The Study on Early-Age Expansion and Shrinkage Model of

Research ArticleThe Study on Early-Age Expansion and Shrinkage Model ofMassive Self-Compacting Concrete Pumped in Steel Tube Column

Zhen-jun He 1 Meng-jia Ding2 Zhen-wei Wang1 Xue-sheng Zhang3 Mei-gen Cao1

and Ming-wei Lei4

1School of Civil Engineering North China University of Technology Beijing 100144 China2College of Architecture and Civil Engineering Beijing University of Technology Beijing 100124 China3Beijing Urban Construction Group Co Ltd Beijing 100016 China4China Xinxing Construction and Development Co Ltd Beijing 100039 China

Correspondence should be addressed to Zhen-jun He zjhencuteducn

Received 24 December 2019 Revised 28 April 2020 Accepted 17 August 2020 Published 15 September 2020

Academic Editor Gang Zhou

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

Massive self-compacting concrete pumped in steel tube columns has been used more andmore widely in super high-rise buildingsand bridge engineering at present +e early-age expansion and shrinkage performance of its core mass concrete is an importantindex to ensure the stress state of triaxial compression and structural safety However no relevant reports have been found In viewof the actual building with the height of 26515 meters the early-age expansion and shrinkage tests of the massive self-compactingconcrete pumped in full-scale columns with the height of 1254m and 1224m and diameter of 13m and 16mwere carried out bymeans of strain gauges embedded in concrete-filled steel tubes (CFSTs) +e early-age variation regularity of the vertical andhorizontal expansion and shrinkage strains for the core concrete with the diameter of steel tube development time temperaturethe pouring pressure expansion stress and so on is given +e calculation model of its early-age deformation strains is presentedin this paper which is in good agreement with the experimental results It provides the basis of experimental and theoreticalanalyses for shrinkage compensation of massive self-compacting concrete pumped in steel tube columns

1 Introduction

As a composite component of steel and concrete it must beensured that its core concrete of concrete-filled steel tube(CFST) is in a complex stress state under three-dimensionalcompression and there is the rigid restraint effect for thecore concrete formed in the steel tube so as to improve thecompressive strength and deformation capacity of the coreconcrete promote the improvement of its plasticity andtoughness and prevent the brittle failure of the coreconcrete in steel tube +erefore the characteristics andchanging regularity of the early-age expansion andshrinkage deformation for the core concrete are particu-larly important which is the premise to ensure both workstogether At present the research on shrinkage and ex-pansion properties of CFST at home and abroad is asfollows

Yang et al [1] stated that the concrete shrinkage andcreep strains in recycled aggregate concrete-filled steel tubes(RACFST) specimens were about 6 to 23 higher thanthose of the corresponding normal CFST specimens Resultsobtained by Abdalhmid et al [2] showed that FA reduced therate of hydration and thus the drying shrinkage of self-compacting concrete (SCC) containing fly ash (FA) wasconsiderably lower than that of the control concrete Yanet al [3] reported that the quantity of ettringite was a verycritical factor in determining the expansion of mortars butmortar structure morphology of ettringite and curinghumidity were also relevant Gonzalez-Corominas andEtxeberria [4] found that the plastic shrinkage of concretesincreased as the employed recycled concrete aggregates(RCA) quality was reduced and the replacement ratio wasincreased However the obtained values for all high-per-formance concrete (HPC) concretes were lower than those

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 5242406 14 pageshttpsdoiorg10115520205242406

required with respect to concrete cracking +e results ofOliveira et al [5] also showed that the curing time wasessential to minimize shrinkage at early ages It caused alower drying mass loss causing a delaying effect in thedevelopment of shrinkage +is was important for earlycracking proneness +e study of Gribniak et al [6] dealtwith concrete shrinkage and accompanying creep influenceon cracking resistance and deformations of structural ele-ments It was found that serviceability characteristics ofreinforced concrete elements at the design stage might beimproved by specifying (1) concrete mixture proportions(2) mechanical properties of aggregates (3) method ofcuring (4) ambient temperature and humidity conditionsand (5) geometry of the structural element It was found thatthe autogenous shrinkage of early-age high-performanceconcrete (HPC) under different curing temperatures couldnot be predicted by the singular application of the equivalentage concept+e possible reason was that the microstructureevolution and apparent activation energy were influenced bytemperature +us investigation on the effect of curingtemperature on cracking resistance of early-age concretemust be further studied [7] +e general trends [8] observedindicated that the American Association of State Highwayand Transportation Officials (AASHTO) method tended tooverpredict shrinkage for both concrete mixtures especiallyat early ages and no method accurately represented thelower shrinkage rate of lightweight self-consolidating con-crete (LWSCC) Benboudjema et al [9] pointed out that thedrying process caused a strong structural effect micro-cracking arises in the concrete skin and attenuates the freedrying shrinkage strain +e amplitude of the structuralstrain was quite large It highlighted the need for an adequatecracking model to separate accurately the intrinsic behaviorof the material from the structural induced effect Never-theless after one year the numerical curve deviated from theexperimental one+is behavior seemed to be intrinsic sincethe adopted mechanical model took into account most of thecharacteristics of cracked concrete +e experimental resultsof Wu et al [10] showed that internal curing was an effectivemeans to reduce the autogenous shrinkage of high-perfor-mance concrete +e results of Persson [11] indicated thatcarbonation shrinkage may be avoided by the addition ofsilica fume Xie et al [12] suggested that from the per-spective of reducing shrinkage the optimal binder-to-sandratio was in the range of 1ndash11 the optimal dosage rate ofshrinkage reducing admixture was 1 and replacing ofmixing water by crushed ice up to 50 by weight had alsoinduced a significant reduction in shrinkageWang et al [13]suggested that the incorporation of 10-Mas expansiveagent was useful to diminish the shrinkage especially by itscombined use with prewetted lightweight aggregates(PLWA) +e results of Oliveira et al [14] also showed apotential for achieving a predefined shrinkage range byusing the combined effect of a set retarder and an expansiveadmixture +e paper [15] presented the main results of aresearch carried out to analyze the mechanical propertiesintrinsic permeability drying shrinkage carbonation andthe self-healing potential of concrete incorporating recycledconcrete aggregates However the effect of curing

temperature on autogenous shrinkage of early-age concretewas not in consistency and how the curing temperatureaffected the cracking resistance of concrete remains lack-ing Analysis of shrinkage stresses of concrete-filled steeltube (CFST) arch bridges showed that the shrinkage self-stress was large and should be taken into account in designcalculation [16] +e results of Cao et al [17] indicated thatthe shrinkage strain of a concrete-filled steel tube wasmainly caused by self-shrinkage and the self-shrinkagestrain was about 1times 10minus4 Zhu et al [18] reported that theshrinkage of a concrete-filled steel tube can be compen-sated well when the amount of expansive agent was 12Chen [19] found that the strains of free shrinkage andlimited shrinkage were 407 times10minus6 and 137 times10minus6 respec-tively at fourteen days

For the massive self-compacting concrete pumped insteel tube column the expansion and shrinkage of thecore concrete affects the stress distribution of concrete-filled steel tubular members to a great extent which canproduce redistribution of internal stress in concrete-filledsteel tubular members including ldquoredistribution of in-ternal stress in the section and internal stress in thesystemrdquo For example during the shrinkage process of thecore concrete in CFST the steel tube is forced to par-ticipate in the work alone resulting in tensile stress in thecore concrete and compressive stress in the steel tuberesulting in redistribution of the internal stress in thesection and the distribution values are large Besideswhen the core concrete shrinks there is a gap between thecore concrete and the steel tube which not only destroysthe joint work between the steel tube and the coreconcrete but also may cause corrosion on the innersurface of the steel tube during use In addition theexcessive expansion of the core massive concrete in thesteel tube will cause serious damage to the steel tube thusmaking the structure in an unsafe state

Based on the above the early-age shrinkage and ex-pansion properties for the massive self-compacting concretepumped in steel columns have been studied in this paper

2 Materials and Experimental Procedures

21 Materials and Mix Proportions +e cementitious ma-terials used for this investigation were Chinese standardPmiddotI425R Portland cement (standard compressive strengthhigher than 425MPa at the age of 28 days) Class I fly ash(fineness of 45 microm not more than 12 water demand rationot greater than 95 and loss on ignition not more than5) and silica fume (the National Standards of the PeoplersquosRepublic of China for Portland Cement and OrdinaryPortland Cement 1999 Fly Ash Used for Cement andConcrete 2005 Silica Fume for Cement Mortar and Con-crete 2012) +e coarse aggregate was a natural crushedstone (diameter 5ndash20mm) the fine aggregate was naturalriver sand (fineness modulus of 27) and tap water was usedfor mixing Tables 1 and 2 respectively show the mixproportions by weight of the mixture and the major pa-rameters of massive self-compaction concrete pumped insteel tube columns

2 Advances in Civil Engineering

22 Samples and Testing Methods

221 Casting Method of Pumped Concrete +e maximumoutlet pressure of HBT10521280RS concrete pump withhigh reliability was designed to be 21MPa and the pressurereserve was 133 +e pumping rates were 35ndash45m3h Inorder to facilitate the removal of gas in the steel tubes it wasnecessary to open 4V20mm vent holes on the wall of steeltubes by every 15ndash2m along the length of the column Testcolumns and their dimensions are shown in Figures 1 and2

222 Apparatus and Testing Methods +e vertical andhorizontal expansion and shrinkage deformation of massiveself-compacting concrete pumped in the core concrete ofCFST were measured by the embedded strain gauges +earrangement of the strain gauges of measurement points isshown in Figure 3 Two pairs of large volume strain gaugesembedded in CFSTwere symmetrically arranged inside eachCFST column +e arrangement distance between thehorizontal position of the strain gauges and the top of theCFST column was 650mm and the vertical and horizontalspacing of the four embedded strain gauges were D4 of thediameter which were 325mm and 400mm respectively asshown in Figure 3 Notes the first number of ldquo1ndash1rdquo standsfor the SYZ-1 test column the second number of ldquo1ndash1rdquostands for the first measuring point

BGK-4210 embedded strain gauges with a standarddistance of 250mm were adopted which was suitable forstrain measurement of massive concrete A total of eightgauges for both CFST columns were needed We ensuredthat the embedded strain gauges were geometrically alignedand placed horizontally After the strain gauges and otherdevices were installed it was necessary to calibrate thembefore the core concrete was poured +e early-age ex-pansion and shrinkage deformation were collected regularlyand continuously every day

Wzp-pt100 armored platinum thermal resistance wasused in the temperature test In consideration of the sym-metry of the test column the temperature test section wastaken as one-half of the diameter for testing In addition toensuring the thermal resistance required by the measuringpoint of the internal temperature of the core concrete atemperature instrument was also set up to measure thetemperature inside and outside the test shed +e specific

layout of 1 to 6 measuring points is shown in Figure 3Measuring point 5 corresponded to the temperature in thetest shed and measuring point 6 corresponded to theoutdoor temperature +e test duration of this hydrationheat temperature was 28 days +e collection interval was 1minute by 24-hour continuous collection When dealingwith data results data points were selected according to therequired time interval

Table 1 Mix proportions of massive self-compacting concrete pumped in steel tube columns

Strengthgrade

Waterbinder ratio

Water(kgm3)

Cement(kgm3)

Fly ash(kgm3)

Silica fume(kgm3)

Fine aggregate(kgm3)

Coarse aggregate(kgm3)

Superplasticizer(kgm3)

C60 031 165 320 180 25 790 850 86

Table 2 Major parameters of massive self-compacting concrete pumped in steel tube columns

Mixture performance (1 hour after the concrete is dischargedfrom the mixer)

Compressive strengthMPa Dry shrinkagetimes10minus6mm

Air contents Slump Slump flow V-shaped funnel test 3 d 7 d 28 d 60 d 3 d 7 d 14 d 28 d 60 d 90 d 180 d32 255mm 700mm 14 s 395 548 789 867 minus79 minus176 minus237 minus305 minus378 minus412 minus431

Figure 1 Test columns

Advances in Civil Engineering 3

BGK-4810 vibrating concrete pressure cells were used inthe test of the pouring pressure and expansion stress of thecore concrete Four pressure cells were arranged for SYZ-1

column with the height of 940mm 4470mm 8650mm and11890mm respectively three pressure cells were arrangedfor SYZ-2 column with the height of 2280mm 6360mm

650 70

70

90 1

10

1254

0

130 650

70110

650 130

1000

100

7 times

150

150

950

1000

10

00

1000

10

00

1000

10

00

1000

10

00

1000

70

0

1000

13

0 6

times 15

0 5

times 20

0 15

0 6

times 15

0 10

0 10

00

130

6 times

150

5 times

200

150

6 times

150

100

1000

15

0 6

times 15

0 4

times 20

0

85

85

85

d = 12 Vent hole

85

70 80

30 3

00 2

00

35

35

35

35

35

35

20

20

20

650

650

d = 12 Vent hole

d = 133

Grouting hole

110

1300

2880

90

(a)

800

1224

0

130 800

70110

800 130

1000

100

7 times

150

150

950

1000

10

00

1000

10

00

1000

10

00

1000

10

00

1000

70

0

1000

13

0 6

times 15

0 5

times 20

0 15

0 6

times 15

0 10

0 10

00

130

6 times

150

5 times

200

150

6 times

150

100

1000

15

0 6

times 15

0 4

times 20

0

85

85

85 d = 12

Vent hole

85

7080

115

115

115

35

35

35

35

35

35

800

650

d = 12 Vent hole

30 3

00 2

00

d = 133

Grouting hole

70 110

1300 70

90

11

0 90

4080

4080

2780

(b)

Figure 2 Design drawings of CFST columns used in engineering (unit mm) (a) SYZ-1 test column (b) SYZ-2 test column


and 10440mm respectively Each height corresponded to1sim4 measuring points respectively Figures 4 and 5 showactual arrangement installation photos of the test instru-ments and equipment

3 Test Results and Analysis

31 Change Laws between Temperature and DevelopmentTime As shown in Figure 6 the relationship between themeasured hydration heat temperature (T) in the cementhydration stage of the core concrete for the CFST testcolumn and development time (t) is given It can be seenfrom Figure 6 that when the daily outdoor temperaturereached the maximum values the temperature curve of 1 to4 measuring point shows a slightly rising inflection pointwhich is the most obvious near the temperature measuringpoints 3 and 4 of the steel tube wall that is to say thehydration rates are greater than those of the heat dissipationat this time and the higher the daily outdoor temperature isthe larger the increasing extent of curve is It can also be seenfrom Figure 6 that with the increase of hydration time thetemperature difference of each measuring point graduallydecreases and finally tends to be the same+is is because thehydration process for each measuring point of the coreconcrete has basically tended to be the same At the sametime with the increase of time the temperature of eachmeasuring point gradually tends to the temperature in thetest shed

As shown in Figure 6 the temperature of eachmeasuringpoint for the core concrete of the test column rises rapidlyfirst because the temperature values of the poured concreteitself are higher than those in the test shed+en it decreasesslightly just because there is a temperature difference be-tween the temperature of the poured concrete into the moldand the temperature in the test shed and there is heattransfer between them At this time the hydration heat has

not been formed to offset this heat loss resulting in a slightdrop in the temperature of the core concrete itself +erelease amount of cement hydration heat does not increaseuntil about 10 hours after pouring concrete and it risesslowly and continuously At this time the rates of hydrationheat are greater than those of heat dissipation When thehydration heat rates and heat dissipation rates reach thebalance the section temperatures of the test columns reachthe peak value for about 38 hours after pouring +en theycontinue to decline until it approaches to the temperature inthe test shed

It can be seen from Table 3 and Figure 6 that the peakvalues of temperature at measuring points 1sim4 of SYZ-1 testcolumn were 337degC 326degC 279degC and 223degC respectively+e peak values of temperature at measuring points 1sim4 forSYZ-2 test column were 391degC 366degC 290degC and 196degCrespectively During the test of hydration heat temperatureafter pouring concrete with the increase of time the tem-perature range in the test shed was minus89sim109degC and theoutdoor temperature range was minus109sim115degC+emeasuredcurve in Figure 6 shows that in the initial stage of pouringconcrete the temperature distribution of the cross sectiongenerally reflects the law that was high in the internal partsand low in the external parts and the temperature differencebetween the center and the outer edge of the section wasbigger+is is because concrete is a kind of material with lowthermal conductivity and it is not easy to dissipate the largeamount of hydration heat produced by cement hydration+us the temperature difference was formed along thediameter direction of the test column resulting in differenttemperature values of measuring points 1ndash4 +e maximumvalue of temperature difference between the center of thecore concrete and its outer edge was about 5degC In the initialstages of pouring concrete the temperature section values ofthe test column were significantly higher than those of theoutdoor temperature and the maximum value of

