seismic response analysis of pier considering durability damage...

Research ArticleSeismic Response Analysis of Pier considering DurabilityDamage Repair

Yan Liang 1 Liangliang Li1 Ruimin Mao2 and Xiaoye Shi1

1School of Civil Engineering Zhengzhou University Zhengzhou 450001 China2Bridge Design Institute Henan Provincial Transportation Planning Survey and Design Institute Zhengzhou 450001 China

Correspondence should be addressed to Yan Liang liangyanzzueducn

Received 11 January 2020 Revised 9 June 2020 Accepted 4 July 2020 Published 22 July 2020

Academic Editor Yann Malecot

Copyright copy 2020 Yan Liang et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

At present most of the research studies on the seismic performance of the durability degraded reinforced concrete structure onlyconsider the influence of a single factor is paper comprehensively considers the factors such as concrete carbonization steelcorrosion and bond slip performance degradation caused by other durability factors and durability damage repair and studies theinfluence of the above factors on the seismic performance of bridge structures Based on the finite element model considering thebond slip and the material parameters of time-varying durability damage the seismic performance analysis model of the pier isestablished considering material durability damage repair in different service periods en the effect of material durabilitydamage repair on the seismic performance of the pier is examinede results show that the displacement of the pier top increasesthe curvature of the pier bottom decreases and the moment-curvature curve pinching phenomenon is further evident whenconsidering the bond slip When considering the durability damage repair of materials the curvature considerably decreases (themaximum value is approximately 1604) with the extension of the service time of the bridge and the pier damage issubstantially reduced

1 Introduction

In recent years the durability of existing bridges has becomea research hotspot With the extension of the service time ofconcrete bridges concrete is carbonated by the influence ofthe surrounding air e change in the chemical composi-tion of the pore solution weakens the passivation andprotection of steel bars Subsequently steel bars are corrodedby the influence of the surrounding chloride ions Corrosionof steel bars in concrete reduces the diameter strength andelasticity modulus of steel bars cracks or even exfoliatesconcrete cover It weakens the bond between steel bars andconcrete [1ndash3]

Most of the offshore bridges are under the conditions ofthe marine environment and warm climate e highchloride ion concentration in air leads to serious corrosionof steel bars and the reduction of bond stress between steelbars and concrete Consequently such phenomenon reducesthe bearing capacity and durability of bridges and seriously

affects the safety and seismic performance of bridge struc-tures in the entire life cycle erefore the damage evolutionlaw of concrete bridges in an offshore environment must beinvestigated and the seismic response of concrete bridgesunder earthquake must be analysed

At present scholars at home and abroad have done a lotof research on carbonation of concrete (influencing factorsof carbonization and the prediction models of carbonizationdepth [4ndash6]) and prediction model of steel corrosion rate[7ndash13] eoretical analysis [14] and experimental research[15ndash17] have been performed on the seismic performance ofreinforced concrete structures after durability damageHowever research on the seismic performance [18] ofdurable degraded reinforced concrete structures [19] mostlyconsiders the single factor of steel corrosion or concretecarbonization It disregards the coupling effects of concretecarbonization steel corrosion degradation of bond slip anddurable damage repair on seismic performance ereforebased on the OpenSees platform a finite element analysis

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 2198310 16 pageshttpsdoiorg10115520202198310

model considering the factors of concrete carbonation re-inforcement corrosion bond slip degradation and materialdurability damage repair is established during the service lifeof the bridge e influence of the above factors on theseismic performance of the structure or components underthe offshore atmospheric environment is studied

2 Brief Introduction to the Project

In this study the Y2 pier of a 6times 60m offshore large-spancontinuous beam bridge is used as the research object epier adopts C50 concrete HRB335 as longitudinal rein-forcement with 32mm diameter and R235 as stirrup with16mm diameter e pier is 364m high the cross section ishexagonal the axial compression ratio is 0197 and thethickness of the concrete cover is 9 cm e geologicalcondition of the bridge site is goode bottom of the pier isa 15m thick expanded foundation and the top is consol-idated with the beam body e surrounding rock is weakweathered rock e base material is C25 concrete e siteconditions of the bridge are as follows 7-degree seismicfortification intensity of the first group and the second-classsite e stress state of concrete has a certain effect on itsstrength [20] Considering the influence of stirrups on theconcrete in the core area the pier concrete section is dividedinto constraint and protective concretes on the basis ofManderrsquos model Figure 1 is a detailed view of the bridge

3 The Finite Element Analysis Model

31Definition of theModel A concrete01 constitutive modelis adopted for the concrete material of the pier Concrete01 isbased on the uniaxial compressive stress-strain relationshipof KentndashScottndashPark concrete with linear unloadingreloading stiffness which ignores the tensile strength ofconcrete

Steel02 constitutive model is used for longitudinal re-inforcement Steel02 material model is a uniaxial isotropicGiuffrendashMenegottondashPinto model [21] which can efficientlysimulate the nonlinear behaviour of reinforcement underseismic load including the degradation of strength andstiffness e skeleton curve is a two-line model eBond_SP01 constitutive model in OpenSees material libraryis used for the bonded slip material

In OpenSees software simulation the pier body is di-vided into 37 nonlinear beam-column elements each ofwhich has three integral control points e lengths of units1 to 36 and 37 are 1 and 044m respectively e expandedfoundation at the pier bottom is consolidated directlywithout considering the interaction between pile and soile zero-length section element is used to simulate thecorner and displacement deformations caused by bond slipat the pier bottom e consolidation between the top andbeam is simplified as a zero-length element Node i repre-sents the pier top and node j represents the contact pointbetween the pier and beam and is consolidated As the piersection is not shaped like a regular rectangle or fan theconcrete should be divided in a quadrilateral Figure 1

presents the bridge details and specific sectional fibre di-vision of the bridge pier

32 Ground Motion Inputting When the time-historyanalysis method is used to analyse the seismic response ofthe bridge structure the reasonable selection of seismic waveis the premise of the seismic analysis To ensure the reliabilityof calculation results an appropriate seismic wave must beselected in combination with site conditions of the bridge

Seismic parameters are the bases of seismic designDifferent bridges have various requirements for seismicsafety evaluation which are mainly determined by bridgetype and safety risk and social impact Based on the zoningmap of ground motion parameters and site conditions(seismic fortification intensity of 7 degrees group I and classII site) of bridge piers in China ten seismic waves with amagnitude of about 7 are selected from the existing strongearthquake records [22] for incremental dynamic analysise selected types should be the same as the site conditionsof the research bridge and their characteristic periodsshould be close or the same [23ndash25]

Peak ground acceleration (PGA) [26ndash30] is used as theindex of ground motion intensity As the selected PGA ofseismic wave is different from the required PGA the am-plitude of the selected PGA should be adjusted using thefollowing equation

aprime(t) AprimeA

a(t) (1)

where aprime(t) and a(t) are time-history curves of the accel-eration of seismic wave after and before amplitude modu-lation respectively and Aprime and A are peak accelerations ofseismic wave after and before amplitude modulationrespectively

Based on the bridge site conditions the PGA of theseven-degree fortification design ground motion is 01 g(015 g) corresponding to the PGA of ground motion whoseexceeding probability is 10 in 50 years To simulate theearthquake that the pier may encounter the selected seismicwave should be adjusted in the calculation model such thatthe vertical and horizontal peak accelerations can satisfy therequirements of E2 seismic action of 03 and 06 g respec-tively Table 1 shows the adjustment of horizontal andvertical ground motions

4 Research on MechanicalProperties of Materials

41 Study on the Properties of Carbonized Concrete Giventhat the bridge structure requires high ductility of the pierthe arrangement of stirrups can effectively restrain coreconcrete and improve the strength and ductility of concretein the core area e restraint effect of stirrups should besimulated during finite element modellinge coefficient ofconstrained effect is considered on the basis of Manderrsquosconstitutive model [31] of constrained concrete e re-straint effect of stirrups on the core concrete is equivalent tothe effective uniform lateral pressure e stress-strain

2 Advances in Civil Engineering

constitutive relationship curve of the core concrete ismodified which can effectively evaluate the ultimate bearingcapacity and ductility of bridge structures

e stochastic process model of concrete carbonationdepth is as follows [32]

X(t) kt

radic

k 3Kco2Kk1Kk2Kk3KFT14

RH15

(1 minus RH)58

fcukminus 0761113888 1113889

KF 10 + 1334F03

(2)

where X(t) is the depth of concrete carbonization t is thetime of carbonization K is the coefficient of carbonizationKco2 is the coefficient of influence of CO2 concentrationand Kk1 is the influence coefficient of position e anglepart is 14 and the nonangle part is 10 Kk2 is the coefficientof influence of curing and pouring and 113 is the coef-ficient of influence of pouring surface Kk3 is the coefficient

of influence of working stress 10 is the coefficient of in-fluence by compression and 12 is the coefficient of in-fluence by tension T is the concrete temperature RH is therelative humidity of the environment KF is the replace-ment coefficient of fly ash fcuk is the cubic compressivestrength of concrete and F is the weight ratio of fly ash

