Effect of Reinforcement on Early-Age Concrete Temperature Stress ...

Research ArticleEffect of Reinforcement on Early-Age ConcreteTemperature Stress Preliminary ExperimentalInvestigation and Analytical Simulation

Jianda Xin1 Siqing Lin2 Nannan Shi1 Jianshu Ouyang1 and Dahai Huang1

1Department of Airport and Pavement Engineering Beihang University Beijing 100191 China2Hekou Reservoir Administration Henan 454650 China

Correspondence should be addressed to Dahai Huang 59703751qqcom

Received 30 January 2015 Accepted 21 May 2015

Academic Editor Luigi Nicolais

Copyright copy 2015 Jianda Xin et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

For concrete under short-term loading effect of reinforcement on concrete crack resistance capability is usually negligible howeverrecent research results show that extension of this viewpoint to concrete under long-term loading (temperature variation) maybe unsuitable In order to investigate this phenomenon this paper presents the experimental and analytical results of early-agereinforced concrete temperature stress development under uniaxial restraint The experiments were carried out on a temperaturestress testing machine (TSTM) Experimental results show that the coupling of reinforcement and concrete creep behaviorinfluenced the concrete temperature stress development and nearly 16 of concrete stress was reduced in the current researchMoreover the cracking time of reinforced concrete was also delayed Finally based on the principle of superposition analyticalsimulations of effect of reinforcement on concrete temperature stress have been performed

1 Introduction

The tensile strength of concrete is relatively low and massconcrete structures after casting are prone to crack at early-age Concrete deformation caused by cement hydration ifrestrained can result in tensile stress during the coolingphase These tensile stresses will cause concrete crackingwhen exceeding the tensile strength

Although many researchers studied the early-age crack-ing behavior of restrained concrete with ring tests [1ndash3] thedefects of this test such as uncertain restraint degree anduncontrolled temperature history limit its use in complexissues To overcome these limits a temperature stress testingmachine (TSTM) which was firstly developed by Springen-schmid et al [4] and then improved by others [5ndash7] was grad-ually used Numerous studies have been performed Tao andWeizu [8] investigated the early-age tensile creep behaviorof high strength concrete with different concrete mixturesIgarashi et al [9] evaluated the effects of waterbinder ratioand silica fume on the early-age concrete stress development

Darquennes et al [10] found that the expansion of slag cementconcrete at early-age greatly relaxes internal stresses

To the authorsrsquo knowledge most studies about the early-age concrete temperature and stress development have beenperformed on unreinforced concrete [11ndash13] Lee et al [11]discussed the thermal stress of reactor containment buildingunder hotcold weather and corresponding cracking riskindexes were given Honorio et al [12] investigated theinfluence of boundary and initial condition on temperaturedevelopment of massive concrete structures Benboudjemaand Torrenti [13] developed a numerical model to predictearly-age cracking of massive concrete structures and severalfactors such as creep damage and hydration have beentaken into account Few researches about the effect ofreinforcement on concrete temperature stress and crackingbehavior can be found [14 15] Observation in practice [16]and research results [14 17] however clearly show the benefitof reinforcement on reduction of concrete cracking riskSule and Van Breugel [14] investigated the effect of rein-forcement on early-age cracking in high strength concrete

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2015 Article ID 231973 9 pageshttpdxdoiorg1011552015231973

2 Advances in Materials Science and Engineering

Figure 1 Uniaxial tension test [18]

and a strain enhancement factor was introduced to quantifythe effect of reinforcement decreasing the risk of early-ageconcrete cracking Briffaut et al [17] studied the early-ageconcrete behavior of massive structures with a thermal activerestrained shrinkage ring and found that the cracking timeof concrete was delayed when concrete was reinforced Itis noted that this phenomenon is not consistent with thecracking behavior of reinforced concrete under short-termloading Usually the usage of reinforcement on concretestructures is not to prevent concrete from cracking [18] butto limit the deflection and crack width [19 20] Obviouslythe effect of reinforcement on cracking behavior of con-crete under long-term loading (temperature variation) is notnegligible It is necessary to investigate how reinforcementinfluences the development of concrete temperature stress

On the other hand concrete deformation closely relatesto the cooling rate and the effect of temperature control onmass concrete casting projects has already been proven [21]A good understanding of the effect of cooling rate on concretetemperature stress development is also of great importance

Thus the following studies have been carried out in thispaper

(1) Temperature stress tests of plain concrete and rein-forced concrete specimens were conducted on aTSTM The effect of reinforcement on concretetemperature stress development has been analyzedMoreover concrete temperature stress developmentsunder different cooling rates were preliminarily stud-ied

(2) Based on the principle of superposition analyticalsimulations of effect of reinforcement on concretetemperature stress were performed on Matlab soft-ware

2 Analysis of Temperature StressDevelopment of TSTM Test

21 Effect of Reinforcement on Concrete Stress under Short-Term Loading Figure 1 shows a traditional uniaxial tensiontest for the determination of concrete cracking load The testis performed under a multistage loading and the applied loadcan be monitored by a load sensor

The cracking load can be estimated by the followingequation

119873cr = 119891119905119860[1+(119864119904

119864119888

minus 1)120588] (1)

where 119891119905is the tensile strength of concrete 119860 is the cross

section area of specimen 119864119904and 119864

119888are the modulus of

reinforcement and concrete respectively and 120588 is the rein-forcement ratio

Equation (1) shows that the cracking load of reinforcedconcrete member is increased as reinforcement can bearadditional load However the effect of reinforcement onconcrete stress evolution is negligible in this test

22 Effect of Reinforcement on Concrete Stress under Long-Term Loading As shown in Figure 2 the total deformationof plain concrete specimen increases when an initial stressapplied and this stress keeps constant thereafter knownas creep However for a reinforced concrete the concretestress decreases with time because of the interaction betweenconcrete and reinforcement during the loading period

