lehmanrsquos column 415 (c) and (d) Moyerand Kowalskyrsquos column 1

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(b)

Figure 11 Pushover analyses considering corrosion induced damage in reinforcing steel and cracked cover concrete (a) Lehmanrsquos column415 (b) Moyer and Kowalskyrsquos column 1

Advances in Materials Science and Engineering 11

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(b)

Figure 12 Pushover analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a)Lehmanrsquos column 415 (b) Moyer and Kowalskyrsquos column 1

influence of corrosion on the confined concrete (throughloss of confining tie reinforcement) This corrosion damageon the confined concrete results in a rapid reduction instrength and ductility of the corroded columns compared tothe previous cases where confined concrete was considered tobe undamaged

Figure 12(b) shows the results of pushover analyses ofMoyer andKowalskyrsquos column 1 In this case the failuremodewas mainly bar buckling and concrete crushing followed byfracture of bars in tension for up to 20 mass loss Howevercorrosion levels beyond 20 mass loss have changed thefailure mode to premature fracture of bars in tension Thisdifference between the behaviour of the two columns is due tothe buckling behaviour of the vertical bars Given that Moyerand Kowalskyrsquos column 1 has much smaller buckling lengththe strength degradation in compression is much smallerthan Lehmanrsquos column 415 Therefore corrosion has more asignificant impact in terms of ductility loss of bars in tensionwhereas in Lehmanrsquos column 415 failure initiates with severebar buckling and concrete crushing then it is followed byfracture of vertical bars in tension

Figure 13 shows the results of cyclic analysis It showsthe cyclic analyses of Lehmanrsquos column 415 and Moyer andKowalskyrsquos column 1 with 10 and 20 mass loss togetherwith the corresponding pushover envelopes Figure 13 showsthat the extent of corrosion damage under cyclic loadingis more severe than monotonic loading The results ofmonotonic analysis showed that considering the ductility lossof corroded bars in tension and confinement reinforcementin compression has a big impact on bar buckling andfracture of reinforcement However cyclic analysis resultsshow that considering cyclic degradation due to low-cyclefatigue is crucial to have a realistic evaluation of the seismicperformance of existing corroded columns

For example in Figures 13(a) and 13(b) the failure ofLehmanrsquos column 415 was governed by bar buckling andconcrete crushing for a corrosion level up to 10 undermonotonic loadingHowever the same corrosion level results

in a much more severe drift capacity loss under cyclicloading due to a reduced low-cycle fatigue life Similarly inFigures 13(c) and 13(d) the failure of Moyer and Kowalskyrsquoscolumn was governed by concrete crushing in compressionfollowed by bar fracture in tension However low-cyclefatigue degradation due to cyclic loading results in prematurefracture of bars and subsequently severe loss of drift capacity

7 Comparison of the NonlinearResponses of Corroded Columns Computedin Different Scenarios

In order to clearly demonstrate the significance of corrosionmodels on the inelastic response of RC columns a com-parison between the computed responses of two columnswith different scenarios has been made The responses ofcolumns with 20 mass loss in monotonic pushover andcyclic analyses are compared and shown in Figure 14

Figure 14 shows the monotonic pushover and cyclicresponses of Lehmanrsquos column 415 andMoyer and Kowalskyrsquoscolumn 1 with 20 mass losses and different corrosiondamage models Figures 14(a) and 14(b) show that if thecorrosion induced damage to confined concrete is ignoredthe predicted failure mode is likely to be the fracture of barsin tension due to their reduced ductility However if thecorrosion induced damage to confined concrete is addedFigure 14(a) shows that the failure mode of Lehmanrsquos column415 will change to concrete crushing and buckling of thevertical bars in compression

Figure 14(b) shows that the failure mode of Moyer andKowalskyrsquos column 1 initiates with concrete crushing andbuckling of bars in compression and then it is followedby fracture of bars in tension This difference in failuremechanism is due to the differences in confinement level thebuckling length of the vertical bars the ratio of longitudinalreinforcement and the axial force ratio on the columnThere-fore in order to predict the nonlinear response accurately adetailed finite element model is required

12 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(d)

Figure 13 Cyclic analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a) and(b) Lehmanrsquos column 415 (c) and (d) Moyer and Kowalskyrsquos column 1

It is found that the failure mode under cyclic loading ismainly governed by the fracture of horizontal bars in tensiondue to reduced low-cycle fatigue life (Figures 14(c) and 14(d))This is a very important finding as it suggests that nonlinearquasistatic pushover analysis on its own is not adequate forperformance assessment of existing corroded bridge piers

With reference to Figure 14 it is evident that consideringthe impact of the corrosion damage on core confined con-crete and low-cycle fatigue degradation is crucial Thereforethey need to be considered when modelling the nonlinearbehaviour of corrosion damaged RC bridge piers underseismic loading This finding is in good agreement with theobserved experimental results by other researchers [12ndash1458]

A series of experimental studies were conducted in [12]on the cyclic behaviour of large-scale corroded cantilever RCbeams Ou et al found that as the level of corrosion increasesthe flexural failure initiates with premature buckling oflongitudinal bars This conclusion is in good agreement withthe numerical results discussed in this paper In another study[13] a series of experimental studies were conducted on cyclicbehaviour of corroded RC columns with varied axial forceMa et al have reported that once the corrosion level increases

beyond about 14 rapid strength and ductility reductionand cyclic degradation in hysteretic loops are seen due toreduced low-cycle fatigue life and premature buckling ofvertical reinforcement This conclusion is in good agreementwith the predicted failure modes using the numerical modelpresented in this paper

The detailed finite element model developed in thispaper can accurately model the nonlinear behaviour ofcorrodedRCcolumns subject to cyclic loading up to completecollapse There is a need to extend the PEER-UW columndatabase to include corroded RC columns so that furthercalibrationvalidation of the material model parameters canbe performed However the modelling technique developedin this paper is able to simulate the multiple failure modesof corroded RC columns simultaneously It represents thecurrent state of the art and as such they provide a novel com-putational framework for the seismic response prediction ofcorroded RC bridges

8 Conclusions

A series of pushover and cyclic analyses on two hypotheticalcorroded RC columns are conducted and these are used

Advances in Materials Science and Engineering 13

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(d)

Figure 14 Comparison of the computed responses of columns with different deterioration models (a) and (c) Lehmanrsquos column 415 undermonotonic and cyclic loading (b) and (d) Moyer and Kowalskyrsquos column 1 under monotonic and cyclic loading

to explore the performance of the proposed computationalframework The impact of corrosion on (i) the verticalreinforcing steel (ii) the tieconfinement (iii) the cover(unconfined) concrete and (iv) the core (confined) concreteis represented through new material models The proposednew steel material model accounts for (i) inelastic nonlinearbuckling of the vertical reinforcement (ii) the corrosion lossof area (iii) the nonuniform corrosion pitting and (iv) low-cycle high amplitude fatigueThenew cover concretematerialmodel includes the influence of internal pressure due tothe build-up of corrosion products (using compression fieldtheory) The new core concrete model includes the influenceof corrosion induced loss of confining reinforcement

The main outcomes of this study can be summarised asfollows

(1) Corrosion has a more significant impact on theductility loss (drift capacity) of RC columns than thestrength loss (plastic moment capacity)

(2) The numerical model developed in this paper is ableto predict the nonlinear flexural response of corrodedRC columns up to complete collapse Results showwhich depends on a cyclic load history that flexuralfailure can be initiated by the buckling of vertical bars

and crushing of core concrete which is then followedby fracture of bars in tension In cases where thebuckling of bars is not an issue or the buckling lengthis too short (119871eff119889

1015840le 5) the failure is governed by the

fracture of the vertical bars in tension due to low-cyclehigh amplitude fatigue

(3) The analyses results show that for the seismic perfor-mance and evaluation of existing corroded bridgesmonotonic pushover analysis is not sufficient Thecyclic degradation due to low-cycle high amplitudefatigue has a significant influence on the response ofcorroded RC columns

(4) The results of this study show that it is inadequate toassume that corrosion only affects the main verticalreinforcement in the column It was found that theconfined concrete with corroded confinement rein-forcement starts crushing much faster than uncor-roded undamaged concrete This changes the failuremode and results in premature buckling of the ver-tical reinforcement This change in the failure modecannot be predicted if the damage in core confinedconcrete due to corrosion of tie reinforcement isignored This is in good agreement with observed

14 Advances in Materials Science and Engineering

experimental results reported by other researchers[12ndash14]

(5) The modelling technique developed in this paper hassignificantly improved the earlier models and canbe used by other researchers in the future researchfor seismic vulnerability and fragility analysis ofcorroded RC bridges

Disclosure

Any findings opinions and recommendations provided inthis paper are only based on the authorsrsquo view

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This research is conducted in collaboration with the Univer-sity of Bristol and the University of Washington while thefirst author was on sabbatical leave in the US The fundingprovided by the World Wide University Network throughthe Research Mobility Program to the first author was muchappreciated The authors would like to thank Professor MarcO Eberhard and Professor John F Stanton for providingvaluable guidance during the course of this research

References

[1] S Hida F I S Ibrahim H A Capers et al ldquoAssuringbridge safety and serviceability in Europerdquo Tech Rep FHWA-PL-10-014 Office of International Programs Federal HighwayAdministration US Department of Transportation AmericanAssociation of State Highway and Transportation Officials2010

[2] ASCE Failure to Act The Economic Impact of Current Invest-ment Trends in Surface Transportation Infrastructure EconomicDevelopment Research Group Inc ASCE 2011

[3] D-E Choe P Gardoni D Rosowsky and T Haukaas ldquoProb-abilistic capacity models and seismic fragility estimates forRC columns subject to corrosionrdquo Reliability Engineering andSystem Safety vol 93 no 3 pp 383ndash393 2008

[4] L Berto R Vitaliani A Saetta and P Simioni ldquoSeismicassessment of existing RC structures affected by degradationphenomenardquo Structural Safety vol 31 no 4 pp 284ndash297 2009

[5] J Ghosh and J E Padgett ldquoAging considerations in the devel-opment of time-dependent seismic fragility curvesrdquo Journal ofStructural Engineering vol 136 no 12 pp 1497ndash1511 2010

[6] A Alipour B Shafei and M Shinozuka ldquoPerformance evalu-ation of deteriorating highway bridges located in high seismicareasrdquo Journal of Bridge Engineering vol 16 no 5 pp 597ndash6112011

[7] F Biondini E Camnasio and A Palermo ldquoLifetime seismicperformance of concrete bridges exposed to corrosionrdquo Struc-ture and Infrastructure Engineering vol 10 no 7 pp 880ndash9002014

[8] M Akiyama D M Frangopol and H Matsuzaki ldquoLife-cyclereliability of RC bridge piers under seismic and airborne chlo-ride hazardsrdquo Earthquake Engineering and Structural Dynamicsvol 40 no 15 pp 1671ndash1687 2011

[9] F Biondini A Palermo and G Toniolo ldquoSeismic performanceof concrete structures exposed to corrosion case studies of low-rise precast buildingsrdquo Structure and Infrastructure Engineeringvol 7 no 1-2 pp 109ndash119 2011

[10] C K Chiu F J Tu and F P Hsiao ldquoLifetime seismic perfor-mance assessment for chloride-corroded reinforced concretebuildingsrdquo Structure and Infrastructure Engineering vol 11 no3 pp 345ndash362 2015

[11] M Sanchez-Silva G-A Klutke and D V Rosowsky ldquoLife-cycleperformance of structures subject to multiple deteriorationmechanismsrdquo Structural Safety vol 33 no 3 pp 206ndash217 2011

[12] Y-C Ou L-L Tsai and H-H Chen ldquoCyclic performance oflarge-scale corroded reinforced concrete beamsrdquo EarthquakeEngineering and StructuralDynamics vol 41 no 4 pp 593ndash6042012

[13] Y Ma Y Che and J Gong ldquoBehavior of corrosion damagedcircular reinforced concrete columns under cyclic loadingrdquoConstruction and Building Materials vol 29 pp 548ndash556 2012

[14] A Meda S Mostosi Z Rinaldi and P Riva ldquoExperimentalevaluation of the corrosion influence on the cyclic behaviour ofRC columnsrdquo Engineering Structures vol 76 pp 112ndash123 2014

[15] A A Almusallam ldquoEffect of degree of corrosion on theproperties of reinforcing steel barsrdquo Construction and BuildingMaterials vol 15 no 8 pp 361ndash368 2001

[16] Y G Du L A Clark and A H C Chan ldquoResidual capacity ofcorroded reinforcing barsrdquoMagazine of Concrete Research vol57 no 3 pp 135ndash147 2005

[17] Y G Du L A Clarkt and A H C Chan ldquoEffect of corrosionon ductility of reinforcing barsrdquoMagazine of Concrete Researchvol 57 no 7 pp 407ndash419 2005

[18] J Cairns G A Plizzari Y Du D W Law and C FranzonildquoMechanical properties of corrosion-damaged reinforcementrdquoACI Materials Journal vol 102 no 4 pp 256ndash264 2005

[19] C A ApostolopoulosM P Papadopoulos and S G PantelakisldquoTensile behavior of corroded reinforcing steel bars BSt 500srdquoConstruction and Building Materials vol 20 no 9 pp 782ndash7892006

[20] C A Apostolopoulos ldquoMechanical behavior of corroded rein-forcing steel bars S500s tempcore under low cycle fatiguerdquoConstruction andBuildingMaterials vol 21 no 7 pp 1447ndash14562007

[21] M M Kashani A J Crewe and N A Alexander ldquoNonlinearstress-strain behaviour of corrosion-damaged reinforcing barsincluding inelastic bucklingrdquo Engineering Structures vol 48 pp417ndash429 2013

[22] M M Kashani A J Crewe and N A Alexander ldquoNonlinearcyclic response of corrosion-damaged reinforcing bars with theeffect of bucklingrdquo Construction and Building Materials vol 41pp 388ndash400 2013

[23] M M Kashani A J Crewe and N A Alexander ldquoUse of a 3Doptical measurement technique for stochastic corrosion patternanalysis of reinforcing bars subjected to accelerated corrosionrdquoCorrosion Science vol 73 pp 208ndash221 2013

[24] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoFinite element investigation of the influence of corrosionpattern on inelastic buckling and cyclic response of corrodedreinforcing barsrdquo Engineering Structures vol 75 pp 113ndash1252014

Advances in Materials Science and Engineering 15

[25] M M Kashani Seismic performance of corroded rc bridge piersdevelopment of a multi-mechanical nonlinear fibre beam-columnmodel [PhD thesis] University of Bristol Bristol UK 2014

[26] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part I Formula-tionrdquo Earthquake Engineering and Structural Dynamics vol 25no 7 pp 711ndash725 1996

[27] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part II Applica-tionsrdquoEarthquake Engineering and Structural Dynamics vol 25no 7 pp 727ndash742 1996

[28] The Open System for Earthquake Engineering Simulation(OpenSees) Pacific Earthquake Engineering Research CentreUniversity of California Berkeley Berkeley Calif USA 2011

[29] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoPhenomenological hysteretic model for corroded reinforcingbars including inelastic buckling and low-cycle fatigue degrada-tionrdquo Computers and Structures vol 156 article 5393 pp 58ndash712015

[30] J Coleman and E Spacone ldquoLocalization issues in force-basedframe elementsrdquo Journal of Structural Engineering vol 127 no11 pp 1257ndash1265 2001

[31] J S Pugh Numerical simulation of walls and seismic designrecommendations for walled buildings [PhD thesis] Universityof Washington Seattle Wash USA 2012

[32] D V Val and R E Melchers ldquoReliability of deteriorating RCslab bridgesrdquo Journal of Structural Engineering vol 123 no 12pp 1638ndash1644 1997

[33] M S Darmawan and M G Stewart ldquoEffect of pitting corro-sion on capacity of prestressing wiresrdquo Magazine of ConcreteResearch vol 59 no 2 pp 131ndash139 2007

[34] R P Dhakal and K Maekawa ldquoReinforcement stability andfracture of cover concrete in reinforced concrete membersrdquoJournal of Structural Engineering vol 128 no 10 pp 1253ndash12622002

[35] C Lee J F Bonacci M D A Thomas et al ldquoAcceleratedcorrosion and repair of reinforced concrete columns usingcarbon fibre reinforced polymer sheetsrdquo Canadian Journal ofCivil Engineering vol 27 no 5 pp 941ndash948 2000

[36] W Aquino Long-term performance of seismically rehabilitatedcorrosion-damaged columns [PhD thesis] University of Illinoisat Urbana-Champaign Champaign Ill USA 2002

[37] S Timoshenko and J Gere Theory of Elastic StabilityMacGraw-Hill New York NY USA 1963

[38] S J Pantazopoulou ldquoDetailing for reinforcement stability in RCmembersrdquo Journal of Structural Engineering vol 124 no 6 pp623ndash632 1998

[39] J B Mander M J N Priestley and R Park ldquoObserved stress-strain behavior of confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1827ndash1849 1988

[40] J B Mander M J Priestley and R Park ldquoTheoretical stress-strain model for confined concreterdquo Journal of Structural Engi-neering (United States) vol 114 no 8 pp 1804ndash1826 1988

[41] S Popovics ldquoAnumerical approach to the complete stress-straincurve of concreterdquo Cement and Concrete Research vol 3 no 5pp 583ndash599 1973

[42] I D Karsan and J O Jirsa ldquoBehavior of concrete undercompressive loadingrdquo Journal of Structural Division vol 95article ST12 1969

[43] M P Berry andMO Eberhard ldquoPerformancemodeling strate-gies for modern reinforced concrete bridge columnsrdquo PEER

Research Report University of California Berkeley BerkeleyCalif USA 2006

[44] B D Scott R Park and M J N Priestley ldquoStress-strainbehavior of concrete confined by overlapping hoops at low andhigh strain ratesrdquo Journal of the American Concrete Institute vol79 no 1 pp 13ndash27 1982

[45] A S Al-Harthy M G Stewart and J Mullard ldquoConcrete covercracking caused by steel reinforcement corrosionrdquoMagazine ofConcrete Research vol 63 no 9 pp 655ndash667 2011

[46] T Vidal A Castel and R Francois ldquoAnalyzing crack width topredict corrosion in reinforced concreterdquo Cement and ConcreteResearch vol 34 no 1 pp 165ndash174 2004

[47] F J Molina C Alonso and C Andrade ldquoCover cracking as afunction of rebar corrosion part 2-numerical modelrdquoMaterialsand Structures vol 26 no 9 pp 532ndash548 1993

[48] F J Vecchio and M P Collins ldquoThe modified compression-field theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[49] D Coronelli and P Gambarova ldquoStructural assessment ofcorroded reinforced concrete beams modeling guidelinesrdquoJournal of Structural Engineering vol 130 no 8 pp 1214ndash12242004

[50] D E Lehman and J P Moehle ldquoSeismic performance of well-confined concrete columnsrdquo PEER Research Report Universityof California at Berkeley 2000

[51] L N Lowes and A Altoontash ldquoModeling reinforced-concretebeam-column joints subjected to cyclic loadingrdquo Journal ofStructural Engineering vol 129 no 12 pp 1686ndash1697 2003

[52] M Berry M Parrish and M Eberhard ldquoPerformance databaseUserrsquos manualrdquo in Pacific Earthquake Engineering ResearchCentre 2004 University of California at Berkeley 2004httpwwwcewashingtonedusimpeera1

[53] A N Kallias and M Imran Rafiq ldquoFinite element investigationof the structural response of corroded RC beamsrdquo EngineeringStructures vol 32 no 9 pp 2984ndash2994 2010

[54] M J Moyer and M J Kowalsky ldquoInfluence of tension strain onbuckling of reinforcement in concrete columnsrdquo ACI StructuralJournal vol 100 no 1 pp 75ndash85 2003

[55] K A T Vu andM G Stewart ldquoStructural reliability of concretebridges including improved chloride-induced corrosion mod-elsrdquo Structural Safety vol 22 no 4 pp 313ndash333 2000

[56] D V Val ldquoFactors affecting life-cycle cost analysis of RCstructures in chloride contaminated environmentsrdquo Journal ofInfrastructure Systems vol 13 no 2 pp 135ndash143 2007

[57] J P BroomfieldCorrosion of Steel in Concrete Taylor amp FrancisLondon UK 2nd edition 2007

[58] M M Kashani P Alagheband R Khan and S Davis ldquoImpactof corrosion on low-cycle fatigue degradation of reinforcingbars with the effect of inelastic bucklingrdquo International Journalof Fatigue vol 77 pp 174ndash185 2015

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

4 Advances in Materials Science and Engineering

Corrodedreinforcement

FracturingPlastic hinge regionzone

Buckling ofcorroded reinforcement

Idealised beam on springbuckling model

Corrosion induced damage

to the column section

Corrosion induced crackin cover concrete

Kt

s

F

Lef

f=

ns

Figure 3 Schematic overview of corrosion induced damage to RC column

bars In this study the proposed models that developed in[23] are used to model the impact of pitting corrosion ongeometrical properties of corroded bars

4 Calculation of the BucklingLength considering the Stiffness ofTie Reinforcement

The detailed discussion and validation of the Dhakal-Maekawa buckling model are available in [25 34] The samemethodology is used here for calculation of the bucklinglength of corroded vertical reinforcement

Figure 3 shows a schematic overview of the extent ofcorrosion damage on a hypothetical RC columnThe damageat section level shown in Figure 3 is based on the observedexperimental tests by [35 36] The corrosion of verticalreinforcement results in longitudinal cracks at the surface ofthe columnparallel to vertical reinforcementThiswill reducethe cross-sectional area and flexural rigidity of the verticalreinforcement which are very important in buckling Corro-sion of horizontal tie reinforcement reduces the volumetricratio of confinement reinforcement which is very importantin providing confinement for core concrete Furthermorethis will result in splitting the core and cover concrete bycreation of horizontal cracks around the perimeter of thecolumn sectionMoreover horizontal ties restrain the verticalbars against buckling and corrosion results in a reduction in

stiffness of these ties Therefore these parameters need to beconsidered in calculation of the buckling length

To account for the effect of corrosion on Dhakal-Maekawa equations the flexural rigidity of the vertical rein-forcement (119864119868) and stiffness of horizontal tie reinforcement(119870119905) are adjusted This is discussed in Sections 41 and 42

41 Influence of Corrosion on Flexural Rigidity of CorrodedBars Thebuckling of reinforcing bars is an inelastic bucklingphenomenon and therefore the elastic flexural rigidity 119864

119904119868

is no longer valid [37] Reference [34] suggested an averageflexural rigidity in which it has been validated against anextensive set of experimental data for uncorroded columnsThis has beenmodified for corroded reinforcement (1198641198681015840) anddefined as

1198641198681015840=1198641199041198681015840

min2

radic1205901015840

119910

400

(1)

where 119864119904and 1205901015840119910are the elastic modulus and yield strength of

the corroded vertical reinforcement inMPa respectively and1198681015840

min is the secondmoment of area of corroded reinforcementThe detailed calculation of 1198681015840min is available in [23]

Corrosion of reinforcing bars affects the second momentof area and yield strength of reinforcement but does nothave any influence on the elastic modulus The yield strength

Advances in Materials Science and Engineering 5

0 10 20 30 40 50 600

025

05

075

1

125

15

Tension envelopemdashuncorroded reinforcementTension envelopemdashcorroded reinforcement

120578=120590120590

y

120585 = 120576120576y

(a)

minus40 minus35 minus30 minus25 minus20 minus15 minus10 minus5 0minus12

minus1

minus08

minus06

minus04

minus02

0

Buckling envelopemdashuncorroded reinforcementBuckling envelopemdashcorroded reinforcement

120578=120590120590

y

120585 = 120576120576y

(b)

Figure 4 Implemented tension and compression envelopes of corroded bars in OpenSees (20 mass loss)

can be modified based on the following empirical equationsuggested by [16]

1205901015840

119910= 120590119910(1 minus 0005120595) (2)

where 120595 is the percentage mass loss of the reinforcement

42 Influence of Corrosion on Stiffness of Tie ReinforcementIn this study the stiffness of the horizontal ties of spiralreinforcement is computed using the following empiricalequation suggested by [38]

119870119905=

4119864sp1198601015840

sp

radic(1199042 + 1198892119888)

(3)

where 119864sp is the elastic modulus 1198601015840sp is the cross-sectionalarea of corroded spiral reinforcement 119904 is the spiral pitch and119889119888is the core diameterThe focus of this paper is on circular columns However

in the case of rectangular section the axial stiffness of tiereinforcement can be computed using

119870119905=119864st1198601015840

st119897119905

(4)

where 119864st is the elastic modulus of tie reinforcement 1198601015840st isthe cross-sectional area of corroded tie reinforcement and 119897

119905

is the length of the rectangular tie reinforcement

5 Description of Uniaxial Material Modelsincluding Corrosion Damage

51 Reinforcing Steel Model Tension and CompressionEnvelopes The uniaxial material model developed by [29] isused to model the reinforcing steel This advanced materialmodel combines the material nonlinearity with geometricalnonlinearity due to inelastic buckling into a single-materialmodel The impact of geometrical nonlinearity on cyclicbehaviour of reinforcing bars is also considered Moreover

the cyclic degradation due to low-cycle fatigue and the impactof corrosion on the tension and compression envelopes(including the postbuckling behaviour) are included Furtherdiscussion about the model development is available in [29]To implement the buckling model in OpenSees the uniaxialHystereticmodel available in OpenSees is modified and used(the detailed discussion is available in [25]) Figure 4 showsour proposed tension and compression envelope curves ofcorroded bars implemented in OpenSees

52 Reinforcing Steel Model Cyclic Response and Low-CycleFatigue Degradation As explained in Section 51 the Hys-teretic material model in OpenSees is modified to define thereinforcing steel model The cyclic response of the Hystereticmodel is defined by two pinch parameters (pinch 119909 andpinch 119910) The pinching effect in the cyclic response ofreinforcing bars is affected by the stiffness of the horizontal tiereinforcementThe optimumvalues of pinch parameters havebeen obtained by a comprehensive parametric study reportedin [25] (the calibrated values are pinch 119909 = 04 and pinch119910 = 06)

The Uniaxial Fatigue model is wrapped to the steelmaterial model to model the low-cycle fatigue degradationof corroded vertical reinforcement The low-cycle fatiguematerial constants are modified to account for the impactof corrosion on the low-cycle fatigue life of corroded barsbased on the model developed by [29] Figure 5 shows anexample cyclic response of the implemented Hysteretic +Fatigue model for the uncorroded and corroded reinforcingsteel Further detailed discussion about modelling combinedfatigue and buckling of reinforcing bars inside RC columns isavailable in [29]

53 Corrosion Damaged Confined Concrete Model The com-pressive behaviour of confined concrete is a function ofvolumetric ratio yield strength and fracture strain of thehorizontal tie reinforcement (ie spiral hoop and transversereinforcement) [39 40] Since tie reinforcement is the nearestto the surface being exposed to chloride attack they may

6 Advances in Materials Science and Engineering

minus30 minus20 minus10 0 10 20 30minus15

minus1

minus05

0

05

1

15

Cyclic response including fatiguemdashuncorrodedCyclic response including fatiguemdashcorroded

120578=120590120590

y

120585 = 120576120576y

Figure 5 Cyclic response of the Hysteretic + Fatigue model inOpenSees (20 mass loss)

start corroding prior to the corrosion initiation of verticalreinforcement As a result the volumetric ratio of tie rein-forcement is decreased due to cross section loss There isalso a reduced yield strength and fracture strain due to thepitting effect Therefore the internal confinement pressureof the core concrete can result in premature fracture of tiereinforcement

To date there has not been any experimental study toquantify and model the effect of corrosion on the nonlinearbehaviour of confined concrete under monotonic compres-sion and cyclic loading Further research is required to under-stand and model the extent of corrosion damage on confinedconcrete behaviour However a simplified methodology isused in this research tomodify the confined concretematerialmodel (which is a function of the percentage mass loss inhorizontal tie reinforcement) to account for the effect ofcorrosion damage

In this study the uniaxial Concrete04 material modelavailable in OpenSees is used to model the concrete ThePopovics curve [41] is used for the compression envelope andthe Karsan-Jirsa model [42] is used to determine the slopeof the curve for unloading and reloading in compressionFor tensile loading an exponential curve is used to definethe envelope to the stress-strain curve Further details areavailable in [43]

The parameters proposed by [40] are used to modelthe effect of confinement on concrete in compression Themaximum compressive stress of the concrete (120590cc) and thestrain at the maximum compressive strain (120576cc) can becalculated using the equations developed in [40]

The maximum crushing strain of the confined concreteis defined by the fracture of the first horizontal tiespiralreinforcement Here the model proposed by [44] is used topredict the concrete crushing strain as defined in

120576cc = 0004 + 14 (120588sc120590119910tie120576119906tie

120590119888

) (5)

where 120576119906tie is the fracture strain of the tiespiral reinforce-

ment 120588sc is the volumetric ratio of spiral reinforcement and120590119910tie is the yield stress of spiral reinforcement

minus20 minus18 minus16 minus14 minus12 minus10 minus8 minus6 minus4 minus2 0minus15

minus125

minus1

minus075

minus05

minus025

0

Original confined concrete modelCorrosion damaged confined concrete

120574=120590120590

c

120595 = 120576120576c0

Figure 6 Corrosion damaged confined concrete model (20 massloss)

It is clear that the confined concrete model is a functionof yield strength volumetric ratio and fracture strain ofthe confinementtie reinforcement Therefore the previouslydefined equations for reinforcing steel can be used to modifythe cross-sectional area yield strength and fracture strain oftie reinforcement as a function of the percentage mass lossAccordingly these modified values can be used to accountfor the impact of corrosion on confined concrete model(Figure 6)

54 Corrosion Damaged Cracked Cover Concrete ModelOnce corrosion initiates the corrosion products accumulatearound the reinforcement Given the volume of the corrosionproducts is bigger than the original reinforcing steel it gener-ates a radial pressureexpansion on the concrete surroundingthe reinforcement This behaviour is like a thick cylinderunder internal pressure that eventually results in fracture ofthe cover concrete [45ndash47] The cracking of cover concreteresults in loss of compressive strength and crushing strainof the concrete in the compressive zone of RC sectionsTherefore consideration needs to be given to model theinfluence of this cracking on the response of cover concretein compression

The response of cracked concrete in compression isdescribed in detail by [48] which is known as compressionfield theory (CFT) Based onCFT the compressive strength ofcracked concrete in compression depends on the magnitudeof the average tensile strain in the transverse direction whichcauses longitudinal microcracks Reference [49] employedthis method in nonlinear finite element analysis of corrosiondamaged RC beams with modified constitutive model forthe cracked cover concrete as a function of percentagemass loss and validated this against experimental resultsTherefore the equations suggested by [49] are employedto model the compression response of crack cover con-crete Figure 7(a) shows the compression envelope and Fig-ure 7(b) shows the tension envelope of the uniaxial materialmodel for corrosion damaged unconfined cover concreteused in the fibre model Further details are available in[49]

Advances in Materials Science and Engineering 7

minus25 minus2 minus15 minus1 minus05 0minus1

minus075

minus05

minus025

0

Original unconfined concrete modelCorrosion induced crack unconfined concrete

120595 = 120576120576c0

120574=120590120590

c

(a)

0 1 2 3 4 5 6 70

005

01

015

02

Original concrete tension envelopeCorrosion induced cracked concrete

120574=120590120590

c

120595 = 120576120576ct

(b)

Figure 7 Corrosion damaged cracked cover concrete model for 20 mass loss (a) compression (b) tension

55 Bond-Slip Model and Zero-Length Element In seismicdesign of RC structures and bridges plastic hinges are formedat the columnbeam ends This will induce a substantialstrain penetration along the longitudinal bars into the jointthat eventually results in slippage of longitudinal bars Thisphenomenon has been observed by other researchers exper-imentally [50] Reference [51] adopted a bar-slip model forthe end slip of longitudinal reinforcement in beam-columnjoints This model has been employed by [25] to model thecyclic behaviour of RC columns and is validated against UW-PEER experimental RC column database [52]

Corrosion affects the reinforcing steel near the surface ofthe concrete due to diffusion of chloride ions from the surfaceandor carbonation of cover concrete In bridge piers thevertical reinforcement bars are anchored to the foundationwell below the foundation surface Therefore the verticalreinforcement does not corrode at this depth and the bar-slipbehaviour of bars at the anchorage zone remains the same asin the uncorroded column This has been observed by otherresearchers experimentally [12ndash14]

It should be pointed out that corrosion does affect thebond strength of corroded vertical reinforcement abovethe foundation level (internal bond-slip within the columnitself) However based on the observed experimental resultsthe reduced bond strength does not govern the failure ofcolumns References [12ndash14] reported that the failure ofcorroded columns and beams under cyclic loading is mainlygovern by fracture of bars in tension due to low-cycle fatigueand buckling of bars and crushing of confined concrete incompression

Reference [53] conducted a comprehensive detailed non-linear finite element analysis of corroded RC beams andvalidated them against experimental results They havereported that reduced bond strength only changes the crackpattern and affects the serviceability of corroded beamsTheyconcluded that reduced bond strength does not affect theultimate capacity of corroded beams Therefore bond-slip ofcorroded vertical bars within the element is not considered inthis research

The detailed discussion and implementation of the zero-length section in modelling the cyclic behaviour of RCcolumns is available in [25]

6 Impact of Corrosion Damage on NonlinearResponse of RC Bridges Piers

In this section the impact of different corrosion damagescenarios on the inelastic response of RC bridge piers isexplored A comparative study on two hypothetical corrodedRC columns with different buckling lengths of vertical barsis conducted The columns are taken from the UW-PEERexperimental RC column database [52] These columns areused to validate and calibrate the basic numerical model forthe uncorroded columns [25]

To investigate the impact of corrosion on drift capacityand strength loss of RC columns a series of nonlinearpushover analyses with varied corrosion levels are conductedTo explore the impact of cyclic degradation nonlinear cyclicanalyses using the load history that was used in the exper-iment are conducted In order to investigate the impact ofdifferent modelling techniques and damage mechanism foreach analysis type three scenarios are considered

(a) Vertical and horizontal tie reinforcement are cor-roded but cover and core concrete are not affected bycorrosion

(b) Vertical and horizontal tie reinforcement are cor-roded and the cover concrete is cracked due tocorrosion but the core concrete is not affected

(c) Vertical and horizontal tie reinforcement are cor-roded the cover concrete is cracked and the coreconcrete is affected due to corrosion of confiningtiereinforcement

These scenarios will highlight the importance of each damagecomponent that needs to be considered in modelling nonlin-ear response of corroded RC columns

8 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008

minus300minus200minus100

0100200300

ExperimentFibre model

Drift ratio

Late

ral f

orce

(kN

)

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

ExperimentFibre model

Drift ratio

Late

ral f

orce

(kN

)

(b)

Figure 8 Comparison of experimental results and calibrated numerical model of uncorroded columns (a) Lehmanrsquos column 415 (b) Moyerand Kowalskyrsquos column 1

Lehmanrsquos column 415 and Moyer and Kowalskyrsquos column1 [50 54] are considered in this study The geometricaldetails material properties and detailed experimental resultsof these columns are available in [50 54] Figure 8 showsa comparison of the numerical model and experimentalresponses of these columns It should be noted that Lehmanrsquoscolumn 415 has 119871eff119889 = 10 and Moyer and Kowalskyrsquoscolumn 1 has 119871eff119889 = 4 The detailed discussion of thenumerical model validation is available in [25] It shouldbe noted that the maximum drift capacity in this paperis considered as the point where the force-displacementresponse of the column starts softening and losing strengthIt is found that the maximum drift capacity of both columnsat uncorroded state is about 6

The buckling lengths of corroded vertical reinforcementare calculated using the methodology described in Section 4The corrosion of horizontal ties is considered in the bucklinglength calculation As discussed previously (Section 4) thebuckling length of the vertical bars is a function of thetie reinforcementrsquos stiffness and the vertical reinforcementrsquosflexural rigidity Corrosion results in a reduction in flexuralrigidity of vertical barsTherefore the required stiffness fromtie reinforcement to restrain vertical bars against bucklingis reduced However corrosion also reduces the stiffness ofthe tie reinforcement For example in Moyer and Kowalskyrsquoscolumn the vertical reinforcement buckled between two tiesIn this case it was found that corrosion did not affect thebuckling length

In Lehmanrsquos column 415 the vertical reinforcementbuckled over five ties However once the corrosion levelexceeds 10 the buckling length reduced and the verticalreinforcement buckled over four ties It should be notedthat although the buckling length is reduced 119871eff119889

1015840 is notnecessarily reduced where 119871eff is the buckling length and 1198891015840is the diameter of the corroded vertical reinforcement Thisis because corrosion also reduces the diameter of verticalbars This change in buckling length is related to the relativecorrosion level and stiffness between the vertical and tiereinforcement

In practice the horizontal tie reinforcement is closer thanthe main vertical reinforcement to the surface of concreteTherefore it might start corroding earlier than verticalreinforcementThis phenomenonmight have an effect on thebuckling length and confined concrete behaviour Howeverthere has not been any research to date to explore thecorrelation between the corrosion levels of the horizontaltie and vertical reinforcement This is an area for futureresearch and therefore in this research in the absence of anyexperimentalfield data the same corrosion is considered forboth vertical and tie reinforcement

It should be noted that the calculation of the time tocorrosion initiation and time-dependent corrosion propaga-tion is out of the scope of this paper There are mathematicalmodels available in the literature that enable an estimationof the time to corrosion initiation and propagation basedon the environmental conditions [55 56] The corrosion ratecan also be measured on site by electrical equipment whichcan then be turned into a mass loss ratio using Faradayrsquoslaw of electrolysis [57] Given that the focus of this paperis on the impact of different mass loss ratios on the seismicperformance of RC columns the corrosion level is modelledby percentage mass loss throughout this paper

61 Scenario (a) Column Nonlinear Behaviour When Cor-rosion Is Assumed Present in Vertical and Horizontal TieReinforcement Only In this scenario it is assumed that thecorrosion damage is only limited to the steel reinforcement(vertical and horizontal tie reinforcement) that is cover con-crete is uncracked and corrosion of confining reinforcementdoes not affect the confined concrete behaviour Here thesteel model described in Section 51 is used which includesthe impact of corrosion on the buckling and postbucklingbehaviour in compression and strength and ductility loss intension

Figure 9 shows the results of monotonic pushover anal-yses Figure 9(a) shows that the failure mode of Lehmanrsquoscolumn 415 is by vertical bar buckling and core confined

Advances in Materials Science and Engineering 9

0 001 002 003 004 005 006 007 0080

50100150200250300350

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

Drift ratio

Late

ral f

orce

(kN

)

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

Drift ratio

Late

ral f

orce

(kN

)

(b)

Figure 9 Pushover analyses considering corrosion induced damage in reinforcing steel (a) Lehmanrsquos column 415 (b) Moyer and Kowalskyrsquoscolumn 1

concrete crushing up to 10 mass loss However as the cor-rosion level increases beyond 10mass loss the failure modechanges from vertical bar bucking and concrete crushing incompression to fracture of the vertical bars in tension

Figure 9(b) shows that Moyer and Kowalskyrsquos column1 has also failed in bar buckling and concrete crushing incompression However because 119871eff119889 = 4 the strength lossis not as significant as that of Lehmanrsquos column 415 with119871eff119889 = 10 under monotonic loading The corrosion levelup to 20 mass loss changes Moyer and Kowalskyrsquos column1 behaviour The failure initiates with bar buckling andconcrete crushing in compression and followed by fracture ofthe vertical reinforcement in tension With corrosion levelsgreater than 20 mass loss failure is by premature fractureof the vertical bars in tension At this point a cascade of barfracture can be seen in the graphs up to complete collapse ofthe columns