D4 D4 D4 D4

D4

D4

D4

D4

D

Embedded strain gauges

ts = 20

(a)

D3 D3 D2

D

45 3

D3

126

Armored platinum thermal resistance

ts = 20

(b)

Figure 3 Arrangement drawings of test instruments for cross section of column (unit mm) (a) Layout of deformation measurementpoints (b) Layout of temperature measurement points


temperature difference between the section center and theoutdoor temperature was 18degC

Based on the above analysis temperature parameters mustbe included in the early-age expansion and shrinkage model ofmassive self-compaction concrete pumped in steel tube column

32ChangeLawsbetween thePouringPressure andExpansionStress and Development Time Figures 7 and 8 respectivelyshow the relationship between the pouring pressure andexpansion stress of the core concrete for SYZ-1 and SYZ-2column and development time As can be seen fromFigures 7(a) and 8(a) the pouring pressure reached themaximum after pouring then as the core concrete graduallysolidified its pressure gradually decreased For each mea-suring point the platform stage before the curve reaches thepeak value is the waiting period of pouring concrete if thereis no waiting time for pouring concrete the curve showscontinuity and the curve does not display the landing steps

It can be seen from Figures 7(b) and 8(b) that for SYZ-1column the compressive stress on the inner wall of steel tubeincreases gradually for nearly 19 hours after pouring and fourmeasuring points reach the maximum peak expansion stress forabout 32 hours after pouring For SYZ-2 column the pressuregradually increased for nearly 20 hours after pouring and themaximumpeak expansion stress was reached at threemeasuring

points for about 39 hours after pouring It can be seen fromTable 4 and Figures 7(b) and 8(b) that the peak value of pouringpressure at measuring points 1sim4 for SYZ-1 column is0025MPa 0094MPa 0197MPa and 0283MPa respectively+e peak value of expansion stress at measuring points 1sim4 forSYZ-1 column is 0407MPa 0505MPa 053MPa and037MPa respectively +e peak value of pouring pressure atmeasuring points 1sim3 for SYZ-2 column is 0208MPa0282MPa and 037MPa respectively +e peak value of ex-pansion stress at 1sim3 measuring points for SYZ-2 column is0657MPa 0712MPa and 0686MPa respectively From theabove test results it can be seen that the pouring pressure is notgreat which will not cause harm to the steel tube wall but thepouring pressure at the joint of the through center plate is greaterthan that of other nonjoint in addition the larger the cross-section size of the steel tube column the greater the expansionstress and the later the time when it reaches the peak expansionstress

From Figures 7(c) and 8(c) it can be seen that for SYZ-1column the pressure of four measuring points basicallytends to be stable in about 3 days after pouring for SYZ-2column the pressure of three measuring points basicallytends to zero in about 15 days after pouring and after thatthe core concrete forms tensile stress on the inner wall of thesteel tube reaching the maximum 015MPa tensile stress inabout 20 days and then tends to zero +e reason is that

Embedded strain gaugesReinforcement of

fixed support

Studs

(a)


Reinforcement of fixed support

Studs

(b)


(c)

Pressure cell

(d)

Figure 4 Arrangement photos of test instruments (a) Deformationmeasurement of SYZ-1 column (b) Deformationmeasurement of SYZ-2 column (c) Temperature measurement (d) Vibrating-wire pressure cell


there is a certain adhesive force between the surface of thepressure cell and the core concrete and the additional in-ternal force generated by the shrinkage deformation of thecore concrete drives the steel pipe which shows a certainamount of tensile stress +erefore it can be seen that theshrinkage of the above SYZ-2 column in the joint area isgreater than that in the nonjoint area

33 Change Laws between the Vertical and Horizontal Strainsand Development Time Figure 9 shows the relationshipbetween the vertical and horizontal strains of the measureddeformation and development time From Figure 9 it can beseen that the vertical and horizontal strains of the measureddeformation of the core concrete in CFSTcolumns similarlychange with development time +e early-age strains of the

0 5 10 15 20 25 30

1-11-31-5

1-21-41-6

ndash15ndash10

ndash505

10152025303540

T (deg

C)

t (d)

(a)

ndash20

ndash10

0

10

20

30

40

0 5 10 15 20 25 30

T (deg

C)

2-12-32-5

2-22-42-6

t (d)

(b)

Figure 6 Test curves of temperature measurement of the core concrete (a) SYZ-1 column (b) SYZ-2 column

(a) (b)

(c) (d)

Figure 5 Test equipment (a) Data collection instrument for vibrating-wire sensor (b) Data collection computer (c) Concrete pump truck(d) Wire saw for cutting


core concrete develop rapidly Its expansion strains firstoccur and then there are shrinkage strains +e expansionstrains occur within 25 days after the core concrete waspoured +e curves of shrinkage strain for both CFST col-umns show a significant turning point around the 9th dayafter pouring +e curves change slowly over time and reachthe peak of shrinkage strains around the 21st day and thenthe curves flatten

It can be seen from Table 5 and Figure 9 that for SYZ-1column the values of the vertical and horizontal expansionstrains are 30295 με and 23792 με 7058 με and 87019 μεrespectively For SYZ-2 column the values of the verticaland horizontal expansion strains are 6824 με and 8777 με31654 με and 38513 με respectively +e values of the

horizontal expansion strains are greater than those of thevertical ones +e values of the two kinds of expansionstrains for a small diameter of CFSTare greater than those oflarge diameter ones

For SYZ-1 column the maximum values of the verticaland horizontal strains for early-age shrinkage of the coreconcrete in 28 days are minus414518 με and minus40206 μεminus36537 με and minus335686 με respectively for SYZ-2 col-umn the maximum values of the vertical and horizontalstrains for it are minus323532 με and minus30218 με 268006 μεand minus269299 με respectively which are much greaterthan those of the two kinds of cross-section sizes in [20]that is vertical and horizontal shrinkage values for squaresteel tubes of 200 times 200mm (1021 με and 915 με) and

Table 3 Maximum values of temperature at each measuring point of the core concrete

Type of steel tube columnMeasuring points

1 2 3 4 5 6SYZ-1 337degC 326degC 279degC 223degC 109degC 115degCSYZ-2 391degC 366degC 290degC 196degC

0

005

01

015

02

025

03

035

0 02 04 06 08 1

P (M

Pa)

t (h)

1-11-2

1-31-4

(a)

ndash01

0

01

02

03

04

05

06

0 1 2 3

t (d)

1-11-2

1-31-4

P (M

Pa)

(b)

ndash01

0

01

02

03

04

05

06

0 5 10 15 20 25 30

P (M

Pa)

t (d)

1-11-2

1-31-4

(c)

Figure 7 Test curves of pouring pressure and expansion stress of the core concrete for SYZ-1 (a) 1 hour (b) 3 days (c) 28 days


1000 times1000mm (472 με and 304 με) were calculated +evalues of the vertical strains for early-age shrinkage aregreater than those of the horizontal ones +e values of thetwo kinds of shrinkage strains of the core concrete forsmall diameter CFST are greater than those of large di-ameter ones

+rough the analysis of the above experimental re-sults it can be concluded that for SYZ-1 column thedifference values between vertical and horizontal

shrinkage deformation are not significant in the first 6days but for SYZ-2 column there was slightly greaterdifference for the above and the difference values tend toincrease with the change of time For the CFST column ofthe same diameter size the values of the vertical shrinkagestrains are much greater than those of the horizontalshrinkage strains at the same time which may be due tothe influence of the self-weight of concrete and spatialeffect on the vertical shrinkage of the core concrete

0

005

01

015

02

025

03

035

04

0 05 1 15 2 25 3 35 4t (h)

2-12-22-3

P (M

Pa)

(a)

0

01

02

03

04

05

06

07

08

0 1 2 3t (d)

2-12-22-3

P (M

Pa)

(b)

ndash02ndash01

00102030405060708

0 5 10 15 20 25 30

t (d)

2-12-22-3

P (M

Pa)

(c)

Figure 8 Test curves of pouring pressure and expansion stress of the core concrete for SYZ-2 (a) 4 hours (b) 3 days (c) 28 days

Table 4 Maximum values of pouring pressure and expansion stress at each measuring point of the core concrete

Type of steel tube column Types of forceMeasuring points

1 2 3 4

SYZ-1 Pouring pressure 0025MPa 0094MPa 0197MPa 0283MPaExpansion stress 0407MPa 0505MPa 0530MPa 0370MPa

SYZ-2 Pouring pressure 0208MPa 0282MPa 0370MPa mdashExpansion stress 0657MPa 0712MPa 0686MPa mdash


+erefore the development trends of the horizontal andvertical shrinkage deformation show some differences+e values of the horizontal strains of temperature ex-pansion are greater than those of its vertical ones at thesame time which is the main reason for the change causedby different spatial constraints +e values of the verticaland horizontal shrinkage strains of temperature expan-sion for small diameter CFST columns are greater thanthose of large diameter ones at the same time

Based on the experimental measurement of hydrationheat temperature expansion pressure expansion andshrinkage strain of the core concrete and through theoreticalanalysis the interaction mechanism of the above three as-pects is as follows at the initial stage of mass concretepouring a large amount of hydration heat is released fromcement hydration reaction which quickly accumulates inthe concrete making the concrete temperature rise and theexpansion volume of concrete increase Temperature stressand temperature difference stress will be generated and theirnumerical sizes also involve many factors such as the planesize of the structure structure thickness constraintscharacteristics of various composite materials of concretephysical and mechanical properties and constructiontechnology with the release of heat and the end of heatexchange with the environment the temperature of concrete

decreases and the volume of concrete shrinks When theshrinkage is constrained tensile stress occurs At this timethe newly poured concrete no matter its tensile strength andforce which are very small is not enough to resist the tensilestress so cracks appear in its concrete

4 Calculation Model of Early-Age Expansionand Shrinkage Deformation

Based on the analysis for the experimental results in thispaper and the existing shrinkage models of concrete at homeand abroad [20ndash22] and in view of the fact that the coreconcrete is sealed in steel tube the variation law of its relativehumidity is different from the general situation +ereforebased on the above comparison and consideration thecalculation model proposed in this paper on the early-ageexpansion and shrinkage for the massive self-compactingconcrete pumped in steel tubes has the followingcharacteristics

(1) +e formula for the calculation model incorporatesfactors such as the limit shrinkage strain (εshu) of thecore concrete in standard state the time-develop-ment function (β(t)) of the early-age expansion andshrinkage and the correction coefficients of various

ndash450ndash400ndash350ndash300ndash250ndash200ndash150ndash100

ndash500

50100

0 5 10 15 20 25 30

Test curve 1 of vertical strainsTest curve 2 of vertical strainsTest curve 1 of horizontal strainsTest curve 2 of horizontal strainsThe model

ε (με

)

t (d)

(a)

ndash350

ndash300

ndash250

ndash200

ndash150

ndash100

ndash50

0

500 5 10 15 20 25 30


t (d)

ε (με

)

(b)

Figure 9 Comparisons between the calculation model and test curves (a) SYZ-1 column (b) SYZ-2 column

Table 5 Maximum values of expansion and shrinkage strains of the core concrete

Type of steel tube column Expansion and shrinkage directions Expansion strains Shrinkage strains

SYZ-1Vertical 30295 με minus414518 με

23792 με minus402060 με

Horizontal 70580 με minus365370 με87019 με minus335686 με


8777 με minus302180 με



influencing factors that determine the early-ageexpansion and shrinkage development of the coreconcrete in nonstandard state that is to say thecorrection coefficients of various influencing factorssuch as the correction coefficients (αVS) of volume-to-surface ratio of steel tubes the types of concrete(αck) and active mineral additions (αfs) should betaken into consideration +erefore the formula ofmulticoefficient model presented in this paper isclear in concept convenient and practical

(2) Although the tests show that the strength of theconcrete itself does not affect the expansion andshrinkage deformation the factors that affect the abovedeformation such as cement content different water-to-binder ratios and aggregate condition are closelyrelated to the concrete strength in varying degrees Sothe influence of these factors can be reflected indirectlyand comprehensively by introducing the compressivestrength of concrete+erefore the formula of ultimateshrinkage strain (εshu) of concrete under standard statecontains 28d average compressive strength parameterfor its core concrete

(3) Based on the analysis of shrinkage test of the coreconcrete pumped in steel tube in [20] the authors in thisarticle hold that the parameters of component size suchas volume-to-surface ratio (VS) not only affect thedevelopment process (β(t)) of the expansion andshrinkage of CFST columns but also affect its finaldeformation values especially the latter So the influ-ence parameter on the VS is included in the correctioncoefficient (αvs) and the β parameter is included in thedevelopment function of shrinkage time (β(t)) In ad-dition the authors in this paper argue that in theGL2000 model [21] the parameter of the volume-to-surface ratio has a greater impact on the time-devel-opment function when it is larger or smaller +ereforein view of the actual influence of the above parametersfor CFST the corresponding correction is made

(4) In recent years high-performance concrete (HPC)has been widely used in the core concrete of CFST+e obvious difference between HPC and ordinaryconcrete is that its composition has the fifth activemineral materials such as fly ash silica fume andslag +erefore in this model there is correctioncoefficient (αfs) of active mineral additions

+e formula is applicable to calculate expansion andshrinkage deformation of the core concrete in CFST+ere isno reinforcement in the core concrete of steel tube +etime-development function of expansion and shrinkage isapplicable for dimensions D ranging from 1000mm to1600mm of CFST sections (D is the outer diameter ofcircular steel tube) +e average compressive strength of thecore concrete for 28 days is more than 60MPa and the valueof water-to-binder ratio is less than 035 cement class is I IIand III as described as follows

εsh β(t) middot εshu middot αVS middot αck middot αfs (1)

where εsh refers to the expansion and shrinkage strain ofthe core concrete at age t εshu is the ultimate shrinkagestrain of the core concrete under standard conditions β(t)is the time-development function of expansion andshrinkage αVS refers to the correction coefficient forvolume-to-surface ratio αck is the correction coefficienton the cement type αfs is the correction coefficient ofactive mineral addition

+e core concrete in CFST belongs to the massiveconcrete that is its section size is from 1000mm to1600mm and its time-development function is as follows

β(t) A0 minus 1

1 +(tα)β + 1

A0

minus00196 times T + 09431 (vertical directions)

minus00358 times T + 12176 (horizontal directions)

⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

(2)

where A0 is the parameter of expansion strains which isrelated to the temperature and expansion stress of the coreconcrete α is the parameter of the turning point for thedevelopment between expansion and shrinkage strainswhose value is the day value in the horizontal coordinatesd β is the trend and magnitude parameter of expansionand shrinkage strain which is related to the section size ofsteel tube and the direction of vertical and horizontalexpansion and shrinkage t is the development time of theexpansion and shrinkage age of the core concrete d β isthe impact index of section size on the development ofvolume-to-surface ratio in the time-development functionof expansion and shrinkage +e calculated results interms of the abovementioned parameters are given inTables 6ndash9

+e final shrinkage value (εshu) of plain concrete informula (1) and the average compressive strength (fcm28) at28 days can be used in view of the formula proposed byGardnerndashLockman model [21] as follows

εshu 30

fcm281113888 1113889

12

middot 10minus3

fcm28 11fck + 5(MPa)

(3)

Figure 9 gives the comparison of the calculation formulaand test results It can be seen from Figure 6 that the early-age expansion and shrinkage model of the massive self-compacting concrete pumped in steel tube columns is ofbetter precision and applicability

5 Discussion

+rough shrinkage test combined with hammering test ofouter-wall of steel tube inspection method of split damagetest and detection of cracks between the inner wall of steeltube and the core concrete by the electronic and visual crackobserver as shown in Figures 5(d) and 10 the followingregularities of shrinkage cracks on the joint surface between


the inner wall of steel tube and the core concrete for massiveself-compacting concrete pumped in steel tube column aresummarized the location of shrinkage cracks on the jointsurface is ldquouncertainrdquo that is to say the location of the abovejoint surface cannot be determined +e shrinkage cracks donot mean that as long as there is shrinkage deformationthere are shrinkage cracks on the joint surface of each lo-cation +e shrinkage deformation of different sections ordifferent locations of the same section has ldquononuniformityrdquothat is to say the shrinkage size of different sections ordifferent positions of the same section cannot be completelydetermined +e shrinkage crack size has ldquononuniformityand uncertaintyrdquo that is to say the size of shrinkage crack forthe joint surface cannot be accurately determined by thevalues of shrinkage deformation but it can only be estimatedroughly when the shrinkage cracks occur+e location of theshrinkage cracks is ldquosymmetricalrdquo that is to say theshrinkage cracks can sometimes occur at the same time ontwo relatively symmetrical planes +ere is ldquouncertaintyrdquobetween the above two which cannot be accurately deter-mined when the shrinkage cracks of the joint surface occur

+erefore the shrinkage deformation of the core concretemust be strictly controlled to ensure structural safety

6 Conclusions

Based on the experimental work and the analysis of the testresults the following conclusions can be drawn

(1) +e values of horizontal strains for early-age tem-peratures expansion are greater than those of thevertical ones +e two kinds of strains of the coreconcrete for small diameter CFST are greater thanthose of large diameter ones

(2) +e values of the vertical strains for early-ageshrinkage are greater than those of the horizontalones+e two kinds of strains of the core concrete forsmall diameter CFST are greater than those of largediameter ones

(3) +e shrinkage deformation of the core concrete inCFST develops rapidly in the early stage and thevalues of its horizontal shrinkage are slightly less

Table 9 Influencing coefficient of cement types on shrinkage [22]

Cement types Ordinary or fast-hardening cement Slow-hardening cement Fast-hardening high-strength cementαck 10 07 115

Table 6 +e parameter values of time-development function for the early-age shrinkage and expansion

Type of steel tubecolumn

Expansion and shrinkagedirection

Time-development function β(t) [(A0 minus1)(1 +(tα)β)] + 1(0le t)

Curve markA 0 α β Days of maximum expansion strains

t0

SYZ-1 Vertical minus015 50 20 18 Model in Figure 9(a)Horizontal minus035 50 20 20 Model in Figure 9(a)

SYZ-2 Vertical minus006 45 15 04 Model in Figure 9(b)Horizontal minus030 45 15 12 Model in Figure 9(b)

It should be explained here that before the day t0 of the maximum expansion strains that can be achieved the parameter A0 is a variable and then it is theconstant value According to the time 0minus t0 in Table 6 the parameter A0 is interpolated linearly according to 0minusA0

Table 7 +e correction coefficient of volume-to-surface ratio of massive self-compacting concrete

Type of steel tube column+e correction coefficient of volume-to-surface ratio αVS

Vertical direction Horizontal direction

SYZ-1 070 055SYZ-2 052 045

Table 8 Influencing coefficient of substitution proportion of fly ash replacing cement [22]

Substitution proportion of fly ash replacing cement 0 10sim20 20sim30αfs 1 095 090


than those of the vertical ones at the same time Butthe deformation rates show a decreasing trend withthe increase of time After 28 days the shrinkagedeformation curves in this paper become horizontalgradually

(4) +e change of section size and volume-to-surfaceratio has a great influence on shrinkage deformationof the core concrete With the increase of sectionsize the shrinkage deformation values of the coreconcrete decrease +e influence of volume-to-sur-face ratio of CFST should be reasonably consideredin calculating shrinkage deformation of the coreconcrete

(5) +e calculation model for the early-age shrinkageand expansion is proposed for the massive self-compacting concrete pumped in steel tube column

Data Availability

All data models or codes generated or used in this paper areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is study was funded by the Yuyou Talent Support Plan ofthe North China University of Technology (Grant no 2018-39)

References

[1] Y F Yang L H Han and X Wu ldquoConcrete shrinkage andcreep in recycled aggregate concrete-filled steel tubesrdquo Ad-vances in Structural Engineering vol 11 no 4 pp 383ndash3962008

[2] J M Abdalhmid A F Ashour and T Sheehan ldquoLong-termdrying shrinkage of self-compacting concrete experimentaland analytical investigationsrdquo Construction and BuildingMaterials vol 202 no 2 pp 825ndash837 2019

[3] P Y Yan F Zheng J Peng et al ldquoRelationship betweendelayed ettringite formation and delayed expansion in

massive shrinkage-compensating concreterdquo Cement andConcrete Composites vol 26 no 6 pp 383ndash396 2004

[4] A Gonzalez-Corominas and M Etxeberria ldquoEffects of usingrecycled concrete aggregates on the shrinkage of high per-formance concreterdquo Construction and Building Materialsvol 115 no 4 pp 32ndash41 2016

[5] M J Oliveira A B Ribeiro and F G Branco ldquoCuring effectin the shrinkage of a lower strength self-compacting con-creterdquo Construction and Building Materials vol 93 no 4pp 1206ndash1215 2015

[6] V Gribniak G Kaklauskas R Kliukas and R JakubovskisldquoShrinkage effect on short-term deformation behavior ofreinforced concrete-when it should not be neglectedrdquo Ma-terials amp Design vol 51 no 9 pp 1060ndash1070 2013

[7] D Shen J Jiang J Shen P Yao and G Jiang ldquoInfluence ofcuring temperature on autogenous shrinkage and crackingresistance of high-performance concrete at an early agerdquoConstruction and BuildingMaterials vol 103 no 1 pp 67ndash762016

[8] A Wendling K Sadhasivam and R W Floyd ldquoCreep andshrinkage of lightweight self-consolidating concrete for pre-stressed membersrdquo Construction and Building Materialsvol 167 no 2 pp 205ndash215 2018

[9] F Benboudjema F Meftah and J M Torrenti ldquoInteractionbetween drying shrinkage creep and cracking phenomena inconcreterdquo Engineering Structures vol 27 no 2 pp 239ndash2502005

[10] L Wu N Farzadnia C Shi Z Zhang and H Wang ldquoAu-togenous shrinkage of high performance concrete a reviewrdquoConstruction and Building Materials vol 149 no 5 pp 62ndash75 2017

[11] B Persson ldquoExperimental studies on shrinkage of high-performance concreterdquo Cement and Concrete Researchvol 28 no 7 pp 1023ndash1036 1998

[12] T Xie C Fang M S Mohamad Ali and P VisintinldquoCharacterizations of autogenous and drying shrinkage ofultra-high performance concrete (UHPC) an experimentalstudyrdquo Cement and Concrete Composites vol 91 no 4pp 156ndash173 2018

[13] X F Wang C Fang W Q Kuang D W Li N X Han andF Xing ldquoExperimental investigation on the compressivestrength and shrinkage of concrete with pre-wetted light-weight aggregatesrdquo Construction and Building Materialsvol 155 no 6 pp 867ndash879 2017

[14] M J Oliveira A B Ribeiro and F G Branco ldquoCombinedeffect of expansive and shrinkage reducing admixtures tocontrol autogenous shrinkage in self-compacting concreterdquo

(a) (b)

Figure 10 Detection of cracks between steel tube wall and the core concrete (a) Detecting by electronic crack observer (b) Detecting byvisual crack observer


Construction and Building Materials vol 52 no 1 pp 267ndash275 2014

[15] S Ribeiro A Z Bendimerad E Roziere and A Loukili ldquoHowdo recycled concrete aggregates modify the shrinkage andself-healing propertiesrdquo Cement and Concrete Compositesvol 86 no 1 pp 72ndash86 2018

[16] B C Chen and Y Lai ldquoShrinkage deformation of concretefilled steel tube and shrinkage stress of concrete filled steeltubular archrdquo Journal of Railway vol 38 no 2 pp 112ndash1232016

[17] G H Cao K Zhang J X Hu et al ldquoCalculation model ofshrinkage for expansive concrete filled steel tuberdquo Journal ofCentral South University (Science and Technology) vol 46no 3 pp 1094ndash1099 2015

[18] H B Zhu Q S Yuan J Xiang et al ldquoExperimental researchon expansive performance of micro-expansive lightweightaggregate concrete filled steel tuberdquo Sichuan Building Sciencevol 43 no 3 pp 135ndash138 2017

[19] W X Chen ldquoResearch on shrinkage and crack resistanceperformance of self-compacting concrete for underwater steelpipe columns of shanghai-nantong yangtze river bridgerdquoRailway Engineering vol 58 no 12 pp 150ndash155 2018

[20] L H Han Concrete Filled Steel Tube Structure-eory andPractice Science Press Beijing China 2007

[21] N J Gardner and M J Lockman ldquoDesign provisions fordrying shrinkage and creep of normal-strength concreterdquoACIMaterials Journal vol 98 no 2 pp 159ndash167 2001

[22] L S Gong M Y Hui B Yang et al ldquoExperimental study onshrinkage and creep of concreterdquo Report on ArchitecturalScience Research China Academy of Building ResearchBeijing China 1987


required with respect to concrete cracking +e results ofOliveira et al [5] also showed that the curing time wasessential to minimize shrinkage at early ages It caused alower drying mass loss causing a delaying effect in thedevelopment of shrinkage +is was important for earlycracking proneness +e study of Gribniak et al [6] dealtwith concrete shrinkage and accompanying creep influenceon cracking resistance and deformations of structural ele-ments It was found that serviceability characteristics ofreinforced concrete elements at the design stage might beimproved by specifying (1) concrete mixture proportions(2) mechanical properties of aggregates (3) method ofcuring (4) ambient temperature and humidity conditionsand (5) geometry of the structural element It was found thatthe autogenous shrinkage of early-age high-performanceconcrete (HPC) under different curing temperatures couldnot be predicted by the singular application of the equivalentage concept+e possible reason was that the microstructureevolution and apparent activation energy were influenced bytemperature +us investigation on the effect of curingtemperature on cracking resistance of early-age concretemust be further studied [7] +e general trends [8] observedindicated that the American Association of State Highwayand Transportation Officials (AASHTO) method tended tooverpredict shrinkage for both concrete mixtures especiallyat early ages and no method accurately represented thelower shrinkage rate of lightweight self-consolidating con-crete (LWSCC) Benboudjema et al [9] pointed out that thedrying process caused a strong structural effect micro-cracking arises in the concrete skin and attenuates the freedrying shrinkage strain +e amplitude of the structuralstrain was quite large It highlighted the need for an adequatecracking model to separate accurately the intrinsic behaviorof the material from the structural induced effect Never-theless after one year the numerical curve deviated from theexperimental one+is behavior seemed to be intrinsic sincethe adopted mechanical model took into account most of thecharacteristics of cracked concrete +e experimental resultsof Wu et al [10] showed that internal curing was an effectivemeans to reduce the autogenous shrinkage of high-perfor-mance concrete +e results of Persson [11] indicated thatcarbonation shrinkage may be avoided by the addition ofsilica fume Xie et al [12] suggested that from the per-spective of reducing shrinkage the optimal binder-to-sandratio was in the range of 1ndash11 the optimal dosage rate ofshrinkage reducing admixture was 1 and replacing ofmixing water by crushed ice up to 50 by weight had alsoinduced a significant reduction in shrinkageWang et al [13]suggested that the incorporation of 10-Mas expansiveagent was useful to diminish the shrinkage especially by itscombined use with prewetted lightweight aggregates(PLWA) +e results of Oliveira et al [14] also showed apotential for achieving a predefined shrinkage range byusing the combined effect of a set retarder and an expansiveadmixture +e paper [15] presented the main results of aresearch carried out to analyze the mechanical propertiesintrinsic permeability drying shrinkage carbonation andthe self-healing potential of concrete incorporating recycledconcrete aggregates However the effect of curing

temperature on autogenous shrinkage of early-age concretewas not in consistency and how the curing temperatureaffected the cracking resistance of concrete remains lack-ing Analysis of shrinkage stresses of concrete-filled steeltube (CFST) arch bridges showed that the shrinkage self-stress was large and should be taken into account in designcalculation [16] +e results of Cao et al [17] indicated thatthe shrinkage strain of a concrete-filled steel tube wasmainly caused by self-shrinkage and the self-shrinkagestrain was about 1times 10minus4 Zhu et al [18] reported that theshrinkage of a concrete-filled steel tube can be compen-sated well when the amount of expansive agent was 12Chen [19] found that the strains of free shrinkage andlimited shrinkage were 407 times10minus6 and 137 times10minus6 respec-tively at fourteen days

For the massive self-compacting concrete pumped insteel tube column the expansion and shrinkage of thecore concrete affects the stress distribution of concrete-filled steel tubular members to a great extent which canproduce redistribution of internal stress in concrete-filledsteel tubular members including ldquoredistribution of in-ternal stress in the section and internal stress in thesystemrdquo For example during the shrinkage process of thecore concrete in CFST the steel tube is forced to par-ticipate in the work alone resulting in tensile stress in thecore concrete and compressive stress in the steel tuberesulting in redistribution of the internal stress in thesection and the distribution values are large Besideswhen the core concrete shrinks there is a gap between thecore concrete and the steel tube which not only destroysthe joint work between the steel tube and the coreconcrete but also may cause corrosion on the innersurface of the steel tube during use In addition theexcessive expansion of the core massive concrete in thesteel tube will cause serious damage to the steel tube thusmaking the structure in an unsafe state

Based on the above the early-age shrinkage and ex-pansion properties for the massive self-compacting concretepumped in steel columns have been studied in this paper

2 Materials and Experimental Procedures

21 Materials and Mix Proportions +e cementitious ma-terials used for this investigation were Chinese standardPmiddotI425R Portland cement (standard compressive strengthhigher than 425MPa at the age of 28 days) Class I fly ash(fineness of 45 microm not more than 12 water demand rationot greater than 95 and loss on ignition not more than5) and silica fume (the National Standards of the PeoplersquosRepublic of China for Portland Cement and OrdinaryPortland Cement 1999 Fly Ash Used for Cement andConcrete 2005 Silica Fume for Cement Mortar and Con-crete 2012) +e coarse aggregate was a natural crushedstone (diameter 5ndash20mm) the fine aggregate was naturalriver sand (fineness modulus of 27) and tap water was usedfor mixing Tables 1 and 2 respectively show the mixproportions by weight of the mixture and the major pa-rameters of massive self-compaction concrete pumped insteel tube columns









Strengthgrade

Waterbinder ratio

Water(kgm3)

Cement(kgm3)

Fly ash(kgm3)

Silica fume(kgm3)




C60 031 165 320 180 25 790 850 86









650 70

70

90 1

10

1254

0

130 650

70110

650 130

1000

100

7 times

150

150

950

1000

10

00

1000

10

00

1000

10

00

1000

10

00

1000

70

0

1000

13

0 6

times 15

0 5

times 20

0 15

0 6

times 15

0 10

0 10

00

130

6 times

150

5 times

200

150

6 times

150

100

1000

15

0 6

times 15

0 4

times 20

0

85

85

85

d = 12 Vent hole

85

70 80

30 3

00 2

00

35

35

35

35

35

35

20

20

20

650

650

d = 12 Vent hole

d = 133

Grouting hole

110

1300

2880

90

(a)

800

1224

0

130 800

70110

800 130

1000

100

7 times

150

150

950

1000

10

00

1000

10

00

1000

10

00

1000

10

00

1000

70

0

1000

13

0 6

times 15

0 5

times 20

0 15

0 6

times 15

0 10

0 10

00

130

6 times

150

5 times

200

150

6 times

150

100

1000

15

0 6

times 15

0 4

times 20

0

85

85

85 d = 12

Vent hole

85

7080

115

115

115

35

35

35

35

35

35

800

650

d = 12 Vent hole

30 3

00 2

00

d = 133

Grouting hole

70 110

1300 70

90

11

0 90

4080

4080

2780

(b)









D4 D4 D4 D4

D4

D4

D4

D4

D


ts = 20

(a)

D3 D3 D2

D

45 3

D3

126


ts = 20

(b)










fixed support

Studs

(a)



Studs

(b)


(c)

Pressure cell

(d)





0 5 10 15 20 25 30

1-11-31-5

1-21-41-6

ndash15ndash10

ndash505

10152025303540

T (deg

C)

t (d)

(a)

ndash20

ndash10

0

10

20

30

40

0 5 10 15 20 25 30

T (deg

C)

2-12-32-5

2-22-42-6

t (d)

(b)


(a) (b)

(c) (d)










0

005

01

015

02

025

03

035

0 02 04 06 08 1

P (M

Pa)

t (h)

1-11-2

1-31-4

(a)

ndash01

0

01

02

03

04

05

06

0 1 2 3

t (d)

1-11-2

1-31-4

P (M

Pa)

(b)

ndash01

0

01

02

03

04

05

06

0 5 10 15 20 25 30

P (M

Pa)

t (d)

1-11-2

1-31-4

(c)






0

005

01

015

02

025

03

035

04

0 05 1 15 2 25 3 35 4t (h)

2-12-22-3

P (M

Pa)

(a)

0

01

02

03

04

05

06

07

08

0 1 2 3t (d)

2-12-22-3

P (M

Pa)

(b)

ndash02ndash01

00102030405060708

0 5 10 15 20 25 30

t (d)

2-12-22-3

P (M

Pa)

(c)




1 2 3 4











ndash500

50100

0 5 10 15 20 25 30


ε (με

)

t (d)

(a)

ndash350

ndash300

ndash250

ndash200

ndash150

ndash100

ndash50

0

500 5 10 15 20 25 30


t (d)

ε (με

)

(b)





23792 με minus402060 με














β(t) A0 minus 1

1 +(tα)β + 1

A0



⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

(2)



εshu 30

fcm281113888 1113889

12

middot 10minus3


(3)


5 Discussion





6 Conclusions












t0







SYZ-1 070 055SYZ-2 052 045







Data Availability




Acknowledgments


References
















(a) (b)




















Strengthgrade

Waterbinder ratio

Water(kgm3)

Cement(kgm3)

Fly ash(kgm3)

Silica fume(kgm3)




C60 031 165 320 180 25 790 850 86









650 70

70

90 1

10

1254

0

130 650

70110

650 130

1000

100

7 times

150

150

950

1000

10

00

1000

10

00

1000

10

00

1000

10

00

1000

70

0

1000

13

0 6

times 15

0 5

times 20

0 15

0 6

times 15

0 10

0 10

00

130

6 times

150

5 times

200

150

6 times

150

100

1000

15

0 6

times 15

0 4

times 20

0

85

85

85

d = 12 Vent hole

85

70 80

30 3

00 2

00

35

35

35

35

35

35

20

20

20

650

650

d = 12 Vent hole

d = 133

Grouting hole

110

1300

2880

90

(a)

800

1224

0

130 800

70110

800 130

1000

100

7 times

150

150

950

1000

10

00

1000

10

00

1000

10

00

1000

10

00

1000

70

0

1000

13

0 6

times 15

0 5

times 20

0 15

0 6

times 15

0 10

0 10

00

130

6 times

150

5 times

200

150

6 times

150

100

1000

15

0 6

times 15

0 4

times 20

0

85

85

85 d = 12

Vent hole

85

7080

115

115

115

35

35

35

35

35

35

800

650

d = 12 Vent hole

30 3

00 2

00

d = 133

Grouting hole

70 110

1300 70

90

11

0 90

4080

4080

2780

(b)









D4 D4 D4 D4

D4

D4

D4

D4

D


ts = 20

(a)

D3 D3 D2

D

45 3

D3

126


ts = 20

(b)










fixed support

Studs

(a)



Studs

(b)


(c)

Pressure cell

(d)





0 5 10 15 20 25 30

1-11-31-5

1-21-41-6

ndash15ndash10

ndash505

10152025303540

T (deg

C)

t (d)

(a)

ndash20

ndash10

0

10

20

30

40

0 5 10 15 20 25 30

T (deg

C)

2-12-32-5

2-22-42-6

t (d)

(b)


(a) (b)

(c) (d)










0

005

01

015

02

025

03

035

0 02 04 06 08 1

P (M

Pa)

t (h)

1-11-2

1-31-4

(a)

ndash01

0

01

02

03

04

05

06

0 1 2 3

t (d)

1-11-2

1-31-4

P (M

Pa)

(b)

ndash01

0

01

02

03

04

05

06

0 5 10 15 20 25 30

P (M

Pa)

t (d)

1-11-2

1-31-4

(c)






0

005

01

015

02

025

03

035

04

0 05 1 15 2 25 3 35 4t (h)

2-12-22-3

P (M

Pa)

(a)

0

01

02

03

04

05

06

07

08

0 1 2 3t (d)

2-12-22-3

P (M

Pa)

(b)

ndash02ndash01

00102030405060708

0 5 10 15 20 25 30

t (d)

2-12-22-3

P (M

Pa)

(c)




1 2 3 4











ndash500

50100

0 5 10 15 20 25 30


ε (με

)

t (d)

(a)

ndash350

ndash300

ndash250

ndash200

ndash150

ndash100

ndash50

0

500 5 10 15 20 25 30


t (d)

ε (με

)

(b)





23792 με minus402060 με














β(t) A0 minus 1

1 +(tα)β + 1

A0



⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

(2)



εshu 30

fcm281113888 1113889

12

middot 10minus3


(3)


5 Discussion





6 Conclusions












t0







SYZ-1 070 055SYZ-2 052 045







Data Availability




Acknowledgments


References
















(a) (b)















650 70

70

90 1

10

1254

0

130 650

70110

650 130

1000

100

7 times

150

150

950

1000

10

00

1000

10

00

1000

10

00

1000

10

00

1000

70

0

1000

13

0 6

times 15

0 5

times 20

0 15

0 6

times 15

0 10

0 10

00

130

6 times

150

5 times

200

150

6 times

150

100

1000

15

0 6

times 15

0 4

times 20

0

85

85

85

d = 12 Vent hole

85

70 80

30 3

00 2

00

35

35

35

35

35

35

20

20

20

650

650

d = 12 Vent hole

d = 133

Grouting hole

110

1300

2880

90

(a)

800

1224

0

130 800

70110

800 130

1000

100

7 times

150

150

950

1000

10

00

1000

10

00

1000

10

00

1000

10

00

1000

70

0

1000

13

0 6

times 15

0 5

times 20

0 15

0 6

times 15

0 10

0 10

00

130

6 times

150

5 times

200

150

6 times

150

100

1000

15

0 6

times 15

0 4

times 20

0

85

85

85 d = 12

Vent hole

85

7080

115

115

115

35

35

35

35

35

35

800

650

d = 12 Vent hole

30 3

00 2

00

d = 133

Grouting hole

70 110

1300 70

90

11

0 90

4080

4080

2780

(b)









D4 D4 D4 D4

D4

D4

D4

D4

D


ts = 20

(a)

D3 D3 D2

D

45 3

D3

126


ts = 20

(b)










fixed support

Studs

(a)



Studs

(b)


(c)

Pressure cell

(d)





0 5 10 15 20 25 30

1-11-31-5

1-21-41-6

ndash15ndash10

ndash505

10152025303540

T (deg

C)

t (d)

(a)

ndash20

ndash10

0

10

20

30

40

0 5 10 15 20 25 30

T (deg

C)

2-12-32-5

2-22-42-6

t (d)

(b)


(a) (b)

(c) (d)










0

005

01

015

02

025

03

035

0 02 04 06 08 1

P (M

Pa)

t (h)

1-11-2

1-31-4

(a)

ndash01

0

01

02

03

04

05

06

0 1 2 3

t (d)

1-11-2

1-31-4

P (M

Pa)

(b)

ndash01

0

01

02

03

04

05

06

0 5 10 15 20 25 30

P (M

Pa)

t (d)

1-11-2

1-31-4

(c)






0

005

01

015

02

025

03

035

04

0 05 1 15 2 25 3 35 4t (h)

2-12-22-3

P (M

Pa)

(a)

0

01

02

03

04

05

06

07

08

0 1 2 3t (d)

2-12-22-3

P (M

Pa)

(b)

ndash02ndash01

00102030405060708

0 5 10 15 20 25 30

t (d)

2-12-22-3

P (M

Pa)

(c)




1 2 3 4











ndash500

50100

0 5 10 15 20 25 30


ε (με

)

t (d)

(a)

ndash350

ndash300

ndash250

ndash200

ndash150

ndash100

ndash50

0

500 5 10 15 20 25 30


t (d)

ε (με

)

(b)





23792 με minus402060 με














β(t) A0 minus 1

1 +(tα)β + 1

A0



⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

(2)



εshu 30

fcm281113888 1113889

12

middot 10minus3


(3)


5 Discussion





6 Conclusions












t0







SYZ-1 070 055SYZ-2 052 045







Data Availability




Acknowledgments


References
















(a) (b)



















D4 D4 D4 D4

D4

D4

D4

D4

D


ts = 20

(a)

D3 D3 D2

D

45 3

D3

126


ts = 20

(b)










fixed support

Studs

(a)



Studs

(b)


(c)

Pressure cell

(d)





0 5 10 15 20 25 30

1-11-31-5

1-21-41-6

ndash15ndash10

ndash505

10152025303540

T (deg

C)

t (d)

(a)

ndash20

ndash10

0

10

20

30

40

0 5 10 15 20 25 30

T (deg

C)

2-12-32-5

2-22-42-6

t (d)

(b)


(a) (b)

(c) (d)










0

005

01

015

02

025

03

035

0 02 04 06 08 1

P (M

Pa)

t (h)

1-11-2

1-31-4

(a)

ndash01

0

01

02

03

04

05

06

0 1 2 3

t (d)

1-11-2

1-31-4

P (M

Pa)

(b)

ndash01

0

01

02

03

04

05

06

0 5 10 15 20 25 30

P (M

Pa)

t (d)

1-11-2

1-31-4

(c)






0

005

01

015

02

025

03

035

04

0 05 1 15 2 25 3 35 4t (h)

2-12-22-3

P (M

Pa)

(a)

0

01

02

03

04

05

06

07

08

0 1 2 3t (d)

2-12-22-3

P (M

Pa)

(b)

ndash02ndash01

00102030405060708

0 5 10 15 20 25 30

t (d)

2-12-22-3

P (M

Pa)

(c)




1 2 3 4











ndash500

50100

0 5 10 15 20 25 30


ε (με

)

t (d)

(a)

ndash350

ndash300

ndash250

ndash200

ndash150

ndash100

ndash50

0

500 5 10 15 20 25 30


t (d)

ε (με

)

(b)





23792 με minus402060 με














β(t) A0 minus 1

1 +(tα)β + 1

A0



⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

(2)



εshu 30

fcm281113888 1113889

12

middot 10minus3


(3)


5 Discussion





6 Conclusions












t0







SYZ-1 070 055SYZ-2 052 045







Data Availability




Acknowledgments


References
















(a) (b)




















fixed support

Studs

(a)



Studs

(b)


(c)

Pressure cell

(d)





0 5 10 15 20 25 30

1-11-31-5

1-21-41-6

ndash15ndash10

ndash505

10152025303540

T (deg

C)

t (d)

(a)

ndash20

ndash10

0

10

20

30

40

0 5 10 15 20 25 30

T (deg

C)

2-12-32-5

2-22-42-6

t (d)

(b)


(a) (b)

(c) (d)










0

005

01

015

02

025

03

035

0 02 04 06 08 1

P (M

Pa)

t (h)

1-11-2

1-31-4

(a)

ndash01

0

01

02

03

04

05

06

0 1 2 3

t (d)

1-11-2

1-31-4

P (M

Pa)

(b)

ndash01

0

01

02

03

04

05

06

0 5 10 15 20 25 30

P (M

Pa)

t (d)

1-11-2

1-31-4

(c)






0

005

01

015

02

025

03

035

04

0 05 1 15 2 25 3 35 4t (h)

2-12-22-3

P (M

Pa)

(a)

0

01

02

03

04

05

06

07

08

0 1 2 3t (d)

2-12-22-3

P (M

Pa)

(b)

ndash02ndash01

00102030405060708

0 5 10 15 20 25 30

t (d)

2-12-22-3

P (M

Pa)

(c)




1 2 3 4











ndash500

50100

0 5 10 15 20 25 30


ε (με

)

t (d)

(a)

ndash350

ndash300

ndash250

ndash200

ndash150

ndash100

ndash50

0

500 5 10 15 20 25 30


t (d)

ε (με

)

(b)





23792 με minus402060 με














β(t) A0 minus 1

1 +(tα)β + 1

A0



⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

(2)



εshu 30

fcm281113888 1113889

12

middot 10minus3


(3)


5 Discussion





6 Conclusions












t0







SYZ-1 070 055SYZ-2 052 045







Data Availability




Acknowledgments


References
















(a) (b)















0 5 10 15 20 25 30

1-11-31-5

1-21-41-6

ndash15ndash10

ndash505

10152025303540

T (deg

C)

t (d)

(a)

ndash20

ndash10

0

10

20

30

40

0 5 10 15 20 25 30

T (deg

C)

2-12-32-5

2-22-42-6

t (d)

(b)


(a) (b)

(c) (d)










0

005

01

015

02

025

03

035

0 02 04 06 08 1

P (M

Pa)

t (h)

1-11-2

1-31-4

(a)

ndash01

0

01

02

03

04

05

06

0 1 2 3

t (d)

1-11-2

1-31-4

P (M

Pa)

(b)

ndash01

0

01

02

03

04

05

06

0 5 10 15 20 25 30

P (M

Pa)

t (d)

1-11-2

1-31-4

(c)






0

005

01

015

02

025

03

035

04

0 05 1 15 2 25 3 35 4t (h)

2-12-22-3

P (M

Pa)

(a)

0

01

02

03

04

05

06

07

08

0 1 2 3t (d)

2-12-22-3

P (M

Pa)

(b)

ndash02ndash01

00102030405060708

0 5 10 15 20 25 30

t (d)

2-12-22-3

P (M

Pa)

(c)




1 2 3 4











ndash500

50100

0 5 10 15 20 25 30


ε (με

)

t (d)

(a)

ndash350

ndash300

ndash250

ndash200

ndash150

ndash100

ndash50

0

500 5 10 15 20 25 30


t (d)

ε (με

)

(b)





23792 με minus402060 με














β(t) A0 minus 1

1 +(tα)β + 1

A0



⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

(2)



εshu 30

fcm281113888 1113889

12

middot 10minus3


(3)


5 Discussion





6 Conclusions












t0







SYZ-1 070 055SYZ-2 052 045







Data Availability




Acknowledgments


References
















(a) (b)




















0

005

01

015

02

025

03

035

0 02 04 06 08 1

P (M

Pa)

t (h)

1-11-2

1-31-4

(a)

ndash01

0

01

02

03

04

05

06

0 1 2 3

t (d)

1-11-2

1-31-4

P (M

Pa)

(b)

ndash01

0

01

02

03

04

05

06

0 5 10 15 20 25 30

P (M

Pa)

t (d)

1-11-2

1-31-4

(c)






0

005

01

015

02

025

03

035

04

0 05 1 15 2 25 3 35 4t (h)

2-12-22-3

P (M

Pa)

(a)

0

01

02

03

04

05

06

07

08

0 1 2 3t (d)

2-12-22-3

P (M

Pa)

(b)

ndash02ndash01

00102030405060708

0 5 10 15 20 25 30

t (d)

2-12-22-3

P (M

Pa)

(c)




1 2 3 4











ndash500

50100

0 5 10 15 20 25 30


ε (με

)

t (d)

(a)

ndash350

ndash300

ndash250

ndash200

ndash150

ndash100

ndash50

0

500 5 10 15 20 25 30


t (d)

ε (με

)

(b)





23792 με minus402060 με














β(t) A0 minus 1

1 +(tα)β + 1

A0



⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

(2)



εshu 30

fcm281113888 1113889

12

middot 10minus3


(3)


5 Discussion





6 Conclusions












t0







SYZ-1 070 055SYZ-2 052 045







Data Availability




Acknowledgments


References
















(a) (b)
















0

005

01

015

02

025

03

035

04

0 05 1 15 2 25 3 35 4t (h)

2-12-22-3

P (M

Pa)

(a)

0

01

02

03

04

05

06

07

08

0 1 2 3t (d)

2-12-22-3

P (M

Pa)

(b)

ndash02ndash01

00102030405060708

0 5 10 15 20 25 30

t (d)

2-12-22-3

P (M

Pa)

(c)




1 2 3 4











ndash500

50100

0 5 10 15 20 25 30


ε (με

)

t (d)

(a)

ndash350

ndash300

ndash250

ndash200

ndash150

ndash100

ndash50

0

500 5 10 15 20 25 30


t (d)

ε (με

)

(b)





23792 με minus402060 με














β(t) A0 minus 1

1 +(tα)β + 1

A0



⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

(2)



εshu 30

fcm281113888 1113889

12

middot 10minus3


(3)


5 Discussion





6 Conclusions












t0







SYZ-1 070 055SYZ-2 052 045







Data Availability




Acknowledgments


References
















(a) (b)




















ndash500

50100

0 5 10 15 20 25 30


ε (με

)

t (d)

(a)

ndash350

ndash300

ndash250

ndash200

ndash150

ndash100

ndash50

0

500 5 10 15 20 25 30


t (d)

ε (με

)

(b)





23792 με minus402060 με














β(t) A0 minus 1

1 +(tα)β + 1

A0



⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

(2)



εshu 30

fcm281113888 1113889

12

middot 10minus3


(3)


5 Discussion





6 Conclusions












t0







SYZ-1 070 055SYZ-2 052 045







Data Availability




Acknowledgments


References
















(a) (b)





















β(t) A0 minus 1

1 +(tα)β + 1

A0



⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭

(2)



εshu 30

fcm281113888 1113889

12

middot 10minus3


(3)


5 Discussion





6 Conclusions












t0







SYZ-1 070 055SYZ-2 052 045







Data Availability




Acknowledgments


References
















(a) (b)















6 Conclusions












t0







SYZ-1 070 055SYZ-2 052 045







Data Availability




Acknowledgments


References
















(a) (b)
















Data Availability




Acknowledgments


References
















(a) (b)























Documents

The Study on Early-Age Expansion and Shrinkage Model of