Research ArticleInverse Analysis of UHPFRC Beams with a Notch to EvaluateTensile Behavior

Seong-Cheol Lee1 Han-Byeol Kim1 and Changbin Joh2

1Department of NPP Engineering KEPCO International Nuclear Graduate School 658-91 Haemaji-ro Seosaeng-myeonUlju-gun Ulsan 45014 Republic of Korea2Structural Engineering Research Institute Korea Institute of Civil Engineering and Building Technology (KICT) 283 Goyang-daeroIlsanseo-gu Goyang-si Gyeonggi-do 10223 Republic of Korea

Correspondence should be addressed to Seong-Cheol Lee scleekingsackr

Received 1 January 2017 Accepted 20 March 2017 Published 3 April 2017

Academic Editor Katsuyuki Kida

Copyright copy 2017 Seong-Cheol Lee et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Recently ultra high performance fiber reinforced concrete (UHPFRC) has been developed to attain considerably increasedcompressive cracking strength and ductile tensile behavior with high tensile strength through adding straight steel fibers in concretemixture Although benefits with UHPFRC were investigated through experimental program it is difficult to predict structuralbehavior ofUHPFRCmembers since theoretical approaches are limited In this paper inverse analysis procedure has been proposedfor a three-point bending test with notched UHPFRC beams so that tensile behavior of UHPFRC could be rationally evaluatedOn the inverse analysis procedure failure mode of the UHPFRC beam was simplified and the simplified diverse embedmentmodel (SDEM) was employed To verify the proposed inverse analysis procedure UHPFRC beams with a notch were analyzedwith the tensile behavior of UHPFRC evaluated through the inverse analysis procedure The analytical predictions showed goodagreement with the load-crack mouth opening displacement (CMOD) responses measured through the three-point bending testConsequently it can be concluded that UHPFRC tensile behavior can be rationally evaluated through the proposed inverse analysisprocedureTheproposed inverse analysis procedure can be useful in relevant research areas such as development of advanced designapproaches or computational methods for UHPFRC members

1 Introduction

To overcome brittle behavior of concrete after cracking anumber of researches have been conducted to use fiber rein-forced concrete as a structural member [1ndash6] It is well knownthat fiber reinforced concrete can exhibit ductile behavioreven after cracking because of fibers bridging cracks Fiberreinforced concrete can be divided into two categories aspresented in Figure 1 [7] conventional fiber reinforced con-crete and high performance fiber reinforced concrete (notedas FRC and HPFRC in the figure resp) Conventional fiberreinforced concrete usually exhibits softening behavior witha single dominant crack since tensile stress due to fibers is lessthan cracking strength of concretematrix On the other handhigh performance fiber reinforced concrete exhibits stiffeningbehavior withmultiple cracks since tensile stress due to fibersis larger than cracking strength of concrete matrix

To predict structural behavior of fiber reinforced concretemembers a simple model is required to represent the tensilebehavior of fiber reinforced concreteThrough literatures [8ndash11] tensile stress attained by fibers was evaluated by consid-ering random distribution of fiber inclination angle andfiber embedment length together In general it was funda-mentally assumed that bond stress along fibers was uniformAdvanced from the previous models the diverse embedmentmodel (DEM) [12 13] and the Simplified DEM (SDEM)[14] have been developed with consideration of fiber typessuch as straight and end-hooked types Based on the DEMand SDEM structural behavior of fiber reinforced concretemembers with rebars could be more rationally predictedthrough considering stress distribution in a member andthrough development of analysis procedure [15 16] Althoughmany models were developed as summarized here they wereprimarily focused on fiber reinforced concrete exhibiting

HindawiAdvances in Materials Science and EngineeringVolume 2017 Article ID 6543175 10 pageshttpsdoiorg10115520176543175

2 Advances in Materials Science and Engineering

Strain deformation

Tens

ile st

ress

Concrete

FRC

HPFRC

Figure 1 Tensile behavior of concrete FRC and HPFRC [7]

softening behavior whereas theoretical models for higherperformance fiber reinforced concrete are still limited

Recently ultra high performance fiber reinforced con-crete (UHPFRC) has been developed in which coarse aggre-gate was not included in mixture [17] UHPFRC can exhibitvery high compressive strength more than 150MPa andductile tensile behavior with well-distributedmultiple cracksOwning to the characteristics of UHPFRC it was investi-gated through experimental programs [18 19] that structuralmembers with UHPFRC exhibited good performance underflexure or shear even with relatively small amount of rebarsAlthough advantages ofUHPFRCwere experimentally inves-tigated theoretical approaches to predict structural behaviorof UHPFRC members are very limited

In this paper to evaluate tensile behavior of UHPFRCwhich is one of the most important aspects in analytical pre-dictions for structural behavior an inverse analysis procedureis proposed so that the tensile behavior of UHPFRC canbe rationally evaluated from three-point bending test resultswith UHPFRC beams which have a notch at the bottom ofthemid-point section To verify the proposed inverse analysisprocedure test results are compared with analytical predic-tions based on the tensile behavior of UHPFRC evaluatedthrough the proposed inverse analysis procedure

2 Inverse Analysis of UHPFRCBeams with a Notch

21 Section Analysis of UHPFRC Beams with a Notch One ofthe most important characteristics of UHPFRC is postcracktensile behavior when structural behavior of members withUHPFRC is theoretically predicted or investigated On eval-uation of tensile behavior of UHPFRC it is preferred toconduct three-point bending test for a notched beam witha rectangular section as adopted by Yang et al [18] sincethe test method is relatively easier than direct tension testwith dog-bone shaped specimens [21] In the case of thebending test the tensile behavior of UHPFRC can be inferredfrom test results such as applied load-CMOD (crack mouthopening displacement) response Recently CEB-FIP ModelCode 2010 (MC10) [22] presented a simple model to evaluate

0 Axial strainat the top

훿

h

P

휀ctop

wcrbot

휃b

2휃b

dc

Δc

L2 L2

Figure 2 Idealized failure mode of UHPFRC beam [20]

tensile stress-crack width response or tensile stress-strainresponse from the three-point bending test results Howeverit was investigated by Lee [20] that effect of fiber type wasnot rationally considered on the simple model tensile stressof fiber reinforced concrete with straight fibers could beoverestimated while one with end-hooked fibers could beunderestimated when crack width is smaller than 1mmTherefore more rational model is required to be developedto represent tensile behavior of UHPFRC

To derive UHPFRC tension model inverse analysis hasbeen conducted in this paper based on section analysisprocedure adopted by Lee [20] It is noted that the sectionanalysis procedure was modified from the analysis methodpresented by Oh et al [23] so that effect of a notch at thebottom of the center in a beam can be rigorously taken intothe account As illustrated in Figure 2 UHPFRC beam witha notch was idealized to exhibit a single dominant crackwhichwas developed fromanotch Because aUHPFRCbeamspecimen subjected to the three-point loading reaches failurethrough the formation of a single dominant flexural crack andopening of a notch the failure configuration can be assumedas presented in Figure 2 In this figure the relationshipbetween the compressive strain 120576119888top and the compressivedeformation Δ 119888 at the top fiber along the section with anotch can be derived as follows

Δ 119888 = int1198710120576119909top119889119909 = 12120576119888top119871 (1)

where 120576119909top is compressive strain at the top fiber in the sectionat the distance of 119909 from the support and 119871 is the pure spanof the specimen

From the geometric conditions illustrated in Figure 2 thecrack mouth opening displacement at the bottom of a notch(CMOD) 119908crbot is 2120579119887(ℎ minus 119889119888) where 119889119888 is depth to neutralaxis from the top fiber 120579119887 is rotation angle of cracked beamFrom the geometric condition 120579119887 can simply be calculatedfrom 120579119887 = Δ 119888(2119889119888) By incorporating these relationships into

Advances in Materials Science and Engineering 3

Notch

Noncrackedstrain

Cracked crack width

(a) (b)

휀ctop

dc

Figure 3 Crack width strain and stress distribution throughthe section with a notch (a) section compatibility and (b) stressdistribution

(1) the relationship between 120576119888top and 119908crbot can be derivedas follows

120576119888top = 2119871 119889119888ℎ minus 119889119888119908crbot (2)

With the above equation the relationship between strainand crack width distributions can be rigorously consideredon section compatibility

22 Constitutive Relations for UHPFRC With the relation-ship presented in (2) the strain and crack width distributionthrough the section with a notch can be evaluated as illus-trated in Figure 3 Stress distribution along the uncrackeddepth in the section with a notch can be evaluated for givenstrain distribution Since UHPFRC exhibits linear stress-strain response before experiencing the compressive strength[17] the following linear relationship between stress 119891119888 andstrain 120576119888 in UHPFRC under compression can be employedfor the prepeak compressive behavior

119891119888 = 120576119888120576co1198911015840119888 = 120576119888119864119888 for 120576co le 120576119888 lt 0 (3)

where 1198911015840119888 is the compressive strength of UHPFRC 120576co isstrain corresponding to 1198911015840119888 and 119864119888 is the elastic modulus ofUHPFRC

As a similar way the tensile behavior in UHPFRC beforecracking can be expressed as follows

119891119888 = 120576119888119864119888 for 0 le 120576119888 lt 120576cr (4)

where 120576cr = 119891cr119864119888 and 119891cr is cracking strength of concretematrix which can be assumed to be 05radic1198911015840119888 when it is notprovided from the test

Along the cracked depth above the notch in the sectiontensile stress of UHPFRC can be calculated as sum of tensilestresses due to tension-softening effect of concretematrix andstraight fibers (119891ct and 119891119891 resp) as follows

119891119888 = 119891ct + 119891119891 (5)

The tensile stress due to the tension-softening effect ofconcrete matrix can be evaluated as follows [9]

119891ct = 119891cr119890minus119888119908cr (6)

where the coefficient 119888 is 30 for UHPFRC since there is nocoarse aggregate in UHPFRC

The tensile stress of UHPFRC can be evaluated for a givencrack width which is calculated from (2) From the SDEM[14] which was simplified from the diverse embedmentmodel (DEM) [12 13] tensile stress due to straight steel fiberscan be calculated for a given crack width 119908cr as follows

119891119891 = 120572119891119881119891119870st120591119891max119897119891119889119891 (1 minus

2119908cr119897119891 )2 (7)

where 120572119891 is fiber orientation factor usually can be taken tobe 05 119881119891 is fiber volumetric ratio 120591119891max is pullout strengthof a straight steel fiber 119897119891 is fiber length 119889119891 is fiber diameterand 119870st is a factor to represent average pullout stress offibers considering random distribution of fibers 119870st can becalculated for a given crack width from the following

119870st =

1205731198913 119908cr119904119891 for 119908cr lt 1199041198911 minus radic 119904119891119908cr

+ 1205731198913 radic 119904119891119908cr for 119908cr ge 119904119891

(8)

where 120573119891 is a coefficient to consider effect of fiber slip whichis 067 and 119904119891 is the fiber slip corresponding to the pulloutstrength of a straight steel fiber which can be taken to be001mm

23 Analysis Algorithm for the Inverse Analysis Among theparameters required to conduct section analysis only thepullout strength of straight steel fiber 120591119891max is an unknownvariable At the beginning of the inverse analysis therefore120591119891max is assumed then the section analysis for the sectionwith a notch can be conducted through an iteration proce-dure finding the neutral axis depth for a given crack mouthopening displacement at the bottomof the notch by satisfyingforce equilibrium along the longitudinal axis On the sectionanalysis strain and crack width distribution along the sectioncan be evaluated from (2) for a given 119908crbot then stressdistribution along the section can be evaluated from (3)sim(8)From the stress distribution the sectional moment 119872 canbe calculated for the section with a notch Finally the appliedload119875 for a given crackmouth opening displacement can becalculated as follows

119875 = 4119872119871 (9)

Consequently with an initially assumed pullout strengthof a straight steel fiber 120591119891max the applied load-crack mouthopening displacement response of UHPFRC beam with anotch can be evaluated through the section analysis with vari-ation of crack mouth opening displacement Then throughcomparing the maximum applied force 119875max with test result

4 Advances in Materials Science and Engineering

Calculate strain and crack width distribution

Calculate stress distribution from Eqs (3)~(8)

Calculate M and P

Check axial forceequilibriumYes

No

with test result

Sect

ion

anal

ysis

the SDEM

Close enoughNot close

Get 휏fmax and UHPFRC tensile behavior from

Compare Pmax

Get P-w response of UHPFRC beam

Assume 휏fmax

along the section from 휀ctop and wcrbot

crbot

Calculate 휀ctop from Eq ( 2)

Assume dc

Set wcrbot

Figure 4 Analysis algorithm for the inverse analysis

the pullout strength of a straight steel fiber 120591119891max can beevaluated Now the tensile stress-crack width response ofUHPFRC can be evaluated from the SDEM which has beenpresented with (5)sim(8)

Details about the inverse analysis algorithm have beenpresented in Figure 4

3 Verification of the ProposedInverse Analysis Procedure

31 Subject Members and Materials In this paper UHPFRCspecimens tested by Yang et al [18] have been consideredfor verification of the proposed inverse analysis procedureIn their study a series of UHPFRC beams with a notch wasfabricated and tested In the experimental program the three-point bending test was conducted to investigate the tensilebehavior of UHPFRC

Figure 5 shows details about the UHPFRC beams Asillustrated in the figure the UHPFRC beams had a height of100mm a width of 100mm a pure span of 300mm and alength of 400mm Each specimen had a notchwith a depth of10mm which was placed at the bottom of the mid-section inthe pure span During the three-point bending test the crackmouth opening displacement was measured through a clipgauge attached to the bottom face of the specimen on eitherside of the notch

50 150 150 50

400

P

100

100

10

Figure 5 Details about the three-point bending test for UHPFRC[18]

Table 1 Mix proportion of UHPFRC by weight ratio [18]

WB Cement Silicafume Filler Fine

aggregate

Water-reducingadmixture

Steel fibervolumetricratio

02 10 025 03 11 002 10 15 20

In Table 1 mix proportion of UHPFRC has been pre-sented As presented in the table no coarse aggregates wereprovided while fine aggregates consisting of sands withdiameters of less than 05mm were added The water-binderratio (WB) was 02 so that high compressive strength couldbe achieved To attain postcrack ductile behavior straightsteel fibers were provided which have a diameter of 02mma length of 13mm and yield strength of 2500MPa Testvariable was fiber volumetric ratio which was varied through10 15 and 20

Representativematerial properties ofUHPFRChave beenpresented in Table 2 including compressive strength andelastic modulus The notation for the specimens means testparameters which are shear span-to-depth ratio (S25 and S34for 25 and 34 resp) fiber volumetric ratio (F10 F15 andF20 for fiber volumetric ratio of 10 15 and 20 resp)and presence or absence of prestress (P0 and PS for presenceand absence of prestress resp) As presented in the table thecompressive strength and elastic modulus were much higherthan normal concrete without fibers 1672sim1930MPa for thecompressive strength and 43400sim47780MPa for the elasticmodulus It is noted that UHPFRC exhibited almost linearstress-strain response before experiencing the compressivestrength since no coarse aggregate was provided In the tablethe maximums on the applied load 119875max measured throughthe three-point bending test have been also presented It isnoted that 119875max in the table was calculated through average of3sim6 test results for each test group

32 Evaluation of the Tensile Behavior of UHPFRC In orderto evaluate the tensile behavior of UHPFRC the pulloutstrength of a straight steel fiber has been evaluated throughthe proposed inverse analysis with the SDEM When thepullout strength was evaluated the maximum applied load119875max measured through the three-point bending test wascompared with ones predicted by the inverse analysis thepullout strength to get the maximum load predicted by the

Advances in Materials Science and Engineering 5

Table 2 Material properties of UHPFRC and the maximum load from the three-point bending test [18]

Specimen Compressive strength MPa Elastic modulus MPa Fiber volumetricratio 119875max from the test kN

S25-F10-P0 1745 43550 10 484S25-F10-PS 1813 45560 10 440S25-F15-P0 1882 45930 15 638S25-F15-PS 1836 45850 15 648S25-F20-P0 1855 47780 20 714S25-F20-PS 1898 45510 20 777S34-F10-P0 1689 43400 10 470S34-F10-PS 1672 44050 10 423S34-F15-P0 1930 46920 15 648S34-F15-PS 1892 45280 155 669S34-F20-P0 1885 46290 20 743S34-F20-PS 1823 45350 20 735

Table 3 Pullout strength of a fiber in UHPFRC evaluated throughthe inverse analysis

Specimen Pullout strength MPaS25-F10-P0 449S25-F10-PS 404S25-F15-P0 405S25-F15-PS 410S25-F20-P0 341S25-F20-PS 379S34-F10-P0 435S34-F10-PS 388S34-F15-P0 410S34-F15-PS 426S34-F20-P0 359S34-F20-PS 356

inverse analysis close enough to the test result Table 3 showsthe pullout strengths evaluated through the proposed inverseanalysis As presented in the table the pullout strengthswere evaluated to be 341sim449 which were much higherthan the suggestions by Voo and Foster [9] in which pulloutstrength of a straight steel fiber was assumed to be 10times of matrix tensile strength in specimens with no coarseaggregate Since UHPFRC mix proportion is quite differentfrom conventional concrete or mortar it can be inferredthat provisions designated for conventional concrete cannotbe employed to evaluate the pullout strength of a fiber inUHPFRC In addition it was investigated that the evaluatedpullout strength for specimens with 20 of fiber volumetricratio was less than ones with 10 or 15 of fiber volumetricratio This result is compatible with the test results observedby Lee et al [21] fiber efficiency generally decreased as fibervolumetric ratio increased This indicates that the pulloutstrength of a fiber is affected not only by fibers and concretemixture but also by fiber volumetric ratio specifically whenfiber volumetric ratio is larger than 15

From the evaluated pullout strengths of a straight steelfiber in UHPFRC the tensile behaviors of UHPFRC wereevaluated based on the SDEMwhich has been expressedwith(5)sim(8)The evaluated tensile stress-crack width responses ofUHPFRC have been presented in Figure 6 As a similar wayto the pullout strength of a straight steel fiber in UHPFRCthe tensile stress of UHPFRC did not proportionally increasewith an increase of fiber volumetric ratio In additionas can be seen in the figures it was evaluated that themaximum tensile stress of UHPFRCwas larger than crackingstrength Therefore it can be inferred that UHPFRC mayexhibit postcrack strain-hardening behavior with distributedmultiple cracks

33 Comparisonwith theThree-Point Bending Test Results Toverify the proposed inverse analysis procedure the sectionanalysis presented with the gray box with dotted lines inFigure 4 was conducted for the section with a notch andthe test results were compared with the tensile stress-CMODresponse predicted by the section analysis in Figure 7It should be noted that the UHPFRC tensile behavior inFigure 6 was employed on the section analysis As can be seenin the figure the tensile stress-CMOD response predicted bythe section analysis showed good agreement with the testresults In the comparisons the test results were scatteredfrom the predictions but this is mainly caused by the natureof fiber reinforced concrete fiber reinforced concrete exhibitsrelatively considerable scattering tensile behavior because ofrandom distribution of fibers [21 24 25]

Figure 8 shows an example for stress distribution alongthe sectionwith a notch It is noted that themaximumappliedloads corresponded to the CMOD around 10mm in thespecimens S25-F10-P0 and S25-F20-P0 As presented in thefigure stress along cracked region decreases with increasingthe opening displacement In addition since S25-F10-P0 andS25-F20-P0 had the cracking strengths of 660 and 681MParespectively it is obvious that maximum tensile stress ofUHPFRCwas larger than cracking strengthThese results arecompatible with the SDEM and the proposed method in thispaper

6 Advances in Materials Science and Engineering

S25F10P0S25F15P0S25F20P0

S25-P0 series

0

5

10

15

20Te

nsile

stre

ss (M

Pa)

2 4 6 8 100Crack width (mm)

0

5

10

15

20

Tens

ile st

ress

(MPa

)

2 4 6 8 100Crack width (mm)

2 4 6 8 100Crack width (mm)

0

5

10

15

20Te

nsile

stre

ss (M

Pa)

0

5

10

15

20

Tens

ile st

ress

(MPa

)

2 4 6 8 100Crack width (mm)

S25F10PSS25F15PSS25F20PS

S25-PS series

S34F10PSS34F15PSS34F20PS

S34-PS series

S34F10P0S34F15P0S34F20P0

S34-P0 series

Figure 6 Tensile behavior of UHPFRC evaluated through the proposed inverse analysis with the SDEM

Consequently it can be concluded that the tensile behav-ior of UHPFRC can be reasonably predicted by the pulloutstrength which is evaluated through the proposed inverseanalysis based on the section analysis with the SDEM

4 Conclusion

In this paper an inverse analysis procedure has been pro-posed to evaluate tensile behavior of UHPFRC from testresults with notched UHPFRC beams subjected to three-point flexural loading The proposed inverse analysis pro-cedure is based on section analysis in which the SDEM isemployed to take into account UHPFRC stress distributionalong the section with a notch Since pullout strength of astraight fiber can be directly evaluated from the maximumload measured through the three-point bending test tensilebehavior of UHPFRC can be easily predicted with the SDEM

To verify the proposed inverse analysis procedureUHPFRC beams with a notch subjected to three-point flex-ural loading have been analyzed with the tensile behavior ofUHPFRC evaluated through the proposed inverse analysisprocedure The analysis results showed good agreement withthe test results expressed to the applied load-CMODresponse It can be concluded that the tensile behavior ofUHPFRC can be reasonably evaluated from the proposedinverse analysis procedure

The proposed inverse analysis procedure can be usefulin evaluating tensile behavior of concrete with other typesof fibers like end-hooked fibers crimped fibers and so onIn addition through simplification of the proposed inverseanalysis procedure it is anticipated that this paper can beuseful in developing advanced design approaches or morerational computational methods for UHPFRC members

Advances in Materials Science and Engineering 7

S25-F10-P0

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 2

Spec 3

Spec 4

Spec 5Spec 6Prediction

S25-F10-PS

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 4

Spec 5Spec 6Prediction

Spec 1

Spec 2

S25-F15-P0

Spec 3

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 6Prediction

Spec 1

Spec 2

Spec 4

S25-F15-PS

0

20

40

60

80Lo

ad (k

N)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

S25-F20-PS

0

20

40

60

100

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

S25-F20-P0

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5

Spec 6Prediction

Spec 1Spec 2

Figure 7 Continued

8 Advances in Materials Science and Engineering

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5PredictionSpec 4

Spec 3

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4Spec 3

0

20

40

60

80Lo

ad (k

N)

0 1 2 3 4 5 6CMOD (mm)

Spec 6Prediction

Spec 1Spec 2Spec 3

Spec 4

0

20

40

60

100

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4Spec 2

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

S34-F10-P0 S34-F10-PS

S34-F15-P0 S34-F15-PS

S34-F20-P0 S34-F20-PS

Figure 7 Comparison on the applied load-CMOD response

Advances in Materials Science and Engineering 9

0

20

40

60

80

100

Dist

ance

from

top

fiber

(mm

)

S25-F10-P0 S25-F20-P0

CMOD =CMOD =

CMOD =

CMOD =

minus100 minus75 minus50 minus25 0 25Stress (MPa)

0

20

40

60

80

100

Dist

ance

from

top

fiber

(mm

)

CMOD =CMOD =

CMOD =

CMOD =

minus100 minus75 minus50 minus25 0 25Stress (MPa)

10mm20mm

30mm50mm

10mm20mm

30mm50mm

Figure 8 Stress distribution along the section with a notch

Conflicts of Interest

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

Acknowledgments

This research was supported by a grant (13SCIPA02) fromSmart Civil Infrastructure Research Program funded byMinistry of Land Infrastructure and Transport (MOLIT)of Korea government and Korea Agency for InfrastructureTechnology Advancement (KAIA)

References

[1] P H Bischoff ldquoTension stiffening and cracking of steel fiber-reinforced concreterdquo Journal of Materials in Civil Engineeringvol 15 no 2 pp 174ndash182 2003

[2] B BaeHChoi B Lee andC Bang ldquoCompressive behavior andmechanical characteristics and their application to stress-strainrelationship of steel fiber-reinforced reactive powder concreterdquoAdvances inMaterials Science and Engineering vol 2016 ArticleID 6465218 11 pages 2016

[3] H H Dinh G J Parra-Montesinos and J K Wight ldquoShearbehavior of steel fiber-reinforced concrete beams without stir-rup reinforcementrdquo ACI Structural Journal vol 107 no 5 pp597ndash606 2010

[4] J Susetyo P Gauvreau and F J Vecchio ldquoEffectiveness of steelfiber as minimum shear reinforcementrdquoACI Structural Journalvol 108 no 4 pp 488ndash496 2011

[5] MHHarajli andA A Rteil ldquoEffect of confinement using fiber-reinforced polymer or fiber-reinforced concrete on seismicperformance of gravity load-designed columnsrdquo ACI StructuralJournal vol 101 no 1 pp 47ndash56 2004

[6] Y ChiaHwan and H JianBo ldquoThe mechanical behavior offiber reinforced PP ECC beams under reverse cyclic loadingrdquo

Advances inMaterials Science and Engineering vol 2014 ArticleID 159790 9 pages 2014

[7] A E Naaman and H W Reinhardt ldquoCharacterization of highperformance fiber reinforced cement composites-HPFRCCrdquo inProceedings of HPFRCC 2 pp 1ndash23 1995

[8] P Marti T Pfyl V Sigrist and T Ulaga ldquoHarmonized testprocedures for steel fiber-reinforced concreterdquo ACI MaterialsJournal vol 96 no 6 pp 676ndash685 1999

[9] J Y L Voo and S J Foster ldquoVariable engagementmodel for fibrereinforced concrete in tensionrdquo UNICIV Report R-420 Schoolof Civil and Environmental Engineering the University of NewSouth Wales Sydney Australia 2003

[10] T Leutbecher and E Fehling ldquoCrack width control for com-bined reinforcement of rebars and fibers exemplified by ultra-high-performance concreterdquo fib Task Group 86 Ultra HighPerformance Fiber Reinforced Concrete-UHPFRC pp 1ndash282008

[11] P Stroeven ldquoStereological principles of spatialmodeling appliedto steel fiber-reinforced concrete in tensionrdquo ACI MaterialsJournal vol 106 no 3 pp 213ndash222 2009

[12] S-C Lee J-Y Cho and F J Vecchio ldquoDiverse embedmentmodel for steel fiber-reinforced concrete in tension modeldevelopmentrdquo ACI Materials Journal vol 108 no 5 pp 516ndash525 2011

[13] S-C Lee J-Y Cho and F J Vecchio ldquoDiverse embedmentmodel for steel fiber-reinforced concrete in tension modelverificationrdquo ACI Materials Journal vol 108 no 5 pp 526ndash5352011

[14] S-C Lee J-Y Cho and F J Vecchio ldquoSimplified diverseembedment model for steel fiber-reinforced concrete elementsin tensionrdquo ACI Materials Journal vol 110 no 4 pp 403ndash4122013

[15] S-C Lee J-Y Cho and F J Vecchio ldquoTension-stiffeningmodelfor steel fiber-reinforced concrete containing conventional rein-forcementrdquo ACI Structural Journal vol 110 no 4 pp 639ndash6482013

10 Advances in Materials Science and Engineering

[16] S-C Lee J-Y Cho and F J Vecchio ldquoAnalysis of steel fiber-reinforced concrete elements subjected to shearrdquoACI StructuralJournal vol 113 no 2 pp 275ndash285 2016

[17] K Kim I Yang and C Joh ldquoMaterial properties and structuralcharacteristics on flexure of steel fiber-reinforced ultra-high-performance concreterdquo Journal of the Korea Concrete Institutevol 28 no 2 pp 177ndash185 2016

[18] I-H Yang C Joh and B-S Kim ldquoShear behaviour of ultra-highperformance fibre-reinforced concrete beams without stir-rupsrdquo Magazine of Concrete Research vol 64 no 11 pp 979ndash993 2012

[19] I H Yang C Joh and B-S Kim ldquoStructural behavior ofultra high performance concrete beams subjected to bendingrdquoEngineering Structures vol 32 no 11 pp 3478ndash3487 2010

[20] S-C Lee ldquoRe-evaluation of fibre-reinforced concrete tensionmodel in CEB-FIP Model Code 2010rdquo Materials ResearchInnovations vol 19 supplement 8 pp 107ndash110 2015

[21] S-C Lee J-H Oh and J-Y Cho ldquoFiber efficiency in SFRCmembers subjected to uniaxial tensionrdquo Construction andBuilding Materials vol 113 pp 479ndash487 2016

[22] International Federation for Structural Concrete (fib) fibModelCode for Concrete Structures 2010 Ernst amp Sohn 2013

[23] B H Oh D G Park J C Kim and Y C Choi ldquoExperimentaland theoretical investigation on the postcracking inelasticbehavior of synthetic fiber reinforced concrete beamsrdquo Cementand Concrete Research vol 35 no 2 pp 384ndash392 2005

[24] S-C Lee J-H Oh and J-Y Cho ldquoFiber orientation factor ona circular cross-section in concrete membersrdquo Journal of theKorea Concrete Institute vol 26 no 3 pp 307ndash313 2014

[25] S-C Lee J-H Oh and J-Y Cho ldquoFiber orientation factor onrectangular cross-section in concrete membersrdquo InternationalJournal of Engineering and Technology vol 7 no 6 pp 470ndash4732015

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Materials Science and Engineering 3

Notch

Noncrackedstrain

Cracked crack width

(a) (b)

휀ctop

dc

Figure 3 Crack width strain and stress distribution throughthe section with a notch (a) section compatibility and (b) stressdistribution

(1) the relationship between 120576119888top and 119908crbot can be derivedas follows

120576119888top = 2119871 119889119888ℎ minus 119889119888119908crbot (2)

With the above equation the relationship between strainand crack width distributions can be rigorously consideredon section compatibility

22 Constitutive Relations for UHPFRC With the relation-ship presented in (2) the strain and crack width distributionthrough the section with a notch can be evaluated as illus-trated in Figure 3 Stress distribution along the uncrackeddepth in the section with a notch can be evaluated for givenstrain distribution Since UHPFRC exhibits linear stress-strain response before experiencing the compressive strength[17] the following linear relationship between stress 119891119888 andstrain 120576119888 in UHPFRC under compression can be employedfor the prepeak compressive behavior

119891119888 = 120576119888120576co1198911015840119888 = 120576119888119864119888 for 120576co le 120576119888 lt 0 (3)

where 1198911015840119888 is the compressive strength of UHPFRC 120576co isstrain corresponding to 1198911015840119888 and 119864119888 is the elastic modulus ofUHPFRC

As a similar way the tensile behavior in UHPFRC beforecracking can be expressed as follows

119891119888 = 120576119888119864119888 for 0 le 120576119888 lt 120576cr (4)

where 120576cr = 119891cr119864119888 and 119891cr is cracking strength of concretematrix which can be assumed to be 05radic1198911015840119888 when it is notprovided from the test

Along the cracked depth above the notch in the sectiontensile stress of UHPFRC can be calculated as sum of tensilestresses due to tension-softening effect of concretematrix andstraight fibers (119891ct and 119891119891 resp) as follows

119891119888 = 119891ct + 119891119891 (5)

The tensile stress due to the tension-softening effect ofconcrete matrix can be evaluated as follows [9]

119891ct = 119891cr119890minus119888119908cr (6)

where the coefficient 119888 is 30 for UHPFRC since there is nocoarse aggregate in UHPFRC

The tensile stress of UHPFRC can be evaluated for a givencrack width which is calculated from (2) From the SDEM[14] which was simplified from the diverse embedmentmodel (DEM) [12 13] tensile stress due to straight steel fiberscan be calculated for a given crack width 119908cr as follows

119891119891 = 120572119891119881119891119870st120591119891max119897119891119889119891 (1 minus

2119908cr119897119891 )2 (7)

where 120572119891 is fiber orientation factor usually can be taken tobe 05 119881119891 is fiber volumetric ratio 120591119891max is pullout strengthof a straight steel fiber 119897119891 is fiber length 119889119891 is fiber diameterand 119870st is a factor to represent average pullout stress offibers considering random distribution of fibers 119870st can becalculated for a given crack width from the following

119870st =

1205731198913 119908cr119904119891 for 119908cr lt 1199041198911 minus radic 119904119891119908cr

+ 1205731198913 radic 119904119891119908cr for 119908cr ge 119904119891

(8)

where 120573119891 is a coefficient to consider effect of fiber slip whichis 067 and 119904119891 is the fiber slip corresponding to the pulloutstrength of a straight steel fiber which can be taken to be001mm

23 Analysis Algorithm for the Inverse Analysis Among theparameters required to conduct section analysis only thepullout strength of straight steel fiber 120591119891max is an unknownvariable At the beginning of the inverse analysis therefore120591119891max is assumed then the section analysis for the sectionwith a notch can be conducted through an iteration proce-dure finding the neutral axis depth for a given crack mouthopening displacement at the bottomof the notch by satisfyingforce equilibrium along the longitudinal axis On the sectionanalysis strain and crack width distribution along the sectioncan be evaluated from (2) for a given 119908crbot then stressdistribution along the section can be evaluated from (3)sim(8)From the stress distribution the sectional moment 119872 canbe calculated for the section with a notch Finally the appliedload119875 for a given crackmouth opening displacement can becalculated as follows

119875 = 4119872119871 (9)

Consequently with an initially assumed pullout strengthof a straight steel fiber 120591119891max the applied load-crack mouthopening displacement response of UHPFRC beam with anotch can be evaluated through the section analysis with vari-ation of crack mouth opening displacement Then throughcomparing the maximum applied force 119875max with test result

4 Advances in Materials Science and Engineering

Calculate strain and crack width distribution

Calculate stress distribution from Eqs (3)~(8)

Calculate M and P

Check axial forceequilibriumYes

No

with test result

Sect

ion

anal

ysis

the SDEM

Close enoughNot close

Get 휏fmax and UHPFRC tensile behavior from

Compare Pmax

Get P-w response of UHPFRC beam

Assume 휏fmax

along the section from 휀ctop and wcrbot

crbot

Calculate 휀ctop from Eq ( 2)

Assume dc

Set wcrbot

Figure 4 Analysis algorithm for the inverse analysis

the pullout strength of a straight steel fiber 120591119891max can beevaluated Now the tensile stress-crack width response ofUHPFRC can be evaluated from the SDEM which has beenpresented with (5)sim(8)

Details about the inverse analysis algorithm have beenpresented in Figure 4

3 Verification of the ProposedInverse Analysis Procedure

31 Subject Members and Materials In this paper UHPFRCspecimens tested by Yang et al [18] have been consideredfor verification of the proposed inverse analysis procedureIn their study a series of UHPFRC beams with a notch wasfabricated and tested In the experimental program the three-point bending test was conducted to investigate the tensilebehavior of UHPFRC

Figure 5 shows details about the UHPFRC beams Asillustrated in the figure the UHPFRC beams had a height of100mm a width of 100mm a pure span of 300mm and alength of 400mm Each specimen had a notchwith a depth of10mm which was placed at the bottom of the mid-section inthe pure span During the three-point bending test the crackmouth opening displacement was measured through a clipgauge attached to the bottom face of the specimen on eitherside of the notch

50 150 150 50

400

P

100

100

10

Figure 5 Details about the three-point bending test for UHPFRC[18]

Table 1 Mix proportion of UHPFRC by weight ratio [18]

WB Cement Silicafume Filler Fine

aggregate

Water-reducingadmixture

Steel fibervolumetricratio

02 10 025 03 11 002 10 15 20

In Table 1 mix proportion of UHPFRC has been pre-sented As presented in the table no coarse aggregates wereprovided while fine aggregates consisting of sands withdiameters of less than 05mm were added The water-binderratio (WB) was 02 so that high compressive strength couldbe achieved To attain postcrack ductile behavior straightsteel fibers were provided which have a diameter of 02mma length of 13mm and yield strength of 2500MPa Testvariable was fiber volumetric ratio which was varied through10 15 and 20

Representativematerial properties ofUHPFRChave beenpresented in Table 2 including compressive strength andelastic modulus The notation for the specimens means testparameters which are shear span-to-depth ratio (S25 and S34for 25 and 34 resp) fiber volumetric ratio (F10 F15 andF20 for fiber volumetric ratio of 10 15 and 20 resp)and presence or absence of prestress (P0 and PS for presenceand absence of prestress resp) As presented in the table thecompressive strength and elastic modulus were much higherthan normal concrete without fibers 1672sim1930MPa for thecompressive strength and 43400sim47780MPa for the elasticmodulus It is noted that UHPFRC exhibited almost linearstress-strain response before experiencing the compressivestrength since no coarse aggregate was provided In the tablethe maximums on the applied load 119875max measured throughthe three-point bending test have been also presented It isnoted that 119875max in the table was calculated through average of3sim6 test results for each test group

32 Evaluation of the Tensile Behavior of UHPFRC In orderto evaluate the tensile behavior of UHPFRC the pulloutstrength of a straight steel fiber has been evaluated throughthe proposed inverse analysis with the SDEM When thepullout strength was evaluated the maximum applied load119875max measured through the three-point bending test wascompared with ones predicted by the inverse analysis thepullout strength to get the maximum load predicted by the

Advances in Materials Science and Engineering 5

Table 2 Material properties of UHPFRC and the maximum load from the three-point bending test [18]

Specimen Compressive strength MPa Elastic modulus MPa Fiber volumetricratio 119875max from the test kN

S25-F10-P0 1745 43550 10 484S25-F10-PS 1813 45560 10 440S25-F15-P0 1882 45930 15 638S25-F15-PS 1836 45850 15 648S25-F20-P0 1855 47780 20 714S25-F20-PS 1898 45510 20 777S34-F10-P0 1689 43400 10 470S34-F10-PS 1672 44050 10 423S34-F15-P0 1930 46920 15 648S34-F15-PS 1892 45280 155 669S34-F20-P0 1885 46290 20 743S34-F20-PS 1823 45350 20 735

Table 3 Pullout strength of a fiber in UHPFRC evaluated throughthe inverse analysis

Specimen Pullout strength MPaS25-F10-P0 449S25-F10-PS 404S25-F15-P0 405S25-F15-PS 410S25-F20-P0 341S25-F20-PS 379S34-F10-P0 435S34-F10-PS 388S34-F15-P0 410S34-F15-PS 426S34-F20-P0 359S34-F20-PS 356

inverse analysis close enough to the test result Table 3 showsthe pullout strengths evaluated through the proposed inverseanalysis As presented in the table the pullout strengthswere evaluated to be 341sim449 which were much higherthan the suggestions by Voo and Foster [9] in which pulloutstrength of a straight steel fiber was assumed to be 10times of matrix tensile strength in specimens with no coarseaggregate Since UHPFRC mix proportion is quite differentfrom conventional concrete or mortar it can be inferredthat provisions designated for conventional concrete cannotbe employed to evaluate the pullout strength of a fiber inUHPFRC In addition it was investigated that the evaluatedpullout strength for specimens with 20 of fiber volumetricratio was less than ones with 10 or 15 of fiber volumetricratio This result is compatible with the test results observedby Lee et al [21] fiber efficiency generally decreased as fibervolumetric ratio increased This indicates that the pulloutstrength of a fiber is affected not only by fibers and concretemixture but also by fiber volumetric ratio specifically whenfiber volumetric ratio is larger than 15

From the evaluated pullout strengths of a straight steelfiber in UHPFRC the tensile behaviors of UHPFRC wereevaluated based on the SDEMwhich has been expressedwith(5)sim(8)The evaluated tensile stress-crack width responses ofUHPFRC have been presented in Figure 6 As a similar wayto the pullout strength of a straight steel fiber in UHPFRCthe tensile stress of UHPFRC did not proportionally increasewith an increase of fiber volumetric ratio In additionas can be seen in the figures it was evaluated that themaximum tensile stress of UHPFRCwas larger than crackingstrength Therefore it can be inferred that UHPFRC mayexhibit postcrack strain-hardening behavior with distributedmultiple cracks

33 Comparisonwith theThree-Point Bending Test Results Toverify the proposed inverse analysis procedure the sectionanalysis presented with the gray box with dotted lines inFigure 4 was conducted for the section with a notch andthe test results were compared with the tensile stress-CMODresponse predicted by the section analysis in Figure 7It should be noted that the UHPFRC tensile behavior inFigure 6 was employed on the section analysis As can be seenin the figure the tensile stress-CMOD response predicted bythe section analysis showed good agreement with the testresults In the comparisons the test results were scatteredfrom the predictions but this is mainly caused by the natureof fiber reinforced concrete fiber reinforced concrete exhibitsrelatively considerable scattering tensile behavior because ofrandom distribution of fibers [21 24 25]

Figure 8 shows an example for stress distribution alongthe sectionwith a notch It is noted that themaximumappliedloads corresponded to the CMOD around 10mm in thespecimens S25-F10-P0 and S25-F20-P0 As presented in thefigure stress along cracked region decreases with increasingthe opening displacement In addition since S25-F10-P0 andS25-F20-P0 had the cracking strengths of 660 and 681MParespectively it is obvious that maximum tensile stress ofUHPFRCwas larger than cracking strengthThese results arecompatible with the SDEM and the proposed method in thispaper

6 Advances in Materials Science and Engineering

S25F10P0S25F15P0S25F20P0

S25-P0 series

0

5

10

15

20Te

nsile

stre

ss (M

Pa)

2 4 6 8 100Crack width (mm)

0

5

10

15

20

Tens

ile st

ress

(MPa

)

2 4 6 8 100Crack width (mm)

2 4 6 8 100Crack width (mm)

0

5

10

15

20Te

nsile

stre

ss (M

Pa)

0

5

10

15

20

Tens

ile st

ress

(MPa

)

2 4 6 8 100Crack width (mm)

S25F10PSS25F15PSS25F20PS

S25-PS series

S34F10PSS34F15PSS34F20PS

S34-PS series

S34F10P0S34F15P0S34F20P0

S34-P0 series

Figure 6 Tensile behavior of UHPFRC evaluated through the proposed inverse analysis with the SDEM

Consequently it can be concluded that the tensile behav-ior of UHPFRC can be reasonably predicted by the pulloutstrength which is evaluated through the proposed inverseanalysis based on the section analysis with the SDEM

4 Conclusion

In this paper an inverse analysis procedure has been pro-posed to evaluate tensile behavior of UHPFRC from testresults with notched UHPFRC beams subjected to three-point flexural loading The proposed inverse analysis pro-cedure is based on section analysis in which the SDEM isemployed to take into account UHPFRC stress distributionalong the section with a notch Since pullout strength of astraight fiber can be directly evaluated from the maximumload measured through the three-point bending test tensilebehavior of UHPFRC can be easily predicted with the SDEM

To verify the proposed inverse analysis procedureUHPFRC beams with a notch subjected to three-point flex-ural loading have been analyzed with the tensile behavior ofUHPFRC evaluated through the proposed inverse analysisprocedure The analysis results showed good agreement withthe test results expressed to the applied load-CMODresponse It can be concluded that the tensile behavior ofUHPFRC can be reasonably evaluated from the proposedinverse analysis procedure

The proposed inverse analysis procedure can be usefulin evaluating tensile behavior of concrete with other typesof fibers like end-hooked fibers crimped fibers and so onIn addition through simplification of the proposed inverseanalysis procedure it is anticipated that this paper can beuseful in developing advanced design approaches or morerational computational methods for UHPFRC members

Advances in Materials Science and Engineering 7

S25-F10-P0

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 2

Spec 3

Spec 4

Spec 5Spec 6Prediction

S25-F10-PS

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 4

Spec 5Spec 6Prediction

Spec 1

Spec 2

S25-F15-P0

Spec 3

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 6Prediction

Spec 1

Spec 2

Spec 4

S25-F15-PS

0

20

40

60

80Lo

ad (k

N)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

S25-F20-PS

0

20

40

60

100

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

S25-F20-P0

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5

Spec 6Prediction

Spec 1Spec 2

Figure 7 Continued

8 Advances in Materials Science and Engineering

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5PredictionSpec 4

Spec 3

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4Spec 3

0

20

40

60

80Lo

ad (k

N)

0 1 2 3 4 5 6CMOD (mm)

Spec 6Prediction

Spec 1Spec 2Spec 3

Spec 4

0

20

40

60

100

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4Spec 2

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

S34-F10-P0 S34-F10-PS

S34-F15-P0 S34-F15-PS

S34-F20-P0 S34-F20-PS

Figure 7 Comparison on the applied load-CMOD response

Advances in Materials Science and Engineering 9

0

20

40

60

80

100

Dist

ance

from

top

fiber

(mm

)

S25-F10-P0 S25-F20-P0

CMOD =CMOD =

CMOD =

CMOD =

minus100 minus75 minus50 minus25 0 25Stress (MPa)

0

20

40

60

80

100

Dist

ance

from

top

fiber

(mm

)

CMOD =CMOD =

CMOD =

CMOD =

minus100 minus75 minus50 minus25 0 25Stress (MPa)

10mm20mm

30mm50mm

10mm20mm

30mm50mm

Figure 8 Stress distribution along the section with a notch

Conflicts of Interest

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

Acknowledgments

This research was supported by a grant (13SCIPA02) fromSmart Civil Infrastructure Research Program funded byMinistry of Land Infrastructure and Transport (MOLIT)of Korea government and Korea Agency for InfrastructureTechnology Advancement (KAIA)

References

[1] P H Bischoff ldquoTension stiffening and cracking of steel fiber-reinforced concreterdquo Journal of Materials in Civil Engineeringvol 15 no 2 pp 174ndash182 2003

[2] B BaeHChoi B Lee andC Bang ldquoCompressive behavior andmechanical characteristics and their application to stress-strainrelationship of steel fiber-reinforced reactive powder concreterdquoAdvances inMaterials Science and Engineering vol 2016 ArticleID 6465218 11 pages 2016

[3] H H Dinh G J Parra-Montesinos and J K Wight ldquoShearbehavior of steel fiber-reinforced concrete beams without stir-rup reinforcementrdquo ACI Structural Journal vol 107 no 5 pp597ndash606 2010

[4] J Susetyo P Gauvreau and F J Vecchio ldquoEffectiveness of steelfiber as minimum shear reinforcementrdquoACI Structural Journalvol 108 no 4 pp 488ndash496 2011

[5] MHHarajli andA A Rteil ldquoEffect of confinement using fiber-reinforced polymer or fiber-reinforced concrete on seismicperformance of gravity load-designed columnsrdquo ACI StructuralJournal vol 101 no 1 pp 47ndash56 2004

[6] Y ChiaHwan and H JianBo ldquoThe mechanical behavior offiber reinforced PP ECC beams under reverse cyclic loadingrdquo

Advances inMaterials Science and Engineering vol 2014 ArticleID 159790 9 pages 2014

[7] A E Naaman and H W Reinhardt ldquoCharacterization of highperformance fiber reinforced cement composites-HPFRCCrdquo inProceedings of HPFRCC 2 pp 1ndash23 1995

[8] P Marti T Pfyl V Sigrist and T Ulaga ldquoHarmonized testprocedures for steel fiber-reinforced concreterdquo ACI MaterialsJournal vol 96 no 6 pp 676ndash685 1999

[9] J Y L Voo and S J Foster ldquoVariable engagementmodel for fibrereinforced concrete in tensionrdquo UNICIV Report R-420 Schoolof Civil and Environmental Engineering the University of NewSouth Wales Sydney Australia 2003

[10] T Leutbecher and E Fehling ldquoCrack width control for com-bined reinforcement of rebars and fibers exemplified by ultra-high-performance concreterdquo fib Task Group 86 Ultra HighPerformance Fiber Reinforced Concrete-UHPFRC pp 1ndash282008

[11] P Stroeven ldquoStereological principles of spatialmodeling appliedto steel fiber-reinforced concrete in tensionrdquo ACI MaterialsJournal vol 106 no 3 pp 213ndash222 2009

[12] S-C Lee J-Y Cho and F J Vecchio ldquoDiverse embedmentmodel for steel fiber-reinforced concrete in tension modeldevelopmentrdquo ACI Materials Journal vol 108 no 5 pp 516ndash525 2011

[13] S-C Lee J-Y Cho and F J Vecchio ldquoDiverse embedmentmodel for steel fiber-reinforced concrete in tension modelverificationrdquo ACI Materials Journal vol 108 no 5 pp 526ndash5352011

[14] S-C Lee J-Y Cho and F J Vecchio ldquoSimplified diverseembedment model for steel fiber-reinforced concrete elementsin tensionrdquo ACI Materials Journal vol 110 no 4 pp 403ndash4122013

[15] S-C Lee J-Y Cho and F J Vecchio ldquoTension-stiffeningmodelfor steel fiber-reinforced concrete containing conventional rein-forcementrdquo ACI Structural Journal vol 110 no 4 pp 639ndash6482013

10 Advances in Materials Science and Engineering

[16] S-C Lee J-Y Cho and F J Vecchio ldquoAnalysis of steel fiber-reinforced concrete elements subjected to shearrdquoACI StructuralJournal vol 113 no 2 pp 275ndash285 2016

[17] K Kim I Yang and C Joh ldquoMaterial properties and structuralcharacteristics on flexure of steel fiber-reinforced ultra-high-performance concreterdquo Journal of the Korea Concrete Institutevol 28 no 2 pp 177ndash185 2016

[18] I-H Yang C Joh and B-S Kim ldquoShear behaviour of ultra-highperformance fibre-reinforced concrete beams without stir-rupsrdquo Magazine of Concrete Research vol 64 no 11 pp 979ndash993 2012

[19] I H Yang C Joh and B-S Kim ldquoStructural behavior ofultra high performance concrete beams subjected to bendingrdquoEngineering Structures vol 32 no 11 pp 3478ndash3487 2010

[20] S-C Lee ldquoRe-evaluation of fibre-reinforced concrete tensionmodel in CEB-FIP Model Code 2010rdquo Materials ResearchInnovations vol 19 supplement 8 pp 107ndash110 2015

[21] S-C Lee J-H Oh and J-Y Cho ldquoFiber efficiency in SFRCmembers subjected to uniaxial tensionrdquo Construction andBuilding Materials vol 113 pp 479ndash487 2016

[22] International Federation for Structural Concrete (fib) fibModelCode for Concrete Structures 2010 Ernst amp Sohn 2013

[23] B H Oh D G Park J C Kim and Y C Choi ldquoExperimentaland theoretical investigation on the postcracking inelasticbehavior of synthetic fiber reinforced concrete beamsrdquo Cementand Concrete Research vol 35 no 2 pp 384ndash392 2005

[24] S-C Lee J-H Oh and J-Y Cho ldquoFiber orientation factor ona circular cross-section in concrete membersrdquo Journal of theKorea Concrete Institute vol 26 no 3 pp 307ndash313 2014

[25] S-C Lee J-H Oh and J-Y Cho ldquoFiber orientation factor onrectangular cross-section in concrete membersrdquo InternationalJournal of Engineering and Technology vol 7 no 6 pp 470ndash4732015

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

4 Advances in Materials Science and Engineering

Calculate strain and crack width distribution

Calculate stress distribution from Eqs (3)~(8)

Calculate M and P

Check axial forceequilibriumYes

No

with test result

Sect

ion

anal

ysis

the SDEM

Close enoughNot close

Get 휏fmax and UHPFRC tensile behavior from

Compare Pmax

Get P-w response of UHPFRC beam

Assume 휏fmax

along the section from 휀ctop and wcrbot

crbot

Calculate 휀ctop from Eq ( 2)

Assume dc

Set wcrbot

Figure 4 Analysis algorithm for the inverse analysis

the pullout strength of a straight steel fiber 120591119891max can beevaluated Now the tensile stress-crack width response ofUHPFRC can be evaluated from the SDEM which has beenpresented with (5)sim(8)

Details about the inverse analysis algorithm have beenpresented in Figure 4

3 Verification of the ProposedInverse Analysis Procedure

31 Subject Members and Materials In this paper UHPFRCspecimens tested by Yang et al [18] have been consideredfor verification of the proposed inverse analysis procedureIn their study a series of UHPFRC beams with a notch wasfabricated and tested In the experimental program the three-point bending test was conducted to investigate the tensilebehavior of UHPFRC

Figure 5 shows details about the UHPFRC beams Asillustrated in the figure the UHPFRC beams had a height of100mm a width of 100mm a pure span of 300mm and alength of 400mm Each specimen had a notchwith a depth of10mm which was placed at the bottom of the mid-section inthe pure span During the three-point bending test the crackmouth opening displacement was measured through a clipgauge attached to the bottom face of the specimen on eitherside of the notch

50 150 150 50

400

P

100

100

10

Figure 5 Details about the three-point bending test for UHPFRC[18]

Table 1 Mix proportion of UHPFRC by weight ratio [18]

WB Cement Silicafume Filler Fine

aggregate

Water-reducingadmixture

Steel fibervolumetricratio

02 10 025 03 11 002 10 15 20

In Table 1 mix proportion of UHPFRC has been pre-sented As presented in the table no coarse aggregates wereprovided while fine aggregates consisting of sands withdiameters of less than 05mm were added The water-binderratio (WB) was 02 so that high compressive strength couldbe achieved To attain postcrack ductile behavior straightsteel fibers were provided which have a diameter of 02mma length of 13mm and yield strength of 2500MPa Testvariable was fiber volumetric ratio which was varied through10 15 and 20

Representativematerial properties ofUHPFRChave beenpresented in Table 2 including compressive strength andelastic modulus The notation for the specimens means testparameters which are shear span-to-depth ratio (S25 and S34for 25 and 34 resp) fiber volumetric ratio (F10 F15 andF20 for fiber volumetric ratio of 10 15 and 20 resp)and presence or absence of prestress (P0 and PS for presenceand absence of prestress resp) As presented in the table thecompressive strength and elastic modulus were much higherthan normal concrete without fibers 1672sim1930MPa for thecompressive strength and 43400sim47780MPa for the elasticmodulus It is noted that UHPFRC exhibited almost linearstress-strain response before experiencing the compressivestrength since no coarse aggregate was provided In the tablethe maximums on the applied load 119875max measured throughthe three-point bending test have been also presented It isnoted that 119875max in the table was calculated through average of3sim6 test results for each test group

32 Evaluation of the Tensile Behavior of UHPFRC In orderto evaluate the tensile behavior of UHPFRC the pulloutstrength of a straight steel fiber has been evaluated throughthe proposed inverse analysis with the SDEM When thepullout strength was evaluated the maximum applied load119875max measured through the three-point bending test wascompared with ones predicted by the inverse analysis thepullout strength to get the maximum load predicted by the

Advances in Materials Science and Engineering 5

Table 2 Material properties of UHPFRC and the maximum load from the three-point bending test [18]

Specimen Compressive strength MPa Elastic modulus MPa Fiber volumetricratio 119875max from the test kN

S25-F10-P0 1745 43550 10 484S25-F10-PS 1813 45560 10 440S25-F15-P0 1882 45930 15 638S25-F15-PS 1836 45850 15 648S25-F20-P0 1855 47780 20 714S25-F20-PS 1898 45510 20 777S34-F10-P0 1689 43400 10 470S34-F10-PS 1672 44050 10 423S34-F15-P0 1930 46920 15 648S34-F15-PS 1892 45280 155 669S34-F20-P0 1885 46290 20 743S34-F20-PS 1823 45350 20 735

Table 3 Pullout strength of a fiber in UHPFRC evaluated throughthe inverse analysis

Specimen Pullout strength MPaS25-F10-P0 449S25-F10-PS 404S25-F15-P0 405S25-F15-PS 410S25-F20-P0 341S25-F20-PS 379S34-F10-P0 435S34-F10-PS 388S34-F15-P0 410S34-F15-PS 426S34-F20-P0 359S34-F20-PS 356

inverse analysis close enough to the test result Table 3 showsthe pullout strengths evaluated through the proposed inverseanalysis As presented in the table the pullout strengthswere evaluated to be 341sim449 which were much higherthan the suggestions by Voo and Foster [9] in which pulloutstrength of a straight steel fiber was assumed to be 10times of matrix tensile strength in specimens with no coarseaggregate Since UHPFRC mix proportion is quite differentfrom conventional concrete or mortar it can be inferredthat provisions designated for conventional concrete cannotbe employed to evaluate the pullout strength of a fiber inUHPFRC In addition it was investigated that the evaluatedpullout strength for specimens with 20 of fiber volumetricratio was less than ones with 10 or 15 of fiber volumetricratio This result is compatible with the test results observedby Lee et al [21] fiber efficiency generally decreased as fibervolumetric ratio increased This indicates that the pulloutstrength of a fiber is affected not only by fibers and concretemixture but also by fiber volumetric ratio specifically whenfiber volumetric ratio is larger than 15

From the evaluated pullout strengths of a straight steelfiber in UHPFRC the tensile behaviors of UHPFRC wereevaluated based on the SDEMwhich has been expressedwith(5)sim(8)The evaluated tensile stress-crack width responses ofUHPFRC have been presented in Figure 6 As a similar wayto the pullout strength of a straight steel fiber in UHPFRCthe tensile stress of UHPFRC did not proportionally increasewith an increase of fiber volumetric ratio In additionas can be seen in the figures it was evaluated that themaximum tensile stress of UHPFRCwas larger than crackingstrength Therefore it can be inferred that UHPFRC mayexhibit postcrack strain-hardening behavior with distributedmultiple cracks

33 Comparisonwith theThree-Point Bending Test Results Toverify the proposed inverse analysis procedure the sectionanalysis presented with the gray box with dotted lines inFigure 4 was conducted for the section with a notch andthe test results were compared with the tensile stress-CMODresponse predicted by the section analysis in Figure 7It should be noted that the UHPFRC tensile behavior inFigure 6 was employed on the section analysis As can be seenin the figure the tensile stress-CMOD response predicted bythe section analysis showed good agreement with the testresults In the comparisons the test results were scatteredfrom the predictions but this is mainly caused by the natureof fiber reinforced concrete fiber reinforced concrete exhibitsrelatively considerable scattering tensile behavior because ofrandom distribution of fibers [21 24 25]

Figure 8 shows an example for stress distribution alongthe sectionwith a notch It is noted that themaximumappliedloads corresponded to the CMOD around 10mm in thespecimens S25-F10-P0 and S25-F20-P0 As presented in thefigure stress along cracked region decreases with increasingthe opening displacement In addition since S25-F10-P0 andS25-F20-P0 had the cracking strengths of 660 and 681MParespectively it is obvious that maximum tensile stress ofUHPFRCwas larger than cracking strengthThese results arecompatible with the SDEM and the proposed method in thispaper

6 Advances in Materials Science and Engineering

S25F10P0S25F15P0S25F20P0

S25-P0 series

0

5

10

15

20Te

nsile

stre

ss (M

Pa)

2 4 6 8 100Crack width (mm)

0

5

10

15

20

Tens

ile st

ress

(MPa

)

2 4 6 8 100Crack width (mm)

2 4 6 8 100Crack width (mm)

0

5

10

15

20Te

nsile

stre

ss (M

Pa)

0

5

10

15

20

Tens

ile st

ress

(MPa

)

2 4 6 8 100Crack width (mm)

S25F10PSS25F15PSS25F20PS

S25-PS series

S34F10PSS34F15PSS34F20PS

S34-PS series

S34F10P0S34F15P0S34F20P0

S34-P0 series

Figure 6 Tensile behavior of UHPFRC evaluated through the proposed inverse analysis with the SDEM

Consequently it can be concluded that the tensile behav-ior of UHPFRC can be reasonably predicted by the pulloutstrength which is evaluated through the proposed inverseanalysis based on the section analysis with the SDEM

4 Conclusion

In this paper an inverse analysis procedure has been pro-posed to evaluate tensile behavior of UHPFRC from testresults with notched UHPFRC beams subjected to three-point flexural loading The proposed inverse analysis pro-cedure is based on section analysis in which the SDEM isemployed to take into account UHPFRC stress distributionalong the section with a notch Since pullout strength of astraight fiber can be directly evaluated from the maximumload measured through the three-point bending test tensilebehavior of UHPFRC can be easily predicted with the SDEM

To verify the proposed inverse analysis procedureUHPFRC beams with a notch subjected to three-point flex-ural loading have been analyzed with the tensile behavior ofUHPFRC evaluated through the proposed inverse analysisprocedure The analysis results showed good agreement withthe test results expressed to the applied load-CMODresponse It can be concluded that the tensile behavior ofUHPFRC can be reasonably evaluated from the proposedinverse analysis procedure

The proposed inverse analysis procedure can be usefulin evaluating tensile behavior of concrete with other typesof fibers like end-hooked fibers crimped fibers and so onIn addition through simplification of the proposed inverseanalysis procedure it is anticipated that this paper can beuseful in developing advanced design approaches or morerational computational methods for UHPFRC members

Advances in Materials Science and Engineering 7

S25-F10-P0

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 2

Spec 3

Spec 4

Spec 5Spec 6Prediction

S25-F10-PS

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 4

Spec 5Spec 6Prediction

Spec 1

Spec 2

S25-F15-P0

Spec 3

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 6Prediction

Spec 1

Spec 2

Spec 4

S25-F15-PS

0

20

40

60

80Lo

ad (k

N)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

S25-F20-PS

0

20

40

60

100

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

S25-F20-P0

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5

Spec 6Prediction

Spec 1Spec 2

Figure 7 Continued

8 Advances in Materials Science and Engineering

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5PredictionSpec 4

Spec 3

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4Spec 3

0

20

40

60

80Lo

ad (k

N)

0 1 2 3 4 5 6CMOD (mm)

Spec 6Prediction

Spec 1Spec 2Spec 3

Spec 4

0

20

40

60

100

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4Spec 2

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

S34-F10-P0 S34-F10-PS

S34-F15-P0 S34-F15-PS

S34-F20-P0 S34-F20-PS

Figure 7 Comparison on the applied load-CMOD response

Advances in Materials Science and Engineering 9

0

20

40

60

80

100

Dist

ance

from

top

fiber

(mm

)

S25-F10-P0 S25-F20-P0

CMOD =CMOD =

CMOD =

CMOD =

minus100 minus75 minus50 minus25 0 25Stress (MPa)

0

20

40

60

80

100

Dist

ance

from

top

fiber

(mm

)

CMOD =CMOD =

CMOD =

CMOD =

minus100 minus75 minus50 minus25 0 25Stress (MPa)

10mm20mm

30mm50mm

10mm20mm

30mm50mm

Figure 8 Stress distribution along the section with a notch

Conflicts of Interest

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

Acknowledgments

This research was supported by a grant (13SCIPA02) fromSmart Civil Infrastructure Research Program funded byMinistry of Land Infrastructure and Transport (MOLIT)of Korea government and Korea Agency for InfrastructureTechnology Advancement (KAIA)

References

[1] P H Bischoff ldquoTension stiffening and cracking of steel fiber-reinforced concreterdquo Journal of Materials in Civil Engineeringvol 15 no 2 pp 174ndash182 2003

[2] B BaeHChoi B Lee andC Bang ldquoCompressive behavior andmechanical characteristics and their application to stress-strainrelationship of steel fiber-reinforced reactive powder concreterdquoAdvances inMaterials Science and Engineering vol 2016 ArticleID 6465218 11 pages 2016

[3] H H Dinh G J Parra-Montesinos and J K Wight ldquoShearbehavior of steel fiber-reinforced concrete beams without stir-rup reinforcementrdquo ACI Structural Journal vol 107 no 5 pp597ndash606 2010

[4] J Susetyo P Gauvreau and F J Vecchio ldquoEffectiveness of steelfiber as minimum shear reinforcementrdquoACI Structural Journalvol 108 no 4 pp 488ndash496 2011

[5] MHHarajli andA A Rteil ldquoEffect of confinement using fiber-reinforced polymer or fiber-reinforced concrete on seismicperformance of gravity load-designed columnsrdquo ACI StructuralJournal vol 101 no 1 pp 47ndash56 2004

[6] Y ChiaHwan and H JianBo ldquoThe mechanical behavior offiber reinforced PP ECC beams under reverse cyclic loadingrdquo

Advances inMaterials Science and Engineering vol 2014 ArticleID 159790 9 pages 2014

[7] A E Naaman and H W Reinhardt ldquoCharacterization of highperformance fiber reinforced cement composites-HPFRCCrdquo inProceedings of HPFRCC 2 pp 1ndash23 1995

[8] P Marti T Pfyl V Sigrist and T Ulaga ldquoHarmonized testprocedures for steel fiber-reinforced concreterdquo ACI MaterialsJournal vol 96 no 6 pp 676ndash685 1999

[9] J Y L Voo and S J Foster ldquoVariable engagementmodel for fibrereinforced concrete in tensionrdquo UNICIV Report R-420 Schoolof Civil and Environmental Engineering the University of NewSouth Wales Sydney Australia 2003

[10] T Leutbecher and E Fehling ldquoCrack width control for com-bined reinforcement of rebars and fibers exemplified by ultra-high-performance concreterdquo fib Task Group 86 Ultra HighPerformance Fiber Reinforced Concrete-UHPFRC pp 1ndash282008

[11] P Stroeven ldquoStereological principles of spatialmodeling appliedto steel fiber-reinforced concrete in tensionrdquo ACI MaterialsJournal vol 106 no 3 pp 213ndash222 2009

[12] S-C Lee J-Y Cho and F J Vecchio ldquoDiverse embedmentmodel for steel fiber-reinforced concrete in tension modeldevelopmentrdquo ACI Materials Journal vol 108 no 5 pp 516ndash525 2011

[13] S-C Lee J-Y Cho and F J Vecchio ldquoDiverse embedmentmodel for steel fiber-reinforced concrete in tension modelverificationrdquo ACI Materials Journal vol 108 no 5 pp 526ndash5352011

[14] S-C Lee J-Y Cho and F J Vecchio ldquoSimplified diverseembedment model for steel fiber-reinforced concrete elementsin tensionrdquo ACI Materials Journal vol 110 no 4 pp 403ndash4122013

[15] S-C Lee J-Y Cho and F J Vecchio ldquoTension-stiffeningmodelfor steel fiber-reinforced concrete containing conventional rein-forcementrdquo ACI Structural Journal vol 110 no 4 pp 639ndash6482013

10 Advances in Materials Science and Engineering

[16] S-C Lee J-Y Cho and F J Vecchio ldquoAnalysis of steel fiber-reinforced concrete elements subjected to shearrdquoACI StructuralJournal vol 113 no 2 pp 275ndash285 2016

[17] K Kim I Yang and C Joh ldquoMaterial properties and structuralcharacteristics on flexure of steel fiber-reinforced ultra-high-performance concreterdquo Journal of the Korea Concrete Institutevol 28 no 2 pp 177ndash185 2016

[18] I-H Yang C Joh and B-S Kim ldquoShear behaviour of ultra-highperformance fibre-reinforced concrete beams without stir-rupsrdquo Magazine of Concrete Research vol 64 no 11 pp 979ndash993 2012

[19] I H Yang C Joh and B-S Kim ldquoStructural behavior ofultra high performance concrete beams subjected to bendingrdquoEngineering Structures vol 32 no 11 pp 3478ndash3487 2010

[20] S-C Lee ldquoRe-evaluation of fibre-reinforced concrete tensionmodel in CEB-FIP Model Code 2010rdquo Materials ResearchInnovations vol 19 supplement 8 pp 107ndash110 2015

[21] S-C Lee J-H Oh and J-Y Cho ldquoFiber efficiency in SFRCmembers subjected to uniaxial tensionrdquo Construction andBuilding Materials vol 113 pp 479ndash487 2016

[22] International Federation for Structural Concrete (fib) fibModelCode for Concrete Structures 2010 Ernst amp Sohn 2013

[23] B H Oh D G Park J C Kim and Y C Choi ldquoExperimentaland theoretical investigation on the postcracking inelasticbehavior of synthetic fiber reinforced concrete beamsrdquo Cementand Concrete Research vol 35 no 2 pp 384ndash392 2005

[24] S-C Lee J-H Oh and J-Y Cho ldquoFiber orientation factor ona circular cross-section in concrete membersrdquo Journal of theKorea Concrete Institute vol 26 no 3 pp 307ndash313 2014

[25] S-C Lee J-H Oh and J-Y Cho ldquoFiber orientation factor onrectangular cross-section in concrete membersrdquo InternationalJournal of Engineering and Technology vol 7 no 6 pp 470ndash4732015

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Materials Science and Engineering 5

Table 2 Material properties of UHPFRC and the maximum load from the three-point bending test [18]

Specimen Compressive strength MPa Elastic modulus MPa Fiber volumetricratio 119875max from the test kN

S25-F10-P0 1745 43550 10 484S25-F10-PS 1813 45560 10 440S25-F15-P0 1882 45930 15 638S25-F15-PS 1836 45850 15 648S25-F20-P0 1855 47780 20 714S25-F20-PS 1898 45510 20 777S34-F10-P0 1689 43400 10 470S34-F10-PS 1672 44050 10 423S34-F15-P0 1930 46920 15 648S34-F15-PS 1892 45280 155 669S34-F20-P0 1885 46290 20 743S34-F20-PS 1823 45350 20 735

Table 3 Pullout strength of a fiber in UHPFRC evaluated throughthe inverse analysis

Specimen Pullout strength MPaS25-F10-P0 449S25-F10-PS 404S25-F15-P0 405S25-F15-PS 410S25-F20-P0 341S25-F20-PS 379S34-F10-P0 435S34-F10-PS 388S34-F15-P0 410S34-F15-PS 426S34-F20-P0 359S34-F20-PS 356

inverse analysis close enough to the test result Table 3 showsthe pullout strengths evaluated through the proposed inverseanalysis As presented in the table the pullout strengthswere evaluated to be 341sim449 which were much higherthan the suggestions by Voo and Foster [9] in which pulloutstrength of a straight steel fiber was assumed to be 10times of matrix tensile strength in specimens with no coarseaggregate Since UHPFRC mix proportion is quite differentfrom conventional concrete or mortar it can be inferredthat provisions designated for conventional concrete cannotbe employed to evaluate the pullout strength of a fiber inUHPFRC In addition it was investigated that the evaluatedpullout strength for specimens with 20 of fiber volumetricratio was less than ones with 10 or 15 of fiber volumetricratio This result is compatible with the test results observedby Lee et al [21] fiber efficiency generally decreased as fibervolumetric ratio increased This indicates that the pulloutstrength of a fiber is affected not only by fibers and concretemixture but also by fiber volumetric ratio specifically whenfiber volumetric ratio is larger than 15

From the evaluated pullout strengths of a straight steelfiber in UHPFRC the tensile behaviors of UHPFRC wereevaluated based on the SDEMwhich has been expressedwith(5)sim(8)The evaluated tensile stress-crack width responses ofUHPFRC have been presented in Figure 6 As a similar wayto the pullout strength of a straight steel fiber in UHPFRCthe tensile stress of UHPFRC did not proportionally increasewith an increase of fiber volumetric ratio In additionas can be seen in the figures it was evaluated that themaximum tensile stress of UHPFRCwas larger than crackingstrength Therefore it can be inferred that UHPFRC mayexhibit postcrack strain-hardening behavior with distributedmultiple cracks

33 Comparisonwith theThree-Point Bending Test Results Toverify the proposed inverse analysis procedure the sectionanalysis presented with the gray box with dotted lines inFigure 4 was conducted for the section with a notch andthe test results were compared with the tensile stress-CMODresponse predicted by the section analysis in Figure 7It should be noted that the UHPFRC tensile behavior inFigure 6 was employed on the section analysis As can be seenin the figure the tensile stress-CMOD response predicted bythe section analysis showed good agreement with the testresults In the comparisons the test results were scatteredfrom the predictions but this is mainly caused by the natureof fiber reinforced concrete fiber reinforced concrete exhibitsrelatively considerable scattering tensile behavior because ofrandom distribution of fibers [21 24 25]

Figure 8 shows an example for stress distribution alongthe sectionwith a notch It is noted that themaximumappliedloads corresponded to the CMOD around 10mm in thespecimens S25-F10-P0 and S25-F20-P0 As presented in thefigure stress along cracked region decreases with increasingthe opening displacement In addition since S25-F10-P0 andS25-F20-P0 had the cracking strengths of 660 and 681MParespectively it is obvious that maximum tensile stress ofUHPFRCwas larger than cracking strengthThese results arecompatible with the SDEM and the proposed method in thispaper

6 Advances in Materials Science and Engineering

S25F10P0S25F15P0S25F20P0

S25-P0 series

0

5

10

15

20Te

nsile

stre

ss (M

Pa)

2 4 6 8 100Crack width (mm)

0

5

10

15

20

Tens

ile st

ress

(MPa

)

2 4 6 8 100Crack width (mm)

2 4 6 8 100Crack width (mm)

0

5

10

15

20Te

nsile

stre

ss (M

Pa)

0

5

10

15

20

Tens

ile st

ress

(MPa

)

2 4 6 8 100Crack width (mm)

S25F10PSS25F15PSS25F20PS

S25-PS series

S34F10PSS34F15PSS34F20PS

S34-PS series

S34F10P0S34F15P0S34F20P0

S34-P0 series

Figure 6 Tensile behavior of UHPFRC evaluated through the proposed inverse analysis with the SDEM

Consequently it can be concluded that the tensile behav-ior of UHPFRC can be reasonably predicted by the pulloutstrength which is evaluated through the proposed inverseanalysis based on the section analysis with the SDEM

4 Conclusion

In this paper an inverse analysis procedure has been pro-posed to evaluate tensile behavior of UHPFRC from testresults with notched UHPFRC beams subjected to three-point flexural loading The proposed inverse analysis pro-cedure is based on section analysis in which the SDEM isemployed to take into account UHPFRC stress distributionalong the section with a notch Since pullout strength of astraight fiber can be directly evaluated from the maximumload measured through the three-point bending test tensilebehavior of UHPFRC can be easily predicted with the SDEM

To verify the proposed inverse analysis procedureUHPFRC beams with a notch subjected to three-point flex-ural loading have been analyzed with the tensile behavior ofUHPFRC evaluated through the proposed inverse analysisprocedure The analysis results showed good agreement withthe test results expressed to the applied load-CMODresponse It can be concluded that the tensile behavior ofUHPFRC can be reasonably evaluated from the proposedinverse analysis procedure

The proposed inverse analysis procedure can be usefulin evaluating tensile behavior of concrete with other typesof fibers like end-hooked fibers crimped fibers and so onIn addition through simplification of the proposed inverseanalysis procedure it is anticipated that this paper can beuseful in developing advanced design approaches or morerational computational methods for UHPFRC members

Advances in Materials Science and Engineering 7

S25-F10-P0

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 2

Spec 3

Spec 4

Spec 5Spec 6Prediction

S25-F10-PS

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 4

Spec 5Spec 6Prediction

Spec 1

Spec 2

S25-F15-P0

Spec 3

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 6Prediction

Spec 1

Spec 2

Spec 4

S25-F15-PS

0

20

40

60

80Lo

ad (k

N)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

S25-F20-PS

0

20

40

60

100

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

S25-F20-P0

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5

Spec 6Prediction

Spec 1Spec 2

Figure 7 Continued

8 Advances in Materials Science and Engineering

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5PredictionSpec 4

Spec 3

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4Spec 3

0

20

40

60

80Lo

ad (k

N)

0 1 2 3 4 5 6CMOD (mm)

Spec 6Prediction

Spec 1Spec 2Spec 3

Spec 4

0

20

40

60

100

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4Spec 2

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

S34-F10-P0 S34-F10-PS

S34-F15-P0 S34-F15-PS

S34-F20-P0 S34-F20-PS

Figure 7 Comparison on the applied load-CMOD response

Advances in Materials Science and Engineering 9

0

20

40

60

80

100

Dist

ance

from

top

fiber

(mm

)

S25-F10-P0 S25-F20-P0

CMOD =CMOD =

CMOD =

CMOD =

minus100 minus75 minus50 minus25 0 25Stress (MPa)

0

20

40

60

80

100

Dist

ance

from

top

fiber

(mm

)

CMOD =CMOD =

CMOD =

CMOD =

minus100 minus75 minus50 minus25 0 25Stress (MPa)

10mm20mm

30mm50mm

10mm20mm

30mm50mm

Figure 8 Stress distribution along the section with a notch

Conflicts of Interest

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

Acknowledgments

This research was supported by a grant (13SCIPA02) fromSmart Civil Infrastructure Research Program funded byMinistry of Land Infrastructure and Transport (MOLIT)of Korea government and Korea Agency for InfrastructureTechnology Advancement (KAIA)

References

[1] P H Bischoff ldquoTension stiffening and cracking of steel fiber-reinforced concreterdquo Journal of Materials in Civil Engineeringvol 15 no 2 pp 174ndash182 2003

[2] B BaeHChoi B Lee andC Bang ldquoCompressive behavior andmechanical characteristics and their application to stress-strainrelationship of steel fiber-reinforced reactive powder concreterdquoAdvances inMaterials Science and Engineering vol 2016 ArticleID 6465218 11 pages 2016

[3] H H Dinh G J Parra-Montesinos and J K Wight ldquoShearbehavior of steel fiber-reinforced concrete beams without stir-rup reinforcementrdquo ACI Structural Journal vol 107 no 5 pp597ndash606 2010

[4] J Susetyo P Gauvreau and F J Vecchio ldquoEffectiveness of steelfiber as minimum shear reinforcementrdquoACI Structural Journalvol 108 no 4 pp 488ndash496 2011

[5] MHHarajli andA A Rteil ldquoEffect of confinement using fiber-reinforced polymer or fiber-reinforced concrete on seismicperformance of gravity load-designed columnsrdquo ACI StructuralJournal vol 101 no 1 pp 47ndash56 2004

[6] Y ChiaHwan and H JianBo ldquoThe mechanical behavior offiber reinforced PP ECC beams under reverse cyclic loadingrdquo

Advances inMaterials Science and Engineering vol 2014 ArticleID 159790 9 pages 2014

[7] A E Naaman and H W Reinhardt ldquoCharacterization of highperformance fiber reinforced cement composites-HPFRCCrdquo inProceedings of HPFRCC 2 pp 1ndash23 1995

[8] P Marti T Pfyl V Sigrist and T Ulaga ldquoHarmonized testprocedures for steel fiber-reinforced concreterdquo ACI MaterialsJournal vol 96 no 6 pp 676ndash685 1999

[9] J Y L Voo and S J Foster ldquoVariable engagementmodel for fibrereinforced concrete in tensionrdquo UNICIV Report R-420 Schoolof Civil and Environmental Engineering the University of NewSouth Wales Sydney Australia 2003

[10] T Leutbecher and E Fehling ldquoCrack width control for com-bined reinforcement of rebars and fibers exemplified by ultra-high-performance concreterdquo fib Task Group 86 Ultra HighPerformance Fiber Reinforced Concrete-UHPFRC pp 1ndash282008

[11] P Stroeven ldquoStereological principles of spatialmodeling appliedto steel fiber-reinforced concrete in tensionrdquo ACI MaterialsJournal vol 106 no 3 pp 213ndash222 2009

[12] S-C Lee J-Y Cho and F J Vecchio ldquoDiverse embedmentmodel for steel fiber-reinforced concrete in tension modeldevelopmentrdquo ACI Materials Journal vol 108 no 5 pp 516ndash525 2011

[13] S-C Lee J-Y Cho and F J Vecchio ldquoDiverse embedmentmodel for steel fiber-reinforced concrete in tension modelverificationrdquo ACI Materials Journal vol 108 no 5 pp 526ndash5352011

[14] S-C Lee J-Y Cho and F J Vecchio ldquoSimplified diverseembedment model for steel fiber-reinforced concrete elementsin tensionrdquo ACI Materials Journal vol 110 no 4 pp 403ndash4122013

[15] S-C Lee J-Y Cho and F J Vecchio ldquoTension-stiffeningmodelfor steel fiber-reinforced concrete containing conventional rein-forcementrdquo ACI Structural Journal vol 110 no 4 pp 639ndash6482013

10 Advances in Materials Science and Engineering

[16] S-C Lee J-Y Cho and F J Vecchio ldquoAnalysis of steel fiber-reinforced concrete elements subjected to shearrdquoACI StructuralJournal vol 113 no 2 pp 275ndash285 2016

[17] K Kim I Yang and C Joh ldquoMaterial properties and structuralcharacteristics on flexure of steel fiber-reinforced ultra-high-performance concreterdquo Journal of the Korea Concrete Institutevol 28 no 2 pp 177ndash185 2016

[18] I-H Yang C Joh and B-S Kim ldquoShear behaviour of ultra-highperformance fibre-reinforced concrete beams without stir-rupsrdquo Magazine of Concrete Research vol 64 no 11 pp 979ndash993 2012

[19] I H Yang C Joh and B-S Kim ldquoStructural behavior ofultra high performance concrete beams subjected to bendingrdquoEngineering Structures vol 32 no 11 pp 3478ndash3487 2010

[20] S-C Lee ldquoRe-evaluation of fibre-reinforced concrete tensionmodel in CEB-FIP Model Code 2010rdquo Materials ResearchInnovations vol 19 supplement 8 pp 107ndash110 2015

[21] S-C Lee J-H Oh and J-Y Cho ldquoFiber efficiency in SFRCmembers subjected to uniaxial tensionrdquo Construction andBuilding Materials vol 113 pp 479ndash487 2016

[22] International Federation for Structural Concrete (fib) fibModelCode for Concrete Structures 2010 Ernst amp Sohn 2013

[23] B H Oh D G Park J C Kim and Y C Choi ldquoExperimentaland theoretical investigation on the postcracking inelasticbehavior of synthetic fiber reinforced concrete beamsrdquo Cementand Concrete Research vol 35 no 2 pp 384ndash392 2005

[24] S-C Lee J-H Oh and J-Y Cho ldquoFiber orientation factor ona circular cross-section in concrete membersrdquo Journal of theKorea Concrete Institute vol 26 no 3 pp 307ndash313 2014

[25] S-C Lee J-H Oh and J-Y Cho ldquoFiber orientation factor onrectangular cross-section in concrete membersrdquo InternationalJournal of Engineering and Technology vol 7 no 6 pp 470ndash4732015

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

6 Advances in Materials Science and Engineering

S25F10P0S25F15P0S25F20P0

S25-P0 series

0

5

10

15

20Te

nsile

stre

ss (M

Pa)

2 4 6 8 100Crack width (mm)

0

5

10

15

20

Tens

ile st

ress

(MPa

)

2 4 6 8 100Crack width (mm)

2 4 6 8 100Crack width (mm)

0

5

10

15

20Te

nsile

stre

ss (M

Pa)

0

5

10

15

20

Tens

ile st

ress

(MPa

)

2 4 6 8 100Crack width (mm)

S25F10PSS25F15PSS25F20PS

S25-PS series

S34F10PSS34F15PSS34F20PS

S34-PS series

S34F10P0S34F15P0S34F20P0

S34-P0 series

Figure 6 Tensile behavior of UHPFRC evaluated through the proposed inverse analysis with the SDEM

Consequently it can be concluded that the tensile behav-ior of UHPFRC can be reasonably predicted by the pulloutstrength which is evaluated through the proposed inverseanalysis based on the section analysis with the SDEM

4 Conclusion

In this paper an inverse analysis procedure has been pro-posed to evaluate tensile behavior of UHPFRC from testresults with notched UHPFRC beams subjected to three-point flexural loading The proposed inverse analysis pro-cedure is based on section analysis in which the SDEM isemployed to take into account UHPFRC stress distributionalong the section with a notch Since pullout strength of astraight fiber can be directly evaluated from the maximumload measured through the three-point bending test tensilebehavior of UHPFRC can be easily predicted with the SDEM

To verify the proposed inverse analysis procedureUHPFRC beams with a notch subjected to three-point flex-ural loading have been analyzed with the tensile behavior ofUHPFRC evaluated through the proposed inverse analysisprocedure The analysis results showed good agreement withthe test results expressed to the applied load-CMODresponse It can be concluded that the tensile behavior ofUHPFRC can be reasonably evaluated from the proposedinverse analysis procedure

The proposed inverse analysis procedure can be usefulin evaluating tensile behavior of concrete with other typesof fibers like end-hooked fibers crimped fibers and so onIn addition through simplification of the proposed inverseanalysis procedure it is anticipated that this paper can beuseful in developing advanced design approaches or morerational computational methods for UHPFRC members

Advances in Materials Science and Engineering 7

S25-F10-P0

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 2

Spec 3

Spec 4

Spec 5Spec 6Prediction

S25-F10-PS

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 4

Spec 5Spec 6Prediction

Spec 1

Spec 2

S25-F15-P0

Spec 3

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 6Prediction

Spec 1

Spec 2

Spec 4

S25-F15-PS

0

20

40

60

80Lo

ad (k

N)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

S25-F20-PS

0

20

40

60

100

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

S25-F20-P0

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5

Spec 6Prediction

Spec 1Spec 2

Figure 7 Continued

8 Advances in Materials Science and Engineering

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5PredictionSpec 4

Spec 3

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4Spec 3

0

20

40

60

80Lo

ad (k

N)

0 1 2 3 4 5 6CMOD (mm)

Spec 6Prediction

Spec 1Spec 2Spec 3

Spec 4

0

20

40

60

100

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4Spec 2

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

S34-F10-P0 S34-F10-PS

S34-F15-P0 S34-F15-PS

S34-F20-P0 S34-F20-PS

Figure 7 Comparison on the applied load-CMOD response

Advances in Materials Science and Engineering 9

0

20

40

60

80

100

Dist

ance

from

top

fiber

(mm

)

S25-F10-P0 S25-F20-P0

CMOD =CMOD =

CMOD =

CMOD =

minus100 minus75 minus50 minus25 0 25Stress (MPa)

0

20

40

60

80

100

Dist

ance

from

top

fiber

(mm

)

CMOD =CMOD =

CMOD =

CMOD =

minus100 minus75 minus50 minus25 0 25Stress (MPa)

10mm20mm

30mm50mm

10mm20mm

30mm50mm

Figure 8 Stress distribution along the section with a notch

Conflicts of Interest

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

Acknowledgments

This research was supported by a grant (13SCIPA02) fromSmart Civil Infrastructure Research Program funded byMinistry of Land Infrastructure and Transport (MOLIT)of Korea government and Korea Agency for InfrastructureTechnology Advancement (KAIA)

References

[1] P H Bischoff ldquoTension stiffening and cracking of steel fiber-reinforced concreterdquo Journal of Materials in Civil Engineeringvol 15 no 2 pp 174ndash182 2003

[2] B BaeHChoi B Lee andC Bang ldquoCompressive behavior andmechanical characteristics and their application to stress-strainrelationship of steel fiber-reinforced reactive powder concreterdquoAdvances inMaterials Science and Engineering vol 2016 ArticleID 6465218 11 pages 2016

[3] H H Dinh G J Parra-Montesinos and J K Wight ldquoShearbehavior of steel fiber-reinforced concrete beams without stir-rup reinforcementrdquo ACI Structural Journal vol 107 no 5 pp597ndash606 2010

[4] J Susetyo P Gauvreau and F J Vecchio ldquoEffectiveness of steelfiber as minimum shear reinforcementrdquoACI Structural Journalvol 108 no 4 pp 488ndash496 2011

[5] MHHarajli andA A Rteil ldquoEffect of confinement using fiber-reinforced polymer or fiber-reinforced concrete on seismicperformance of gravity load-designed columnsrdquo ACI StructuralJournal vol 101 no 1 pp 47ndash56 2004

[6] Y ChiaHwan and H JianBo ldquoThe mechanical behavior offiber reinforced PP ECC beams under reverse cyclic loadingrdquo

Advances inMaterials Science and Engineering vol 2014 ArticleID 159790 9 pages 2014

[7] A E Naaman and H W Reinhardt ldquoCharacterization of highperformance fiber reinforced cement composites-HPFRCCrdquo inProceedings of HPFRCC 2 pp 1ndash23 1995

[8] P Marti T Pfyl V Sigrist and T Ulaga ldquoHarmonized testprocedures for steel fiber-reinforced concreterdquo ACI MaterialsJournal vol 96 no 6 pp 676ndash685 1999

[9] J Y L Voo and S J Foster ldquoVariable engagementmodel for fibrereinforced concrete in tensionrdquo UNICIV Report R-420 Schoolof Civil and Environmental Engineering the University of NewSouth Wales Sydney Australia 2003

[10] T Leutbecher and E Fehling ldquoCrack width control for com-bined reinforcement of rebars and fibers exemplified by ultra-high-performance concreterdquo fib Task Group 86 Ultra HighPerformance Fiber Reinforced Concrete-UHPFRC pp 1ndash282008

[11] P Stroeven ldquoStereological principles of spatialmodeling appliedto steel fiber-reinforced concrete in tensionrdquo ACI MaterialsJournal vol 106 no 3 pp 213ndash222 2009

[12] S-C Lee J-Y Cho and F J Vecchio ldquoDiverse embedmentmodel for steel fiber-reinforced concrete in tension modeldevelopmentrdquo ACI Materials Journal vol 108 no 5 pp 516ndash525 2011

[13] S-C Lee J-Y Cho and F J Vecchio ldquoDiverse embedmentmodel for steel fiber-reinforced concrete in tension modelverificationrdquo ACI Materials Journal vol 108 no 5 pp 526ndash5352011

[14] S-C Lee J-Y Cho and F J Vecchio ldquoSimplified diverseembedment model for steel fiber-reinforced concrete elementsin tensionrdquo ACI Materials Journal vol 110 no 4 pp 403ndash4122013

[15] S-C Lee J-Y Cho and F J Vecchio ldquoTension-stiffeningmodelfor steel fiber-reinforced concrete containing conventional rein-forcementrdquo ACI Structural Journal vol 110 no 4 pp 639ndash6482013

10 Advances in Materials Science and Engineering

[16] S-C Lee J-Y Cho and F J Vecchio ldquoAnalysis of steel fiber-reinforced concrete elements subjected to shearrdquoACI StructuralJournal vol 113 no 2 pp 275ndash285 2016

[17] K Kim I Yang and C Joh ldquoMaterial properties and structuralcharacteristics on flexure of steel fiber-reinforced ultra-high-performance concreterdquo Journal of the Korea Concrete Institutevol 28 no 2 pp 177ndash185 2016

[18] I-H Yang C Joh and B-S Kim ldquoShear behaviour of ultra-highperformance fibre-reinforced concrete beams without stir-rupsrdquo Magazine of Concrete Research vol 64 no 11 pp 979ndash993 2012

[19] I H Yang C Joh and B-S Kim ldquoStructural behavior ofultra high performance concrete beams subjected to bendingrdquoEngineering Structures vol 32 no 11 pp 3478ndash3487 2010

[20] S-C Lee ldquoRe-evaluation of fibre-reinforced concrete tensionmodel in CEB-FIP Model Code 2010rdquo Materials ResearchInnovations vol 19 supplement 8 pp 107ndash110 2015

[21] S-C Lee J-H Oh and J-Y Cho ldquoFiber efficiency in SFRCmembers subjected to uniaxial tensionrdquo Construction andBuilding Materials vol 113 pp 479ndash487 2016

[22] International Federation for Structural Concrete (fib) fibModelCode for Concrete Structures 2010 Ernst amp Sohn 2013

[23] B H Oh D G Park J C Kim and Y C Choi ldquoExperimentaland theoretical investigation on the postcracking inelasticbehavior of synthetic fiber reinforced concrete beamsrdquo Cementand Concrete Research vol 35 no 2 pp 384ndash392 2005

[24] S-C Lee J-H Oh and J-Y Cho ldquoFiber orientation factor ona circular cross-section in concrete membersrdquo Journal of theKorea Concrete Institute vol 26 no 3 pp 307ndash313 2014

[25] S-C Lee J-H Oh and J-Y Cho ldquoFiber orientation factor onrectangular cross-section in concrete membersrdquo InternationalJournal of Engineering and Technology vol 7 no 6 pp 470ndash4732015

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Materials Science and Engineering 7

S25-F10-P0

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 2

Spec 3

Spec 4

Spec 5Spec 6Prediction

S25-F10-PS

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 4

Spec 5Spec 6Prediction

Spec 1

Spec 2

S25-F15-P0

Spec 3

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 6Prediction

Spec 1

Spec 2

Spec 4

S25-F15-PS

0

20

40

60

80Lo

ad (k

N)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

S25-F20-PS

0

20

40

60

100

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

S25-F20-P0

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5

Spec 6Prediction

Spec 1Spec 2

Figure 7 Continued

8 Advances in Materials Science and Engineering

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5PredictionSpec 4

Spec 3

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4Spec 3

0

20

40

60

80Lo

ad (k

N)

0 1 2 3 4 5 6CMOD (mm)

Spec 6Prediction

Spec 1Spec 2Spec 3

Spec 4

0

20

40

60

100

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4Spec 2

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

S34-F10-P0 S34-F10-PS

S34-F15-P0 S34-F15-PS

S34-F20-P0 S34-F20-PS

Figure 7 Comparison on the applied load-CMOD response

Advances in Materials Science and Engineering 9

0

20

40

60

80

100

Dist

ance

from

top

fiber

(mm

)

S25-F10-P0 S25-F20-P0

CMOD =CMOD =

CMOD =

CMOD =

minus100 minus75 minus50 minus25 0 25Stress (MPa)

0

20

40

60

80

100

Dist

ance

from

top

fiber

(mm

)

CMOD =CMOD =

CMOD =

CMOD =

minus100 minus75 minus50 minus25 0 25Stress (MPa)

10mm20mm

30mm50mm

10mm20mm

30mm50mm

Figure 8 Stress distribution along the section with a notch

Conflicts of Interest

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

Acknowledgments

This research was supported by a grant (13SCIPA02) fromSmart Civil Infrastructure Research Program funded byMinistry of Land Infrastructure and Transport (MOLIT)of Korea government and Korea Agency for InfrastructureTechnology Advancement (KAIA)

References

[1] P H Bischoff ldquoTension stiffening and cracking of steel fiber-reinforced concreterdquo Journal of Materials in Civil Engineeringvol 15 no 2 pp 174ndash182 2003

[2] B BaeHChoi B Lee andC Bang ldquoCompressive behavior andmechanical characteristics and their application to stress-strainrelationship of steel fiber-reinforced reactive powder concreterdquoAdvances inMaterials Science and Engineering vol 2016 ArticleID 6465218 11 pages 2016

[3] H H Dinh G J Parra-Montesinos and J K Wight ldquoShearbehavior of steel fiber-reinforced concrete beams without stir-rup reinforcementrdquo ACI Structural Journal vol 107 no 5 pp597ndash606 2010

[4] J Susetyo P Gauvreau and F J Vecchio ldquoEffectiveness of steelfiber as minimum shear reinforcementrdquoACI Structural Journalvol 108 no 4 pp 488ndash496 2011

[5] MHHarajli andA A Rteil ldquoEffect of confinement using fiber-reinforced polymer or fiber-reinforced concrete on seismicperformance of gravity load-designed columnsrdquo ACI StructuralJournal vol 101 no 1 pp 47ndash56 2004

[6] Y ChiaHwan and H JianBo ldquoThe mechanical behavior offiber reinforced PP ECC beams under reverse cyclic loadingrdquo

Advances inMaterials Science and Engineering vol 2014 ArticleID 159790 9 pages 2014

[7] A E Naaman and H W Reinhardt ldquoCharacterization of highperformance fiber reinforced cement composites-HPFRCCrdquo inProceedings of HPFRCC 2 pp 1ndash23 1995

[8] P Marti T Pfyl V Sigrist and T Ulaga ldquoHarmonized testprocedures for steel fiber-reinforced concreterdquo ACI MaterialsJournal vol 96 no 6 pp 676ndash685 1999

[9] J Y L Voo and S J Foster ldquoVariable engagementmodel for fibrereinforced concrete in tensionrdquo UNICIV Report R-420 Schoolof Civil and Environmental Engineering the University of NewSouth Wales Sydney Australia 2003

[10] T Leutbecher and E Fehling ldquoCrack width control for com-bined reinforcement of rebars and fibers exemplified by ultra-high-performance concreterdquo fib Task Group 86 Ultra HighPerformance Fiber Reinforced Concrete-UHPFRC pp 1ndash282008

[11] P Stroeven ldquoStereological principles of spatialmodeling appliedto steel fiber-reinforced concrete in tensionrdquo ACI MaterialsJournal vol 106 no 3 pp 213ndash222 2009

[12] S-C Lee J-Y Cho and F J Vecchio ldquoDiverse embedmentmodel for steel fiber-reinforced concrete in tension modeldevelopmentrdquo ACI Materials Journal vol 108 no 5 pp 516ndash525 2011

[13] S-C Lee J-Y Cho and F J Vecchio ldquoDiverse embedmentmodel for steel fiber-reinforced concrete in tension modelverificationrdquo ACI Materials Journal vol 108 no 5 pp 526ndash5352011

[14] S-C Lee J-Y Cho and F J Vecchio ldquoSimplified diverseembedment model for steel fiber-reinforced concrete elementsin tensionrdquo ACI Materials Journal vol 110 no 4 pp 403ndash4122013

[15] S-C Lee J-Y Cho and F J Vecchio ldquoTension-stiffeningmodelfor steel fiber-reinforced concrete containing conventional rein-forcementrdquo ACI Structural Journal vol 110 no 4 pp 639ndash6482013

10 Advances in Materials Science and Engineering

[16] S-C Lee J-Y Cho and F J Vecchio ldquoAnalysis of steel fiber-reinforced concrete elements subjected to shearrdquoACI StructuralJournal vol 113 no 2 pp 275ndash285 2016

[17] K Kim I Yang and C Joh ldquoMaterial properties and structuralcharacteristics on flexure of steel fiber-reinforced ultra-high-performance concreterdquo Journal of the Korea Concrete Institutevol 28 no 2 pp 177ndash185 2016

[18] I-H Yang C Joh and B-S Kim ldquoShear behaviour of ultra-highperformance fibre-reinforced concrete beams without stir-rupsrdquo Magazine of Concrete Research vol 64 no 11 pp 979ndash993 2012

[19] I H Yang C Joh and B-S Kim ldquoStructural behavior ofultra high performance concrete beams subjected to bendingrdquoEngineering Structures vol 32 no 11 pp 3478ndash3487 2010

[20] S-C Lee ldquoRe-evaluation of fibre-reinforced concrete tensionmodel in CEB-FIP Model Code 2010rdquo Materials ResearchInnovations vol 19 supplement 8 pp 107ndash110 2015

[21] S-C Lee J-H Oh and J-Y Cho ldquoFiber efficiency in SFRCmembers subjected to uniaxial tensionrdquo Construction andBuilding Materials vol 113 pp 479ndash487 2016

[22] International Federation for Structural Concrete (fib) fibModelCode for Concrete Structures 2010 Ernst amp Sohn 2013

[23] B H Oh D G Park J C Kim and Y C Choi ldquoExperimentaland theoretical investigation on the postcracking inelasticbehavior of synthetic fiber reinforced concrete beamsrdquo Cementand Concrete Research vol 35 no 2 pp 384ndash392 2005

[24] S-C Lee J-H Oh and J-Y Cho ldquoFiber orientation factor ona circular cross-section in concrete membersrdquo Journal of theKorea Concrete Institute vol 26 no 3 pp 307ndash313 2014

[25] S-C Lee J-H Oh and J-Y Cho ldquoFiber orientation factor onrectangular cross-section in concrete membersrdquo InternationalJournal of Engineering and Technology vol 7 no 6 pp 470ndash4732015

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

8 Advances in Materials Science and Engineering

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5PredictionSpec 4

Spec 3

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4Spec 3

0

20

40

60

80Lo

ad (k

N)

0 1 2 3 4 5 6CMOD (mm)

Spec 6Prediction

Spec 1Spec 2Spec 3

Spec 4

0

20

40

60

100

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4Spec 2

0

20

40

60

80

Load

(kN

)

0 1 2 3 4 5 6CMOD (mm)

Spec 5Spec 6Prediction

Spec 1

Spec 4

Spec 2Spec 3

S34-F10-P0 S34-F10-PS

S34-F15-P0 S34-F15-PS

S34-F20-P0 S34-F20-PS

Figure 7 Comparison on the applied load-CMOD response

Advances in Materials Science and Engineering 9

0

20

40

60

80

100

Dist

ance

from

top

fiber

(mm

)

S25-F10-P0 S25-F20-P0

CMOD =CMOD =

CMOD =

CMOD =

minus100 minus75 minus50 minus25 0 25Stress (MPa)

0

20

40

60

80

100

Dist

ance

from

top

fiber

(mm

)

CMOD =CMOD =

CMOD =

CMOD =

minus100 minus75 minus50 minus25 0 25Stress (MPa)

10mm20mm

30mm50mm

10mm20mm

30mm50mm

Figure 8 Stress distribution along the section with a notch

Conflicts of Interest

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

Acknowledgments

This research was supported by a grant (13SCIPA02) fromSmart Civil Infrastructure Research Program funded byMinistry of Land Infrastructure and Transport (MOLIT)of Korea government and Korea Agency for InfrastructureTechnology Advancement (KAIA)

References

[1] P H Bischoff ldquoTension stiffening and cracking of steel fiber-reinforced concreterdquo Journal of Materials in Civil Engineeringvol 15 no 2 pp 174ndash182 2003

[2] B BaeHChoi B Lee andC Bang ldquoCompressive behavior andmechanical characteristics and their application to stress-strainrelationship of steel fiber-reinforced reactive powder concreterdquoAdvances inMaterials Science and Engineering vol 2016 ArticleID 6465218 11 pages 2016

[3] H H Dinh G J Parra-Montesinos and J K Wight ldquoShearbehavior of steel fiber-reinforced concrete beams without stir-rup reinforcementrdquo ACI Structural Journal vol 107 no 5 pp597ndash606 2010

[4] J Susetyo P Gauvreau and F J Vecchio ldquoEffectiveness of steelfiber as minimum shear reinforcementrdquoACI Structural Journalvol 108 no 4 pp 488ndash496 2011

[5] MHHarajli andA A Rteil ldquoEffect of confinement using fiber-reinforced polymer or fiber-reinforced concrete on seismicperformance of gravity load-designed columnsrdquo ACI StructuralJournal vol 101 no 1 pp 47ndash56 2004

[6] Y ChiaHwan and H JianBo ldquoThe mechanical behavior offiber reinforced PP ECC beams under reverse cyclic loadingrdquo

Advances inMaterials Science and Engineering vol 2014 ArticleID 159790 9 pages 2014

[7] A E Naaman and H W Reinhardt ldquoCharacterization of highperformance fiber reinforced cement composites-HPFRCCrdquo inProceedings of HPFRCC 2 pp 1ndash23 1995

[8] P Marti T Pfyl V Sigrist and T Ulaga ldquoHarmonized testprocedures for steel fiber-reinforced concreterdquo ACI MaterialsJournal vol 96 no 6 pp 676ndash685 1999

[9] J Y L Voo and S J Foster ldquoVariable engagementmodel for fibrereinforced concrete in tensionrdquo UNICIV Report R-420 Schoolof Civil and Environmental Engineering the University of NewSouth Wales Sydney Australia 2003

[10] T Leutbecher and E Fehling ldquoCrack width control for com-bined reinforcement of rebars and fibers exemplified by ultra-high-performance concreterdquo fib Task Group 86 Ultra HighPerformance Fiber Reinforced Concrete-UHPFRC pp 1ndash282008

[11] P Stroeven ldquoStereological principles of spatialmodeling appliedto steel fiber-reinforced concrete in tensionrdquo ACI MaterialsJournal vol 106 no 3 pp 213ndash222 2009

[12] S-C Lee J-Y Cho and F J Vecchio ldquoDiverse embedmentmodel for steel fiber-reinforced concrete in tension modeldevelopmentrdquo ACI Materials Journal vol 108 no 5 pp 516ndash525 2011

[13] S-C Lee J-Y Cho and F J Vecchio ldquoDiverse embedmentmodel for steel fiber-reinforced concrete in tension modelverificationrdquo ACI Materials Journal vol 108 no 5 pp 526ndash5352011

[14] S-C Lee J-Y Cho and F J Vecchio ldquoSimplified diverseembedment model for steel fiber-reinforced concrete elementsin tensionrdquo ACI Materials Journal vol 110 no 4 pp 403ndash4122013

[15] S-C Lee J-Y Cho and F J Vecchio ldquoTension-stiffeningmodelfor steel fiber-reinforced concrete containing conventional rein-forcementrdquo ACI Structural Journal vol 110 no 4 pp 639ndash6482013

10 Advances in Materials Science and Engineering

[16] S-C Lee J-Y Cho and F J Vecchio ldquoAnalysis of steel fiber-reinforced concrete elements subjected to shearrdquoACI StructuralJournal vol 113 no 2 pp 275ndash285 2016

[17] K Kim I Yang and C Joh ldquoMaterial properties and structuralcharacteristics on flexure of steel fiber-reinforced ultra-high-performance concreterdquo Journal of the Korea Concrete Institutevol 28 no 2 pp 177ndash185 2016

[18] I-H Yang C Joh and B-S Kim ldquoShear behaviour of ultra-highperformance fibre-reinforced concrete beams without stir-rupsrdquo Magazine of Concrete Research vol 64 no 11 pp 979ndash993 2012

[19] I H Yang C Joh and B-S Kim ldquoStructural behavior ofultra high performance concrete beams subjected to bendingrdquoEngineering Structures vol 32 no 11 pp 3478ndash3487 2010

[20] S-C Lee ldquoRe-evaluation of fibre-reinforced concrete tensionmodel in CEB-FIP Model Code 2010rdquo Materials ResearchInnovations vol 19 supplement 8 pp 107ndash110 2015

[21] S-C Lee J-H Oh and J-Y Cho ldquoFiber efficiency in SFRCmembers subjected to uniaxial tensionrdquo Construction andBuilding Materials vol 113 pp 479ndash487 2016

[22] International Federation for Structural Concrete (fib) fibModelCode for Concrete Structures 2010 Ernst amp Sohn 2013

[23] B H Oh D G Park J C Kim and Y C Choi ldquoExperimentaland theoretical investigation on the postcracking inelasticbehavior of synthetic fiber reinforced concrete beamsrdquo Cementand Concrete Research vol 35 no 2 pp 384ndash392 2005

[24] S-C Lee J-H Oh and J-Y Cho ldquoFiber orientation factor ona circular cross-section in concrete membersrdquo Journal of theKorea Concrete Institute vol 26 no 3 pp 307ndash313 2014

[25] S-C Lee J-H Oh and J-Y Cho ldquoFiber orientation factor onrectangular cross-section in concrete membersrdquo InternationalJournal of Engineering and Technology vol 7 no 6 pp 470ndash4732015

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Materials Science and Engineering 9

0

20

40

60

80

100

Dist

ance

from

top

fiber

(mm

)

S25-F10-P0 S25-F20-P0

CMOD =CMOD =

CMOD =

CMOD =

minus100 minus75 minus50 minus25 0 25Stress (MPa)

0

20

40

60

80

100

Dist

ance

from

top

fiber

(mm

)

CMOD =CMOD =

CMOD =

CMOD =

minus100 minus75 minus50 minus25 0 25Stress (MPa)

10mm20mm

30mm50mm

10mm20mm

30mm50mm

Figure 8 Stress distribution along the section with a notch

Conflicts of Interest

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

Acknowledgments

This research was supported by a grant (13SCIPA02) fromSmart Civil Infrastructure Research Program funded byMinistry of Land Infrastructure and Transport (MOLIT)of Korea government and Korea Agency for InfrastructureTechnology Advancement (KAIA)

References

[1] P H Bischoff ldquoTension stiffening and cracking of steel fiber-reinforced concreterdquo Journal of Materials in Civil Engineeringvol 15 no 2 pp 174ndash182 2003

[2] B BaeHChoi B Lee andC Bang ldquoCompressive behavior andmechanical characteristics and their application to stress-strainrelationship of steel fiber-reinforced reactive powder concreterdquoAdvances inMaterials Science and Engineering vol 2016 ArticleID 6465218 11 pages 2016

[3] H H Dinh G J Parra-Montesinos and J K Wight ldquoShearbehavior of steel fiber-reinforced concrete beams without stir-rup reinforcementrdquo ACI Structural Journal vol 107 no 5 pp597ndash606 2010

[4] J Susetyo P Gauvreau and F J Vecchio ldquoEffectiveness of steelfiber as minimum shear reinforcementrdquoACI Structural Journalvol 108 no 4 pp 488ndash496 2011

[5] MHHarajli andA A Rteil ldquoEffect of confinement using fiber-reinforced polymer or fiber-reinforced concrete on seismicperformance of gravity load-designed columnsrdquo ACI StructuralJournal vol 101 no 1 pp 47ndash56 2004

[6] Y ChiaHwan and H JianBo ldquoThe mechanical behavior offiber reinforced PP ECC beams under reverse cyclic loadingrdquo

Advances inMaterials Science and Engineering vol 2014 ArticleID 159790 9 pages 2014

[7] A E Naaman and H W Reinhardt ldquoCharacterization of highperformance fiber reinforced cement composites-HPFRCCrdquo inProceedings of HPFRCC 2 pp 1ndash23 1995

[8] P Marti T Pfyl V Sigrist and T Ulaga ldquoHarmonized testprocedures for steel fiber-reinforced concreterdquo ACI MaterialsJournal vol 96 no 6 pp 676ndash685 1999

[9] J Y L Voo and S J Foster ldquoVariable engagementmodel for fibrereinforced concrete in tensionrdquo UNICIV Report R-420 Schoolof Civil and Environmental Engineering the University of NewSouth Wales Sydney Australia 2003

[10] T Leutbecher and E Fehling ldquoCrack width control for com-bined reinforcement of rebars and fibers exemplified by ultra-high-performance concreterdquo fib Task Group 86 Ultra HighPerformance Fiber Reinforced Concrete-UHPFRC pp 1ndash282008

[11] P Stroeven ldquoStereological principles of spatialmodeling appliedto steel fiber-reinforced concrete in tensionrdquo ACI MaterialsJournal vol 106 no 3 pp 213ndash222 2009

[12] S-C Lee J-Y Cho and F J Vecchio ldquoDiverse embedmentmodel for steel fiber-reinforced concrete in tension modeldevelopmentrdquo ACI Materials Journal vol 108 no 5 pp 516ndash525 2011

[13] S-C Lee J-Y Cho and F J Vecchio ldquoDiverse embedmentmodel for steel fiber-reinforced concrete in tension modelverificationrdquo ACI Materials Journal vol 108 no 5 pp 526ndash5352011

[14] S-C Lee J-Y Cho and F J Vecchio ldquoSimplified diverseembedment model for steel fiber-reinforced concrete elementsin tensionrdquo ACI Materials Journal vol 110 no 4 pp 403ndash4122013

[15] S-C Lee J-Y Cho and F J Vecchio ldquoTension-stiffeningmodelfor steel fiber-reinforced concrete containing conventional rein-forcementrdquo ACI Structural Journal vol 110 no 4 pp 639ndash6482013

10 Advances in Materials Science and Engineering

[16] S-C Lee J-Y Cho and F J Vecchio ldquoAnalysis of steel fiber-reinforced concrete elements subjected to shearrdquoACI StructuralJournal vol 113 no 2 pp 275ndash285 2016

[17] K Kim I Yang and C Joh ldquoMaterial properties and structuralcharacteristics on flexure of steel fiber-reinforced ultra-high-performance concreterdquo Journal of the Korea Concrete Institutevol 28 no 2 pp 177ndash185 2016

[18] I-H Yang C Joh and B-S Kim ldquoShear behaviour of ultra-highperformance fibre-reinforced concrete beams without stir-rupsrdquo Magazine of Concrete Research vol 64 no 11 pp 979ndash993 2012

[19] I H Yang C Joh and B-S Kim ldquoStructural behavior ofultra high performance concrete beams subjected to bendingrdquoEngineering Structures vol 32 no 11 pp 3478ndash3487 2010

[20] S-C Lee ldquoRe-evaluation of fibre-reinforced concrete tensionmodel in CEB-FIP Model Code 2010rdquo Materials ResearchInnovations vol 19 supplement 8 pp 107ndash110 2015

[21] S-C Lee J-H Oh and J-Y Cho ldquoFiber efficiency in SFRCmembers subjected to uniaxial tensionrdquo Construction andBuilding Materials vol 113 pp 479ndash487 2016

[22] International Federation for Structural Concrete (fib) fibModelCode for Concrete Structures 2010 Ernst amp Sohn 2013

[23] B H Oh D G Park J C Kim and Y C Choi ldquoExperimentaland theoretical investigation on the postcracking inelasticbehavior of synthetic fiber reinforced concrete beamsrdquo Cementand Concrete Research vol 35 no 2 pp 384ndash392 2005

[24] S-C Lee J-H Oh and J-Y Cho ldquoFiber orientation factor ona circular cross-section in concrete membersrdquo Journal of theKorea Concrete Institute vol 26 no 3 pp 307ndash313 2014

[25] S-C Lee J-H Oh and J-Y Cho ldquoFiber orientation factor onrectangular cross-section in concrete membersrdquo InternationalJournal of Engineering and Technology vol 7 no 6 pp 470ndash4732015

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

10 Advances in Materials Science and Engineering

[16] S-C Lee J-Y Cho and F J Vecchio ldquoAnalysis of steel fiber-reinforced concrete elements subjected to shearrdquoACI StructuralJournal vol 113 no 2 pp 275ndash285 2016

[17] K Kim I Yang and C Joh ldquoMaterial properties and structuralcharacteristics on flexure of steel fiber-reinforced ultra-high-performance concreterdquo Journal of the Korea Concrete Institutevol 28 no 2 pp 177ndash185 2016

[18] I-H Yang C Joh and B-S Kim ldquoShear behaviour of ultra-highperformance fibre-reinforced concrete beams without stir-rupsrdquo Magazine of Concrete Research vol 64 no 11 pp 979ndash993 2012

[19] I H Yang C Joh and B-S Kim ldquoStructural behavior ofultra high performance concrete beams subjected to bendingrdquoEngineering Structures vol 32 no 11 pp 3478ndash3487 2010

[20] S-C Lee ldquoRe-evaluation of fibre-reinforced concrete tensionmodel in CEB-FIP Model Code 2010rdquo Materials ResearchInnovations vol 19 supplement 8 pp 107ndash110 2015

[21] S-C Lee J-H Oh and J-Y Cho ldquoFiber efficiency in SFRCmembers subjected to uniaxial tensionrdquo Construction andBuilding Materials vol 113 pp 479ndash487 2016

[22] International Federation for Structural Concrete (fib) fibModelCode for Concrete Structures 2010 Ernst amp Sohn 2013

[23] B H Oh D G Park J C Kim and Y C Choi ldquoExperimentaland theoretical investigation on the postcracking inelasticbehavior of synthetic fiber reinforced concrete beamsrdquo Cementand Concrete Research vol 35 no 2 pp 384ndash392 2005

[24] S-C Lee J-H Oh and J-Y Cho ldquoFiber orientation factor ona circular cross-section in concrete membersrdquo Journal of theKorea Concrete Institute vol 26 no 3 pp 307ndash313 2014

[25] S-C Lee J-H Oh and J-Y Cho ldquoFiber orientation factor onrectangular cross-section in concrete membersrdquo InternationalJournal of Engineering and Technology vol 7 no 6 pp 470ndash4732015

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014