Figures 10(a) and 10(b) show Lehmanrsquos column 415 with10 and 20 mass losses under cyclic loading respectivelyComparing the monotonic and cyclic responses (the samecyclic load protocol as the experiment) shows that low-cyclefatigue has a significant impact on the column responseThe monotonic analysis showed that 10 mass loss did notresult in vertical bar fracture in tension and the failure wasgoverned by bar buckling and concrete crushing However incyclic analysis the failuremode is combined bar buckling andconcrete crushing in compression (failure initiation) followedby bar fracture in tension due to low-cycle fatigue

Here we have a system that does not technically fail incrushing and buckling but survives a little longer until thenext cycle when the vertical reinforcement fails in tensionIt was found that a mass loss ratio greater than 10 has asignificant impact on the nonlinear response of the corrodedcolumn due to reduced low-cycle fatigue life Figure 10(b)shows that at 20 mass loss resulted in bar fracture at 005drift ratio in pushover analysis but it resulted in bar fractureat 003 drift ratio under cyclic loading due to low-cycle fatiguefailure

Figures 10(c) and 10(d) show a similar result for Moyerand Kowalskyrsquos column 1 Overall Moyer and Kowalskyrsquoscolumn 1 has slightly less pinched cyclic responseThis is dueto the influence of the buckling length of the vertical bars andits cyclic degradation due to buckling [25]

62 Scenario (b) Column Nonlinear Behaviour When Corro-sion Is Assumed Present in Vertical and Horizontal Tie Rein-forcement and Cover Concrete Is Cracked In this scenarioit is assumed that the reinforcing steel (vertical and tie) iscorroded and the cover concrete is cracked due to corrosionof vertical reinforcementThe results of the pushover analysesare shown in Figure 11 The results in this case are almostidentical to the previous case (Section 61) where the damagein cover concrete was not considered Therefore in canbe concluded that whether or not we seek to model thecorrosion induced cracking of cover concrete it does not havea significant impact on the nonlinear response of corrodedcolumns Further discussion and comparison of this scenariowith other damage scenarios are available in Section 63

63 Scenario (c) Column Seismic Behaviour When Cor-rosion Is Assumed Present in Vertical and Horizontal TieReinforcement and Both Cover and Confined Concrete AreDamaged In this scenario it is assumed that the reinforc-ing steel (vertical and tie) is corroded cover concrete iscracked and the core confined concrete is affected by thecorrosion of horizontal tie reinforcement (as described inSection 53) Figure 12(a) shows the results of monotonicpushover analyses of Lehmanrsquos column 415 The results showthat the failure mechanism of this column for up to 10mass loss is bar buckling and core confined concrete crushingin compression However for corrosion levels beyond 10the failure mode changes This is a loss of drift capacitywhich starts with bar buckling and concrete crushing incompression and it is followed by bar fracture in tensionThese analyses demonstrate the importance of modelling the

10 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

Drift ratio

Late

ral f

orce

(kN

)

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

Drift ratio

Late

ral f

orce

(kN

)

(b)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

(c)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

(d)

Figure 10 Cyclic analyses considering corrosion induced damage in reinforcing steel (a) and (b) Lehmanrsquos column 415 (c) and (d) Moyerand Kowalskyrsquos column 1

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(b)

Figure 11 Pushover analyses considering corrosion induced damage in reinforcing steel and cracked cover concrete (a) Lehmanrsquos column415 (b) Moyer and Kowalskyrsquos column 1

Advances in Materials Science and Engineering 11

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(b)

Figure 12 Pushover analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a)Lehmanrsquos column 415 (b) Moyer and Kowalskyrsquos column 1

influence of corrosion on the confined concrete (throughloss of confining tie reinforcement) This corrosion damageon the confined concrete results in a rapid reduction instrength and ductility of the corroded columns compared tothe previous cases where confined concrete was considered tobe undamaged

Figure 12(b) shows the results of pushover analyses ofMoyer andKowalskyrsquos column 1 In this case the failuremodewas mainly bar buckling and concrete crushing followed byfracture of bars in tension for up to 20 mass loss Howevercorrosion levels beyond 20 mass loss have changed thefailure mode to premature fracture of bars in tension Thisdifference between the behaviour of the two columns is due tothe buckling behaviour of the vertical bars Given that Moyerand Kowalskyrsquos column 1 has much smaller buckling lengththe strength degradation in compression is much smallerthan Lehmanrsquos column 415 Therefore corrosion has more asignificant impact in terms of ductility loss of bars in tensionwhereas in Lehmanrsquos column 415 failure initiates with severebar buckling and concrete crushing then it is followed byfracture of vertical bars in tension

Figure 13 shows the results of cyclic analysis It showsthe cyclic analyses of Lehmanrsquos column 415 and Moyer andKowalskyrsquos column 1 with 10 and 20 mass loss togetherwith the corresponding pushover envelopes Figure 13 showsthat the extent of corrosion damage under cyclic loadingis more severe than monotonic loading The results ofmonotonic analysis showed that considering the ductility lossof corroded bars in tension and confinement reinforcementin compression has a big impact on bar buckling andfracture of reinforcement However cyclic analysis resultsshow that considering cyclic degradation due to low-cyclefatigue is crucial to have a realistic evaluation of the seismicperformance of existing corroded columns

For example in Figures 13(a) and 13(b) the failure ofLehmanrsquos column 415 was governed by bar buckling andconcrete crushing for a corrosion level up to 10 undermonotonic loadingHowever the same corrosion level results

in a much more severe drift capacity loss under cyclicloading due to a reduced low-cycle fatigue life Similarly inFigures 13(c) and 13(d) the failure of Moyer and Kowalskyrsquoscolumn was governed by concrete crushing in compressionfollowed by bar fracture in tension However low-cyclefatigue degradation due to cyclic loading results in prematurefracture of bars and subsequently severe loss of drift capacity

7 Comparison of the NonlinearResponses of Corroded Columns Computedin Different Scenarios

In order to clearly demonstrate the significance of corrosionmodels on the inelastic response of RC columns a com-parison between the computed responses of two columnswith different scenarios has been made The responses ofcolumns with 20 mass loss in monotonic pushover andcyclic analyses are compared and shown in Figure 14

Figure 14 shows the monotonic pushover and cyclicresponses of Lehmanrsquos column 415 andMoyer and Kowalskyrsquoscolumn 1 with 20 mass losses and different corrosiondamage models Figures 14(a) and 14(b) show that if thecorrosion induced damage to confined concrete is ignoredthe predicted failure mode is likely to be the fracture of barsin tension due to their reduced ductility However if thecorrosion induced damage to confined concrete is addedFigure 14(a) shows that the failure mode of Lehmanrsquos column415 will change to concrete crushing and buckling of thevertical bars in compression

Figure 14(b) shows that the failure mode of Moyer andKowalskyrsquos column 1 initiates with concrete crushing andbuckling of bars in compression and then it is followedby fracture of bars in tension This difference in failuremechanism is due to the differences in confinement level thebuckling length of the vertical bars the ratio of longitudinalreinforcement and the axial force ratio on the columnThere-fore in order to predict the nonlinear response accurately adetailed finite element model is required

12 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(d)

Figure 13 Cyclic analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a) and(b) Lehmanrsquos column 415 (c) and (d) Moyer and Kowalskyrsquos column 1

It is found that the failure mode under cyclic loading ismainly governed by the fracture of horizontal bars in tensiondue to reduced low-cycle fatigue life (Figures 14(c) and 14(d))This is a very important finding as it suggests that nonlinearquasistatic pushover analysis on its own is not adequate forperformance assessment of existing corroded bridge piers

With reference to Figure 14 it is evident that consideringthe impact of the corrosion damage on core confined con-crete and low-cycle fatigue degradation is crucial Thereforethey need to be considered when modelling the nonlinearbehaviour of corrosion damaged RC bridge piers underseismic loading This finding is in good agreement with theobserved experimental results by other researchers [12ndash1458]

A series of experimental studies were conducted in [12]on the cyclic behaviour of large-scale corroded cantilever RCbeams Ou et al found that as the level of corrosion increasesthe flexural failure initiates with premature buckling oflongitudinal bars This conclusion is in good agreement withthe numerical results discussed in this paper In another study[13] a series of experimental studies were conducted on cyclicbehaviour of corroded RC columns with varied axial forceMa et al have reported that once the corrosion level increases

beyond about 14 rapid strength and ductility reductionand cyclic degradation in hysteretic loops are seen due toreduced low-cycle fatigue life and premature buckling ofvertical reinforcement This conclusion is in good agreementwith the predicted failure modes using the numerical modelpresented in this paper

The detailed finite element model developed in thispaper can accurately model the nonlinear behaviour ofcorrodedRCcolumns subject to cyclic loading up to completecollapse There is a need to extend the PEER-UW columndatabase to include corroded RC columns so that furthercalibrationvalidation of the material model parameters canbe performed However the modelling technique developedin this paper is able to simulate the multiple failure modesof corroded RC columns simultaneously It represents thecurrent state of the art and as such they provide a novel com-putational framework for the seismic response prediction ofcorroded RC bridges

8 Conclusions

A series of pushover and cyclic analyses on two hypotheticalcorroded RC columns are conducted and these are used

Advances in Materials Science and Engineering 13

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(d)

Figure 14 Comparison of the computed responses of columns with different deterioration models (a) and (c) Lehmanrsquos column 415 undermonotonic and cyclic loading (b) and (d) Moyer and Kowalskyrsquos column 1 under monotonic and cyclic loading

to explore the performance of the proposed computationalframework The impact of corrosion on (i) the verticalreinforcing steel (ii) the tieconfinement (iii) the cover(unconfined) concrete and (iv) the core (confined) concreteis represented through new material models The proposednew steel material model accounts for (i) inelastic nonlinearbuckling of the vertical reinforcement (ii) the corrosion lossof area (iii) the nonuniform corrosion pitting and (iv) low-cycle high amplitude fatigueThenew cover concretematerialmodel includes the influence of internal pressure due tothe build-up of corrosion products (using compression fieldtheory) The new core concrete model includes the influenceof corrosion induced loss of confining reinforcement

The main outcomes of this study can be summarised asfollows

(1) Corrosion has a more significant impact on theductility loss (drift capacity) of RC columns than thestrength loss (plastic moment capacity)

(2) The numerical model developed in this paper is ableto predict the nonlinear flexural response of corrodedRC columns up to complete collapse Results showwhich depends on a cyclic load history that flexuralfailure can be initiated by the buckling of vertical bars

and crushing of core concrete which is then followedby fracture of bars in tension In cases where thebuckling of bars is not an issue or the buckling lengthis too short (119871eff119889

1015840le 5) the failure is governed by the

fracture of the vertical bars in tension due to low-cyclehigh amplitude fatigue

(3) The analyses results show that for the seismic perfor-mance and evaluation of existing corroded bridgesmonotonic pushover analysis is not sufficient Thecyclic degradation due to low-cycle high amplitudefatigue has a significant influence on the response ofcorroded RC columns

(4) The results of this study show that it is inadequate toassume that corrosion only affects the main verticalreinforcement in the column It was found that theconfined concrete with corroded confinement rein-forcement starts crushing much faster than uncor-roded undamaged concrete This changes the failuremode and results in premature buckling of the ver-tical reinforcement This change in the failure modecannot be predicted if the damage in core confinedconcrete due to corrosion of tie reinforcement isignored This is in good agreement with observed

14 Advances in Materials Science and Engineering

experimental results reported by other researchers[12ndash14]

(5) The modelling technique developed in this paper hassignificantly improved the earlier models and canbe used by other researchers in the future researchfor seismic vulnerability and fragility analysis ofcorroded RC bridges

Disclosure

Any findings opinions and recommendations provided inthis paper are only based on the authorsrsquo view

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This research is conducted in collaboration with the Univer-sity of Bristol and the University of Washington while thefirst author was on sabbatical leave in the US The fundingprovided by the World Wide University Network throughthe Research Mobility Program to the first author was muchappreciated The authors would like to thank Professor MarcO Eberhard and Professor John F Stanton for providingvaluable guidance during the course of this research

References

[1] S Hida F I S Ibrahim H A Capers et al ldquoAssuringbridge safety and serviceability in Europerdquo Tech Rep FHWA-PL-10-014 Office of International Programs Federal HighwayAdministration US Department of Transportation AmericanAssociation of State Highway and Transportation Officials2010

[2] ASCE Failure to Act The Economic Impact of Current Invest-ment Trends in Surface Transportation Infrastructure EconomicDevelopment Research Group Inc ASCE 2011

[3] D-E Choe P Gardoni D Rosowsky and T Haukaas ldquoProb-abilistic capacity models and seismic fragility estimates forRC columns subject to corrosionrdquo Reliability Engineering andSystem Safety vol 93 no 3 pp 383ndash393 2008

[4] L Berto R Vitaliani A Saetta and P Simioni ldquoSeismicassessment of existing RC structures affected by degradationphenomenardquo Structural Safety vol 31 no 4 pp 284ndash297 2009

[5] J Ghosh and J E Padgett ldquoAging considerations in the devel-opment of time-dependent seismic fragility curvesrdquo Journal ofStructural Engineering vol 136 no 12 pp 1497ndash1511 2010

[6] A Alipour B Shafei and M Shinozuka ldquoPerformance evalu-ation of deteriorating highway bridges located in high seismicareasrdquo Journal of Bridge Engineering vol 16 no 5 pp 597ndash6112011

[7] F Biondini E Camnasio and A Palermo ldquoLifetime seismicperformance of concrete bridges exposed to corrosionrdquo Struc-ture and Infrastructure Engineering vol 10 no 7 pp 880ndash9002014

[8] M Akiyama D M Frangopol and H Matsuzaki ldquoLife-cyclereliability of RC bridge piers under seismic and airborne chlo-ride hazardsrdquo Earthquake Engineering and Structural Dynamicsvol 40 no 15 pp 1671ndash1687 2011

[9] F Biondini A Palermo and G Toniolo ldquoSeismic performanceof concrete structures exposed to corrosion case studies of low-rise precast buildingsrdquo Structure and Infrastructure Engineeringvol 7 no 1-2 pp 109ndash119 2011

[10] C K Chiu F J Tu and F P Hsiao ldquoLifetime seismic perfor-mance assessment for chloride-corroded reinforced concretebuildingsrdquo Structure and Infrastructure Engineering vol 11 no3 pp 345ndash362 2015

[11] M Sanchez-Silva G-A Klutke and D V Rosowsky ldquoLife-cycleperformance of structures subject to multiple deteriorationmechanismsrdquo Structural Safety vol 33 no 3 pp 206ndash217 2011

[12] Y-C Ou L-L Tsai and H-H Chen ldquoCyclic performance oflarge-scale corroded reinforced concrete beamsrdquo EarthquakeEngineering and StructuralDynamics vol 41 no 4 pp 593ndash6042012

[13] Y Ma Y Che and J Gong ldquoBehavior of corrosion damagedcircular reinforced concrete columns under cyclic loadingrdquoConstruction and Building Materials vol 29 pp 548ndash556 2012

[14] A Meda S Mostosi Z Rinaldi and P Riva ldquoExperimentalevaluation of the corrosion influence on the cyclic behaviour ofRC columnsrdquo Engineering Structures vol 76 pp 112ndash123 2014

[15] A A Almusallam ldquoEffect of degree of corrosion on theproperties of reinforcing steel barsrdquo Construction and BuildingMaterials vol 15 no 8 pp 361ndash368 2001

[16] Y G Du L A Clark and A H C Chan ldquoResidual capacity ofcorroded reinforcing barsrdquoMagazine of Concrete Research vol57 no 3 pp 135ndash147 2005

[17] Y G Du L A Clarkt and A H C Chan ldquoEffect of corrosionon ductility of reinforcing barsrdquoMagazine of Concrete Researchvol 57 no 7 pp 407ndash419 2005

[18] J Cairns G A Plizzari Y Du D W Law and C FranzonildquoMechanical properties of corrosion-damaged reinforcementrdquoACI Materials Journal vol 102 no 4 pp 256ndash264 2005

[19] C A ApostolopoulosM P Papadopoulos and S G PantelakisldquoTensile behavior of corroded reinforcing steel bars BSt 500srdquoConstruction and Building Materials vol 20 no 9 pp 782ndash7892006

[20] C A Apostolopoulos ldquoMechanical behavior of corroded rein-forcing steel bars S500s tempcore under low cycle fatiguerdquoConstruction andBuildingMaterials vol 21 no 7 pp 1447ndash14562007

[21] M M Kashani A J Crewe and N A Alexander ldquoNonlinearstress-strain behaviour of corrosion-damaged reinforcing barsincluding inelastic bucklingrdquo Engineering Structures vol 48 pp417ndash429 2013

[22] M M Kashani A J Crewe and N A Alexander ldquoNonlinearcyclic response of corrosion-damaged reinforcing bars with theeffect of bucklingrdquo Construction and Building Materials vol 41pp 388ndash400 2013

[23] M M Kashani A J Crewe and N A Alexander ldquoUse of a 3Doptical measurement technique for stochastic corrosion patternanalysis of reinforcing bars subjected to accelerated corrosionrdquoCorrosion Science vol 73 pp 208ndash221 2013

[24] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoFinite element investigation of the influence of corrosionpattern on inelastic buckling and cyclic response of corrodedreinforcing barsrdquo Engineering Structures vol 75 pp 113ndash1252014

Advances in Materials Science and Engineering 15

[25] M M Kashani Seismic performance of corroded rc bridge piersdevelopment of a multi-mechanical nonlinear fibre beam-columnmodel [PhD thesis] University of Bristol Bristol UK 2014

[26] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part I Formula-tionrdquo Earthquake Engineering and Structural Dynamics vol 25no 7 pp 711ndash725 1996

[27] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part II Applica-tionsrdquoEarthquake Engineering and Structural Dynamics vol 25no 7 pp 727ndash742 1996

[28] The Open System for Earthquake Engineering Simulation(OpenSees) Pacific Earthquake Engineering Research CentreUniversity of California Berkeley Berkeley Calif USA 2011

[29] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoPhenomenological hysteretic model for corroded reinforcingbars including inelastic buckling and low-cycle fatigue degrada-tionrdquo Computers and Structures vol 156 article 5393 pp 58ndash712015

[30] J Coleman and E Spacone ldquoLocalization issues in force-basedframe elementsrdquo Journal of Structural Engineering vol 127 no11 pp 1257ndash1265 2001

[31] J S Pugh Numerical simulation of walls and seismic designrecommendations for walled buildings [PhD thesis] Universityof Washington Seattle Wash USA 2012

[32] D V Val and R E Melchers ldquoReliability of deteriorating RCslab bridgesrdquo Journal of Structural Engineering vol 123 no 12pp 1638ndash1644 1997

[33] M S Darmawan and M G Stewart ldquoEffect of pitting corro-sion on capacity of prestressing wiresrdquo Magazine of ConcreteResearch vol 59 no 2 pp 131ndash139 2007

[34] R P Dhakal and K Maekawa ldquoReinforcement stability andfracture of cover concrete in reinforced concrete membersrdquoJournal of Structural Engineering vol 128 no 10 pp 1253ndash12622002

[35] C Lee J F Bonacci M D A Thomas et al ldquoAcceleratedcorrosion and repair of reinforced concrete columns usingcarbon fibre reinforced polymer sheetsrdquo Canadian Journal ofCivil Engineering vol 27 no 5 pp 941ndash948 2000

[36] W Aquino Long-term performance of seismically rehabilitatedcorrosion-damaged columns [PhD thesis] University of Illinoisat Urbana-Champaign Champaign Ill USA 2002

[37] S Timoshenko and J Gere Theory of Elastic StabilityMacGraw-Hill New York NY USA 1963

[38] S J Pantazopoulou ldquoDetailing for reinforcement stability in RCmembersrdquo Journal of Structural Engineering vol 124 no 6 pp623ndash632 1998

[39] J B Mander M J N Priestley and R Park ldquoObserved stress-strain behavior of confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1827ndash1849 1988

[40] J B Mander M J Priestley and R Park ldquoTheoretical stress-strain model for confined concreterdquo Journal of Structural Engi-neering (United States) vol 114 no 8 pp 1804ndash1826 1988

[41] S Popovics ldquoAnumerical approach to the complete stress-straincurve of concreterdquo Cement and Concrete Research vol 3 no 5pp 583ndash599 1973

[42] I D Karsan and J O Jirsa ldquoBehavior of concrete undercompressive loadingrdquo Journal of Structural Division vol 95article ST12 1969

[43] M P Berry andMO Eberhard ldquoPerformancemodeling strate-gies for modern reinforced concrete bridge columnsrdquo PEER

Research Report University of California Berkeley BerkeleyCalif USA 2006

[44] B D Scott R Park and M J N Priestley ldquoStress-strainbehavior of concrete confined by overlapping hoops at low andhigh strain ratesrdquo Journal of the American Concrete Institute vol79 no 1 pp 13ndash27 1982

[45] A S Al-Harthy M G Stewart and J Mullard ldquoConcrete covercracking caused by steel reinforcement corrosionrdquoMagazine ofConcrete Research vol 63 no 9 pp 655ndash667 2011

[46] T Vidal A Castel and R Francois ldquoAnalyzing crack width topredict corrosion in reinforced concreterdquo Cement and ConcreteResearch vol 34 no 1 pp 165ndash174 2004

[47] F J Molina C Alonso and C Andrade ldquoCover cracking as afunction of rebar corrosion part 2-numerical modelrdquoMaterialsand Structures vol 26 no 9 pp 532ndash548 1993

[48] F J Vecchio and M P Collins ldquoThe modified compression-field theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[49] D Coronelli and P Gambarova ldquoStructural assessment ofcorroded reinforced concrete beams modeling guidelinesrdquoJournal of Structural Engineering vol 130 no 8 pp 1214ndash12242004

[50] D E Lehman and J P Moehle ldquoSeismic performance of well-confined concrete columnsrdquo PEER Research Report Universityof California at Berkeley 2000

[51] L N Lowes and A Altoontash ldquoModeling reinforced-concretebeam-column joints subjected to cyclic loadingrdquo Journal ofStructural Engineering vol 129 no 12 pp 1686ndash1697 2003

[52] M Berry M Parrish and M Eberhard ldquoPerformance databaseUserrsquos manualrdquo in Pacific Earthquake Engineering ResearchCentre 2004 University of California at Berkeley 2004httpwwwcewashingtonedusimpeera1

[53] A N Kallias and M Imran Rafiq ldquoFinite element investigationof the structural response of corroded RC beamsrdquo EngineeringStructures vol 32 no 9 pp 2984ndash2994 2010

[54] M J Moyer and M J Kowalsky ldquoInfluence of tension strain onbuckling of reinforcement in concrete columnsrdquo ACI StructuralJournal vol 100 no 1 pp 75ndash85 2003

[55] K A T Vu andM G Stewart ldquoStructural reliability of concretebridges including improved chloride-induced corrosion mod-elsrdquo Structural Safety vol 22 no 4 pp 313ndash333 2000

[56] D V Val ldquoFactors affecting life-cycle cost analysis of RCstructures in chloride contaminated environmentsrdquo Journal ofInfrastructure Systems vol 13 no 2 pp 135ndash143 2007

[57] J P BroomfieldCorrosion of Steel in Concrete Taylor amp FrancisLondon UK 2nd edition 2007

[58] M M Kashani P Alagheband R Khan and S Davis ldquoImpactof corrosion on low-cycle fatigue degradation of reinforcingbars with the effect of inelastic bucklingrdquo International Journalof Fatigue vol 77 pp 174ndash185 2015

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 5

0 10 20 30 40 50 600

025

05

075

1

125

15

Tension envelopemdashuncorroded reinforcementTension envelopemdashcorroded reinforcement

120578=120590120590

y

120585 = 120576120576y

(a)

minus40 minus35 minus30 minus25 minus20 minus15 minus10 minus5 0minus12

minus1

minus08

minus06

minus04

minus02

0

Buckling envelopemdashuncorroded reinforcementBuckling envelopemdashcorroded reinforcement

120578=120590120590

y

120585 = 120576120576y

(b)

Figure 4 Implemented tension and compression envelopes of corroded bars in OpenSees (20 mass loss)

can be modified based on the following empirical equationsuggested by [16]

1205901015840

119910= 120590119910(1 minus 0005120595) (2)

where 120595 is the percentage mass loss of the reinforcement

42 Influence of Corrosion on Stiffness of Tie ReinforcementIn this study the stiffness of the horizontal ties of spiralreinforcement is computed using the following empiricalequation suggested by [38]

119870119905=

4119864sp1198601015840

sp

radic(1199042 + 1198892119888)

(3)

where 119864sp is the elastic modulus 1198601015840sp is the cross-sectionalarea of corroded spiral reinforcement 119904 is the spiral pitch and119889119888is the core diameterThe focus of this paper is on circular columns However

in the case of rectangular section the axial stiffness of tiereinforcement can be computed using

119870119905=119864st1198601015840

st119897119905

(4)

where 119864st is the elastic modulus of tie reinforcement 1198601015840st isthe cross-sectional area of corroded tie reinforcement and 119897

119905

is the length of the rectangular tie reinforcement

5 Description of Uniaxial Material Modelsincluding Corrosion Damage

51 Reinforcing Steel Model Tension and CompressionEnvelopes The uniaxial material model developed by [29] isused to model the reinforcing steel This advanced materialmodel combines the material nonlinearity with geometricalnonlinearity due to inelastic buckling into a single-materialmodel The impact of geometrical nonlinearity on cyclicbehaviour of reinforcing bars is also considered Moreover

the cyclic degradation due to low-cycle fatigue and the impactof corrosion on the tension and compression envelopes(including the postbuckling behaviour) are included Furtherdiscussion about the model development is available in [29]To implement the buckling model in OpenSees the uniaxialHystereticmodel available in OpenSees is modified and used(the detailed discussion is available in [25]) Figure 4 showsour proposed tension and compression envelope curves ofcorroded bars implemented in OpenSees

52 Reinforcing Steel Model Cyclic Response and Low-CycleFatigue Degradation As explained in Section 51 the Hys-teretic material model in OpenSees is modified to define thereinforcing steel model The cyclic response of the Hystereticmodel is defined by two pinch parameters (pinch 119909 andpinch 119910) The pinching effect in the cyclic response ofreinforcing bars is affected by the stiffness of the horizontal tiereinforcementThe optimumvalues of pinch parameters havebeen obtained by a comprehensive parametric study reportedin [25] (the calibrated values are pinch 119909 = 04 and pinch119910 = 06)

The Uniaxial Fatigue model is wrapped to the steelmaterial model to model the low-cycle fatigue degradationof corroded vertical reinforcement The low-cycle fatiguematerial constants are modified to account for the impactof corrosion on the low-cycle fatigue life of corroded barsbased on the model developed by [29] Figure 5 shows anexample cyclic response of the implemented Hysteretic +Fatigue model for the uncorroded and corroded reinforcingsteel Further detailed discussion about modelling combinedfatigue and buckling of reinforcing bars inside RC columns isavailable in [29]

53 Corrosion Damaged Confined Concrete Model The com-pressive behaviour of confined concrete is a function ofvolumetric ratio yield strength and fracture strain of thehorizontal tie reinforcement (ie spiral hoop and transversereinforcement) [39 40] Since tie reinforcement is the nearestto the surface being exposed to chloride attack they may

6 Advances in Materials Science and Engineering

minus30 minus20 minus10 0 10 20 30minus15

minus1

minus05

0

05

1

15

Cyclic response including fatiguemdashuncorrodedCyclic response including fatiguemdashcorroded

120578=120590120590

y

120585 = 120576120576y

Figure 5 Cyclic response of the Hysteretic + Fatigue model inOpenSees (20 mass loss)

start corroding prior to the corrosion initiation of verticalreinforcement As a result the volumetric ratio of tie rein-forcement is decreased due to cross section loss There isalso a reduced yield strength and fracture strain due to thepitting effect Therefore the internal confinement pressureof the core concrete can result in premature fracture of tiereinforcement

To date there has not been any experimental study toquantify and model the effect of corrosion on the nonlinearbehaviour of confined concrete under monotonic compres-sion and cyclic loading Further research is required to under-stand and model the extent of corrosion damage on confinedconcrete behaviour However a simplified methodology isused in this research tomodify the confined concretematerialmodel (which is a function of the percentage mass loss inhorizontal tie reinforcement) to account for the effect ofcorrosion damage

In this study the uniaxial Concrete04 material modelavailable in OpenSees is used to model the concrete ThePopovics curve [41] is used for the compression envelope andthe Karsan-Jirsa model [42] is used to determine the slopeof the curve for unloading and reloading in compressionFor tensile loading an exponential curve is used to definethe envelope to the stress-strain curve Further details areavailable in [43]

The parameters proposed by [40] are used to modelthe effect of confinement on concrete in compression Themaximum compressive stress of the concrete (120590cc) and thestrain at the maximum compressive strain (120576cc) can becalculated using the equations developed in [40]

The maximum crushing strain of the confined concreteis defined by the fracture of the first horizontal tiespiralreinforcement Here the model proposed by [44] is used topredict the concrete crushing strain as defined in

120576cc = 0004 + 14 (120588sc120590119910tie120576119906tie

120590119888

) (5)

where 120576119906tie is the fracture strain of the tiespiral reinforce-

ment 120588sc is the volumetric ratio of spiral reinforcement and120590119910tie is the yield stress of spiral reinforcement

minus20 minus18 minus16 minus14 minus12 minus10 minus8 minus6 minus4 minus2 0minus15

minus125

minus1

minus075

minus05

minus025

0

Original confined concrete modelCorrosion damaged confined concrete

120574=120590120590

c

120595 = 120576120576c0

Figure 6 Corrosion damaged confined concrete model (20 massloss)

It is clear that the confined concrete model is a functionof yield strength volumetric ratio and fracture strain ofthe confinementtie reinforcement Therefore the previouslydefined equations for reinforcing steel can be used to modifythe cross-sectional area yield strength and fracture strain oftie reinforcement as a function of the percentage mass lossAccordingly these modified values can be used to accountfor the impact of corrosion on confined concrete model(Figure 6)

54 Corrosion Damaged Cracked Cover Concrete ModelOnce corrosion initiates the corrosion products accumulatearound the reinforcement Given the volume of the corrosionproducts is bigger than the original reinforcing steel it gener-ates a radial pressureexpansion on the concrete surroundingthe reinforcement This behaviour is like a thick cylinderunder internal pressure that eventually results in fracture ofthe cover concrete [45ndash47] The cracking of cover concreteresults in loss of compressive strength and crushing strainof the concrete in the compressive zone of RC sectionsTherefore consideration needs to be given to model theinfluence of this cracking on the response of cover concretein compression

The response of cracked concrete in compression isdescribed in detail by [48] which is known as compressionfield theory (CFT) Based onCFT the compressive strength ofcracked concrete in compression depends on the magnitudeof the average tensile strain in the transverse direction whichcauses longitudinal microcracks Reference [49] employedthis method in nonlinear finite element analysis of corrosiondamaged RC beams with modified constitutive model forthe cracked cover concrete as a function of percentagemass loss and validated this against experimental resultsTherefore the equations suggested by [49] are employedto model the compression response of crack cover con-crete Figure 7(a) shows the compression envelope and Fig-ure 7(b) shows the tension envelope of the uniaxial materialmodel for corrosion damaged unconfined cover concreteused in the fibre model Further details are available in[49]

Advances in Materials Science and Engineering 7

minus25 minus2 minus15 minus1 minus05 0minus1

minus075

minus05

minus025

0

Original unconfined concrete modelCorrosion induced crack unconfined concrete

120595 = 120576120576c0

120574=120590120590

c

(a)

0 1 2 3 4 5 6 70

005

01

015

02

Original concrete tension envelopeCorrosion induced cracked concrete

120574=120590120590

c

120595 = 120576120576ct

(b)

Figure 7 Corrosion damaged cracked cover concrete model for 20 mass loss (a) compression (b) tension

55 Bond-Slip Model and Zero-Length Element In seismicdesign of RC structures and bridges plastic hinges are formedat the columnbeam ends This will induce a substantialstrain penetration along the longitudinal bars into the jointthat eventually results in slippage of longitudinal bars Thisphenomenon has been observed by other researchers exper-imentally [50] Reference [51] adopted a bar-slip model forthe end slip of longitudinal reinforcement in beam-columnjoints This model has been employed by [25] to model thecyclic behaviour of RC columns and is validated against UW-PEER experimental RC column database [52]

Corrosion affects the reinforcing steel near the surface ofthe concrete due to diffusion of chloride ions from the surfaceandor carbonation of cover concrete In bridge piers thevertical reinforcement bars are anchored to the foundationwell below the foundation surface Therefore the verticalreinforcement does not corrode at this depth and the bar-slipbehaviour of bars at the anchorage zone remains the same asin the uncorroded column This has been observed by otherresearchers experimentally [12ndash14]

It should be pointed out that corrosion does affect thebond strength of corroded vertical reinforcement abovethe foundation level (internal bond-slip within the columnitself) However based on the observed experimental resultsthe reduced bond strength does not govern the failure ofcolumns References [12ndash14] reported that the failure ofcorroded columns and beams under cyclic loading is mainlygovern by fracture of bars in tension due to low-cycle fatigueand buckling of bars and crushing of confined concrete incompression

Reference [53] conducted a comprehensive detailed non-linear finite element analysis of corroded RC beams andvalidated them against experimental results They havereported that reduced bond strength only changes the crackpattern and affects the serviceability of corroded beamsTheyconcluded that reduced bond strength does not affect theultimate capacity of corroded beams Therefore bond-slip ofcorroded vertical bars within the element is not considered inthis research

The detailed discussion and implementation of the zero-length section in modelling the cyclic behaviour of RCcolumns is available in [25]

6 Impact of Corrosion Damage on NonlinearResponse of RC Bridges Piers

In this section the impact of different corrosion damagescenarios on the inelastic response of RC bridge piers isexplored A comparative study on two hypothetical corrodedRC columns with different buckling lengths of vertical barsis conducted The columns are taken from the UW-PEERexperimental RC column database [52] These columns areused to validate and calibrate the basic numerical model forthe uncorroded columns [25]

To investigate the impact of corrosion on drift capacityand strength loss of RC columns a series of nonlinearpushover analyses with varied corrosion levels are conductedTo explore the impact of cyclic degradation nonlinear cyclicanalyses using the load history that was used in the exper-iment are conducted In order to investigate the impact ofdifferent modelling techniques and damage mechanism foreach analysis type three scenarios are considered

(a) Vertical and horizontal tie reinforcement are cor-roded but cover and core concrete are not affected bycorrosion

(b) Vertical and horizontal tie reinforcement are cor-roded and the cover concrete is cracked due tocorrosion but the core concrete is not affected

(c) Vertical and horizontal tie reinforcement are cor-roded the cover concrete is cracked and the coreconcrete is affected due to corrosion of confiningtiereinforcement

These scenarios will highlight the importance of each damagecomponent that needs to be considered in modelling nonlin-ear response of corroded RC columns

8 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008

minus300minus200minus100

0100200300

ExperimentFibre model

Drift ratio

Late

ral f

orce

(kN

)

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

ExperimentFibre model

Drift ratio

Late

ral f

orce

(kN

)

(b)

Figure 8 Comparison of experimental results and calibrated numerical model of uncorroded columns (a) Lehmanrsquos column 415 (b) Moyerand Kowalskyrsquos column 1

Lehmanrsquos column 415 and Moyer and Kowalskyrsquos column1 [50 54] are considered in this study The geometricaldetails material properties and detailed experimental resultsof these columns are available in [50 54] Figure 8 showsa comparison of the numerical model and experimentalresponses of these columns It should be noted that Lehmanrsquoscolumn 415 has 119871eff119889 = 10 and Moyer and Kowalskyrsquoscolumn 1 has 119871eff119889 = 4 The detailed discussion of thenumerical model validation is available in [25] It shouldbe noted that the maximum drift capacity in this paperis considered as the point where the force-displacementresponse of the column starts softening and losing strengthIt is found that the maximum drift capacity of both columnsat uncorroded state is about 6

The buckling lengths of corroded vertical reinforcementare calculated using the methodology described in Section 4The corrosion of horizontal ties is considered in the bucklinglength calculation As discussed previously (Section 4) thebuckling length of the vertical bars is a function of thetie reinforcementrsquos stiffness and the vertical reinforcementrsquosflexural rigidity Corrosion results in a reduction in flexuralrigidity of vertical barsTherefore the required stiffness fromtie reinforcement to restrain vertical bars against bucklingis reduced However corrosion also reduces the stiffness ofthe tie reinforcement For example in Moyer and Kowalskyrsquoscolumn the vertical reinforcement buckled between two tiesIn this case it was found that corrosion did not affect thebuckling length

In Lehmanrsquos column 415 the vertical reinforcementbuckled over five ties However once the corrosion levelexceeds 10 the buckling length reduced and the verticalreinforcement buckled over four ties It should be notedthat although the buckling length is reduced 119871eff119889

1015840 is notnecessarily reduced where 119871eff is the buckling length and 1198891015840is the diameter of the corroded vertical reinforcement Thisis because corrosion also reduces the diameter of verticalbars This change in buckling length is related to the relativecorrosion level and stiffness between the vertical and tiereinforcement

In practice the horizontal tie reinforcement is closer thanthe main vertical reinforcement to the surface of concreteTherefore it might start corroding earlier than verticalreinforcementThis phenomenonmight have an effect on thebuckling length and confined concrete behaviour Howeverthere has not been any research to date to explore thecorrelation between the corrosion levels of the horizontaltie and vertical reinforcement This is an area for futureresearch and therefore in this research in the absence of anyexperimentalfield data the same corrosion is considered forboth vertical and tie reinforcement

It should be noted that the calculation of the time tocorrosion initiation and time-dependent corrosion propaga-tion is out of the scope of this paper There are mathematicalmodels available in the literature that enable an estimationof the time to corrosion initiation and propagation basedon the environmental conditions [55 56] The corrosion ratecan also be measured on site by electrical equipment whichcan then be turned into a mass loss ratio using Faradayrsquoslaw of electrolysis [57] Given that the focus of this paperis on the impact of different mass loss ratios on the seismicperformance of RC columns the corrosion level is modelledby percentage mass loss throughout this paper

61 Scenario (a) Column Nonlinear Behaviour When Cor-rosion Is Assumed Present in Vertical and Horizontal TieReinforcement Only In this scenario it is assumed that thecorrosion damage is only limited to the steel reinforcement(vertical and horizontal tie reinforcement) that is cover con-crete is uncracked and corrosion of confining reinforcementdoes not affect the confined concrete behaviour Here thesteel model described in Section 51 is used which includesthe impact of corrosion on the buckling and postbucklingbehaviour in compression and strength and ductility loss intension

Figure 9 shows the results of monotonic pushover anal-yses Figure 9(a) shows that the failure mode of Lehmanrsquoscolumn 415 is by vertical bar buckling and core confined

Advances in Materials Science and Engineering 9

0 001 002 003 004 005 006 007 0080

50100150200250300350

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

Drift ratio

Late

ral f

orce

(kN

)

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

Drift ratio

Late

ral f

orce

(kN

)

(b)

Figure 9 Pushover analyses considering corrosion induced damage in reinforcing steel (a) Lehmanrsquos column 415 (b) Moyer and Kowalskyrsquoscolumn 1

concrete crushing up to 10 mass loss However as the cor-rosion level increases beyond 10mass loss the failure modechanges from vertical bar bucking and concrete crushing incompression to fracture of the vertical bars in tension