Based on the bridge design construction and siteselection in this paper Kco2 12 Kk1 10Kk2 12Kk3 10 T 165degC RH 77 and F 0 Fromthis we can get the carbonization coefficient of C50concrete k 0541mm

a

radic

Existing research results [33] indicate that the con-crete carbonization rate often uses the carbonizationdepth as a parameter However the same carbonizationdepth in the structure or component of different cross-sectional areas has a great influence on the structuralproperties e environment with different surfaces of thesame structure after carbonization is not the same euse of carbonization depth as parameter ignores thecross-sectional size effect and environmental impact ofthe actual component To consider the size effect ofcomponent sections and reasonably reflect the evolutionlaw of mechanical properties of concrete after

j

60m 60m 60m 60m 60m 60m

Y1

Y2 Y3

Y4Y5

(a)373635343332

54321

iZero-length

elements

Nonlinearbeam-column

elements

(b) (c)

Cover concrete

Confined concrete

Figure 1 e bridge details (a) bridge schematic (b) the simplified model of bridge pier (c) pier cross section

Table 1 Horizontal and vertical time-history analysis of seismic wave adjustment

Seismic wave Magnitude PGA (g) Adjustment coefficient of PGA(03 g)

Adjustment coefficient of PGA(06 g)

Loma Prieta America 1989 693 0076 395 789Northridge 01 America 1994 669 035 086 171Cape Mendocino America 1992 701 019 158 316Landers America 1992 728 004 750 1500Hector Mine America 1999 713 005 600 1200Coalinga 01 America 1983 636 012 250 500Taiwan SMART1 (45) Taiwan China1986 73 016 188 375

Chi-Chi Taiwan China 1999 762 006 500 1000Duzce Turkey 1999 714 001 3000 6000Kocaeli Turkey 1999 751 031 097 194

Advances in Civil Engineering 3

carbonization the relative carbonization area [34] of theconcrete section is selected as the parameter to study theperformance of carbonized concrete

e carbonation rate of concrete can be calculated usingthe following equation

S Ac

A (3)

where S is the relative carbonization area Ac is the car-bonization area and A is the total area of the structure orcomponent section

According to the above formula when the service life is0 30 50 70 100 and 120 years the carbonation depth of thepier is 0 296 383 453 541 and 593mm respectively andthe carbonation rate of the corresponding cover concrete is0 039 050 059 071 and 078 respectivelyTable 2 shows the elastic modulus and shear modulus of C50in different service periods

42 Studyon theProperties ofCorrodedSteel Bars In offshoreenvironments reinforced concrete structures are susceptibleto corrosion damage because of high chloride content ecorrosion damage process can be divided into three stages[35] diffusion propagation and degradation e ductilityand yield strength of reinforcement will degenerate with thedecrease in reinforcement area and the internal expansionof the structure caused by corrosion will result in thecracking of concrete materials leading to the spalling ofconcrete cover In the past when evaluating the seismicperformance of degraded bridge structures cracks caused bysteel corrosion are often repaired in practical projectsHence the corrosion rate of the important index in steelcorrosion analysis becomes relatively different from theactual situation Before studying the corrosion of steel barsin concrete bridge structures in the offshore environment itis necessary to consider the repair problem when the crackwidth of the cover concrete reaches a critical value

Fickrsquos second diffusion law [36] is often used to fit theprocess of steel bar corrosion affected by air composition inan offshore environment Wu et al [37] stated that therelated parameters will change with variations in time andthe air environment such as the initial time of steel cor-rosion (tinit) the chloride ion concentration on the concretesurface (Cs) and the critical chloride ion concentration onsteel corrosion (Ccr) To some extent these parameters canbe regarded as random variables obeying normaldistribution

According to the calculation models of Vu and Stewart[38] and Du et al [39] we can get the change law of steel bardiameter steel bar yield strength and steel bar corrosion ratewith time steel bar diameter and steel bar yield strengthgradually decrease with time and the steel bar corrosion rategradually increases As the stirrup protection layer isthinner the mechanical properties of the reinforcement aremore degraded e characteristic values of steel bars indifferent service periods are shown in Table 3

is paper refers to the ldquoStandard for Durability As-sessment of Concrete Structuresrdquo (CECS 220-2007) [40] to

estimate the variation law of steel corrosion under a chlorideion erosion environment Without considering the changein chloride ion diffusion coefficient with time the time ofsteel bar corrosion can be estimated using the followingequations

tiprime c

K1113872 1113873

2times 10minus 6 (4)

ti tiprime + 02t1 (5)

where tiprime is the initial corrosion time of reinforcing steelwithout considering the chloride ion diffusion coefficientti is the initial corrosion time of reinforcing steel underoffshore environment t1 is the accumulated time ofchloride ion reaching a stable value on the concretesurface c is the thickness of the concrete cover and K isthe chloride ion corrosion coefficient and according toTable 4 t1(a) is 125 e initial corrosion time of lon-gitudinal reinforcement is 2177 years and that of stirrupsis 1553 years

In the absence of effective measured data the chloride ionconcentration Ms on the surface of concrete in the offshoreatmospheric environment can be estimated according toequation (6) It is assumed that the distance between the bridgestructure to the coastline is 05 km

Ms Msprime k (6)

where Ms is the chloride ion concentration on the concretesurfaceMsprime is the chloride ion concentration on the concretesurface at 01 km away from the coast as shown in Table 5and k is the position correction factor for the distance fromthe coastline as shown in Table 6

e variations in diameter yield strength elasticitymodulus and corrosion rate of steel bars can be obtained usingthe following equations

tcr ti + tc (7)

tc δcr

λcl

(8)

δcr 0012c

d+ 000084fcuk + 0018 (9)

λcl 116 times i times 10minus 3 (10)

ln i 8617 + 0618 ln Msl minus3034

T + 273minus 5 times 10minus 3ρ + ln mcl

(11)

Msl Ms0 + Ms minus Ms0( 1113857 1 minus erfc times 10minus 3

2Dtcr

11139681113888 11138891113890 1113891 (12)

Table 2 Elastic modulus and shear modulus of C50 in differentservice periods

Service life (years) 0 30 50 70 100 120Elasticity modulus(times104MPa) 3450 3457 3458 3460 3462 3463

Shear modulus(times104MPa) 1437 1440 1441 1442 1443 1443


ρ kρ 18 minus Mucl( 1113857 + 10(RH minus 1)

2+ 4 (13)

λcll 45 minus 26λcl( 1113857 times λcl (14)When λcll lt 18λcl λcll 18λcl

d(t)

d0 tleTi

d0 minus 2λ t minus Ti( 1113857 Ti le tleTcr

0 tgeTcr

⎧⎪⎪⎨

⎪⎪⎩(15)

fyc (1 minus 0339ρ)fy (16)

Ex (1 minus 1166ρ)Es (17)

where tc is the time from steel bar corrosion to concretecracking δcr is the depth of steel bar corrosion when theconcrete cracks λcl is the average annual corrosion rate ofsteel bar before concrete cracking d is the diameter of thesteel bar fcuk is the standard value of the concrete cubecompressive strength i is the corrosion current density ofthe steel bar Msl is the chloride ion concentration on thesurface of the steel bar T is the atmospheric environmenttemperature ρ is the concrete resistivity mcl is the localenvironmental coefficient Ms0 is the chloride ion contentadded during concrete preparation Kρ is the coefficientwhen the water cement ratio is 03ndash04 or the concrete isC40ndashC50 K is 111 Mu

cl is the average chloride ion con-centration of the concrete cover RH is the environmentalrelative humidity λcll is the average annual corrosion rate ofthe steel bar after concrete cracking fyc is the yield strengthof corroded steel bars fy is the yield strength of steel barsbefore corrosion Ex is the elastic modulus of steel bars after

corrosion and Es is the elastic modulus of steel bars beforecorrosion

e above two methods of calculating the corrosion rateboth show that the initial corrosion time of stirrups is earlierthan that of the longitudinal bars and the corrosion rate ofstirrups is much higher than that of the longitudinal barsafter the cracking of the cover concrete According to thecalculation method proposed by Vu and Du the corrosionrate of cover concrete after cracking is higher than thatcalculated in the CECS 220-2007ere is a certain deviationbetween the two methods e degradation process of theconcrete structure under the environment is very compli-cated and the various environmental factors are relativelyrandome ldquoCECS 220-2007rdquo is compiled by accumulatinga large amount of engineering practice data and engineeringpractice experience which is more suitable for the appli-cation Due to the research on the durability of concretestructures in Chinarsquos offshore environment this paper usesthe calculation method of ldquoCECS 220-2007rdquo to study thedurability of materials