For plain concrete if loaded and totally restrained stresswill decrease in the concrete also known as relaxation(Figure 3) However for reinforced concrete the evolutionof concrete stress will still be the same as that of plainconcrete because no deformation is generated and the effectof reinforcement will not be activated

23 Temperature Stress Development of TSTM Test Usuallythe deformation of TSTM specimen is not always zero butwithin a threshold 1205760 [5]The specimen will be pushedpulledto the original position when the absolute deformationexceeds the threshold (Figure 4(a))The evolution of concretetemperature stress is illustrated in Figure 4(b) if a perfectbond between concrete and reinforcement is assumed thenstress decrement Δ120590

119894of concrete is transferred to reinforce-

ment because of concrete creep behavior during each cycle(eg the time periods 119905

119894minus1 to 119905119894 119905119894 to 119905119894+1) on the other handstress increment Δ1205901015840

119894of concrete is loaded to maintain the

original length of the specimen at the time of 119905119894minus1 119905119894 and 119905119894+1

and so forth Both concrete stress reduction and creep strainincrease with the number of cycles The TSTM test consistsof numerous cycles and concrete temperature stress can bereduced in each cycle These minor changes will add up overtime and the total change may be considerable (Figure 5)

As mentioned in Section 22 the reduction of concretestress is accompanied by the deformation of concrete indi-cating that concrete creep behavior is crucial for assessingconcrete temperature stress development For a TSTM testtwo identical specimens are tested in the same time Oneis free to deform while the other is restrained The inducedload can be recorded from restrained specimen and shrinkagedeformation can be measured from free deformed specimenand the concrete creep can be easily deduced frommeasureddeformation data The particularly designed TSTM systemmakes it possible to resolve concrete creep behavior

Once concrete creep is known the effect of reinforcementon concrete temperature stress development can be quantita-tively assessed

3 Experimental Program

31 Mechanical Property Test According to the Chinese codeGBT 50081-2002 [22] the mechanical properties of concretemixtures at the ages of 3 days 7 days and 28 days were

Advances in Materials Science and Engineering 3

120590c(t0)

120590c(t0)

120590s(t0) 120590s(t1) gt 120590s(t0)

120590c(t1) lt 120590c(t0)

120590c(t1) = 120590c(t0)

Δ120576

Figure 2 Effect of reinforcement on concrete stress in creep tests (120590119888 concrete stress 120590

119904 reinforcement stress)

120590c(t1) lt 120590c(t0)120590c(t1) lt 120590c(t0)

120590c(t0)120590c(t0)

120576 = 0

120590s(t0)

120590s(t1) = 120590s(t0)

Figure 3 Effect of reinforcement on concrete stress in relaxation tests (120590119888 concrete stress 120590


timinus1

1205760

ti

ti

ti+1

ti+1

Δ120590i

Δ120590998400i

Δ120590i+1

Δ120590998400i+1

(a)

120590c

timinus1 ti ti+1 tn

timinus1 ti ti+1 tnt

t

120576

1205760

(b)

Figure 4 Evolution of (a) deformation and (b) concrete stress of reinforced concrete

120576

1205760

Δ120590

120576creep

t

sumΔ120590

Figure 5 Evolution of creep strain and stress reduction of concrete

measured on specimens of 100mm times 100mm times 300mm forelastic modulus test and 100mm times 100mm times 100mm forsplitting tensile test

Figure 6 Temperature stress testing machine

32 TSTM Test The specimens were tested on a TSTM(Figure 6) Concrete was directly cast in the TSTM mouldand the top surfaces of all specimens were then covered witha plastic sheet to maintain a constant humidity Details oftemperature stress testing procedure can be found elsewhere[4 5]


Table 1 Mix proportion of concrete (kgm3)

Mix Cement Fly ash Sand Gravel Water Water reducer Air entrainingMass 255 85 748 1133 146 4074 0068

150

1501500

Figure 7 Dimensions of the TSTM specimen (mm)

Table 2 Specimen numbers and parameters

Specimen Reinforcement configuration Cooling rateC-0-1 mdash 033∘ChC-0-2 mdash 021∘ChC-0-3 mdash 033∘ChC-1-1 412059312 033∘ChC-1-2 412059312 033∘ChNote C-0-3 and C-1-1 are free deformed C-0-1 C-0-2 and C-1-2 are fullyrestrained

Table 1 shows the mix proportion of concrete Theconcrete mixture (wcm = 043) was made with ordinaryPortland cement natural sand and crushed stone with amaximum particle size of 30mm The steel reinforcementused in this research is with an elastic modulus of 200GPaand a yield strength of 235MPa

The dimension of specimens is illustrated in Figure 7Numbers of specimen are listed in Table 2 Specimens of

TSTM tests were cast from the same batch of concrete andthe reinforcement ratio of reinforced specimens is 20 Thespecimens went through a three-phase temperature variation(Figure 8(a)) an adiabatic temperature phase an isothermaltemperature phase and a cooling temperature phase Thetemperature decrease rate of the massive wall structures isapproximately with a linear decrease of 035∘Ch [17] andthe evolution of temperature of concrete structures dependson several factors such as concrete mix wind and castingtemperature therefore two cooling rates were selected andthe cooling phase lasts until the concrete cracks

4 Experimental Results and Discussions

41 Mechanical Properties Mechanical property test resultsare listed in Table 3

Table 3 Mechanical properties of concrete

Agedays Splitting tensilestrengthMPa Elastic modulusGPa

3 181 19397 287 275128 321 3130

42 Deformation Behavior

421 Free Strain Figure 8(b) shows a typical strain evolutionof free specimen (solid line) It can be seen that the free strainincreased rapidly during the adiabatic temperature phase (inthe first 24 h) the variation of free strain was not distinctwhen the temperature was kept constant (isothermal temper-ature phase) At the last stage the free strain simultaneouslydecreased with the dropping temperature