Figure 9(b) shows that Moyer and Kowalskyrsquos column1 has also failed in bar buckling and concrete crushing incompression However because 119871eff119889 = 4 the strength lossis not as significant as that of Lehmanrsquos column 415 with119871eff119889 = 10 under monotonic loading The corrosion levelup to 20 mass loss changes Moyer and Kowalskyrsquos column1 behaviour The failure initiates with bar buckling andconcrete crushing in compression and followed by fracture ofthe vertical reinforcement in tension With corrosion levelsgreater than 20 mass loss failure is by premature fractureof the vertical bars in tension At this point a cascade of barfracture can be seen in the graphs up to complete collapse ofthe columns

Figures 10(a) and 10(b) show Lehmanrsquos column 415 with10 and 20 mass losses under cyclic loading respectivelyComparing the monotonic and cyclic responses (the samecyclic load protocol as the experiment) shows that low-cyclefatigue has a significant impact on the column responseThe monotonic analysis showed that 10 mass loss did notresult in vertical bar fracture in tension and the failure wasgoverned by bar buckling and concrete crushing However incyclic analysis the failuremode is combined bar buckling andconcrete crushing in compression (failure initiation) followedby bar fracture in tension due to low-cycle fatigue

Here we have a system that does not technically fail incrushing and buckling but survives a little longer until thenext cycle when the vertical reinforcement fails in tensionIt was found that a mass loss ratio greater than 10 has asignificant impact on the nonlinear response of the corrodedcolumn due to reduced low-cycle fatigue life Figure 10(b)shows that at 20 mass loss resulted in bar fracture at 005drift ratio in pushover analysis but it resulted in bar fractureat 003 drift ratio under cyclic loading due to low-cycle fatiguefailure

Figures 10(c) and 10(d) show a similar result for Moyerand Kowalskyrsquos column 1 Overall Moyer and Kowalskyrsquoscolumn 1 has slightly less pinched cyclic responseThis is dueto the influence of the buckling length of the vertical bars andits cyclic degradation due to buckling [25]

62 Scenario (b) Column Nonlinear Behaviour When Corro-sion Is Assumed Present in Vertical and Horizontal Tie Rein-forcement and Cover Concrete Is Cracked In this scenarioit is assumed that the reinforcing steel (vertical and tie) iscorroded and the cover concrete is cracked due to corrosionof vertical reinforcementThe results of the pushover analysesare shown in Figure 11 The results in this case are almostidentical to the previous case (Section 61) where the damagein cover concrete was not considered Therefore in canbe concluded that whether or not we seek to model thecorrosion induced cracking of cover concrete it does not havea significant impact on the nonlinear response of corrodedcolumns Further discussion and comparison of this scenariowith other damage scenarios are available in Section 63

63 Scenario (c) Column Seismic Behaviour When Cor-rosion Is Assumed Present in Vertical and Horizontal TieReinforcement and Both Cover and Confined Concrete AreDamaged In this scenario it is assumed that the reinforc-ing steel (vertical and tie) is corroded cover concrete iscracked and the core confined concrete is affected by thecorrosion of horizontal tie reinforcement (as described inSection 53) Figure 12(a) shows the results of monotonicpushover analyses of Lehmanrsquos column 415 The results showthat the failure mechanism of this column for up to 10mass loss is bar buckling and core confined concrete crushingin compression However for corrosion levels beyond 10the failure mode changes This is a loss of drift capacitywhich starts with bar buckling and concrete crushing incompression and it is followed by bar fracture in tensionThese analyses demonstrate the importance of modelling the

10 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

Drift ratio

Late

ral f

orce

(kN

)

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

Drift ratio

Late

ral f

orce

(kN

)

(b)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

(c)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

(d)

Figure 10 Cyclic analyses considering corrosion induced damage in reinforcing steel (a) and (b) Lehmanrsquos column 415 (c) and (d) Moyerand Kowalskyrsquos column 1

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(b)

Figure 11 Pushover analyses considering corrosion induced damage in reinforcing steel and cracked cover concrete (a) Lehmanrsquos column415 (b) Moyer and Kowalskyrsquos column 1

Advances in Materials Science and Engineering 11

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(b)

Figure 12 Pushover analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a)Lehmanrsquos column 415 (b) Moyer and Kowalskyrsquos column 1

influence of corrosion on the confined concrete (throughloss of confining tie reinforcement) This corrosion damageon the confined concrete results in a rapid reduction instrength and ductility of the corroded columns compared tothe previous cases where confined concrete was considered tobe undamaged

Figure 12(b) shows the results of pushover analyses ofMoyer andKowalskyrsquos column 1 In this case the failuremodewas mainly bar buckling and concrete crushing followed byfracture of bars in tension for up to 20 mass loss Howevercorrosion levels beyond 20 mass loss have changed thefailure mode to premature fracture of bars in tension Thisdifference between the behaviour of the two columns is due tothe buckling behaviour of the vertical bars Given that Moyerand Kowalskyrsquos column 1 has much smaller buckling lengththe strength degradation in compression is much smallerthan Lehmanrsquos column 415 Therefore corrosion has more asignificant impact in terms of ductility loss of bars in tensionwhereas in Lehmanrsquos column 415 failure initiates with severebar buckling and concrete crushing then it is followed byfracture of vertical bars in tension

Figure 13 shows the results of cyclic analysis It showsthe cyclic analyses of Lehmanrsquos column 415 and Moyer andKowalskyrsquos column 1 with 10 and 20 mass loss togetherwith the corresponding pushover envelopes Figure 13 showsthat the extent of corrosion damage under cyclic loadingis more severe than monotonic loading The results ofmonotonic analysis showed that considering the ductility lossof corroded bars in tension and confinement reinforcementin compression has a big impact on bar buckling andfracture of reinforcement However cyclic analysis resultsshow that considering cyclic degradation due to low-cyclefatigue is crucial to have a realistic evaluation of the seismicperformance of existing corroded columns

For example in Figures 13(a) and 13(b) the failure ofLehmanrsquos column 415 was governed by bar buckling andconcrete crushing for a corrosion level up to 10 undermonotonic loadingHowever the same corrosion level results

in a much more severe drift capacity loss under cyclicloading due to a reduced low-cycle fatigue life Similarly inFigures 13(c) and 13(d) the failure of Moyer and Kowalskyrsquoscolumn was governed by concrete crushing in compressionfollowed by bar fracture in tension However low-cyclefatigue degradation due to cyclic loading results in prematurefracture of bars and subsequently severe loss of drift capacity

7 Comparison of the NonlinearResponses of Corroded Columns Computedin Different Scenarios

In order to clearly demonstrate the significance of corrosionmodels on the inelastic response of RC columns a com-parison between the computed responses of two columnswith different scenarios has been made The responses ofcolumns with 20 mass loss in monotonic pushover andcyclic analyses are compared and shown in Figure 14

Figure 14 shows the monotonic pushover and cyclicresponses of Lehmanrsquos column 415 andMoyer and Kowalskyrsquoscolumn 1 with 20 mass losses and different corrosiondamage models Figures 14(a) and 14(b) show that if thecorrosion induced damage to confined concrete is ignoredthe predicted failure mode is likely to be the fracture of barsin tension due to their reduced ductility However if thecorrosion induced damage to confined concrete is addedFigure 14(a) shows that the failure mode of Lehmanrsquos column415 will change to concrete crushing and buckling of thevertical bars in compression

Figure 14(b) shows that the failure mode of Moyer andKowalskyrsquos column 1 initiates with concrete crushing andbuckling of bars in compression and then it is followedby fracture of bars in tension This difference in failuremechanism is due to the differences in confinement level thebuckling length of the vertical bars the ratio of longitudinalreinforcement and the axial force ratio on the columnThere-fore in order to predict the nonlinear response accurately adetailed finite element model is required

12 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(d)

Figure 13 Cyclic analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a) and(b) Lehmanrsquos column 415 (c) and (d) Moyer and Kowalskyrsquos column 1

It is found that the failure mode under cyclic loading ismainly governed by the fracture of horizontal bars in tensiondue to reduced low-cycle fatigue life (Figures 14(c) and 14(d))This is a very important finding as it suggests that nonlinearquasistatic pushover analysis on its own is not adequate forperformance assessment of existing corroded bridge piers

With reference to Figure 14 it is evident that consideringthe impact of the corrosion damage on core confined con-crete and low-cycle fatigue degradation is crucial Thereforethey need to be considered when modelling the nonlinearbehaviour of corrosion damaged RC bridge piers underseismic loading This finding is in good agreement with theobserved experimental results by other researchers [12ndash1458]

A series of experimental studies were conducted in [12]on the cyclic behaviour of large-scale corroded cantilever RCbeams Ou et al found that as the level of corrosion increasesthe flexural failure initiates with premature buckling oflongitudinal bars This conclusion is in good agreement withthe numerical results discussed in this paper In another study[13] a series of experimental studies were conducted on cyclicbehaviour of corroded RC columns with varied axial forceMa et al have reported that once the corrosion level increases

beyond about 14 rapid strength and ductility reductionand cyclic degradation in hysteretic loops are seen due toreduced low-cycle fatigue life and premature buckling ofvertical reinforcement This conclusion is in good agreementwith the predicted failure modes using the numerical modelpresented in this paper

The detailed finite element model developed in thispaper can accurately model the nonlinear behaviour ofcorrodedRCcolumns subject to cyclic loading up to completecollapse There is a need to extend the PEER-UW columndatabase to include corroded RC columns so that furthercalibrationvalidation of the material model parameters canbe performed However the modelling technique developedin this paper is able to simulate the multiple failure modesof corroded RC columns simultaneously It represents thecurrent state of the art and as such they provide a novel com-putational framework for the seismic response prediction ofcorroded RC bridges

8 Conclusions

A series of pushover and cyclic analyses on two hypotheticalcorroded RC columns are conducted and these are used

Advances in Materials Science and Engineering 13

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(d)

Figure 14 Comparison of the computed responses of columns with different deterioration models (a) and (c) Lehmanrsquos column 415 undermonotonic and cyclic loading (b) and (d) Moyer and Kowalskyrsquos column 1 under monotonic and cyclic loading

to explore the performance of the proposed computationalframework The impact of corrosion on (i) the verticalreinforcing steel (ii) the tieconfinement (iii) the cover(unconfined) concrete and (iv) the core (confined) concreteis represented through new material models The proposednew steel material model accounts for (i) inelastic nonlinearbuckling of the vertical reinforcement (ii) the corrosion lossof area (iii) the nonuniform corrosion pitting and (iv) low-cycle high amplitude fatigueThenew cover concretematerialmodel includes the influence of internal pressure due tothe build-up of corrosion products (using compression fieldtheory) The new core concrete model includes the influenceof corrosion induced loss of confining reinforcement

The main outcomes of this study can be summarised asfollows

(1) Corrosion has a more significant impact on theductility loss (drift capacity) of RC columns than thestrength loss (plastic moment capacity)

(2) The numerical model developed in this paper is ableto predict the nonlinear flexural response of corrodedRC columns up to complete collapse Results showwhich depends on a cyclic load history that flexuralfailure can be initiated by the buckling of vertical bars

and crushing of core concrete which is then followedby fracture of bars in tension In cases where thebuckling of bars is not an issue or the buckling lengthis too short (119871eff119889

1015840le 5) the failure is governed by the

fracture of the vertical bars in tension due to low-cyclehigh amplitude fatigue

(3) The analyses results show that for the seismic perfor-mance and evaluation of existing corroded bridgesmonotonic pushover analysis is not sufficient Thecyclic degradation due to low-cycle high amplitudefatigue has a significant influence on the response ofcorroded RC columns

(4) The results of this study show that it is inadequate toassume that corrosion only affects the main verticalreinforcement in the column It was found that theconfined concrete with corroded confinement rein-forcement starts crushing much faster than uncor-roded undamaged concrete This changes the failuremode and results in premature buckling of the ver-tical reinforcement This change in the failure modecannot be predicted if the damage in core confinedconcrete due to corrosion of tie reinforcement isignored This is in good agreement with observed

14 Advances in Materials Science and Engineering

experimental results reported by other researchers[12ndash14]

(5) The modelling technique developed in this paper hassignificantly improved the earlier models and canbe used by other researchers in the future researchfor seismic vulnerability and fragility analysis ofcorroded RC bridges

Disclosure

Any findings opinions and recommendations provided inthis paper are only based on the authorsrsquo view

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This research is conducted in collaboration with the Univer-sity of Bristol and the University of Washington while thefirst author was on sabbatical leave in the US The fundingprovided by the World Wide University Network throughthe Research Mobility Program to the first author was muchappreciated The authors would like to thank Professor MarcO Eberhard and Professor John F Stanton for providingvaluable guidance during the course of this research

References

[1] S Hida F I S Ibrahim H A Capers et al ldquoAssuringbridge safety and serviceability in Europerdquo Tech Rep FHWA-PL-10-014 Office of International Programs Federal HighwayAdministration US Department of Transportation AmericanAssociation of State Highway and Transportation Officials2010

[2] ASCE Failure to Act The Economic Impact of Current Invest-ment Trends in Surface Transportation Infrastructure EconomicDevelopment Research Group Inc ASCE 2011

[3] D-E Choe P Gardoni D Rosowsky and T Haukaas ldquoProb-abilistic capacity models and seismic fragility estimates forRC columns subject to corrosionrdquo Reliability Engineering andSystem Safety vol 93 no 3 pp 383ndash393 2008

[4] L Berto R Vitaliani A Saetta and P Simioni ldquoSeismicassessment of existing RC structures affected by degradationphenomenardquo Structural Safety vol 31 no 4 pp 284ndash297 2009

[5] J Ghosh and J E Padgett ldquoAging considerations in the devel-opment of time-dependent seismic fragility curvesrdquo Journal ofStructural Engineering vol 136 no 12 pp 1497ndash1511 2010

[6] A Alipour B Shafei and M Shinozuka ldquoPerformance evalu-ation of deteriorating highway bridges located in high seismicareasrdquo Journal of Bridge Engineering vol 16 no 5 pp 597ndash6112011

[7] F Biondini E Camnasio and A Palermo ldquoLifetime seismicperformance of concrete bridges exposed to corrosionrdquo Struc-ture and Infrastructure Engineering vol 10 no 7 pp 880ndash9002014

[8] M Akiyama D M Frangopol and H Matsuzaki ldquoLife-cyclereliability of RC bridge piers under seismic and airborne chlo-ride hazardsrdquo Earthquake Engineering and Structural Dynamicsvol 40 no 15 pp 1671ndash1687 2011

[9] F Biondini A Palermo and G Toniolo ldquoSeismic performanceof concrete structures exposed to corrosion case studies of low-rise precast buildingsrdquo Structure and Infrastructure Engineeringvol 7 no 1-2 pp 109ndash119 2011

[10] C K Chiu F J Tu and F P Hsiao ldquoLifetime seismic perfor-mance assessment for chloride-corroded reinforced concretebuildingsrdquo Structure and Infrastructure Engineering vol 11 no3 pp 345ndash362 2015

[11] M Sanchez-Silva G-A Klutke and D V Rosowsky ldquoLife-cycleperformance of structures subject to multiple deteriorationmechanismsrdquo Structural Safety vol 33 no 3 pp 206ndash217 2011

[12] Y-C Ou L-L Tsai and H-H Chen ldquoCyclic performance oflarge-scale corroded reinforced concrete beamsrdquo EarthquakeEngineering and StructuralDynamics vol 41 no 4 pp 593ndash6042012

[13] Y Ma Y Che and J Gong ldquoBehavior of corrosion damagedcircular reinforced concrete columns under cyclic loadingrdquoConstruction and Building Materials vol 29 pp 548ndash556 2012

[14] A Meda S Mostosi Z Rinaldi and P Riva ldquoExperimentalevaluation of the corrosion influence on the cyclic behaviour ofRC columnsrdquo Engineering Structures vol 76 pp 112ndash123 2014

[15] A A Almusallam ldquoEffect of degree of corrosion on theproperties of reinforcing steel barsrdquo Construction and BuildingMaterials vol 15 no 8 pp 361ndash368 2001

[16] Y G Du L A Clark and A H C Chan ldquoResidual capacity ofcorroded reinforcing barsrdquoMagazine of Concrete Research vol57 no 3 pp 135ndash147 2005

[17] Y G Du L A Clarkt and A H C Chan ldquoEffect of corrosionon ductility of reinforcing barsrdquoMagazine of Concrete Researchvol 57 no 7 pp 407ndash419 2005

[18] J Cairns G A Plizzari Y Du D W Law and C FranzonildquoMechanical properties of corrosion-damaged reinforcementrdquoACI Materials Journal vol 102 no 4 pp 256ndash264 2005

[19] C A ApostolopoulosM P Papadopoulos and S G PantelakisldquoTensile behavior of corroded reinforcing steel bars BSt 500srdquoConstruction and Building Materials vol 20 no 9 pp 782ndash7892006

[20] C A Apostolopoulos ldquoMechanical behavior of corroded rein-forcing steel bars S500s tempcore under low cycle fatiguerdquoConstruction andBuildingMaterials vol 21 no 7 pp 1447ndash14562007

[21] M M Kashani A J Crewe and N A Alexander ldquoNonlinearstress-strain behaviour of corrosion-damaged reinforcing barsincluding inelastic bucklingrdquo Engineering Structures vol 48 pp417ndash429 2013

[22] M M Kashani A J Crewe and N A Alexander ldquoNonlinearcyclic response of corrosion-damaged reinforcing bars with theeffect of bucklingrdquo Construction and Building Materials vol 41pp 388ndash400 2013

[23] M M Kashani A J Crewe and N A Alexander ldquoUse of a 3Doptical measurement technique for stochastic corrosion patternanalysis of reinforcing bars subjected to accelerated corrosionrdquoCorrosion Science vol 73 pp 208ndash221 2013

[24] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoFinite element investigation of the influence of corrosionpattern on inelastic buckling and cyclic response of corrodedreinforcing barsrdquo Engineering Structures vol 75 pp 113ndash1252014

Advances in Materials Science and Engineering 15

[25] M M Kashani Seismic performance of corroded rc bridge piersdevelopment of a multi-mechanical nonlinear fibre beam-columnmodel [PhD thesis] University of Bristol Bristol UK 2014

[26] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part I Formula-tionrdquo Earthquake Engineering and Structural Dynamics vol 25no 7 pp 711ndash725 1996

[27] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part II Applica-tionsrdquoEarthquake Engineering and Structural Dynamics vol 25no 7 pp 727ndash742 1996

[28] The Open System for Earthquake Engineering Simulation(OpenSees) Pacific Earthquake Engineering Research CentreUniversity of California Berkeley Berkeley Calif USA 2011

[29] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoPhenomenological hysteretic model for corroded reinforcingbars including inelastic buckling and low-cycle fatigue degrada-tionrdquo Computers and Structures vol 156 article 5393 pp 58ndash712015

[30] J Coleman and E Spacone ldquoLocalization issues in force-basedframe elementsrdquo Journal of Structural Engineering vol 127 no11 pp 1257ndash1265 2001

[31] J S Pugh Numerical simulation of walls and seismic designrecommendations for walled buildings [PhD thesis] Universityof Washington Seattle Wash USA 2012

[32] D V Val and R E Melchers ldquoReliability of deteriorating RCslab bridgesrdquo Journal of Structural Engineering vol 123 no 12pp 1638ndash1644 1997

[33] M S Darmawan and M G Stewart ldquoEffect of pitting corro-sion on capacity of prestressing wiresrdquo Magazine of ConcreteResearch vol 59 no 2 pp 131ndash139 2007

[34] R P Dhakal and K Maekawa ldquoReinforcement stability andfracture of cover concrete in reinforced concrete membersrdquoJournal of Structural Engineering vol 128 no 10 pp 1253ndash12622002

[35] C Lee J F Bonacci M D A Thomas et al ldquoAcceleratedcorrosion and repair of reinforced concrete columns usingcarbon fibre reinforced polymer sheetsrdquo Canadian Journal ofCivil Engineering vol 27 no 5 pp 941ndash948 2000

[36] W Aquino Long-term performance of seismically rehabilitatedcorrosion-damaged columns [PhD thesis] University of Illinoisat Urbana-Champaign Champaign Ill USA 2002

[37] S Timoshenko and J Gere Theory of Elastic StabilityMacGraw-Hill New York NY USA 1963

[38] S J Pantazopoulou ldquoDetailing for reinforcement stability in RCmembersrdquo Journal of Structural Engineering vol 124 no 6 pp623ndash632 1998

[39] J B Mander M J N Priestley and R Park ldquoObserved stress-strain behavior of confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1827ndash1849 1988

[40] J B Mander M J Priestley and R Park ldquoTheoretical stress-strain model for confined concreterdquo Journal of Structural Engi-neering (United States) vol 114 no 8 pp 1804ndash1826 1988

[41] S Popovics ldquoAnumerical approach to the complete stress-straincurve of concreterdquo Cement and Concrete Research vol 3 no 5pp 583ndash599 1973

[42] I D Karsan and J O Jirsa ldquoBehavior of concrete undercompressive loadingrdquo Journal of Structural Division vol 95article ST12 1969

[43] M P Berry andMO Eberhard ldquoPerformancemodeling strate-gies for modern reinforced concrete bridge columnsrdquo PEER

Research Report University of California Berkeley BerkeleyCalif USA 2006

[44] B D Scott R Park and M J N Priestley ldquoStress-strainbehavior of concrete confined by overlapping hoops at low andhigh strain ratesrdquo Journal of the American Concrete Institute vol79 no 1 pp 13ndash27 1982

[45] A S Al-Harthy M G Stewart and J Mullard ldquoConcrete covercracking caused by steel reinforcement corrosionrdquoMagazine ofConcrete Research vol 63 no 9 pp 655ndash667 2011

[46] T Vidal A Castel and R Francois ldquoAnalyzing crack width topredict corrosion in reinforced concreterdquo Cement and ConcreteResearch vol 34 no 1 pp 165ndash174 2004

[47] F J Molina C Alonso and C Andrade ldquoCover cracking as afunction of rebar corrosion part 2-numerical modelrdquoMaterialsand Structures vol 26 no 9 pp 532ndash548 1993

[48] F J Vecchio and M P Collins ldquoThe modified compression-field theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[49] D Coronelli and P Gambarova ldquoStructural assessment ofcorroded reinforced concrete beams modeling guidelinesrdquoJournal of Structural Engineering vol 130 no 8 pp 1214ndash12242004

[50] D E Lehman and J P Moehle ldquoSeismic performance of well-confined concrete columnsrdquo PEER Research Report Universityof California at Berkeley 2000

[51] L N Lowes and A Altoontash ldquoModeling reinforced-concretebeam-column joints subjected to cyclic loadingrdquo Journal ofStructural Engineering vol 129 no 12 pp 1686ndash1697 2003

[52] M Berry M Parrish and M Eberhard ldquoPerformance databaseUserrsquos manualrdquo in Pacific Earthquake Engineering ResearchCentre 2004 University of California at Berkeley 2004httpwwwcewashingtonedusimpeera1

[53] A N Kallias and M Imran Rafiq ldquoFinite element investigationof the structural response of corroded RC beamsrdquo EngineeringStructures vol 32 no 9 pp 2984ndash2994 2010

[54] M J Moyer and M J Kowalsky ldquoInfluence of tension strain onbuckling of reinforcement in concrete columnsrdquo ACI StructuralJournal vol 100 no 1 pp 75ndash85 2003

[55] K A T Vu andM G Stewart ldquoStructural reliability of concretebridges including improved chloride-induced corrosion mod-elsrdquo Structural Safety vol 22 no 4 pp 313ndash333 2000

[56] D V Val ldquoFactors affecting life-cycle cost analysis of RCstructures in chloride contaminated environmentsrdquo Journal ofInfrastructure Systems vol 13 no 2 pp 135ndash143 2007

[57] J P BroomfieldCorrosion of Steel in Concrete Taylor amp FrancisLondon UK 2nd edition 2007

[58] M M Kashani P Alagheband R Khan and S Davis ldquoImpactof corrosion on low-cycle fatigue degradation of reinforcingbars with the effect of inelastic bucklingrdquo International Journalof Fatigue vol 77 pp 174ndash185 2015

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

6 Advances in Materials Science and Engineering

minus30 minus20 minus10 0 10 20 30minus15

minus1

minus05

0

05

1

15

Cyclic response including fatiguemdashuncorrodedCyclic response including fatiguemdashcorroded

120578=120590120590

y

120585 = 120576120576y

Figure 5 Cyclic response of the Hysteretic + Fatigue model inOpenSees (20 mass loss)

start corroding prior to the corrosion initiation of verticalreinforcement As a result the volumetric ratio of tie rein-forcement is decreased due to cross section loss There isalso a reduced yield strength and fracture strain due to thepitting effect Therefore the internal confinement pressureof the core concrete can result in premature fracture of tiereinforcement

To date there has not been any experimental study toquantify and model the effect of corrosion on the nonlinearbehaviour of confined concrete under monotonic compres-sion and cyclic loading Further research is required to under-stand and model the extent of corrosion damage on confinedconcrete behaviour However a simplified methodology isused in this research tomodify the confined concretematerialmodel (which is a function of the percentage mass loss inhorizontal tie reinforcement) to account for the effect ofcorrosion damage

In this study the uniaxial Concrete04 material modelavailable in OpenSees is used to model the concrete ThePopovics curve [41] is used for the compression envelope andthe Karsan-Jirsa model [42] is used to determine the slopeof the curve for unloading and reloading in compressionFor tensile loading an exponential curve is used to definethe envelope to the stress-strain curve Further details areavailable in [43]

The parameters proposed by [40] are used to modelthe effect of confinement on concrete in compression Themaximum compressive stress of the concrete (120590cc) and thestrain at the maximum compressive strain (120576cc) can becalculated using the equations developed in [40]

The maximum crushing strain of the confined concreteis defined by the fracture of the first horizontal tiespiralreinforcement Here the model proposed by [44] is used topredict the concrete crushing strain as defined in

120576cc = 0004 + 14 (120588sc120590119910tie120576119906tie

120590119888

) (5)

where 120576119906tie is the fracture strain of the tiespiral reinforce-

ment 120588sc is the volumetric ratio of spiral reinforcement and120590119910tie is the yield stress of spiral reinforcement

minus20 minus18 minus16 minus14 minus12 minus10 minus8 minus6 minus4 minus2 0minus15

minus125

minus1

minus075

minus05

minus025

0

Original confined concrete modelCorrosion damaged confined concrete

120574=120590120590

c

120595 = 120576120576c0

Figure 6 Corrosion damaged confined concrete model (20 massloss)

It is clear that the confined concrete model is a functionof yield strength volumetric ratio and fracture strain ofthe confinementtie reinforcement Therefore the previouslydefined equations for reinforcing steel can be used to modifythe cross-sectional area yield strength and fracture strain oftie reinforcement as a function of the percentage mass lossAccordingly these modified values can be used to accountfor the impact of corrosion on confined concrete model(Figure 6)

54 Corrosion Damaged Cracked Cover Concrete ModelOnce corrosion initiates the corrosion products accumulatearound the reinforcement Given the volume of the corrosionproducts is bigger than the original reinforcing steel it gener-ates a radial pressureexpansion on the concrete surroundingthe reinforcement This behaviour is like a thick cylinderunder internal pressure that eventually results in fracture ofthe cover concrete [45ndash47] The cracking of cover concreteresults in loss of compressive strength and crushing strainof the concrete in the compressive zone of RC sectionsTherefore consideration needs to be given to model theinfluence of this cracking on the response of cover concretein compression

The response of cracked concrete in compression isdescribed in detail by [48] which is known as compressionfield theory (CFT) Based onCFT the compressive strength ofcracked concrete in compression depends on the magnitudeof the average tensile strain in the transverse direction whichcauses longitudinal microcracks Reference [49] employedthis method in nonlinear finite element analysis of corrosiondamaged RC beams with modified constitutive model forthe cracked cover concrete as a function of percentagemass loss and validated this against experimental resultsTherefore the equations suggested by [49] are employedto model the compression response of crack cover con-crete Figure 7(a) shows the compression envelope and Fig-ure 7(b) shows the tension envelope of the uniaxial materialmodel for corrosion damaged unconfined cover concreteused in the fibre model Further details are available in[49]

Advances in Materials Science and Engineering 7

minus25 minus2 minus15 minus1 minus05 0minus1

minus075

minus05

minus025

0

Original unconfined concrete modelCorrosion induced crack unconfined concrete

120595 = 120576120576c0

120574=120590120590

c

(a)

0 1 2 3 4 5 6 70

005

01

015

02

Original concrete tension envelopeCorrosion induced cracked concrete

120574=120590120590

c

120595 = 120576120576ct

(b)

Figure 7 Corrosion damaged cracked cover concrete model for 20 mass loss (a) compression (b) tension

55 Bond-Slip Model and Zero-Length Element In seismicdesign of RC structures and bridges plastic hinges are formedat the columnbeam ends This will induce a substantialstrain penetration along the longitudinal bars into the jointthat eventually results in slippage of longitudinal bars Thisphenomenon has been observed by other researchers exper-imentally [50] Reference [51] adopted a bar-slip model forthe end slip of longitudinal reinforcement in beam-columnjoints This model has been employed by [25] to model thecyclic behaviour of RC columns and is validated against UW-PEER experimental RC column database [52]

Corrosion affects the reinforcing steel near the surface ofthe concrete due to diffusion of chloride ions from the surfaceandor carbonation of cover concrete In bridge piers thevertical reinforcement bars are anchored to the foundationwell below the foundation surface Therefore the verticalreinforcement does not corrode at this depth and the bar-slipbehaviour of bars at the anchorage zone remains the same asin the uncorroded column This has been observed by otherresearchers experimentally [12ndash14]

It should be pointed out that corrosion does affect thebond strength of corroded vertical reinforcement abovethe foundation level (internal bond-slip within the columnitself) However based on the observed experimental resultsthe reduced bond strength does not govern the failure ofcolumns References [12ndash14] reported that the failure ofcorroded columns and beams under cyclic loading is mainlygovern by fracture of bars in tension due to low-cycle fatigueand buckling of bars and crushing of confined concrete incompression

Reference [53] conducted a comprehensive detailed non-linear finite element analysis of corroded RC beams andvalidated them against experimental results They havereported that reduced bond strength only changes the crackpattern and affects the serviceability of corroded beamsTheyconcluded that reduced bond strength does not affect theultimate capacity of corroded beams Therefore bond-slip ofcorroded vertical bars within the element is not considered inthis research

The detailed discussion and implementation of the zero-length section in modelling the cyclic behaviour of RCcolumns is available in [25]

6 Impact of Corrosion Damage on NonlinearResponse of RC Bridges Piers

In this section the impact of different corrosion damagescenarios on the inelastic response of RC bridge piers isexplored A comparative study on two hypothetical corrodedRC columns with different buckling lengths of vertical barsis conducted The columns are taken from the UW-PEERexperimental RC column database [52] These columns areused to validate and calibrate the basic numerical model forthe uncorroded columns [25]

To investigate the impact of corrosion on drift capacityand strength loss of RC columns a series of nonlinearpushover analyses with varied corrosion levels are conductedTo explore the impact of cyclic degradation nonlinear cyclicanalyses using the load history that was used in the exper-iment are conducted In order to investigate the impact ofdifferent modelling techniques and damage mechanism foreach analysis type three scenarios are considered

(a) Vertical and horizontal tie reinforcement are cor-roded but cover and core concrete are not affected bycorrosion

(b) Vertical and horizontal tie reinforcement are cor-roded and the cover concrete is cracked due tocorrosion but the core concrete is not affected

(c) Vertical and horizontal tie reinforcement are cor-roded the cover concrete is cracked and the coreconcrete is affected due to corrosion of confiningtiereinforcement

These scenarios will highlight the importance of each damagecomponent that needs to be considered in modelling nonlin-ear response of corroded RC columns

8 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008

minus300minus200minus100

0100200300

ExperimentFibre model

Drift ratio

Late

ral f

orce

(kN

)

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

ExperimentFibre model

Drift ratio

Late

ral f

orce

(kN

)

(b)

Figure 8 Comparison of experimental results and calibrated numerical model of uncorroded columns (a) Lehmanrsquos column 415 (b) Moyerand Kowalskyrsquos column 1

Lehmanrsquos column 415 and Moyer and Kowalskyrsquos column1 [50 54] are considered in this study The geometricaldetails material properties and detailed experimental resultsof these columns are available in [50 54] Figure 8 showsa comparison of the numerical model and experimentalresponses of these columns It should be noted that Lehmanrsquoscolumn 415 has 119871eff119889 = 10 and Moyer and Kowalskyrsquoscolumn 1 has 119871eff119889 = 4 The detailed discussion of thenumerical model validation is available in [25] It shouldbe noted that the maximum drift capacity in this paperis considered as the point where the force-displacementresponse of the column starts softening and losing strengthIt is found that the maximum drift capacity of both columnsat uncorroded state is about 6

The buckling lengths of corroded vertical reinforcementare calculated using the methodology described in Section 4The corrosion of horizontal ties is considered in the bucklinglength calculation As discussed previously (Section 4) thebuckling length of the vertical bars is a function of thetie reinforcementrsquos stiffness and the vertical reinforcementrsquosflexural rigidity Corrosion results in a reduction in flexuralrigidity of vertical barsTherefore the required stiffness fromtie reinforcement to restrain vertical bars against bucklingis reduced However corrosion also reduces the stiffness ofthe tie reinforcement For example in Moyer and Kowalskyrsquoscolumn the vertical reinforcement buckled between two tiesIn this case it was found that corrosion did not affect thebuckling length

In Lehmanrsquos column 415 the vertical reinforcementbuckled over five ties However once the corrosion levelexceeds 10 the buckling length reduced and the verticalreinforcement buckled over four ties It should be notedthat although the buckling length is reduced 119871eff119889

1015840 is notnecessarily reduced where 119871eff is the buckling length and 1198891015840is the diameter of the corroded vertical reinforcement Thisis because corrosion also reduces the diameter of verticalbars This change in buckling length is related to the relativecorrosion level and stiffness between the vertical and tiereinforcement

In practice the horizontal tie reinforcement is closer thanthe main vertical reinforcement to the surface of concreteTherefore it might start corroding earlier than verticalreinforcementThis phenomenonmight have an effect on thebuckling length and confined concrete behaviour Howeverthere has not been any research to date to explore thecorrelation between the corrosion levels of the horizontaltie and vertical reinforcement This is an area for futureresearch and therefore in this research in the absence of anyexperimentalfield data the same corrosion is considered forboth vertical and tie reinforcement

It should be noted that the calculation of the time tocorrosion initiation and time-dependent corrosion propaga-tion is out of the scope of this paper There are mathematicalmodels available in the literature that enable an estimationof the time to corrosion initiation and propagation basedon the environmental conditions [55 56] The corrosion ratecan also be measured on site by electrical equipment whichcan then be turned into a mass loss ratio using Faradayrsquoslaw of electrolysis [57] Given that the focus of this paperis on the impact of different mass loss ratios on the seismicperformance of RC columns the corrosion level is modelledby percentage mass loss throughout this paper

61 Scenario (a) Column Nonlinear Behaviour When Cor-rosion Is Assumed Present in Vertical and Horizontal TieReinforcement Only In this scenario it is assumed that thecorrosion damage is only limited to the steel reinforcement(vertical and horizontal tie reinforcement) that is cover con-crete is uncracked and corrosion of confining reinforcementdoes not affect the confined concrete behaviour Here thesteel model described in Section 51 is used which includesthe impact of corrosion on the buckling and postbucklingbehaviour in compression and strength and ductility loss intension

Figure 9 shows the results of monotonic pushover anal-yses Figure 9(a) shows that the failure mode of Lehmanrsquoscolumn 415 is by vertical bar buckling and core confined

Advances in Materials Science and Engineering 9

0 001 002 003 004 005 006 007 0080

50100150200250300350

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

Drift ratio

Late

ral f

orce

(kN

)

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

Drift ratio

Late

ral f

orce

(kN

)

(b)

Figure 9 Pushover analyses considering corrosion induced damage in reinforcing steel (a) Lehmanrsquos column 415 (b) Moyer and Kowalskyrsquoscolumn 1

concrete crushing up to 10 mass loss However as the cor-rosion level increases beyond 10mass loss the failure modechanges from vertical bar bucking and concrete crushing incompression to fracture of the vertical bars in tension

Figure 9(b) shows that Moyer and Kowalskyrsquos column1 has also failed in bar buckling and concrete crushing incompression However because 119871eff119889 = 4 the strength lossis not as significant as that of Lehmanrsquos column 415 with119871eff119889 = 10 under monotonic loading The corrosion levelup to 20 mass loss changes Moyer and Kowalskyrsquos column1 behaviour The failure initiates with bar buckling andconcrete crushing in compression and followed by fracture ofthe vertical reinforcement in tension With corrosion levelsgreater than 20 mass loss failure is by premature fractureof the vertical bars in tension At this point a cascade of barfracture can be seen in the graphs up to complete collapse ofthe columns

Figures 10(a) and 10(b) show Lehmanrsquos column 415 with10 and 20 mass losses under cyclic loading respectivelyComparing the monotonic and cyclic responses (the samecyclic load protocol as the experiment) shows that low-cyclefatigue has a significant impact on the column responseThe monotonic analysis showed that 10 mass loss did notresult in vertical bar fracture in tension and the failure wasgoverned by bar buckling and concrete crushing However incyclic analysis the failuremode is combined bar buckling andconcrete crushing in compression (failure initiation) followedby bar fracture in tension due to low-cycle fatigue

Here we have a system that does not technically fail incrushing and buckling but survives a little longer until thenext cycle when the vertical reinforcement fails in tensionIt was found that a mass loss ratio greater than 10 has asignificant impact on the nonlinear response of the corrodedcolumn due to reduced low-cycle fatigue life Figure 10(b)shows that at 20 mass loss resulted in bar fracture at 005drift ratio in pushover analysis but it resulted in bar fractureat 003 drift ratio under cyclic loading due to low-cycle fatiguefailure

Figures 10(c) and 10(d) show a similar result for Moyerand Kowalskyrsquos column 1 Overall Moyer and Kowalskyrsquoscolumn 1 has slightly less pinched cyclic responseThis is dueto the influence of the buckling length of the vertical bars andits cyclic degradation due to buckling [25]

62 Scenario (b) Column Nonlinear Behaviour When Corro-sion Is Assumed Present in Vertical and Horizontal Tie Rein-forcement and Cover Concrete Is Cracked In this scenarioit is assumed that the reinforcing steel (vertical and tie) iscorroded and the cover concrete is cracked due to corrosionof vertical reinforcementThe results of the pushover analysesare shown in Figure 11 The results in this case are almostidentical to the previous case (Section 61) where the damagein cover concrete was not considered Therefore in canbe concluded that whether or not we seek to model thecorrosion induced cracking of cover concrete it does not havea significant impact on the nonlinear response of corrodedcolumns Further discussion and comparison of this scenariowith other damage scenarios are available in Section 63

63 Scenario (c) Column Seismic Behaviour When Cor-rosion Is Assumed Present in Vertical and Horizontal TieReinforcement and Both Cover and Confined Concrete AreDamaged In this scenario it is assumed that the reinforc-ing steel (vertical and tie) is corroded cover concrete iscracked and the core confined concrete is affected by thecorrosion of horizontal tie reinforcement (as described inSection 53) Figure 12(a) shows the results of monotonicpushover analyses of Lehmanrsquos column 415 The results showthat the failure mechanism of this column for up to 10mass loss is bar buckling and core confined concrete crushingin compression However for corrosion levels beyond 10the failure mode changes This is a loss of drift capacitywhich starts with bar buckling and concrete crushing incompression and it is followed by bar fracture in tensionThese analyses demonstrate the importance of modelling the