5 Seismic Response Analysis of the Bridge Pier

51 Seismic Response Analysis in Different Directions ofSeismic Action e pier model is established using Open-Sees software [41] e adjusted horizontal and verticalwaves which are divided into longitudinal lateral simul-taneous longitudinal and lateral simultaneous vertical andlongitudinal and simultaneous vertical and lateral actionsare input as ground motions e displacement momentcurvature and axial force responses of the pier model arecalculated e influence of seismic wave in different di-rections on the seismic response of the pier is analysed

Figure 2 shows the maximum displacement of the piertop corresponding to 10 waves in 5 different seismic actioncombinations e graph indicates that under longitudinalseismic action the longitudinal peak displacement of thepier top is considerably larger than the transverse andvertical displacements e maximum values of the longi-tudinal transverse and vertical displacements of theLanders wave pier top are 4716 0 and 251mm

Table 3 e characteristic values of steel bars corresponding to different service periods

Service life (years) 0 30 50 70 100 120Yield strength of stirrup (MPa) 235 18432 16675 15350 13904 13212Diameter of stirrup (mm) 16 1197 1021 865 653 522Corrosion rate of stirrup () 0 1487 4001 5635 7354 8182Yield strength of longitudinal bar (MPa) 335 32686 32359 32083 31732 31528Diameter of longitudinal bar (mm) 32 2858 2708 2575 2395 2284Corrosion rate of longitudinal bar () 0 0 1338 2299 3403 4017

Table 4 Environmental grade and parameters of chloride erosion

Environmental category Environmental grade Environmental condition t1(a)

Offshore atmospheric environment

IIIa Within one kilometer from the coast 20sim30IIIb Within one kilometer from the coast 15sim20IIIc Within one kilometer from the coast 10sim15IIId Within one kilometer from the coast 10

Table 5 Chlorine ion concentration Msprime at 01 km from the coast

fcuk (MPa) 40 30 25 20Msprime (kgm3) 32 40 46 52

Table 6 Correction coefficient k of chloride ion concentration

Distance from the coast(km)

Near thecoastline 01 025 05 10

Correction factor 196 10 066 044 033


0

200

400

600

800

1000D

ispla

cem

ent o

f pie

r top

(mm

)

2 4 6 8 100Seismic wavenumber

Longitudinal displacementTransverse displacementVertical displacement

(a)

0

600

1200

1800

Disp

lace

men

t of p

ier t

op (m

m)



(b)

0

600

1200

1800

Disp

lace

men

t of p

ier t

op (m

m)



(c)

0

200

400

600

800D

ispla

cem

ent o

f pie

r top

(mm

)



(d)

0

600

1200

1800

2400

Disp

lace

men

t of p

ier t

op (m

m)



(e)

Figure 2 Maximum displacement of pier top under different seismic action combinations (a) longitudinal action (b) transverse action(c) longitudinal and transverse simultaneous action (d) longitudinal and vertical simultaneous action (e) transverse and vertical si-multaneous action


respectively Under the effect of transverse earthquakes thetransverse peak displacement of the pier top is considerablylarger than the longitudinal and vertical peak displacementse maximum longitudinal transverse and vertical dis-placements of the pier top of the Landers wave are 0 9330and 390mm respectively e direction of the main dis-placement of the pier is consistent with that of groundmotion Under the simultaneous action of longitudinal andtransverse earthquakes the maximum longitudinal trans-verse and vertical displacements of the pier top corre-sponding to the Landers wave are 4638 8470 and 382mmrespectively e transverse displacement of the pier top isconsiderably larger than the longitudinal and vertical dis-placements e transverse seismic response of the high pierdeserves attention due to the small transverse stiffnessUnder the simultaneous action of longitudinal and verticalearthquakes the maximum longitudinal and vertical dis-placements of the pier top corresponding to the Landerswave are 4717 and 266mm respectively e maximumtransverse and vertical displacements of the pier top cor-responding to the Landers wave are 12451 and 551mmrespectively under the simultaneous action of transverseand vertical earthquakes Vertical seismic action signifi-cantly increases the vertical seismic response

It can be obtained through analysis that the peakmoment and curvature of the pier bottom under the actionof the longitudinal earthquake and the simultaneous actionof longitudinal and transverse earthquakes are larger thanthose under the simultaneous action of longitudinal andvertical earthquakes e moment-curvature curves underthese three types of ground motion are compared andanalysed and the other two are not discussed

Figure 3 presents the moment-curvature curve of thepier bottom of 10 seismic waves e analysis shows thatthe moment-curvature curve of the pier bottom is fullunder the simultaneous action of longitudinal andtransverse earthquakes and no remarkable pinchingphenomenon was observed e curvature value of thepier bottom is considerably increased compared with thatof longitudinal earthquakes e maximum curvature ofthe pier bottom under longitudinal earthquake is 0029and that under the simultaneous action of longitudinaland transverse earthquakes is 0044 Under the simulta-neous action of vertical and longitudinal earthquakes andtransverse and vertical earthquakes the moment-curva-ture curve has no evident difference compared with theaction of a longitudinal earthquake e maximum valueunder the simultaneous action of vertical and longitudinalearthquakes is 0030 Under the action of transverse andvertical earthquakes the maximum curvature value is0033 It can be seen that the pier is most sensitive tolongitudinal and transverse seismic waves

Under longitudinal seismic action the displacement ofthe pier top of the Landers wave is the largest among the tenseismic waves with a value of 4716mm Figures 4(a) and4(b) show the displacement time-history curve of the piertop and the curvature time-history curve of the pier bottomunder the Landers wave respectively Under the action ofother seismic waves the displacement time-history curve of

the pier top and the curvature time-history curve of the pierbottom have the same law which is not described here epictures show that under the action of the Landers wavethe maximum displacement of the pier top and the max-imum curvature of pier bottom occur at 3378 s efluctuation law of the two time-history curves is the same

6 Seismic Response Analysis consideringBond Slip

Given the limited space this paper only presents the effect ofbond slip on the seismic response of the pier under theaction of a longitudinal earthquake In this paper threewaves are selected to analyse the displacement of the pier topand the moment-curvature curves at the bottom of the pier

ere are obvious differences in the three-pier topdisplacement time-history curves in Figure 5 Whetherconsidering or not considering the bond slip the maximumdisplacement of the pier top occurs at the same time For theNorthridge wave the corresponding maximum displace-ments of the two models are 2492 and 3181mm (276increase) For the Taiwan wave the corresponding maxi-mum displacements of the two models are 2816 and3544mm (259 increase) For the Duzce wave the cor-responding maximum displacements of the two models are3065 and 3948mm (288 increase) In Figure 6 thelongitudinal peak displacements of 10 waves with the bondslip model are larger than those without the bond slip modeland are increased by 268 276 147 274 293308 259 266 288 and 259 and the displace-ment is relatively different e deformation of the pier topcan be underestimated if the influence of bond slip at the pierbottom is ignored in the seismic calculation of the pierUnder the action of the longitudinal earthquake the max-imum displacement of the pier top is 4807mm the yielddisplacement of the pier is 2766mm and the ultimatedisplacement is 9831mm e pier has not reached theultimate state which indicates that the pier can still play acertain function under the action of a rare earthquake

Figure 7 is the moment-curvature curve of theNorthridge wave the Taiwan wave and the Duzce waveObviously the curvature of the pier bottom considering thebond slip model is considerably smaller than that withoutconsidering the bond slip For the Northridge wave thepeak curvatures before and after considering the bond slipare 00139 and 00106 (237 decrease) respectively epeak moments are 467761 and 465143MPa (06 de-crease) respectively For the Taiwan wave the peak cur-vatures before and after considering the bond slip are00189 and 00156 (175 decrease) respectively e peakmoments are 469268 and 461787MPa (16 decrease)respectively For the Duzce wave the peak curvaturesbefore and after considering the bond slip are 00246 and00219 (110 decrease) respectively e peak momentsare 487202 and 482233MPa (10 decrease) respectivelye moment-curvature curve pinching phenomenon isfurther evident when considering the bond slip model ofthe pier If the influence factors of the bond slip are


neglected in the simulation calculation the energy dissi-pation capacity of the structure or component will beoverestimated

7 Seismic Response Analysis consideringDurability Damage Repair

In previous theoretical studies on steel corrosion the repair ofconcrete cracks in the concrete cover is generally ignored in

practical projects e corrosion rate of steel after the concretecover cracks is higher than the actual value which affects thesubsequent research results of concrete structures e as-sumption is that under the action of chloride ion erosion thecracks of concrete cover will be repaired when they reach1mm After repair the corrosion rate of steel bars in the pierwill be the same as that before cracking Vida et al [42] ob-tained the calculation method of crack width by studying thecorrosion of reinforced concrete structure as follows

6

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)

ndash005 0 005Curvature (1m)

LengthwaysLongitudinal and transverse

times104

(a)

6

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)

LengthwaysLongitudinal and vertical

ndash004 004ndash002 0020Curvature (1m)

times104

(b)

6

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104

LengthwaysTransverse and vertical

(c)

Figure 3 Moment-curvature curves of 10 waves at the pier bottom (a) longitudinal and lateral simultaneous action (b) vertical andlongitudinal simultaneous action (c) transverse and vertical simultaneous action


w k ΔAs minus ΔAs0( 1113857

ΔAs π4

2αxcorrds0 minus α2xcorr2

1113872 1113873

ΔAs0 As 1 minus 1 minusα

ds0753 + 932

X

ds01113888 1113889 times 10minus 3

1113890 1113891

2⎡⎣ ⎤⎦

(18)

whereW is the crack width k is the coefficient with a value of00575 and α is the corrosion coefficient (α1 for uniformrust and α 4 for nonuniform rust) ds0 is the bar diameterXis the concrete cover depth ∆As0 and ∆As are the steel cross-section losses As is the sound steel cross section and xcorr isthe corrosion depth

e influence of chloride ion on offshore bridges israndom us the corrosion coefficient is 4 According toVidarsquos calculation method the width of concrete cover fromcrack to crack is 1mm which lasts for 0759 yearsAccording to the CECS 220-2007 the longitudinal steel barsbegin rusting to crack the concrete covere average annualcorrosion rate of steel bars is 0015mmyear e averagecorrosion rate is 0061mmyear after concrete covercracking When the crack width reaches 1mm the crack isrepaired e corrosion rate of repaired steel bars should beconsistent with that before concrete cover cracking Figure 8shows the corrosion rate of steel bars considering crackrepaire corrosion rate of steel bars in the service period ofthe bridge decreases significantly when considering therepair When the bridge is in service for 120 years thecorrosion rate of longitudinal steel bars decreases by 6599and the corrosion rate of stirrups decreases by 5748Hence the effect of the crack repair of the concrete cover onthe durability of concrete structures should be considered infuture durability evaluations

Based on the above calculation method we can obtainthe various rules of the diameter yield strength and elasticmodulus of longitudinal stress bars with time when

considering the crack repair of concrete cover As shown inFigure 9 after considering the crack repair of concrete coverthe longitudinal reinforcement diameter yield strength andelastic modulus are considerably reduced e bridge is inservice for 120 yearse diameter yield strength and elasticmodulus of longitudinal reinforcement decreases by 823508 and 1866 respectively

In the offshore environment the corrosion of steel barsin the longitudinal direction will not directly affect themechanical properties of confined concrete However thedegradation of stirrup material will reduce its confinementto core concrete which will change the peak stress and strainof confined concrete e corresponding diameter and yieldstrength of stirrups can be calculated based on the corrosionrate of stirrups in different service periods Subsequently thepeak stress peak strain and other mechanical properties ofconfined concrete can be calculated using Manderrsquos modele calculation basis and process are the same as above andwill not be repeated here

To study the effect of the crack repair of the concretecover on the pier seismic response the pier models withcorresponding service lives of 0 30 50 70 100 and 120years were modified on the basis of the bond slip model andtime-varying material parameters e seismic actions arethe same as above e seismic response of pier under theTaiwan wave with different service lives is listed here

Figure 10 shows the curvature time-history curve andmoment-curvature curve corresponding to different serviceperiods under Taiwan wave It can be seen that under thelongitudinal action of Taiwan wave the newly built bridgepier after 0 years of service is unaffected by the surroundingenvironment and the structure is intact e moment-curvature curve coincides completely with that withoutconsidering the damage repair model When the bridge pieris in service for 30 years the pier is subjected to concretecarbonization and chloride ion erosion for a relatively shorttime e material is slightly damaged and the structureremains intact e two curves almost completely coincide

500

250

0

ndash250

ndash500

Disp

lace

men

t (m

m)

0 10 20 30 40 50t (s)

(a)

0 10 20 30 40 50t (s)

004

002

0

ndash002

ndash004

Curv

atur

e (1

m)

(b)

Figure 4 Time-history curve of displacement and curvature of the pier top of Landers wave (a) displacement time-history curve(b) curvature time-history curve


400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45t (s)

Bond slip is not consideredConsidering bond slip

(a)

400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45t (s)


(b)

400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45 50t (s)


(c)

Figure 5 Displacement time-history curves of the pier top (a) Northridge wave (b) Taiwan wave (c) Duzce wave


0

100

200

300

400

500

600

700

Disp

lace

men

t (m

m)

100 6 82 4Seismic wavenumber


Figure 6 Longitudinal peak displacement of 10 waves

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)

ndash0015 ndash001 ndash0005 0 0005 001Curvature (1m)

times104


(a)

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002

Curvature (1m)


times104

(b)

Figure 7 Continued


When serving for 50 years the pier is seriously damaged andits structural performance is reduced e maximum cur-vature of the bridge pier is reduced from 00162 to 00158(22 reduction) after considering repairing the damageWhen serving for 70 years pier is seriously damaged emaximum curvature of the bridge pier is reduced from 0017to 0016 (53 reduction) after considering repairing thedamage

When serving for 100 years the pier is seriously dam-aged e maximum curvature of the bridge pier is reducedfrom 00185 to 00164 (113 reduction) after consideringrepairing the damage When serving for 120 years the pier isseriously damaged due to the long-term marine environ-ment e maximum curvature is decreased from 0024 to0020 (160 reduction) after considering damage repairand the pier damage is considerable

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)

Curvature (1m)ndash002 ndash001 0 001 002

times104


(c)

Figure 7 Analysis of moment-curvature curves (a) Northridge wave (b) Taiwan wave (c) Duzce wave

0

5

10

15

20

25

Cor

rosio

n ra

te o

f lon

gitu

dina

l bar

s (

)

20 40 60 80 100 1200Service life (years)

Considering crack repairCrack repair is not considered

(a)

0

10

20

30

40

50

60

70

Cor

rosio

n ra

te o

f stir

rup

()



(b)

Figure 8 Corrosion rate of steel bars (a) corrosion rate of longitudinal bars (b) corrosion rate of stirrups


28

29

30

31

32

Dia

met

er o

f lon

gitu

dina

l bar

(mm

)

20 10060 80 1200 40Service life (years)


(a)

310

315

320

325

330

335

Yiel

d str

engt

h of

long

itudi

nal

bars

(mm

)



(b)

14

15

16

17

18

19

20

Elas

tic m

odul

us o

f lon

gitu

dina

lba

rs (times

10e5

MPa

)



(c)

Figure 9 Change in longitudinal steel characteristics (a) change in diameter (b) change in yield strength (c) change in elasticity modulus

6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002

Curvature (1m)

times104

Damage repair is not consideredConsidering damage repair

(a)

6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002Curvature (1m)

times104


(b)

Figure 10 Continued


8 Conclusions

is study uses the pier of a large-span continuous beambridge in offshore as the research object e effects ofdifferent seismic action directions bond slip and the du-rability damage repair of materials on the seismic perfor-mance of the pier are investigated using OpenSees softwaree main research results are summarized as follows

(1) e corrosion rate of steel bars calculated by differentmethods is obviously different In this paper themore practical CECS method is adopted Accordingto the calculation method proposed by Vu and Duthe corrosion rate of steel bars after cracking ofconcrete cover is greater than that calculated by theCECS 220-2007 ere is a certain deviation betweenthe two methods

(2) Under the simultaneous action of longitudinal andtransverse earthquakes the maximum values of thelongitudinal transverse and vertical displacementsof the Landers wave corresponding to the pier top are4638 8470 and 382mm respectively e trans-verse displacement of the pier top is considerablylarger than the longitudinal and vertical displace-ments e transverse seismic response of the highpier deserves attention due to the small transversestiffness

(3) When considering the bond slip the displacement ofthe pier top is considerably increased e maximumand minimum displacements are increased by 308and 147 respectively e displacement is relativelydifferent Under the action of the Taiwan wave themaximum curvature values obtained without

6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


8

(c)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(d)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(e)

ndash002ndash003 ndash001 0 001 002Curvature (1m)

times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

(f )