Figure 9 shows the free strain evolution of plain andreinforced concrete It was found that the free strains of plainand reinforced concrete were almost the same indicating thatthe thermal expansion coefficients of concrete and reinforce-ment are about the same in the current research MeanwhileFigure 9 also indicates that the effect of autogenous shrinkageis minor for concrete mixture with high wc [14] and thethermal strain caused by temperature variation is the key partof free strain measured in the tests

422 Creep Strain For a restrained specimen the total strainconsists of elastic strain 120576

119890 thermal strain 120576ther shrinkage

strain 120576sh and tensile creep strain 120576creep The elastic strainis recorded by the computer during the test (dash line inFigure 8(b)) For a full restraint test 120576tot = 0 and thusthe concrete creep strain can be calculated by subtractingaccumulated elastic strain from free strain and this method(Figure 10) is also used by other researchers [5 6]

43 Temperature Stress Development Figure 11 shows a typ-ical stress evolution of plain concrete specimen Compres-sive stress increased due to thermal expansion caused bycement hydration and this stress decreased after the peakof temperature Finally the tensile stress was generated at acritical moment also known as point of ldquothe second zerostressrdquo [23] The concrete tensile stress still increased withthe dropping temperature and ultimately exceeded tensilestrength of concrete The whole process can be divided intotwo phases a compression time zone (phase 1) and a tensiontime zone (phase 2) Since the tensile stress of concrete isstrongly related to the cracking at early-age attention will bepaid to phase 2

The mechanical properties of concrete are strongly influ-enced by the temperature variation and an equivalent age


0 50 100 150

20

30

40

50

Phase 3Phase 2

Time (hour)

Temperature

Phase 1Te

mpe

ratu

re (∘

C)

(a)

0

50

100

150

Total strain of free specimenElastic strain of restrained specimen

50 100 150 200Time (hour)

minus150

minus100

minus50

Stra

in (120583

120576)

(b)

Figure 8 A typical evolution of (a) temperature and (b) strain

0 50 100 150 2000

50

100

150

Time (hour)

C-1-1C-0-3

minus100

minus50

Stra

in (120583

120576)

Figure 9 Free strain evolution of C-0-3 and C-1-1

Free strain

Cumulative strain

Creep

Compensation cycles

Strain

Time

Figure 10 Creep strain calculation method [5]

30 60 90 120 150 1800

1

2

3

Phase 2

Con

cret

e stre

ss (M

Pa)

Time (hour)

Concrete stress

Phase 1

minus1

Figure 11 A typical stress evolution

concept [24] should be adopted to calculate related param-eters For an arbitrary temperature history 119879(119905) concreteage can be converted to equivalent age 119905

119890via Arrhenius law

[25]

119905119890= int exp [

119864ℎ

119877(11198790minus1119879)]119889119905 (2)

where 119864ℎis the activation energy (Jmol) 119877 is the ideal gas

constant (JmolK) 1198790 is the reference temperature and 119879is the actual temperature (K) 119864

ℎequals 33500 Jmol for the

temperature 119879 ge 20∘C and 33500 + 1470(20 minus 119879) Jmolfor the temperature 119879 lt 20∘C [25] 1198790 equals 29315 K


0 50 100 150 200 25000

05

10

15

20

25

30

Con

cret

e stre

ss (M

Pa)

Time (hour)

C-0-1C-0-2

Figure 12 Concrete stress curves of C-0-1 and C-0-2

The temperature variation (Figure 8(a)) takes the followingexpression

120579 (119905)

=

27315 + 1205790 (1 minus exp (minus119886 (119905119887))) 0 le 119905 le 119905127315 + 120579max 1199051 lt 119905 le 1199052

27315 + 120579max minus 119896119905 1199052 lt 119905

(3)

where 1205790 120579max 119886 and 119887 are parameters fitted by experimentaldata 1199051 and 1199052 are critical points of different temperaturephases respectively and 119896 is the cooling rate

Figure 12 presents the stress curves of C-0-1 and C-0-2 The stress curve at a cooling rate of 033∘Ch is steeperindicating that larger deformation of concrete caused bytemperature variation leads to greater tensile stress Theslower cooling rate when applied at the cooling phase leadsto longer cracking time A decrease in stress before the peakvalue of C-0-2 is visible and the possible explanation is thatconcrete does not crack thoroughly The cracking stresses ofC-0-1 and C-0-2 are 254MPa and 274MPa respectively Asmall cracking stress decrease is noted as the cooling rateincreases This phenomenon may be explained by the factthat the nonuniform stress distribution in concrete can beimproved with a slow stress increase The calculated ratios ofcracking stress to tensile strength of C-0-1 and C-0-2 are 081and 086 respectively Under long-term loading microcrackspropagate and the mechanical properties of concrete maydeteriorate until concrete fails

The nominal stress of specimen is calculated via

120590nom

=119875

119860 (4)

where 119860 is the cross section area of specimen and 119875 is theultimate load of specimen

The nominal tensile stress curves are plotted in Figure 13One interesting phenomenon shown in Figure 13 is that

0 50 100 150 200 25000

05

10

15

20

25

30

35

Nom

inal

stre

ss (M

Pa)

Time (hour)

C-0-1C-1-2

Figure 13 Nominal tensile stress of C-0-1 and C-1-2

the cracking time of C-1-2 was delayed indicating thatthe reinforcement improved the crack resistance ability ofconcrete in the current research