10 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

Drift ratio

Late

ral f

orce

(kN

)

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

Drift ratio

Late

ral f

orce

(kN

)

(b)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

(c)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

(d)

Figure 10 Cyclic analyses considering corrosion induced damage in reinforcing steel (a) and (b) Lehmanrsquos column 415 (c) and (d) Moyerand Kowalskyrsquos column 1

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(b)

Figure 11 Pushover analyses considering corrosion induced damage in reinforcing steel and cracked cover concrete (a) Lehmanrsquos column415 (b) Moyer and Kowalskyrsquos column 1

Advances in Materials Science and Engineering 11

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(b)

Figure 12 Pushover analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a)Lehmanrsquos column 415 (b) Moyer and Kowalskyrsquos column 1

influence of corrosion on the confined concrete (throughloss of confining tie reinforcement) This corrosion damageon the confined concrete results in a rapid reduction instrength and ductility of the corroded columns compared tothe previous cases where confined concrete was considered tobe undamaged

Figure 12(b) shows the results of pushover analyses ofMoyer andKowalskyrsquos column 1 In this case the failuremodewas mainly bar buckling and concrete crushing followed byfracture of bars in tension for up to 20 mass loss Howevercorrosion levels beyond 20 mass loss have changed thefailure mode to premature fracture of bars in tension Thisdifference between the behaviour of the two columns is due tothe buckling behaviour of the vertical bars Given that Moyerand Kowalskyrsquos column 1 has much smaller buckling lengththe strength degradation in compression is much smallerthan Lehmanrsquos column 415 Therefore corrosion has more asignificant impact in terms of ductility loss of bars in tensionwhereas in Lehmanrsquos column 415 failure initiates with severebar buckling and concrete crushing then it is followed byfracture of vertical bars in tension

Figure 13 shows the results of cyclic analysis It showsthe cyclic analyses of Lehmanrsquos column 415 and Moyer andKowalskyrsquos column 1 with 10 and 20 mass loss togetherwith the corresponding pushover envelopes Figure 13 showsthat the extent of corrosion damage under cyclic loadingis more severe than monotonic loading The results ofmonotonic analysis showed that considering the ductility lossof corroded bars in tension and confinement reinforcementin compression has a big impact on bar buckling andfracture of reinforcement However cyclic analysis resultsshow that considering cyclic degradation due to low-cyclefatigue is crucial to have a realistic evaluation of the seismicperformance of existing corroded columns

For example in Figures 13(a) and 13(b) the failure ofLehmanrsquos column 415 was governed by bar buckling andconcrete crushing for a corrosion level up to 10 undermonotonic loadingHowever the same corrosion level results

in a much more severe drift capacity loss under cyclicloading due to a reduced low-cycle fatigue life Similarly inFigures 13(c) and 13(d) the failure of Moyer and Kowalskyrsquoscolumn was governed by concrete crushing in compressionfollowed by bar fracture in tension However low-cyclefatigue degradation due to cyclic loading results in prematurefracture of bars and subsequently severe loss of drift capacity

7 Comparison of the NonlinearResponses of Corroded Columns Computedin Different Scenarios

In order to clearly demonstrate the significance of corrosionmodels on the inelastic response of RC columns a com-parison between the computed responses of two columnswith different scenarios has been made The responses ofcolumns with 20 mass loss in monotonic pushover andcyclic analyses are compared and shown in Figure 14

Figure 14 shows the monotonic pushover and cyclicresponses of Lehmanrsquos column 415 andMoyer and Kowalskyrsquoscolumn 1 with 20 mass losses and different corrosiondamage models Figures 14(a) and 14(b) show that if thecorrosion induced damage to confined concrete is ignoredthe predicted failure mode is likely to be the fracture of barsin tension due to their reduced ductility However if thecorrosion induced damage to confined concrete is addedFigure 14(a) shows that the failure mode of Lehmanrsquos column415 will change to concrete crushing and buckling of thevertical bars in compression

Figure 14(b) shows that the failure mode of Moyer andKowalskyrsquos column 1 initiates with concrete crushing andbuckling of bars in compression and then it is followedby fracture of bars in tension This difference in failuremechanism is due to the differences in confinement level thebuckling length of the vertical bars the ratio of longitudinalreinforcement and the axial force ratio on the columnThere-fore in order to predict the nonlinear response accurately adetailed finite element model is required

12 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(d)

Figure 13 Cyclic analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a) and(b) Lehmanrsquos column 415 (c) and (d) Moyer and Kowalskyrsquos column 1

It is found that the failure mode under cyclic loading ismainly governed by the fracture of horizontal bars in tensiondue to reduced low-cycle fatigue life (Figures 14(c) and 14(d))This is a very important finding as it suggests that nonlinearquasistatic pushover analysis on its own is not adequate forperformance assessment of existing corroded bridge piers

With reference to Figure 14 it is evident that consideringthe impact of the corrosion damage on core confined con-crete and low-cycle fatigue degradation is crucial Thereforethey need to be considered when modelling the nonlinearbehaviour of corrosion damaged RC bridge piers underseismic loading This finding is in good agreement with theobserved experimental results by other researchers [12ndash1458]

A series of experimental studies were conducted in [12]on the cyclic behaviour of large-scale corroded cantilever RCbeams Ou et al found that as the level of corrosion increasesthe flexural failure initiates with premature buckling oflongitudinal bars This conclusion is in good agreement withthe numerical results discussed in this paper In another study[13] a series of experimental studies were conducted on cyclicbehaviour of corroded RC columns with varied axial forceMa et al have reported that once the corrosion level increases

beyond about 14 rapid strength and ductility reductionand cyclic degradation in hysteretic loops are seen due toreduced low-cycle fatigue life and premature buckling ofvertical reinforcement This conclusion is in good agreementwith the predicted failure modes using the numerical modelpresented in this paper

The detailed finite element model developed in thispaper can accurately model the nonlinear behaviour ofcorrodedRCcolumns subject to cyclic loading up to completecollapse There is a need to extend the PEER-UW columndatabase to include corroded RC columns so that furthercalibrationvalidation of the material model parameters canbe performed However the modelling technique developedin this paper is able to simulate the multiple failure modesof corroded RC columns simultaneously It represents thecurrent state of the art and as such they provide a novel com-putational framework for the seismic response prediction ofcorroded RC bridges

8 Conclusions

A series of pushover and cyclic analyses on two hypotheticalcorroded RC columns are conducted and these are used

Advances in Materials Science and Engineering 13

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(d)

Figure 14 Comparison of the computed responses of columns with different deterioration models (a) and (c) Lehmanrsquos column 415 undermonotonic and cyclic loading (b) and (d) Moyer and Kowalskyrsquos column 1 under monotonic and cyclic loading

to explore the performance of the proposed computationalframework The impact of corrosion on (i) the verticalreinforcing steel (ii) the tieconfinement (iii) the cover(unconfined) concrete and (iv) the core (confined) concreteis represented through new material models The proposednew steel material model accounts for (i) inelastic nonlinearbuckling of the vertical reinforcement (ii) the corrosion lossof area (iii) the nonuniform corrosion pitting and (iv) low-cycle high amplitude fatigueThenew cover concretematerialmodel includes the influence of internal pressure due tothe build-up of corrosion products (using compression fieldtheory) The new core concrete model includes the influenceof corrosion induced loss of confining reinforcement

The main outcomes of this study can be summarised asfollows

(1) Corrosion has a more significant impact on theductility loss (drift capacity) of RC columns than thestrength loss (plastic moment capacity)

(2) The numerical model developed in this paper is ableto predict the nonlinear flexural response of corrodedRC columns up to complete collapse Results showwhich depends on a cyclic load history that flexuralfailure can be initiated by the buckling of vertical bars

and crushing of core concrete which is then followedby fracture of bars in tension In cases where thebuckling of bars is not an issue or the buckling lengthis too short (119871eff119889

1015840le 5) the failure is governed by the

fracture of the vertical bars in tension due to low-cyclehigh amplitude fatigue

(3) The analyses results show that for the seismic perfor-mance and evaluation of existing corroded bridgesmonotonic pushover analysis is not sufficient Thecyclic degradation due to low-cycle high amplitudefatigue has a significant influence on the response ofcorroded RC columns

(4) The results of this study show that it is inadequate toassume that corrosion only affects the main verticalreinforcement in the column It was found that theconfined concrete with corroded confinement rein-forcement starts crushing much faster than uncor-roded undamaged concrete This changes the failuremode and results in premature buckling of the ver-tical reinforcement This change in the failure modecannot be predicted if the damage in core confinedconcrete due to corrosion of tie reinforcement isignored This is in good agreement with observed

14 Advances in Materials Science and Engineering

experimental results reported by other researchers[12ndash14]

(5) The modelling technique developed in this paper hassignificantly improved the earlier models and canbe used by other researchers in the future researchfor seismic vulnerability and fragility analysis ofcorroded RC bridges

Disclosure

Any findings opinions and recommendations provided inthis paper are only based on the authorsrsquo view

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This research is conducted in collaboration with the Univer-sity of Bristol and the University of Washington while thefirst author was on sabbatical leave in the US The fundingprovided by the World Wide University Network throughthe Research Mobility Program to the first author was muchappreciated The authors would like to thank Professor MarcO Eberhard and Professor John F Stanton for providingvaluable guidance during the course of this research

References

[1] S Hida F I S Ibrahim H A Capers et al ldquoAssuringbridge safety and serviceability in Europerdquo Tech Rep FHWA-PL-10-014 Office of International Programs Federal HighwayAdministration US Department of Transportation AmericanAssociation of State Highway and Transportation Officials2010

[2] ASCE Failure to Act The Economic Impact of Current Invest-ment Trends in Surface Transportation Infrastructure EconomicDevelopment Research Group Inc ASCE 2011

[3] D-E Choe P Gardoni D Rosowsky and T Haukaas ldquoProb-abilistic capacity models and seismic fragility estimates forRC columns subject to corrosionrdquo Reliability Engineering andSystem Safety vol 93 no 3 pp 383ndash393 2008

[4] L Berto R Vitaliani A Saetta and P Simioni ldquoSeismicassessment of existing RC structures affected by degradationphenomenardquo Structural Safety vol 31 no 4 pp 284ndash297 2009

[5] J Ghosh and J E Padgett ldquoAging considerations in the devel-opment of time-dependent seismic fragility curvesrdquo Journal ofStructural Engineering vol 136 no 12 pp 1497ndash1511 2010

[6] A Alipour B Shafei and M Shinozuka ldquoPerformance evalu-ation of deteriorating highway bridges located in high seismicareasrdquo Journal of Bridge Engineering vol 16 no 5 pp 597ndash6112011

[7] F Biondini E Camnasio and A Palermo ldquoLifetime seismicperformance of concrete bridges exposed to corrosionrdquo Struc-ture and Infrastructure Engineering vol 10 no 7 pp 880ndash9002014

[8] M Akiyama D M Frangopol and H Matsuzaki ldquoLife-cyclereliability of RC bridge piers under seismic and airborne chlo-ride hazardsrdquo Earthquake Engineering and Structural Dynamicsvol 40 no 15 pp 1671ndash1687 2011

[9] F Biondini A Palermo and G Toniolo ldquoSeismic performanceof concrete structures exposed to corrosion case studies of low-rise precast buildingsrdquo Structure and Infrastructure Engineeringvol 7 no 1-2 pp 109ndash119 2011

[10] C K Chiu F J Tu and F P Hsiao ldquoLifetime seismic perfor-mance assessment for chloride-corroded reinforced concretebuildingsrdquo Structure and Infrastructure Engineering vol 11 no3 pp 345ndash362 2015

[11] M Sanchez-Silva G-A Klutke and D V Rosowsky ldquoLife-cycleperformance of structures subject to multiple deteriorationmechanismsrdquo Structural Safety vol 33 no 3 pp 206ndash217 2011

[12] Y-C Ou L-L Tsai and H-H Chen ldquoCyclic performance oflarge-scale corroded reinforced concrete beamsrdquo EarthquakeEngineering and StructuralDynamics vol 41 no 4 pp 593ndash6042012

[13] Y Ma Y Che and J Gong ldquoBehavior of corrosion damagedcircular reinforced concrete columns under cyclic loadingrdquoConstruction and Building Materials vol 29 pp 548ndash556 2012

[14] A Meda S Mostosi Z Rinaldi and P Riva ldquoExperimentalevaluation of the corrosion influence on the cyclic behaviour ofRC columnsrdquo Engineering Structures vol 76 pp 112ndash123 2014

[15] A A Almusallam ldquoEffect of degree of corrosion on theproperties of reinforcing steel barsrdquo Construction and BuildingMaterials vol 15 no 8 pp 361ndash368 2001

[16] Y G Du L A Clark and A H C Chan ldquoResidual capacity ofcorroded reinforcing barsrdquoMagazine of Concrete Research vol57 no 3 pp 135ndash147 2005

[17] Y G Du L A Clarkt and A H C Chan ldquoEffect of corrosionon ductility of reinforcing barsrdquoMagazine of Concrete Researchvol 57 no 7 pp 407ndash419 2005

[18] J Cairns G A Plizzari Y Du D W Law and C FranzonildquoMechanical properties of corrosion-damaged reinforcementrdquoACI Materials Journal vol 102 no 4 pp 256ndash264 2005

[19] C A ApostolopoulosM P Papadopoulos and S G PantelakisldquoTensile behavior of corroded reinforcing steel bars BSt 500srdquoConstruction and Building Materials vol 20 no 9 pp 782ndash7892006

[20] C A Apostolopoulos ldquoMechanical behavior of corroded rein-forcing steel bars S500s tempcore under low cycle fatiguerdquoConstruction andBuildingMaterials vol 21 no 7 pp 1447ndash14562007

[21] M M Kashani A J Crewe and N A Alexander ldquoNonlinearstress-strain behaviour of corrosion-damaged reinforcing barsincluding inelastic bucklingrdquo Engineering Structures vol 48 pp417ndash429 2013

[22] M M Kashani A J Crewe and N A Alexander ldquoNonlinearcyclic response of corrosion-damaged reinforcing bars with theeffect of bucklingrdquo Construction and Building Materials vol 41pp 388ndash400 2013

[23] M M Kashani A J Crewe and N A Alexander ldquoUse of a 3Doptical measurement technique for stochastic corrosion patternanalysis of reinforcing bars subjected to accelerated corrosionrdquoCorrosion Science vol 73 pp 208ndash221 2013

[24] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoFinite element investigation of the influence of corrosionpattern on inelastic buckling and cyclic response of corrodedreinforcing barsrdquo Engineering Structures vol 75 pp 113ndash1252014

Advances in Materials Science and Engineering 15

[25] M M Kashani Seismic performance of corroded rc bridge piersdevelopment of a multi-mechanical nonlinear fibre beam-columnmodel [PhD thesis] University of Bristol Bristol UK 2014

[26] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part I Formula-tionrdquo Earthquake Engineering and Structural Dynamics vol 25no 7 pp 711ndash725 1996

[27] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part II Applica-tionsrdquoEarthquake Engineering and Structural Dynamics vol 25no 7 pp 727ndash742 1996

[28] The Open System for Earthquake Engineering Simulation(OpenSees) Pacific Earthquake Engineering Research CentreUniversity of California Berkeley Berkeley Calif USA 2011

[29] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoPhenomenological hysteretic model for corroded reinforcingbars including inelastic buckling and low-cycle fatigue degrada-tionrdquo Computers and Structures vol 156 article 5393 pp 58ndash712015

[30] J Coleman and E Spacone ldquoLocalization issues in force-basedframe elementsrdquo Journal of Structural Engineering vol 127 no11 pp 1257ndash1265 2001

[31] J S Pugh Numerical simulation of walls and seismic designrecommendations for walled buildings [PhD thesis] Universityof Washington Seattle Wash USA 2012

[32] D V Val and R E Melchers ldquoReliability of deteriorating RCslab bridgesrdquo Journal of Structural Engineering vol 123 no 12pp 1638ndash1644 1997

[33] M S Darmawan and M G Stewart ldquoEffect of pitting corro-sion on capacity of prestressing wiresrdquo Magazine of ConcreteResearch vol 59 no 2 pp 131ndash139 2007

[34] R P Dhakal and K Maekawa ldquoReinforcement stability andfracture of cover concrete in reinforced concrete membersrdquoJournal of Structural Engineering vol 128 no 10 pp 1253ndash12622002

[35] C Lee J F Bonacci M D A Thomas et al ldquoAcceleratedcorrosion and repair of reinforced concrete columns usingcarbon fibre reinforced polymer sheetsrdquo Canadian Journal ofCivil Engineering vol 27 no 5 pp 941ndash948 2000

[36] W Aquino Long-term performance of seismically rehabilitatedcorrosion-damaged columns [PhD thesis] University of Illinoisat Urbana-Champaign Champaign Ill USA 2002

[37] S Timoshenko and J Gere Theory of Elastic StabilityMacGraw-Hill New York NY USA 1963

[38] S J Pantazopoulou ldquoDetailing for reinforcement stability in RCmembersrdquo Journal of Structural Engineering vol 124 no 6 pp623ndash632 1998

[39] J B Mander M J N Priestley and R Park ldquoObserved stress-strain behavior of confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1827ndash1849 1988

[40] J B Mander M J Priestley and R Park ldquoTheoretical stress-strain model for confined concreterdquo Journal of Structural Engi-neering (United States) vol 114 no 8 pp 1804ndash1826 1988

[41] S Popovics ldquoAnumerical approach to the complete stress-straincurve of concreterdquo Cement and Concrete Research vol 3 no 5pp 583ndash599 1973

[42] I D Karsan and J O Jirsa ldquoBehavior of concrete undercompressive loadingrdquo Journal of Structural Division vol 95article ST12 1969

[43] M P Berry andMO Eberhard ldquoPerformancemodeling strate-gies for modern reinforced concrete bridge columnsrdquo PEER

Research Report University of California Berkeley BerkeleyCalif USA 2006

[44] B D Scott R Park and M J N Priestley ldquoStress-strainbehavior of concrete confined by overlapping hoops at low andhigh strain ratesrdquo Journal of the American Concrete Institute vol79 no 1 pp 13ndash27 1982

[45] A S Al-Harthy M G Stewart and J Mullard ldquoConcrete covercracking caused by steel reinforcement corrosionrdquoMagazine ofConcrete Research vol 63 no 9 pp 655ndash667 2011

[46] T Vidal A Castel and R Francois ldquoAnalyzing crack width topredict corrosion in reinforced concreterdquo Cement and ConcreteResearch vol 34 no 1 pp 165ndash174 2004

[47] F J Molina C Alonso and C Andrade ldquoCover cracking as afunction of rebar corrosion part 2-numerical modelrdquoMaterialsand Structures vol 26 no 9 pp 532ndash548 1993

[48] F J Vecchio and M P Collins ldquoThe modified compression-field theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[49] D Coronelli and P Gambarova ldquoStructural assessment ofcorroded reinforced concrete beams modeling guidelinesrdquoJournal of Structural Engineering vol 130 no 8 pp 1214ndash12242004

[50] D E Lehman and J P Moehle ldquoSeismic performance of well-confined concrete columnsrdquo PEER Research Report Universityof California at Berkeley 2000

[51] L N Lowes and A Altoontash ldquoModeling reinforced-concretebeam-column joints subjected to cyclic loadingrdquo Journal ofStructural Engineering vol 129 no 12 pp 1686ndash1697 2003

[52] M Berry M Parrish and M Eberhard ldquoPerformance databaseUserrsquos manualrdquo in Pacific Earthquake Engineering ResearchCentre 2004 University of California at Berkeley 2004httpwwwcewashingtonedusimpeera1

[53] A N Kallias and M Imran Rafiq ldquoFinite element investigationof the structural response of corroded RC beamsrdquo EngineeringStructures vol 32 no 9 pp 2984ndash2994 2010

[54] M J Moyer and M J Kowalsky ldquoInfluence of tension strain onbuckling of reinforcement in concrete columnsrdquo ACI StructuralJournal vol 100 no 1 pp 75ndash85 2003

[55] K A T Vu andM G Stewart ldquoStructural reliability of concretebridges including improved chloride-induced corrosion mod-elsrdquo Structural Safety vol 22 no 4 pp 313ndash333 2000

[56] D V Val ldquoFactors affecting life-cycle cost analysis of RCstructures in chloride contaminated environmentsrdquo Journal ofInfrastructure Systems vol 13 no 2 pp 135ndash143 2007

[57] J P BroomfieldCorrosion of Steel in Concrete Taylor amp FrancisLondon UK 2nd edition 2007

[58] M M Kashani P Alagheband R Khan and S Davis ldquoImpactof corrosion on low-cycle fatigue degradation of reinforcingbars with the effect of inelastic bucklingrdquo International Journalof Fatigue vol 77 pp 174ndash185 2015

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 7

minus25 minus2 minus15 minus1 minus05 0minus1

minus075

minus05

minus025

0

Original unconfined concrete modelCorrosion induced crack unconfined concrete

120595 = 120576120576c0

120574=120590120590

c

(a)

0 1 2 3 4 5 6 70

005

01

015

02

Original concrete tension envelopeCorrosion induced cracked concrete

120574=120590120590

c

120595 = 120576120576ct

(b)

Figure 7 Corrosion damaged cracked cover concrete model for 20 mass loss (a) compression (b) tension

55 Bond-Slip Model and Zero-Length Element In seismicdesign of RC structures and bridges plastic hinges are formedat the columnbeam ends This will induce a substantialstrain penetration along the longitudinal bars into the jointthat eventually results in slippage of longitudinal bars Thisphenomenon has been observed by other researchers exper-imentally [50] Reference [51] adopted a bar-slip model forthe end slip of longitudinal reinforcement in beam-columnjoints This model has been employed by [25] to model thecyclic behaviour of RC columns and is validated against UW-PEER experimental RC column database [52]

Corrosion affects the reinforcing steel near the surface ofthe concrete due to diffusion of chloride ions from the surfaceandor carbonation of cover concrete In bridge piers thevertical reinforcement bars are anchored to the foundationwell below the foundation surface Therefore the verticalreinforcement does not corrode at this depth and the bar-slipbehaviour of bars at the anchorage zone remains the same asin the uncorroded column This has been observed by otherresearchers experimentally [12ndash14]

It should be pointed out that corrosion does affect thebond strength of corroded vertical reinforcement abovethe foundation level (internal bond-slip within the columnitself) However based on the observed experimental resultsthe reduced bond strength does not govern the failure ofcolumns References [12ndash14] reported that the failure ofcorroded columns and beams under cyclic loading is mainlygovern by fracture of bars in tension due to low-cycle fatigueand buckling of bars and crushing of confined concrete incompression

Reference [53] conducted a comprehensive detailed non-linear finite element analysis of corroded RC beams andvalidated them against experimental results They havereported that reduced bond strength only changes the crackpattern and affects the serviceability of corroded beamsTheyconcluded that reduced bond strength does not affect theultimate capacity of corroded beams Therefore bond-slip ofcorroded vertical bars within the element is not considered inthis research

The detailed discussion and implementation of the zero-length section in modelling the cyclic behaviour of RCcolumns is available in [25]

6 Impact of Corrosion Damage on NonlinearResponse of RC Bridges Piers

In this section the impact of different corrosion damagescenarios on the inelastic response of RC bridge piers isexplored A comparative study on two hypothetical corrodedRC columns with different buckling lengths of vertical barsis conducted The columns are taken from the UW-PEERexperimental RC column database [52] These columns areused to validate and calibrate the basic numerical model forthe uncorroded columns [25]

To investigate the impact of corrosion on drift capacityand strength loss of RC columns a series of nonlinearpushover analyses with varied corrosion levels are conductedTo explore the impact of cyclic degradation nonlinear cyclicanalyses using the load history that was used in the exper-iment are conducted In order to investigate the impact ofdifferent modelling techniques and damage mechanism foreach analysis type three scenarios are considered

(a) Vertical and horizontal tie reinforcement are cor-roded but cover and core concrete are not affected bycorrosion

(b) Vertical and horizontal tie reinforcement are cor-roded and the cover concrete is cracked due tocorrosion but the core concrete is not affected

(c) Vertical and horizontal tie reinforcement are cor-roded the cover concrete is cracked and the coreconcrete is affected due to corrosion of confiningtiereinforcement

These scenarios will highlight the importance of each damagecomponent that needs to be considered in modelling nonlin-ear response of corroded RC columns

8 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008

minus300minus200minus100

0100200300

ExperimentFibre model

Drift ratio

Late

ral f

orce

(kN

)

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

ExperimentFibre model

Drift ratio

Late

ral f

orce

(kN

)

(b)

Figure 8 Comparison of experimental results and calibrated numerical model of uncorroded columns (a) Lehmanrsquos column 415 (b) Moyerand Kowalskyrsquos column 1

Lehmanrsquos column 415 and Moyer and Kowalskyrsquos column1 [50 54] are considered in this study The geometricaldetails material properties and detailed experimental resultsof these columns are available in [50 54] Figure 8 showsa comparison of the numerical model and experimentalresponses of these columns It should be noted that Lehmanrsquoscolumn 415 has 119871eff119889 = 10 and Moyer and Kowalskyrsquoscolumn 1 has 119871eff119889 = 4 The detailed discussion of thenumerical model validation is available in [25] It shouldbe noted that the maximum drift capacity in this paperis considered as the point where the force-displacementresponse of the column starts softening and losing strengthIt is found that the maximum drift capacity of both columnsat uncorroded state is about 6

The buckling lengths of corroded vertical reinforcementare calculated using the methodology described in Section 4The corrosion of horizontal ties is considered in the bucklinglength calculation As discussed previously (Section 4) thebuckling length of the vertical bars is a function of thetie reinforcementrsquos stiffness and the vertical reinforcementrsquosflexural rigidity Corrosion results in a reduction in flexuralrigidity of vertical barsTherefore the required stiffness fromtie reinforcement to restrain vertical bars against bucklingis reduced However corrosion also reduces the stiffness ofthe tie reinforcement For example in Moyer and Kowalskyrsquoscolumn the vertical reinforcement buckled between two tiesIn this case it was found that corrosion did not affect thebuckling length

In Lehmanrsquos column 415 the vertical reinforcementbuckled over five ties However once the corrosion levelexceeds 10 the buckling length reduced and the verticalreinforcement buckled over four ties It should be notedthat although the buckling length is reduced 119871eff119889

1015840 is notnecessarily reduced where 119871eff is the buckling length and 1198891015840is the diameter of the corroded vertical reinforcement Thisis because corrosion also reduces the diameter of verticalbars This change in buckling length is related to the relativecorrosion level and stiffness between the vertical and tiereinforcement

In practice the horizontal tie reinforcement is closer thanthe main vertical reinforcement to the surface of concreteTherefore it might start corroding earlier than verticalreinforcementThis phenomenonmight have an effect on thebuckling length and confined concrete behaviour Howeverthere has not been any research to date to explore thecorrelation between the corrosion levels of the horizontaltie and vertical reinforcement This is an area for futureresearch and therefore in this research in the absence of anyexperimentalfield data the same corrosion is considered forboth vertical and tie reinforcement

It should be noted that the calculation of the time tocorrosion initiation and time-dependent corrosion propaga-tion is out of the scope of this paper There are mathematicalmodels available in the literature that enable an estimationof the time to corrosion initiation and propagation basedon the environmental conditions [55 56] The corrosion ratecan also be measured on site by electrical equipment whichcan then be turned into a mass loss ratio using Faradayrsquoslaw of electrolysis [57] Given that the focus of this paperis on the impact of different mass loss ratios on the seismicperformance of RC columns the corrosion level is modelledby percentage mass loss throughout this paper

61 Scenario (a) Column Nonlinear Behaviour When Cor-rosion Is Assumed Present in Vertical and Horizontal TieReinforcement Only In this scenario it is assumed that thecorrosion damage is only limited to the steel reinforcement(vertical and horizontal tie reinforcement) that is cover con-crete is uncracked and corrosion of confining reinforcementdoes not affect the confined concrete behaviour Here thesteel model described in Section 51 is used which includesthe impact of corrosion on the buckling and postbucklingbehaviour in compression and strength and ductility loss intension

Figure 9 shows the results of monotonic pushover anal-yses Figure 9(a) shows that the failure mode of Lehmanrsquoscolumn 415 is by vertical bar buckling and core confined

Advances in Materials Science and Engineering 9

0 001 002 003 004 005 006 007 0080

50100150200250300350

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

Drift ratio

Late

ral f

orce

(kN

)

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

Drift ratio

Late

ral f

orce

(kN

)

(b)

Figure 9 Pushover analyses considering corrosion induced damage in reinforcing steel (a) Lehmanrsquos column 415 (b) Moyer and Kowalskyrsquoscolumn 1

concrete crushing up to 10 mass loss However as the cor-rosion level increases beyond 10mass loss the failure modechanges from vertical bar bucking and concrete crushing incompression to fracture of the vertical bars in tension

Figure 9(b) shows that Moyer and Kowalskyrsquos column1 has also failed in bar buckling and concrete crushing incompression However because 119871eff119889 = 4 the strength lossis not as significant as that of Lehmanrsquos column 415 with119871eff119889 = 10 under monotonic loading The corrosion levelup to 20 mass loss changes Moyer and Kowalskyrsquos column1 behaviour The failure initiates with bar buckling andconcrete crushing in compression and followed by fracture ofthe vertical reinforcement in tension With corrosion levelsgreater than 20 mass loss failure is by premature fractureof the vertical bars in tension At this point a cascade of barfracture can be seen in the graphs up to complete collapse ofthe columns

Figures 10(a) and 10(b) show Lehmanrsquos column 415 with10 and 20 mass losses under cyclic loading respectivelyComparing the monotonic and cyclic responses (the samecyclic load protocol as the experiment) shows that low-cyclefatigue has a significant impact on the column responseThe monotonic analysis showed that 10 mass loss did notresult in vertical bar fracture in tension and the failure wasgoverned by bar buckling and concrete crushing However incyclic analysis the failuremode is combined bar buckling andconcrete crushing in compression (failure initiation) followedby bar fracture in tension due to low-cycle fatigue

Here we have a system that does not technically fail incrushing and buckling but survives a little longer until thenext cycle when the vertical reinforcement fails in tensionIt was found that a mass loss ratio greater than 10 has asignificant impact on the nonlinear response of the corrodedcolumn due to reduced low-cycle fatigue life Figure 10(b)shows that at 20 mass loss resulted in bar fracture at 005drift ratio in pushover analysis but it resulted in bar fractureat 003 drift ratio under cyclic loading due to low-cycle fatiguefailure

Figures 10(c) and 10(d) show a similar result for Moyerand Kowalskyrsquos column 1 Overall Moyer and Kowalskyrsquoscolumn 1 has slightly less pinched cyclic responseThis is dueto the influence of the buckling length of the vertical bars andits cyclic degradation due to buckling [25]

62 Scenario (b) Column Nonlinear Behaviour When Corro-sion Is Assumed Present in Vertical and Horizontal Tie Rein-forcement and Cover Concrete Is Cracked In this scenarioit is assumed that the reinforcing steel (vertical and tie) iscorroded and the cover concrete is cracked due to corrosionof vertical reinforcementThe results of the pushover analysesare shown in Figure 11 The results in this case are almostidentical to the previous case (Section 61) where the damagein cover concrete was not considered Therefore in canbe concluded that whether or not we seek to model thecorrosion induced cracking of cover concrete it does not havea significant impact on the nonlinear response of corrodedcolumns Further discussion and comparison of this scenariowith other damage scenarios are available in Section 63

63 Scenario (c) Column Seismic Behaviour When Cor-rosion Is Assumed Present in Vertical and Horizontal TieReinforcement and Both Cover and Confined Concrete AreDamaged In this scenario it is assumed that the reinforc-ing steel (vertical and tie) is corroded cover concrete iscracked and the core confined concrete is affected by thecorrosion of horizontal tie reinforcement (as described inSection 53) Figure 12(a) shows the results of monotonicpushover analyses of Lehmanrsquos column 415 The results showthat the failure mechanism of this column for up to 10mass loss is bar buckling and core confined concrete crushingin compression However for corrosion levels beyond 10the failure mode changes This is a loss of drift capacitywhich starts with bar buckling and concrete crushing incompression and it is followed by bar fracture in tensionThese analyses demonstrate the importance of modelling the

10 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

Drift ratio

Late

ral f

orce

(kN

)

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

Drift ratio

Late

ral f

orce

(kN

)

(b)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

(c)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

(d)

Figure 10 Cyclic analyses considering corrosion induced damage in reinforcing steel (a) and (b) Lehmanrsquos column 415 (c) and (d) Moyerand Kowalskyrsquos column 1

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(b)

Figure 11 Pushover analyses considering corrosion induced damage in reinforcing steel and cracked cover concrete (a) Lehmanrsquos column415 (b) Moyer and Kowalskyrsquos column 1

Advances in Materials Science and Engineering 11

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(b)

Figure 12 Pushover analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a)Lehmanrsquos column 415 (b) Moyer and Kowalskyrsquos column 1

influence of corrosion on the confined concrete (throughloss of confining tie reinforcement) This corrosion damageon the confined concrete results in a rapid reduction instrength and ductility of the corroded columns compared tothe previous cases where confined concrete was considered tobe undamaged

Figure 12(b) shows the results of pushover analyses ofMoyer andKowalskyrsquos column 1 In this case the failuremodewas mainly bar buckling and concrete crushing followed byfracture of bars in tension for up to 20 mass loss Howevercorrosion levels beyond 20 mass loss have changed thefailure mode to premature fracture of bars in tension Thisdifference between the behaviour of the two columns is due tothe buckling behaviour of the vertical bars Given that Moyerand Kowalskyrsquos column 1 has much smaller buckling lengththe strength degradation in compression is much smallerthan Lehmanrsquos column 415 Therefore corrosion has more asignificant impact in terms of ductility loss of bars in tensionwhereas in Lehmanrsquos column 415 failure initiates with severebar buckling and concrete crushing then it is followed byfracture of vertical bars in tension

Figure 13 shows the results of cyclic analysis It showsthe cyclic analyses of Lehmanrsquos column 415 and Moyer andKowalskyrsquos column 1 with 10 and 20 mass loss togetherwith the corresponding pushover envelopes Figure 13 showsthat the extent of corrosion damage under cyclic loadingis more severe than monotonic loading The results ofmonotonic analysis showed that considering the ductility lossof corroded bars in tension and confinement reinforcementin compression has a big impact on bar buckling andfracture of reinforcement However cyclic analysis resultsshow that considering cyclic degradation due to low-cyclefatigue is crucial to have a realistic evaluation of the seismicperformance of existing corroded columns

For example in Figures 13(a) and 13(b) the failure ofLehmanrsquos column 415 was governed by bar buckling andconcrete crushing for a corrosion level up to 10 undermonotonic loadingHowever the same corrosion level results

in a much more severe drift capacity loss under cyclicloading due to a reduced low-cycle fatigue life Similarly inFigures 13(c) and 13(d) the failure of Moyer and Kowalskyrsquoscolumn was governed by concrete crushing in compressionfollowed by bar fracture in tension However low-cyclefatigue degradation due to cyclic loading results in prematurefracture of bars and subsequently severe loss of drift capacity

7 Comparison of the NonlinearResponses of Corroded Columns Computedin Different Scenarios

In order to clearly demonstrate the significance of corrosionmodels on the inelastic response of RC columns a com-parison between the computed responses of two columnswith different scenarios has been made The responses ofcolumns with 20 mass loss in monotonic pushover andcyclic analyses are compared and shown in Figure 14

Figure 14 shows the monotonic pushover and cyclicresponses of Lehmanrsquos column 415 andMoyer and Kowalskyrsquoscolumn 1 with 20 mass losses and different corrosiondamage models Figures 14(a) and 14(b) show that if thecorrosion induced damage to confined concrete is ignoredthe predicted failure mode is likely to be the fracture of barsin tension due to their reduced ductility However if thecorrosion induced damage to confined concrete is addedFigure 14(a) shows that the failure mode of Lehmanrsquos column415 will change to concrete crushing and buckling of thevertical bars in compression

Figure 14(b) shows that the failure mode of Moyer andKowalskyrsquos column 1 initiates with concrete crushing andbuckling of bars in compression and then it is followedby fracture of bars in tension This difference in failuremechanism is due to the differences in confinement level thebuckling length of the vertical bars the ratio of longitudinalreinforcement and the axial force ratio on the columnThere-fore in order to predict the nonlinear response accurately adetailed finite element model is required

12 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(d)

Figure 13 Cyclic analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a) and(b) Lehmanrsquos column 415 (c) and (d) Moyer and Kowalskyrsquos column 1

It is found that the failure mode under cyclic loading ismainly governed by the fracture of horizontal bars in tensiondue to reduced low-cycle fatigue life (Figures 14(c) and 14(d))This is a very important finding as it suggests that nonlinearquasistatic pushover analysis on its own is not adequate forperformance assessment of existing corroded bridge piers

With reference to Figure 14 it is evident that consideringthe impact of the corrosion damage on core confined con-crete and low-cycle fatigue degradation is crucial Thereforethey need to be considered when modelling the nonlinearbehaviour of corrosion damaged RC bridge piers underseismic loading This finding is in good agreement with theobserved experimental results by other researchers [12ndash1458]

A series of experimental studies were conducted in [12]on the cyclic behaviour of large-scale corroded cantilever RCbeams Ou et al found that as the level of corrosion increasesthe flexural failure initiates with premature buckling oflongitudinal bars This conclusion is in good agreement withthe numerical results discussed in this paper In another study[13] a series of experimental studies were conducted on cyclicbehaviour of corroded RC columns with varied axial forceMa et al have reported that once the corrosion level increases

beyond about 14 rapid strength and ductility reductionand cyclic degradation in hysteretic loops are seen due toreduced low-cycle fatigue life and premature buckling ofvertical reinforcement This conclusion is in good agreementwith the predicted failure modes using the numerical modelpresented in this paper

The detailed finite element model developed in thispaper can accurately model the nonlinear behaviour ofcorrodedRCcolumns subject to cyclic loading up to completecollapse There is a need to extend the PEER-UW columndatabase to include corroded RC columns so that furthercalibrationvalidation of the material model parameters canbe performed However the modelling technique developedin this paper is able to simulate the multiple failure modesof corroded RC columns simultaneously It represents thecurrent state of the art and as such they provide a novel com-putational framework for the seismic response prediction ofcorroded RC bridges

8 Conclusions

A series of pushover and cyclic analyses on two hypotheticalcorroded RC columns are conducted and these are used

Advances in Materials Science and Engineering 13

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(d)

Figure 14 Comparison of the computed responses of columns with different deterioration models (a) and (c) Lehmanrsquos column 415 undermonotonic and cyclic loading (b) and (d) Moyer and Kowalskyrsquos column 1 under monotonic and cyclic loading

to explore the performance of the proposed computationalframework The impact of corrosion on (i) the verticalreinforcing steel (ii) the tieconfinement (iii) the cover(unconfined) concrete and (iv) the core (confined) concreteis represented through new material models The proposednew steel material model accounts for (i) inelastic nonlinearbuckling of the vertical reinforcement (ii) the corrosion lossof area (iii) the nonuniform corrosion pitting and (iv) low-cycle high amplitude fatigueThenew cover concretematerialmodel includes the influence of internal pressure due tothe build-up of corrosion products (using compression fieldtheory) The new core concrete model includes the influenceof corrosion induced loss of confining reinforcement