Figure 10 Moment-curvature curves of the Taiwan wave in different service lifes (a) 0 years (b) 30 years (c) 50 years (d) 70 years (e) 100years (f ) 120 years


considering and considering the bond slip are 00189and 00156 respectively e maximum curvature ofthe pier is decreased by 175 It shows that whenconsidering the bond slip the bottom curvature issubstantially decreased and the pinching phenomenonof moment-curvature curve is further evident ere-fore the influence of the bond slip cannot be ignored inthe seismic performance analysis of the bridge

(4) With the increase in the service life of bridges theoffshore pier suffers increasingly serious concretecarbonation and chloride ion erosion Consideringthe durability damage repair of materials the cur-vature is increasingly substantially decreased emaximum curvature can be reduced by 160 Afterrepairing the damage of the pier the damage of thepier is obviously reduced which is of great signifi-cance for the safety and economy of the pier

Data Availability

e data sets used to support the findings of this study areincluded within the article

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

is research was supported by the National Natural ScienceFoundation of China (Grant no 51608488) and Scientificand Technological Project of Henan Province China(192102210185)

References

[1] S J Williamson and L A Clark ldquoPressure required to causecover cracking of concrete due to reinforcement corrosionrdquoMagazine of Concrete Research vol 52 no 6 pp 455ndash467 2000

[2] Y Tian J Liu H Xiao et al ldquoExperimental study on bondperformance and damage detection of corroded reinforcedconcrete specimensrdquo Advances in Civil Engineering vol 2020Article ID 7658623 15 pages 2020

[3] C A Apostolopoulos K F Koulouris and A C ApostolopoulosldquoCorrelation of surface cracks of concrete due to corrosion andbond strength (between steel bar and concrete)rdquoAdvances in CivilEngineering vol 2019 Article ID 3438743 12 pages 2019

[4] J H M Visser ldquoInfluence of the carbon dioxide concen-tration on the resistance to carbonation of concreterdquo Con-struction and Building Materials vol 67 pp 8ndash13 2014

[5] G Li L Dong Z A Bai M Lei and J Du ldquoPredictingcarbonation depth for concrete with organic film coatingscombined with ageing effectsrdquo Construction and BuildingMaterials vol 142 pp 59ndash65 2017

[6] Y Chen P Liu and Z Yu ldquoEffects of environmental factorson concrete carbonation depth and compressive strengthrdquoMaterials vol 11 no 11 2018

[7] D Baweja H Roper and V Sirivivatnanon ldquoImprovedelectrochemical determinations of chloride-induced steel

corrosion in concreterdquo Materials Journal vol 100 pp 228ndash238 2003

[8] S Morinaga Prediction of Service Lives of Reinforced ConcreteBuildings Based on Rate of Corrosion of Reinforcing Steel vol23 Shimizu Corporation Tokyo Japan 1988

[9] C Alonso C Andrade and J A Gonzalez ldquoRelation betweenresistivity and corrosion rate of reinforcements in carbonatedmortar made with several cement typesrdquo Cement and Con-crete Research vol 18 no 5 pp 687ndash698 1988

[10] Z Ding Z Qihui H Baohong Z Jin and T Yuchen ldquoldquoTime-varying modelrdquo and macroscopicmicrocosmic mechanismanalysis based on corroded steel mechanical property of bridgedurabilityrdquo Ferroelectrics vol 529 no 1 pp 128ndash134 2018

[11] I C A Esteves R AMedeiros-Junior andM H F MedeirosldquoNDT for bridges durability assessment on urban-industrialenvironment in Brazilrdquo International Journal of BuildingPathology and Adaptation vol 36 no 5 pp 500ndash515 2018

[12] M Raupach ldquoInvestigations on the influence of oxygen oncorrosion of steel in concrete-Part 2rdquo Materials and Struc-tures vol 29 no 4 pp 226ndash232 1996

[13] N Hearn and J Aiello ldquoEffect of mechanical restraint on therate of corrosion in concreterdquo Canadian Journal of CivilEngineering vol 25 no 1 pp 81ndash86 1998

[14] H Yalciner S Sensoy and O Eren ldquoTime-dependent seismicperformance assessment of a single-degree-of-freedom framesubject to corrosionrdquo Engineering Failure Analysis vol 19pp 109ndash122 2012

[15] S Gadve A Mukherjee and S N Malhotra ldquoCorrosion of steelreinforcements embedded in FRP wrapped concreterdquo Con-struction and BuildingMaterials vol 23 no1 pp153ndash161 2009

[16] H-S Lee T Kage T Noguchi and F Tomosawa ldquoAn ex-perimental study on the retrofitting effects of reinforcedconcrete columns damaged by rebar corrosion strengthenedwith carbon fiber sheetsrdquo Cement and Concrete Researchvol 33 no 4 pp 563ndash570 2003

[17] W Aquino and N M Hawkins ldquoSeismic retrofitting ofcorroded reinforced concrete columns using carbon com-positesrdquo Aci Structural Journal vol 104 pp 348ndash356 2007

[18] M Zhang R Liu Y Li and G Zhao ldquoSeismic performance ofa corroded reinforce concrete frame structure using pushovermethodrdquo Advances in Civil Engineering vol 2018 Article ID7208031 12 pages 2018

[19] G Zhao J Xu Y Li andM Zhang ldquoNumerical analysis of thedegradation characteristics of bearing capacity of a corrodedreinforced concrete beamrdquo Advances in Civil Engineeringvol 2018 Article ID 2492350 10 pages 2018

[20] Y Malecot L Daudeville F Dupray C Poinard andE Buzaud ldquoStrength and damage of concrete under hightriaxial loadingrdquo European Journal of Environmental and CivilEngineering vol 14 no 6-7 pp 777ndash803 2010

[21] M Menegotto ldquoMethod of analysis for cyclically loaded RCplane frames including changes in geometry and non-elasticbehavior of elements under combined normal force andbendingrdquo in Proceedings of the IABSE Symposium on Resis-tance and Ultimate Deformability of Structures Acted on byWell Defined Repeated Loads Lisbon Portugal 1973

[22] N Shome C A Cornell P Bazzurro and J E CarballoldquoEarthquakes records and nonlinear responsesrdquo EarthquakeSpectra vol 14 no 3 pp 469ndash500 1998

[23] International Code Council International Building Code2009 Cengage Learning Boston MA USA 2009

[24] R T Conrad and S R C Winkel Design Guide to the 1997Uniform Building Code John Wiley amp Sons Hoboken NJUSA 1998


[25] American Society of Civil Engineers Minimum Design Loadsfor Buildings and Other Structures American Society of CivilEngineers Reston VA USA 2006

[26] B Wei C Li and X He ldquoe applicability of differentearthquake intensity measures to the seismic vulnerability of ahigh-speed railway continuous bridgerdquo International Journalof Civil Engineering vol 17 no 7 pp 981ndash997 2019

[27] J E Padgett B G Nielson and R DesRoches ldquoSelection ofoptimal intensity measures in probabilistic seismic demandmodels of highway bridge portfoliosrdquo Earthquake Engineeringamp Structural Dynamics vol 37 no 5 pp 711ndash725 2008

[28] N Xiang and M S Alam ldquoComparative seismic fragilityassessment of an existing isolated continuous bridge retro-fitted with different energy dissipation devicesrdquo Journal ofBridge Engineering vol 24 no 8 Article ID 4019070 2019

[29] S Shekhar J Ghosh and S Ghosh ldquoImpact of design codeevolution on failure mechanism and seismic fragility ofhighway bridge piersrdquo Journal of Bridge Engineering vol 25no 2 Article ID 4019140 2020

[30] S Misra and J E Padgett ldquoSeismic fragility of railway bridgeclasses methods models and comparison with the state of theartrdquo Journal of Bridge Engineering vol 24 no 12 Article ID4019116 2019

[31] J B Mander M J N Priestley and R Park ldquoeoreticalstress-strain model for confined concreterdquo Journal of Struc-tural Engineering vol 114 no 8 pp 1804ndash1826 1988

[32] D Niu Durability and Life Prediction of Concrete StructuresScience Press Henderson NV USA 2003

[33] L Lam Y L Wong and C S Poon ldquoDegree of hydration andgelspace ratio of high-volume fly ashcement systemsrdquo Ce-ment and Concrete Research vol 30 no 5 pp 747ndash756 2000

[34] M Ozaki A Okazaki K Tomomoto et al ldquoImproved re-sponse factor methods for seismic fragility of reactor build-ingrdquo Nuclear Engineering and Design vol 185 no 2-3pp 277ndash291 1998

[35] Y Liu and R E Weyers ldquoModeling time-to-corrosioncracking in chloride contaminated reinforced concretestructuresrdquo ACI Materials Journal vol 96 1999

[36] P J Missel ldquoFinite element modeling of diffusion and par-titioning in biological systems the infinite composite mediumproblemrdquo Annals of Biomedical Engineering vol 28 no 11pp 1307ndash1317 2000

