seismicdamageandcollapseassessmentofreinforcedconcret...

Research ArticleSeismic Damage and Collapse Assessment of Reinforced ConcreteFrame Structures Using a Component-ClassificationWeighted Algorithm

Jizhi Su Boquan Liu Guohua Xing Yudong Ma and Jiao Huang

School of Civil Engineering Changrsquoan University Xirsquoan 710061 China

Correspondence should be addressed to Boquan Liu bqliuchdeducn

Received 9 April 2019 Revised 20 June 2019 Accepted 25 July 2019 Published 18 August 2019

Academic Editor Alberto Cavallo

Copyright copy 2019 Jizhi Su et al(is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

(e seismic performance of reinforced concrete members under earthquake excitation is different from that of whole structurescollapse mechanism may occur because of severe damage to individual members even if the structural damage is not significant(erefore the potential seismic damage of each member should be investigated specifically apart from that of overall structure Inthis study a global damage model based on component classification is proposed to analyze the structural damage evolution ruleand failure mechanism then the computed damage is compared with the experimental phenomena of three 13-scale models ofthree-storey three-bay reinforced concrete frame structures under low-reversed cyclic loading In addition a probabilisticapproach is finally adopted to quantify the seismic performance of RC frame structures based on the proposed global damagemodel Results indicate that the structures with lower vertical axial force and beam-to-column linear stiffness ratio still maintain acertain load-bearing capacity even when the interstorey drift angle exceeds the elastoplastic limit value and the cumulative damageof structures is mainly concentrated on the beam ends and column bottoms of the first floor at final collapse Moreover thestructural failure probability at different performance levels would increase significantly if reinforced concrete frame structuressuffer ground motions higher than the design fortification intensity even up to eight times

1 Introduction

Structural collapse refers to the loss of capacity to resistgravity loads and dynamic instability in a side-way modewhen subjected to seismic excitation which is usually causedby the deterioration in stiffness and strength of componentsand P-Δ effects Protection has been the major target ofseismic design as collapse being the main reason for casu-alties and property losses thus reasonable provisions andconstructional measures have been given in current buildingcodes and standards to alleviate seismic damage and preventstructural collapse but frame structures still suffer severedamage even designed according to modern building codesstrictly [1] (e aforementioned problems have been at-tributed to the lack of perception in structural damageevolution rule and failure mechanism and then definingthe collapse as an acceptable storey drift or a limit value ofindividual component deformation but this assumption

could not reflect the fact that the capacity of global structureto resist deformation is significantly greater than that ofindividual members(emain goal of this study is to presenta methodology for evaluating the collapse state of de-teriorating reinforced concrete frame structures and thenstudying the failure mechanism

Researches on collapse assessment have been developedon several respects during last decades (e experiment onthe seismic performance of frame structures is the mostdirect method to study the failure rule and a large number ofexperiments have been carried out [2ndash10] For instanceZaharia et al tested two full-scale 3-storey RC structureswith flat slab under pseudodynamic loading and concludedthat the deformations mainly concentrated in the slab-column connections and column bases Bousias et al testedtwo 2-storey RC structures with one bay in each directionunder earthquake loading (e results indicated thatstructural damage modified its fundamental frequency

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 6438450 19 pageshttpsdoiorg10115520196438450

Yavari et al carried out a shaking table test on a two-storeytwo-bay frame to evaluate the effect of axial load and jointconfinement reinforcement on the seismic performance ofRC frames (e previous researches mostly focused on theglobal performance of frame structures although they maynot be significantly affected by some alterations in earthquakecharacteristics the performance of individual componentsmay change dramatically Hence it is necessary to specificallyassess the seismic performance of columns beams and beam-to-column joints in addition to the global response ofstructures(is could be achieved by carrying out a multileveldamage assessment of each individual component

Experimental studies also indicate that the hystereticbehavior of the structure is mainly dependent on the pa-rameters that affect the characteristics of deformation andenergy dissipation (us the development of smooth hys-teretic degrading model [11 12] was performed to replacethe bilinear elastic-plastic hysteresis model which waswidely used for their advantage of simplicity Analyticalinvestigation based on numerical simulation is an effectivesupplement to assess structural collapse [13ndash16] For ex-ample Haselton et al studied the influences of axial com-pression ratio strong column weak-beam ratio and P-Δeffect on the collapse risk of special moment-frame (SMF)buildings based on nonlinear dynamic analyses (e resultsshowed that the plastic deformation capacity of columns andP-Δ effect were the most important factors affecting theinterstorey displacement Shi et al evaluated the collapse-resistant capacities and safety margins against collapse ofmultistorey reinforced concrete frames with different seis-mic fortification levels based on incremental dynamicanalysis (IDA)(e influences of axial compression ratio andfailure mode on the collapse-resistant capacity of RC frameswere discussed by taking the loss of vertical bearing capacityas the evaluation index

Damage indices could quantify the damage degree ofstructures and provide a theoretical basis for postearthquakerepairing schemes At present it is generally agreed thatglobal damage indices defined as weighted average com-ponent level indices referring to the damage degree of asingle member are more precise than those defined in termsof global property variation before and after earthquake[17ndash19] which could provide reasonable evaluation of theoverall damage level at the premise that the damage dis-tributes evenly However the global damage models definedas weighted individual component indices in previous re-searches tended to give more weight to the members at lowerstories [20ndash24] but failed to take the negative influence ofdifferent types of damaged components on the structuralseismic performance into account (e effect of localizedcolumn failure on structural collapse is more obvious thanthat of beam failure or other components thus the defi-nition of weighted coefficients should consider the differ-ences particularly

In this study three 13-scale models of three-storeythree-bay reinforced concrete frame structures are testedunder low-reversed cyclic loading which could syntheticallyreflect the force characteristics of components in sidespanandmidspan at the bottom floor middle floor and top floor

Based on experimental results the damage distribution ofindividual components is investigated and the damagequantitative deduction of overall structures is accomplishedthrough a proposed global damage model (is modelconsiders the different influences of component types on thedeterioration of overall seismic performance and dividesstructural components into different types expressed ascomponent classification In addition a probabilistic as-sessment relied on nonlinear dynamic simulation is con-ducted to exhibit the further application of the globaldamage model in predicting the failure probability ofreinforced concrete frame structures

2 Specimens and Test Setup

21 Specimen Design (e prototype structure was a typicalRC moment-resisting frame structure located in an earth-quake-prone region with seismic fortification intensity 8 sitesoil class II and design group 1(e criteria of strong-columnweak-beam were adopted in the structural design accordingto the Chinese Code for Seismic Design of Buildings [25] toensure that the test frames would fail in the flexural modeunder combined lateral displacement and axial compressionload (us the cross-sectional areas of frame columns weredesigned to a larger size (600times 600mm) while those ofbeams were 300times 600mm (e component sizes in the testspecimens were defined according to the geometric reducedscale of prototype ones as 200times 200mm for columns and100times 200mm for beams respectively

To investigate the ultimate elastoplastic interstorey driftangle for preventing building collapse under strong earth-quake the test specimens with excellent ductile deformationwere designed through reasonable construction measures(e specimens were optimized by properly raising thelongitudinal reinforcement ratio of frame columns in orderto facilitate the formation of structural ldquobeam-hingerdquo failurepattern under low-reversed cyclic loading (e sum of ul-timate flexural capacity of columns framing into jointsshould be larger than that of beams in the same plane andthe overstrength factors of exterior joints at the first floorand second floor were 323 and 295 respectively whilethose of interior joints were 269 and 253 meeting theconclusions in previous researches that the strong-columnweak-beam ratio ranging from 20 to 30 is beneficial to theformation of the ldquobeam-hingerdquo mechanism [14 26ndash30] (eoverstrength factors of joints at the third floor were ignoredfor the reason that the interference effect of the loadingdevice on the strength of beams was inevitable

For the model design of overall structures the specimensare mostly scaled models due to the limitations of testingequipment and manufacturing cost Hence the lower threelayers of a single plane frame in the central axis were selectedas the prototype substructure and three 13-scale models ofthree-storey three-bay RC frames were constructed (escaled models could accurately reflect the seismic behaviorof prototypes such as the failure pattern the appearanceorder of plastic hinges the ultimate bearing capacity and theultimate deformation capacity with the method of keepingthe reinforcement ratio and material strength constant

2 Mathematical Problems in Engineering

before and after scaling (e similarity relation of me-chanical behavior during the cracking process betweenmodels and prototypes was difficult to fulfill because theinfluence factors such as steel diameter reinforcement ratioand cover thickness as well as relevant variables could not bescaled completely according to geometric similarity [31] butthis shortcoming could be improved through the methodadopted above(e details of Specimen KJ-1 are presented asan illustration in Figure 1

In order to study the influence of axial compression ratioon the ultimate deformability and seismic performance ofstructures the axial compression loads applied on the top ofexterior columns and interior columns in Specimen KJ-1were 262 kN and 330 kN respectively determined based onthe experimental axial compression ratio converted from theprototype structural design axial compression ratio 045 witha ratio of 1 168 [32] while those in Specimen KJ-2 andSpecimen KJ-3 were 421 kN and 566 kN which were cor-responding to the limiting value of axial compression ratiofor Aseismic Grade II To study the influence of beam-to-column stiffness ratio the height of the first storey inSpecimen KJ-1 and Specimen KJ-2 was 11m for both whilethat in Specimen KJ-3 was 15m

(e commercial concrete and steel used for the testmodels were C40 and HRB400 respectively According tothe results of material sampling tests little variation wasfound in mechanical properties among the specimens (eaverage compressive strength of 150mm concrete cubes wasmeasured as 305MPa after curing at an ambient temper-ature for 28 days 6 bars 8 bars and 10 bars were used as thelongitudinal reinforcements in columns and beams theactual yield and ultimate strength of longitudinal re-inforcement with a diameter of 6mm were 4712MPa and6062MPa respectively while those with the diameter of8mm were 5489MPa and 6402MPa and those with thediameter of 10mm were 5392MPa and 5937MPa 4 low-carbon steel wires were used as the stirrups in both columnsand beams and the actual ultimate strength of steel wireswas 6786MPa

22 Test Setup and Loading Procedure (e model frameswere tested under constant vertical loads and lateral low-reversed cyclic loads in the Earthquake Engineering Labo-ratory of Changrsquoan University (e test setup and in-strumentation are illustrated in Figure 2 Two rigid steelbeams were used to brace the specimens in the out-of-planedirection with frictionless rollers at the top beam level toallow the free in-plane motion of frames (e lateral cyclicloads were applied to the top beam by using a horizontalMTS electrohydraulic servosystem the force was trans-mitted by using four high-strength threaded rods attachingthe actuator and connecting two sides of each column withsleeves and fixtures (e actuator was arranged to movealong the guild rail freely so that the P-Δ effect could beconsidered with great precision Constant vertical loads wereapplied to the top of steel distributive girders by two 300 telectrohydraulic jacks with small sliding plates (e axialloads were obtained from 1168 design axial compression

ratio measured strength of concrete material and scaledmember sizes and transferred to each column by using two100 t manual-hydraulic jacks (located in the interior col-umns) and two 50 t manual-hydraulic jacks (located in theexterior columns) with pressure sensors for each to facilitatereal-time monitoring of vertical loads (e vertical force wascompensated by the manual-hydraulic jacks to ensure theloads remained constant during the whole loading processAll the hydraulic jacks could move with the structural de-formation during the loading history

To examine the allowable values of interstorey drift anglecorresponding to different performance levels specified instandards (1550 for operational level 1250 for slight damagelevel 1120 for medium damage level 150 for seriousdamage level and 125 for collapse level respectively)through the comparison with the experimental failure phe-nomena this paper makes some improvements to the loadingprotocol based on the basic principles in specification forearthquake-resistant buildings [31] the lateral displacementvaried from 0mm to 18mm which is the structural yieldingdisplacement obtained from the finite element simulationahead of conducting the experiment with an interval of 3mm(the corresponding drift ratio is 11100) and one loading cyclefor each displacement amplitude to catch the yielding featurepoints then some damage phenomenon occurred and thetest specimens went into the plastic stage and subsequentlythree full loading cycles were applied for each displacementamplitude with an increment of 9mm which was the half ofstructural yielding displacement (12times18mm 9mm) toapproach the allowable values for the five performance levelsas far as possible Until the roof drift angle reached 125 thetest frame structures were supposed to collapse In this ex-periment the roof drift angle was defined as DΔH whereH was the total height of structure and Δ was the lateral roofdisplacement (e lateral loading as presented in Figure 3was applied to the centerline of top-floor beams in the form ofa displacement-control mode

Two kinds of measurement methods were used in theexperiment One was the traditional data acquisition in-strument such as resistance strain gauges and linear variabledifferential transformers (LVDTs) to obtain the steel strainsforce and displacement during the testing process as il-lustrated in Figure 4 Strain gauges were installed on thelongitudinal and transverse steel bars at the sections of100mm from component ends and transverse steel bars atthe middle position of each beam-column joint to monitorthe section strains LVDTs were used to record the de-formation of members and the displacement at each floorTwo wide-ranging LVDTs were placed at each floor level tomeasure the lateral displacement and one LVDT wasarranged at the basebeam level to monitor the potentialsliding LVDTs with a lower range were placed vertically atthe ends of beams in each floor to obtain the beam-to-column relative rotation and two LVDTs were placed di-agonally to one joint to measure the joint shear responseAnother measurement technique named digital imagecorrelation (DIC) which is an emerging noncontact opticaltechnique for measuring displacement and strain [33] wasalso used on the south side of test frames as presented in

Mathematical Problems in Engineering 3

Figure 5 All the concrete surfaces of test frames were madespeckled pattern artificially with an approximate diameter of4sim8mm and five high-resolution cameras were used to

capture the undeformed image before loading and the de-formed images at every loading stage An open sourcesoftware Ncorr-V12 [34] was introduced to analyze the

3550

400

1100

1100

1100

250

200

200

1200

500

400

300

300 300500

300

400

600 600

600 2000 2000 2000 6007200

Oslash450Oslash475

Oslash475

10100

Oslash450Oslash4100

Oslash450

Oslash450Oslash4100

Oslash4150

1 2 21 5

5

4

43

3

(a)

135 degree hooksAltemate location of hooks35mm extensions




4mm oslash ties20mm clear cover tolongitudinal bars




200

200

200

200

400

100 400

100

1-1(2-2)

1 8(6)

2

12

2

10

8

10

4-4

3-3

5-5

8

3 6

83

63

186

186

(b)

Figure 1 Test specimen and reinforcement details

Gantry

Distributivegirders

mTS

read rod withle and right screws

(connecting with sleevesthread engagement length

150mm)

Electrohydraulicjacks

Slide plate

Manual hydraulicjacks

L-type steelconnector

Frame

Anchoragedevices

Figure 2 Overview of test setup

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95ndash180

ndash150

ndash120

ndash90

ndash60

30

ndash30

0

60

90

120

150

1801251120 12612813013313614115015216117311221250

Operational

Interstorey dri angle 1550

Load

ing

disp

lace

men

t (m

m)

Step

Operational

Slight damage

Medium damage

Serious damageCollapse

Figure 3 Cyclic loading history


acquired digital images and obtain the local deformation ofstructural components

3 Damage Observation

Specimens were considered to fail when the roof drift anglereached 1262 and then the loading continued until severedamage occurred For an accurate description the parts oftest frames are named as shown in Figure 6 where columnsare assigned by the axis and the storey number and beamsare assigned by the axis on both sides and the storey numberBased on the limit value of interstorey drift angle at differentperformance levels the test frames were assumed to gothrough five periods ie operational slight damage me-dium damage serious damage and collapse respectively

Minor flexural cracks first occurred at the beam endswith a maximum width of 004mm at the roof drift ratio of009 (ere were no visible cracks on columns and jointsAs the roof drift ratio increased to 018 hairlike horizontalcracks occurred at the bottom of first-storey and second-storey columns in Specimen KJ-1 (e cracks at the beamends of Specimen KJ-2 continued to increase and extendedtoward the midposition but the number of cracks remainedrelatively low In Specimen KJ-3 the cracks formed at themidspan of beams partly and increased in length andnumber with the width within the range of 006sim012mm(operational level)

For all the three specimens the number and width ofcracks at the beam ends increased substantially as the roofdrift ratio rose to 027(e length extended to 5sim10 cm andthe width was 008sim024mm and a few penetrating cracksformed at the bottom of beam ends New cracks appeared atthe bottom of first-storey columns in Specimens KJ-2 andKJ-3 but no cracks occurred at the joints in the same cycle(slight damage level)

When the roof drift ratio reached 082 the number ofpenetrating cracks at the beam ends of the three specimensincreased drastically and those at the midspan developedwith the width of 012sim044mm Concrete peeling initiatedat the beam-column interface of the second storey inSpecimens KJ-1 and KJ-2 Hairlike horizontal cracksaligning with the top of beams were detected at the jointsand a small amount of penetrating cracks were observed atthe bottom of first-storey columns in Specimen KJ-2 (edevelopment of cracks at the beam ends of Specimen KJ-3was lower than that of Specimen KJ-1 and KJ-2 but thecracks at the bottom of first-storey columns developedsignificantly with numerous penetrating cracks on both theeast and west sides (medium damage level)

(e concrete at the beam ends of the three specimensspalled to different degrees at the roof drift ratio of 191Minor concrete crushing occurred at the left side of Beam-AB2 in Specimens KJ-1 and KJ-2 which caused the exposureof longitudinal reinforcements (e damage degree of thecolumn bottoms in Specimen KJ-2 was more severe thanthat of Specimen KJ-1 with the phenomena that massivepenetrating cracks formed at the bottom of first-storeycolumns and concrete peeled at Column-A1 and Column-D1 (e concrete at Beam-AB1 Beam-AB2 Column-B1and Column-C1 of Specimen KJ-3 was crushed and peeledmeanwhile horizontal cracks aligning with the top surface ofbeams appeared at Joint J-3 (serious damage level)

In Specimens KJ-1 and KJ-2 buckling of the nakedlongitudinal reinforcements at the left side of Beam-AB1 andBeam-AB2 occurred when the roof drift ratio reached 273and massive concrete flaked away at the other beams in-ducing the exposure of longitudinal reinforcements BesidesSpecimen KJ-2 showed a larger extent of concrete spalling atthe bottom of first-storey columns and the longitudinal

MTS

Figure 4 Traditional instrumentation

Figure 5 DIC instrumentation

Foundation beamEast

Beam AB1

J-1 J-2 J-3 J-4

J-8J-5 J-6 J-7

Beam BC1

Beam BC2

Beam CD1

Beam CD2Beam AB2

Col

umn

A1

Col

umn

A2

Col

umn

A3

Col

umn

B1C

olum

n B2

Col

umn

B3

Col

umn

C1C

olum

n C2

Col

umn

C3

Col

umn

D1

Col

umn

D2

Col

umn

D3

West

Figure 6 Components of test frames


reinforcements and stirrups inside could be observed clearly(e damage degree at the beam ends of Specimen KJ-3 waslighter than that of Specimens KJ-1 and KJ-2 although thelongitudinal reinforcements were exposed there was nobuckling (Beam-CD2 right side Beam-AB1 left side andBeam-BC1 left side) (e concrete at the bottom of Column-A1 Column-B1 and Column-C1 was crushed as severely asthat of Specimen KJ-2 (e naked longitudinal reinforce-ments at the beam ends (Beam-AB2 left side Beam-AB1 leftside and Beam-BC1 left side) of Specimen KJ-1 fractured atthe roof drift ratio of 300(e longitudinal reinforcementsand stirrups at the column bottoms were exposed withoutbuckling and the joints remained intact as the roof driftratio rose almost as high as 409 (e test loading wasterminated at this displacement amplitude to ensure theexperimental safety of Specimen KJ-1(e bending degree ofthe buckling longitudinal reinforcements at the beam ends(Beam-CD2 right side Beam-AB2 left side and Beam-BC1right side) of Specimens KJ-2 and KJ-3 increased as thedisplacement amplitude increased but there was no fractureat the end of loading(e concrete at the bottom of Column-B1 and Column-C1 in Specimen KJ-2 was crushed to a largescale the longitudinal reinforcements and stirrups with largedeformation ruptured at the roof drift ratio of 361Specimen KJ-2 collapsed due to the severe loss of verticalbearing capacity (e damage degree of the column bottomsin Specimen KJ-3 was lighter than that in Specimen KJ-2and the concrete at the bottom of Column-B1 and Column-C1 was crushed and the longitudinal reinforcements andstirrups bended without rupturing Loading was haltedimmediately owing to the sudden drop in the structuralvertical bearing ability to ensure safety Figures 7 and 8illustrated the damage characteristics and the force distri-bution of the specimens at the end of loading respectively(collapse level)

In general the experimental phenomena of the threetest frames were almost identical at the small-loading stage(operational slight damage and medium damage) in spiteof the difference in design parameters Cracks at beam endswere observed obviously while those at the column bot-toms appeared laggingly ie only slight horizontal crackswere detected in the joint areas At the large-loading stage(Serious Damage and Collapse) all the three test framesexhibited different failure process and failure pattern Fromthe perspective of failure phenomena the influence of cyclenumber increase on the structural damage was slightlygreater than that of displacement amplitude increase (eforce condition of columns and beams alternated betweentension and compression under multiple positive andnegative loads especially in the position of beam-columnjunction and the connection of ground beam-column endat the first floor (e serious failure phenomena such as thebending and fracture of steel bars or massive peeling ofconcrete occurred due to uncoordinated deformationcaused by the stiffness difference of members While theP-Δ effect highlighted when the structures approachedthe collapse level then the influence of displacementamplitude increase on the structural failure became moreserious relatively From the perspective of plastic hinge

development the test specimens presented the similardamage characteristics with actual seismic failure of framestructures (e plastic hinges in the columns formed mostlysubsequent to those at the beam ends though the growth ofcolumn hinges was faster than that of the beam hinges Whenthe specimens approached the ultimate state of the collapselevel the plastic hinges at the bottom of first-storey columnsfully developed and the P-Δ effect highlighted at the sametime and subsequently the structures collapsed due to thesudden loss of vertical bearing capacity which arose from themassive concrete crushing at first-storey column bottoms(e failure characteristics indicated that the structures stillpossessed a certain vertical bearing capacity and were far fromreaching the limit state of collapse even the interstorey driftangle exceeded 150 which is specified as the elasto-plasticlimit value in the Chinese Code for Design of ConcreteStructures [35]

4 Proposed Seismic Damage Model

41 Component Level Computational expressions takinginternal force parameters or deformation parameters asvariables are widely used in the evaluation of componentdamage numerous damage models specific to the com-ponent-level have been established by both local and in-ternational scholars to reflect the influence of earthquakeexcitation on component failure [18 36ndash45] (eMehannyndashDeierlein damage model is selected as thequantitative expression for component level in this articleowing to the easy acquisition of local deformation datagauged by the digital image correlation method (e effectof the loading path on component failure is taken intoconsideration in this model accompanied with stablecomputational convergence [46] (e formula is shown asfollows

D+θ

θ+p

11138681113868111386811138681113868currentPHC1113874 1113875

α+ 1113936

n+

i1θ+p

11138681113868111386811138681113868FHCi1113874 1113875

β

θ+pu1113872 1113873

α+ 1113936

n+

i1θ+p

11138681113868111386811138681113868FHCi1113874 1113875

β (1)

Dminusθ

θminusp

11138681113868111386811138681113868currentPHC1113874 1113875

α+ 1113936

nminus

i1θminusp

11138681113868111386811138681113868FHCi1113874 1113875

β

θminuspu1113872 1113873

α+ 1113936

nminus

i1θminusp

11138681113868111386811138681113868FHCi1113874 1113875

β (2)

D D+( )c + Dminus( )cc

1113968 (3)

where θp∣currentPHC is the inelastic component deformationreferring to any half cycle whose amplitude exceeds that ofprevious cycles θp∣FHCj is the inelastic component de-formation referring to all the subsequent cycles of smalleramplitude θpu is the associated capacity under monotonicloading and α β and c are the calibration coefficients andthe values are α 1 β 15 c 6 for reinforced concretemembers

42 Storey Level Quantifying component damage is toevaluate the damage degree of overall structure eventually


so it is necessary to establish a combination mode withsimple calculation for component damage Storey damage isusually used as a transition to deliver component damage tostructural collapse In this paper the components in RCframe structures are divided into two types and the corre-sponding storey-weighted coefficients are defined as theconcept of damage indices [47]

Dbstoreyminus i

1113936mj1 Db

ji1113872 11138732

1113936mj1D

bji

(4)

Dcstoreyminus i

1113936nx1 Dc

ji1113872 11138732

1113936nx1D

cji

(5)

where Dbstoreyminus i Dc

storeyminus i are the storey damage indices forbeam and column members in the i-th floor respectively mand n are the number of beam and columnmembers in the i-th floor respectively Db

ji and Dcji are the damage indices of

individual beam and column members respectively

43 Structure Level (e storey damage indices for differenttypes of components should be summed up in order toevaluate the seismic performance of the overall structureStructure-weighted coefficients referring to the damageseverity and the relative position of storeys are defined toestablish the relation between storey damage and structuraldamage

ζ i ζDi middot ζFi

1113936Ni1ζDi middot ζFi

(6)

ζDi Dstoreyminus i

1113936Ni1Dstoreyminus i

(7)

ζFi N minus i + 1

1113936Ni1i

(8)

where ζi is the total weighted coefficient ζDi is theweighted coefficient referring to the damage degree of thestorey ζFi is the weighted coefficient referring to therelative position of the storey and N is the entire floor ofbuilding structure

Structural components are divided into three types inthe Chinese Technical Specification for Concrete Structureof Tall Buildings [48] namely ldquokey componentsrdquo ldquonormalvertical componentsrdquo and ldquoenergy dissipation compo-nentsrdquo to highlight the importance of different componenttypes to structural stability According to the detaileddescription in code the ldquokey componentsrdquo and ldquonormalvertical componentsrdquo are referred to as ldquovertical membersrdquoin this article and the global damage model is defined asfollows

Dtotal λh 1113944

N

i1ζ iD

bstoreyminus i + λv 1113944

N

i1ζ iD

cstoreyminus i (9)

where Dtotal is the global damage indices for overall struc-ture λh and λv are the importance coefficients for ldquoverticalmembersrdquo and ldquohorizontal membersrdquo respectively

Component damage could be accumulated into struc-tural damage through abovementioned the calculationtheory however defining the importance coefficients fordifferent types of components becomes the key to solving theproblem (e definition of importance factors should satisfythe following requirements (1) (e weighted coefficient ofldquovertical membersrdquo should be larger than that of ldquohorizontalmembersrdquo for the reason that the failure of vertical bearingmembers under earthquake excitation would have a

Figure 7 Failure modes of test frames

ndash001

0

001

002

003

004

005

(a)

0

001

002

003

004

005

(b)

ndash000500005001001500200250030035004

(c)

Figure 8 DIC nephograms at structural collapse (a) KJ-1 (b) KJ-2 (c) KJ-3


catastrophic effect on structural collapse (2) (e globaldamage model based on component classification shouldmaintain a good consistency with the damage model definedas global property parameter variation [49] in respect ofreflecting the damage degree (e correlation betweendamage indices and damage states is shown in Table 1 (3)(e damage indices should be larger than 100 once thestructure collapses

In compliance with the principles above the importancecoefficients for different types of components are givenbased on the statistical results of a series of elastoplastictime-history analysis (e initial combination values are setas λh 100 and λv 100 and the combination is supposedto be reasonable if most evaluation results of these twodamage models (global damage model based on componentclassification and damage model based on structural energydissipation capability) are in good agreement On thecontrary the combination values vary with an interval of025 and the operation mentioned above repeats Afterseveral trial calculations the importance coefficients arevalued as λh 050 and λv 125 tentatively which guar-antees the consistency of evaluation results in most workingconditions (e proposed global damage model reflects theinherent relation between local component damage andglobal structure collapse (e cumulative damage andloading path are represented as the ratio of cross-sectionalrotation angle during the loading process to the maximumrotation capacity meanwhile the different influence of el-ement types damage degree and relative position of storeyson structural deterioration is also taken into consideration toexplain the physical behavior reasonably

44 Model Verification (e global damage model Dtotalbased on component classification is verified by comparingit with the final softening model DT [50] and the stiffnessdamage model Dk [51] in the form of evaluating the damagedegree of RC test frames presentedin the following sections(e results are shown in Table 2

It is concluded that the evaluation results of the threedamage models Dtotal DT and Dk are almost identical in theaspect of determining the damage degree although the valuesdiffer owing to separate performance level division All thevalues based on Dtotal are larger than 100 at structuralfailure which indicates that the global damage model basedon component classification could assess the structuraldamage degree accurately and reflect the collapse failurelogically

5 Damage Assessment and Failure Analysis

51 Component Damage Evaluation (e MehannyndashDeierlein damage model is expressed as the ratio of maxi-mum deformation during the loading process to the inelasticdeformation capacity (e deformation capacity refers to thedisparity between the ultimate rotation and the yield rota-tion of member sections (e formulas differ for componenttypes

Columns

θpu θu minus θy ϕu minus ϕy1113872 1113873lp

ϕy 1957εy

h

ϕu 1587εcu

(02 + n)h

εcu 0004 +09ρvfyh

300

lp 008l + 0022dfy

(10)

where ϕy and ϕu are the yield curvature and the ultimatecurvature of column respectively lp is the length of plastichinge εy and fy are the yield strain and the yield strength oflongitudinal reinforcement respectively d is the diameter oflongitudinal reinforcement h is the section height in cal-culation direction εcu is the ultimate strain of concrete n isthe axial compression ratio ρv is the volumetric percentageof stirrup and fyh is the yield strength of stirrup

Beams

θy ϕyls3

+ 00025 + ast025εydfy

h0 minus h1( 1113857fc

1113968

ϕy fyprime

Es(1 minus ξ)h0

θu αstαcy 1 +ast

231113874 111387502]

max 001 ρprimefyprimefc1113872 11138731113872 1113873

max 001 ρfyfc1113872 11138731113872 1113873fc

⎡⎢⎣ ⎤⎥⎦

0275

middotls

h1113888 1113889

045

11 100αρsxfyhfc

1113872 111387313 100ρd( )

(11)

where ϕu is the yield curvature of beam ls is the shear-spanlength h0 is the effective height of section h1 is the distancebetween the centroid of compression reinforcement and theedge of concrete fc is the axial compressive strength ofconcrete fy and fyprime are the yield strength of compressionreinforcement and tensile reinforcement respectively Es isthe elastic modulus of steel αst is the steel type coefficientvalued as 125 for hot-rolled bar αcy is the load type co-efficient valued as 1 and 06 for static loading and cyclic loadrespectively ρ and ρprime are the reinforcement ratios ofcompression reinforcement and tensile reinforcement re-spectively α is the restriction coefficient of stirrup ρd is thereinforcement ratio of web bars

(e inelastic deformation capacity of structural columnsand beams is shown in Table 3 (e damage distribution of


three RC test frame structures at different performance levelsis obtained by substituting DIC data into equations (1) to (3)as presented in Figure 9 It is found that the seismic damageinitiated at the local position of structural columns andbeams in the three test frame structures at the operationalperformance level with the damage indices of columnsvarying in the range 0sim010 and that of beams generallyexceeding 010 (e number and width of cracks at the beamends were larger than those at the column ends obviously inactual test phenomena the damage degree of the three testframe structures is different at the slight damage level andmedium damage level

(e damage at the beam ends of Specimens KJ-1 and KJ-2 increases faster than that at the column ends with thedamage indices of columns being about 020 while that of

beams exceeds 040 In comparison with Specimens KJ-1 andKJ-2 the damage degree of beams in Specimen KJ-3 de-velops slowly but the damage to columns develops fasterindicating that the structural failure path deteriorates owingto the ldquovertical componentsrdquo breaking anterior to theldquohorizontal componentsrdquo gradually From the seriousdamage level to the point of collapse the damage degree ofbeam ends is larger than that of column ends all the time inSpecimen KJ-1 with all the damage indices of beams ex-ceeding 100 at the end of loading On the contrary thedamage indices of beams in Specimens KJ-2 and KJ-3 arelower than the limit value while the damage indices ofcolumns exceed 100 that is to say these two test framestructures no longer have the ability to withstand the verticalbearing capacity and have reached the limit state of collapse

Table 1 Correlation between damage indices and damage states

Damage states Operational performance Slight damage Medium damage Serious damage CollapseDenergy 0sim015 015sim030 030sim060 060sim080 gt080Dtotal 0sim010 010sim025 025sim040 040sim100 gt100

Table 2 Comparison of evaluation results

KJ-1

Load (mm) 0 6 12 27 63 99 135Dtotal mdash 005 014 030 077 106 121

Performance level mdash Operational Slight damage Medium damage Serious damage Collapse CollapseDT mdash 002 013 024 051 063 077

Performance level mdash Operational Slight damage Medium damage Serious damage Serious damage CollapseDk mdash 001 012 026 054 074 083

Performance level mdash Slight damage Slight damage Medium damage Serious damage Serious damage Collapse

KJ-2



Performance level mdash Operational Slight damage Medium damage Serious damage Collapse CollapseDk mdash 004 007 028 059 076 084


KJ-3




Performance level mdash Slight damage Slight damage Medium damage Serious damage Serious damage CollapseNote only the values corresponding to limit points of performance levels are listed in the table due to space limitation

Table 3 Inelastic deformation capacity of components

Specimen NO Components ϕu ndash ϕy (radmm) lp (mm) θu ndash θy (mm)

KJ-1Column-A (D) 372times10minus 5 13200 491times 10minus 3

Column-B (C) 364times10minus 5 13200 480times10minus 3

Beam-AB (BC CD) mdash mdash 511times 10minus 3




KJ-3

F1-column-A (D) 304times10minus 5 14800 450times10minus 3

F1-column-B (C) 291times 10minus 5 14800 431times 10minus 3

F1-beam-AB (BC CD) mdash mdash 544times10minus 3

F23-column-A (D) 349times10minus 5 14800 461times 10minus 3

F23-column-B (C) 335times10minus 5 14800 442times10minus 3

F23-beam-AB (BC CD) mdash mdash 511times 10minus 3


It is also noteworthy that the damage degree of Specimen KJ-3 is lighter than that of Specimen KJ-2 in the end because ofthe larger beam-to-column stiffness ratio

It could be observed from the damage distribution of thethree RC test frame structures that the damage indices ofbottom members are generally larger than that of the upper

ones To illustrate with Specimen KJ-2 the average damageindices of columns in the first floor second floor and third-floor are 097 062 and 015 respectively and those of beamsare 095 086 and 074 at the final collapse which indicatesthat the structural cumulative damage proceeds from bot-tom storey to top storey under seismic excitation Besides

005002

004

005

006

004

009

016

016

025

035

025

047

016

026

045

056

036

053

014

014

034

055

026

045

019

020

060

063

155

095

011

021

051062

064094

011

019

051052

072092

009

011

051071

072097

013

015

035

046

046

050

003

004

005

007

004

005

002

007

003

006

008

011

007

004

004

009

006

011

004

007

008

007

014

014

003

006

003

008

014

015

004

007

008

018

009

022

005

008

007

012

016

023

013

007

008

018

015

014

006

004

015

015

017

019

004

007

008

006

008

017

002

005

004

004

005

014

014

021 014 019 012 015 013

010 010

003 006

013 013

007

016

003 004

055 059 054 051 054 052 059 067 064 071 072 073

102 118 115 109 106 113

110 105 109 110 108 106075 086 065 075 084 072

075 103 095 107 096 106

041 033 049 044 048 044

056 055 046 046 059 062

056 060 049 049 055 060

018 017 019 021 018 022

033 025 022 026 029 033

029 044 032 032 029 023

(a)

002

004

004

004

006

006

010

016

039

046

039

057

008

012

039

063

039

052

016

023

057

068

062

115

012

024

055

075

078

117

006

014

058

068

090

123

012

016

041

077

078

110

010

015

042

056

048

061

014

021

034

060

046

064

001

003

004

007

005

009

003

006

006

006

007

011

005

007

006

009

010

016

005

008

009

008

013

014

002

006

007

011

008

011

005

009

011

012

010

019

009

014

009

013

015

021

008

012

011

015

016

018

006

008

014

017

014

016

002

005

004

005

009

010

003

003

003

006

007

012

004 007 006 004 005 006

045 053 048 041 047 044

083 097 084 104 095 104

086 087 085 080 083 094

076 069 072 076 076 078

052 062 055 059 061 056

060 086 075 086 085 087

012 015 014 018 016 016 031 029 042 032 041 040

049 046 035 042 055 052

040 055 041 042 049 051024 033 026 028 024 021

025 022 015 018 019 023012 012 008 012 011 010

016 013 015 015 012 017

(b)

002

003

005

007

005

008

014

022

035

051

047

061

018

024

040

056

054

077

012

019

034

065

043

067

019

027

065

074

069

107

015

021

046

068

073

124

016

021

051

083

084

099

011

023

064

073

076

112

011

023

037

049

055

070

003

006

002

005

006

012

004

008

005

007

008

016

004

007

005

009

010

012

007

016

009

015

018

026

006

017

012

016

014

020

004

007

019

018

015

017

008

011

010

014

012

024

003

006

006

009

013

016

003

005

005

006

006

013

003

005

002

006

003

007

002

004

005

008

004

006

005 006 006 007 008 005

043 057 069 051 042 048

055 073 064 077 069 076

044 050 038 035 033 028

013 005 012 012 019 018

020 024 012 022 019 013

010 012 011 014 014 012 023 019 022 020 024 033

061 051 054 057 063 068

080 075 079 080 068 076

072 078 115 089 086 073

032 040 035 029 034 042

037 025 022 033 029 038

011 009 012 011 007 014

012 014 015 010 013 014

(c)

Figure 9 Damage distribution of test frames (a) KJ-1 (A) Operational (IDR1550) (B) Slight damage (IDR1360) (C) Medium damage(IDR1120) (D) Serious damage (IDR150) (E) Collapse (IDR124) (b) KJ-2 (A) Operational (IDR1550) (B) Slight damage (IDR1360) (C) Medium damage (IDR1120) (D) Serious damage (IDR150) (E) Collapse (IDR128) (c) KJ-3 (A) Operational (IDR1550)(B) Slight damage (IDR1360) (C) Medium damage (IDR1120) (D) Serious damage (IDR150) (E) Collapse (IDR126)


the damage degree of beam ends is more serious than that ofcolumn ends in the specimen with smaller vertical loadhowever the cumulative damage of column ends increasesrapidly in the structure with larger beam-to-column linearstiffness

52 Storey Damage Evaluation (e damage distributionalong the floors is obtained by substituting the damageindices of components into equations (4) to (5) as shown inFigure 10

It is found that the storey damage of beams is evenlydistributed with test results showing that the damage indicesof the first storey in Specimen KJ-1 are about 1391 and3913 larger than that of the second storey and third storeyrespectively (for Specimen KJ-2 1274 and 2549 forSpecimen KJ-3 1771 and 3542) at final collapse (edamage degree of columns increases slowly with lowerdisplacement amplitude but increases rapidly as the am-plitude and cycle times rise the damage is mainly con-centrated on the bottom floor of structures with test resultsshowing that the damage indices of the first storey inSpecimen KJ-1 are about 3473 and 6947 larger than thatof the second storey and third storey respectively (forSpecimen KJ-2 3846 and 7436 for Specimen KJ-33243 and 7387) at final collapse reflecting the fact thatthe structural collapse arose from the local accumulation ofdamage at the bottom of columns

53 Structure Damage Evaluation (e damage evolutioncurves of overall structures are obtained by substituting thestorey damage indices into eequations (6) to (9) as shown inFigure 11

It is found that the damage evolution curves of the threetest frame structures show a similar trend the slope is flatwhen the displacement loading is small and gradually be-comes steeper as the amplitude increases (is phenomenonindicates that the beams acting as energy-consumingcomponents have positive effects on delaying the progres-sion of damage in the overall structure at the small-loadingstage while the columns gradually replace the beams andbegin to consume the seismic energy as seriously damagedbeams lose their functions with the displacement amplitudeand cycle times increasing (e damaged columns sub-sequently induce a sharp decline in the structural energydissipation capacity and then aggravate the degradation ofseismic performance at the large-loading stage

(e members including beams and columns consumethe seismic energy through the method of changing theirdeformation Large deformation occurred to dissipate en-ergy when the displacement amplitude increased obviousfailure phenomena were found once the deformationexceeded a certain limiting value (e strength and stiffnessof members degraded after several repeated deformationswhen suffering cyclic loading at the same amplitude andthen the energy dissipation capacity declined sharply andserious failure phenomena occurred along with the nextlarger displacement amplitude

Comparing the damage evolution curves of the threespecimens it is found that the curve of Specimen KJ-1 isflatter than that of Specimens KJ-2 and KJ-3 (e damageindices of Specimen KJ-1 for the final collapse is the smallestwhich indicates that the full development of ldquobeam hingerdquo isbeneficial to postpone the collapse process of integralstructure and mitigate the damage degree at failure (ecurves of Specimen KJ-2 and KJ-3 are both steeper with fewdifferences between them there are several feature pointspresented in the form of slope variation in the Specimen KJ-2curve which is related to the alternation of ldquobeam hingefailurerdquo and ldquocolumn hinge failurerdquo While the slope of theSpecimen KJ-3 curve is almost unchanged during theloading process for the reason that the plastic hinges at thebeam ends are not fully formed and the columns consume aconsiderable part of seismic energy due to the larger beam-to-column linear stiffness ratio (e damage indices ofSpecimen KJ-2 are a little larger than those of KJ-3 at finalcollapse indicating that the influence of axial compressionratio increasing on the degradation of seismic performanceis greater than that of the beam-to-column linear stiffnessratio

In conclusion the global damage model based oncomponent classification could reflect the structural damageevolution rule and the different influence of componenttypes on the seismic performance of overall structure

6 Seismic Vulnerability Assessment

Over the past decade efforts to develop performance-basedseismic evaluation have progressed and resulted in guidelinedocuments such as ASCESEI 41-06 (2006) and FEMA 356(2000) [52] FEMA-356 (2000) proposes a probabilisticdescription of the performance level on establishing aquantitative evaluation of damage states which is accom-plished by nonlinear elasto-plastic methods As numerousstudies have shown ground motion characteristics is thelargest source of uncertainty in structural seismic responsehence three ground motion parameters that affect thestructural response are considered Response parameterssuch as plastic rotation are also interpreted into a damageform (D) through the global damage model presented in theprevious section and the probabilistic approach resulting inthe fragility surfaces that characterize the conditionalprobability of predicted demand and performance state iscarried out

61 Nonlinear Simulation Model In this section probabi-listic seismic demand analysis is performed using AbaqusExplicit finite element program to study the seismic vul-nerability of archetype RC frame structure (e momentframe is designed to resist both gravity loads and lateralloads satisfying all the seismic criteria regarding strengthand deformation limits according to the codes

Compared with the implicit method it is not necessaryto form or invert stiffness matrices in the explicit dynamicanalysis and the displacements are calculated at the be-ginning of each time increment so it is efficient for highly


nonlinear problems such as structural dynamic collapse(efiber-beam element B31 in the Abaqus element library isselected to simulate the beams and columns of a structureand the rectangular cross-sectional shape is defined for beam

property (is type of element is suitable for exhibiting thenonlinear materials where large deformation and rotationoccur At each time increment the stress over cross section isintegrated numerically to follow the development of indi-vidual elastoplastic response (e section is divided intomultifiber bundles with the uniaxial stress-strain relation-ship of concrete material imparted on each fiber and steelreinforcements are inserted into each element by definitionat appropriate depth of cross section using the keywordlowastREBAR to ensure computational convergence as shown inFigure 12

(e material property is simulated using the subroutinePQ-Fiber [53] through the converter program UMATUConcrete02 is used for the concrete to consider the con-fined effect of stirrups in this paper because the hoops cannotbe defined directly in fiber-beam element It is an isotropicelastoplastic concrete material with the character of confinedconcrete which defines the modified Kent-Park model[54 55] as compression constitutive relation and the bilinearmodel with a softening segment as tension constitutiverelation as shown in Figure 13 Eight parameters are definedin this model axial compressive strength correspondingcompressive strain ultimate compressive strength ultimatecompressive strain the ratio of unloading stiffness to initialelasticity modulus axial tensile strength tensile softening

6mm9mm27mm

6mm9mm27mm

6mm9mm27mm

63mm126mm

63mm126mm

63mm126mm

Floo

r

Floo

r

Floo

r

02 04 06 08 1000Damage indices

02 04 06 08 10 1200Damage indices

0

1

2

3

0

1

2

3

02 04 06 08 10 1200Damage indices

0

1

2

3

(a)

6mm9mm27mm

6mm9mm27mm

6mm9mm27mm

63mm126mm

63mm119mm

63mm126mm

Floo

r

Floo

r

0

1

2

3

Floo

r

0

1

2

3

02 04 06 08 10 1200Damage indices


0

1

2

3

02 04 06 08 10 1200Damage indices

(b)

Figure 10 Damage distribution along the floors (a) KJ-1 (A) Column damage distribution (B) Beam damage distribution (b) KJ-2 (A)Column damage distribution (B) Beam damage distribution (c) KJ-3 (A) Column damage distribution (B) Beam damage distribution

Collapse

Serious damage

Medium damage

Slight damage

KJ-1KJ-2KJ-3

00

03

06

09

12

15

Dto

tal

20 40 60 80 100 120 1400Displacement (mm)

Operational

Figure 11 Damage evolution curves of test frames


modulus and yield strain of steel bars in the section All thevalues of these parameters are related to the measuredstrength of the concrete material as described in Section 2Usteel02 is used for steel to consider the Bauschinger effectcaused by stiffness degradation and the bending capacityattenuation caused by cumulative damage It is the improvedform of the proposed maximum point-oriented bilinearmodel [56] as shown in Figure 14 Four parameters are usedin this material elasticity modulus yield strength the ratioof postyield stiffness to elasticity modulus and ultimateplastic deformation rate Similar with adopted values inUConcrete02 these parameters are obtained frommeasuredvalues and default values Besides the material nonlinearityin beams and columns the option of geometric nonlinearityin the Step Module of Abaqus is selected in simulatingstructural collapse due to the large deformation (P-Δ) effectsexperienced during the strong earthquake (e axial loads ofbeams are negligible but imposed at column tops in eachfloor as concentrated forces

(ree analysis steps including initial step for fixedconstraints of column bottoms at the first floor Step-1 foraxial loads applying and Step-2 for seismic records in-putting are set to complete the applied loads in order toensure the boundary condition and loading sequence of thenumerical model being consistent with the experimentalspecimens (e initial time and the minimum time step areset as 0001 s and 10minus 5 respectively (e seismic loading isdefined as the acceleration field acting on the wholestructure with the consideration of fixed support in thefoundation (e numerical results are compared with the

experimental results of Specimen KJ-1 to verify the reliabilityof simulation method as shown in Figure 15

It can be seen that the analytical hysteresis loop liesreasonably close to the experimental one but the energydissipation capacity of simulated frame structure is slightlysmaller than that of experimental specimen

(e major reason for the difference may attribute to themethod of defining the embedded steel bars that is to saythe keyword ldquolowastrebarrdquo treats concrete material and steelmaterial as a whole thus the energy dissipation ability ofsteel could not be made full use However in actual ex-periment the bond slip in the interface between concreteand steel bars occurs under low-reversed cycle loading thusthe tensile and energy dissipation properties of steel barscould be utilized sufficiently After comprehensive consid-eration the numerical model for the experimental prototypestructure (a multilayer RC office building) is establishedbased on the simulation method above

(e selection of seismic intensity parameters has agreater impact on the accuracy of seismic vulnerabilityanalysis results Considering the complexity of structuralfailure mechanism under earthquake action a single seismicintensity parameter is not sufficient to reflect the influence ofearthquake characteristics on the structural failure proba-bility (erefore three seismic intensity parameters iePGD (in relation to the amplitude characteristics) M (inrelation to the spectrum characteristics) and SA1 (com-monly used in time-history analysis) are selected in thissection to carry out the seismic reliability evaluation of RCframe structures (e time-history analysis is accomplished

Concrete fiber Beam sectionintegration point

Inserted reinforcementintegral point

Reinforcementfiber

Figure 12 Section of fiber-beam element

05dcE0

dcE0

dcE0

γsE0

E0

σ

εce εR εimax

ε

R

E0

Figure 13 Constitutive model of concrete material

02fimax

05E0

02fimax

fyfy2

fy2

fy

fy3 E0

E0

εy

εf

ε

σ

Figure 14 Constitutive model of steel material


by using a set of 50 ground motions from PEER GroundMotion Database to reduce the biases in structural response(ese 50 ground motions involve a wide range of magni-tudes (50ndash76) epicentral distances (06 kmndash2224 km) siteclassification (types AndashD) and spectral range

62 Collapse Resistance Assessment Fragility surface rep-resents the conditional probability that structural responseparameterD reaches or exceeds the structural resistance C ata certain performance level when the intensity parametersIM1 and IM2 take different values (e formula could beexpressed as follows

Pf P CDle 1 ∣ IM1 i1 IM2 i2( 1113857 (12)

Assuming that the parameters C and D are independentrandom variables obeying log-normal distribution then thefailure probability of the structure at a specific performancelevel could be expressed as follows

Pf P CDle 1I ∣M1 i1 IM2 i2( 1113857 Φln(C) minus ln(D)

σ1113888 1113889

(13)

where Φ(x) is the normal distribution function and thevalue could be obtained by consulting relevant tables and σis the standard deviation

(e structural aseismic capacity at different performancelevels (characterized by global damage indices based oncomponent classification) are shown in Table 1 (e linearregression equation between two seismic intensity param-eters (IM1 IM2) and the global damage indices Dtotal (Ta-ble 4) is setup as follows

ln Dtotal( 1113857 a + b ln IM1( 1113857 + c ln IM1( 1113857( 11138572

+ d ln IM2( 1113857

+ e ln IM2( 1113857( 11138572

+ f ln IM1( 1113857ln IM2( 1113857

(14)

where a b c d e and f are the regression coefficients

It could be seen in Figure 16 that the failure probabilitythat RC structural seismic response exceeding differentdamage levels is affected by PGD and SA1 simultaneouslyfurthermore SA1 has a greater influence on the structuralfailure probability at the operational level and slight damagelevel (e fragility surface also indicates that the probabilityof structural damage exceeding the serious damage level is7280 based on equations (23) and (25)

In the fragility surface composed of SA1 and M asshown in Figure 17 the failure probability of RC structuralseismic response exceeding different damage levels ismainly affected by SA1 however M has little impact onthe structural failure probability (e fragility surfaceindicates that the probability of structural damage ex-ceeding the serious damage level is 7059 based onequations (24) and (26)

(e failure probability of RC frame structures under 8-degree and 9-degree design fortification intensity is alsoinvestigated in this section

Based on the relevant parameters of selected 50 groundmotions the PGD is set as 1m 3m 6m and 10m re-spectively and theM is set as 5 6 7 and 8 respectively(evalue of SA1 is taken as the standard proposal ie10271 cms2 for frequent earthquake 26962 cms2 forbasic fortification and 57776 cms2 for rare earthquakerespectively corresponding to 8-degree fortification in-tensity and 20542 cms2 for frequent earthquake51356 cms2 for basic fortification and 89874 cms2 forrare earthquake respectively corresponding to 9-degreefortification intensity (e structural failure probabilityunder different performance levels is obtained via equa-tions (25) and (26) and the calculation results are shown inTables 5sim6

It could be seen in Table 5 that the failure probability ofRC frame structure subjected to frequent earthquake is01ndash25 for operational level 0ndash10 for slight damagelevel 0ndash06 for medium damage level and 0ndash02 forserious damage level corresponding to 8-degree fortificationintensity when PGD is assumed to be 100sim1000 cm thefailure probability is 335ndash885 69ndash638 46ndash269 and 20ndash160 respectively for RC frame structuresubjected to rare earthquake at the same fortification

ndash150 ndash100 ndash50 0 50 100 150

Test resultsSimulation results

ndash200

ndash150

ndash100

ndash50

0

50

100

150

200F

(kN

)

Δ (mm)

Figure 15 Comparison of hysteretic curves in the test specimenand numerical model

Table 4 Structural damage indices under different groundmotions

No Dtotal No Dtotal No Dtotal No Dtotal

1 068 14 061 27 038 40 0882 093 15 048 28 029 41 0483 098 16 097 29 044 42 0724 086 17 099 30 043 43 1125 033 18 033 31 011 44 0406 068 19 094 32 055 45 0527 099 20 098 33 032 46 0888 108 21 098 34 098 47 0899 071 22 031 35 097 48 09510 086 23 090 36 099 49 03011 099 24 092 37 034 50 03012 095 25 097 38 054 mdash mdash13 027 26 077 39 040 mdash mdash


intensity (e failure probability of RC frame structuresubjected to frequent earthquake is 4ndash246 for opera-tional level 16ndash143 for slight damage level 1ndash103for medium damage level and 03ndash5 for serious damagelevel corresponding to 9-degree fortification intensity whenPGD is assumed to be 100sim1000 cm

(e failure probability is 711ndash973 318ndash752184ndash476 and 39ndash343 respectively for RC framestructure subjected to rare earthquake at the same fortifi-cation intensity

It could be seen in Table 6 that the failure probability ofRC frame structure subjected to frequent earthquake is24ndash40 for operational level 11ndash20 for slightdamage level 07ndash14 for medium damage level and03ndash06 for serious damage level corresponding to 8-degree fortification intensity whenM is assumed to be 5sim8the failure probability is 461ndash692 173ndash30091ndash135 and 51ndash80 respectively for RC frame

structure subjected to rare earthquake at the same forti-fication intensity (e failure probability of RC framestructure subjected to frequent earthquake is 96ndash141for operational level 53ndash84 for slight damage level38ndash62 for medium damage level and 19ndash33 forserious damage level corresponding to 9-degree fortifica-tion intensity when M is assumed to be 5sim8 the failureprobability is 758ndash960 185ndash754 206ndash346and 87ndash230 respectively for RC frame structuresubjected to rare earthquake at the same fortificationintensity

Based on the information presented above it is foundthat the failure probability of RC frame structure underdifferent performance levels would increase significantlyonce the structure is subjected to earthquake excitationhigher than the initial design fortification intensity andthe increasing amplitude could rise as much as eighttimes

Table 6 Failure probability corresponding to different fortification intensities (SA1 and M)

Performance level Earthquake magnitudeFortification intensity 8 Fortification intensity 9

SA1 (cms2)M

SA1 (cms2)M

M 8 M 7 M 6 M 5 M 8 M 7 M 6 M 5

Operational performanceFrequent earthquake 81 0040 0033 0028 0024 175 0141 0122 0107 0096Basic fortification 158 0123 0106 0093 0082 316 0721 0633 0510 0392Rare earthquake 316 0692 0510 0433 0461 491 0960 0857 0800 0758

Slight damageFrequent earthquake 81 0020 0016 0013 0011 175 0084 0071 0061 0053Basic fortification 158 0072 0060 0052 0045 316 0373 0351 0233 0120Rare earthquake 316 0300 0133 0151 0173 491 0754 0626 0503 0185

Medium damageFrequent earthquake 81 0014 0011 0009 0007 175 0062 0052 0044 0038Basic fortification 158 0053 0044 0037 0032 316 0135 0117 0103 0091Rare earthquake 316 0135 0117 0103 0091 491 0206 0181 0162 0346

Serious damageFrequent earthquake 81 0006 0005 0004 0003 175 0033 0027 0022 0019Basic fortification 158 0027 0022 0018 0015 316 0080 0067 0058 0051Rare earthquake 316 0080 0067 0058 0051 491 0230 0212 0140 0087

Table 5 Failure probability corresponding to different fortification intensities (SA1 and PGD)

Performancelevel

Earthquakemagnitude

Fortification intensity 8 Fortification intensity 9

SA1(cms2)

PGD SA1(cms2)

PGD100 cm 300 cm 600 cm 1000 cm 100 cm 300 cm 600 cm 1000 cm

Operationalperformance

Frequentearthquake 81 0001 0001 0002 0025 175 0040 0043 0052 0246

Basic fortification 158 0029 0032 0039 0204 316 0335 0544 0665 0815Rare earthquake 316 0335 0444 0665 0885 491 0711 0822 0949 0973

Slight damage



Mediumdamage



Serious damage




081

060402

0

0 200 400 600 800 1000

Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(a)

0 200 400 600 800 1000

081

060402

0Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(b)

0 200 400 600 8001000

45

67

8

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(c)

0 200 400 600 800 1000

445

555

6

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(d)

Figure 17 Fragility surfaces based on intensity parameters SA1 andM (a) Operational (b) Slight Damage (c) MediumDamage (d) SeriousDamage

500

108060402

0

00 200 400 600 800 10001000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(a)

500

0 0 200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(b)

500

00200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(c)

500

0 0200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(d)

Figure 16 Fragility surfaces based on intensity parameters PGD and SA1 (a) Operational (b) Slight Damage (c) Medium Damage(d) Serious Damage


7 Conclusion

An experimental study was conducted on three 13-scalemodels of three-storey three-bay reinforced concrete framestructures under low-reversed cyclic loading and a proposedglobal damage model based on component classification wasestablished to investigate the damage evolution rule bydiscussing the relationship between local damage andstructural collapse Further application of the global damagemodel was introduced in terms of assessing the failureprobability of RC frame structure at different damage levelsthe following conclusions can be drawn from this study

(1) (e structural damage develops from the bottomstorey to top storey under earthquake excitation andthe damage distribution is mainly concentrated onthe beam ends and column bottoms of the first floorat final collapse(e anticipated beam-hinged failuremechanism is easier to achieve in the structures withlower vertical axial force and the structures stillmaintain a certain load-bearing capacity even whenthe interstorey drift angle exceeds the elastoplasticlimit value (e damage degree of columns increasesrapidly in structures with larger beam-to-columnlinear stiffness which is harmful to integral ductilityand deformation capacity

(2) (e damage distribution along the floors varies di-rectly with component types (e damage of beams isdistributed along the floor evenly but that of columnsis concentrated(e full development of plastic hingesat the beam ends has positive effect on delaying thedamage growth of the integral structure and miti-gating the damage degree besides the influence of theaxial compression ratio increasing on the seismicperformance degradation is greater than that of thebeam-to-column linear stiffness ratio increasing

(3) (e formula ln(Dtotal) a+ bln(IM1) + c(ln(IM1))2 +dln(IM2) + e(ln(IM2))2 + f ln(IM1) ln(IM2) could beused to reveal the relationship between the twoseismic intensity parameters and global damagemodel based on component classification From thisequation fragility surfaces with different intensityparameter combinations are drawn showing that theprobability of structural damage exceeding the se-rious damage level ranges from 7059 to 7280

(4) (e maximum failure probabilities of structuraldamage exceeding operational level slight damagelevel medium damage level and serious damage levelare 40 20 14 and 06 respectively when RCframe structure suffers the frequent earthquake at 8-degree fortification intensity failure probabilities are885 638 269 and 160 respectively whenthe structure suffers the rare earthquake at the samefortification intensity (e failure probabilities wouldincrease significantly once the structure encounteringground motions higher than the initial design forti-fication intensity and the increasing amplitude rea-ches as much as eight times

Data Availability

(e data given in Table 2 and Figure 9 used to support thefindings of this study were related to the original data ofexperiments funded by the National Natural ScienceFoundation of China and so cannot be made freely availableconcerning legal restrictions Requests for access to thesedata should be made to the leader of this academic project(email address bqliuchdeducn) (e data in Tables 6ndash9and Figures 16 and 17 used to support the findings of thisstudy were based on the groundmotions selected from PEERGround Motion Database (website ngawest2berkeleyedu)and calculated by commercial software SeismoSignalAbaqus and Matlab (e results are presented in the article(e other data used to support the findings of this study wereobtained through equations presented in article and thecalculation methods were included within the paper

Conflicts of Interest

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

Acknowledgments

(is research was partially supported by the NationalNatural Science Foundation of China (Grant no 51578077)and the International Science and Technology CooperationProject of Shaanxi Province (Grant no 2016KW-056)

References

[1] H N Li S Y Xiao and L S Huo ldquoDamage investigation andanalysis of engineering structure in Wenchuan earthquakerdquoJournal of Xirsquoan of Building Structures vol 41 pp 606ndash6112008

[2] R Zaharia Pseudodynamic Earthquake Tests on a Full-ScaleRC Flat-Slab Building structure Joint Research Centre IspraItaly 2006

[3] A Hashemi and K M Mosalam ldquoShake-table experiment onreinforced concrete structure containing masonry infill wallrdquoEarthquake Engineering amp Structural Dynamics vol 35no 14 pp 1827ndash1852 2006

[4] S N Bousias M N Fardis A-L Spathis and A J KosmopoulosldquoPseudodynamic response of torsionally unbalanced two-storeytest structurerdquo Earthquake Engineering amp Structural Dynamicsvol 36 no 8 pp 1065ndash1087 2007

[5] K J Elwood and J P Moehle ldquoDynamic collapse analysis fora reinforced concrete frame sustaining shear and axial fail-uresrdquo Earthquake Engineering amp Structural Dynamics vol 37no 7 pp 991ndash1012 2008

[6] S Yavari K J Elwood S H Lin C L Wu S J Hwang andJ P Moehle ldquoExperimental study on dynamic behavior ofmulti-story reinforced concrete frames with non-seismicdetailingrdquo in Proceedings of the Improving the Seismic Per-formance of Existing Buildings and Other Structurespp 489ndash499 San Francisco CA USA December 2010

[7] W M Ghannoum and J P Moehle ldquoShake-table tests of aconcrete frame sustaining column axial failuresrdquo ACIStructural Journal vol 109 pp 393ndash402 2012


[8] D G Lignos T Hikino Y Matsuoka and M NakashimaldquoCollapse assessment of steel moment frames based onE-defense full-scale shake table collapse testsrdquo Journal ofStructural Engineering vol 139 no 1 pp 120ndash132 2013

[9] Y-L Chung T Nagae T Hitaka and M Nakashima ldquoSeismicresistance capacity of high-rise buildings subjected to long-period ground motions E-defense shaking table testrdquo Journalof Structural Engineering vol 136 no 6 pp 637ndash644 2010

[10] Y-L Chung T Nagae T Matsumiya and M NakashimaldquoSeismic resistance capacity of beam-column connections in high-rise buildings E-defense shaking table testrdquo Earthquake Engi-neering amp Structural Dynamics vol 40 no 6 pp 605ndash622 2011

[11] M V Sivaselvan and A M Reinhorn ldquoHysteretic models fordeteriorating inelastic structuresrdquo Journal of EngineeringMechanics vol 126 no 6 pp 633ndash640 2000

[12] J K Song and J A Pincheira ldquoSpectral displacement de-mands of stiffnessmdashand strengthmdashdegrading systemsrdquoEarthquake Spectra vol 16 no 4 pp 817ndash851 2000

[13] C B Haselton A B Liel G G Deierlein B S Dean andJ H Chou ldquoSeismic collapse safety of reinforced concretebuildings I assessment of ductile moment framesrdquo Journal ofStructural Engineering vol 137 no 4 pp 481ndash491 2010

[14] A B Liel C B Haselton G G Deierlein B S Dean andJ H Chou ldquoSeismic collapse safety of reinforced concretebuildings II comparative assessment of nonductile andductile moment framesrdquo Journal of Structural Engineeringvol 137 no 4 pp 492ndash502 2010

[15] W Shi L P Ye and X Z Lu ldquoStudy on the collasp-resistantcapacity of RC frames with different seismic fortificationlevelsrdquo Engineering Mechanics vol 28 no 3 pp 41ndash48 2011

[16] B Wang H J Dai Y T Bai and K Xiao ldquoInfluencemechanism of steel diagonal braces onmechanical behavior ofsteel truss-RC tubular column hybrid structurerdquo Journal ofEarthquake Engineering pp 1ndash27 2019

[17] E B Williamson ldquoEvaluation of damage and P-Δ effects forsystems under earthquake excitationrdquo Journal of StructuralEngineering vol 129 no 8 pp 1036ndash1046 2003

[18] Y J Park A H S Ang and Y K Wen ldquoSeismic damageanalysis of reinforced concrete buildingsrdquo Journal of Struc-tural Engineering vol 111 no 4 pp 740ndash757 1985

[19] M S L Roufaiel and C Meyer ldquoAnalytical modeling ofhysteretic behavior of RC framesrdquo Journal of StructuralEngineering vol 113 no 3 pp 429ndash444 1987

[20] S Rodriguez-Gomez and A S Cakmak ldquoEvaluation of seismicdamage indices for RC structuresrdquo Technical Report NCEER-90-0022 National Center for Earthquake Engineering Re-search State University of New York Buffalo NY USA 1990

[21] E DiPasquale and A S Cakmak ldquoOn the relation betweenlocal and global damage indicesrdquo Technical Report NCEER-89-0034 National Center for Earthquake Engineering Re-search State University of New York Buffalo NY USA 1989

[22] Y J Park AM Reinhorn and S K Kunnath ldquoSeismic damageanalysis of rc buildingsrdquo in Proceedings of Fe Ninth WorldConference on Earthquake Engineering Tokyo Japan 1988

[23] Y S Chung C Meyer and M Shinozuka ldquoModeling ofconcrete damagerdquo ACI Structural Journal vol 86 pp 259ndash271 1989

[24] F Legeron P Paultre and J Mazars ldquoDamage mechanicsmodeling of nonlinear seismic behavior of concrete struc-turesrdquo Journal of Structural Engineering vol 131 no 6pp 946ndash955 2005

[25] China Architecture and Building Press GB50011-2010 Codefor Seismic Design of Buildings China Architecture andBuilding Press Beijing China 2010

[26] M Nakashima and S Sawaizumi ldquoColumn-to-beam strengthratio required for ensuring beam-collapse mechanisms inearthquake responses of steel moment framesrdquo in Proceedingsof the 12th World Conference on Earthquake Engineeringvol 38 pp 52ndash29 Auckland New Zealand February 2000

[27] K L Dooley and J M Bracci ldquoSeismic evaluation of column-to-beam strength ratios in reinforced concrete framesrdquo ACIStructural Journal vol 98 no 6 pp 834ndash851 2001

[28] G L Kuntz and J Browning ldquoReduction of column yieldingduring earthquakes for reinforced concrete framesrdquo ACIStructural Journal vol 100 no 5 pp 573ndash580 2003

[29] R A Medina and H Krawinkler ldquoStrength demand issuesrelevant for the seismic design of moment-resisting framesrdquoEarthquake Spectra vol 21 no 2 pp 415ndash439 2005

[30] L F Ibarra and H Krawinkler ldquoGlobal collapse of framestructures under seismic excitationsrdquo Dissertation StanfordUniversity San Francisco CA USA 2005

[31] W J Yi and W X Zhang Architectural Structure Experi-mentation China Architecture and Building Press BeijingChina 2014

[32] B Q Liu ldquoAbout a few problems in aseismic design ofreinforced concrete framesrdquo Journal of Northwestern Institudeof Architectural Engineering vol 1 pp 1ndash3 1994

[33] S-W Khoo S Karuppanan and C-S Tan ldquoA review ofsurface deformation and strain measurement using two-di-mensional digital image correlationrdquo Metrology and Mea-surement Systems vol 23 no 3 pp 461ndash480 2016

[34] J Blaber B Adair and A Antoniou ldquoNcorr open-source 2Ddigital image correlation matlab softwarerdquo ExperimentalMechanics vol 55 no 6 pp 1105ndash1122 2015

[35] China Architecture And Building Press GB50010 Code forDesign of Concrete Structures China Architecture andBuilding Press Beijing China 2010

[36] D Dawin and C K Nmai ldquoEnergy dissipation in RC beamsunder cyclic loadrdquo Journal of Structural Engineering vol 112pp 1829ndash1846 1986

[37] S L Mccabe and W J Hall ldquoDamage and reserve capacity ofstructures subjected to strong earthquake ground motionrdquo inProceedings of 10th World Conference on EarthquakeEngineering Madrid Spain July 1992

[38] S Kumar and T Usami ldquoDamage evaluation in steel boxcolumns by cyclic loading testsrdquo Journal of Structural Engi-neering vol 122 no 6 pp 626ndash634 1996

[39] B Q Liu S L Bai and M Liu ldquoEquivalent ductility damagecriteria of earthquake-resistant structures and their verifica-tion by substructure methodrdquo Earthquake Engineering andEngineering Vibration vol 17 pp 78ndash84 1997

[40] G H Powell and R Allchabadi ldquoSeismic damage predictionby deterministic method concept and proceduresrdquo Earth-quake Engineering and Structural Dynamics vol 16 no 5pp 719ndash734 1998

[41] P S Rao B S Sarms and N Lakshmanan ldquoDamage modelfor reinforced concrete elements under cyclic loadingrdquo ACIMaterials Journal vol 95 no 6 pp 682ndash690 1998

[42] K J Elwood Shake Table Tests and Analytical Studies on theGravity Load Collapse of Reinforced Concrete Frames Dis-sertation University of California Berkeley CA USA 2002

[43] T Mohamed and K M Mosalam ldquoTowards modeling pro-gressive collapse in reinforced concrete buildingsrdquo in Pro-ceedings of Sessions of the 2007 Structures Congress LongBeach CA USA May 2007

[44] H-S Kim J Kim and D-W An ldquoDevelopment of integratedsystem for progressive collapse analysis of building structures


considering dynamic effectsrdquo Advances in Engineering Soft-ware vol 40 no 1 pp 1ndash8 2009

[45] G Siddhartha D Debarati and A A Katakdhond ldquoEsti-mation of the Park-Ang damage index for planar multi-storeyframes usingequivalent single-degree systemsrdquo EngineeringStructures vol 33 no 9 pp 2509ndash2524 2011

[46] S S F Mehanny and G G Deierlein ldquoSeismic damage andcollapse assessment of composite moment framesrdquo Journal ofStructural Engineering vol 127 no 9 pp 1045ndash1053 2001

[47] J M Bracci A M Reinhorn J B Mander and S K KunnathldquoDeterministic model for seismic damage evaluation of RCstructuresrdquo Technical Report NCEER-89ndash0033 vol 89 P33State University of New York New York NY USA 1989

[48] China Architecture and Building Press JGJ-3 TechnicalSpecification for Concrete Structure of Tall Building ChinaArchitecture and Building Press Beijing China 2010

[49] Z F Liu Q Zhou and K Chen ldquoQuantitative analysis ofseismic damage based on structural energy dissipation andstorage capabilityrdquo Engineering Mechanics vol 30 pp 169ndash189 2013

[50] E Dipasquale and A S Cakmak Identification of the Ser-viceability Limit State and Detection of Seismic StructuralDamage National Center for Earthquake Engineering Re-search New York NY USA 1988

[51] A Ghobarah H Abou-Elfath and A Biddah ldquoResponse-based damage assessment of structuresrdquo Earthquake Engi-neering amp Structural Dynamics vol 28 no 1 pp 79ndash1041999

[52] FEMA356 Prestandard and Commentary for the SeismicRehabilitation of Buildings Federal Emergency ManagementAgency Washington DC USA 2000

[53] Z Qu and L P Ye ldquoStrength deterioration model based oneffective hysteretic energy dissipation for RC members undercyclic loadingrdquo Engineering Mechanics vol 28 pp 45ndash512011

[54] D C Kent and R Park ldquoFlexural members with confinedconcreterdquo Journal of the Structural Division vol 97pp 1969ndash1990 1971

[55] B D Scott R Park and M J N Priestley ldquoStress-strainbehavior of concrete confined by overlapping hoops at lowand high strain ratesrdquo ACI Structural Journal vol 79pp 13ndash27 1982

[56] R W Clough ldquoEffect of stiffness degradation on earthquakeductility requirementsrdquo Dissertation University of Cal-ifornia Berkeley CA USA 1966


Hindawiwwwhindawicom Volume 2018

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Submit your manuscripts atwwwhindawicom

Yavari et al carried out a shaking table test on a two-storeytwo-bay frame to evaluate the effect of axial load and jointconfinement reinforcement on the seismic performance ofRC frames (e previous researches mostly focused on theglobal performance of frame structures although they maynot be significantly affected by some alterations in earthquakecharacteristics the performance of individual componentsmay change dramatically Hence it is necessary to specificallyassess the seismic performance of columns beams and beam-to-column joints in addition to the global response ofstructures(is could be achieved by carrying out a multileveldamage assessment of each individual component

Experimental studies also indicate that the hystereticbehavior of the structure is mainly dependent on the pa-rameters that affect the characteristics of deformation andenergy dissipation (us the development of smooth hys-teretic degrading model [11 12] was performed to replacethe bilinear elastic-plastic hysteresis model which waswidely used for their advantage of simplicity Analyticalinvestigation based on numerical simulation is an effectivesupplement to assess structural collapse [13ndash16] For ex-ample Haselton et al studied the influences of axial com-pression ratio strong column weak-beam ratio and P-Δeffect on the collapse risk of special moment-frame (SMF)buildings based on nonlinear dynamic analyses (e resultsshowed that the plastic deformation capacity of columns andP-Δ effect were the most important factors affecting theinterstorey displacement Shi et al evaluated the collapse-resistant capacities and safety margins against collapse ofmultistorey reinforced concrete frames with different seis-mic fortification levels based on incremental dynamicanalysis (IDA)(e influences of axial compression ratio andfailure mode on the collapse-resistant capacity of RC frameswere discussed by taking the loss of vertical bearing capacityas the evaluation index

Damage indices could quantify the damage degree ofstructures and provide a theoretical basis for postearthquakerepairing schemes At present it is generally agreed thatglobal damage indices defined as weighted average com-ponent level indices referring to the damage degree of asingle member are more precise than those defined in termsof global property variation before and after earthquake[17ndash19] which could provide reasonable evaluation of theoverall damage level at the premise that the damage dis-tributes evenly However the global damage models definedas weighted individual component indices in previous re-searches tended to give more weight to the members at lowerstories [20ndash24] but failed to take the negative influence ofdifferent types of damaged components on the structuralseismic performance into account (e effect of localizedcolumn failure on structural collapse is more obvious thanthat of beam failure or other components thus the defi-nition of weighted coefficients should consider the differ-ences particularly

In this study three 13-scale models of three-storeythree-bay reinforced concrete frame structures are testedunder low-reversed cyclic loading which could syntheticallyreflect the force characteristics of components in sidespanandmidspan at the bottom floor middle floor and top floor

Based on experimental results the damage distribution ofindividual components is investigated and the damagequantitative deduction of overall structures is accomplishedthrough a proposed global damage model (is modelconsiders the different influences of component types on thedeterioration of overall seismic performance and dividesstructural components into different types expressed ascomponent classification In addition a probabilistic as-sessment relied on nonlinear dynamic simulation is con-ducted to exhibit the further application of the globaldamage model in predicting the failure probability ofreinforced concrete frame structures

2 Specimens and Test Setup

21 Specimen Design (e prototype structure was a typicalRC moment-resisting frame structure located in an earth-quake-prone region with seismic fortification intensity 8 sitesoil class II and design group 1(e criteria of strong-columnweak-beam were adopted in the structural design accordingto the Chinese Code for Seismic Design of Buildings [25] toensure that the test frames would fail in the flexural modeunder combined lateral displacement and axial compressionload (us the cross-sectional areas of frame columns weredesigned to a larger size (600times 600mm) while those ofbeams were 300times 600mm (e component sizes in the testspecimens were defined according to the geometric reducedscale of prototype ones as 200times 200mm for columns and100times 200mm for beams respectively

To investigate the ultimate elastoplastic interstorey driftangle for preventing building collapse under strong earth-quake the test specimens with excellent ductile deformationwere designed through reasonable construction measures(e specimens were optimized by properly raising thelongitudinal reinforcement ratio of frame columns in orderto facilitate the formation of structural ldquobeam-hingerdquo failurepattern under low-reversed cyclic loading (e sum of ul-timate flexural capacity of columns framing into jointsshould be larger than that of beams in the same plane andthe overstrength factors of exterior joints at the first floorand second floor were 323 and 295 respectively whilethose of interior joints were 269 and 253 meeting theconclusions in previous researches that the strong-columnweak-beam ratio ranging from 20 to 30 is beneficial to theformation of the ldquobeam-hingerdquo mechanism [14 26ndash30] (eoverstrength factors of joints at the third floor were ignoredfor the reason that the interference effect of the loadingdevice on the strength of beams was inevitable

For the model design of overall structures the specimensare mostly scaled models due to the limitations of testingequipment and manufacturing cost Hence the lower threelayers of a single plane frame in the central axis were selectedas the prototype substructure and three 13-scale models ofthree-storey three-bay RC frames were constructed (escaled models could accurately reflect the seismic behaviorof prototypes such as the failure pattern the appearanceorder of plastic hinges the ultimate bearing capacity and theultimate deformation capacity with the method of keepingthe reinforcement ratio and material strength constant












3550

400

1100

1100

1100

250

200

200

1200

500

400

300

300 300500

300

400

600 600

600 2000 2000 2000 6007200

Oslash450Oslash475

Oslash475

10100

Oslash450Oslash4100

Oslash450

Oslash450Oslash4100

Oslash4150

1 2 21 5

5

4

43

3

(a)









200

200

200

200

400

100 400

100

1-1(2-2)

1 8(6)

2

12

2

10

8

10

4-4

3-3

5-5

8

3 6

83

63

186

186

(b)


Gantry

Distributivegirders

mTS



150mm)


Slide plate



Frame

Anchoragedevices


0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95ndash180

ndash150

ndash120

ndash90

ndash60

30

ndash30

0

60

90

120

150

1801251120 12612813013313614115015216117311221250

Operational


Load

ing

disp

lace

men

t (m

m)

Step

Operational

Slight damage

Medium damage












MTS



Foundation beamEast

Beam AB1

J-1 J-2 J-3 J-4

J-8J-5 J-6 J-7

Beam BC1

Beam BC2

Beam CD1

Beam CD2Beam AB2

Col

umn

A1

Col

umn

A2

Col

umn

A3

Col

umn

B1C

olum

n B2

Col

umn

B3

Col

umn

C1C

olum

n C2

Col

umn

C3

Col

umn

D1

Col

umn

D2

Col

umn

D3

West








D+θ

θ+p

11138681113868111386811138681113868currentPHC1113874 1113875

α+ 1113936

n+

i1θ+p

11138681113868111386811138681113868FHCi1113874 1113875

β

θ+pu1113872 1113873

α+ 1113936

n+

i1θ+p

11138681113868111386811138681113868FHCi1113874 1113875

β (1)

Dminusθ

θminusp

11138681113868111386811138681113868currentPHC1113874 1113875

α+ 1113936

nminus

i1θminusp

11138681113868111386811138681113868FHCi1113874 1113875

β

θminuspu1113872 1113873

α+ 1113936

nminus

i1θminusp

11138681113868111386811138681113868FHCi1113874 1113875

β (2)


1113968 (3)





Dbstoreyminus i

1113936mj1 Db

ji1113872 11138732

1113936mj1D

bji

(4)

Dcstoreyminus i

1113936nx1 Dc

ji1113872 11138732

1113936nx1D

cji

(5)








(6)

ζDi Dstoreyminus i


(7)

ζFi N minus i + 1

1113936Ni1i

(8)



Dtotal λh 1113944

N

i1ζ iD


N

i1ζ iD

cstoreyminus i (9)




ndash001

0

001

002

003

004

005

(a)

0

001

002

003

004

005

(b)

ndash000500005001001500200250030035004

(c)









Columns


ϕy 1957εy

h

ϕu 1587εcu

(02 + n)h

εcu 0004 +09ρvfyh

300

lp 008l + 0022dfy

(10)


Beams

θy ϕyls3

+ 00025 + ast025εydfy


1113968

ϕy fyprime

Es(1 minus ξ)h0

θu αstαcy 1 +ast

231113874 111387502]


max 001 ρfyfc1113872 11138731113872 1113873fc

⎡⎢⎣ ⎤⎥⎦

0275

middotls

h1113888 1113889

045

11 100αρsxfyhfc

1113872 111387313 100ρd( )

(11)










KJ-1





KJ-2





KJ-3













KJ-3











005002

004

005

006

004

009

016

016

025

035

025

047

016

026

045

056

036

053

014

014

034

055

026

045

019

020

060

063

155

095

011

021

051062

064094

011

019

051052

072092

009

011

051071

072097

013

015

035

046

046

050

003

004

005

007

004

005

002

007

003

006

008

011

007

004

004

009

006

011

004

007

008

007

014

014

003

006

003

008

014

015

004

007

008

018

009

022

005

008

007

012

016

023

013

007

008

018

015

014

006

004

015

015

017

019

004

007

008

006

008

017

002

005

004

004

005

014

014

021 014 019 012 015 013

010 010

003 006

013 013

007

016

003 004

055 059 054 051 054 052 059 067 064 071 072 073

102 118 115 109 106 113

110 105 109 110 108 106075 086 065 075 084 072

075 103 095 107 096 106

041 033 049 044 048 044

056 055 046 046 059 062

056 060 049 049 055 060

018 017 019 021 018 022

033 025 022 026 029 033

029 044 032 032 029 023

(a)

002

004

004

004

006

006

010

016

039

046

039

057

008

012

039

063

039

052

016

023

057

068

062

115

012

024

055

075

078

117

006

014

058

068

090

123

012

016

041

077

078

110

010

015

042

056

048

061

014

021

034

060

046

064

001

003

004

007

005

009

003

006

006

006

007

011

005

007

006

009

010

016

005

008

009

008

013

014

002

006

007

011

008

011

005

009

011

012

010

019

009

014

009

013

015

021

008

012

011

015

016

018

006

008

014

017

014

016

002

005

004

005

009

010

003

003

003

006

007

012

004 007 006 004 005 006

045 053 048 041 047 044

083 097 084 104 095 104

086 087 085 080 083 094

076 069 072 076 076 078

052 062 055 059 061 056

060 086 075 086 085 087

012 015 014 018 016 016 031 029 042 032 041 040

049 046 035 042 055 052

040 055 041 042 049 051024 033 026 028 024 021

025 022 015 018 019 023012 012 008 012 011 010

016 013 015 015 012 017

(b)

002

003

005

007

005

008

014

022

035

051

047

061

018

024

040

056

054

077

012

019

034

065

043

067

019

027

065

074

069

107

015

021

046

068

073

124

016

021

051

083

084

099

011

023

064

073

076

112

011

023

037

049

055

070

003

006

002

005

006

012

004

008

005

007

008

016

004

007

005

009

010

012

007

016

009

015

018

026

006

017

012

016

014

020

004

007

019

018

015

017

008

011

010

014

012

024

003

006

006

009

013

016

003

005

005

006

006

013

003

005

002

006

003

007

002

004

005

008

004

006

005 006 006 007 008 005

043 057 069 051 042 048

055 073 064 077 069 076

044 050 038 035 033 028

013 005 012 012 019 018

020 024 012 022 019 013

010 012 011 014 014 012 023 019 022 020 024 033

061 051 054 057 063 068

080 075 079 080 068 076

072 078 115 089 086 073

032 040 035 029 034 042

037 025 022 033 029 038

011 009 012 011 007 014

012 014 015 010 013 014

(c)



















6mm9mm27mm

6mm9mm27mm

6mm9mm27mm

63mm126mm

63mm126mm

63mm126mm

Floo

r

Floo

r

Floo

r


02 04 06 08 10 1200Damage indices

0

1

2

3

0

1

2

3

02 04 06 08 10 1200Damage indices

0

1

2

3

(a)

6mm9mm27mm

6mm9mm27mm

6mm9mm27mm

63mm126mm

63mm119mm

63mm126mm

Floo

r

Floo

r

0

1

2

3

Floo

r

0

1

2

3

02 04 06 08 10 1200Damage indices


0

1

2

3

02 04 06 08 10 1200Damage indices

(b)


Collapse

Serious damage

Medium damage

Slight damage

KJ-1KJ-2KJ-3

00

03

06

09

12

15

Dto

tal

20 40 60 80 100 120 1400Displacement (mm)

Operational











Reinforcementfiber


05dcE0

dcE0

dcE0

γsE0

E0

σ

εce εR εimax

ε

R

E0


02fimax

05E0

02fimax

fyfy2

fy2

fy

fy3 E0

E0

εy

εf

ε

σ





Pf P CDle 1 ∣ IM1 i1 IM2 i2( 1113857 (12)



σ1113888 1113889

(13)




+ d ln IM2( 1113857

+ e ln IM2( 1113857( 11138572

+ f ln IM1( 1113857ln IM2( 1113857

(14)









ndash200

ndash150

ndash100

ndash50

0

50

100

150

200F

(kN

)

Δ (mm)













SA1 (cms2)M

SA1 (cms2)M

M 8 M 7 M 6 M 5 M 8 M 7 M 6 M 5






Performancelevel

Earthquakemagnitude


SA1(cms2)

PGD SA1(cms2)





Slight damage



Mediumdamage



Serious damage




081

060402

0

0 200 400 600 800 1000

Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(a)

0 200 400 600 800 1000

081

060402

0Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(b)

0 200 400 600 8001000

45

67

8

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(c)

0 200 400 600 800 1000

445

555

6

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(d)


500

108060402

0

00 200 400 600 800 10001000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(a)

500

0 0 200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(b)

500

00200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(c)

500

0 0200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(d)



7 Conclusion






Data Availability




Acknowledgments


References




































































Journal of












Journal of







Volume 2018






Volume 2018


















3550

400

1100

1100

1100

250

200

200

1200

500

400

300

300 300500

300

400

600 600

600 2000 2000 2000 6007200

Oslash450Oslash475

Oslash475

10100

Oslash450Oslash4100

Oslash450

Oslash450Oslash4100

Oslash4150

1 2 21 5

5

4

43

3

(a)









200

200

200

200

400

100 400

100

1-1(2-2)

1 8(6)

2

12

2

10

8

10

4-4

3-3

5-5

8

3 6

83

63

186

186

(b)


Gantry

Distributivegirders

mTS



150mm)


Slide plate



Frame

Anchoragedevices


0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95ndash180

ndash150

ndash120

ndash90

ndash60

30

ndash30

0

60

90

120

150

1801251120 12612813013313614115015216117311221250

Operational


Load

ing

disp

lace

men

t (m

m)

Step

Operational

Slight damage

Medium damage












MTS



Foundation beamEast

Beam AB1

J-1 J-2 J-3 J-4

J-8J-5 J-6 J-7

Beam BC1

Beam BC2

Beam CD1

Beam CD2Beam AB2

Col

umn

A1

Col

umn

A2

Col

umn

A3

Col

umn

B1C

olum

n B2

Col

umn

B3

Col

umn

C1C

olum

n C2

Col

umn

C3

Col

umn

D1

Col

umn

D2

Col

umn

D3

West








D+θ

θ+p

11138681113868111386811138681113868currentPHC1113874 1113875

α+ 1113936

n+

i1θ+p

11138681113868111386811138681113868FHCi1113874 1113875

β

θ+pu1113872 1113873

α+ 1113936

n+

i1θ+p

11138681113868111386811138681113868FHCi1113874 1113875

β (1)

Dminusθ

θminusp

11138681113868111386811138681113868currentPHC1113874 1113875

α+ 1113936

nminus

i1θminusp

11138681113868111386811138681113868FHCi1113874 1113875

β

θminuspu1113872 1113873

α+ 1113936

nminus

i1θminusp

11138681113868111386811138681113868FHCi1113874 1113875

β (2)


1113968 (3)





Dbstoreyminus i

1113936mj1 Db

ji1113872 11138732

1113936mj1D

bji

(4)

Dcstoreyminus i

1113936nx1 Dc

ji1113872 11138732

1113936nx1D

cji

(5)








(6)

ζDi Dstoreyminus i


(7)

ζFi N minus i + 1

1113936Ni1i

(8)



Dtotal λh 1113944

N

i1ζ iD


N

i1ζ iD

cstoreyminus i (9)




ndash001

0

001

002

003

004

005

(a)

0

001

002

003

004

005

(b)

ndash000500005001001500200250030035004

(c)









Columns


ϕy 1957εy

h

ϕu 1587εcu

(02 + n)h

εcu 0004 +09ρvfyh

300

lp 008l + 0022dfy

(10)


Beams

θy ϕyls3

+ 00025 + ast025εydfy


1113968

ϕy fyprime

Es(1 minus ξ)h0

θu αstαcy 1 +ast

231113874 111387502]


max 001 ρfyfc1113872 11138731113872 1113873fc

⎡⎢⎣ ⎤⎥⎦

0275

middotls

h1113888 1113889

045

11 100αρsxfyhfc

1113872 111387313 100ρd( )

(11)










KJ-1





KJ-2





KJ-3













KJ-3











005002

004

005

006

004

009

016

016

025

035

025

047

016

026

045

056

036

053

014

014

034

055

026

045

019

020

060

063

155

095

011

021

051062

064094

011

019

051052

072092

009

011

051071

072097

013

015

035

046

046

050

003

004

005

007

004

005

002

007

003

006

008

011

007

004

004

009

006

011

004

007

008

007

014

014

003

006

003

008

014

015

004

007

008

018

009

022

005

008

007

012

016

023

013

007

008

018

015

014

006

004

015

015

017

019

004

007

008

006

008

017

002

005

004

004

005

014

014

021 014 019 012 015 013

010 010

003 006

013 013

007

016

003 004

055 059 054 051 054 052 059 067 064 071 072 073

102 118 115 109 106 113

110 105 109 110 108 106075 086 065 075 084 072

075 103 095 107 096 106

041 033 049 044 048 044

056 055 046 046 059 062

056 060 049 049 055 060

018 017 019 021 018 022

033 025 022 026 029 033

029 044 032 032 029 023

(a)

002

004

004

004

006

006

010

016

039

046

039

057

008

012

039

063

039

052

016

023

057

068

062

115

012

024

055

075

078

117

006

014

058

068

090

123

012

016

041

077

078

110

010

015

042

056

048

061

014

021

034

060

046

064

001

003

004

007

005

009

003

006

006

006

007

011

005

007

006

009

010

016

005

008

009

008

013

014

002

006

007

011

008

011

005

009

011

012

010

019

009

014

009

013

015

021

008

012

011

015

016

018

006

008

014

017

014

016

002

005

004

005

009

010

003

003

003

006

007

012

004 007 006 004 005 006

045 053 048 041 047 044

083 097 084 104 095 104

086 087 085 080 083 094

076 069 072 076 076 078

052 062 055 059 061 056

060 086 075 086 085 087

012 015 014 018 016 016 031 029 042 032 041 040

049 046 035 042 055 052

040 055 041 042 049 051024 033 026 028 024 021

025 022 015 018 019 023012 012 008 012 011 010

016 013 015 015 012 017

(b)

002

003

005

007

005

008

014

022

035

051

047

061

018

024

040

056

054

077

012

019

034

065

043

067

019

027

065

074

069

107

015

021

046

068

073

124

016

021

051

083

084

099

011

023

064

073

076

112

011

023

037

049

055

070

003

006

002

005

006

012

004

008

005

007

008

016

004

007

005

009

010

012

007

016

009

015

018

026

006

017

012

016

014

020

004

007

019

018

015

017

008

011

010

014

012

024

003

006

006

009

013

016

003

005

005

006

006

013

003

005

002

006

003

007

002

004

005

008

004

006

005 006 006 007 008 005

043 057 069 051 042 048

055 073 064 077 069 076

044 050 038 035 033 028

013 005 012 012 019 018

020 024 012 022 019 013

010 012 011 014 014 012 023 019 022 020 024 033

061 051 054 057 063 068

080 075 079 080 068 076

072 078 115 089 086 073

032 040 035 029 034 042

037 025 022 033 029 038

011 009 012 011 007 014

012 014 015 010 013 014

(c)



















6mm9mm27mm

6mm9mm27mm

6mm9mm27mm

63mm126mm

63mm126mm

63mm126mm

Floo

r

Floo

r

Floo

r


02 04 06 08 10 1200Damage indices

0

1

2

3

0

1

2

3

02 04 06 08 10 1200Damage indices

0

1

2

3

(a)

6mm9mm27mm

6mm9mm27mm

6mm9mm27mm

63mm126mm

63mm119mm

63mm126mm

Floo

r

Floo

r

0

1

2

3

Floo

r

0

1

2

3

02 04 06 08 10 1200Damage indices


0

1

2

3

02 04 06 08 10 1200Damage indices

(b)


Collapse

Serious damage

Medium damage

Slight damage

KJ-1KJ-2KJ-3

00

03

06

09

12

15

Dto

tal

20 40 60 80 100 120 1400Displacement (mm)

Operational











Reinforcementfiber


05dcE0

dcE0

dcE0

γsE0

E0

σ

εce εR εimax

ε

R

E0


02fimax

05E0

02fimax

fyfy2

fy2

fy

fy3 E0

E0

εy

εf

ε

σ





Pf P CDle 1 ∣ IM1 i1 IM2 i2( 1113857 (12)



σ1113888 1113889

(13)




+ d ln IM2( 1113857

+ e ln IM2( 1113857( 11138572

+ f ln IM1( 1113857ln IM2( 1113857

(14)









ndash200

ndash150

ndash100

ndash50

0

50

100

150

200F

(kN

)

Δ (mm)













SA1 (cms2)M

SA1 (cms2)M

M 8 M 7 M 6 M 5 M 8 M 7 M 6 M 5






Performancelevel

Earthquakemagnitude


SA1(cms2)

PGD SA1(cms2)





Slight damage



Mediumdamage



Serious damage




081

060402

0

0 200 400 600 800 1000

Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(a)

0 200 400 600 800 1000

081

060402

0Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(b)

0 200 400 600 8001000

45

67

8

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(c)

0 200 400 600 800 1000

445

555

6

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(d)


500

108060402

0

00 200 400 600 800 10001000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(a)

500

0 0 200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(b)

500

00200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(c)

500

0 0200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(d)



7 Conclusion






Data Availability




Acknowledgments


References




































































Journal of












Journal of







Volume 2018






Volume 2018
















MTS



Foundation beamEast

Beam AB1

J-1 J-2 J-3 J-4

J-8J-5 J-6 J-7

Beam BC1

Beam BC2

Beam CD1

Beam CD2Beam AB2

Col

umn

A1

Col

umn

A2

Col

umn

A3

Col

umn

B1C

olum

n B2

Col

umn

B3

Col

umn

C1C

olum

n C2

Col

umn

C3

Col

umn

D1

Col

umn

D2

Col

umn

D3

West








D+θ

θ+p

11138681113868111386811138681113868currentPHC1113874 1113875

α+ 1113936

n+

i1θ+p

11138681113868111386811138681113868FHCi1113874 1113875

β

θ+pu1113872 1113873

α+ 1113936

n+

i1θ+p

11138681113868111386811138681113868FHCi1113874 1113875

β (1)

Dminusθ

θminusp

11138681113868111386811138681113868currentPHC1113874 1113875

α+ 1113936

nminus

i1θminusp

11138681113868111386811138681113868FHCi1113874 1113875

β

θminuspu1113872 1113873

α+ 1113936

nminus

i1θminusp

11138681113868111386811138681113868FHCi1113874 1113875

β (2)


1113968 (3)





Dbstoreyminus i

1113936mj1 Db

ji1113872 11138732

1113936mj1D

bji

(4)

Dcstoreyminus i

1113936nx1 Dc

ji1113872 11138732

1113936nx1D

cji

(5)








(6)

ζDi Dstoreyminus i


(7)

ζFi N minus i + 1

1113936Ni1i

(8)



Dtotal λh 1113944

N

i1ζ iD


N

i1ζ iD

cstoreyminus i (9)




ndash001

0

001

002

003

004

005

(a)

0

001

002

003

004

005

(b)

ndash000500005001001500200250030035004

(c)









Columns


ϕy 1957εy

h

ϕu 1587εcu

(02 + n)h

εcu 0004 +09ρvfyh

300

lp 008l + 0022dfy

(10)


Beams

θy ϕyls3

+ 00025 + ast025εydfy


1113968

ϕy fyprime

Es(1 minus ξ)h0

θu αstαcy 1 +ast

231113874 111387502]


max 001 ρfyfc1113872 11138731113872 1113873fc

⎡⎢⎣ ⎤⎥⎦

0275

middotls

h1113888 1113889

045

11 100αρsxfyhfc

1113872 111387313 100ρd( )

(11)










KJ-1





KJ-2





KJ-3













KJ-3











005002

004

005

006

004

009

016

016

025

035

025

047

016

026

045

056

036

053

014

014

034

055

026

045

019

020

060

063

155

095

011

021

051062

064094

011

019

051052

072092

009

011

051071

072097

013

015

035

046

046

050

003

004

005

007

004

005

002

007

003

006

008

011

007

004

004

009

006

011

004

007

008

007

014

014

003

006

003

008

014

015

004

007

008

018

009

022

005

008

007

012

016

023

013

007

008

018

015

014

006

004

015

015

017

019

004

007

008

006

008

017

002

005

004

004

005

014

014

021 014 019 012 015 013

010 010

003 006

013 013

007

016

003 004

055 059 054 051 054 052 059 067 064 071 072 073

102 118 115 109 106 113

110 105 109 110 108 106075 086 065 075 084 072

075 103 095 107 096 106

041 033 049 044 048 044

056 055 046 046 059 062

056 060 049 049 055 060

018 017 019 021 018 022

033 025 022 026 029 033

029 044 032 032 029 023

(a)

002

004

004

004

006

006

010

016

039

046

039

057

008

012

039

063

039

052

016

023

057

068

062

115

012

024

055

075

078

117

006

014

058

068

090

123

012

016

041

077

078

110

010

015

042

056

048

061

014

021

034

060

046

064

001

003

004

007

005

009

003

006

006

006

007

011

005

007

006

009

010

016

005

008

009

008

013

014

002

006

007

011

008

011

005

009

011

012

010

019

009

014

009

013

015

021

008

012

011

015

016

018

006

008

014

017

014

016

002

005

004

005

009

010

003

003

003

006

007

012

004 007 006 004 005 006

045 053 048 041 047 044

083 097 084 104 095 104

086 087 085 080 083 094

076 069 072 076 076 078

052 062 055 059 061 056

060 086 075 086 085 087

012 015 014 018 016 016 031 029 042 032 041 040

049 046 035 042 055 052

040 055 041 042 049 051024 033 026 028 024 021

025 022 015 018 019 023012 012 008 012 011 010

016 013 015 015 012 017

(b)

002

003

005

007

005

008

014

022

035

051

047

061

018

024

040

056

054

077

012

019

034

065

043

067

019

027

065

074

069

107

015

021

046

068

073

124

016

021

051

083

084

099

011

023

064

073

076

112

011

023

037

049

055

070

003

006

002

005

006

012

004

008

005

007

008

016

004

007

005

009

010

012

007

016

009

015

018

026

006

017

012

016

014

020

004

007

019

018

015

017

008

011

010

014

012

024

003

006

006

009

013

016

003

005

005

006

006

013

003

005

002

006

003

007

002

004

005

008

004

006

005 006 006 007 008 005

043 057 069 051 042 048

055 073 064 077 069 076

044 050 038 035 033 028

013 005 012 012 019 018

020 024 012 022 019 013

010 012 011 014 014 012 023 019 022 020 024 033

061 051 054 057 063 068

080 075 079 080 068 076

072 078 115 089 086 073

032 040 035 029 034 042

037 025 022 033 029 038

011 009 012 011 007 014

012 014 015 010 013 014

(c)



















6mm9mm27mm

6mm9mm27mm

6mm9mm27mm

63mm126mm

63mm126mm

63mm126mm

Floo

r

Floo

r

Floo

r


02 04 06 08 10 1200Damage indices

0

1

2

3

0

1

2

3

02 04 06 08 10 1200Damage indices

0

1

2

3

(a)

6mm9mm27mm

6mm9mm27mm

6mm9mm27mm

63mm126mm

63mm119mm

63mm126mm

Floo

r

Floo

r

0

1

2

3

Floo

r

0

1

2

3

02 04 06 08 10 1200Damage indices


0

1

2

3

02 04 06 08 10 1200Damage indices

(b)


Collapse

Serious damage

Medium damage

Slight damage

KJ-1KJ-2KJ-3

00

03

06

09

12

15

Dto

tal

20 40 60 80 100 120 1400Displacement (mm)

Operational











Reinforcementfiber


05dcE0

dcE0

dcE0

γsE0

E0

σ

εce εR εimax

ε

R

E0


02fimax

05E0

02fimax

fyfy2

fy2

fy

fy3 E0

E0

εy

εf

ε

σ





Pf P CDle 1 ∣ IM1 i1 IM2 i2( 1113857 (12)



σ1113888 1113889

(13)




+ d ln IM2( 1113857

+ e ln IM2( 1113857( 11138572

+ f ln IM1( 1113857ln IM2( 1113857

(14)









ndash200

ndash150

ndash100

ndash50

0

50

100

150

200F

(kN

)

Δ (mm)













SA1 (cms2)M

SA1 (cms2)M

M 8 M 7 M 6 M 5 M 8 M 7 M 6 M 5






Performancelevel

Earthquakemagnitude


SA1(cms2)

PGD SA1(cms2)





Slight damage



Mediumdamage



Serious damage




081

060402

0

0 200 400 600 800 1000

Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(a)

0 200 400 600 800 1000

081

060402

0Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(b)

0 200 400 600 8001000

45

67

8

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(c)

0 200 400 600 800 1000

445

555

6

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(d)


500

108060402

0

00 200 400 600 800 10001000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(a)

500

0 0 200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(b)

500

00200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(c)

500

0 0200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(d)



7 Conclusion






Data Availability




Acknowledgments


References




































































Journal of












Journal of







Volume 2018






Volume 2018













D+θ

θ+p

11138681113868111386811138681113868currentPHC1113874 1113875

α+ 1113936

n+

i1θ+p

11138681113868111386811138681113868FHCi1113874 1113875

β

θ+pu1113872 1113873

α+ 1113936

n+

i1θ+p

11138681113868111386811138681113868FHCi1113874 1113875

β (1)

Dminusθ

θminusp

11138681113868111386811138681113868currentPHC1113874 1113875

α+ 1113936

nminus

i1θminusp

11138681113868111386811138681113868FHCi1113874 1113875

β

θminuspu1113872 1113873

α+ 1113936

nminus

i1θminusp

11138681113868111386811138681113868FHCi1113874 1113875

β (2)


1113968 (3)





Dbstoreyminus i

1113936mj1 Db

ji1113872 11138732

1113936mj1D

bji

(4)

Dcstoreyminus i

1113936nx1 Dc

ji1113872 11138732

1113936nx1D

cji

(5)








(6)

ζDi Dstoreyminus i


(7)

ζFi N minus i + 1

1113936Ni1i

(8)



Dtotal λh 1113944

N

i1ζ iD


N

i1ζ iD

cstoreyminus i (9)




ndash001

0

001

002

003

004

005

(a)

0

001

002

003

004

005

(b)

ndash000500005001001500200250030035004

(c)









Columns


ϕy 1957εy

h

ϕu 1587εcu

(02 + n)h

εcu 0004 +09ρvfyh

300

lp 008l + 0022dfy

(10)


Beams

θy ϕyls3

+ 00025 + ast025εydfy


1113968

ϕy fyprime

Es(1 minus ξ)h0

θu αstαcy 1 +ast

231113874 111387502]


max 001 ρfyfc1113872 11138731113872 1113873fc

⎡⎢⎣ ⎤⎥⎦

0275

middotls

h1113888 1113889

045

11 100αρsxfyhfc

1113872 111387313 100ρd( )

(11)










KJ-1





KJ-2





KJ-3













KJ-3











005002

004

005

006

004

009

016

016

025

035

025

047

016

026

045

056

036

053

014

014

034

055

026

045

019

020

060

063

155

095

011

021

051062

064094

011

019

051052

072092

009

011

051071

072097

013

015

035

046

046

050

003

004

005

007

004

005

002

007

003

006

008

011

007

004

004

009

006

011

004

007

008

007

014

014

003

006

003

008

014

015

004

007

008

018

009

022

005

008

007

012

016

023

013

007

008

018

015

014

006

004

015

015

017

019

004

007

008

006

008

017

002

005

004

004

005

014

014

021 014 019 012 015 013

010 010

003 006

013 013

007

016

003 004

055 059 054 051 054 052 059 067 064 071 072 073

102 118 115 109 106 113

110 105 109 110 108 106075 086 065 075 084 072

075 103 095 107 096 106

041 033 049 044 048 044

056 055 046 046 059 062

056 060 049 049 055 060

018 017 019 021 018 022

033 025 022 026 029 033

029 044 032 032 029 023

(a)

002

004

004

004

006

006

010

016

039

046

039

057

008

012

039

063

039

052

016

023

057

068

062

115

012

024

055

075

078

117

006

014

058

068

090

123

012

016

041

077

078

110

010

015

042

056

048

061

014

021

034

060

046

064

001

003

004

007

005

009

003

006

006

006

007

011

005

007

006

009

010

016

005

008

009

008

013

014

002

006

007

011

008

011

005

009

011

012

010

019

009

014

009

013

015

021

008

012

011

015

016

018

006

008

014

017

014

016

002

005

004

005

009

010

003

003

003

006

007

012

004 007 006 004 005 006

045 053 048 041 047 044

083 097 084 104 095 104

086 087 085 080 083 094

076 069 072 076 076 078

052 062 055 059 061 056

060 086 075 086 085 087

012 015 014 018 016 016 031 029 042 032 041 040

049 046 035 042 055 052

040 055 041 042 049 051024 033 026 028 024 021

025 022 015 018 019 023012 012 008 012 011 010

016 013 015 015 012 017

(b)

002

003

005

007

005

008

014

022

035

051

047

061

018

024

040

056

054

077

012

019

034

065

043

067

019

027

065

074

069

107

015

021

046

068

073

124

016

021

051

083

084

099

011

023

064

073

076

112

011

023

037

049

055

070

003

006

002

005

006

012

004

008

005

007

008

016

004

007

005

009

010

012

007

016

009

015

018

026

006

017

012

016

014

020

004

007

019

018

015

017

008

011

010

014

012

024

003

006

006

009

013

016

003

005

005

006

006

013

003

005

002

006

003

007

002

004

005

008

004

006

005 006 006 007 008 005

043 057 069 051 042 048

055 073 064 077 069 076

044 050 038 035 033 028

013 005 012 012 019 018

020 024 012 022 019 013

010 012 011 014 014 012 023 019 022 020 024 033

061 051 054 057 063 068

080 075 079 080 068 076

072 078 115 089 086 073

032 040 035 029 034 042

037 025 022 033 029 038

011 009 012 011 007 014

012 014 015 010 013 014

(c)



















6mm9mm27mm

6mm9mm27mm

6mm9mm27mm

63mm126mm

63mm126mm

63mm126mm

Floo

r

Floo

r

Floo

r


02 04 06 08 10 1200Damage indices

0

1

2

3

0

1

2

3

02 04 06 08 10 1200Damage indices

0

1

2

3

(a)

6mm9mm27mm

6mm9mm27mm

6mm9mm27mm

63mm126mm

63mm119mm

63mm126mm

Floo

r

Floo

r

0

1

2

3

Floo

r

0

1

2

3

02 04 06 08 10 1200Damage indices


0

1

2

3

02 04 06 08 10 1200Damage indices

(b)


Collapse

Serious damage

Medium damage

Slight damage

KJ-1KJ-2KJ-3

00

03

06

09

12

15

Dto

tal

20 40 60 80 100 120 1400Displacement (mm)

Operational











Reinforcementfiber


05dcE0

dcE0

dcE0

γsE0

E0

σ

εce εR εimax

ε

R

E0


02fimax

05E0

02fimax

fyfy2

fy2

fy

fy3 E0

E0

εy

εf

ε

σ





Pf P CDle 1 ∣ IM1 i1 IM2 i2( 1113857 (12)



σ1113888 1113889

(13)




+ d ln IM2( 1113857

+ e ln IM2( 1113857( 11138572

+ f ln IM1( 1113857ln IM2( 1113857

(14)









ndash200

ndash150

ndash100

ndash50

0

50

100

150

200F

(kN

)

Δ (mm)













SA1 (cms2)M

SA1 (cms2)M

M 8 M 7 M 6 M 5 M 8 M 7 M 6 M 5






Performancelevel

Earthquakemagnitude


SA1(cms2)

PGD SA1(cms2)





Slight damage



Mediumdamage



Serious damage




081

060402

0

0 200 400 600 800 1000

Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(a)

0 200 400 600 800 1000

081

060402

0Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(b)

0 200 400 600 8001000

45

67

8

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(c)

0 200 400 600 800 1000

445

555

6

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(d)


500

108060402

0

00 200 400 600 800 10001000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(a)

500

0 0 200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(b)

500

00200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(c)

500

0 0200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(d)



7 Conclusion






Data Availability




Acknowledgments


References




































































Journal of












Journal of







Volume 2018






Volume 2018









Dbstoreyminus i

1113936mj1 Db

ji1113872 11138732

1113936mj1D

bji

(4)

Dcstoreyminus i

1113936nx1 Dc

ji1113872 11138732

1113936nx1D

cji

(5)








(6)

ζDi Dstoreyminus i


(7)

ζFi N minus i + 1

1113936Ni1i

(8)



Dtotal λh 1113944

N

i1ζ iD


N

i1ζ iD

cstoreyminus i (9)




ndash001

0

001

002

003

004

005

(a)

0

001

002

003

004

005

(b)

ndash000500005001001500200250030035004

(c)









Columns


ϕy 1957εy

h

ϕu 1587εcu

(02 + n)h

εcu 0004 +09ρvfyh

300

lp 008l + 0022dfy

(10)


Beams

θy ϕyls3

+ 00025 + ast025εydfy


1113968

ϕy fyprime

Es(1 minus ξ)h0

θu αstαcy 1 +ast

231113874 111387502]


max 001 ρfyfc1113872 11138731113872 1113873fc

⎡⎢⎣ ⎤⎥⎦

0275

middotls

h1113888 1113889

045

11 100αρsxfyhfc

1113872 111387313 100ρd( )

(11)










KJ-1





KJ-2





KJ-3













KJ-3











005002

004

005

006

004

009

016

016

025

035

025

047

016

026

045

056

036

053

014

014

034

055

026

045

019

020

060

063

155

095

011

021

051062

064094

011

019

051052

072092

009

011

051071

072097

013

015

035

046

046

050

003

004

005

007

004

005

002

007

003

006

008

011

007

004

004

009

006

011

004

007

008

007

014

014

003

006

003

008

014

015

004

007

008

018

009

022

005

008

007

012

016

023

013

007

008

018

015

014

006

004

015

015

017

019

004

007

008

006

008

017

002

005

004

004

005

014

014

021 014 019 012 015 013

010 010

003 006

013 013

007

016

003 004

055 059 054 051 054 052 059 067 064 071 072 073

102 118 115 109 106 113

110 105 109 110 108 106075 086 065 075 084 072

075 103 095 107 096 106

041 033 049 044 048 044

056 055 046 046 059 062

056 060 049 049 055 060

018 017 019 021 018 022

033 025 022 026 029 033

029 044 032 032 029 023

(a)

002

004

004

004

006

006

010

016

039

046

039

057

008

012

039

063

039

052

016

023

057

068

062

115

012

024

055

075

078

117

006

014

058

068

090

123

012

016

041

077

078

110

010

015

042

056

048

061

014

021

034

060

046

064

001

003

004

007

005

009

003

006

006

006

007

011

005

007

006

009

010

016

005

008

009

008

013

014

002

006

007

011

008

011

005

009

011

012

010

019

009

014

009

013

015

021

008

012

011

015

016

018

006

008

014

017

014

016

002

005

004

005

009

010

003

003

003

006

007

012

004 007 006 004 005 006

045 053 048 041 047 044

083 097 084 104 095 104

086 087 085 080 083 094

076 069 072 076 076 078

052 062 055 059 061 056

060 086 075 086 085 087

012 015 014 018 016 016 031 029 042 032 041 040

049 046 035 042 055 052

040 055 041 042 049 051024 033 026 028 024 021

025 022 015 018 019 023012 012 008 012 011 010

016 013 015 015 012 017

(b)

002

003

005

007

005

008

014

022

035

051

047

061

018

024

040

056

054

077

012

019

034

065

043

067

019

027

065

074

069

107

015

021

046

068

073

124

016

021

051

083

084

099

011

023

064

073

076

112

011

023

037

049

055

070

003

006

002

005

006

012

004

008

005

007

008

016

004

007

005

009

010

012

007

016

009

015

018

026

006

017

012

016

014

020

004

007

019

018

015

017

008

011

010

014

012

024

003

006

006

009

013

016

003

005

005

006

006

013

003

005

002

006

003

007

002

004

005

008

004

006

005 006 006 007 008 005

043 057 069 051 042 048

055 073 064 077 069 076

044 050 038 035 033 028

013 005 012 012 019 018

020 024 012 022 019 013

010 012 011 014 014 012 023 019 022 020 024 033

061 051 054 057 063 068

080 075 079 080 068 076

072 078 115 089 086 073

032 040 035 029 034 042

037 025 022 033 029 038

011 009 012 011 007 014

012 014 015 010 013 014

(c)



















6mm9mm27mm

6mm9mm27mm

6mm9mm27mm

63mm126mm

63mm126mm

63mm126mm

Floo

r

Floo

r

Floo

r


02 04 06 08 10 1200Damage indices

0

1

2

3

0

1

2

3

02 04 06 08 10 1200Damage indices

0

1

2

3

(a)

6mm9mm27mm

6mm9mm27mm

6mm9mm27mm

63mm126mm

63mm119mm

63mm126mm

Floo

r

Floo

r

0

1

2

3

Floo

r

0

1

2

3

02 04 06 08 10 1200Damage indices


0

1

2

3

02 04 06 08 10 1200Damage indices

(b)


Collapse

Serious damage

Medium damage

Slight damage

KJ-1KJ-2KJ-3

00

03

06

09

12

15

Dto

tal

20 40 60 80 100 120 1400Displacement (mm)

Operational











Reinforcementfiber


05dcE0

dcE0

dcE0

γsE0

E0

σ

εce εR εimax

ε

R

E0


02fimax

05E0

02fimax

fyfy2

fy2

fy

fy3 E0

E0

εy

εf

ε

σ





Pf P CDle 1 ∣ IM1 i1 IM2 i2( 1113857 (12)



σ1113888 1113889

(13)




+ d ln IM2( 1113857

+ e ln IM2( 1113857( 11138572

+ f ln IM1( 1113857ln IM2( 1113857

(14)









ndash200

ndash150

ndash100

ndash50

0

50

100

150

200F

(kN

)

Δ (mm)













SA1 (cms2)M

SA1 (cms2)M

M 8 M 7 M 6 M 5 M 8 M 7 M 6 M 5






Performancelevel

Earthquakemagnitude


SA1(cms2)

PGD SA1(cms2)





Slight damage



Mediumdamage



Serious damage




081

060402

0

0 200 400 600 800 1000

Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(a)

0 200 400 600 800 1000

081

060402

0Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(b)

0 200 400 600 8001000

45

67

8

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(c)

0 200 400 600 800 1000

445

555

6

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(d)


500

108060402

0

00 200 400 600 800 10001000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(a)

500

0 0 200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(b)

500

00200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(c)

500

0 0200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(d)



7 Conclusion






Data Availability




Acknowledgments


References




































































Journal of












Journal of







Volume 2018






Volume 2018














Columns


ϕy 1957εy

h

ϕu 1587εcu

(02 + n)h

εcu 0004 +09ρvfyh

300

lp 008l + 0022dfy

(10)


Beams

θy ϕyls3

+ 00025 + ast025εydfy


1113968

ϕy fyprime

Es(1 minus ξ)h0

θu αstαcy 1 +ast

231113874 111387502]


max 001 ρfyfc1113872 11138731113872 1113873fc

⎡⎢⎣ ⎤⎥⎦

0275

middotls

h1113888 1113889

045

11 100αρsxfyhfc

1113872 111387313 100ρd( )

(11)










KJ-1





KJ-2





KJ-3













KJ-3











005002

004

005

006

004

009

016

016

025

035

025

047

016

026

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055 059 054 051 054 052 059 067 064 071 072 073

102 118 115 109 106 113

110 105 109 110 108 106075 086 065 075 084 072

075 103 095 107 096 106

041 033 049 044 048 044

056 055 046 046 059 062

056 060 049 049 055 060

018 017 019 021 018 022

033 025 022 026 029 033

029 044 032 032 029 023

(a)

002

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086 087 085 080 083 094

076 069 072 076 076 078

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060 086 075 086 085 087

012 015 014 018 016 016 031 029 042 032 041 040

049 046 035 042 055 052

040 055 041 042 049 051024 033 026 028 024 021

025 022 015 018 019 023012 012 008 012 011 010

016 013 015 015 012 017

(b)

002

003

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055 073 064 077 069 076

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020 024 012 022 019 013

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061 051 054 057 063 068

080 075 079 080 068 076

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032 040 035 029 034 042

037 025 022 033 029 038

011 009 012 011 007 014

012 014 015 010 013 014

(c)



















6mm9mm27mm

6mm9mm27mm

6mm9mm27mm

63mm126mm

63mm126mm

63mm126mm

Floo

r

Floo

r

Floo

r


02 04 06 08 10 1200Damage indices

0

1

2

3

0

1

2

3

02 04 06 08 10 1200Damage indices

0

1

2

3

(a)

6mm9mm27mm

6mm9mm27mm

6mm9mm27mm

63mm126mm

63mm119mm

63mm126mm

Floo

r

Floo

r

0

1

2

3

Floo

r

0

1

2

3

02 04 06 08 10 1200Damage indices


0

1

2

3

02 04 06 08 10 1200Damage indices

(b)


Collapse

Serious damage

Medium damage

Slight damage

KJ-1KJ-2KJ-3

00

03

06

09

12

15

Dto

tal

20 40 60 80 100 120 1400Displacement (mm)

Operational











Reinforcementfiber


05dcE0

dcE0

dcE0

γsE0

E0

σ

εce εR εimax

ε

R

E0


02fimax

05E0

02fimax

fyfy2

fy2

fy

fy3 E0

E0

εy

εf

ε

σ





Pf P CDle 1 ∣ IM1 i1 IM2 i2( 1113857 (12)



σ1113888 1113889

(13)




+ d ln IM2( 1113857

+ e ln IM2( 1113857( 11138572

+ f ln IM1( 1113857ln IM2( 1113857

(14)









ndash200

ndash150

ndash100

ndash50

0

50

100

150

200F

(kN

)

Δ (mm)













SA1 (cms2)M

SA1 (cms2)M

M 8 M 7 M 6 M 5 M 8 M 7 M 6 M 5






Performancelevel

Earthquakemagnitude


SA1(cms2)

PGD SA1(cms2)





Slight damage



Mediumdamage



Serious damage




081

060402

0

0 200 400 600 800 1000

Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(a)

0 200 400 600 800 1000

081

060402

0Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(b)

0 200 400 600 8001000

45

67

8

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(c)

0 200 400 600 800 1000

445

555

6

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(d)


500

108060402

0

00 200 400 600 800 10001000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(a)

500

0 0 200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(b)

500

00200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(c)

500

0 0200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(d)



7 Conclusion






Data Availability




Acknowledgments


References




































































Journal of












Journal of







Volume 2018






Volume 2018














KJ-1





KJ-2





KJ-3













KJ-3











005002

004

005

006

004

009

016

016

025

035

025

047

016

026

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055 059 054 051 054 052 059 067 064 071 072 073

102 118 115 109 106 113

110 105 109 110 108 106075 086 065 075 084 072

075 103 095 107 096 106

041 033 049 044 048 044

056 055 046 046 059 062

056 060 049 049 055 060

018 017 019 021 018 022

033 025 022 026 029 033

029 044 032 032 029 023

(a)

002

004

004

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006

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012 015 014 018 016 016 031 029 042 032 041 040

049 046 035 042 055 052

040 055 041 042 049 051024 033 026 028 024 021

025 022 015 018 019 023012 012 008 012 011 010

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(b)

002

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043 057 069 051 042 048

055 073 064 077 069 076

044 050 038 035 033 028

013 005 012 012 019 018

020 024 012 022 019 013

010 012 011 014 014 012 023 019 022 020 024 033

061 051 054 057 063 068

080 075 079 080 068 076

072 078 115 089 086 073

032 040 035 029 034 042

037 025 022 033 029 038

011 009 012 011 007 014

012 014 015 010 013 014

(c)



















6mm9mm27mm

6mm9mm27mm

6mm9mm27mm

63mm126mm

63mm126mm

63mm126mm

Floo

r

Floo

r

Floo

r


02 04 06 08 10 1200Damage indices

0

1

2

3

0

1

2

3

02 04 06 08 10 1200Damage indices

0

1

2

3

(a)

6mm9mm27mm

6mm9mm27mm

6mm9mm27mm

63mm126mm

63mm119mm

63mm126mm

Floo

r

Floo

r

0

1

2

3

Floo

r

0

1

2

3

02 04 06 08 10 1200Damage indices


0

1

2

3

02 04 06 08 10 1200Damage indices

(b)


Collapse

Serious damage

Medium damage

Slight damage

KJ-1KJ-2KJ-3

00

03

06

09

12

15

Dto

tal

20 40 60 80 100 120 1400Displacement (mm)

Operational











Reinforcementfiber


05dcE0

dcE0

dcE0

γsE0

E0

σ

εce εR εimax

ε

R

E0


02fimax

05E0

02fimax

fyfy2

fy2

fy

fy3 E0

E0

εy

εf

ε

σ





Pf P CDle 1 ∣ IM1 i1 IM2 i2( 1113857 (12)



σ1113888 1113889

(13)




+ d ln IM2( 1113857

+ e ln IM2( 1113857( 11138572

+ f ln IM1( 1113857ln IM2( 1113857

(14)









ndash200

ndash150

ndash100

ndash50

0

50

100

150

200F

(kN

)

Δ (mm)













SA1 (cms2)M

SA1 (cms2)M

M 8 M 7 M 6 M 5 M 8 M 7 M 6 M 5






Performancelevel

Earthquakemagnitude


SA1(cms2)

PGD SA1(cms2)





Slight damage



Mediumdamage



Serious damage




081

060402

0

0 200 400 600 800 1000

Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(a)

0 200 400 600 800 1000

081

060402

0Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(b)

0 200 400 600 8001000

45

67

8

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(c)

0 200 400 600 800 1000

445

555

6

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(d)


500

108060402

0

00 200 400 600 800 10001000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(a)

500

0 0 200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(b)

500

00200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(c)

500

0 0200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(d)



7 Conclusion






Data Availability




Acknowledgments


References




































































Journal of












Journal of







Volume 2018






Volume 2018











005002

004

005

006

004

009

016

016

025

035

025

047

016

026

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056

036

053

014

014

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075 103 095 107 096 106

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(a)

002

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040 055 041 042 049 051024 033 026 028 024 021

025 022 015 018 019 023012 012 008 012 011 010

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(b)

002

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005 006 006 007 008 005

043 057 069 051 042 048

055 073 064 077 069 076

044 050 038 035 033 028

013 005 012 012 019 018

020 024 012 022 019 013

010 012 011 014 014 012 023 019 022 020 024 033

061 051 054 057 063 068

080 075 079 080 068 076

072 078 115 089 086 073

032 040 035 029 034 042

037 025 022 033 029 038

011 009 012 011 007 014

012 014 015 010 013 014

(c)



















6mm9mm27mm

6mm9mm27mm

6mm9mm27mm

63mm126mm

63mm126mm

63mm126mm

Floo

r

Floo

r

Floo

r


02 04 06 08 10 1200Damage indices

0

1

2

3

0

1

2

3

02 04 06 08 10 1200Damage indices

0

1

2

3

(a)

6mm9mm27mm

6mm9mm27mm

6mm9mm27mm

63mm126mm

63mm119mm

63mm126mm

Floo

r

Floo

r

0

1

2

3

Floo

r

0

1

2

3

02 04 06 08 10 1200Damage indices


0

1

2

3

02 04 06 08 10 1200Damage indices

(b)


Collapse

Serious damage

Medium damage

Slight damage

KJ-1KJ-2KJ-3

00

03

06

09

12

15

Dto

tal

20 40 60 80 100 120 1400Displacement (mm)

Operational











Reinforcementfiber


05dcE0

dcE0

dcE0

γsE0

E0

σ

εce εR εimax

ε

R

E0


02fimax

05E0

02fimax

fyfy2

fy2

fy

fy3 E0

E0

εy

εf

ε

σ





Pf P CDle 1 ∣ IM1 i1 IM2 i2( 1113857 (12)



σ1113888 1113889

(13)




+ d ln IM2( 1113857

+ e ln IM2( 1113857( 11138572

+ f ln IM1( 1113857ln IM2( 1113857

(14)









ndash200

ndash150

ndash100

ndash50

0

50

100

150

200F

(kN

)

Δ (mm)













SA1 (cms2)M

SA1 (cms2)M

M 8 M 7 M 6 M 5 M 8 M 7 M 6 M 5






Performancelevel

Earthquakemagnitude


SA1(cms2)

PGD SA1(cms2)





Slight damage



Mediumdamage



Serious damage




081

060402

0

0 200 400 600 800 1000

Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(a)

0 200 400 600 800 1000

081

060402

0Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(b)

0 200 400 600 8001000

45

67

8

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(c)

0 200 400 600 800 1000

445

555

6

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(d)


500

108060402

0

00 200 400 600 800 10001000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(a)

500

0 0 200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(b)

500

00200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(c)

500

0 0200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(d)



7 Conclusion






Data Availability




Acknowledgments


References




































































Journal of












Journal of







Volume 2018






Volume 2018
























6mm9mm27mm

6mm9mm27mm

6mm9mm27mm

63mm126mm

63mm126mm

63mm126mm

Floo

r

Floo

r

Floo

r


02 04 06 08 10 1200Damage indices

0

1

2

3

0

1

2

3

02 04 06 08 10 1200Damage indices

0

1

2

3

(a)

6mm9mm27mm

6mm9mm27mm

6mm9mm27mm

63mm126mm

63mm119mm

63mm126mm

Floo

r

Floo

r

0

1

2

3

Floo

r

0

1

2

3

02 04 06 08 10 1200Damage indices


0

1

2

3

02 04 06 08 10 1200Damage indices

(b)


Collapse

Serious damage

Medium damage

Slight damage

KJ-1KJ-2KJ-3

00

03

06

09

12

15

Dto

tal

20 40 60 80 100 120 1400Displacement (mm)

Operational











Reinforcementfiber


05dcE0

dcE0

dcE0

γsE0

E0

σ

εce εR εimax

ε

R

E0


02fimax

05E0

02fimax

fyfy2

fy2

fy

fy3 E0

E0

εy

εf

ε

σ





Pf P CDle 1 ∣ IM1 i1 IM2 i2( 1113857 (12)



σ1113888 1113889

(13)




+ d ln IM2( 1113857

+ e ln IM2( 1113857( 11138572

+ f ln IM1( 1113857ln IM2( 1113857

(14)









ndash200

ndash150

ndash100

ndash50

0

50

100

150

200F

(kN

)

Δ (mm)













SA1 (cms2)M

SA1 (cms2)M

M 8 M 7 M 6 M 5 M 8 M 7 M 6 M 5






Performancelevel

Earthquakemagnitude


SA1(cms2)

PGD SA1(cms2)





Slight damage



Mediumdamage



Serious damage




081

060402

0

0 200 400 600 800 1000

Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(a)

0 200 400 600 800 1000

081

060402

0Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(b)

0 200 400 600 8001000

45

67

8

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(c)

0 200 400 600 800 1000

445

555

6

081

060402

0Exce

edin

g pr

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ility

P

M (Mw) SA1 (cms2)

(d)


500

108060402

0

00 200 400 600 800 10001000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(a)

500

0 0 200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(b)

500

00200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(c)

500

0 0200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(d)



7 Conclusion






Data Availability




Acknowledgments


References




































































Journal of












Journal of







Volume 2018






Volume 2018
















Reinforcementfiber


05dcE0

dcE0

dcE0

γsE0

E0

σ

εce εR εimax

ε

R

E0


02fimax

05E0

02fimax

fyfy2

fy2

fy

fy3 E0

E0

εy

εf

ε

σ





Pf P CDle 1 ∣ IM1 i1 IM2 i2( 1113857 (12)



σ1113888 1113889

(13)




+ d ln IM2( 1113857

+ e ln IM2( 1113857( 11138572

+ f ln IM1( 1113857ln IM2( 1113857

(14)









ndash200

ndash150

ndash100

ndash50

0

50

100

150

200F

(kN

)

Δ (mm)













SA1 (cms2)M

SA1 (cms2)M

M 8 M 7 M 6 M 5 M 8 M 7 M 6 M 5






Performancelevel

Earthquakemagnitude


SA1(cms2)

PGD SA1(cms2)





Slight damage



Mediumdamage



Serious damage




081

060402

0

0 200 400 600 800 1000

Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(a)

0 200 400 600 800 1000

081

060402

0Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(b)

0 200 400 600 8001000

45

67

8

081

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0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(c)

0 200 400 600 800 1000

445

555

6

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(d)


500

108060402

0

00 200 400 600 800 10001000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(a)

500

0 0 200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(b)

500

00200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(c)

500

0 0200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(d)



7 Conclusion






Data Availability




Acknowledgments


References




































































Journal of












Journal of







Volume 2018






Volume 2018










Pf P CDle 1 ∣ IM1 i1 IM2 i2( 1113857 (12)



σ1113888 1113889

(13)




+ d ln IM2( 1113857

+ e ln IM2( 1113857( 11138572

+ f ln IM1( 1113857ln IM2( 1113857

(14)









ndash200

ndash150

ndash100

ndash50

0

50

100

150

200F

(kN

)

Δ (mm)













SA1 (cms2)M

SA1 (cms2)M

M 8 M 7 M 6 M 5 M 8 M 7 M 6 M 5






Performancelevel

Earthquakemagnitude


SA1(cms2)

PGD SA1(cms2)





Slight damage



Mediumdamage



Serious damage




081

060402

0

0 200 400 600 800 1000

Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(a)

0 200 400 600 800 1000

081

060402

0Exce

edin

g pr

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ility

P

45

67

8

M (Mw) SA1 (cms2)

(b)

0 200 400 600 8001000

45

67

8

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(c)

0 200 400 600 800 1000

445

555

6

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(d)


500

108060402

0

00 200 400 600 800 10001000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(a)

500

0 0 200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(b)

500

00200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(c)

500

0 0200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(d)



7 Conclusion






Data Availability




Acknowledgments


References




































































Journal of












Journal of







Volume 2018






Volume 2018















SA1 (cms2)M

SA1 (cms2)M

M 8 M 7 M 6 M 5 M 8 M 7 M 6 M 5






Performancelevel

Earthquakemagnitude


SA1(cms2)

PGD SA1(cms2)





Slight damage



Mediumdamage



Serious damage




081

060402

0

0 200 400 600 800 1000

Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(a)

0 200 400 600 800 1000

081

060402

0Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(b)

0 200 400 600 8001000

45

67

8

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(c)

0 200 400 600 800 1000

445

555

6

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(d)


500

108060402

0

00 200 400 600 800 10001000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(a)

500

0 0 200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(b)

500

00200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(c)

500

0 0200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(d)



7 Conclusion






Data Availability




Acknowledgments


References




































































Journal of












Journal of







Volume 2018






Volume 2018








081

060402

0

0 200 400 600 800 1000

Exce

edin

g pr

obab

ility

P

45

67

8

M (Mw) SA1 (cms2)

(a)

0 200 400 600 800 1000

081

060402

0Exce

edin

g pr

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ility

P

45

67

8

M (Mw) SA1 (cms2)

(b)

0 200 400 600 8001000

45

67

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0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(c)

0 200 400 600 800 1000

445

555

6

081

060402

0Exce

edin

g pr

obab

ility

P

M (Mw) SA1 (cms2)

(d)


500

108060402

0

00 200 400 600 800 10001000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(a)

500

0 0 200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(b)

500

00200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(c)

500

0 0200 400 600 800 1000

108060402

01000Ex

ceed

ing

prob

abili

ty P

PGD (cm) SA1 (cms2)

(d)



7 Conclusion






Data Availability




Acknowledgments


References




































































Journal of












Journal of







Volume 2018






Volume 2018








7 Conclusion






Data Availability




Acknowledgments


References




































































Journal of












Journal of







Volume 2018






Volume 2018



































































Journal of












Journal of







Volume 2018






Volume 2018








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