The main outcomes of this study can be summarised asfollows

(1) Corrosion has a more significant impact on theductility loss (drift capacity) of RC columns than thestrength loss (plastic moment capacity)

(2) The numerical model developed in this paper is ableto predict the nonlinear flexural response of corrodedRC columns up to complete collapse Results showwhich depends on a cyclic load history that flexuralfailure can be initiated by the buckling of vertical bars

and crushing of core concrete which is then followedby fracture of bars in tension In cases where thebuckling of bars is not an issue or the buckling lengthis too short (119871eff119889

1015840le 5) the failure is governed by the

fracture of the vertical bars in tension due to low-cyclehigh amplitude fatigue

(3) The analyses results show that for the seismic perfor-mance and evaluation of existing corroded bridgesmonotonic pushover analysis is not sufficient Thecyclic degradation due to low-cycle high amplitudefatigue has a significant influence on the response ofcorroded RC columns

(4) The results of this study show that it is inadequate toassume that corrosion only affects the main verticalreinforcement in the column It was found that theconfined concrete with corroded confinement rein-forcement starts crushing much faster than uncor-roded undamaged concrete This changes the failuremode and results in premature buckling of the ver-tical reinforcement This change in the failure modecannot be predicted if the damage in core confinedconcrete due to corrosion of tie reinforcement isignored This is in good agreement with observed

14 Advances in Materials Science and Engineering

experimental results reported by other researchers[12ndash14]

(5) The modelling technique developed in this paper hassignificantly improved the earlier models and canbe used by other researchers in the future researchfor seismic vulnerability and fragility analysis ofcorroded RC bridges

Disclosure

Any findings opinions and recommendations provided inthis paper are only based on the authorsrsquo view

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This research is conducted in collaboration with the Univer-sity of Bristol and the University of Washington while thefirst author was on sabbatical leave in the US The fundingprovided by the World Wide University Network throughthe Research Mobility Program to the first author was muchappreciated The authors would like to thank Professor MarcO Eberhard and Professor John F Stanton for providingvaluable guidance during the course of this research

References

[1] S Hida F I S Ibrahim H A Capers et al ldquoAssuringbridge safety and serviceability in Europerdquo Tech Rep FHWA-PL-10-014 Office of International Programs Federal HighwayAdministration US Department of Transportation AmericanAssociation of State Highway and Transportation Officials2010

[2] ASCE Failure to Act The Economic Impact of Current Invest-ment Trends in Surface Transportation Infrastructure EconomicDevelopment Research Group Inc ASCE 2011

[3] D-E Choe P Gardoni D Rosowsky and T Haukaas ldquoProb-abilistic capacity models and seismic fragility estimates forRC columns subject to corrosionrdquo Reliability Engineering andSystem Safety vol 93 no 3 pp 383ndash393 2008

[4] L Berto R Vitaliani A Saetta and P Simioni ldquoSeismicassessment of existing RC structures affected by degradationphenomenardquo Structural Safety vol 31 no 4 pp 284ndash297 2009

[5] J Ghosh and J E Padgett ldquoAging considerations in the devel-opment of time-dependent seismic fragility curvesrdquo Journal ofStructural Engineering vol 136 no 12 pp 1497ndash1511 2010

[6] A Alipour B Shafei and M Shinozuka ldquoPerformance evalu-ation of deteriorating highway bridges located in high seismicareasrdquo Journal of Bridge Engineering vol 16 no 5 pp 597ndash6112011

[7] F Biondini E Camnasio and A Palermo ldquoLifetime seismicperformance of concrete bridges exposed to corrosionrdquo Struc-ture and Infrastructure Engineering vol 10 no 7 pp 880ndash9002014

[8] M Akiyama D M Frangopol and H Matsuzaki ldquoLife-cyclereliability of RC bridge piers under seismic and airborne chlo-ride hazardsrdquo Earthquake Engineering and Structural Dynamicsvol 40 no 15 pp 1671ndash1687 2011

[9] F Biondini A Palermo and G Toniolo ldquoSeismic performanceof concrete structures exposed to corrosion case studies of low-rise precast buildingsrdquo Structure and Infrastructure Engineeringvol 7 no 1-2 pp 109ndash119 2011

[10] C K Chiu F J Tu and F P Hsiao ldquoLifetime seismic perfor-mance assessment for chloride-corroded reinforced concretebuildingsrdquo Structure and Infrastructure Engineering vol 11 no3 pp 345ndash362 2015

[11] M Sanchez-Silva G-A Klutke and D V Rosowsky ldquoLife-cycleperformance of structures subject to multiple deteriorationmechanismsrdquo Structural Safety vol 33 no 3 pp 206ndash217 2011

[12] Y-C Ou L-L Tsai and H-H Chen ldquoCyclic performance oflarge-scale corroded reinforced concrete beamsrdquo EarthquakeEngineering and StructuralDynamics vol 41 no 4 pp 593ndash6042012

[13] Y Ma Y Che and J Gong ldquoBehavior of corrosion damagedcircular reinforced concrete columns under cyclic loadingrdquoConstruction and Building Materials vol 29 pp 548ndash556 2012

[14] A Meda S Mostosi Z Rinaldi and P Riva ldquoExperimentalevaluation of the corrosion influence on the cyclic behaviour ofRC columnsrdquo Engineering Structures vol 76 pp 112ndash123 2014

[15] A A Almusallam ldquoEffect of degree of corrosion on theproperties of reinforcing steel barsrdquo Construction and BuildingMaterials vol 15 no 8 pp 361ndash368 2001

[16] Y G Du L A Clark and A H C Chan ldquoResidual capacity ofcorroded reinforcing barsrdquoMagazine of Concrete Research vol57 no 3 pp 135ndash147 2005

[17] Y G Du L A Clarkt and A H C Chan ldquoEffect of corrosionon ductility of reinforcing barsrdquoMagazine of Concrete Researchvol 57 no 7 pp 407ndash419 2005

[18] J Cairns G A Plizzari Y Du D W Law and C FranzonildquoMechanical properties of corrosion-damaged reinforcementrdquoACI Materials Journal vol 102 no 4 pp 256ndash264 2005

[19] C A ApostolopoulosM P Papadopoulos and S G PantelakisldquoTensile behavior of corroded reinforcing steel bars BSt 500srdquoConstruction and Building Materials vol 20 no 9 pp 782ndash7892006

[20] C A Apostolopoulos ldquoMechanical behavior of corroded rein-forcing steel bars S500s tempcore under low cycle fatiguerdquoConstruction andBuildingMaterials vol 21 no 7 pp 1447ndash14562007

[21] M M Kashani A J Crewe and N A Alexander ldquoNonlinearstress-strain behaviour of corrosion-damaged reinforcing barsincluding inelastic bucklingrdquo Engineering Structures vol 48 pp417ndash429 2013

[22] M M Kashani A J Crewe and N A Alexander ldquoNonlinearcyclic response of corrosion-damaged reinforcing bars with theeffect of bucklingrdquo Construction and Building Materials vol 41pp 388ndash400 2013

[23] M M Kashani A J Crewe and N A Alexander ldquoUse of a 3Doptical measurement technique for stochastic corrosion patternanalysis of reinforcing bars subjected to accelerated corrosionrdquoCorrosion Science vol 73 pp 208ndash221 2013

[24] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoFinite element investigation of the influence of corrosionpattern on inelastic buckling and cyclic response of corrodedreinforcing barsrdquo Engineering Structures vol 75 pp 113ndash1252014

Advances in Materials Science and Engineering 15

[25] M M Kashani Seismic performance of corroded rc bridge piersdevelopment of a multi-mechanical nonlinear fibre beam-columnmodel [PhD thesis] University of Bristol Bristol UK 2014

[26] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part I Formula-tionrdquo Earthquake Engineering and Structural Dynamics vol 25no 7 pp 711ndash725 1996

[27] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part II Applica-tionsrdquoEarthquake Engineering and Structural Dynamics vol 25no 7 pp 727ndash742 1996

[28] The Open System for Earthquake Engineering Simulation(OpenSees) Pacific Earthquake Engineering Research CentreUniversity of California Berkeley Berkeley Calif USA 2011

[29] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoPhenomenological hysteretic model for corroded reinforcingbars including inelastic buckling and low-cycle fatigue degrada-tionrdquo Computers and Structures vol 156 article 5393 pp 58ndash712015

[30] J Coleman and E Spacone ldquoLocalization issues in force-basedframe elementsrdquo Journal of Structural Engineering vol 127 no11 pp 1257ndash1265 2001

[31] J S Pugh Numerical simulation of walls and seismic designrecommendations for walled buildings [PhD thesis] Universityof Washington Seattle Wash USA 2012

[32] D V Val and R E Melchers ldquoReliability of deteriorating RCslab bridgesrdquo Journal of Structural Engineering vol 123 no 12pp 1638ndash1644 1997

[33] M S Darmawan and M G Stewart ldquoEffect of pitting corro-sion on capacity of prestressing wiresrdquo Magazine of ConcreteResearch vol 59 no 2 pp 131ndash139 2007

[34] R P Dhakal and K Maekawa ldquoReinforcement stability andfracture of cover concrete in reinforced concrete membersrdquoJournal of Structural Engineering vol 128 no 10 pp 1253ndash12622002

[35] C Lee J F Bonacci M D A Thomas et al ldquoAcceleratedcorrosion and repair of reinforced concrete columns usingcarbon fibre reinforced polymer sheetsrdquo Canadian Journal ofCivil Engineering vol 27 no 5 pp 941ndash948 2000

[36] W Aquino Long-term performance of seismically rehabilitatedcorrosion-damaged columns [PhD thesis] University of Illinoisat Urbana-Champaign Champaign Ill USA 2002

[37] S Timoshenko and J Gere Theory of Elastic StabilityMacGraw-Hill New York NY USA 1963

[38] S J Pantazopoulou ldquoDetailing for reinforcement stability in RCmembersrdquo Journal of Structural Engineering vol 124 no 6 pp623ndash632 1998

[39] J B Mander M J N Priestley and R Park ldquoObserved stress-strain behavior of confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1827ndash1849 1988

[40] J B Mander M J Priestley and R Park ldquoTheoretical stress-strain model for confined concreterdquo Journal of Structural Engi-neering (United States) vol 114 no 8 pp 1804ndash1826 1988

[41] S Popovics ldquoAnumerical approach to the complete stress-straincurve of concreterdquo Cement and Concrete Research vol 3 no 5pp 583ndash599 1973

[42] I D Karsan and J O Jirsa ldquoBehavior of concrete undercompressive loadingrdquo Journal of Structural Division vol 95article ST12 1969

[43] M P Berry andMO Eberhard ldquoPerformancemodeling strate-gies for modern reinforced concrete bridge columnsrdquo PEER

Research Report University of California Berkeley BerkeleyCalif USA 2006

[44] B D Scott R Park and M J N Priestley ldquoStress-strainbehavior of concrete confined by overlapping hoops at low andhigh strain ratesrdquo Journal of the American Concrete Institute vol79 no 1 pp 13ndash27 1982

[45] A S Al-Harthy M G Stewart and J Mullard ldquoConcrete covercracking caused by steel reinforcement corrosionrdquoMagazine ofConcrete Research vol 63 no 9 pp 655ndash667 2011

[46] T Vidal A Castel and R Francois ldquoAnalyzing crack width topredict corrosion in reinforced concreterdquo Cement and ConcreteResearch vol 34 no 1 pp 165ndash174 2004

[47] F J Molina C Alonso and C Andrade ldquoCover cracking as afunction of rebar corrosion part 2-numerical modelrdquoMaterialsand Structures vol 26 no 9 pp 532ndash548 1993

[48] F J Vecchio and M P Collins ldquoThe modified compression-field theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[49] D Coronelli and P Gambarova ldquoStructural assessment ofcorroded reinforced concrete beams modeling guidelinesrdquoJournal of Structural Engineering vol 130 no 8 pp 1214ndash12242004

[50] D E Lehman and J P Moehle ldquoSeismic performance of well-confined concrete columnsrdquo PEER Research Report Universityof California at Berkeley 2000

[51] L N Lowes and A Altoontash ldquoModeling reinforced-concretebeam-column joints subjected to cyclic loadingrdquo Journal ofStructural Engineering vol 129 no 12 pp 1686ndash1697 2003

[52] M Berry M Parrish and M Eberhard ldquoPerformance databaseUserrsquos manualrdquo in Pacific Earthquake Engineering ResearchCentre 2004 University of California at Berkeley 2004httpwwwcewashingtonedusimpeera1

[53] A N Kallias and M Imran Rafiq ldquoFinite element investigationof the structural response of corroded RC beamsrdquo EngineeringStructures vol 32 no 9 pp 2984ndash2994 2010

[54] M J Moyer and M J Kowalsky ldquoInfluence of tension strain onbuckling of reinforcement in concrete columnsrdquo ACI StructuralJournal vol 100 no 1 pp 75ndash85 2003

[55] K A T Vu andM G Stewart ldquoStructural reliability of concretebridges including improved chloride-induced corrosion mod-elsrdquo Structural Safety vol 22 no 4 pp 313ndash333 2000

[56] D V Val ldquoFactors affecting life-cycle cost analysis of RCstructures in chloride contaminated environmentsrdquo Journal ofInfrastructure Systems vol 13 no 2 pp 135ndash143 2007

[57] J P BroomfieldCorrosion of Steel in Concrete Taylor amp FrancisLondon UK 2nd edition 2007

[58] M M Kashani P Alagheband R Khan and S Davis ldquoImpactof corrosion on low-cycle fatigue degradation of reinforcingbars with the effect of inelastic bucklingrdquo International Journalof Fatigue vol 77 pp 174ndash185 2015

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

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MetallurgyJournal of

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BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

8 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008

minus300minus200minus100

0100200300

ExperimentFibre model

Drift ratio

Late

ral f

orce

(kN

)

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

ExperimentFibre model

Drift ratio

Late

ral f

orce

(kN

)

(b)

Figure 8 Comparison of experimental results and calibrated numerical model of uncorroded columns (a) Lehmanrsquos column 415 (b) Moyerand Kowalskyrsquos column 1

Lehmanrsquos column 415 and Moyer and Kowalskyrsquos column1 [50 54] are considered in this study The geometricaldetails material properties and detailed experimental resultsof these columns are available in [50 54] Figure 8 showsa comparison of the numerical model and experimentalresponses of these columns It should be noted that Lehmanrsquoscolumn 415 has 119871eff119889 = 10 and Moyer and Kowalskyrsquoscolumn 1 has 119871eff119889 = 4 The detailed discussion of thenumerical model validation is available in [25] It shouldbe noted that the maximum drift capacity in this paperis considered as the point where the force-displacementresponse of the column starts softening and losing strengthIt is found that the maximum drift capacity of both columnsat uncorroded state is about 6

The buckling lengths of corroded vertical reinforcementare calculated using the methodology described in Section 4The corrosion of horizontal ties is considered in the bucklinglength calculation As discussed previously (Section 4) thebuckling length of the vertical bars is a function of thetie reinforcementrsquos stiffness and the vertical reinforcementrsquosflexural rigidity Corrosion results in a reduction in flexuralrigidity of vertical barsTherefore the required stiffness fromtie reinforcement to restrain vertical bars against bucklingis reduced However corrosion also reduces the stiffness ofthe tie reinforcement For example in Moyer and Kowalskyrsquoscolumn the vertical reinforcement buckled between two tiesIn this case it was found that corrosion did not affect thebuckling length

In Lehmanrsquos column 415 the vertical reinforcementbuckled over five ties However once the corrosion levelexceeds 10 the buckling length reduced and the verticalreinforcement buckled over four ties It should be notedthat although the buckling length is reduced 119871eff119889

1015840 is notnecessarily reduced where 119871eff is the buckling length and 1198891015840is the diameter of the corroded vertical reinforcement Thisis because corrosion also reduces the diameter of verticalbars This change in buckling length is related to the relativecorrosion level and stiffness between the vertical and tiereinforcement

In practice the horizontal tie reinforcement is closer thanthe main vertical reinforcement to the surface of concreteTherefore it might start corroding earlier than verticalreinforcementThis phenomenonmight have an effect on thebuckling length and confined concrete behaviour Howeverthere has not been any research to date to explore thecorrelation between the corrosion levels of the horizontaltie and vertical reinforcement This is an area for futureresearch and therefore in this research in the absence of anyexperimentalfield data the same corrosion is considered forboth vertical and tie reinforcement

It should be noted that the calculation of the time tocorrosion initiation and time-dependent corrosion propaga-tion is out of the scope of this paper There are mathematicalmodels available in the literature that enable an estimationof the time to corrosion initiation and propagation basedon the environmental conditions [55 56] The corrosion ratecan also be measured on site by electrical equipment whichcan then be turned into a mass loss ratio using Faradayrsquoslaw of electrolysis [57] Given that the focus of this paperis on the impact of different mass loss ratios on the seismicperformance of RC columns the corrosion level is modelledby percentage mass loss throughout this paper

61 Scenario (a) Column Nonlinear Behaviour When Cor-rosion Is Assumed Present in Vertical and Horizontal TieReinforcement Only In this scenario it is assumed that thecorrosion damage is only limited to the steel reinforcement(vertical and horizontal tie reinforcement) that is cover con-crete is uncracked and corrosion of confining reinforcementdoes not affect the confined concrete behaviour Here thesteel model described in Section 51 is used which includesthe impact of corrosion on the buckling and postbucklingbehaviour in compression and strength and ductility loss intension

Figure 9 shows the results of monotonic pushover anal-yses Figure 9(a) shows that the failure mode of Lehmanrsquoscolumn 415 is by vertical bar buckling and core confined

Advances in Materials Science and Engineering 9

0 001 002 003 004 005 006 007 0080

50100150200250300350

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

Drift ratio

Late

ral f

orce

(kN

)

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

Drift ratio

Late

ral f

orce

(kN

)

(b)

Figure 9 Pushover analyses considering corrosion induced damage in reinforcing steel (a) Lehmanrsquos column 415 (b) Moyer and Kowalskyrsquoscolumn 1

concrete crushing up to 10 mass loss However as the cor-rosion level increases beyond 10mass loss the failure modechanges from vertical bar bucking and concrete crushing incompression to fracture of the vertical bars in tension

Figure 9(b) shows that Moyer and Kowalskyrsquos column1 has also failed in bar buckling and concrete crushing incompression However because 119871eff119889 = 4 the strength lossis not as significant as that of Lehmanrsquos column 415 with119871eff119889 = 10 under monotonic loading The corrosion levelup to 20 mass loss changes Moyer and Kowalskyrsquos column1 behaviour The failure initiates with bar buckling andconcrete crushing in compression and followed by fracture ofthe vertical reinforcement in tension With corrosion levelsgreater than 20 mass loss failure is by premature fractureof the vertical bars in tension At this point a cascade of barfracture can be seen in the graphs up to complete collapse ofthe columns

Figures 10(a) and 10(b) show Lehmanrsquos column 415 with10 and 20 mass losses under cyclic loading respectivelyComparing the monotonic and cyclic responses (the samecyclic load protocol as the experiment) shows that low-cyclefatigue has a significant impact on the column responseThe monotonic analysis showed that 10 mass loss did notresult in vertical bar fracture in tension and the failure wasgoverned by bar buckling and concrete crushing However incyclic analysis the failuremode is combined bar buckling andconcrete crushing in compression (failure initiation) followedby bar fracture in tension due to low-cycle fatigue

Here we have a system that does not technically fail incrushing and buckling but survives a little longer until thenext cycle when the vertical reinforcement fails in tensionIt was found that a mass loss ratio greater than 10 has asignificant impact on the nonlinear response of the corrodedcolumn due to reduced low-cycle fatigue life Figure 10(b)shows that at 20 mass loss resulted in bar fracture at 005drift ratio in pushover analysis but it resulted in bar fractureat 003 drift ratio under cyclic loading due to low-cycle fatiguefailure

Figures 10(c) and 10(d) show a similar result for Moyerand Kowalskyrsquos column 1 Overall Moyer and Kowalskyrsquoscolumn 1 has slightly less pinched cyclic responseThis is dueto the influence of the buckling length of the vertical bars andits cyclic degradation due to buckling [25]

62 Scenario (b) Column Nonlinear Behaviour When Corro-sion Is Assumed Present in Vertical and Horizontal Tie Rein-forcement and Cover Concrete Is Cracked In this scenarioit is assumed that the reinforcing steel (vertical and tie) iscorroded and the cover concrete is cracked due to corrosionof vertical reinforcementThe results of the pushover analysesare shown in Figure 11 The results in this case are almostidentical to the previous case (Section 61) where the damagein cover concrete was not considered Therefore in canbe concluded that whether or not we seek to model thecorrosion induced cracking of cover concrete it does not havea significant impact on the nonlinear response of corrodedcolumns Further discussion and comparison of this scenariowith other damage scenarios are available in Section 63

63 Scenario (c) Column Seismic Behaviour When Cor-rosion Is Assumed Present in Vertical and Horizontal TieReinforcement and Both Cover and Confined Concrete AreDamaged In this scenario it is assumed that the reinforc-ing steel (vertical and tie) is corroded cover concrete iscracked and the core confined concrete is affected by thecorrosion of horizontal tie reinforcement (as described inSection 53) Figure 12(a) shows the results of monotonicpushover analyses of Lehmanrsquos column 415 The results showthat the failure mechanism of this column for up to 10mass loss is bar buckling and core confined concrete crushingin compression However for corrosion levels beyond 10the failure mode changes This is a loss of drift capacitywhich starts with bar buckling and concrete crushing incompression and it is followed by bar fracture in tensionThese analyses demonstrate the importance of modelling the

10 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

Drift ratio

Late

ral f

orce

(kN

)

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

Drift ratio

Late

ral f

orce

(kN

)

(b)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

(c)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

(d)

Figure 10 Cyclic analyses considering corrosion induced damage in reinforcing steel (a) and (b) Lehmanrsquos column 415 (c) and (d) Moyerand Kowalskyrsquos column 1

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(b)

Figure 11 Pushover analyses considering corrosion induced damage in reinforcing steel and cracked cover concrete (a) Lehmanrsquos column415 (b) Moyer and Kowalskyrsquos column 1

Advances in Materials Science and Engineering 11

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(b)

Figure 12 Pushover analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a)Lehmanrsquos column 415 (b) Moyer and Kowalskyrsquos column 1

influence of corrosion on the confined concrete (throughloss of confining tie reinforcement) This corrosion damageon the confined concrete results in a rapid reduction instrength and ductility of the corroded columns compared tothe previous cases where confined concrete was considered tobe undamaged

Figure 12(b) shows the results of pushover analyses ofMoyer andKowalskyrsquos column 1 In this case the failuremodewas mainly bar buckling and concrete crushing followed byfracture of bars in tension for up to 20 mass loss Howevercorrosion levels beyond 20 mass loss have changed thefailure mode to premature fracture of bars in tension Thisdifference between the behaviour of the two columns is due tothe buckling behaviour of the vertical bars Given that Moyerand Kowalskyrsquos column 1 has much smaller buckling lengththe strength degradation in compression is much smallerthan Lehmanrsquos column 415 Therefore corrosion has more asignificant impact in terms of ductility loss of bars in tensionwhereas in Lehmanrsquos column 415 failure initiates with severebar buckling and concrete crushing then it is followed byfracture of vertical bars in tension

Figure 13 shows the results of cyclic analysis It showsthe cyclic analyses of Lehmanrsquos column 415 and Moyer andKowalskyrsquos column 1 with 10 and 20 mass loss togetherwith the corresponding pushover envelopes Figure 13 showsthat the extent of corrosion damage under cyclic loadingis more severe than monotonic loading The results ofmonotonic analysis showed that considering the ductility lossof corroded bars in tension and confinement reinforcementin compression has a big impact on bar buckling andfracture of reinforcement However cyclic analysis resultsshow that considering cyclic degradation due to low-cyclefatigue is crucial to have a realistic evaluation of the seismicperformance of existing corroded columns

For example in Figures 13(a) and 13(b) the failure ofLehmanrsquos column 415 was governed by bar buckling andconcrete crushing for a corrosion level up to 10 undermonotonic loadingHowever the same corrosion level results

in a much more severe drift capacity loss under cyclicloading due to a reduced low-cycle fatigue life Similarly inFigures 13(c) and 13(d) the failure of Moyer and Kowalskyrsquoscolumn was governed by concrete crushing in compressionfollowed by bar fracture in tension However low-cyclefatigue degradation due to cyclic loading results in prematurefracture of bars and subsequently severe loss of drift capacity

7 Comparison of the NonlinearResponses of Corroded Columns Computedin Different Scenarios

In order to clearly demonstrate the significance of corrosionmodels on the inelastic response of RC columns a com-parison between the computed responses of two columnswith different scenarios has been made The responses ofcolumns with 20 mass loss in monotonic pushover andcyclic analyses are compared and shown in Figure 14

Figure 14 shows the monotonic pushover and cyclicresponses of Lehmanrsquos column 415 andMoyer and Kowalskyrsquoscolumn 1 with 20 mass losses and different corrosiondamage models Figures 14(a) and 14(b) show that if thecorrosion induced damage to confined concrete is ignoredthe predicted failure mode is likely to be the fracture of barsin tension due to their reduced ductility However if thecorrosion induced damage to confined concrete is addedFigure 14(a) shows that the failure mode of Lehmanrsquos column415 will change to concrete crushing and buckling of thevertical bars in compression

Figure 14(b) shows that the failure mode of Moyer andKowalskyrsquos column 1 initiates with concrete crushing andbuckling of bars in compression and then it is followedby fracture of bars in tension This difference in failuremechanism is due to the differences in confinement level thebuckling length of the vertical bars the ratio of longitudinalreinforcement and the axial force ratio on the columnThere-fore in order to predict the nonlinear response accurately adetailed finite element model is required

12 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(d)

Figure 13 Cyclic analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a) and(b) Lehmanrsquos column 415 (c) and (d) Moyer and Kowalskyrsquos column 1

It is found that the failure mode under cyclic loading ismainly governed by the fracture of horizontal bars in tensiondue to reduced low-cycle fatigue life (Figures 14(c) and 14(d))This is a very important finding as it suggests that nonlinearquasistatic pushover analysis on its own is not adequate forperformance assessment of existing corroded bridge piers

With reference to Figure 14 it is evident that consideringthe impact of the corrosion damage on core confined con-crete and low-cycle fatigue degradation is crucial Thereforethey need to be considered when modelling the nonlinearbehaviour of corrosion damaged RC bridge piers underseismic loading This finding is in good agreement with theobserved experimental results by other researchers [12ndash1458]

A series of experimental studies were conducted in [12]on the cyclic behaviour of large-scale corroded cantilever RCbeams Ou et al found that as the level of corrosion increasesthe flexural failure initiates with premature buckling oflongitudinal bars This conclusion is in good agreement withthe numerical results discussed in this paper In another study[13] a series of experimental studies were conducted on cyclicbehaviour of corroded RC columns with varied axial forceMa et al have reported that once the corrosion level increases

beyond about 14 rapid strength and ductility reductionand cyclic degradation in hysteretic loops are seen due toreduced low-cycle fatigue life and premature buckling ofvertical reinforcement This conclusion is in good agreementwith the predicted failure modes using the numerical modelpresented in this paper

The detailed finite element model developed in thispaper can accurately model the nonlinear behaviour ofcorrodedRCcolumns subject to cyclic loading up to completecollapse There is a need to extend the PEER-UW columndatabase to include corroded RC columns so that furthercalibrationvalidation of the material model parameters canbe performed However the modelling technique developedin this paper is able to simulate the multiple failure modesof corroded RC columns simultaneously It represents thecurrent state of the art and as such they provide a novel com-putational framework for the seismic response prediction ofcorroded RC bridges

8 Conclusions

A series of pushover and cyclic analyses on two hypotheticalcorroded RC columns are conducted and these are used

Advances in Materials Science and Engineering 13

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(d)

Figure 14 Comparison of the computed responses of columns with different deterioration models (a) and (c) Lehmanrsquos column 415 undermonotonic and cyclic loading (b) and (d) Moyer and Kowalskyrsquos column 1 under monotonic and cyclic loading

to explore the performance of the proposed computationalframework The impact of corrosion on (i) the verticalreinforcing steel (ii) the tieconfinement (iii) the cover(unconfined) concrete and (iv) the core (confined) concreteis represented through new material models The proposednew steel material model accounts for (i) inelastic nonlinearbuckling of the vertical reinforcement (ii) the corrosion lossof area (iii) the nonuniform corrosion pitting and (iv) low-cycle high amplitude fatigueThenew cover concretematerialmodel includes the influence of internal pressure due tothe build-up of corrosion products (using compression fieldtheory) The new core concrete model includes the influenceof corrosion induced loss of confining reinforcement

The main outcomes of this study can be summarised asfollows

(1) Corrosion has a more significant impact on theductility loss (drift capacity) of RC columns than thestrength loss (plastic moment capacity)

(2) The numerical model developed in this paper is ableto predict the nonlinear flexural response of corrodedRC columns up to complete collapse Results showwhich depends on a cyclic load history that flexuralfailure can be initiated by the buckling of vertical bars

and crushing of core concrete which is then followedby fracture of bars in tension In cases where thebuckling of bars is not an issue or the buckling lengthis too short (119871eff119889

1015840le 5) the failure is governed by the

fracture of the vertical bars in tension due to low-cyclehigh amplitude fatigue

(3) The analyses results show that for the seismic perfor-mance and evaluation of existing corroded bridgesmonotonic pushover analysis is not sufficient Thecyclic degradation due to low-cycle high amplitudefatigue has a significant influence on the response ofcorroded RC columns

(4) The results of this study show that it is inadequate toassume that corrosion only affects the main verticalreinforcement in the column It was found that theconfined concrete with corroded confinement rein-forcement starts crushing much faster than uncor-roded undamaged concrete This changes the failuremode and results in premature buckling of the ver-tical reinforcement This change in the failure modecannot be predicted if the damage in core confinedconcrete due to corrosion of tie reinforcement isignored This is in good agreement with observed

14 Advances in Materials Science and Engineering

experimental results reported by other researchers[12ndash14]

(5) The modelling technique developed in this paper hassignificantly improved the earlier models and canbe used by other researchers in the future researchfor seismic vulnerability and fragility analysis ofcorroded RC bridges

Disclosure

Any findings opinions and recommendations provided inthis paper are only based on the authorsrsquo view

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This research is conducted in collaboration with the Univer-sity of Bristol and the University of Washington while thefirst author was on sabbatical leave in the US The fundingprovided by the World Wide University Network throughthe Research Mobility Program to the first author was muchappreciated The authors would like to thank Professor MarcO Eberhard and Professor John F Stanton for providingvaluable guidance during the course of this research

References

[1] S Hida F I S Ibrahim H A Capers et al ldquoAssuringbridge safety and serviceability in Europerdquo Tech Rep FHWA-PL-10-014 Office of International Programs Federal HighwayAdministration US Department of Transportation AmericanAssociation of State Highway and Transportation Officials2010

[2] ASCE Failure to Act The Economic Impact of Current Invest-ment Trends in Surface Transportation Infrastructure EconomicDevelopment Research Group Inc ASCE 2011

[3] D-E Choe P Gardoni D Rosowsky and T Haukaas ldquoProb-abilistic capacity models and seismic fragility estimates forRC columns subject to corrosionrdquo Reliability Engineering andSystem Safety vol 93 no 3 pp 383ndash393 2008

[4] L Berto R Vitaliani A Saetta and P Simioni ldquoSeismicassessment of existing RC structures affected by degradationphenomenardquo Structural Safety vol 31 no 4 pp 284ndash297 2009

[5] J Ghosh and J E Padgett ldquoAging considerations in the devel-opment of time-dependent seismic fragility curvesrdquo Journal ofStructural Engineering vol 136 no 12 pp 1497ndash1511 2010

[6] A Alipour B Shafei and M Shinozuka ldquoPerformance evalu-ation of deteriorating highway bridges located in high seismicareasrdquo Journal of Bridge Engineering vol 16 no 5 pp 597ndash6112011

[7] F Biondini E Camnasio and A Palermo ldquoLifetime seismicperformance of concrete bridges exposed to corrosionrdquo Struc-ture and Infrastructure Engineering vol 10 no 7 pp 880ndash9002014

[8] M Akiyama D M Frangopol and H Matsuzaki ldquoLife-cyclereliability of RC bridge piers under seismic and airborne chlo-ride hazardsrdquo Earthquake Engineering and Structural Dynamicsvol 40 no 15 pp 1671ndash1687 2011

[9] F Biondini A Palermo and G Toniolo ldquoSeismic performanceof concrete structures exposed to corrosion case studies of low-rise precast buildingsrdquo Structure and Infrastructure Engineeringvol 7 no 1-2 pp 109ndash119 2011

[10] C K Chiu F J Tu and F P Hsiao ldquoLifetime seismic perfor-mance assessment for chloride-corroded reinforced concretebuildingsrdquo Structure and Infrastructure Engineering vol 11 no3 pp 345ndash362 2015

[11] M Sanchez-Silva G-A Klutke and D V Rosowsky ldquoLife-cycleperformance of structures subject to multiple deteriorationmechanismsrdquo Structural Safety vol 33 no 3 pp 206ndash217 2011

[12] Y-C Ou L-L Tsai and H-H Chen ldquoCyclic performance oflarge-scale corroded reinforced concrete beamsrdquo EarthquakeEngineering and StructuralDynamics vol 41 no 4 pp 593ndash6042012

[13] Y Ma Y Che and J Gong ldquoBehavior of corrosion damagedcircular reinforced concrete columns under cyclic loadingrdquoConstruction and Building Materials vol 29 pp 548ndash556 2012

[14] A Meda S Mostosi Z Rinaldi and P Riva ldquoExperimentalevaluation of the corrosion influence on the cyclic behaviour ofRC columnsrdquo Engineering Structures vol 76 pp 112ndash123 2014

[15] A A Almusallam ldquoEffect of degree of corrosion on theproperties of reinforcing steel barsrdquo Construction and BuildingMaterials vol 15 no 8 pp 361ndash368 2001

[16] Y G Du L A Clark and A H C Chan ldquoResidual capacity ofcorroded reinforcing barsrdquoMagazine of Concrete Research vol57 no 3 pp 135ndash147 2005

[17] Y G Du L A Clarkt and A H C Chan ldquoEffect of corrosionon ductility of reinforcing barsrdquoMagazine of Concrete Researchvol 57 no 7 pp 407ndash419 2005

[18] J Cairns G A Plizzari Y Du D W Law and C FranzonildquoMechanical properties of corrosion-damaged reinforcementrdquoACI Materials Journal vol 102 no 4 pp 256ndash264 2005

[19] C A ApostolopoulosM P Papadopoulos and S G PantelakisldquoTensile behavior of corroded reinforcing steel bars BSt 500srdquoConstruction and Building Materials vol 20 no 9 pp 782ndash7892006

[20] C A Apostolopoulos ldquoMechanical behavior of corroded rein-forcing steel bars S500s tempcore under low cycle fatiguerdquoConstruction andBuildingMaterials vol 21 no 7 pp 1447ndash14562007

[21] M M Kashani A J Crewe and N A Alexander ldquoNonlinearstress-strain behaviour of corrosion-damaged reinforcing barsincluding inelastic bucklingrdquo Engineering Structures vol 48 pp417ndash429 2013

[22] M M Kashani A J Crewe and N A Alexander ldquoNonlinearcyclic response of corrosion-damaged reinforcing bars with theeffect of bucklingrdquo Construction and Building Materials vol 41pp 388ndash400 2013

[23] M M Kashani A J Crewe and N A Alexander ldquoUse of a 3Doptical measurement technique for stochastic corrosion patternanalysis of reinforcing bars subjected to accelerated corrosionrdquoCorrosion Science vol 73 pp 208ndash221 2013

[24] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoFinite element investigation of the influence of corrosionpattern on inelastic buckling and cyclic response of corrodedreinforcing barsrdquo Engineering Structures vol 75 pp 113ndash1252014

Advances in Materials Science and Engineering 15

[25] M M Kashani Seismic performance of corroded rc bridge piersdevelopment of a multi-mechanical nonlinear fibre beam-columnmodel [PhD thesis] University of Bristol Bristol UK 2014

[26] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part I Formula-tionrdquo Earthquake Engineering and Structural Dynamics vol 25no 7 pp 711ndash725 1996

[27] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part II Applica-tionsrdquoEarthquake Engineering and Structural Dynamics vol 25no 7 pp 727ndash742 1996

[28] The Open System for Earthquake Engineering Simulation(OpenSees) Pacific Earthquake Engineering Research CentreUniversity of California Berkeley Berkeley Calif USA 2011

[29] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoPhenomenological hysteretic model for corroded reinforcingbars including inelastic buckling and low-cycle fatigue degrada-tionrdquo Computers and Structures vol 156 article 5393 pp 58ndash712015

[30] J Coleman and E Spacone ldquoLocalization issues in force-basedframe elementsrdquo Journal of Structural Engineering vol 127 no11 pp 1257ndash1265 2001

[31] J S Pugh Numerical simulation of walls and seismic designrecommendations for walled buildings [PhD thesis] Universityof Washington Seattle Wash USA 2012

[32] D V Val and R E Melchers ldquoReliability of deteriorating RCslab bridgesrdquo Journal of Structural Engineering vol 123 no 12pp 1638ndash1644 1997

[33] M S Darmawan and M G Stewart ldquoEffect of pitting corro-sion on capacity of prestressing wiresrdquo Magazine of ConcreteResearch vol 59 no 2 pp 131ndash139 2007

[34] R P Dhakal and K Maekawa ldquoReinforcement stability andfracture of cover concrete in reinforced concrete membersrdquoJournal of Structural Engineering vol 128 no 10 pp 1253ndash12622002

[35] C Lee J F Bonacci M D A Thomas et al ldquoAcceleratedcorrosion and repair of reinforced concrete columns usingcarbon fibre reinforced polymer sheetsrdquo Canadian Journal ofCivil Engineering vol 27 no 5 pp 941ndash948 2000

[36] W Aquino Long-term performance of seismically rehabilitatedcorrosion-damaged columns [PhD thesis] University of Illinoisat Urbana-Champaign Champaign Ill USA 2002

[37] S Timoshenko and J Gere Theory of Elastic StabilityMacGraw-Hill New York NY USA 1963

[38] S J Pantazopoulou ldquoDetailing for reinforcement stability in RCmembersrdquo Journal of Structural Engineering vol 124 no 6 pp623ndash632 1998

[39] J B Mander M J N Priestley and R Park ldquoObserved stress-strain behavior of confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1827ndash1849 1988

[40] J B Mander M J Priestley and R Park ldquoTheoretical stress-strain model for confined concreterdquo Journal of Structural Engi-neering (United States) vol 114 no 8 pp 1804ndash1826 1988

[41] S Popovics ldquoAnumerical approach to the complete stress-straincurve of concreterdquo Cement and Concrete Research vol 3 no 5pp 583ndash599 1973

[42] I D Karsan and J O Jirsa ldquoBehavior of concrete undercompressive loadingrdquo Journal of Structural Division vol 95article ST12 1969

[43] M P Berry andMO Eberhard ldquoPerformancemodeling strate-gies for modern reinforced concrete bridge columnsrdquo PEER

Research Report University of California Berkeley BerkeleyCalif USA 2006

[44] B D Scott R Park and M J N Priestley ldquoStress-strainbehavior of concrete confined by overlapping hoops at low andhigh strain ratesrdquo Journal of the American Concrete Institute vol79 no 1 pp 13ndash27 1982