[37] W Wu L Li X Shao and S Hu ldquoSeismic evaluation of theaged high-pier and long-span bridges subjected to extremelyhalobiotic conditionrdquo in Proceedings of the 7th InternationalConference on Bridge Maintenance Safety and ManagementShanghai China 2014

[38] K A T Vu and M G Stewart ldquoStructural reliability ofconcrete bridges including improved chloride-induced cor-rosion modelsrdquo Structural Safety vol 22 no 4 pp 313ndash3332000

[39] Y G Du L A Clark and A H C Chan ldquoResidual capacity ofcorroded reinforcing barsrdquo Magazine of Concrete Researchvol 57 no 3 pp 135ndash147 2005

[40] Architecture and Building Press Standard for DurabilityAssessment of Concrete Structures (CECS220-2007) Archi-tecture amp Building Press Beijing China 2007

[41] S Mazzoni F McKenna M H Scott and G L FenvesOpenSees Command Language Manual vol 264 PacificEarthquake Engineering Research (PEER) Center BerkeleyCA USA 2006

[42] T Vidal A Castel and R Franccedilois ldquoAnalyzing crack width topredict corrosion in reinforced concreterdquo Cement and Con-crete Research vol 34 no 1 pp 165ndash174 2004


model considering the factors of concrete carbonation re-inforcement corrosion bond slip degradation and materialdurability damage repair is established during the service lifeof the bridge e influence of the above factors on theseismic performance of the structure or components underthe offshore atmospheric environment is studied

2 Brief Introduction to the Project

In this study the Y2 pier of a 6times 60m offshore large-spancontinuous beam bridge is used as the research object epier adopts C50 concrete HRB335 as longitudinal rein-forcement with 32mm diameter and R235 as stirrup with16mm diameter e pier is 364m high the cross section ishexagonal the axial compression ratio is 0197 and thethickness of the concrete cover is 9 cm e geologicalcondition of the bridge site is goode bottom of the pier isa 15m thick expanded foundation and the top is consol-idated with the beam body e surrounding rock is weakweathered rock e base material is C25 concrete e siteconditions of the bridge are as follows 7-degree seismicfortification intensity of the first group and the second-classsite e stress state of concrete has a certain effect on itsstrength [20] Considering the influence of stirrups on theconcrete in the core area the pier concrete section is dividedinto constraint and protective concretes on the basis ofManderrsquos model Figure 1 is a detailed view of the bridge

3 The Finite Element Analysis Model

31Definition of theModel A concrete01 constitutive modelis adopted for the concrete material of the pier Concrete01 isbased on the uniaxial compressive stress-strain relationshipof KentndashScottndashPark concrete with linear unloadingreloading stiffness which ignores the tensile strength ofconcrete

Steel02 constitutive model is used for longitudinal re-inforcement Steel02 material model is a uniaxial isotropicGiuffrendashMenegottondashPinto model [21] which can efficientlysimulate the nonlinear behaviour of reinforcement underseismic load including the degradation of strength andstiffness e skeleton curve is a two-line model eBond_SP01 constitutive model in OpenSees material libraryis used for the bonded slip material

In OpenSees software simulation the pier body is di-vided into 37 nonlinear beam-column elements each ofwhich has three integral control points e lengths of units1 to 36 and 37 are 1 and 044m respectively e expandedfoundation at the pier bottom is consolidated directlywithout considering the interaction between pile and soile zero-length section element is used to simulate thecorner and displacement deformations caused by bond slipat the pier bottom e consolidation between the top andbeam is simplified as a zero-length element Node i repre-sents the pier top and node j represents the contact pointbetween the pier and beam and is consolidated As the piersection is not shaped like a regular rectangle or fan theconcrete should be divided in a quadrilateral Figure 1

presents the bridge details and specific sectional fibre di-vision of the bridge pier

32 Ground Motion Inputting When the time-historyanalysis method is used to analyse the seismic response ofthe bridge structure the reasonable selection of seismic waveis the premise of the seismic analysis To ensure the reliabilityof calculation results an appropriate seismic wave must beselected in combination with site conditions of the bridge

Seismic parameters are the bases of seismic designDifferent bridges have various requirements for seismicsafety evaluation which are mainly determined by bridgetype and safety risk and social impact Based on the zoningmap of ground motion parameters and site conditions(seismic fortification intensity of 7 degrees group I and classII site) of bridge piers in China ten seismic waves with amagnitude of about 7 are selected from the existing strongearthquake records [22] for incremental dynamic analysise selected types should be the same as the site conditionsof the research bridge and their characteristic periodsshould be close or the same [23ndash25]

Peak ground acceleration (PGA) [26ndash30] is used as theindex of ground motion intensity As the selected PGA ofseismic wave is different from the required PGA the am-plitude of the selected PGA should be adjusted using thefollowing equation

aprime(t) AprimeA

a(t) (1)

where aprime(t) and a(t) are time-history curves of the accel-eration of seismic wave after and before amplitude modu-lation respectively and Aprime and A are peak accelerations ofseismic wave after and before amplitude modulationrespectively

Based on the bridge site conditions the PGA of theseven-degree fortification design ground motion is 01 g(015 g) corresponding to the PGA of ground motion whoseexceeding probability is 10 in 50 years To simulate theearthquake that the pier may encounter the selected seismicwave should be adjusted in the calculation model such thatthe vertical and horizontal peak accelerations can satisfy therequirements of E2 seismic action of 03 and 06 g respec-tively Table 1 shows the adjustment of horizontal andvertical ground motions

4 Research on MechanicalProperties of Materials

41 Study on the Properties of Carbonized Concrete Giventhat the bridge structure requires high ductility of the pierthe arrangement of stirrups can effectively restrain coreconcrete and improve the strength and ductility of concretein the core area e restraint effect of stirrups should besimulated during finite element modellinge coefficient ofconstrained effect is considered on the basis of Manderrsquosconstitutive model [31] of constrained concrete e re-straint effect of stirrups on the core concrete is equivalent tothe effective uniform lateral pressure e stress-strain




X(t) kt

radic


RH15

(1 minus RH)58

fcukminus 0761113888 1113889

KF 10 + 1334F03

(2)




a

radic


j

60m 60m 60m 60m 60m 60m

Y1

Y2 Y3

Y4Y5

(a)373635343332

54321

iZero-length

elements


elements

(b) (c)

Cover concrete

Confined concrete










S Ac

A (3)








tiprime c

K1113872 1113873





Ms Msprime k (6)



tcr ti + tc (7)

tc δcr

λcl

(8)

δcr 0012c

d+ 000084fcuk + 0018 (9)


ln i 8617 + 0618 ln Msl minus3034


(11)


2Dtcr

11139681113888 11138891113890 1113891 (12)






2+ 4 (13)


d(t)

d0 tleTi


0 tgeTcr

⎧⎪⎪⎨

⎪⎪⎩(15)























0

200

400

600

800

1000D

ispla

cem

ent o

f pie

r top

(mm

)



(a)

0

600

1200

1800

Disp

lace

men

t of p

ier t

op (m

m)



(b)

0

600

1200

1800

Disp

lace

men

t of p

ier t

op (m

m)



(c)

0

200

400

600

800D

ispla

cem

ent o

f pie

r top

(mm

)



(d)

0

600

1200

1800

2400

Disp

lace

men

t of p

ier t

op (m

m)



(e)

















6

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)



times104

(a)

6

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)



times104

(b)

6

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(c)




ΔAs π4


1113872 1113873


ds0753 + 932

X

ds01113888 1113889 times 10minus 3

1113890 1113891

2⎡⎣ ⎤⎦

(18)








500

250

0

ndash250

ndash500

Disp

lace

men

t (m

m)

0 10 20 30 40 50t (s)

(a)

0 10 20 30 40 50t (s)

004

002

0

ndash002

ndash004

Curv

atur

e (1

m)

(b)



400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45t (s)


(a)

400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45t (s)


(b)

400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45 50t (s)


(c)



0

100

200

300

400

500

600

700

Disp

lace

men

t (m

m)




4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(a)

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002

Curvature (1m)


times104

(b)

Figure 7 Continued




4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(c)


0

5

10

15

20

25

Cor

rosio

n ra

te o

f lon

gitu

dina

l bar

s (

)



(a)

0

10

20

30

40

50

60

70

Cor

rosio

n ra

te o

f stir

rup

()



(b)



28

29

30

31

32

Dia

met

er o

f lon

gitu

dina

l bar

(mm

)



(a)

310

315

320

325

330

335

Yiel

d str

engt

h of

long

itudi

nal

bars

(mm

)



(b)

14

15

16

17

18

19

20

Elas

tic m

odul

us o

f lon

gitu

dina

lba

rs (times

10e5

MPa

)



(c)


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002

Curvature (1m)

times104


(a)

6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


(b)

Figure 10 Continued


8 Conclusions





6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


8

(c)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(d)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(e)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

(f )





Data Availability




Acknowledgments


References
















































X(t) kt

radic


RH15

(1 minus RH)58

fcukminus 0761113888 1113889

KF 10 + 1334F03

(2)




a

radic


j

60m 60m 60m 60m 60m 60m

Y1

Y2 Y3

Y4Y5

(a)373635343332

54321

iZero-length

elements


elements

(b) (c)

Cover concrete

Confined concrete










S Ac

A (3)








tiprime c

K1113872 1113873





Ms Msprime k (6)



tcr ti + tc (7)

tc δcr

λcl

(8)

δcr 0012c

d+ 000084fcuk + 0018 (9)


ln i 8617 + 0618 ln Msl minus3034


(11)


2Dtcr

11139681113888 11138891113890 1113891 (12)






2+ 4 (13)


d(t)

d0 tleTi


0 tgeTcr

⎧⎪⎪⎨

⎪⎪⎩(15)























0

200

400

600

800

1000D

ispla

cem

ent o

f pie

r top

(mm

)



(a)

0

600

1200

1800

Disp

lace

men

t of p

ier t

op (m

m)



(b)

0

600

1200

1800

Disp

lace

men

t of p

ier t

op (m

m)



(c)

0

200

400

600

800D

ispla

cem

ent o

f pie

r top

(mm

)



(d)

0

600

1200

1800

2400

Disp

lace

men

t of p

ier t

op (m

m)



(e)

















6

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)



times104

(a)

6

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)



times104

(b)

6

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(c)




ΔAs π4


1113872 1113873


ds0753 + 932

X

ds01113888 1113889 times 10minus 3

1113890 1113891

2⎡⎣ ⎤⎦

(18)








500

250

0

ndash250

ndash500

Disp

lace

men

t (m

m)

0 10 20 30 40 50t (s)

(a)

0 10 20 30 40 50t (s)

004

002

0

ndash002

ndash004

Curv

atur

e (1

m)

(b)



400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45t (s)


(a)

400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45t (s)


(b)

400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45 50t (s)


(c)



0

100

200

300

400

500

600

700

Disp

lace

men

t (m

m)




4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(a)

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002

Curvature (1m)


times104

(b)

Figure 7 Continued




4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(c)


0

5

10

15

20

25

Cor

rosio

n ra

te o

f lon

gitu

dina

l bar

s (

)



(a)

0

10

20

30

40

50

60

70

Cor

rosio

n ra

te o

f stir

rup

()



(b)



28

29

30

31

32

Dia

met

er o

f lon

gitu

dina

l bar

(mm

)



(a)

310

315

320

325

330

335

Yiel

d str

engt

h of

long

itudi

nal

bars

(mm

)



(b)

14

15

16

17

18

19

20

Elas

tic m

odul

us o

f lon

gitu

dina

lba

rs (times

10e5

MPa

)



(c)


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002

Curvature (1m)

times104


(a)

6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


(b)

Figure 10 Continued


8 Conclusions





6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


8

(c)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(d)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(e)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

(f )





Data Availability




Acknowledgments


References
















































S Ac

A (3)








tiprime c

K1113872 1113873





Ms Msprime k (6)



tcr ti + tc (7)

tc δcr

λcl

(8)

δcr 0012c

d+ 000084fcuk + 0018 (9)


ln i 8617 + 0618 ln Msl minus3034


(11)


2Dtcr

11139681113888 11138891113890 1113891 (12)






2+ 4 (13)


d(t)

d0 tleTi


0 tgeTcr

⎧⎪⎪⎨

⎪⎪⎩(15)























0

200

400

600

800

1000D

ispla

cem

ent o

f pie

r top

(mm

)



(a)

0

600

1200

1800

Disp

lace

men

t of p

ier t

op (m

m)



(b)

0

600

1200

1800

Disp

lace

men

t of p

ier t

op (m

m)



(c)

0

200

400

600

800D

ispla

cem

ent o

f pie

r top

(mm

)



(d)

0

600

1200

1800

2400

Disp

lace

men

t of p

ier t

op (m

m)



(e)

















6

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)



times104

(a)

6

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)



times104

(b)

6

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(c)




ΔAs π4


1113872 1113873


ds0753 + 932

X

ds01113888 1113889 times 10minus 3

1113890 1113891

2⎡⎣ ⎤⎦

(18)








500

250

0

ndash250

ndash500

Disp

lace

men

t (m

m)

0 10 20 30 40 50t (s)

(a)

0 10 20 30 40 50t (s)

004

002

0

ndash002

ndash004

Curv

atur

e (1

m)

(b)



400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45t (s)


(a)

400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45t (s)


(b)

400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45 50t (s)


(c)



0

100

200

300

400

500

600

700

Disp

lace

men

t (m

m)




4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(a)

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002

Curvature (1m)


times104

(b)

Figure 7 Continued




4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(c)


0

5

10

15

20

25

Cor

rosio

n ra

te o

f lon

gitu

dina

l bar

s (

)



(a)

0

10

20

30

40

50

60

70

Cor

rosio

n ra

te o

f stir

rup

()



(b)



28

29

30

31

32

Dia

met

er o

f lon

gitu

dina

l bar

(mm

)



(a)

310

315

320

325

330

335

Yiel

d str

engt

h of

long

itudi

nal

bars

(mm

)



(b)

14

15

16

17

18

19

20

Elas

tic m

odul

us o

f lon

gitu

dina

lba

rs (times

10e5

MPa

)



(c)


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002

Curvature (1m)

times104


(a)

6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


(b)

Figure 10 Continued


8 Conclusions





6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


8

(c)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(d)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(e)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

(f )





Data Availability




Acknowledgments


References















































2+ 4 (13)


d(t)

d0 tleTi


0 tgeTcr

⎧⎪⎪⎨

⎪⎪⎩(15)























0

200

400

600

800

1000D

ispla

cem

ent o

f pie

r top

(mm

)



(a)

0

600

1200

1800

Disp

lace

men

t of p

ier t

op (m

m)



(b)

0

600

1200

1800

Disp

lace

men

t of p

ier t

op (m

m)



(c)

0

200

400

600

800D

ispla

cem

ent o

f pie

r top

(mm

)



(d)

0

600

1200

1800

2400

Disp

lace

men

t of p

ier t

op (m

m)



(e)

















6

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)



times104

(a)

6

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)



times104

(b)

6

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(c)




ΔAs π4


1113872 1113873


ds0753 + 932

X

ds01113888 1113889 times 10minus 3

1113890 1113891

2⎡⎣ ⎤⎦

(18)








500

250

0

ndash250

ndash500

Disp

lace

men

t (m

m)

0 10 20 30 40 50t (s)

(a)

0 10 20 30 40 50t (s)

004

002

0

ndash002

ndash004

Curv

atur

e (1

m)

(b)



400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45t (s)


(a)

400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45t (s)


(b)

400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45 50t (s)


(c)



0

100

200

300

400

500

600

700

Disp

lace

men

t (m

m)




4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(a)

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002

Curvature (1m)


times104

(b)

Figure 7 Continued




4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(c)


0

5

10

15

20

25

Cor

rosio

n ra

te o

f lon

gitu

dina

l bar

s (

)



(a)

0

10

20

30

40

50

60

70

Cor

rosio

n ra

te o

f stir

rup

()



(b)



28

29

30

31

32

Dia

met

er o

f lon

gitu

dina

l bar

(mm

)



(a)

310

315

320

325

330

335

Yiel

d str

engt

h of

long

itudi

nal

bars

(mm

)



(b)

14

15

16

17

18

19

20

Elas

tic m

odul

us o

f lon

gitu

dina

lba

rs (times

10e5

MPa

)



(c)


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002

Curvature (1m)

times104


(a)

6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


(b)

Figure 10 Continued


8 Conclusions





6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


8

(c)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(d)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(e)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

(f )





Data Availability




Acknowledgments


References














































0

200

400

600

800

1000D

ispla

cem

ent o

f pie

r top

(mm

)



(a)

0

600

1200

1800

Disp

lace

men

t of p

ier t

op (m

m)



(b)

0

600

1200

1800

Disp

lace

men

t of p

ier t

op (m

m)



(c)

0

200

400

600

800D

ispla

cem

ent o

f pie

r top

(mm

)



(d)

0

600

1200

1800

2400

Disp

lace

men

t of p

ier t

op (m

m)



(e)

















6

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)



times104

(a)

6

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)



times104

(b)

6

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(c)




ΔAs π4


1113872 1113873


ds0753 + 932

X

ds01113888 1113889 times 10minus 3

1113890 1113891

2⎡⎣ ⎤⎦

(18)