Based on the principle of deformation compatibility thevalue of Δ120590

119888and the concrete cracking stress 120590crack can be

calculated by the following expressions

Δ120590119888=

120576creep119864119904119860 119904

119860119888

120590crack =120590nom

119860 minus 120576119890119864119904119860119904

119860119888

(5)

where 120576creep is creep strain and can be calculated in Section 42and 120576119890is the elastic strain recorded by the computer

In the current research the calculated Δ120590119888and 120590crack are

051MPa and 265MPa respectively and a stress transferfactor can be defined to describe the effect of reinforcement

120574 =Δ120590119888

Δ120590119888+ 120590crack

= 16 (6)

Thanks to the reinforcement and concrete creep behavior thecracking time of concrete was also delayed to some extent

5 Analytical Simulation of Effect ofReinforcement on Concrete TemperatureStress Development

51 Methodology Reinforcement restrains concrete time-dependent deformation caused by creep behavior resultingin stress transfer between concrete and reinforcement Theconcrete temperature stress can be calculated based on theprinciple of superposition [26] and deformation compatibil-ity The flow chart of calculation is given in Figure 14 and theprogramming has been performed on Matlab software


Start

Elastic modulus E(t)Specific creep C(t 120591)Shrinkage strain 120576sh(t)

Thermal strain 120576ther(t)

Δ120590998400c

Δ120576Δ120590998400c + Δ120590c

120576lt120576 0

120576 ge 1205760120590c = sumΔ120590998400c + Δ120590c 120576 = sumΔ120576

Figure 14 Flow chart of stress calculation

t

Recoverablecreep

creepNonrecoverable

120591

C(t 120591)

t

Figure 15 A general description of specific creep

52 Comparison with Experimental Results Literature [27]reported that the thermal expansion coefficient of concretebecame stable (10minus5∘C) after one day and this value isadopted for assessing thermal deformation of concrete inthe current research A specific creep expression in literature[26] is adopted Equation (7) is an exponential functionwhich is beneficial for programming as well as reductionof calculation amount The first term of (7) representsnonrecoverable creep and the second term of (7) representsrecoverable creep A general description of specific creep isshown in Figure 15 Creep parameters are given in Table 4Consider

119862 (119905 120591) =

2sum

119894=1(119891119894+119892119894120591minus119901119894) [1minus 119890minus119903119894(119905minus120591)] (7)

where 120591 is the loading age and 119905 is the concrete ageFigure 16 shows the comparison between analytical

results and experimental results It can be seen that the

Table 4 Parameters of specific creep [26]

Parameter 119891119894(10minus4) 119892

119894(10minus4) 119901

119894119903119894

119894 = 1 01045 09614 07 03119894 = 2 02360 04012 07 0005

00

05

10

15

20

25

30

35

Nom

inal

stre

ss (M

Pa)

80 100 120 140 160 180 200 220 240 260Time (hour)

Measured results of C-0-1Measured results of C-1-2Simulated results of C-1-2

Figure 16 Comparison of experimental results and analyticalsimulation

benefit of reinforcement has been observed in this prelimi-nary analysis The differences between measured results andanalytical results are due to inaccuracy of creep parametersandmeasurement errorsMore experimental tests are neededfor further investigation

Extended analytical results are drawn for different rein-forcement ratios and the results have been normalized basedon the experimental reinforcement ratio (1205880 = 2) Asillustrated in Figure 17 the stress transfer factor 120574 increaseswith reinforcement ratio while the rate becomes slower withthe increasing reinforcement ratio

6 Conclusions

Effect of reinforcement on concrete temperature stress devel-opment has been investigated and the following conclusionscan be drawn in this paper

(1) A small concrete cracking stress increase wasobserved when slower cooling rate was applied at thecooling phase The nonuniform stress distribution inconcrete can be improved with a slow stress increase

(2) Concrete temperature stress can be reduced in eachcycle of TSTM test due to the interaction betweenconcrete and reinforcement These minor reductionsadded up over time and almost 16 of concrete tem-perature stress was reduced in the current researchMoreover the cracking time of reinforced concretewas also delayed It should be noted that this paper


0 1 2 3 4 500

05

10

15

20

25

30

y = minus3374 lowast exp(minusx318) + 3374

R2 = 099

1205881205880

120574120574

0

Figure 17 Effect of reinforcement ratio on reduction of concretestress

provides only limited experimental evidence andpreliminary results More experiments are needed

(3) Analytical simulations of effect of reinforcement showan agreement with the experimental results Theinfluences of reinforcement ratio on reduction ofconcrete temperature stress were investigated and acorrelation was developed between the reinforcementratio and the reduction of concrete temperature stress

For practice the deformation of early-age concrete is nottotally restrained by the rock foundation or the adjoiningstructures and this feature provides a possibility for theinteraction between reinforcement and concrete The effectof reinforcement on reduction of concrete temperature stressmay be activated in realistic reinforced concrete structuresunder long-term loading (temperature variation) and thecracking probability of reinforced concrete structures islowered when the effect of reinforcement has been taken intoconsideration

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This study was part of a research project supported by ChinaThree Gorges Corporation (Grant no TGC-2012746379) andHekoucun reservoir concrete engineering projects (Grant noHKCSK-KY-01)

References

[1] A M Soliman and M L Nehdi ldquoEffects of shrinkage reducingadmixture and wollastonite microfiber on early-age behaviorof ultra-high performance concreterdquo Cement and ConcreteComposites vol 46 pp 81ndash89 2014

[2] H T See E K Attiogbe and M A Miltenberger ldquoShrinkagecracking characteristics of concrete using ring specimensrdquo ACIMaterials Journal vol 100 no 3 pp 239ndash245 2003

[3] A B Hossain and J Weiss ldquoAssessing residual stress develop-ment and stress relaxation in restrained concrete ring speci-mensrdquo Cement and Concrete Composites vol 26 no 5 pp 531ndash540 2004

[4] R Springenschmid R Breitenbucher andMMangold ldquoDevel-opment of the cracking frame and the temperature-stress testingmachinerdquo in Thermal Cracking in Concrete at Early Ages RSpringenschmid Ed pp 37ndash144 E amp FN Spon London UK1994

[5] K Kovler ldquoTesting system for determining the mechanicalbehaviour of early age concrete under restrained and freeuniaxial shrinkagerdquo Materials and Structures vol 27 no 6 pp324ndash330 1994

[6] ZH LinQuantitative evaluation of the effectiveness of expansiveconcrete as a countermeasure for thermal cracking and thedevelopment of its practical application [PhD thesis] Universityof Tokyo Tokyo Japan 2006

[7] S A Altoubat and D A Lange ldquoCreep shrinkage and crackingof restrained concrete at early-agerdquo ACI Materials Journal vol98 no 4 pp 323ndash331 2001

[8] Z Tao and Q Weizu ldquoTensile creep due to restraining stressesin high-strength concrete at early agesrdquo Cement and ConcreteResearch vol 36 no 3 pp 584ndash591 2006

[9] S-I Igarashi A Bentur and K Kovler ldquoAutogenous shrinkageand induced restraining stresses in high-strength concretesrdquoCement and Concrete Research vol 30 no 11 pp 1701ndash17072000

[10] A Darquennes S Staquet M-P Delplancke-Ogletree and BEspion ldquoEffect of autogenous deformation on the cracking riskof slag cement concretesrdquoCement and Concrete Composites vol33 no 3 pp 368ndash379 2011

[11] Y Lee Y-Y Kim J-H Hyun and D-G Kim ldquoThermal stressanalysis of reactor containment building considering severeweather conditionrdquo Nuclear Engineering and Design vol 270pp 152ndash161 2014

[12] T Honorio B Bary and F Benboudjema ldquoEvaluation of thecontribution of boundary and initial conditions in the chemo-thermal analysis of a massive concrete structurerdquo EngineeringStructures vol 80 pp 173ndash188 2014

[13] F Benboudjema and J M Torrenti ldquoEarly-age behaviourof concrete nuclear containmentsrdquo Nuclear Engineering andDesign vol 238 no 10 pp 2495ndash2506 2008

[14] M S Sule andKVanBreugel ldquoEffect of reinforcement on early-age cracking in high strength concreterdquoHeron vol 49 no 3 pp273ndash292 2004

[15] N Shi J Ouyang R Zhang and D Huang ldquoExperimentalstudy on early-age crack of mass concrete under the controlledtemperature historyrdquo Advances in Materials Science and Engi-neering vol 2014 Article ID 671795 10 pages 2014

[16] W Q Fu and S F Han ldquoThe prevention and control of crack inconcrete structuresrdquo Concrete no 5 pp 3ndash14 2003 (Chinese)

[17] M Briffaut F Benboudjema J M Torrenti and G NahasldquoA thermal active restrained shrinkage ring test to study theearly age concrete behaviour ofmassive structuresrdquoCement andConcrete Research vol 41 no 1 pp 56ndash63 2011

[18] W Song Y Yuan and J Gong ldquoExperimental research ontensile performance of reinforced concreterdquo Journal of SoutheastUniversity (Natural Science Edition) vol 32 pp 98ndash101 2002(Chinese)


[19] D Han M Keuser X Zhao and B Langer ldquoInfluence oftransverse reinforcing bar spacing on flexural crack spacing onreinforced concreterdquo Procedia Engineering vol 14 pp 2238ndash2245 2011

[20] V Colotti and G Spadea ldquoAn analytical model for crack con-trol in reinforced concrete elements under combined forcesrdquoCement and Concrete Composites vol 27 no 4 pp 503ndash5142005

[21] P Mehta and J Monteiro Concrete Microstructure Propertiesand Materials McGraw-Hill New York NY USA 2005

[22] China StandardsGBT50081-2002 Test Standards andMethodsfor Mechanical Properties of Normal Concrete Peoplersquos Republicof China Beijing China 2002

[23] M LarsonThermal crack estimation in early age concrete [PhDthesis] Lulea University of Technology Lulea Sweden 2003

[24] I A Rubinsky ldquoHeat of hydration in concreterdquo Magazine ofConcrete Research vol 6 no 17 pp 79ndash92 1954

[25] P F Hansen and E J Pedersen ldquoMaturity computer forcontrolled curing and hardening of concreterdquo Nordisk Betongvol 1 pp 21ndash25 1977

[26] B F Zhu Thermal Stressed and Temperature Control of MassConcrete China Electric Power Press Beijing China 2003

[27] I Shimasaki K Rokugo andHMorimoto ldquoOn thermal expan-sion coefficient of concrete at very early agesrdquo in Proceedings ofthe International Workshop on Control of Cracking in Early-ageConcrete pp 49ndash56 Sendai Japan 2000

Submit your manuscripts athttpwwwhindawicom

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Figure 1 Uniaxial tension test [18]

and a strain enhancement factor was introduced to quantifythe effect of reinforcement decreasing the risk of early-ageconcrete cracking Briffaut et al [17] studied the early-ageconcrete behavior of massive structures with a thermal activerestrained shrinkage ring and found that the cracking timeof concrete was delayed when concrete was reinforced Itis noted that this phenomenon is not consistent with thecracking behavior of reinforced concrete under short-termloading Usually the usage of reinforcement on concretestructures is not to prevent concrete from cracking [18] butto limit the deflection and crack width [19 20] Obviouslythe effect of reinforcement on cracking behavior of con-crete under long-term loading (temperature variation) is notnegligible It is necessary to investigate how reinforcementinfluences the development of concrete temperature stress

On the other hand concrete deformation closely relatesto the cooling rate and the effect of temperature control onmass concrete casting projects has already been proven [21]A good understanding of the effect of cooling rate on concretetemperature stress development is also of great importance

Thus the following studies have been carried out in thispaper

(1) Temperature stress tests of plain concrete and rein-forced concrete specimens were conducted on aTSTM The effect of reinforcement on concretetemperature stress development has been analyzedMoreover concrete temperature stress developmentsunder different cooling rates were preliminarily stud-ied

(2) Based on the principle of superposition analyticalsimulations of effect of reinforcement on concretetemperature stress were performed on Matlab soft-ware

2 Analysis of Temperature StressDevelopment of TSTM Test

21 Effect of Reinforcement on Concrete Stress under Short-Term Loading Figure 1 shows a traditional uniaxial tensiontest for the determination of concrete cracking load The testis performed under a multistage loading and the applied loadcan be monitored by a load sensor

The cracking load can be estimated by the followingequation

119873cr = 119891119905119860[1+(119864119904

119864119888

minus 1)120588] (1)

where 119891119905is the tensile strength of concrete 119860 is the cross

section area of specimen 119864119904and 119864

119888are the modulus of

reinforcement and concrete respectively and 120588 is the rein-forcement ratio

Equation (1) shows that the cracking load of reinforcedconcrete member is increased as reinforcement can bearadditional load However the effect of reinforcement onconcrete stress evolution is negligible in this test

22 Effect of Reinforcement on Concrete Stress under Long-Term Loading As shown in Figure 2 the total deformationof plain concrete specimen increases when an initial stressapplied and this stress keeps constant thereafter knownas creep However for a reinforced concrete the concretestress decreases with time because of the interaction betweenconcrete and reinforcement during the loading period

For plain concrete if loaded and totally restrained stresswill decrease in the concrete also known as relaxation(Figure 3) However for reinforced concrete the evolutionof concrete stress will still be the same as that of plainconcrete because no deformation is generated and the effectof reinforcement will not be activated

23 Temperature Stress Development of TSTM Test Usuallythe deformation of TSTM specimen is not always zero butwithin a threshold 1205760 [5]The specimen will be pushedpulledto the original position when the absolute deformationexceeds the threshold (Figure 4(a))The evolution of concretetemperature stress is illustrated in Figure 4(b) if a perfectbond between concrete and reinforcement is assumed thenstress decrement Δ120590

119894of concrete is transferred to reinforce-

ment because of concrete creep behavior during each cycle(eg the time periods 119905

119894minus1 to 119905119894 119905119894 to 119905119894+1) on the other handstress increment Δ1205901015840

119894of concrete is loaded to maintain the

original length of the specimen at the time of 119905119894minus1 119905119894 and 119905119894+1

and so forth Both concrete stress reduction and creep strainincrease with the number of cycles The TSTM test consistsof numerous cycles and concrete temperature stress can bereduced in each cycle These minor changes will add up overtime and the total change may be considerable (Figure 5)

As mentioned in Section 22 the reduction of concretestress is accompanied by the deformation of concrete indi-cating that concrete creep behavior is crucial for assessingconcrete temperature stress development For a TSTM testtwo identical specimens are tested in the same time Oneis free to deform while the other is restrained The inducedload can be recorded from restrained specimen and shrinkagedeformation can be measured from free deformed specimenand the concrete creep can be easily deduced frommeasureddeformation data The particularly designed TSTM systemmakes it possible to resolve concrete creep behavior

Once concrete creep is known the effect of reinforcementon concrete temperature stress development can be quantita-tively assessed

3 Experimental Program

31 Mechanical Property Test According to the Chinese codeGBT 50081-2002 [22] the mechanical properties of concretemixtures at the ages of 3 days 7 days and 28 days were


120590c(t0)

120590c(t0)

120590s(t0) 120590s(t1) gt 120590s(t0)

120590c(t1) lt 120590c(t0)

120590c(t1) = 120590c(t0)

Δ120576



120590c(t1) lt 120590c(t0)120590c(t1) lt 120590c(t0)

120590c(t0)120590c(t0)

120576 = 0

120590s(t0)

120590s(t1) = 120590s(t0)



timinus1

1205760

ti

ti

ti+1

ti+1

Δ120590i

Δ120590998400i

Δ120590i+1

Δ120590998400i+1

(a)

120590c

timinus1 ti ti+1 tn


t

120576

1205760

(b)


120576

1205760

Δ120590

120576creep

t

sumΔ120590








150

1501500











3 181 19397 287 275128 321 3130










0 50 100 150

20

30

40

50

Phase 3Phase 2

Time (hour)

Temperature

Phase 1Te

mpe

ratu

re (∘

C)

(a)

0

50

100

150


50 100 150 200Time (hour)

minus150

minus100

minus50

Stra

in (120583

120576)

(b)


0 50 100 150 2000

50

100

150

Time (hour)

C-1-1C-0-3

minus100

minus50

Stra

in (120583

120576)


Free strain

Cumulative strain

Creep

Compensation cycles

Strain

Time


30 60 90 120 150 1800

1

2

3

Phase 2

Con

cret

e stre

ss (M

Pa)

Time (hour)

Concrete stress

Phase 1

minus1




[25]

119905119890= int exp [

119864ℎ

119877(11198790minus1119879)]119889119905 (2)






0 50 100 150 200 25000

05

10

15

20

25

30

Con

cret

e stre

ss (M

Pa)

Time (hour)

C-0-1C-0-2



120579 (119905)

=


27315 + 120579max minus 119896119905 1199052 lt 119905

(3)




120590nom

=119875

119860 (4)



0 50 100 150 200 25000

05

10

15

20

25

30

35

Nom

inal

stre

ss (M

Pa)

Time (hour)

C-0-1C-1-2






Δ120590119888=

120576creep119864119904119860 119904

119860119888

120590crack =120590nom

119860 minus 120576119890119864119904119860119904

119860119888

(5)




120574 =Δ120590119888

Δ120590119888+ 120590crack

= 16 (6)





Start



Δ120590998400c

Δ120576Δ120590998400c + Δ120590c

120576lt120576 0

120576 ge 1205760120590c = sumΔ120590998400c + Δ120590c 120576 = sumΔ120576


t

Recoverablecreep

creepNonrecoverable

120591

C(t 120591)

t



119862 (119905 120591) =

2sum





Parameter 119891119894(10minus4) 119892

119894(10minus4) 119901

119894119903119894

119894 = 1 01045 09614 07 03119894 = 2 02360 04012 07 0005

00

05

10

15

20

25

30

35

Nom

inal

stre

ss (M

Pa)

80 100 120 140 160 180 200 220 240 260Time (hour)





6 Conclusions





0 1 2 3 4 500

05

10

15

20

25

30


R2 = 099

1205881205880

120574120574

0







Acknowledgments


References




































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




120590c(t0)

120590c(t0)

120590s(t0) 120590s(t1) gt 120590s(t0)

120590c(t1) lt 120590c(t0)

120590c(t1) = 120590c(t0)

Δ120576



120590c(t1) lt 120590c(t0)120590c(t1) lt 120590c(t0)

120590c(t0)120590c(t0)

120576 = 0

120590s(t0)

120590s(t1) = 120590s(t0)



timinus1

1205760

ti

ti

ti+1

ti+1

Δ120590i

Δ120590998400i

Δ120590i+1

Δ120590998400i+1

(a)

120590c

timinus1 ti ti+1 tn


t

120576

1205760

(b)


120576

1205760

Δ120590

120576creep

t

sumΔ120590








150

1501500











3 181 19397 287 275128 321 3130










0 50 100 150

20

30

40

50

Phase 3Phase 2

Time (hour)

Temperature

Phase 1Te

mpe

ratu

re (∘

C)

(a)

0

50

100

150


50 100 150 200Time (hour)

minus150

minus100

minus50

Stra

in (120583

120576)

(b)


0 50 100 150 2000

50

100

150

Time (hour)

C-1-1C-0-3

minus100

minus50

Stra

in (120583

120576)


Free strain

Cumulative strain

Creep

Compensation cycles

Strain

Time


30 60 90 120 150 1800

1

2

3

Phase 2

Con

cret

e stre

ss (M

Pa)

Time (hour)

Concrete stress

Phase 1

minus1




[25]

119905119890= int exp [

119864ℎ

119877(11198790minus1119879)]119889119905 (2)






0 50 100 150 200 25000

05

10

15

20

25

30

Con

cret

e stre

ss (M

Pa)

Time (hour)

C-0-1C-0-2



120579 (119905)

=


27315 + 120579max minus 119896119905 1199052 lt 119905

(3)




120590nom

=119875

119860 (4)



0 50 100 150 200 25000

05

10

15

20

25

30

35

Nom

inal

stre

ss (M

Pa)

Time (hour)

C-0-1C-1-2






Δ120590119888=

120576creep119864119904119860 119904

119860119888

120590crack =120590nom

119860 minus 120576119890119864119904119860119904

119860119888

(5)




120574 =Δ120590119888

Δ120590119888+ 120590crack

= 16 (6)





Start



Δ120590998400c

Δ120576Δ120590998400c + Δ120590c

120576lt120576 0

120576 ge 1205760120590c = sumΔ120590998400c + Δ120590c 120576 = sumΔ120576


t

Recoverablecreep

creepNonrecoverable

120591

C(t 120591)

t



119862 (119905 120591) =

2sum





Parameter 119891119894(10minus4) 119892

119894(10minus4) 119901

119894119903119894

119894 = 1 01045 09614 07 03119894 = 2 02360 04012 07 0005

00

05

10

15

20

25

30

35

Nom

inal

stre

ss (M

Pa)

80 100 120 140 160 180 200 220 240 260Time (hour)





6 Conclusions





0 1 2 3 4 500

05

10

15

20

25

30


R2 = 099

1205881205880

120574120574

0







Acknowledgments


References




































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






150

1501500











3 181 19397 287 275128 321 3130










0 50 100 150

20

30

40

50

Phase 3Phase 2

Time (hour)

Temperature

Phase 1Te

mpe

ratu

re (∘

C)

(a)

0

50

100

150


50 100 150 200Time (hour)

minus150

minus100

minus50

Stra

in (120583

120576)

(b)


0 50 100 150 2000

50

100

150

Time (hour)

C-1-1C-0-3

minus100

minus50

Stra

in (120583

120576)


Free strain

Cumulative strain

Creep

Compensation cycles

Strain

Time


30 60 90 120 150 1800

1

2

3

Phase 2

Con

cret

e stre

ss (M

Pa)

Time (hour)

Concrete stress

Phase 1

minus1




[25]

119905119890= int exp [

119864ℎ

119877(11198790minus1119879)]119889119905 (2)






0 50 100 150 200 25000

05

10

15

20

25

30

Con

cret

e stre

ss (M

Pa)

Time (hour)

C-0-1C-0-2



120579 (119905)

=


27315 + 120579max minus 119896119905 1199052 lt 119905

(3)




120590nom

=119875

119860 (4)



0 50 100 150 200 25000

05

10

15

20

25

30

35

Nom

inal

stre

ss (M

Pa)

Time (hour)

C-0-1C-1-2






Δ120590119888=

120576creep119864119904119860 119904

119860119888

120590crack =120590nom

119860 minus 120576119890119864119904119860119904

119860119888

(5)




120574 =Δ120590119888

Δ120590119888+ 120590crack

= 16 (6)





Start



Δ120590998400c

Δ120576Δ120590998400c + Δ120590c

120576lt120576 0

120576 ge 1205760120590c = sumΔ120590998400c + Δ120590c 120576 = sumΔ120576


t

Recoverablecreep

creepNonrecoverable

120591

C(t 120591)

t



119862 (119905 120591) =

2sum





Parameter 119891119894(10minus4) 119892

119894(10minus4) 119901

119894119903119894

119894 = 1 01045 09614 07 03119894 = 2 02360 04012 07 0005

00

05

10

15

20

25

30

35

Nom

inal

stre

ss (M

Pa)

80 100 120 140 160 180 200 220 240 260Time (hour)





6 Conclusions





0 1 2 3 4 500

05

10

15

20

25

30


R2 = 099

1205881205880

120574120574

0







Acknowledgments


References




































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0 50 100 150

20

30

40

50

Phase 3Phase 2

Time (hour)

Temperature

Phase 1Te

mpe

ratu

re (∘

C)

(a)

0

50

100

150


50 100 150 200Time (hour)

minus150

minus100

minus50

Stra

in (120583

120576)

(b)


0 50 100 150 2000

50

100

150

Time (hour)

C-1-1C-0-3

minus100

minus50

Stra

in (120583

120576)


Free strain

Cumulative strain

Creep

Compensation cycles

Strain

Time


30 60 90 120 150 1800

1

2

3

Phase 2

Con

cret

e stre

ss (M

Pa)

Time (hour)

Concrete stress

Phase 1

minus1




[25]

119905119890= int exp [

119864ℎ

119877(11198790minus1119879)]119889119905 (2)






0 50 100 150 200 25000

05

10

15

20

25

30

Con

cret

e stre

ss (M

Pa)

Time (hour)

C-0-1C-0-2



120579 (119905)

=


27315 + 120579max minus 119896119905 1199052 lt 119905

(3)




120590nom

=119875

119860 (4)



0 50 100 150 200 25000

05

10

15

20

25

30

35

Nom

inal

stre

ss (M

Pa)

Time (hour)

C-0-1C-1-2






Δ120590119888=

120576creep119864119904119860 119904

119860119888

120590crack =120590nom

119860 minus 120576119890119864119904119860119904

119860119888

(5)




120574 =Δ120590119888

Δ120590119888+ 120590crack

= 16 (6)





Start



Δ120590998400c

Δ120576Δ120590998400c + Δ120590c

120576lt120576 0

120576 ge 1205760120590c = sumΔ120590998400c + Δ120590c 120576 = sumΔ120576


t

Recoverablecreep

creepNonrecoverable

120591

C(t 120591)

t



119862 (119905 120591) =

2sum





Parameter 119891119894(10minus4) 119892

119894(10minus4) 119901

119894119903119894

119894 = 1 01045 09614 07 03119894 = 2 02360 04012 07 0005

00

05

10

15

20

25

30

35

Nom

inal

stre

ss (M

Pa)

80 100 120 140 160 180 200 220 240 260Time (hour)





6 Conclusions





0 1 2 3 4 500

05

10

15

20

25

30


R2 = 099

1205881205880

120574120574

0







Acknowledgments


References




































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0 50 100 150 200 25000

05

10

15

20

25

30

Con

cret

e stre

ss (M

Pa)

Time (hour)

C-0-1C-0-2



120579 (119905)

=


27315 + 120579max minus 119896119905 1199052 lt 119905

(3)




120590nom

=119875

119860 (4)



0 50 100 150 200 25000

05

10

15

20

25

30

35

Nom

inal

stre

ss (M

Pa)

Time (hour)

C-0-1C-1-2






Δ120590119888=

120576creep119864119904119860 119904

119860119888

120590crack =120590nom

119860 minus 120576119890119864119904119860119904

119860119888

(5)




120574 =Δ120590119888

Δ120590119888+ 120590crack

= 16 (6)





Start



Δ120590998400c

Δ120576Δ120590998400c + Δ120590c

120576lt120576 0

120576 ge 1205760120590c = sumΔ120590998400c + Δ120590c 120576 = sumΔ120576


t

Recoverablecreep

creepNonrecoverable

120591

C(t 120591)

t



119862 (119905 120591) =

2sum





Parameter 119891119894(10minus4) 119892

119894(10minus4) 119901

119894119903119894

119894 = 1 01045 09614 07 03119894 = 2 02360 04012 07 0005

00

05

10

15

20

25

30

35

Nom

inal

stre

ss (M

Pa)

80 100 120 140 160 180 200 220 240 260Time (hour)





6 Conclusions





0 1 2 3 4 500

05

10

15

20

25

30


R2 = 099

1205881205880

120574120574

0







Acknowledgments


References




































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Start



Δ120590998400c

Δ120576Δ120590998400c + Δ120590c

120576lt120576 0

120576 ge 1205760120590c = sumΔ120590998400c + Δ120590c 120576 = sumΔ120576


t

Recoverablecreep

creepNonrecoverable

120591

C(t 120591)

t



119862 (119905 120591) =

2sum





Parameter 119891119894(10minus4) 119892

119894(10minus4) 119901

119894119903119894

119894 = 1 01045 09614 07 03119894 = 2 02360 04012 07 0005

00

05

10

15

20

25

30

35

Nom

inal

stre

ss (M

Pa)

80 100 120 140 160 180 200 220 240 260Time (hour)





6 Conclusions





0 1 2 3 4 500

05

10

15

20

25

30


R2 = 099

1205881205880

120574120574

0







Acknowledgments


References




































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0 1 2 3 4 500

05

10

15

20

25

30


R2 = 099

1205881205880

120574120574

0







Acknowledgments


References




































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




















CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



Effect of Reinforcement on Early-Age Concrete Temperature Stress ...

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Transcript of Effect of Reinforcement on Early-Age Concrete Temperature Stress ...