[45] A S Al-Harthy M G Stewart and J Mullard ldquoConcrete covercracking caused by steel reinforcement corrosionrdquoMagazine ofConcrete Research vol 63 no 9 pp 655ndash667 2011

[46] T Vidal A Castel and R Francois ldquoAnalyzing crack width topredict corrosion in reinforced concreterdquo Cement and ConcreteResearch vol 34 no 1 pp 165ndash174 2004

[47] F J Molina C Alonso and C Andrade ldquoCover cracking as afunction of rebar corrosion part 2-numerical modelrdquoMaterialsand Structures vol 26 no 9 pp 532ndash548 1993

[48] F J Vecchio and M P Collins ldquoThe modified compression-field theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[49] D Coronelli and P Gambarova ldquoStructural assessment ofcorroded reinforced concrete beams modeling guidelinesrdquoJournal of Structural Engineering vol 130 no 8 pp 1214ndash12242004

[50] D E Lehman and J P Moehle ldquoSeismic performance of well-confined concrete columnsrdquo PEER Research Report Universityof California at Berkeley 2000

[51] L N Lowes and A Altoontash ldquoModeling reinforced-concretebeam-column joints subjected to cyclic loadingrdquo Journal ofStructural Engineering vol 129 no 12 pp 1686ndash1697 2003

[52] M Berry M Parrish and M Eberhard ldquoPerformance databaseUserrsquos manualrdquo in Pacific Earthquake Engineering ResearchCentre 2004 University of California at Berkeley 2004httpwwwcewashingtonedusimpeera1

[53] A N Kallias and M Imran Rafiq ldquoFinite element investigationof the structural response of corroded RC beamsrdquo EngineeringStructures vol 32 no 9 pp 2984ndash2994 2010

[54] M J Moyer and M J Kowalsky ldquoInfluence of tension strain onbuckling of reinforcement in concrete columnsrdquo ACI StructuralJournal vol 100 no 1 pp 75ndash85 2003

[55] K A T Vu andM G Stewart ldquoStructural reliability of concretebridges including improved chloride-induced corrosion mod-elsrdquo Structural Safety vol 22 no 4 pp 313ndash333 2000

[56] D V Val ldquoFactors affecting life-cycle cost analysis of RCstructures in chloride contaminated environmentsrdquo Journal ofInfrastructure Systems vol 13 no 2 pp 135ndash143 2007

[57] J P BroomfieldCorrosion of Steel in Concrete Taylor amp FrancisLondon UK 2nd edition 2007

[58] M M Kashani P Alagheband R Khan and S Davis ldquoImpactof corrosion on low-cycle fatigue degradation of reinforcingbars with the effect of inelastic bucklingrdquo International Journalof Fatigue vol 77 pp 174ndash185 2015

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 9

0 001 002 003 004 005 006 007 0080

50100150200250300350

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

Drift ratio

Late

ral f

orce

(kN

)

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

Drift ratio

Late

ral f

orce

(kN

)

(b)

Figure 9 Pushover analyses considering corrosion induced damage in reinforcing steel (a) Lehmanrsquos column 415 (b) Moyer and Kowalskyrsquoscolumn 1

concrete crushing up to 10 mass loss However as the cor-rosion level increases beyond 10mass loss the failure modechanges from vertical bar bucking and concrete crushing incompression to fracture of the vertical bars in tension

Figure 9(b) shows that Moyer and Kowalskyrsquos column1 has also failed in bar buckling and concrete crushing incompression However because 119871eff119889 = 4 the strength lossis not as significant as that of Lehmanrsquos column 415 with119871eff119889 = 10 under monotonic loading The corrosion levelup to 20 mass loss changes Moyer and Kowalskyrsquos column1 behaviour The failure initiates with bar buckling andconcrete crushing in compression and followed by fracture ofthe vertical reinforcement in tension With corrosion levelsgreater than 20 mass loss failure is by premature fractureof the vertical bars in tension At this point a cascade of barfracture can be seen in the graphs up to complete collapse ofthe columns

Figures 10(a) and 10(b) show Lehmanrsquos column 415 with10 and 20 mass losses under cyclic loading respectivelyComparing the monotonic and cyclic responses (the samecyclic load protocol as the experiment) shows that low-cyclefatigue has a significant impact on the column responseThe monotonic analysis showed that 10 mass loss did notresult in vertical bar fracture in tension and the failure wasgoverned by bar buckling and concrete crushing However incyclic analysis the failuremode is combined bar buckling andconcrete crushing in compression (failure initiation) followedby bar fracture in tension due to low-cycle fatigue

Here we have a system that does not technically fail incrushing and buckling but survives a little longer until thenext cycle when the vertical reinforcement fails in tensionIt was found that a mass loss ratio greater than 10 has asignificant impact on the nonlinear response of the corrodedcolumn due to reduced low-cycle fatigue life Figure 10(b)shows that at 20 mass loss resulted in bar fracture at 005drift ratio in pushover analysis but it resulted in bar fractureat 003 drift ratio under cyclic loading due to low-cycle fatiguefailure

Figures 10(c) and 10(d) show a similar result for Moyerand Kowalskyrsquos column 1 Overall Moyer and Kowalskyrsquoscolumn 1 has slightly less pinched cyclic responseThis is dueto the influence of the buckling length of the vertical bars andits cyclic degradation due to buckling [25]

62 Scenario (b) Column Nonlinear Behaviour When Corro-sion Is Assumed Present in Vertical and Horizontal Tie Rein-forcement and Cover Concrete Is Cracked In this scenarioit is assumed that the reinforcing steel (vertical and tie) iscorroded and the cover concrete is cracked due to corrosionof vertical reinforcementThe results of the pushover analysesare shown in Figure 11 The results in this case are almostidentical to the previous case (Section 61) where the damagein cover concrete was not considered Therefore in canbe concluded that whether or not we seek to model thecorrosion induced cracking of cover concrete it does not havea significant impact on the nonlinear response of corrodedcolumns Further discussion and comparison of this scenariowith other damage scenarios are available in Section 63

63 Scenario (c) Column Seismic Behaviour When Cor-rosion Is Assumed Present in Vertical and Horizontal TieReinforcement and Both Cover and Confined Concrete AreDamaged In this scenario it is assumed that the reinforc-ing steel (vertical and tie) is corroded cover concrete iscracked and the core confined concrete is affected by thecorrosion of horizontal tie reinforcement (as described inSection 53) Figure 12(a) shows the results of monotonicpushover analyses of Lehmanrsquos column 415 The results showthat the failure mechanism of this column for up to 10mass loss is bar buckling and core confined concrete crushingin compression However for corrosion levels beyond 10the failure mode changes This is a loss of drift capacitywhich starts with bar buckling and concrete crushing incompression and it is followed by bar fracture in tensionThese analyses demonstrate the importance of modelling the

10 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

Drift ratio

Late

ral f

orce

(kN

)

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

Drift ratio

Late

ral f

orce

(kN

)

(b)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

(c)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

(d)

Figure 10 Cyclic analyses considering corrosion induced damage in reinforcing steel (a) and (b) Lehmanrsquos column 415 (c) and (d) Moyerand Kowalskyrsquos column 1

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(b)

Figure 11 Pushover analyses considering corrosion induced damage in reinforcing steel and cracked cover concrete (a) Lehmanrsquos column415 (b) Moyer and Kowalskyrsquos column 1

Advances in Materials Science and Engineering 11

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(b)

Figure 12 Pushover analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a)Lehmanrsquos column 415 (b) Moyer and Kowalskyrsquos column 1

influence of corrosion on the confined concrete (throughloss of confining tie reinforcement) This corrosion damageon the confined concrete results in a rapid reduction instrength and ductility of the corroded columns compared tothe previous cases where confined concrete was considered tobe undamaged

Figure 12(b) shows the results of pushover analyses ofMoyer andKowalskyrsquos column 1 In this case the failuremodewas mainly bar buckling and concrete crushing followed byfracture of bars in tension for up to 20 mass loss Howevercorrosion levels beyond 20 mass loss have changed thefailure mode to premature fracture of bars in tension Thisdifference between the behaviour of the two columns is due tothe buckling behaviour of the vertical bars Given that Moyerand Kowalskyrsquos column 1 has much smaller buckling lengththe strength degradation in compression is much smallerthan Lehmanrsquos column 415 Therefore corrosion has more asignificant impact in terms of ductility loss of bars in tensionwhereas in Lehmanrsquos column 415 failure initiates with severebar buckling and concrete crushing then it is followed byfracture of vertical bars in tension

Figure 13 shows the results of cyclic analysis It showsthe cyclic analyses of Lehmanrsquos column 415 and Moyer andKowalskyrsquos column 1 with 10 and 20 mass loss togetherwith the corresponding pushover envelopes Figure 13 showsthat the extent of corrosion damage under cyclic loadingis more severe than monotonic loading The results ofmonotonic analysis showed that considering the ductility lossof corroded bars in tension and confinement reinforcementin compression has a big impact on bar buckling andfracture of reinforcement However cyclic analysis resultsshow that considering cyclic degradation due to low-cyclefatigue is crucial to have a realistic evaluation of the seismicperformance of existing corroded columns

For example in Figures 13(a) and 13(b) the failure ofLehmanrsquos column 415 was governed by bar buckling andconcrete crushing for a corrosion level up to 10 undermonotonic loadingHowever the same corrosion level results

in a much more severe drift capacity loss under cyclicloading due to a reduced low-cycle fatigue life Similarly inFigures 13(c) and 13(d) the failure of Moyer and Kowalskyrsquoscolumn was governed by concrete crushing in compressionfollowed by bar fracture in tension However low-cyclefatigue degradation due to cyclic loading results in prematurefracture of bars and subsequently severe loss of drift capacity

7 Comparison of the NonlinearResponses of Corroded Columns Computedin Different Scenarios

In order to clearly demonstrate the significance of corrosionmodels on the inelastic response of RC columns a com-parison between the computed responses of two columnswith different scenarios has been made The responses ofcolumns with 20 mass loss in monotonic pushover andcyclic analyses are compared and shown in Figure 14

Figure 14 shows the monotonic pushover and cyclicresponses of Lehmanrsquos column 415 andMoyer and Kowalskyrsquoscolumn 1 with 20 mass losses and different corrosiondamage models Figures 14(a) and 14(b) show that if thecorrosion induced damage to confined concrete is ignoredthe predicted failure mode is likely to be the fracture of barsin tension due to their reduced ductility However if thecorrosion induced damage to confined concrete is addedFigure 14(a) shows that the failure mode of Lehmanrsquos column415 will change to concrete crushing and buckling of thevertical bars in compression

Figure 14(b) shows that the failure mode of Moyer andKowalskyrsquos column 1 initiates with concrete crushing andbuckling of bars in compression and then it is followedby fracture of bars in tension This difference in failuremechanism is due to the differences in confinement level thebuckling length of the vertical bars the ratio of longitudinalreinforcement and the axial force ratio on the columnThere-fore in order to predict the nonlinear response accurately adetailed finite element model is required

12 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(d)

Figure 13 Cyclic analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a) and(b) Lehmanrsquos column 415 (c) and (d) Moyer and Kowalskyrsquos column 1

It is found that the failure mode under cyclic loading ismainly governed by the fracture of horizontal bars in tensiondue to reduced low-cycle fatigue life (Figures 14(c) and 14(d))This is a very important finding as it suggests that nonlinearquasistatic pushover analysis on its own is not adequate forperformance assessment of existing corroded bridge piers

With reference to Figure 14 it is evident that consideringthe impact of the corrosion damage on core confined con-crete and low-cycle fatigue degradation is crucial Thereforethey need to be considered when modelling the nonlinearbehaviour of corrosion damaged RC bridge piers underseismic loading This finding is in good agreement with theobserved experimental results by other researchers [12ndash1458]

A series of experimental studies were conducted in [12]on the cyclic behaviour of large-scale corroded cantilever RCbeams Ou et al found that as the level of corrosion increasesthe flexural failure initiates with premature buckling oflongitudinal bars This conclusion is in good agreement withthe numerical results discussed in this paper In another study[13] a series of experimental studies were conducted on cyclicbehaviour of corroded RC columns with varied axial forceMa et al have reported that once the corrosion level increases

beyond about 14 rapid strength and ductility reductionand cyclic degradation in hysteretic loops are seen due toreduced low-cycle fatigue life and premature buckling ofvertical reinforcement This conclusion is in good agreementwith the predicted failure modes using the numerical modelpresented in this paper

The detailed finite element model developed in thispaper can accurately model the nonlinear behaviour ofcorrodedRCcolumns subject to cyclic loading up to completecollapse There is a need to extend the PEER-UW columndatabase to include corroded RC columns so that furthercalibrationvalidation of the material model parameters canbe performed However the modelling technique developedin this paper is able to simulate the multiple failure modesof corroded RC columns simultaneously It represents thecurrent state of the art and as such they provide a novel com-putational framework for the seismic response prediction ofcorroded RC bridges

8 Conclusions

A series of pushover and cyclic analyses on two hypotheticalcorroded RC columns are conducted and these are used

Advances in Materials Science and Engineering 13

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(d)

Figure 14 Comparison of the computed responses of columns with different deterioration models (a) and (c) Lehmanrsquos column 415 undermonotonic and cyclic loading (b) and (d) Moyer and Kowalskyrsquos column 1 under monotonic and cyclic loading

to explore the performance of the proposed computationalframework The impact of corrosion on (i) the verticalreinforcing steel (ii) the tieconfinement (iii) the cover(unconfined) concrete and (iv) the core (confined) concreteis represented through new material models The proposednew steel material model accounts for (i) inelastic nonlinearbuckling of the vertical reinforcement (ii) the corrosion lossof area (iii) the nonuniform corrosion pitting and (iv) low-cycle high amplitude fatigueThenew cover concretematerialmodel includes the influence of internal pressure due tothe build-up of corrosion products (using compression fieldtheory) The new core concrete model includes the influenceof corrosion induced loss of confining reinforcement

The main outcomes of this study can be summarised asfollows

(1) Corrosion has a more significant impact on theductility loss (drift capacity) of RC columns than thestrength loss (plastic moment capacity)

(2) The numerical model developed in this paper is ableto predict the nonlinear flexural response of corrodedRC columns up to complete collapse Results showwhich depends on a cyclic load history that flexuralfailure can be initiated by the buckling of vertical bars

and crushing of core concrete which is then followedby fracture of bars in tension In cases where thebuckling of bars is not an issue or the buckling lengthis too short (119871eff119889

1015840le 5) the failure is governed by the

fracture of the vertical bars in tension due to low-cyclehigh amplitude fatigue

(3) The analyses results show that for the seismic perfor-mance and evaluation of existing corroded bridgesmonotonic pushover analysis is not sufficient Thecyclic degradation due to low-cycle high amplitudefatigue has a significant influence on the response ofcorroded RC columns

(4) The results of this study show that it is inadequate toassume that corrosion only affects the main verticalreinforcement in the column It was found that theconfined concrete with corroded confinement rein-forcement starts crushing much faster than uncor-roded undamaged concrete This changes the failuremode and results in premature buckling of the ver-tical reinforcement This change in the failure modecannot be predicted if the damage in core confinedconcrete due to corrosion of tie reinforcement isignored This is in good agreement with observed

14 Advances in Materials Science and Engineering

experimental results reported by other researchers[12ndash14]

(5) The modelling technique developed in this paper hassignificantly improved the earlier models and canbe used by other researchers in the future researchfor seismic vulnerability and fragility analysis ofcorroded RC bridges

Disclosure

Any findings opinions and recommendations provided inthis paper are only based on the authorsrsquo view

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This research is conducted in collaboration with the Univer-sity of Bristol and the University of Washington while thefirst author was on sabbatical leave in the US The fundingprovided by the World Wide University Network throughthe Research Mobility Program to the first author was muchappreciated The authors would like to thank Professor MarcO Eberhard and Professor John F Stanton for providingvaluable guidance during the course of this research

References

[1] S Hida F I S Ibrahim H A Capers et al ldquoAssuringbridge safety and serviceability in Europerdquo Tech Rep FHWA-PL-10-014 Office of International Programs Federal HighwayAdministration US Department of Transportation AmericanAssociation of State Highway and Transportation Officials2010

[2] ASCE Failure to Act The Economic Impact of Current Invest-ment Trends in Surface Transportation Infrastructure EconomicDevelopment Research Group Inc ASCE 2011

[3] D-E Choe P Gardoni D Rosowsky and T Haukaas ldquoProb-abilistic capacity models and seismic fragility estimates forRC columns subject to corrosionrdquo Reliability Engineering andSystem Safety vol 93 no 3 pp 383ndash393 2008

[4] L Berto R Vitaliani A Saetta and P Simioni ldquoSeismicassessment of existing RC structures affected by degradationphenomenardquo Structural Safety vol 31 no 4 pp 284ndash297 2009

[5] J Ghosh and J E Padgett ldquoAging considerations in the devel-opment of time-dependent seismic fragility curvesrdquo Journal ofStructural Engineering vol 136 no 12 pp 1497ndash1511 2010

[6] A Alipour B Shafei and M Shinozuka ldquoPerformance evalu-ation of deteriorating highway bridges located in high seismicareasrdquo Journal of Bridge Engineering vol 16 no 5 pp 597ndash6112011

[7] F Biondini E Camnasio and A Palermo ldquoLifetime seismicperformance of concrete bridges exposed to corrosionrdquo Struc-ture and Infrastructure Engineering vol 10 no 7 pp 880ndash9002014

[8] M Akiyama D M Frangopol and H Matsuzaki ldquoLife-cyclereliability of RC bridge piers under seismic and airborne chlo-ride hazardsrdquo Earthquake Engineering and Structural Dynamicsvol 40 no 15 pp 1671ndash1687 2011

[9] F Biondini A Palermo and G Toniolo ldquoSeismic performanceof concrete structures exposed to corrosion case studies of low-rise precast buildingsrdquo Structure and Infrastructure Engineeringvol 7 no 1-2 pp 109ndash119 2011

[10] C K Chiu F J Tu and F P Hsiao ldquoLifetime seismic perfor-mance assessment for chloride-corroded reinforced concretebuildingsrdquo Structure and Infrastructure Engineering vol 11 no3 pp 345ndash362 2015

[11] M Sanchez-Silva G-A Klutke and D V Rosowsky ldquoLife-cycleperformance of structures subject to multiple deteriorationmechanismsrdquo Structural Safety vol 33 no 3 pp 206ndash217 2011

[12] Y-C Ou L-L Tsai and H-H Chen ldquoCyclic performance oflarge-scale corroded reinforced concrete beamsrdquo EarthquakeEngineering and StructuralDynamics vol 41 no 4 pp 593ndash6042012

[13] Y Ma Y Che and J Gong ldquoBehavior of corrosion damagedcircular reinforced concrete columns under cyclic loadingrdquoConstruction and Building Materials vol 29 pp 548ndash556 2012

[14] A Meda S Mostosi Z Rinaldi and P Riva ldquoExperimentalevaluation of the corrosion influence on the cyclic behaviour ofRC columnsrdquo Engineering Structures vol 76 pp 112ndash123 2014

[15] A A Almusallam ldquoEffect of degree of corrosion on theproperties of reinforcing steel barsrdquo Construction and BuildingMaterials vol 15 no 8 pp 361ndash368 2001

[16] Y G Du L A Clark and A H C Chan ldquoResidual capacity ofcorroded reinforcing barsrdquoMagazine of Concrete Research vol57 no 3 pp 135ndash147 2005

[17] Y G Du L A Clarkt and A H C Chan ldquoEffect of corrosionon ductility of reinforcing barsrdquoMagazine of Concrete Researchvol 57 no 7 pp 407ndash419 2005

[18] J Cairns G A Plizzari Y Du D W Law and C FranzonildquoMechanical properties of corrosion-damaged reinforcementrdquoACI Materials Journal vol 102 no 4 pp 256ndash264 2005

[19] C A ApostolopoulosM P Papadopoulos and S G PantelakisldquoTensile behavior of corroded reinforcing steel bars BSt 500srdquoConstruction and Building Materials vol 20 no 9 pp 782ndash7892006

[20] C A Apostolopoulos ldquoMechanical behavior of corroded rein-forcing steel bars S500s tempcore under low cycle fatiguerdquoConstruction andBuildingMaterials vol 21 no 7 pp 1447ndash14562007

[21] M M Kashani A J Crewe and N A Alexander ldquoNonlinearstress-strain behaviour of corrosion-damaged reinforcing barsincluding inelastic bucklingrdquo Engineering Structures vol 48 pp417ndash429 2013

[22] M M Kashani A J Crewe and N A Alexander ldquoNonlinearcyclic response of corrosion-damaged reinforcing bars with theeffect of bucklingrdquo Construction and Building Materials vol 41pp 388ndash400 2013

[23] M M Kashani A J Crewe and N A Alexander ldquoUse of a 3Doptical measurement technique for stochastic corrosion patternanalysis of reinforcing bars subjected to accelerated corrosionrdquoCorrosion Science vol 73 pp 208ndash221 2013

[24] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoFinite element investigation of the influence of corrosionpattern on inelastic buckling and cyclic response of corrodedreinforcing barsrdquo Engineering Structures vol 75 pp 113ndash1252014

Advances in Materials Science and Engineering 15

[25] M M Kashani Seismic performance of corroded rc bridge piersdevelopment of a multi-mechanical nonlinear fibre beam-columnmodel [PhD thesis] University of Bristol Bristol UK 2014

[26] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part I Formula-tionrdquo Earthquake Engineering and Structural Dynamics vol 25no 7 pp 711ndash725 1996

[27] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part II Applica-tionsrdquoEarthquake Engineering and Structural Dynamics vol 25no 7 pp 727ndash742 1996

[28] The Open System for Earthquake Engineering Simulation(OpenSees) Pacific Earthquake Engineering Research CentreUniversity of California Berkeley Berkeley Calif USA 2011

[29] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoPhenomenological hysteretic model for corroded reinforcingbars including inelastic buckling and low-cycle fatigue degrada-tionrdquo Computers and Structures vol 156 article 5393 pp 58ndash712015

[30] J Coleman and E Spacone ldquoLocalization issues in force-basedframe elementsrdquo Journal of Structural Engineering vol 127 no11 pp 1257ndash1265 2001

[31] J S Pugh Numerical simulation of walls and seismic designrecommendations for walled buildings [PhD thesis] Universityof Washington Seattle Wash USA 2012

[32] D V Val and R E Melchers ldquoReliability of deteriorating RCslab bridgesrdquo Journal of Structural Engineering vol 123 no 12pp 1638ndash1644 1997

[33] M S Darmawan and M G Stewart ldquoEffect of pitting corro-sion on capacity of prestressing wiresrdquo Magazine of ConcreteResearch vol 59 no 2 pp 131ndash139 2007

[34] R P Dhakal and K Maekawa ldquoReinforcement stability andfracture of cover concrete in reinforced concrete membersrdquoJournal of Structural Engineering vol 128 no 10 pp 1253ndash12622002

[35] C Lee J F Bonacci M D A Thomas et al ldquoAcceleratedcorrosion and repair of reinforced concrete columns usingcarbon fibre reinforced polymer sheetsrdquo Canadian Journal ofCivil Engineering vol 27 no 5 pp 941ndash948 2000

[36] W Aquino Long-term performance of seismically rehabilitatedcorrosion-damaged columns [PhD thesis] University of Illinoisat Urbana-Champaign Champaign Ill USA 2002

[37] S Timoshenko and J Gere Theory of Elastic StabilityMacGraw-Hill New York NY USA 1963

[38] S J Pantazopoulou ldquoDetailing for reinforcement stability in RCmembersrdquo Journal of Structural Engineering vol 124 no 6 pp623ndash632 1998

[39] J B Mander M J N Priestley and R Park ldquoObserved stress-strain behavior of confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1827ndash1849 1988

[40] J B Mander M J Priestley and R Park ldquoTheoretical stress-strain model for confined concreterdquo Journal of Structural Engi-neering (United States) vol 114 no 8 pp 1804ndash1826 1988

[41] S Popovics ldquoAnumerical approach to the complete stress-straincurve of concreterdquo Cement and Concrete Research vol 3 no 5pp 583ndash599 1973

[42] I D Karsan and J O Jirsa ldquoBehavior of concrete undercompressive loadingrdquo Journal of Structural Division vol 95article ST12 1969

[43] M P Berry andMO Eberhard ldquoPerformancemodeling strate-gies for modern reinforced concrete bridge columnsrdquo PEER

Research Report University of California Berkeley BerkeleyCalif USA 2006

[44] B D Scott R Park and M J N Priestley ldquoStress-strainbehavior of concrete confined by overlapping hoops at low andhigh strain ratesrdquo Journal of the American Concrete Institute vol79 no 1 pp 13ndash27 1982

[45] A S Al-Harthy M G Stewart and J Mullard ldquoConcrete covercracking caused by steel reinforcement corrosionrdquoMagazine ofConcrete Research vol 63 no 9 pp 655ndash667 2011

[46] T Vidal A Castel and R Francois ldquoAnalyzing crack width topredict corrosion in reinforced concreterdquo Cement and ConcreteResearch vol 34 no 1 pp 165ndash174 2004

[47] F J Molina C Alonso and C Andrade ldquoCover cracking as afunction of rebar corrosion part 2-numerical modelrdquoMaterialsand Structures vol 26 no 9 pp 532ndash548 1993

[48] F J Vecchio and M P Collins ldquoThe modified compression-field theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[49] D Coronelli and P Gambarova ldquoStructural assessment ofcorroded reinforced concrete beams modeling guidelinesrdquoJournal of Structural Engineering vol 130 no 8 pp 1214ndash12242004

[50] D E Lehman and J P Moehle ldquoSeismic performance of well-confined concrete columnsrdquo PEER Research Report Universityof California at Berkeley 2000

[51] L N Lowes and A Altoontash ldquoModeling reinforced-concretebeam-column joints subjected to cyclic loadingrdquo Journal ofStructural Engineering vol 129 no 12 pp 1686ndash1697 2003

[52] M Berry M Parrish and M Eberhard ldquoPerformance databaseUserrsquos manualrdquo in Pacific Earthquake Engineering ResearchCentre 2004 University of California at Berkeley 2004httpwwwcewashingtonedusimpeera1

[53] A N Kallias and M Imran Rafiq ldquoFinite element investigationof the structural response of corroded RC beamsrdquo EngineeringStructures vol 32 no 9 pp 2984ndash2994 2010

[54] M J Moyer and M J Kowalsky ldquoInfluence of tension strain onbuckling of reinforcement in concrete columnsrdquo ACI StructuralJournal vol 100 no 1 pp 75ndash85 2003

[55] K A T Vu andM G Stewart ldquoStructural reliability of concretebridges including improved chloride-induced corrosion mod-elsrdquo Structural Safety vol 22 no 4 pp 313ndash333 2000

[56] D V Val ldquoFactors affecting life-cycle cost analysis of RCstructures in chloride contaminated environmentsrdquo Journal ofInfrastructure Systems vol 13 no 2 pp 135ndash143 2007

[57] J P BroomfieldCorrosion of Steel in Concrete Taylor amp FrancisLondon UK 2nd edition 2007

[58] M M Kashani P Alagheband R Khan and S Davis ldquoImpactof corrosion on low-cycle fatigue degradation of reinforcingbars with the effect of inelastic bucklingrdquo International Journalof Fatigue vol 77 pp 174ndash185 2015

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

10 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

Drift ratio

Late

ral f

orce

(kN

)

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

Drift ratio

Late

ral f

orce

(kN

)

(b)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

(c)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

(d)

Figure 10 Cyclic analyses considering corrosion induced damage in reinforcing steel (a) and (b) Lehmanrsquos column 415 (c) and (d) Moyerand Kowalskyrsquos column 1

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(b)

Figure 11 Pushover analyses considering corrosion induced damage in reinforcing steel and cracked cover concrete (a) Lehmanrsquos column415 (b) Moyer and Kowalskyrsquos column 1

Advances in Materials Science and Engineering 11

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(b)

Figure 12 Pushover analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a)Lehmanrsquos column 415 (b) Moyer and Kowalskyrsquos column 1

influence of corrosion on the confined concrete (throughloss of confining tie reinforcement) This corrosion damageon the confined concrete results in a rapid reduction instrength and ductility of the corroded columns compared tothe previous cases where confined concrete was considered tobe undamaged

Figure 12(b) shows the results of pushover analyses ofMoyer andKowalskyrsquos column 1 In this case the failuremodewas mainly bar buckling and concrete crushing followed byfracture of bars in tension for up to 20 mass loss Howevercorrosion levels beyond 20 mass loss have changed thefailure mode to premature fracture of bars in tension Thisdifference between the behaviour of the two columns is due tothe buckling behaviour of the vertical bars Given that Moyerand Kowalskyrsquos column 1 has much smaller buckling lengththe strength degradation in compression is much smallerthan Lehmanrsquos column 415 Therefore corrosion has more asignificant impact in terms of ductility loss of bars in tensionwhereas in Lehmanrsquos column 415 failure initiates with severebar buckling and concrete crushing then it is followed byfracture of vertical bars in tension

Figure 13 shows the results of cyclic analysis It showsthe cyclic analyses of Lehmanrsquos column 415 and Moyer andKowalskyrsquos column 1 with 10 and 20 mass loss togetherwith the corresponding pushover envelopes Figure 13 showsthat the extent of corrosion damage under cyclic loadingis more severe than monotonic loading The results ofmonotonic analysis showed that considering the ductility lossof corroded bars in tension and confinement reinforcementin compression has a big impact on bar buckling andfracture of reinforcement However cyclic analysis resultsshow that considering cyclic degradation due to low-cyclefatigue is crucial to have a realistic evaluation of the seismicperformance of existing corroded columns

For example in Figures 13(a) and 13(b) the failure ofLehmanrsquos column 415 was governed by bar buckling andconcrete crushing for a corrosion level up to 10 undermonotonic loadingHowever the same corrosion level results

in a much more severe drift capacity loss under cyclicloading due to a reduced low-cycle fatigue life Similarly inFigures 13(c) and 13(d) the failure of Moyer and Kowalskyrsquoscolumn was governed by concrete crushing in compressionfollowed by bar fracture in tension However low-cyclefatigue degradation due to cyclic loading results in prematurefracture of bars and subsequently severe loss of drift capacity

7 Comparison of the NonlinearResponses of Corroded Columns Computedin Different Scenarios

In order to clearly demonstrate the significance of corrosionmodels on the inelastic response of RC columns a com-parison between the computed responses of two columnswith different scenarios has been made The responses ofcolumns with 20 mass loss in monotonic pushover andcyclic analyses are compared and shown in Figure 14

Figure 14 shows the monotonic pushover and cyclicresponses of Lehmanrsquos column 415 andMoyer and Kowalskyrsquoscolumn 1 with 20 mass losses and different corrosiondamage models Figures 14(a) and 14(b) show that if thecorrosion induced damage to confined concrete is ignoredthe predicted failure mode is likely to be the fracture of barsin tension due to their reduced ductility However if thecorrosion induced damage to confined concrete is addedFigure 14(a) shows that the failure mode of Lehmanrsquos column415 will change to concrete crushing and buckling of thevertical bars in compression

Figure 14(b) shows that the failure mode of Moyer andKowalskyrsquos column 1 initiates with concrete crushing andbuckling of bars in compression and then it is followedby fracture of bars in tension This difference in failuremechanism is due to the differences in confinement level thebuckling length of the vertical bars the ratio of longitudinalreinforcement and the axial force ratio on the columnThere-fore in order to predict the nonlinear response accurately adetailed finite element model is required

12 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(d)

Figure 13 Cyclic analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a) and(b) Lehmanrsquos column 415 (c) and (d) Moyer and Kowalskyrsquos column 1

It is found that the failure mode under cyclic loading ismainly governed by the fracture of horizontal bars in tensiondue to reduced low-cycle fatigue life (Figures 14(c) and 14(d))This is a very important finding as it suggests that nonlinearquasistatic pushover analysis on its own is not adequate forperformance assessment of existing corroded bridge piers

With reference to Figure 14 it is evident that consideringthe impact of the corrosion damage on core confined con-crete and low-cycle fatigue degradation is crucial Thereforethey need to be considered when modelling the nonlinearbehaviour of corrosion damaged RC bridge piers underseismic loading This finding is in good agreement with theobserved experimental results by other researchers [12ndash1458]

A series of experimental studies were conducted in [12]on the cyclic behaviour of large-scale corroded cantilever RCbeams Ou et al found that as the level of corrosion increasesthe flexural failure initiates with premature buckling oflongitudinal bars This conclusion is in good agreement withthe numerical results discussed in this paper In another study[13] a series of experimental studies were conducted on cyclicbehaviour of corroded RC columns with varied axial forceMa et al have reported that once the corrosion level increases

beyond about 14 rapid strength and ductility reductionand cyclic degradation in hysteretic loops are seen due toreduced low-cycle fatigue life and premature buckling ofvertical reinforcement This conclusion is in good agreementwith the predicted failure modes using the numerical modelpresented in this paper

The detailed finite element model developed in thispaper can accurately model the nonlinear behaviour ofcorrodedRCcolumns subject to cyclic loading up to completecollapse There is a need to extend the PEER-UW columndatabase to include corroded RC columns so that furthercalibrationvalidation of the material model parameters canbe performed However the modelling technique developedin this paper is able to simulate the multiple failure modesof corroded RC columns simultaneously It represents thecurrent state of the art and as such they provide a novel com-putational framework for the seismic response prediction ofcorroded RC bridges

8 Conclusions

A series of pushover and cyclic analyses on two hypotheticalcorroded RC columns are conducted and these are used

Advances in Materials Science and Engineering 13

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(d)

Figure 14 Comparison of the computed responses of columns with different deterioration models (a) and (c) Lehmanrsquos column 415 undermonotonic and cyclic loading (b) and (d) Moyer and Kowalskyrsquos column 1 under monotonic and cyclic loading

to explore the performance of the proposed computationalframework The impact of corrosion on (i) the verticalreinforcing steel (ii) the tieconfinement (iii) the cover(unconfined) concrete and (iv) the core (confined) concreteis represented through new material models The proposednew steel material model accounts for (i) inelastic nonlinearbuckling of the vertical reinforcement (ii) the corrosion lossof area (iii) the nonuniform corrosion pitting and (iv) low-cycle high amplitude fatigueThenew cover concretematerialmodel includes the influence of internal pressure due tothe build-up of corrosion products (using compression fieldtheory) The new core concrete model includes the influenceof corrosion induced loss of confining reinforcement

The main outcomes of this study can be summarised asfollows

(1) Corrosion has a more significant impact on theductility loss (drift capacity) of RC columns than thestrength loss (plastic moment capacity)

(2) The numerical model developed in this paper is ableto predict the nonlinear flexural response of corrodedRC columns up to complete collapse Results showwhich depends on a cyclic load history that flexuralfailure can be initiated by the buckling of vertical bars

and crushing of core concrete which is then followedby fracture of bars in tension In cases where thebuckling of bars is not an issue or the buckling lengthis too short (119871eff119889

1015840le 5) the failure is governed by the

fracture of the vertical bars in tension due to low-cyclehigh amplitude fatigue

(3) The analyses results show that for the seismic perfor-mance and evaluation of existing corroded bridgesmonotonic pushover analysis is not sufficient Thecyclic degradation due to low-cycle high amplitudefatigue has a significant influence on the response ofcorroded RC columns

(4) The results of this study show that it is inadequate toassume that corrosion only affects the main verticalreinforcement in the column It was found that theconfined concrete with corroded confinement rein-forcement starts crushing much faster than uncor-roded undamaged concrete This changes the failuremode and results in premature buckling of the ver-tical reinforcement This change in the failure modecannot be predicted if the damage in core confinedconcrete due to corrosion of tie reinforcement isignored This is in good agreement with observed

14 Advances in Materials Science and Engineering

experimental results reported by other researchers[12ndash14]

(5) The modelling technique developed in this paper hassignificantly improved the earlier models and canbe used by other researchers in the future researchfor seismic vulnerability and fragility analysis ofcorroded RC bridges

Disclosure

Any findings opinions and recommendations provided inthis paper are only based on the authorsrsquo view

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This research is conducted in collaboration with the Univer-sity of Bristol and the University of Washington while thefirst author was on sabbatical leave in the US The fundingprovided by the World Wide University Network throughthe Research Mobility Program to the first author was muchappreciated The authors would like to thank Professor MarcO Eberhard and Professor John F Stanton for providingvaluable guidance during the course of this research

References

[1] S Hida F I S Ibrahim H A Capers et al ldquoAssuringbridge safety and serviceability in Europerdquo Tech Rep FHWA-PL-10-014 Office of International Programs Federal HighwayAdministration US Department of Transportation AmericanAssociation of State Highway and Transportation Officials2010

[2] ASCE Failure to Act The Economic Impact of Current Invest-ment Trends in Surface Transportation Infrastructure EconomicDevelopment Research Group Inc ASCE 2011

[3] D-E Choe P Gardoni D Rosowsky and T Haukaas ldquoProb-abilistic capacity models and seismic fragility estimates forRC columns subject to corrosionrdquo Reliability Engineering andSystem Safety vol 93 no 3 pp 383ndash393 2008

[4] L Berto R Vitaliani A Saetta and P Simioni ldquoSeismicassessment of existing RC structures affected by degradationphenomenardquo Structural Safety vol 31 no 4 pp 284ndash297 2009

[5] J Ghosh and J E Padgett ldquoAging considerations in the devel-opment of time-dependent seismic fragility curvesrdquo Journal ofStructural Engineering vol 136 no 12 pp 1497ndash1511 2010

[6] A Alipour B Shafei and M Shinozuka ldquoPerformance evalu-ation of deteriorating highway bridges located in high seismicareasrdquo Journal of Bridge Engineering vol 16 no 5 pp 597ndash6112011

[7] F Biondini E Camnasio and A Palermo ldquoLifetime seismicperformance of concrete bridges exposed to corrosionrdquo Struc-ture and Infrastructure Engineering vol 10 no 7 pp 880ndash9002014

[8] M Akiyama D M Frangopol and H Matsuzaki ldquoLife-cyclereliability of RC bridge piers under seismic and airborne chlo-ride hazardsrdquo Earthquake Engineering and Structural Dynamicsvol 40 no 15 pp 1671ndash1687 2011

[9] F Biondini A Palermo and G Toniolo ldquoSeismic performanceof concrete structures exposed to corrosion case studies of low-rise precast buildingsrdquo Structure and Infrastructure Engineeringvol 7 no 1-2 pp 109ndash119 2011

[10] C K Chiu F J Tu and F P Hsiao ldquoLifetime seismic perfor-mance assessment for chloride-corroded reinforced concretebuildingsrdquo Structure and Infrastructure Engineering vol 11 no3 pp 345ndash362 2015

[11] M Sanchez-Silva G-A Klutke and D V Rosowsky ldquoLife-cycleperformance of structures subject to multiple deteriorationmechanismsrdquo Structural Safety vol 33 no 3 pp 206ndash217 2011

[12] Y-C Ou L-L Tsai and H-H Chen ldquoCyclic performance oflarge-scale corroded reinforced concrete beamsrdquo EarthquakeEngineering and StructuralDynamics vol 41 no 4 pp 593ndash6042012

[13] Y Ma Y Che and J Gong ldquoBehavior of corrosion damagedcircular reinforced concrete columns under cyclic loadingrdquoConstruction and Building Materials vol 29 pp 548ndash556 2012