500

250

0

ndash250

ndash500

Disp

lace

men

t (m

m)

0 10 20 30 40 50t (s)

(a)

0 10 20 30 40 50t (s)

004

002

0

ndash002

ndash004

Curv

atur

e (1

m)

(b)



400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45t (s)


(a)

400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45t (s)


(b)

400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45 50t (s)


(c)



0

100

200

300

400

500

600

700

Disp

lace

men

t (m

m)




4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(a)

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002

Curvature (1m)


times104

(b)

Figure 7 Continued




4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(c)


0

5

10

15

20

25

Cor

rosio

n ra

te o

f lon

gitu

dina

l bar

s (

)



(a)

0

10

20

30

40

50

60

70

Cor

rosio

n ra

te o

f stir

rup

()



(b)



28

29

30

31

32

Dia

met

er o

f lon

gitu

dina

l bar

(mm

)



(a)

310

315

320

325

330

335

Yiel

d str

engt

h of

long

itudi

nal

bars

(mm

)



(b)

14

15

16

17

18

19

20

Elas

tic m

odul

us o

f lon

gitu

dina

lba

rs (times

10e5

MPa

)



(c)


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002

Curvature (1m)

times104


(a)

6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


(b)

Figure 10 Continued


8 Conclusions





6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


8

(c)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(d)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(e)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

(f )





Data Availability




Acknowledgments


References




























































6

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)



times104

(a)

6

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)



times104

(b)

6

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(c)




ΔAs π4


1113872 1113873


ds0753 + 932

X

ds01113888 1113889 times 10minus 3

1113890 1113891

2⎡⎣ ⎤⎦

(18)








500

250

0

ndash250

ndash500

Disp

lace

men

t (m

m)

0 10 20 30 40 50t (s)

(a)

0 10 20 30 40 50t (s)

004

002

0

ndash002

ndash004

Curv

atur

e (1

m)

(b)



400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45t (s)


(a)

400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45t (s)


(b)

400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45 50t (s)


(c)



0

100

200

300

400

500

600

700

Disp

lace

men

t (m

m)




4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(a)

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002

Curvature (1m)


times104

(b)

Figure 7 Continued




4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(c)


0

5

10

15

20

25

Cor

rosio

n ra

te o

f lon

gitu

dina

l bar

s (

)



(a)

0

10

20

30

40

50

60

70

Cor

rosio

n ra

te o

f stir

rup

()



(b)



28

29

30

31

32

Dia

met

er o

f lon

gitu

dina

l bar

(mm

)



(a)

310

315

320

325

330

335

Yiel

d str

engt

h of

long

itudi

nal

bars

(mm

)



(b)

14

15

16

17

18

19

20

Elas

tic m

odul

us o

f lon

gitu

dina

lba

rs (times

10e5

MPa

)



(c)


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002

Curvature (1m)

times104


(a)

6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


(b)

Figure 10 Continued


8 Conclusions





6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


8

(c)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(d)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(e)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

(f )





Data Availability




Acknowledgments


References















































ΔAs π4


1113872 1113873


ds0753 + 932

X

ds01113888 1113889 times 10minus 3

1113890 1113891

2⎡⎣ ⎤⎦

(18)








500

250

0

ndash250

ndash500

Disp

lace

men

t (m

m)

0 10 20 30 40 50t (s)

(a)

0 10 20 30 40 50t (s)

004

002

0

ndash002

ndash004

Curv

atur

e (1

m)

(b)



400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45t (s)


(a)

400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45t (s)


(b)

400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45 50t (s)


(c)



0

100

200

300

400

500

600

700

Disp

lace

men

t (m

m)




4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(a)

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002

Curvature (1m)


times104

(b)

Figure 7 Continued




4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(c)


0

5

10

15

20

25

Cor

rosio

n ra

te o

f lon

gitu

dina

l bar

s (

)



(a)

0

10

20

30

40

50

60

70

Cor

rosio

n ra

te o

f stir

rup

()



(b)



28

29

30

31

32

Dia

met

er o

f lon

gitu

dina

l bar

(mm

)



(a)

310

315

320

325

330

335

Yiel

d str

engt

h of

long

itudi

nal

bars

(mm

)



(b)

14

15

16

17

18

19

20

Elas

tic m

odul

us o

f lon

gitu

dina

lba

rs (times

10e5

MPa

)



(c)


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002

Curvature (1m)

times104


(a)

6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


(b)

Figure 10 Continued


8 Conclusions





6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


8

(c)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(d)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(e)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

(f )





Data Availability




Acknowledgments


References














































400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45t (s)


(a)

400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45t (s)


(b)

400

300

200

100

0

ndash100

ndash200

ndash300

ndash400

Disp

lace

men

t (m

m)

0 5 10 15 20 25 30 35 40 45 50t (s)


(c)



0

100

200

300

400

500

600

700

Disp

lace

men

t (m

m)




4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(a)

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002

Curvature (1m)


times104

(b)

Figure 7 Continued




4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(c)


0

5

10

15

20

25

Cor

rosio

n ra

te o

f lon

gitu

dina

l bar

s (

)



(a)

0

10

20

30

40

50

60

70

Cor

rosio

n ra

te o

f stir

rup

()



(b)



28

29

30

31

32

Dia

met

er o

f lon

gitu

dina

l bar

(mm

)



(a)

310

315

320

325

330

335

Yiel

d str

engt

h of

long

itudi

nal

bars

(mm

)



(b)

14

15

16

17

18

19

20

Elas

tic m

odul

us o

f lon

gitu

dina

lba

rs (times

10e5

MPa

)



(c)


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002

Curvature (1m)

times104


(a)

6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


(b)

Figure 10 Continued


8 Conclusions





6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


8

(c)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(d)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(e)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

(f )





Data Availability




Acknowledgments


References














































0

100

200

300

400

500

600

700

Disp

lace

men

t (m

m)




4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(a)

4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002

Curvature (1m)


times104

(b)

Figure 7 Continued




4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(c)


0

5

10

15

20

25

Cor

rosio

n ra

te o

f lon

gitu

dina

l bar

s (

)



(a)

0

10

20

30

40

50

60

70

Cor

rosio

n ra

te o

f stir

rup

()



(b)



28

29

30

31

32

Dia

met

er o

f lon

gitu

dina

l bar

(mm

)



(a)

310

315

320

325

330

335

Yiel

d str

engt

h of

long

itudi

nal

bars

(mm

)



(b)

14

15

16

17

18

19

20

Elas

tic m

odul

us o

f lon

gitu

dina

lba

rs (times

10e5

MPa

)



(c)


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002

Curvature (1m)

times104


(a)

6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


(b)

Figure 10 Continued


8 Conclusions





6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


8

(c)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(d)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(e)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

(f )





Data Availability




Acknowledgments


References
















































4

2

0

ndash2

ndash4

ndash6

ndash8

Mom

ent (

kNmiddotm

)


times104


(c)


0

5

10

15

20

25

Cor

rosio

n ra

te o

f lon

gitu

dina

l bar

s (

)



(a)

0

10

20

30

40

50

60

70

Cor

rosio

n ra

te o

f stir

rup

()



(b)



28

29

30

31

32

Dia

met

er o

f lon

gitu

dina

l bar

(mm

)



(a)

310

315

320

325

330

335

Yiel

d str

engt

h of

long

itudi

nal

bars

(mm

)



(b)

14

15

16

17

18

19

20

Elas

tic m

odul

us o

f lon

gitu

dina

lba

rs (times

10e5

MPa

)



(c)


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002

Curvature (1m)

times104


(a)

6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


(b)

Figure 10 Continued


8 Conclusions





6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


8

(c)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(d)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(e)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

(f )





Data Availability




Acknowledgments


References














































28

29

30

31

32

Dia

met

er o

f lon

gitu

dina

l bar

(mm

)



(a)

310

315

320

325

330

335

Yiel

d str

engt

h of

long

itudi

nal

bars

(mm

)



(b)

14

15

16

17

18

19

20

Elas

tic m

odul

us o

f lon

gitu

dina

lba

rs (times

10e5

MPa

)



(c)


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

ndash002 ndash001 0 001 002

Curvature (1m)

times104


(a)

6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


(b)

Figure 10 Continued


8 Conclusions





6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


8

(c)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(d)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(e)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

(f )





Data Availability




Acknowledgments


References














































8 Conclusions





6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)


times104


8

(c)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(d)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

8

(e)


times104


6

4

2

0

ndash4

ndash2

Mom

ent (

kNmiddotm

)

(f )





Data Availability




Acknowledgments


References
















































Data Availability




Acknowledgments


References














































seismic response analysis of pier considering durability damage...

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