[14] A Meda S Mostosi Z Rinaldi and P Riva ldquoExperimentalevaluation of the corrosion influence on the cyclic behaviour ofRC columnsrdquo Engineering Structures vol 76 pp 112ndash123 2014

[15] A A Almusallam ldquoEffect of degree of corrosion on theproperties of reinforcing steel barsrdquo Construction and BuildingMaterials vol 15 no 8 pp 361ndash368 2001

[16] Y G Du L A Clark and A H C Chan ldquoResidual capacity ofcorroded reinforcing barsrdquoMagazine of Concrete Research vol57 no 3 pp 135ndash147 2005

[17] Y G Du L A Clarkt and A H C Chan ldquoEffect of corrosionon ductility of reinforcing barsrdquoMagazine of Concrete Researchvol 57 no 7 pp 407ndash419 2005

[18] J Cairns G A Plizzari Y Du D W Law and C FranzonildquoMechanical properties of corrosion-damaged reinforcementrdquoACI Materials Journal vol 102 no 4 pp 256ndash264 2005

[19] C A ApostolopoulosM P Papadopoulos and S G PantelakisldquoTensile behavior of corroded reinforcing steel bars BSt 500srdquoConstruction and Building Materials vol 20 no 9 pp 782ndash7892006

[20] C A Apostolopoulos ldquoMechanical behavior of corroded rein-forcing steel bars S500s tempcore under low cycle fatiguerdquoConstruction andBuildingMaterials vol 21 no 7 pp 1447ndash14562007

[21] M M Kashani A J Crewe and N A Alexander ldquoNonlinearstress-strain behaviour of corrosion-damaged reinforcing barsincluding inelastic bucklingrdquo Engineering Structures vol 48 pp417ndash429 2013

[22] M M Kashani A J Crewe and N A Alexander ldquoNonlinearcyclic response of corrosion-damaged reinforcing bars with theeffect of bucklingrdquo Construction and Building Materials vol 41pp 388ndash400 2013

[23] M M Kashani A J Crewe and N A Alexander ldquoUse of a 3Doptical measurement technique for stochastic corrosion patternanalysis of reinforcing bars subjected to accelerated corrosionrdquoCorrosion Science vol 73 pp 208ndash221 2013

[24] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoFinite element investigation of the influence of corrosionpattern on inelastic buckling and cyclic response of corrodedreinforcing barsrdquo Engineering Structures vol 75 pp 113ndash1252014

Advances in Materials Science and Engineering 15

[25] M M Kashani Seismic performance of corroded rc bridge piersdevelopment of a multi-mechanical nonlinear fibre beam-columnmodel [PhD thesis] University of Bristol Bristol UK 2014

[26] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part I Formula-tionrdquo Earthquake Engineering and Structural Dynamics vol 25no 7 pp 711ndash725 1996

[27] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part II Applica-tionsrdquoEarthquake Engineering and Structural Dynamics vol 25no 7 pp 727ndash742 1996

[28] The Open System for Earthquake Engineering Simulation(OpenSees) Pacific Earthquake Engineering Research CentreUniversity of California Berkeley Berkeley Calif USA 2011

[29] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoPhenomenological hysteretic model for corroded reinforcingbars including inelastic buckling and low-cycle fatigue degrada-tionrdquo Computers and Structures vol 156 article 5393 pp 58ndash712015

[30] J Coleman and E Spacone ldquoLocalization issues in force-basedframe elementsrdquo Journal of Structural Engineering vol 127 no11 pp 1257ndash1265 2001

[31] J S Pugh Numerical simulation of walls and seismic designrecommendations for walled buildings [PhD thesis] Universityof Washington Seattle Wash USA 2012

[32] D V Val and R E Melchers ldquoReliability of deteriorating RCslab bridgesrdquo Journal of Structural Engineering vol 123 no 12pp 1638ndash1644 1997

[33] M S Darmawan and M G Stewart ldquoEffect of pitting corro-sion on capacity of prestressing wiresrdquo Magazine of ConcreteResearch vol 59 no 2 pp 131ndash139 2007

[34] R P Dhakal and K Maekawa ldquoReinforcement stability andfracture of cover concrete in reinforced concrete membersrdquoJournal of Structural Engineering vol 128 no 10 pp 1253ndash12622002

[35] C Lee J F Bonacci M D A Thomas et al ldquoAcceleratedcorrosion and repair of reinforced concrete columns usingcarbon fibre reinforced polymer sheetsrdquo Canadian Journal ofCivil Engineering vol 27 no 5 pp 941ndash948 2000

[36] W Aquino Long-term performance of seismically rehabilitatedcorrosion-damaged columns [PhD thesis] University of Illinoisat Urbana-Champaign Champaign Ill USA 2002

[37] S Timoshenko and J Gere Theory of Elastic StabilityMacGraw-Hill New York NY USA 1963

[38] S J Pantazopoulou ldquoDetailing for reinforcement stability in RCmembersrdquo Journal of Structural Engineering vol 124 no 6 pp623ndash632 1998

[39] J B Mander M J N Priestley and R Park ldquoObserved stress-strain behavior of confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1827ndash1849 1988

[40] J B Mander M J Priestley and R Park ldquoTheoretical stress-strain model for confined concreterdquo Journal of Structural Engi-neering (United States) vol 114 no 8 pp 1804ndash1826 1988

[41] S Popovics ldquoAnumerical approach to the complete stress-straincurve of concreterdquo Cement and Concrete Research vol 3 no 5pp 583ndash599 1973

[42] I D Karsan and J O Jirsa ldquoBehavior of concrete undercompressive loadingrdquo Journal of Structural Division vol 95article ST12 1969

[43] M P Berry andMO Eberhard ldquoPerformancemodeling strate-gies for modern reinforced concrete bridge columnsrdquo PEER

Research Report University of California Berkeley BerkeleyCalif USA 2006

[44] B D Scott R Park and M J N Priestley ldquoStress-strainbehavior of concrete confined by overlapping hoops at low andhigh strain ratesrdquo Journal of the American Concrete Institute vol79 no 1 pp 13ndash27 1982

[45] A S Al-Harthy M G Stewart and J Mullard ldquoConcrete covercracking caused by steel reinforcement corrosionrdquoMagazine ofConcrete Research vol 63 no 9 pp 655ndash667 2011

[46] T Vidal A Castel and R Francois ldquoAnalyzing crack width topredict corrosion in reinforced concreterdquo Cement and ConcreteResearch vol 34 no 1 pp 165ndash174 2004

[47] F J Molina C Alonso and C Andrade ldquoCover cracking as afunction of rebar corrosion part 2-numerical modelrdquoMaterialsand Structures vol 26 no 9 pp 532ndash548 1993

[48] F J Vecchio and M P Collins ldquoThe modified compression-field theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[49] D Coronelli and P Gambarova ldquoStructural assessment ofcorroded reinforced concrete beams modeling guidelinesrdquoJournal of Structural Engineering vol 130 no 8 pp 1214ndash12242004

[50] D E Lehman and J P Moehle ldquoSeismic performance of well-confined concrete columnsrdquo PEER Research Report Universityof California at Berkeley 2000

[51] L N Lowes and A Altoontash ldquoModeling reinforced-concretebeam-column joints subjected to cyclic loadingrdquo Journal ofStructural Engineering vol 129 no 12 pp 1686ndash1697 2003

[52] M Berry M Parrish and M Eberhard ldquoPerformance databaseUserrsquos manualrdquo in Pacific Earthquake Engineering ResearchCentre 2004 University of California at Berkeley 2004httpwwwcewashingtonedusimpeera1

[53] A N Kallias and M Imran Rafiq ldquoFinite element investigationof the structural response of corroded RC beamsrdquo EngineeringStructures vol 32 no 9 pp 2984ndash2994 2010

[54] M J Moyer and M J Kowalsky ldquoInfluence of tension strain onbuckling of reinforcement in concrete columnsrdquo ACI StructuralJournal vol 100 no 1 pp 75ndash85 2003

[55] K A T Vu andM G Stewart ldquoStructural reliability of concretebridges including improved chloride-induced corrosion mod-elsrdquo Structural Safety vol 22 no 4 pp 313ndash333 2000

[56] D V Val ldquoFactors affecting life-cycle cost analysis of RCstructures in chloride contaminated environmentsrdquo Journal ofInfrastructure Systems vol 13 no 2 pp 135ndash143 2007

[57] J P BroomfieldCorrosion of Steel in Concrete Taylor amp FrancisLondon UK 2nd edition 2007

[58] M M Kashani P Alagheband R Khan and S Davis ldquoImpactof corrosion on low-cycle fatigue degradation of reinforcingbars with the effect of inelastic bucklingrdquo International Journalof Fatigue vol 77 pp 174ndash185 2015

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 11

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Control10 mass loss20 mass loss30 mass loss

40 mass loss

Bar fracture in tensionBar buckling and concrete crushing

(b)

Figure 12 Pushover analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a)Lehmanrsquos column 415 (b) Moyer and Kowalskyrsquos column 1

influence of corrosion on the confined concrete (throughloss of confining tie reinforcement) This corrosion damageon the confined concrete results in a rapid reduction instrength and ductility of the corroded columns compared tothe previous cases where confined concrete was considered tobe undamaged

Figure 12(b) shows the results of pushover analyses ofMoyer andKowalskyrsquos column 1 In this case the failuremodewas mainly bar buckling and concrete crushing followed byfracture of bars in tension for up to 20 mass loss Howevercorrosion levels beyond 20 mass loss have changed thefailure mode to premature fracture of bars in tension Thisdifference between the behaviour of the two columns is due tothe buckling behaviour of the vertical bars Given that Moyerand Kowalskyrsquos column 1 has much smaller buckling lengththe strength degradation in compression is much smallerthan Lehmanrsquos column 415 Therefore corrosion has more asignificant impact in terms of ductility loss of bars in tensionwhereas in Lehmanrsquos column 415 failure initiates with severebar buckling and concrete crushing then it is followed byfracture of vertical bars in tension

Figure 13 shows the results of cyclic analysis It showsthe cyclic analyses of Lehmanrsquos column 415 and Moyer andKowalskyrsquos column 1 with 10 and 20 mass loss togetherwith the corresponding pushover envelopes Figure 13 showsthat the extent of corrosion damage under cyclic loadingis more severe than monotonic loading The results ofmonotonic analysis showed that considering the ductility lossof corroded bars in tension and confinement reinforcementin compression has a big impact on bar buckling andfracture of reinforcement However cyclic analysis resultsshow that considering cyclic degradation due to low-cyclefatigue is crucial to have a realistic evaluation of the seismicperformance of existing corroded columns

For example in Figures 13(a) and 13(b) the failure ofLehmanrsquos column 415 was governed by bar buckling andconcrete crushing for a corrosion level up to 10 undermonotonic loadingHowever the same corrosion level results

in a much more severe drift capacity loss under cyclicloading due to a reduced low-cycle fatigue life Similarly inFigures 13(c) and 13(d) the failure of Moyer and Kowalskyrsquoscolumn was governed by concrete crushing in compressionfollowed by bar fracture in tension However low-cyclefatigue degradation due to cyclic loading results in prematurefracture of bars and subsequently severe loss of drift capacity

7 Comparison of the NonlinearResponses of Corroded Columns Computedin Different Scenarios

In order to clearly demonstrate the significance of corrosionmodels on the inelastic response of RC columns a com-parison between the computed responses of two columnswith different scenarios has been made The responses ofcolumns with 20 mass loss in monotonic pushover andcyclic analyses are compared and shown in Figure 14

Figure 14 shows the monotonic pushover and cyclicresponses of Lehmanrsquos column 415 andMoyer and Kowalskyrsquoscolumn 1 with 20 mass losses and different corrosiondamage models Figures 14(a) and 14(b) show that if thecorrosion induced damage to confined concrete is ignoredthe predicted failure mode is likely to be the fracture of barsin tension due to their reduced ductility However if thecorrosion induced damage to confined concrete is addedFigure 14(a) shows that the failure mode of Lehmanrsquos column415 will change to concrete crushing and buckling of thevertical bars in compression

Figure 14(b) shows that the failure mode of Moyer andKowalskyrsquos column 1 initiates with concrete crushing andbuckling of bars in compression and then it is followedby fracture of bars in tension This difference in failuremechanism is due to the differences in confinement level thebuckling length of the vertical bars the ratio of longitudinalreinforcement and the axial force ratio on the columnThere-fore in order to predict the nonlinear response accurately adetailed finite element model is required

12 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(d)

Figure 13 Cyclic analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a) and(b) Lehmanrsquos column 415 (c) and (d) Moyer and Kowalskyrsquos column 1

It is found that the failure mode under cyclic loading ismainly governed by the fracture of horizontal bars in tensiondue to reduced low-cycle fatigue life (Figures 14(c) and 14(d))This is a very important finding as it suggests that nonlinearquasistatic pushover analysis on its own is not adequate forperformance assessment of existing corroded bridge piers

With reference to Figure 14 it is evident that consideringthe impact of the corrosion damage on core confined con-crete and low-cycle fatigue degradation is crucial Thereforethey need to be considered when modelling the nonlinearbehaviour of corrosion damaged RC bridge piers underseismic loading This finding is in good agreement with theobserved experimental results by other researchers [12ndash1458]

A series of experimental studies were conducted in [12]on the cyclic behaviour of large-scale corroded cantilever RCbeams Ou et al found that as the level of corrosion increasesthe flexural failure initiates with premature buckling oflongitudinal bars This conclusion is in good agreement withthe numerical results discussed in this paper In another study[13] a series of experimental studies were conducted on cyclicbehaviour of corroded RC columns with varied axial forceMa et al have reported that once the corrosion level increases

beyond about 14 rapid strength and ductility reductionand cyclic degradation in hysteretic loops are seen due toreduced low-cycle fatigue life and premature buckling ofvertical reinforcement This conclusion is in good agreementwith the predicted failure modes using the numerical modelpresented in this paper

The detailed finite element model developed in thispaper can accurately model the nonlinear behaviour ofcorrodedRCcolumns subject to cyclic loading up to completecollapse There is a need to extend the PEER-UW columndatabase to include corroded RC columns so that furthercalibrationvalidation of the material model parameters canbe performed However the modelling technique developedin this paper is able to simulate the multiple failure modesof corroded RC columns simultaneously It represents thecurrent state of the art and as such they provide a novel com-putational framework for the seismic response prediction ofcorroded RC bridges

8 Conclusions

A series of pushover and cyclic analyses on two hypotheticalcorroded RC columns are conducted and these are used

Advances in Materials Science and Engineering 13

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(d)

Figure 14 Comparison of the computed responses of columns with different deterioration models (a) and (c) Lehmanrsquos column 415 undermonotonic and cyclic loading (b) and (d) Moyer and Kowalskyrsquos column 1 under monotonic and cyclic loading

to explore the performance of the proposed computationalframework The impact of corrosion on (i) the verticalreinforcing steel (ii) the tieconfinement (iii) the cover(unconfined) concrete and (iv) the core (confined) concreteis represented through new material models The proposednew steel material model accounts for (i) inelastic nonlinearbuckling of the vertical reinforcement (ii) the corrosion lossof area (iii) the nonuniform corrosion pitting and (iv) low-cycle high amplitude fatigueThenew cover concretematerialmodel includes the influence of internal pressure due tothe build-up of corrosion products (using compression fieldtheory) The new core concrete model includes the influenceof corrosion induced loss of confining reinforcement

The main outcomes of this study can be summarised asfollows

(1) Corrosion has a more significant impact on theductility loss (drift capacity) of RC columns than thestrength loss (plastic moment capacity)

(2) The numerical model developed in this paper is ableto predict the nonlinear flexural response of corrodedRC columns up to complete collapse Results showwhich depends on a cyclic load history that flexuralfailure can be initiated by the buckling of vertical bars

and crushing of core concrete which is then followedby fracture of bars in tension In cases where thebuckling of bars is not an issue or the buckling lengthis too short (119871eff119889

1015840le 5) the failure is governed by the

fracture of the vertical bars in tension due to low-cyclehigh amplitude fatigue

(3) The analyses results show that for the seismic perfor-mance and evaluation of existing corroded bridgesmonotonic pushover analysis is not sufficient Thecyclic degradation due to low-cycle high amplitudefatigue has a significant influence on the response ofcorroded RC columns

(4) The results of this study show that it is inadequate toassume that corrosion only affects the main verticalreinforcement in the column It was found that theconfined concrete with corroded confinement rein-forcement starts crushing much faster than uncor-roded undamaged concrete This changes the failuremode and results in premature buckling of the ver-tical reinforcement This change in the failure modecannot be predicted if the damage in core confinedconcrete due to corrosion of tie reinforcement isignored This is in good agreement with observed

14 Advances in Materials Science and Engineering

experimental results reported by other researchers[12ndash14]

(5) The modelling technique developed in this paper hassignificantly improved the earlier models and canbe used by other researchers in the future researchfor seismic vulnerability and fragility analysis ofcorroded RC bridges

Disclosure

Any findings opinions and recommendations provided inthis paper are only based on the authorsrsquo view

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This research is conducted in collaboration with the Univer-sity of Bristol and the University of Washington while thefirst author was on sabbatical leave in the US The fundingprovided by the World Wide University Network throughthe Research Mobility Program to the first author was muchappreciated The authors would like to thank Professor MarcO Eberhard and Professor John F Stanton for providingvaluable guidance during the course of this research

References

[1] S Hida F I S Ibrahim H A Capers et al ldquoAssuringbridge safety and serviceability in Europerdquo Tech Rep FHWA-PL-10-014 Office of International Programs Federal HighwayAdministration US Department of Transportation AmericanAssociation of State Highway and Transportation Officials2010

[2] ASCE Failure to Act The Economic Impact of Current Invest-ment Trends in Surface Transportation Infrastructure EconomicDevelopment Research Group Inc ASCE 2011

[3] D-E Choe P Gardoni D Rosowsky and T Haukaas ldquoProb-abilistic capacity models and seismic fragility estimates forRC columns subject to corrosionrdquo Reliability Engineering andSystem Safety vol 93 no 3 pp 383ndash393 2008

[4] L Berto R Vitaliani A Saetta and P Simioni ldquoSeismicassessment of existing RC structures affected by degradationphenomenardquo Structural Safety vol 31 no 4 pp 284ndash297 2009

[5] J Ghosh and J E Padgett ldquoAging considerations in the devel-opment of time-dependent seismic fragility curvesrdquo Journal ofStructural Engineering vol 136 no 12 pp 1497ndash1511 2010

[6] A Alipour B Shafei and M Shinozuka ldquoPerformance evalu-ation of deteriorating highway bridges located in high seismicareasrdquo Journal of Bridge Engineering vol 16 no 5 pp 597ndash6112011

[7] F Biondini E Camnasio and A Palermo ldquoLifetime seismicperformance of concrete bridges exposed to corrosionrdquo Struc-ture and Infrastructure Engineering vol 10 no 7 pp 880ndash9002014

[8] M Akiyama D M Frangopol and H Matsuzaki ldquoLife-cyclereliability of RC bridge piers under seismic and airborne chlo-ride hazardsrdquo Earthquake Engineering and Structural Dynamicsvol 40 no 15 pp 1671ndash1687 2011

[9] F Biondini A Palermo and G Toniolo ldquoSeismic performanceof concrete structures exposed to corrosion case studies of low-rise precast buildingsrdquo Structure and Infrastructure Engineeringvol 7 no 1-2 pp 109ndash119 2011

[10] C K Chiu F J Tu and F P Hsiao ldquoLifetime seismic perfor-mance assessment for chloride-corroded reinforced concretebuildingsrdquo Structure and Infrastructure Engineering vol 11 no3 pp 345ndash362 2015

[11] M Sanchez-Silva G-A Klutke and D V Rosowsky ldquoLife-cycleperformance of structures subject to multiple deteriorationmechanismsrdquo Structural Safety vol 33 no 3 pp 206ndash217 2011

[12] Y-C Ou L-L Tsai and H-H Chen ldquoCyclic performance oflarge-scale corroded reinforced concrete beamsrdquo EarthquakeEngineering and StructuralDynamics vol 41 no 4 pp 593ndash6042012

[13] Y Ma Y Che and J Gong ldquoBehavior of corrosion damagedcircular reinforced concrete columns under cyclic loadingrdquoConstruction and Building Materials vol 29 pp 548ndash556 2012

[14] A Meda S Mostosi Z Rinaldi and P Riva ldquoExperimentalevaluation of the corrosion influence on the cyclic behaviour ofRC columnsrdquo Engineering Structures vol 76 pp 112ndash123 2014

[15] A A Almusallam ldquoEffect of degree of corrosion on theproperties of reinforcing steel barsrdquo Construction and BuildingMaterials vol 15 no 8 pp 361ndash368 2001

[16] Y G Du L A Clark and A H C Chan ldquoResidual capacity ofcorroded reinforcing barsrdquoMagazine of Concrete Research vol57 no 3 pp 135ndash147 2005

[17] Y G Du L A Clarkt and A H C Chan ldquoEffect of corrosionon ductility of reinforcing barsrdquoMagazine of Concrete Researchvol 57 no 7 pp 407ndash419 2005

[18] J Cairns G A Plizzari Y Du D W Law and C FranzonildquoMechanical properties of corrosion-damaged reinforcementrdquoACI Materials Journal vol 102 no 4 pp 256ndash264 2005

[19] C A ApostolopoulosM P Papadopoulos and S G PantelakisldquoTensile behavior of corroded reinforcing steel bars BSt 500srdquoConstruction and Building Materials vol 20 no 9 pp 782ndash7892006

[20] C A Apostolopoulos ldquoMechanical behavior of corroded rein-forcing steel bars S500s tempcore under low cycle fatiguerdquoConstruction andBuildingMaterials vol 21 no 7 pp 1447ndash14562007

[21] M M Kashani A J Crewe and N A Alexander ldquoNonlinearstress-strain behaviour of corrosion-damaged reinforcing barsincluding inelastic bucklingrdquo Engineering Structures vol 48 pp417ndash429 2013

[22] M M Kashani A J Crewe and N A Alexander ldquoNonlinearcyclic response of corrosion-damaged reinforcing bars with theeffect of bucklingrdquo Construction and Building Materials vol 41pp 388ndash400 2013

[23] M M Kashani A J Crewe and N A Alexander ldquoUse of a 3Doptical measurement technique for stochastic corrosion patternanalysis of reinforcing bars subjected to accelerated corrosionrdquoCorrosion Science vol 73 pp 208ndash221 2013

[24] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoFinite element investigation of the influence of corrosionpattern on inelastic buckling and cyclic response of corrodedreinforcing barsrdquo Engineering Structures vol 75 pp 113ndash1252014

Advances in Materials Science and Engineering 15

[25] M M Kashani Seismic performance of corroded rc bridge piersdevelopment of a multi-mechanical nonlinear fibre beam-columnmodel [PhD thesis] University of Bristol Bristol UK 2014

[26] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part I Formula-tionrdquo Earthquake Engineering and Structural Dynamics vol 25no 7 pp 711ndash725 1996

[27] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part II Applica-tionsrdquoEarthquake Engineering and Structural Dynamics vol 25no 7 pp 727ndash742 1996

[28] The Open System for Earthquake Engineering Simulation(OpenSees) Pacific Earthquake Engineering Research CentreUniversity of California Berkeley Berkeley Calif USA 2011

[29] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoPhenomenological hysteretic model for corroded reinforcingbars including inelastic buckling and low-cycle fatigue degrada-tionrdquo Computers and Structures vol 156 article 5393 pp 58ndash712015

[30] J Coleman and E Spacone ldquoLocalization issues in force-basedframe elementsrdquo Journal of Structural Engineering vol 127 no11 pp 1257ndash1265 2001

[31] J S Pugh Numerical simulation of walls and seismic designrecommendations for walled buildings [PhD thesis] Universityof Washington Seattle Wash USA 2012

[32] D V Val and R E Melchers ldquoReliability of deteriorating RCslab bridgesrdquo Journal of Structural Engineering vol 123 no 12pp 1638ndash1644 1997

[33] M S Darmawan and M G Stewart ldquoEffect of pitting corro-sion on capacity of prestressing wiresrdquo Magazine of ConcreteResearch vol 59 no 2 pp 131ndash139 2007

[34] R P Dhakal and K Maekawa ldquoReinforcement stability andfracture of cover concrete in reinforced concrete membersrdquoJournal of Structural Engineering vol 128 no 10 pp 1253ndash12622002

[35] C Lee J F Bonacci M D A Thomas et al ldquoAcceleratedcorrosion and repair of reinforced concrete columns usingcarbon fibre reinforced polymer sheetsrdquo Canadian Journal ofCivil Engineering vol 27 no 5 pp 941ndash948 2000

[36] W Aquino Long-term performance of seismically rehabilitatedcorrosion-damaged columns [PhD thesis] University of Illinoisat Urbana-Champaign Champaign Ill USA 2002

[37] S Timoshenko and J Gere Theory of Elastic StabilityMacGraw-Hill New York NY USA 1963

[38] S J Pantazopoulou ldquoDetailing for reinforcement stability in RCmembersrdquo Journal of Structural Engineering vol 124 no 6 pp623ndash632 1998

[39] J B Mander M J N Priestley and R Park ldquoObserved stress-strain behavior of confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1827ndash1849 1988

[40] J B Mander M J Priestley and R Park ldquoTheoretical stress-strain model for confined concreterdquo Journal of Structural Engi-neering (United States) vol 114 no 8 pp 1804ndash1826 1988

[41] S Popovics ldquoAnumerical approach to the complete stress-straincurve of concreterdquo Cement and Concrete Research vol 3 no 5pp 583ndash599 1973

[42] I D Karsan and J O Jirsa ldquoBehavior of concrete undercompressive loadingrdquo Journal of Structural Division vol 95article ST12 1969

[43] M P Berry andMO Eberhard ldquoPerformancemodeling strate-gies for modern reinforced concrete bridge columnsrdquo PEER

Research Report University of California Berkeley BerkeleyCalif USA 2006

[44] B D Scott R Park and M J N Priestley ldquoStress-strainbehavior of concrete confined by overlapping hoops at low andhigh strain ratesrdquo Journal of the American Concrete Institute vol79 no 1 pp 13ndash27 1982

[45] A S Al-Harthy M G Stewart and J Mullard ldquoConcrete covercracking caused by steel reinforcement corrosionrdquoMagazine ofConcrete Research vol 63 no 9 pp 655ndash667 2011

[46] T Vidal A Castel and R Francois ldquoAnalyzing crack width topredict corrosion in reinforced concreterdquo Cement and ConcreteResearch vol 34 no 1 pp 165ndash174 2004

[47] F J Molina C Alonso and C Andrade ldquoCover cracking as afunction of rebar corrosion part 2-numerical modelrdquoMaterialsand Structures vol 26 no 9 pp 532ndash548 1993

[48] F J Vecchio and M P Collins ldquoThe modified compression-field theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[49] D Coronelli and P Gambarova ldquoStructural assessment ofcorroded reinforced concrete beams modeling guidelinesrdquoJournal of Structural Engineering vol 130 no 8 pp 1214ndash12242004

[50] D E Lehman and J P Moehle ldquoSeismic performance of well-confined concrete columnsrdquo PEER Research Report Universityof California at Berkeley 2000

[51] L N Lowes and A Altoontash ldquoModeling reinforced-concretebeam-column joints subjected to cyclic loadingrdquo Journal ofStructural Engineering vol 129 no 12 pp 1686ndash1697 2003

[52] M Berry M Parrish and M Eberhard ldquoPerformance databaseUserrsquos manualrdquo in Pacific Earthquake Engineering ResearchCentre 2004 University of California at Berkeley 2004httpwwwcewashingtonedusimpeera1

[53] A N Kallias and M Imran Rafiq ldquoFinite element investigationof the structural response of corroded RC beamsrdquo EngineeringStructures vol 32 no 9 pp 2984ndash2994 2010

[54] M J Moyer and M J Kowalsky ldquoInfluence of tension strain onbuckling of reinforcement in concrete columnsrdquo ACI StructuralJournal vol 100 no 1 pp 75ndash85 2003

[55] K A T Vu andM G Stewart ldquoStructural reliability of concretebridges including improved chloride-induced corrosion mod-elsrdquo Structural Safety vol 22 no 4 pp 313ndash333 2000

[56] D V Val ldquoFactors affecting life-cycle cost analysis of RCstructures in chloride contaminated environmentsrdquo Journal ofInfrastructure Systems vol 13 no 2 pp 135ndash143 2007

[57] J P BroomfieldCorrosion of Steel in Concrete Taylor amp FrancisLondon UK 2nd edition 2007

[58] M M Kashani P Alagheband R Khan and S Davis ldquoImpactof corrosion on low-cycle fatigue degradation of reinforcingbars with the effect of inelastic bucklingrdquo International Journalof Fatigue vol 77 pp 174ndash185 2015

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

12 Advances in Materials Science and Engineering

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(a)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 10 mass lossPushover response 10 mass loss

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Cyclic response uncorrodedCyclic response 20 mass loss Pushover response 20 mass loss

(d)

Figure 13 Cyclic analyses considering corrosion induced damage in reinforcing steel cracked cover concrete and confined concrete (a) and(b) Lehmanrsquos column 415 (c) and (d) Moyer and Kowalskyrsquos column 1

It is found that the failure mode under cyclic loading ismainly governed by the fracture of horizontal bars in tensiondue to reduced low-cycle fatigue life (Figures 14(c) and 14(d))This is a very important finding as it suggests that nonlinearquasistatic pushover analysis on its own is not adequate forperformance assessment of existing corroded bridge piers

With reference to Figure 14 it is evident that consideringthe impact of the corrosion damage on core confined con-crete and low-cycle fatigue degradation is crucial Thereforethey need to be considered when modelling the nonlinearbehaviour of corrosion damaged RC bridge piers underseismic loading This finding is in good agreement with theobserved experimental results by other researchers [12ndash1458]

A series of experimental studies were conducted in [12]on the cyclic behaviour of large-scale corroded cantilever RCbeams Ou et al found that as the level of corrosion increasesthe flexural failure initiates with premature buckling oflongitudinal bars This conclusion is in good agreement withthe numerical results discussed in this paper In another study[13] a series of experimental studies were conducted on cyclicbehaviour of corroded RC columns with varied axial forceMa et al have reported that once the corrosion level increases

beyond about 14 rapid strength and ductility reductionand cyclic degradation in hysteretic loops are seen due toreduced low-cycle fatigue life and premature buckling ofvertical reinforcement This conclusion is in good agreementwith the predicted failure modes using the numerical modelpresented in this paper

The detailed finite element model developed in thispaper can accurately model the nonlinear behaviour ofcorrodedRCcolumns subject to cyclic loading up to completecollapse There is a need to extend the PEER-UW columndatabase to include corroded RC columns so that furthercalibrationvalidation of the material model parameters canbe performed However the modelling technique developedin this paper is able to simulate the multiple failure modesof corroded RC columns simultaneously It represents thecurrent state of the art and as such they provide a novel com-putational framework for the seismic response prediction ofcorroded RC bridges

8 Conclusions

A series of pushover and cyclic analyses on two hypotheticalcorroded RC columns are conducted and these are used

Advances in Materials Science and Engineering 13

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(d)

Figure 14 Comparison of the computed responses of columns with different deterioration models (a) and (c) Lehmanrsquos column 415 undermonotonic and cyclic loading (b) and (d) Moyer and Kowalskyrsquos column 1 under monotonic and cyclic loading

to explore the performance of the proposed computationalframework The impact of corrosion on (i) the verticalreinforcing steel (ii) the tieconfinement (iii) the cover(unconfined) concrete and (iv) the core (confined) concreteis represented through new material models The proposednew steel material model accounts for (i) inelastic nonlinearbuckling of the vertical reinforcement (ii) the corrosion lossof area (iii) the nonuniform corrosion pitting and (iv) low-cycle high amplitude fatigueThenew cover concretematerialmodel includes the influence of internal pressure due tothe build-up of corrosion products (using compression fieldtheory) The new core concrete model includes the influenceof corrosion induced loss of confining reinforcement

The main outcomes of this study can be summarised asfollows

(1) Corrosion has a more significant impact on theductility loss (drift capacity) of RC columns than thestrength loss (plastic moment capacity)

(2) The numerical model developed in this paper is ableto predict the nonlinear flexural response of corrodedRC columns up to complete collapse Results showwhich depends on a cyclic load history that flexuralfailure can be initiated by the buckling of vertical bars

and crushing of core concrete which is then followedby fracture of bars in tension In cases where thebuckling of bars is not an issue or the buckling lengthis too short (119871eff119889

1015840le 5) the failure is governed by the

fracture of the vertical bars in tension due to low-cyclehigh amplitude fatigue

(3) The analyses results show that for the seismic perfor-mance and evaluation of existing corroded bridgesmonotonic pushover analysis is not sufficient Thecyclic degradation due to low-cycle high amplitudefatigue has a significant influence on the response ofcorroded RC columns

(4) The results of this study show that it is inadequate toassume that corrosion only affects the main verticalreinforcement in the column It was found that theconfined concrete with corroded confinement rein-forcement starts crushing much faster than uncor-roded undamaged concrete This changes the failuremode and results in premature buckling of the ver-tical reinforcement This change in the failure modecannot be predicted if the damage in core confinedconcrete due to corrosion of tie reinforcement isignored This is in good agreement with observed

14 Advances in Materials Science and Engineering

experimental results reported by other researchers[12ndash14]

(5) The modelling technique developed in this paper hassignificantly improved the earlier models and canbe used by other researchers in the future researchfor seismic vulnerability and fragility analysis ofcorroded RC bridges

Disclosure

Any findings opinions and recommendations provided inthis paper are only based on the authorsrsquo view

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This research is conducted in collaboration with the Univer-sity of Bristol and the University of Washington while thefirst author was on sabbatical leave in the US The fundingprovided by the World Wide University Network throughthe Research Mobility Program to the first author was muchappreciated The authors would like to thank Professor MarcO Eberhard and Professor John F Stanton for providingvaluable guidance during the course of this research

References

[1] S Hida F I S Ibrahim H A Capers et al ldquoAssuringbridge safety and serviceability in Europerdquo Tech Rep FHWA-PL-10-014 Office of International Programs Federal HighwayAdministration US Department of Transportation AmericanAssociation of State Highway and Transportation Officials2010

[2] ASCE Failure to Act The Economic Impact of Current Invest-ment Trends in Surface Transportation Infrastructure EconomicDevelopment Research Group Inc ASCE 2011

[3] D-E Choe P Gardoni D Rosowsky and T Haukaas ldquoProb-abilistic capacity models and seismic fragility estimates forRC columns subject to corrosionrdquo Reliability Engineering andSystem Safety vol 93 no 3 pp 383ndash393 2008

[4] L Berto R Vitaliani A Saetta and P Simioni ldquoSeismicassessment of existing RC structures affected by degradationphenomenardquo Structural Safety vol 31 no 4 pp 284ndash297 2009

[5] J Ghosh and J E Padgett ldquoAging considerations in the devel-opment of time-dependent seismic fragility curvesrdquo Journal ofStructural Engineering vol 136 no 12 pp 1497ndash1511 2010

[6] A Alipour B Shafei and M Shinozuka ldquoPerformance evalu-ation of deteriorating highway bridges located in high seismicareasrdquo Journal of Bridge Engineering vol 16 no 5 pp 597ndash6112011

[7] F Biondini E Camnasio and A Palermo ldquoLifetime seismicperformance of concrete bridges exposed to corrosionrdquo Struc-ture and Infrastructure Engineering vol 10 no 7 pp 880ndash9002014

[8] M Akiyama D M Frangopol and H Matsuzaki ldquoLife-cyclereliability of RC bridge piers under seismic and airborne chlo-ride hazardsrdquo Earthquake Engineering and Structural Dynamicsvol 40 no 15 pp 1671ndash1687 2011

[9] F Biondini A Palermo and G Toniolo ldquoSeismic performanceof concrete structures exposed to corrosion case studies of low-rise precast buildingsrdquo Structure and Infrastructure Engineeringvol 7 no 1-2 pp 109ndash119 2011

[10] C K Chiu F J Tu and F P Hsiao ldquoLifetime seismic perfor-mance assessment for chloride-corroded reinforced concretebuildingsrdquo Structure and Infrastructure Engineering vol 11 no3 pp 345ndash362 2015

[11] M Sanchez-Silva G-A Klutke and D V Rosowsky ldquoLife-cycleperformance of structures subject to multiple deteriorationmechanismsrdquo Structural Safety vol 33 no 3 pp 206ndash217 2011

[12] Y-C Ou L-L Tsai and H-H Chen ldquoCyclic performance oflarge-scale corroded reinforced concrete beamsrdquo EarthquakeEngineering and StructuralDynamics vol 41 no 4 pp 593ndash6042012

[13] Y Ma Y Che and J Gong ldquoBehavior of corrosion damagedcircular reinforced concrete columns under cyclic loadingrdquoConstruction and Building Materials vol 29 pp 548ndash556 2012

[14] A Meda S Mostosi Z Rinaldi and P Riva ldquoExperimentalevaluation of the corrosion influence on the cyclic behaviour ofRC columnsrdquo Engineering Structures vol 76 pp 112ndash123 2014

[15] A A Almusallam ldquoEffect of degree of corrosion on theproperties of reinforcing steel barsrdquo Construction and BuildingMaterials vol 15 no 8 pp 361ndash368 2001

[16] Y G Du L A Clark and A H C Chan ldquoResidual capacity ofcorroded reinforcing barsrdquoMagazine of Concrete Research vol57 no 3 pp 135ndash147 2005

[17] Y G Du L A Clarkt and A H C Chan ldquoEffect of corrosionon ductility of reinforcing barsrdquoMagazine of Concrete Researchvol 57 no 7 pp 407ndash419 2005

[18] J Cairns G A Plizzari Y Du D W Law and C FranzonildquoMechanical properties of corrosion-damaged reinforcementrdquoACI Materials Journal vol 102 no 4 pp 256ndash264 2005

[19] C A ApostolopoulosM P Papadopoulos and S G PantelakisldquoTensile behavior of corroded reinforcing steel bars BSt 500srdquoConstruction and Building Materials vol 20 no 9 pp 782ndash7892006

[20] C A Apostolopoulos ldquoMechanical behavior of corroded rein-forcing steel bars S500s tempcore under low cycle fatiguerdquoConstruction andBuildingMaterials vol 21 no 7 pp 1447ndash14562007

[21] M M Kashani A J Crewe and N A Alexander ldquoNonlinearstress-strain behaviour of corrosion-damaged reinforcing barsincluding inelastic bucklingrdquo Engineering Structures vol 48 pp417ndash429 2013

[22] M M Kashani A J Crewe and N A Alexander ldquoNonlinearcyclic response of corrosion-damaged reinforcing bars with theeffect of bucklingrdquo Construction and Building Materials vol 41pp 388ndash400 2013

[23] M M Kashani A J Crewe and N A Alexander ldquoUse of a 3Doptical measurement technique for stochastic corrosion patternanalysis of reinforcing bars subjected to accelerated corrosionrdquoCorrosion Science vol 73 pp 208ndash221 2013

[24] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoFinite element investigation of the influence of corrosionpattern on inelastic buckling and cyclic response of corrodedreinforcing barsrdquo Engineering Structures vol 75 pp 113ndash1252014

Advances in Materials Science and Engineering 15

[25] M M Kashani Seismic performance of corroded rc bridge piersdevelopment of a multi-mechanical nonlinear fibre beam-columnmodel [PhD thesis] University of Bristol Bristol UK 2014

[26] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part I Formula-tionrdquo Earthquake Engineering and Structural Dynamics vol 25no 7 pp 711ndash725 1996

[27] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part II Applica-tionsrdquoEarthquake Engineering and Structural Dynamics vol 25no 7 pp 727ndash742 1996

[28] The Open System for Earthquake Engineering Simulation(OpenSees) Pacific Earthquake Engineering Research CentreUniversity of California Berkeley Berkeley Calif USA 2011

[29] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoPhenomenological hysteretic model for corroded reinforcingbars including inelastic buckling and low-cycle fatigue degrada-tionrdquo Computers and Structures vol 156 article 5393 pp 58ndash712015

[30] J Coleman and E Spacone ldquoLocalization issues in force-basedframe elementsrdquo Journal of Structural Engineering vol 127 no11 pp 1257ndash1265 2001

[31] J S Pugh Numerical simulation of walls and seismic designrecommendations for walled buildings [PhD thesis] Universityof Washington Seattle Wash USA 2012

[32] D V Val and R E Melchers ldquoReliability of deteriorating RCslab bridgesrdquo Journal of Structural Engineering vol 123 no 12pp 1638ndash1644 1997

[33] M S Darmawan and M G Stewart ldquoEffect of pitting corro-sion on capacity of prestressing wiresrdquo Magazine of ConcreteResearch vol 59 no 2 pp 131ndash139 2007

[34] R P Dhakal and K Maekawa ldquoReinforcement stability andfracture of cover concrete in reinforced concrete membersrdquoJournal of Structural Engineering vol 128 no 10 pp 1253ndash12622002

[35] C Lee J F Bonacci M D A Thomas et al ldquoAcceleratedcorrosion and repair of reinforced concrete columns usingcarbon fibre reinforced polymer sheetsrdquo Canadian Journal ofCivil Engineering vol 27 no 5 pp 941ndash948 2000

[36] W Aquino Long-term performance of seismically rehabilitatedcorrosion-damaged columns [PhD thesis] University of Illinoisat Urbana-Champaign Champaign Ill USA 2002

[37] S Timoshenko and J Gere Theory of Elastic StabilityMacGraw-Hill New York NY USA 1963

[38] S J Pantazopoulou ldquoDetailing for reinforcement stability in RCmembersrdquo Journal of Structural Engineering vol 124 no 6 pp623ndash632 1998

[39] J B Mander M J N Priestley and R Park ldquoObserved stress-strain behavior of confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1827ndash1849 1988

[40] J B Mander M J Priestley and R Park ldquoTheoretical stress-strain model for confined concreterdquo Journal of Structural Engi-neering (United States) vol 114 no 8 pp 1804ndash1826 1988

[41] S Popovics ldquoAnumerical approach to the complete stress-straincurve of concreterdquo Cement and Concrete Research vol 3 no 5pp 583ndash599 1973

[42] I D Karsan and J O Jirsa ldquoBehavior of concrete undercompressive loadingrdquo Journal of Structural Division vol 95article ST12 1969

[43] M P Berry andMO Eberhard ldquoPerformancemodeling strate-gies for modern reinforced concrete bridge columnsrdquo PEER

Research Report University of California Berkeley BerkeleyCalif USA 2006

[44] B D Scott R Park and M J N Priestley ldquoStress-strainbehavior of concrete confined by overlapping hoops at low andhigh strain ratesrdquo Journal of the American Concrete Institute vol79 no 1 pp 13ndash27 1982

[45] A S Al-Harthy M G Stewart and J Mullard ldquoConcrete covercracking caused by steel reinforcement corrosionrdquoMagazine ofConcrete Research vol 63 no 9 pp 655ndash667 2011

[46] T Vidal A Castel and R Francois ldquoAnalyzing crack width topredict corrosion in reinforced concreterdquo Cement and ConcreteResearch vol 34 no 1 pp 165ndash174 2004

[47] F J Molina C Alonso and C Andrade ldquoCover cracking as afunction of rebar corrosion part 2-numerical modelrdquoMaterialsand Structures vol 26 no 9 pp 532ndash548 1993

[48] F J Vecchio and M P Collins ldquoThe modified compression-field theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[49] D Coronelli and P Gambarova ldquoStructural assessment ofcorroded reinforced concrete beams modeling guidelinesrdquoJournal of Structural Engineering vol 130 no 8 pp 1214ndash12242004

[50] D E Lehman and J P Moehle ldquoSeismic performance of well-confined concrete columnsrdquo PEER Research Report Universityof California at Berkeley 2000

[51] L N Lowes and A Altoontash ldquoModeling reinforced-concretebeam-column joints subjected to cyclic loadingrdquo Journal ofStructural Engineering vol 129 no 12 pp 1686ndash1697 2003

[52] M Berry M Parrish and M Eberhard ldquoPerformance databaseUserrsquos manualrdquo in Pacific Earthquake Engineering ResearchCentre 2004 University of California at Berkeley 2004httpwwwcewashingtonedusimpeera1

[53] A N Kallias and M Imran Rafiq ldquoFinite element investigationof the structural response of corroded RC beamsrdquo EngineeringStructures vol 32 no 9 pp 2984ndash2994 2010

[54] M J Moyer and M J Kowalsky ldquoInfluence of tension strain onbuckling of reinforcement in concrete columnsrdquo ACI StructuralJournal vol 100 no 1 pp 75ndash85 2003

[55] K A T Vu andM G Stewart ldquoStructural reliability of concretebridges including improved chloride-induced corrosion mod-elsrdquo Structural Safety vol 22 no 4 pp 313ndash333 2000

[56] D V Val ldquoFactors affecting life-cycle cost analysis of RCstructures in chloride contaminated environmentsrdquo Journal ofInfrastructure Systems vol 13 no 2 pp 135ndash143 2007

[57] J P BroomfieldCorrosion of Steel in Concrete Taylor amp FrancisLondon UK 2nd edition 2007

[58] M M Kashani P Alagheband R Khan and S Davis ldquoImpactof corrosion on low-cycle fatigue degradation of reinforcingbars with the effect of inelastic bucklingrdquo International Journalof Fatigue vol 77 pp 174ndash185 2015

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 13

0 001 002 003 004 005 006 007 0080

50100150200250300350

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(a)

0 001 002 003 004 005 006 007 0080

50

100

150

200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(b)

minus008 minus006 minus004 minus002 0 002 004 006 008minus400minus300minus200minus100

0100200300400

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(c)

minus008 minus006 minus004 minus002 0 002 004 006 008minus200minus150minus100

minus500

50100150200

Drift ratio

Late

ral f

orce

(kN

)

Uncorroded20 mass lossmdashsteel corroded20 mass lossmdashsteel corroded + cover cracked20 mass lossmdashsteel corroded +cover cracked + core concrete damaged

(d)

Figure 14 Comparison of the computed responses of columns with different deterioration models (a) and (c) Lehmanrsquos column 415 undermonotonic and cyclic loading (b) and (d) Moyer and Kowalskyrsquos column 1 under monotonic and cyclic loading

to explore the performance of the proposed computationalframework The impact of corrosion on (i) the verticalreinforcing steel (ii) the tieconfinement (iii) the cover(unconfined) concrete and (iv) the core (confined) concreteis represented through new material models The proposednew steel material model accounts for (i) inelastic nonlinearbuckling of the vertical reinforcement (ii) the corrosion lossof area (iii) the nonuniform corrosion pitting and (iv) low-cycle high amplitude fatigueThenew cover concretematerialmodel includes the influence of internal pressure due tothe build-up of corrosion products (using compression fieldtheory) The new core concrete model includes the influenceof corrosion induced loss of confining reinforcement

The main outcomes of this study can be summarised asfollows

(1) Corrosion has a more significant impact on theductility loss (drift capacity) of RC columns than thestrength loss (plastic moment capacity)

(2) The numerical model developed in this paper is ableto predict the nonlinear flexural response of corrodedRC columns up to complete collapse Results showwhich depends on a cyclic load history that flexuralfailure can be initiated by the buckling of vertical bars

and crushing of core concrete which is then followedby fracture of bars in tension In cases where thebuckling of bars is not an issue or the buckling lengthis too short (119871eff119889

1015840le 5) the failure is governed by the

fracture of the vertical bars in tension due to low-cyclehigh amplitude fatigue

(3) The analyses results show that for the seismic perfor-mance and evaluation of existing corroded bridgesmonotonic pushover analysis is not sufficient Thecyclic degradation due to low-cycle high amplitudefatigue has a significant influence on the response ofcorroded RC columns

(4) The results of this study show that it is inadequate toassume that corrosion only affects the main verticalreinforcement in the column It was found that theconfined concrete with corroded confinement rein-forcement starts crushing much faster than uncor-roded undamaged concrete This changes the failuremode and results in premature buckling of the ver-tical reinforcement This change in the failure modecannot be predicted if the damage in core confinedconcrete due to corrosion of tie reinforcement isignored This is in good agreement with observed

14 Advances in Materials Science and Engineering

experimental results reported by other researchers[12ndash14]

(5) The modelling technique developed in this paper hassignificantly improved the earlier models and canbe used by other researchers in the future researchfor seismic vulnerability and fragility analysis ofcorroded RC bridges

Disclosure

Any findings opinions and recommendations provided inthis paper are only based on the authorsrsquo view

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This research is conducted in collaboration with the Univer-sity of Bristol and the University of Washington while thefirst author was on sabbatical leave in the US The fundingprovided by the World Wide University Network throughthe Research Mobility Program to the first author was muchappreciated The authors would like to thank Professor MarcO Eberhard and Professor John F Stanton for providingvaluable guidance during the course of this research

References

[1] S Hida F I S Ibrahim H A Capers et al ldquoAssuringbridge safety and serviceability in Europerdquo Tech Rep FHWA-PL-10-014 Office of International Programs Federal HighwayAdministration US Department of Transportation AmericanAssociation of State Highway and Transportation Officials2010

[2] ASCE Failure to Act The Economic Impact of Current Invest-ment Trends in Surface Transportation Infrastructure EconomicDevelopment Research Group Inc ASCE 2011

[3] D-E Choe P Gardoni D Rosowsky and T Haukaas ldquoProb-abilistic capacity models and seismic fragility estimates forRC columns subject to corrosionrdquo Reliability Engineering andSystem Safety vol 93 no 3 pp 383ndash393 2008

[4] L Berto R Vitaliani A Saetta and P Simioni ldquoSeismicassessment of existing RC structures affected by degradationphenomenardquo Structural Safety vol 31 no 4 pp 284ndash297 2009

[5] J Ghosh and J E Padgett ldquoAging considerations in the devel-opment of time-dependent seismic fragility curvesrdquo Journal ofStructural Engineering vol 136 no 12 pp 1497ndash1511 2010

[6] A Alipour B Shafei and M Shinozuka ldquoPerformance evalu-ation of deteriorating highway bridges located in high seismicareasrdquo Journal of Bridge Engineering vol 16 no 5 pp 597ndash6112011

[7] F Biondini E Camnasio and A Palermo ldquoLifetime seismicperformance of concrete bridges exposed to corrosionrdquo Struc-ture and Infrastructure Engineering vol 10 no 7 pp 880ndash9002014

[8] M Akiyama D M Frangopol and H Matsuzaki ldquoLife-cyclereliability of RC bridge piers under seismic and airborne chlo-ride hazardsrdquo Earthquake Engineering and Structural Dynamicsvol 40 no 15 pp 1671ndash1687 2011

[9] F Biondini A Palermo and G Toniolo ldquoSeismic performanceof concrete structures exposed to corrosion case studies of low-rise precast buildingsrdquo Structure and Infrastructure Engineeringvol 7 no 1-2 pp 109ndash119 2011

[10] C K Chiu F J Tu and F P Hsiao ldquoLifetime seismic perfor-mance assessment for chloride-corroded reinforced concretebuildingsrdquo Structure and Infrastructure Engineering vol 11 no3 pp 345ndash362 2015

[11] M Sanchez-Silva G-A Klutke and D V Rosowsky ldquoLife-cycleperformance of structures subject to multiple deteriorationmechanismsrdquo Structural Safety vol 33 no 3 pp 206ndash217 2011

[12] Y-C Ou L-L Tsai and H-H Chen ldquoCyclic performance oflarge-scale corroded reinforced concrete beamsrdquo EarthquakeEngineering and StructuralDynamics vol 41 no 4 pp 593ndash6042012

[13] Y Ma Y Che and J Gong ldquoBehavior of corrosion damagedcircular reinforced concrete columns under cyclic loadingrdquoConstruction and Building Materials vol 29 pp 548ndash556 2012

[14] A Meda S Mostosi Z Rinaldi and P Riva ldquoExperimentalevaluation of the corrosion influence on the cyclic behaviour ofRC columnsrdquo Engineering Structures vol 76 pp 112ndash123 2014

[15] A A Almusallam ldquoEffect of degree of corrosion on theproperties of reinforcing steel barsrdquo Construction and BuildingMaterials vol 15 no 8 pp 361ndash368 2001

[16] Y G Du L A Clark and A H C Chan ldquoResidual capacity ofcorroded reinforcing barsrdquoMagazine of Concrete Research vol57 no 3 pp 135ndash147 2005

[17] Y G Du L A Clarkt and A H C Chan ldquoEffect of corrosionon ductility of reinforcing barsrdquoMagazine of Concrete Researchvol 57 no 7 pp 407ndash419 2005

[18] J Cairns G A Plizzari Y Du D W Law and C FranzonildquoMechanical properties of corrosion-damaged reinforcementrdquoACI Materials Journal vol 102 no 4 pp 256ndash264 2005

[19] C A ApostolopoulosM P Papadopoulos and S G PantelakisldquoTensile behavior of corroded reinforcing steel bars BSt 500srdquoConstruction and Building Materials vol 20 no 9 pp 782ndash7892006

[20] C A Apostolopoulos ldquoMechanical behavior of corroded rein-forcing steel bars S500s tempcore under low cycle fatiguerdquoConstruction andBuildingMaterials vol 21 no 7 pp 1447ndash14562007

[21] M M Kashani A J Crewe and N A Alexander ldquoNonlinearstress-strain behaviour of corrosion-damaged reinforcing barsincluding inelastic bucklingrdquo Engineering Structures vol 48 pp417ndash429 2013

[22] M M Kashani A J Crewe and N A Alexander ldquoNonlinearcyclic response of corrosion-damaged reinforcing bars with theeffect of bucklingrdquo Construction and Building Materials vol 41pp 388ndash400 2013

[23] M M Kashani A J Crewe and N A Alexander ldquoUse of a 3Doptical measurement technique for stochastic corrosion patternanalysis of reinforcing bars subjected to accelerated corrosionrdquoCorrosion Science vol 73 pp 208ndash221 2013

[24] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoFinite element investigation of the influence of corrosionpattern on inelastic buckling and cyclic response of corrodedreinforcing barsrdquo Engineering Structures vol 75 pp 113ndash1252014

Advances in Materials Science and Engineering 15

[25] M M Kashani Seismic performance of corroded rc bridge piersdevelopment of a multi-mechanical nonlinear fibre beam-columnmodel [PhD thesis] University of Bristol Bristol UK 2014

[26] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part I Formula-tionrdquo Earthquake Engineering and Structural Dynamics vol 25no 7 pp 711ndash725 1996

[27] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part II Applica-tionsrdquoEarthquake Engineering and Structural Dynamics vol 25no 7 pp 727ndash742 1996

[28] The Open System for Earthquake Engineering Simulation(OpenSees) Pacific Earthquake Engineering Research CentreUniversity of California Berkeley Berkeley Calif USA 2011

[29] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoPhenomenological hysteretic model for corroded reinforcingbars including inelastic buckling and low-cycle fatigue degrada-tionrdquo Computers and Structures vol 156 article 5393 pp 58ndash712015

[30] J Coleman and E Spacone ldquoLocalization issues in force-basedframe elementsrdquo Journal of Structural Engineering vol 127 no11 pp 1257ndash1265 2001

[31] J S Pugh Numerical simulation of walls and seismic designrecommendations for walled buildings [PhD thesis] Universityof Washington Seattle Wash USA 2012

[32] D V Val and R E Melchers ldquoReliability of deteriorating RCslab bridgesrdquo Journal of Structural Engineering vol 123 no 12pp 1638ndash1644 1997

[33] M S Darmawan and M G Stewart ldquoEffect of pitting corro-sion on capacity of prestressing wiresrdquo Magazine of ConcreteResearch vol 59 no 2 pp 131ndash139 2007

[34] R P Dhakal and K Maekawa ldquoReinforcement stability andfracture of cover concrete in reinforced concrete membersrdquoJournal of Structural Engineering vol 128 no 10 pp 1253ndash12622002

[35] C Lee J F Bonacci M D A Thomas et al ldquoAcceleratedcorrosion and repair of reinforced concrete columns usingcarbon fibre reinforced polymer sheetsrdquo Canadian Journal ofCivil Engineering vol 27 no 5 pp 941ndash948 2000

[36] W Aquino Long-term performance of seismically rehabilitatedcorrosion-damaged columns [PhD thesis] University of Illinoisat Urbana-Champaign Champaign Ill USA 2002

[37] S Timoshenko and J Gere Theory of Elastic StabilityMacGraw-Hill New York NY USA 1963

[38] S J Pantazopoulou ldquoDetailing for reinforcement stability in RCmembersrdquo Journal of Structural Engineering vol 124 no 6 pp623ndash632 1998

[39] J B Mander M J N Priestley and R Park ldquoObserved stress-strain behavior of confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1827ndash1849 1988

[40] J B Mander M J Priestley and R Park ldquoTheoretical stress-strain model for confined concreterdquo Journal of Structural Engi-neering (United States) vol 114 no 8 pp 1804ndash1826 1988

[41] S Popovics ldquoAnumerical approach to the complete stress-straincurve of concreterdquo Cement and Concrete Research vol 3 no 5pp 583ndash599 1973

[42] I D Karsan and J O Jirsa ldquoBehavior of concrete undercompressive loadingrdquo Journal of Structural Division vol 95article ST12 1969

[43] M P Berry andMO Eberhard ldquoPerformancemodeling strate-gies for modern reinforced concrete bridge columnsrdquo PEER

Research Report University of California Berkeley BerkeleyCalif USA 2006

[44] B D Scott R Park and M J N Priestley ldquoStress-strainbehavior of concrete confined by overlapping hoops at low andhigh strain ratesrdquo Journal of the American Concrete Institute vol79 no 1 pp 13ndash27 1982

[45] A S Al-Harthy M G Stewart and J Mullard ldquoConcrete covercracking caused by steel reinforcement corrosionrdquoMagazine ofConcrete Research vol 63 no 9 pp 655ndash667 2011

[46] T Vidal A Castel and R Francois ldquoAnalyzing crack width topredict corrosion in reinforced concreterdquo Cement and ConcreteResearch vol 34 no 1 pp 165ndash174 2004

[47] F J Molina C Alonso and C Andrade ldquoCover cracking as afunction of rebar corrosion part 2-numerical modelrdquoMaterialsand Structures vol 26 no 9 pp 532ndash548 1993

[48] F J Vecchio and M P Collins ldquoThe modified compression-field theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[49] D Coronelli and P Gambarova ldquoStructural assessment ofcorroded reinforced concrete beams modeling guidelinesrdquoJournal of Structural Engineering vol 130 no 8 pp 1214ndash12242004

[50] D E Lehman and J P Moehle ldquoSeismic performance of well-confined concrete columnsrdquo PEER Research Report Universityof California at Berkeley 2000

[51] L N Lowes and A Altoontash ldquoModeling reinforced-concretebeam-column joints subjected to cyclic loadingrdquo Journal ofStructural Engineering vol 129 no 12 pp 1686ndash1697 2003

[52] M Berry M Parrish and M Eberhard ldquoPerformance databaseUserrsquos manualrdquo in Pacific Earthquake Engineering ResearchCentre 2004 University of California at Berkeley 2004httpwwwcewashingtonedusimpeera1

[53] A N Kallias and M Imran Rafiq ldquoFinite element investigationof the structural response of corroded RC beamsrdquo EngineeringStructures vol 32 no 9 pp 2984ndash2994 2010

[54] M J Moyer and M J Kowalsky ldquoInfluence of tension strain onbuckling of reinforcement in concrete columnsrdquo ACI StructuralJournal vol 100 no 1 pp 75ndash85 2003

[55] K A T Vu andM G Stewart ldquoStructural reliability of concretebridges including improved chloride-induced corrosion mod-elsrdquo Structural Safety vol 22 no 4 pp 313ndash333 2000

[56] D V Val ldquoFactors affecting life-cycle cost analysis of RCstructures in chloride contaminated environmentsrdquo Journal ofInfrastructure Systems vol 13 no 2 pp 135ndash143 2007

[57] J P BroomfieldCorrosion of Steel in Concrete Taylor amp FrancisLondon UK 2nd edition 2007

[58] M M Kashani P Alagheband R Khan and S Davis ldquoImpactof corrosion on low-cycle fatigue degradation of reinforcingbars with the effect of inelastic bucklingrdquo International Journalof Fatigue vol 77 pp 174ndash185 2015

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

14 Advances in Materials Science and Engineering

experimental results reported by other researchers[12ndash14]

(5) The modelling technique developed in this paper hassignificantly improved the earlier models and canbe used by other researchers in the future researchfor seismic vulnerability and fragility analysis ofcorroded RC bridges

Disclosure

Any findings opinions and recommendations provided inthis paper are only based on the authorsrsquo view

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This research is conducted in collaboration with the Univer-sity of Bristol and the University of Washington while thefirst author was on sabbatical leave in the US The fundingprovided by the World Wide University Network throughthe Research Mobility Program to the first author was muchappreciated The authors would like to thank Professor MarcO Eberhard and Professor John F Stanton for providingvaluable guidance during the course of this research

References

[1] S Hida F I S Ibrahim H A Capers et al ldquoAssuringbridge safety and serviceability in Europerdquo Tech Rep FHWA-PL-10-014 Office of International Programs Federal HighwayAdministration US Department of Transportation AmericanAssociation of State Highway and Transportation Officials2010

[2] ASCE Failure to Act The Economic Impact of Current Invest-ment Trends in Surface Transportation Infrastructure EconomicDevelopment Research Group Inc ASCE 2011

[3] D-E Choe P Gardoni D Rosowsky and T Haukaas ldquoProb-abilistic capacity models and seismic fragility estimates forRC columns subject to corrosionrdquo Reliability Engineering andSystem Safety vol 93 no 3 pp 383ndash393 2008

[4] L Berto R Vitaliani A Saetta and P Simioni ldquoSeismicassessment of existing RC structures affected by degradationphenomenardquo Structural Safety vol 31 no 4 pp 284ndash297 2009

[5] J Ghosh and J E Padgett ldquoAging considerations in the devel-opment of time-dependent seismic fragility curvesrdquo Journal ofStructural Engineering vol 136 no 12 pp 1497ndash1511 2010

[6] A Alipour B Shafei and M Shinozuka ldquoPerformance evalu-ation of deteriorating highway bridges located in high seismicareasrdquo Journal of Bridge Engineering vol 16 no 5 pp 597ndash6112011

[7] F Biondini E Camnasio and A Palermo ldquoLifetime seismicperformance of concrete bridges exposed to corrosionrdquo Struc-ture and Infrastructure Engineering vol 10 no 7 pp 880ndash9002014

[8] M Akiyama D M Frangopol and H Matsuzaki ldquoLife-cyclereliability of RC bridge piers under seismic and airborne chlo-ride hazardsrdquo Earthquake Engineering and Structural Dynamicsvol 40 no 15 pp 1671ndash1687 2011

[9] F Biondini A Palermo and G Toniolo ldquoSeismic performanceof concrete structures exposed to corrosion case studies of low-rise precast buildingsrdquo Structure and Infrastructure Engineeringvol 7 no 1-2 pp 109ndash119 2011

[10] C K Chiu F J Tu and F P Hsiao ldquoLifetime seismic perfor-mance assessment for chloride-corroded reinforced concretebuildingsrdquo Structure and Infrastructure Engineering vol 11 no3 pp 345ndash362 2015

[11] M Sanchez-Silva G-A Klutke and D V Rosowsky ldquoLife-cycleperformance of structures subject to multiple deteriorationmechanismsrdquo Structural Safety vol 33 no 3 pp 206ndash217 2011

[12] Y-C Ou L-L Tsai and H-H Chen ldquoCyclic performance oflarge-scale corroded reinforced concrete beamsrdquo EarthquakeEngineering and StructuralDynamics vol 41 no 4 pp 593ndash6042012

[13] Y Ma Y Che and J Gong ldquoBehavior of corrosion damagedcircular reinforced concrete columns under cyclic loadingrdquoConstruction and Building Materials vol 29 pp 548ndash556 2012

[14] A Meda S Mostosi Z Rinaldi and P Riva ldquoExperimentalevaluation of the corrosion influence on the cyclic behaviour ofRC columnsrdquo Engineering Structures vol 76 pp 112ndash123 2014

[15] A A Almusallam ldquoEffect of degree of corrosion on theproperties of reinforcing steel barsrdquo Construction and BuildingMaterials vol 15 no 8 pp 361ndash368 2001

[16] Y G Du L A Clark and A H C Chan ldquoResidual capacity ofcorroded reinforcing barsrdquoMagazine of Concrete Research vol57 no 3 pp 135ndash147 2005

[17] Y G Du L A Clarkt and A H C Chan ldquoEffect of corrosionon ductility of reinforcing barsrdquoMagazine of Concrete Researchvol 57 no 7 pp 407ndash419 2005

[18] J Cairns G A Plizzari Y Du D W Law and C FranzonildquoMechanical properties of corrosion-damaged reinforcementrdquoACI Materials Journal vol 102 no 4 pp 256ndash264 2005

[19] C A ApostolopoulosM P Papadopoulos and S G PantelakisldquoTensile behavior of corroded reinforcing steel bars BSt 500srdquoConstruction and Building Materials vol 20 no 9 pp 782ndash7892006

[20] C A Apostolopoulos ldquoMechanical behavior of corroded rein-forcing steel bars S500s tempcore under low cycle fatiguerdquoConstruction andBuildingMaterials vol 21 no 7 pp 1447ndash14562007

[21] M M Kashani A J Crewe and N A Alexander ldquoNonlinearstress-strain behaviour of corrosion-damaged reinforcing barsincluding inelastic bucklingrdquo Engineering Structures vol 48 pp417ndash429 2013

[22] M M Kashani A J Crewe and N A Alexander ldquoNonlinearcyclic response of corrosion-damaged reinforcing bars with theeffect of bucklingrdquo Construction and Building Materials vol 41pp 388ndash400 2013

[23] M M Kashani A J Crewe and N A Alexander ldquoUse of a 3Doptical measurement technique for stochastic corrosion patternanalysis of reinforcing bars subjected to accelerated corrosionrdquoCorrosion Science vol 73 pp 208ndash221 2013

[24] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoFinite element investigation of the influence of corrosionpattern on inelastic buckling and cyclic response of corrodedreinforcing barsrdquo Engineering Structures vol 75 pp 113ndash1252014

Advances in Materials Science and Engineering 15

[25] M M Kashani Seismic performance of corroded rc bridge piersdevelopment of a multi-mechanical nonlinear fibre beam-columnmodel [PhD thesis] University of Bristol Bristol UK 2014

[26] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part I Formula-tionrdquo Earthquake Engineering and Structural Dynamics vol 25no 7 pp 711ndash725 1996

[27] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part II Applica-tionsrdquoEarthquake Engineering and Structural Dynamics vol 25no 7 pp 727ndash742 1996

[28] The Open System for Earthquake Engineering Simulation(OpenSees) Pacific Earthquake Engineering Research CentreUniversity of California Berkeley Berkeley Calif USA 2011

[29] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoPhenomenological hysteretic model for corroded reinforcingbars including inelastic buckling and low-cycle fatigue degrada-tionrdquo Computers and Structures vol 156 article 5393 pp 58ndash712015

[30] J Coleman and E Spacone ldquoLocalization issues in force-basedframe elementsrdquo Journal of Structural Engineering vol 127 no11 pp 1257ndash1265 2001

[31] J S Pugh Numerical simulation of walls and seismic designrecommendations for walled buildings [PhD thesis] Universityof Washington Seattle Wash USA 2012

[32] D V Val and R E Melchers ldquoReliability of deteriorating RCslab bridgesrdquo Journal of Structural Engineering vol 123 no 12pp 1638ndash1644 1997

[33] M S Darmawan and M G Stewart ldquoEffect of pitting corro-sion on capacity of prestressing wiresrdquo Magazine of ConcreteResearch vol 59 no 2 pp 131ndash139 2007

[34] R P Dhakal and K Maekawa ldquoReinforcement stability andfracture of cover concrete in reinforced concrete membersrdquoJournal of Structural Engineering vol 128 no 10 pp 1253ndash12622002

[35] C Lee J F Bonacci M D A Thomas et al ldquoAcceleratedcorrosion and repair of reinforced concrete columns usingcarbon fibre reinforced polymer sheetsrdquo Canadian Journal ofCivil Engineering vol 27 no 5 pp 941ndash948 2000

[36] W Aquino Long-term performance of seismically rehabilitatedcorrosion-damaged columns [PhD thesis] University of Illinoisat Urbana-Champaign Champaign Ill USA 2002

[37] S Timoshenko and J Gere Theory of Elastic StabilityMacGraw-Hill New York NY USA 1963

[38] S J Pantazopoulou ldquoDetailing for reinforcement stability in RCmembersrdquo Journal of Structural Engineering vol 124 no 6 pp623ndash632 1998

[39] J B Mander M J N Priestley and R Park ldquoObserved stress-strain behavior of confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1827ndash1849 1988

[40] J B Mander M J Priestley and R Park ldquoTheoretical stress-strain model for confined concreterdquo Journal of Structural Engi-neering (United States) vol 114 no 8 pp 1804ndash1826 1988

[41] S Popovics ldquoAnumerical approach to the complete stress-straincurve of concreterdquo Cement and Concrete Research vol 3 no 5pp 583ndash599 1973

[42] I D Karsan and J O Jirsa ldquoBehavior of concrete undercompressive loadingrdquo Journal of Structural Division vol 95article ST12 1969

[43] M P Berry andMO Eberhard ldquoPerformancemodeling strate-gies for modern reinforced concrete bridge columnsrdquo PEER

Research Report University of California Berkeley BerkeleyCalif USA 2006

[44] B D Scott R Park and M J N Priestley ldquoStress-strainbehavior of concrete confined by overlapping hoops at low andhigh strain ratesrdquo Journal of the American Concrete Institute vol79 no 1 pp 13ndash27 1982

[45] A S Al-Harthy M G Stewart and J Mullard ldquoConcrete covercracking caused by steel reinforcement corrosionrdquoMagazine ofConcrete Research vol 63 no 9 pp 655ndash667 2011

[46] T Vidal A Castel and R Francois ldquoAnalyzing crack width topredict corrosion in reinforced concreterdquo Cement and ConcreteResearch vol 34 no 1 pp 165ndash174 2004

[47] F J Molina C Alonso and C Andrade ldquoCover cracking as afunction of rebar corrosion part 2-numerical modelrdquoMaterialsand Structures vol 26 no 9 pp 532ndash548 1993

[48] F J Vecchio and M P Collins ldquoThe modified compression-field theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[49] D Coronelli and P Gambarova ldquoStructural assessment ofcorroded reinforced concrete beams modeling guidelinesrdquoJournal of Structural Engineering vol 130 no 8 pp 1214ndash12242004

[50] D E Lehman and J P Moehle ldquoSeismic performance of well-confined concrete columnsrdquo PEER Research Report Universityof California at Berkeley 2000

[51] L N Lowes and A Altoontash ldquoModeling reinforced-concretebeam-column joints subjected to cyclic loadingrdquo Journal ofStructural Engineering vol 129 no 12 pp 1686ndash1697 2003

[52] M Berry M Parrish and M Eberhard ldquoPerformance databaseUserrsquos manualrdquo in Pacific Earthquake Engineering ResearchCentre 2004 University of California at Berkeley 2004httpwwwcewashingtonedusimpeera1

[53] A N Kallias and M Imran Rafiq ldquoFinite element investigationof the structural response of corroded RC beamsrdquo EngineeringStructures vol 32 no 9 pp 2984ndash2994 2010

[54] M J Moyer and M J Kowalsky ldquoInfluence of tension strain onbuckling of reinforcement in concrete columnsrdquo ACI StructuralJournal vol 100 no 1 pp 75ndash85 2003

[55] K A T Vu andM G Stewart ldquoStructural reliability of concretebridges including improved chloride-induced corrosion mod-elsrdquo Structural Safety vol 22 no 4 pp 313ndash333 2000

[56] D V Val ldquoFactors affecting life-cycle cost analysis of RCstructures in chloride contaminated environmentsrdquo Journal ofInfrastructure Systems vol 13 no 2 pp 135ndash143 2007

[57] J P BroomfieldCorrosion of Steel in Concrete Taylor amp FrancisLondon UK 2nd edition 2007

[58] M M Kashani P Alagheband R Khan and S Davis ldquoImpactof corrosion on low-cycle fatigue degradation of reinforcingbars with the effect of inelastic bucklingrdquo International Journalof Fatigue vol 77 pp 174ndash185 2015

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 15

[25] M M Kashani Seismic performance of corroded rc bridge piersdevelopment of a multi-mechanical nonlinear fibre beam-columnmodel [PhD thesis] University of Bristol Bristol UK 2014

[26] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part I Formula-tionrdquo Earthquake Engineering and Structural Dynamics vol 25no 7 pp 711ndash725 1996

[27] E Spacone F C Filippou and F F Taucer ldquoFibre beam-columnmodel for non-linear analysis of RC frames part II Applica-tionsrdquoEarthquake Engineering and Structural Dynamics vol 25no 7 pp 727ndash742 1996

[28] The Open System for Earthquake Engineering Simulation(OpenSees) Pacific Earthquake Engineering Research CentreUniversity of California Berkeley Berkeley Calif USA 2011

[29] M M Kashani L N Lowes A J Crewe and N A AlexanderldquoPhenomenological hysteretic model for corroded reinforcingbars including inelastic buckling and low-cycle fatigue degrada-tionrdquo Computers and Structures vol 156 article 5393 pp 58ndash712015

[30] J Coleman and E Spacone ldquoLocalization issues in force-basedframe elementsrdquo Journal of Structural Engineering vol 127 no11 pp 1257ndash1265 2001

[31] J S Pugh Numerical simulation of walls and seismic designrecommendations for walled buildings [PhD thesis] Universityof Washington Seattle Wash USA 2012

[32] D V Val and R E Melchers ldquoReliability of deteriorating RCslab bridgesrdquo Journal of Structural Engineering vol 123 no 12pp 1638ndash1644 1997

[33] M S Darmawan and M G Stewart ldquoEffect of pitting corro-sion on capacity of prestressing wiresrdquo Magazine of ConcreteResearch vol 59 no 2 pp 131ndash139 2007

[34] R P Dhakal and K Maekawa ldquoReinforcement stability andfracture of cover concrete in reinforced concrete membersrdquoJournal of Structural Engineering vol 128 no 10 pp 1253ndash12622002

[35] C Lee J F Bonacci M D A Thomas et al ldquoAcceleratedcorrosion and repair of reinforced concrete columns usingcarbon fibre reinforced polymer sheetsrdquo Canadian Journal ofCivil Engineering vol 27 no 5 pp 941ndash948 2000

[36] W Aquino Long-term performance of seismically rehabilitatedcorrosion-damaged columns [PhD thesis] University of Illinoisat Urbana-Champaign Champaign Ill USA 2002

[37] S Timoshenko and J Gere Theory of Elastic StabilityMacGraw-Hill New York NY USA 1963

[38] S J Pantazopoulou ldquoDetailing for reinforcement stability in RCmembersrdquo Journal of Structural Engineering vol 124 no 6 pp623ndash632 1998

[39] J B Mander M J N Priestley and R Park ldquoObserved stress-strain behavior of confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1827ndash1849 1988

[40] J B Mander M J Priestley and R Park ldquoTheoretical stress-strain model for confined concreterdquo Journal of Structural Engi-neering (United States) vol 114 no 8 pp 1804ndash1826 1988

[41] S Popovics ldquoAnumerical approach to the complete stress-straincurve of concreterdquo Cement and Concrete Research vol 3 no 5pp 583ndash599 1973

[42] I D Karsan and J O Jirsa ldquoBehavior of concrete undercompressive loadingrdquo Journal of Structural Division vol 95article ST12 1969

[43] M P Berry andMO Eberhard ldquoPerformancemodeling strate-gies for modern reinforced concrete bridge columnsrdquo PEER

Research Report University of California Berkeley BerkeleyCalif USA 2006

[44] B D Scott R Park and M J N Priestley ldquoStress-strainbehavior of concrete confined by overlapping hoops at low andhigh strain ratesrdquo Journal of the American Concrete Institute vol79 no 1 pp 13ndash27 1982

[45] A S Al-Harthy M G Stewart and J Mullard ldquoConcrete covercracking caused by steel reinforcement corrosionrdquoMagazine ofConcrete Research vol 63 no 9 pp 655ndash667 2011

[46] T Vidal A Castel and R Francois ldquoAnalyzing crack width topredict corrosion in reinforced concreterdquo Cement and ConcreteResearch vol 34 no 1 pp 165ndash174 2004

[47] F J Molina C Alonso and C Andrade ldquoCover cracking as afunction of rebar corrosion part 2-numerical modelrdquoMaterialsand Structures vol 26 no 9 pp 532ndash548 1993

[48] F J Vecchio and M P Collins ldquoThe modified compression-field theory for reinforced concrete elements subjected to shearrdquoJournal of the American Concrete Institute vol 83 no 2 pp 219ndash231 1986

[49] D Coronelli and P Gambarova ldquoStructural assessment ofcorroded reinforced concrete beams modeling guidelinesrdquoJournal of Structural Engineering vol 130 no 8 pp 1214ndash12242004

[50] D E Lehman and J P Moehle ldquoSeismic performance of well-confined concrete columnsrdquo PEER Research Report Universityof California at Berkeley 2000

[51] L N Lowes and A Altoontash ldquoModeling reinforced-concretebeam-column joints subjected to cyclic loadingrdquo Journal ofStructural Engineering vol 129 no 12 pp 1686ndash1697 2003

[52] M Berry M Parrish and M Eberhard ldquoPerformance databaseUserrsquos manualrdquo in Pacific Earthquake Engineering ResearchCentre 2004 University of California at Berkeley 2004httpwwwcewashingtonedusimpeera1

[53] A N Kallias and M Imran Rafiq ldquoFinite element investigationof the structural response of corroded RC beamsrdquo EngineeringStructures vol 32 no 9 pp 2984ndash2994 2010

[54] M J Moyer and M J Kowalsky ldquoInfluence of tension strain onbuckling of reinforcement in concrete columnsrdquo ACI StructuralJournal vol 100 no 1 pp 75ndash85 2003

[55] K A T Vu andM G Stewart ldquoStructural reliability of concretebridges including improved chloride-induced corrosion mod-elsrdquo Structural Safety vol 22 no 4 pp 313ndash333 2000

[56] D V Val ldquoFactors affecting life-cycle cost analysis of RCstructures in chloride contaminated environmentsrdquo Journal ofInfrastructure Systems vol 13 no 2 pp 135ndash143 2007

[57] J P BroomfieldCorrosion of Steel in Concrete Taylor amp FrancisLondon UK 2nd edition 2007

[58] M M Kashani P Alagheband R Khan and S Davis ldquoImpactof corrosion on low-cycle fatigue degradation of reinforcingbars with the effect of inelastic bucklingrdquo International Journalof Fatigue vol 77 pp 174ndash185 2015

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials