Research ArticleThe Study on Cracking Strength of AIJs to Releasethe Early-Age Stress of Mass Concrete

Xiaogang Zhang1 Chengqiang Wang2 Shuping Wang3 Feng Xing1 and Ronghua Zhu4

1Guangdong Provincial Key Laboratory of Durability for Marine Civil Engineering College of Civil EngineeringShenzhen University Shenzhen 518060 China2Department of Materials and Structural Engineering Nanjing Hydraulic Research Institute Nanjing 210024 China3Department of Building Materials Chalmers University of Technology 41296 Gothenburg Sweden4China Ming Yang Wind Power Group Limited Zhongshan 528437 China

Correspondence should be addressed to Xiaogang Zhang szzxgszueducn and Shuping Wang shupingchalmersse

Received 18 April 2015 Revised 30 August 2015 Accepted 31 August 2015

Academic Editor Hossein Moayedi

Copyright copy 2015 Xiaogang Zhang et alThis is an open access article distributed under theCreativeCommonsAttributionLicensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper aims to theoretically and numerically assess the effect of setting artificial-induced joints (AIJs) during constructionperiod of amass concrete structure to release the early-stage thermal stressWith respect to the coupling influences of various factorssuch as size and boundary of AIJs an analytical model for its cracking strength on the setting section of mass concrete is proposedbased on double-parameter fracture theory A kind of hyper-finite element analysis (FEA) for many array AIJs in simplified planepate is also presented by using bilinear cohesive force distribution The results from the present model and numerical simulationwere compared to those of experimental data to prove the efficiency and accuracy of the analytical model and FEA The modelpresented in this study for the cracking strength of AIJs provides a simple useful tool to accurately evaluate how many early stressAIJs reducedThe theoretical solution and FEA results could also be significantly contributed to find the ldquojustrdquo and ldquoperfectrdquo releaseof the temperature stress and to improve the design level of AIJs in mass concrete structure

1 Introduction

In the past decades mass concrete structures such as superlong underground sidewall large basement slab and rollercompacted concrete (RCC) have been widely used in thepractical construction like subway station [1] high-risebuilding [2] and RCC arch dam [3] The early irregularcracks caused by the thermal stress of mass concrete duringconstruction period are a worldwide problem to the structure[4 5] andhow to effectively control the early-age temperaturecracks in the mass concrete structure is significantly con-cerned by researchers [6ndash8] Up to now many methods havebeen introduced and applied to eliminate these early randomcracks such as adopting deformation joints [9] setting post-poured strips [2] and using high performance materials[10ndash13] Although the above methods to some extent caninhibit the growth of random early-age cracks there are stillproblems during the realistic applications [2 10 14]

Recently therefore more attention has been paid to anew method of setting artificial-induced joints (AIJs) in

construction period to reduce the early-age thermal stress ofmass concrete [1 15 16] Figure 1 illustrates the joint treatmentby this new method for different types of mass concrete (iesuper long underground sidewall large basement slab andRCC arch dam) As can be seen from Figure 1(c) the crosssection of mass concrete consists of many embedded gapsphase-to-phase arrayed if the setting of AIJs in RCC is takenas an example in the present studyThe size of each embeddedgap is 2119886times2119888 the vertical andhorizontal distance between twoadjacent embedded gap centres are 2119887 and 2119889 respectivelyCross section embedded AIJs are expected to be crackedprior to avoiding random cracks in other partssections ofthe structures when the early temperature rises in massconcrete due to the heat of cement hydration (Figure 1(c))Then backfill grouting is applied in the cracking section whenthe chemical reaction of hydration heat has been done duringthe construction period of mass concrete structures

The cracking strength of AIJs which is related to the sizethe shape of each embedded gap the distance between two

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2015 Article ID 623215 8 pageshttpdxdoiorg1011552015623215

2 Advances in Materials Science and Engineering

Medium buried rubber waterstop

Caulking factis

(a) AIJs in super long underground sidewall

Sticking type of waterstop

Medium buried rubber waterstop

(b) AIJs in large basement slab

2a

2b2c

2d

The cross section AIJs embedded

120590120590

(c) AIJs in RCC

Figure 1 The detailed joint treatments of AIJs for different mass concrete

cross section embeddedAIJs and so forth is themost key andimportant parameter in the study of AIJs in mass concreteThis is because only the right value of cracking strength can beexpected to avoid random cracks in other partssections andthereby to ldquojustrdquo and ldquoperfectlyrdquo release temperature stress inmass concrete If the value of cracking strength is too smallor large the cross section embedded AIJs cannot be crackedfirstly or cannot completely reduce the early stress of otherpartssections In this situation the setting of AIJs to inhibitthe growth of random early-age cracks will to some extentbe limited Therefore it is of great importance to accuratelypredict the cracking strength of AIJs in evaluating the effectof controlling the early stress in mass concrete structuresUp to now the accurately analytical solution of crackingstrength to ldquojustrdquo and ldquoperfectlyrdquo release temperature stressin mass concrete is still not yet available although someexperimental investigation theoretical model and numericalsimulation have been carried out [15ndash17] This is becausethere are so many complex factors such as boundary ofcross section different size shape of AIJs concrete strengthand construction schedule which affect the cracking strength[16 17] Therefore it is necessary and of great importanceto illustrate the highly precise model and accurate FEA forthe prediction of cracking strength of AIJs so as to be able toevaluate its effect on releasing the early stress [18ndash20]

In this paper an analytical model of the cracking strengthof AIJs in RCC is studied and improved after considering thevarious factors such as size and boundary of AIJsThen a kindof hyper-finite element method along with the experimental

2a

2w

middot middot middot

Figure 2 Model of penetrated crack in infinite plate

data is present The results from the present model andnumerical simulation are discussed and further verified Themodel presented in this study for the cracking strength is asimple and useful tool to accurately evaluate the reductionof early-age stress The theoretical solution and FEA resultscould also be contributed to find the ldquojustrdquo and ldquoperfectrdquorelease of the temperature stress and to improve the designlevel of AIJs in mass concrete structure

2 Analytical Model of CrackingStrength for AIJs

The analytical solution of cracking strength for AIJs inFigure 1(c) can be simplified as a problem of penetratedcrack in an infinite plate due to the fact that the lengthof arch direction is often hundreds of meters (Figure 2)The vertical distance between two adjacent embedded gapcentres in Figure 2 is 2119908 Similar to the development of

Advances in Materials Science and Engineering 3

Table 1 The indexes for cracking process of AIJ

Fracture energy parameters Cracking strength parameters Crack length parameters Phase of process119866 lt 119866

119904120590 lt 120590

119904119886 = 1198860

Before cracking initiation119866119904le 119866 le 119866

119906120590119904le 120590 le 120590max 119886

0⩽ 119886 ⩽ 119886

119888Stable growth

119866 gt 119866119906

120590 gt 120590max 119886 gt 119886119888

Unstable propagation

other cracks in concretes the AIJs also include crackinginitiation stable growth and unstable propagation processfor mass concrete As assumed 120590 is the tensile strength alongthe arch direction and 120590

119904and 120590max represent initial and

unstable cracking strength respectively The propagation ofAIJs occurredwhen thermal stress away from theAIJs is up to120590119904 thereby weakening the cross sections Similarly AIJs start

to be unstably fractured as thermal stress comes to unstablecracking strength 120590max Apparently one can find that there isa stable propagation stage of the cracking of AIJs between 120590

119904

and 120590maxAs mentioned above the values of 120590

119904and 120590max are

influenced by many factors [16 17] In the present study thecoupling effect of these factors such as boundary of crosssection different size and concrete strength on the crackingstrength of AIJs can be expressed as the following equations[16 17]

120590 = 119860 (1205720) 119891119905(1 + 119861 (120572

0)

119886

119886lowast

infin

)

minus12

(1)

119861 (1205720) = [

119860 (1205720)119884(1205720)

112]

2

(2)

119886lowast

infin=

119864119866119865

12551205871198912

119905

(3)

where1205720is the ratio of initiation crack length to depth and119866

119865

is the fracture energy of concretematerials119891119905and119864 represent

the tensile strength and elastic modulus of RCC respectively119860(1205720) and 119884(120572

0) are the functions of 120572

0and can be varied

from different types of structureAlthough the fracture energy 119866

119865in (3) can be generally

used to describe the average amount of energy consumedduring the breaking down process of AIJs in mass concreteit cannot effectively express the respective consumption ofenergy during two important stages of cracking expansionnamely the stable growth and unstable propagation pro-cess [21] To characterize the energy release ratio in theabove different crack expanding periods 119866

119865is divided into

two fracture parameters initiation fracture energy 119866119904and

unstable fracture energy 119866119906 119866119904is associated with cracking

initiation stress 120590119904and initial crack length 120572

0 while 119866

119906is

related to maximum stress 120590max and critical effective cracklength 119886

119888 More information about the parameters is shown

in Table 1The solution of 119866

119906can be determined by experimental

test of the three-point bending beams [21]

119866119906=

31198752

max1198782

4119861211986331198641198811015840

(120572) (4)

120590(120590ft)

ft(10)

O ws(c1) w0(10)

w(ww0)

120590s(c2)

Figure 3 Bilinear cohesive force model of mass concrete

where 119861 and 119878 are the specimen thickness and loading spanrespectively 120572 = 119886

119888119863 is the ratio of the critical effective crack

length to beam depth119863119875max is themaximum load and119881(120572)

is a coefficient related to 120572

1198811015840

(120572) =2120572

(1 minus 120572)3[558 minus 1957120572 + 3682120572

2

minus 34941205723

+ 12771205724

] + (120572

1 minus 120572)

2

(minus1957 + 7364120572

minus 104821205722

+ 51081205723

)

(5)

If the contribution of energy due to cohesive forces isdefined as 119866

119888 the initiation fracture energy 119866

119904can also be

given as

119866119904= 119866119906minus 119866119888 (6)

where 119866119888can be obtained by integration method of cohesive

forces on the crack surfaceAccording to fracture theory the softening models of

concrete [21] can be simplified into the bilinear cohesive forcemodel to describe the cracking behaviors of mass concrete asillustrated in Figure 3 The expression is

119886119888= 1198860+ Δ119886lowast

119888= 1198860+

41199030

1198881+ 1198882

minus 1199030 (7)

In (7) Δ119886lowast119888is the effective crack propagation length w is the

crack opening displacement and 1199080is the critical value of

119908 1199030can be regarded as crevice genesis zone which can be

evaluated by the following expression

1199030=

119864119866119906

21205871198912

119905

(8)

The stress distribution of the cross section where AIJsembedded will be more affected by the plasticity of concrete

4 Advances in Materials Science and Engineering

CrackCOD

y

x

120590(r)R2

R1

120579

r

o

Figure 4 Crack-singular-analytical element loaded by the linearcohesive force

materials with the lager values of the fracture energy ofRCC As a result the initiation cracking strength 120590

119904and the

unstable cracking strength 120590max of AIJs in mass concrete canbe determined by the above values of 119866

119904and 119866

119906in (4) and

(6) The initiation cracking strength 120590119904can be given as

120590119904= (

119864119866119904

2119882)

12

[tan(120587

2

119886

119882)]

minus12

(9)

After the stable growth and unstable propagation stage ofAIJs the critical value of unstable cracking strength 120590max canalso be written as

120590max = (119864119866119906

2119882)

12

[tan(120587

2

119886119888

119882)]

minus12

(10)

3 The Hyper-Finite Element Analysis for AIJs

Among the fracturemodels of concretematerials proposed byresearchers the fictitious crack model is famous and widelyused It is especially suitable for FEM analysis of AIJs in massconcrete However there still exist many difficulties to obtainaccurate stress distribution on the vicinity of the crack tipeven though a refined mesh is used [21] An effective way tosolve the problem in this study is to apply a hyperelement onthe vicinity of AIJs tip based on the Hamiltonian theory ofelasticity Thereafter the cracking strength of FEM analysisfor AIJs inmass concrete is described when the hyperelementis combined with general finite elements

For bilinear cohesive force distribution in fictitious crackmodel shown in Figure 4 the propagation process of AIJsin mass concrete can be considered as propagation of elasticcracks which is a function of a cohesive distribution closeforce 120590(119909) along the propagation length Δ119886 The regionof cross section embedded AIJs is dispersed with a ringhyperelement surrounding the crack tip and also ordinaryfinite elements around the hyperelement as is illustrated inFigure 4 The equation of variation in the form of Hamilto-nian for the crack-ring-singular element loaded by the linearcohesive force can be expressed as

120575int

120587

0

int

ln1198772

ln1198771119878119903

120597119906

120597120585+ 119878119903120579

120597V120597120585

+ ]119878119903(119906 +

120597V120597120579

) + 119878119903120579(120597119906

120597120579minus V) +

119864

2(119906 +

120597V120597120579

)

2

minus1

2119864[(1 minus ]2) 1198782

119903+ 2 (1 + ]) 1198782

119903120579] 119889120585 119889120579

minus int

ln1198772

ln1198771[1198963exp (2120585) + 119896

4exp (120585)] ∙ V

120579=120587119889120585 = 0

(11)

where 119906 and V are the radial and tangential displacementrespectively 119902 = 119906 V119879 is its displacement vector 119878

119903= 119903120590119903

119878119903120579

= 119903120591119903120579 and 119901 = 119878

119903 119878119903120579119879 is the dual vector

The parameters 120577 1198963 1198964are obtained by

120585 = ln 119903

1198963= minus

(120590119904minus 120590 (119908))

(1198772minus 1198771)

1198964=

(120590119904minus 120590 (119908) 119877

2)

(1198772minus 1198771)

(12)

where 1198771= Δ119886119888and 119877

2= 119886 minus 119886

0

Assuming that there are 119899119903nodes on the hyperelement

and the unknown variables of each node are displacements of119906 V except for the node at 120579 = 0 which has only one variable119906 so the hyperelement has 2119899

119903minus 1 degrees of freedom If 120583

119894

is Eigen value and 120595119894= 119902119894 119901119894119879 is Eigen-function vector the

complete state function vector expansion is expressed as

V (120585 120579) = 119902 119901119879

= 119906 V 119878119903 119878119903120579119879

= 119888120572119894

2119899119903minus1

sum

119894=1

119906120572119894 V120572119894 119878119903120572119894

119878119903120579120572119894

119879

+ 119888120573119894

2119899119903minus1

sum

119894=1

119906120573119894 V120573119894 119878119903120573119894

119878119903120579120573119894

119879

+ V (120585 120579)

= 1198881205721V01+

2119899119903minus2

sum

119894=1

119888120572119894+1

120595120572119894exp (120583

119894120585) + 1198881205731V02

+

2119899119903minus2

sum

119894=1

119888120573119894+1

120595120573119894exp (minus120583

119894120585) + V (120585 120579)

(13)

Advances in Materials Science and Engineering 5

where 119888120572119894 119888120573119894

(119894 = 1 2 119871 2119899119903minus 1) are unknown generalized

constants and V(120585 120579) is a special solution

V (120585 120579) = V 119878119903 119878119903120579119879

= 1198964exp (120585)

1 minus ]119864

0 1 0

119879

minus 1198963exp (2120585)

sdot 1 minus 3]6119864

cos 120579 5 + ]6119864

sin 1205791

3cos 120579 1

3sin 120579

119879

(14)

If 119888 and 119889 are the generalized constant vector andthe nodal displacement vector respectively the relationshipbetween 119888 and 119889 is

(119889 minus 119889) = 119879 ∙ 119888 119888 = 119879minus1

∙ (119889 minus 119889) (15)

where 119888 = 1198881205721 1198881205722 119888

1205722119899119903minus1 1198881205731 1198881205732 119888

1205732119899119903minus1119879 119889 =

11990611 11990612 V12 119906

1119899119903 V1119899119903

11990621 11990622 V22 119906

2119899119903 V2119899119903

119879 119889 =

1198891 1198892119879 =

11 12 V12

1119899119903 V1119899119903

21 22 V22

2119899119903

V2119899119903

119879 and 119889 is the value vector of special solution at the

nodesThe components of the inverse of matrix 119879 are

119879 = [

11987911

11987912

11987921

11987922

] (16)

where

(11987911)119895119894= 119906120572119894

1003816100381610038161003816

120585=ln1198771120579=1205791=0

119895 = 1 119894 = 1 2 2119899119903minus 1

(11987911)119895119894= 119906120572119894

1003816100381610038161003816

120585=ln1198771120579=120579119896

119895 = 2119896 minus 2 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987911)119895119894= V120572119894

1003816100381610038161003816

120585=ln1198771120579=120579119896

119895 = 2119896 minus 1 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987912)119895119894= 119906120573119894

10038161003816100381610038161003816

120585=ln1198771120579=1205791=0

119895 = 1 119894 = 1 2 2119899119903minus 1

(11987912)119895119894= 119906120573119894

10038161003816100381610038161003816

120585=ln1198771120579=120579119896

119895 = 2119896 minus 2 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987912)119895119894= V120573119894

10038161003816100381610038161003816

120585=ln1198771120579=120579119896

119895 = 2119896 minus 1 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987921)119895119894= 119906120572119894

1003816100381610038161003816

120585=ln1198772120579=1205791=0

119895 = 1 119894 = 1 2 2119899119903minus 1

(11987921)119895119894= 119906120572119894

1003816100381610038161003816

120585=ln1198772120579=120579119896

119895 = 2119896 minus 2 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987921)119895119894= V120572119894

1003816100381610038161003816

120585=ln1198772120579=120579119896

119895 = 2119896 minus 1 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987922)119895119894= 119906120573119894

10038161003816100381610038161003816

120585=ln1198772120579=1205791=0

119895 = 1 119894 = 1 2 2119899119903minus 1

(11987922)119895119894= 119906120573119894

10038161003816100381610038161003816

120585=ln1198772120579=120579119896

119895 = 2119896 minus 2 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987922)119895119894= V120573119894

10038161003816100381610038161003816

120585=ln1198772120579=120579119896

119895 = 2119896 minus 1 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(17)

where 120579119896(119896 = 1 2 119871119899

119903) are tangential coordinates of node 120579

The solution can be carried out by iterating over (13) and(11) 119877

0and load vector 119865

0can be obtained by the integration

of partial stiffness matrix of hyperelement

1198770= 119879minus119879

∙ 119877119888∙ 119879minus1

119877119888= [

11987711

11987712

11987721

11987722

]

1198770= 119879minus119879

∙ (119865119888+ 119877119888∙ 119879minus1

∙ 119889) 119865119888= [1198651 1198652]119879

(18)

where 1198770and 119865

0are

(11987711)119895119894= int

120587

0

[119878119903120572119894

(120585 120579) 119906120572119895(120585 120579)

+ 119878119903120579120572119894

(120585 120579) V120572119895(120585 120579)]

10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(11987712)119895119894= int

120587

0

[119878119903120573119894

(120585 120579) 119906120572119895(120585 120579)

+ 119878119903120579120573119894

(120585 120579) V120572119895(120585 120579)]

10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(11987721)119895119894= int

120587

0

[119878119903120572119894

(120585 120579) 119906120573119895(120585 120579)

+ 119878119903120579120572119894

(120585 120579) V120573119895(120585 120579)]

10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(11987722)119895119894= int

120587

0

[119878119903120573119894

(120585 120579) 119906120573119895(120585 120579)

+ 119878119903120579120573119894

(120585 120579) V120573119895(120585 120579)]

10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(1198651)119895= minusint

120587

0

[119878119903119906120572119895

+ 119878119903120579V120572119895]10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(1198652)119895= minusint

120587

0

[119878119903119906120573119895

+ 119878119903120579V120573119895]10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

119894 = 1 2 2119899119903minus 1 119895 = 1 2 2119899

119903minus 1

(19)

6 Advances in Materials Science and Engineering

Table 2 The FEM and experimental results of unstable fractureenergy 119866

119906(Nm)

Specimen designation Experimental value FEMA1 6495 6133A2 6205 6325A3 6208 6222B1 6844 6682B2 5767 6437B3 6606 6592

4 Efficiency and Accuracy ofthe Present Method

To obtain parameters of fracture energy (119866119904and 119866

119906) for AIJs

of mass concrete two types of beams with sizes of 800 times

200 times 100mm and 1600 times 400 times 200mm were prepared forthree-point bendingmeasurementThenumerical results andlaboratory measurement were then compared to verify theanalytical model developed in this study as well as investigatethe accuracy of FEM analysis for prediction According tothe experimental data of RCC and (4)-(5) the values for119866119904and 119866

119906are shown in Figure 5 It can be seen that the

evaluated values of 119866119904and 119866

119906are independent of both size

and boundaryThe average values of119866119904and119866

119906for both series

are 1532Nm and 6482Nm respectively And these valuesare applied to calculate the cracking strength for AIJs in thefollowing discussions

41 FEM Simulation of Three-Point Bending Beams For theFEM simulation of three-point bending beams the tangentialstress distribution near the crack tip is illustrated in Figure 6Here the critical crack length for stable propagation andunstable propagation is 30mm and 50mm respectively Thenumerical results of unstable fracture energy 119866

119906for three-

point bending beams as well as its experimental resultsare present in Table 2 It can be seen that the predictiongiven by the present FEM is in a good agreement with theexperimental data which demonstrates that the FEManalysisis efficient and accurate for 119866

119906prediction

42 Results of Cracking Strength for AIJs in Mass ConcreteWhether AIJs in the early period ofmass concrete will inducecrack or not is important because there is no longer effect ifsetting of AIJs on the cross section is carried out after thermalstress is released As a result the ldquojustrdquo and ldquoperfectlyrdquocracking strength of AIJs in depositing concrete constructionperiod is a key parameter alongwith the increase of altitude ofmass concrete like RCC Taking into account representativealtitude of RCC the cross section embedded AIJs of massconcrete can be considered as penetrated cracks in infiniteplate for the simplification of hyper-finite element analysis(Figure 2)The typical local mesh for artificial-induced jointsis shown in Figure 7

The cracking strength for AIJs in mass concrete predictedby the present model is listed in Table 3 It can be found fromTable 3 that the results fromFEAare in consistencewith those

1489151014961540

1342

1556

Series A of specimensSeries B of specimens

(a) Values for 119866119904(Nm)

649562056208

6844

5767

6606

Series A of specimensSeries B of specimens

(b) Values for 119866119906(Nm)

Figure 5 Experimental data for 119866119904and 119866

119906of RCC three-point

bending beams series A 800times200times100mm series B 1600times400times

200mm

from analytical models indicating that the proposed modelcan be used to accurately assess the effects of AIJs on releasingthe early stress in mass concrete One can also see when therelative cracking strength of AIJs (ie 120590

119904119891119905and 120590max119891119905 for

2119886 = 03m 2119887 = 06m to 09m) reaches about 30ndash36 and55ndash58 separately the AIJs will be initiated to propagateand to be in unstable propagation process respectivelyWhilefor 2119886 = 06m 2119887 = 12m to 15m the above two values ofrelative cracking strength slightly decrease to about 23ndash28

Advances in Materials Science and Engineering 7

Table 3 Cracking strength for AIJs in mass concrete

Analytical model FEM Analytical model FEM

Cracking strength 2119886 = 03m2119887 = 06m 2119887 = 09m

120590max 1294 1339 1374 1365120590max119891119905 0552 0571 0586 0582120590119904

0788 0693 0837 0851120590119904119891119905

0336 0296 0357 0363

Cracking strength 2119886 = 06m2119887 = 12m 2119887 = 15m

120590max 1102 1293 1113 1019120590max119891119905 0470 0551 0475 0435120590119904

0557 0612 0578 0658120590119904119891119905

0237 0261 0247 0281

3

2

1

0minus40 minus20 0 20 40

Coh

esiv

e for

ce (M

Pa)

Propagation length (mm)

(a)

3

2

1

00 10 20 30 40 50

Coh

esiv

e for

ce (M

Pa)

minus50 minus40 minus30 minus20 minus10

minus1Propagation length (mm)

(b)

Figure 6 Tangential stress distribution near the crack tip (a)the subcritical point under maximum load and (b) an unstablepropagation point

and 43ndash55 These results can be considered as the basicfindings to assess the reduction of early stress of AIJs in massconcrete structure

5 Conclusions

The effect of setting artificial-induced joints (AIJs) during theconstruction period of mass concrete structures to releasethe early-stage thermal stress is theoretically and numericallyassessed in this study An analytical model which is relatedto the cracking strength of AIJs on the setting section ofmass concrete along with its hyper-finite element analysisin simplified plane pate is also proposed based on theconsideration on coupling influence of various factors such

Figure 7 Local mesh of hyper-FEM for AIJs (number of hyperele-ment 41 radius 0175m nodes 4420 and elements 8138)

as size and boundary effect The numerical results togetherwith the experimental data prove that the analytical modelsuggested in this study is efficient and accurate in assessingthe cracking strength of AIJs The basic findings can also beused to describe the effects of AIJs on ldquojustrdquo and ldquoperfectrdquoreleasing the early-age stress as well as further improve thedesign level of AIJs in the mass concrete

Conflict of Interests

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

Acknowledgments

This research was supported by the National NaturalScience Foundation of China (51278304) the NationalBasic Research Program (973 Program) of China (2011-CB013604) and the Technology Research and Develop-ment Program (basic research project) of Shenzhen China(JCYJ20120613174456685 and JCYJ20130329143859418) Theauthors greatly appreciate these supports

8 Advances in Materials Science and Engineering

References

[1] X G Zhang Y P Song and Z M Wu ldquoCalculation modelof equivalent strength for induced crack based on double-Kfracture theory and its optimizing setting in RCC arch damrdquoTransactions of Tianjin University vol 1 pp 8ndash15 2005

[2] J-H Ha Y S Jung and Y-G Cho ldquoThermal crack controlin mass concrete structure using an automated curing systemrdquoAutomation in Construction vol 45 pp 16ndash24 2014

[3] K D Hansen ldquoRoller compacted concrete a civil engineeringinnovation concreterdquo International Design amp Construction vol18 no 3 pp 25ndash31 1996

[4] Y Yuan and Z L Wan ldquoPrediction of cracking within early-ageconcrete due to thermal drying and creep behaviorrdquo Cementand Concrete Research vol 32 no 7 pp 1053ndash1059 2002

[5] N Liu and G-T Liu ldquoTime-dependent reliability assessmentfor mass concrete structuresrdquo Structural Safety vol 21 no 1 pp23ndash43 1999

[6] S H Chen P F Su and I Shahrour ldquoComposite elementalgorithm for the thermal analysis of mass concrete simulationof lift jointrdquo Finite Elements in Analysis and Design vol 47 no5 pp 536ndash542 2011

[7] YWu and R Luna ldquoNumerical implementation of temperatureand creep in mass concreterdquo Finite Elements in Analysis andDesign vol 37 no 2 pp 97ndash106 2001

[8] Z Yunchuana B Liangb Y Shengyuana and C Gutinga ldquoSim-ulation analysis of mass concrete temperature fieldrdquo ProcediaEarth and Planetary Science vol 5 pp 5ndash12 2012

[9] J Yang YHu Z Zuo F Jin andQ Li ldquoThermal analysis ofmassconcrete embedded with double-layer staggered heterogeneouscooling water pipesrdquo Applied Thermal Engineering vol 35 no1 pp 145ndash156 2012

[10] B I Yoshitake H Wong T Ishida and A Y Nassif ldquoThermalstress of high volume fly-ash (HVFA) concrete made withlimestone aggregaterdquo Construction and Building Materials vol71 pp 216ndash225 2014

[11] O Kayali and M Sharfuddin Ahmed ldquoAssessment of highvolume replacement fly ash concrete-concept of performanceindexrdquo Construction and Building Materials vol 39 pp 71ndash762013

[12] D Jeon Y Jun Y Jeong and J E Oh ldquoMicrostructuraland strength improvements through the use of Na

2CO3in a

cementless Ca(OH)2-activated class F fly ash systemrdquo Cement

and Concrete Research vol 67 pp 215ndash225 2015[13] J Tikkanen A Cwirzen and V Penttala ldquoEffects of mineral

powders on hydration process and hydration products innormal strength concreterdquoConstruction and BuildingMaterialsvol 72 pp 7ndash14 2014

[14] F LoMonte and P G Gambarova ldquoThermo-mechanical behav-ior of baritic concrete exposed to high temperaturerdquo Cement ampConcrete Composites vol 53 pp 305ndash315 2014

[15] X-ZWang Y-P Song J-K Dong and Z-Q Huang ldquoStudy onequivalent strength for crack directors of RCC arch dam basedon size effect rulerdquo Journal of Harbin Institute of Technology vol16 no 2 pp 149ndash153 2009

[16] K Duan X Z Hu and F H Wittmann ldquoBoundary effect onconcrete fracture and non-constant fracture energy distribu-tionrdquo Engineering Fracture Mechanics vol 70 no 16 pp 2257ndash2268 2003

[17] K Duan X-Z Hu and F H Wittmann ldquoSize effect onfracture resistance and fracture energy of concreterdquo Materialsand Structures vol 36 no 256 pp 73ndash80 2003

[18] Y Ballim ldquoA numerical model and associated calorimeter forpredicting temperature profiles in mass concreterdquo Cement ampConcrete Composites vol 26 no 6 pp 695ndash703 2004

[19] Y Li L Nie and B Wang ldquoA numerical simulation of thetemperature cracking propagation process when pouring massconcreterdquo Automation in Construction vol 37 pp 203ndash2102014

[20] I Chu Y Lee M N Amin B-S Jang and J-K Kim ldquoApplica-tion of a thermal stress device for the prediction of stresses dueto hydration heat in mass concrete structurerdquo Construction andBuilding Materials vol 45 pp 192ndash198 2013

[21] H W Reinhardt and S L Xu ldquoCrack extension resistancebased on the cohesive force in concreterdquo Engineering FractureMechanics vol 64 no 5 pp 563ndash587 1999

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

2 Advances in Materials Science and Engineering

Medium buried rubber waterstop

Caulking factis

(a) AIJs in super long underground sidewall

Sticking type of waterstop

Medium buried rubber waterstop

(b) AIJs in large basement slab

2a

2b2c

2d

The cross section AIJs embedded

120590120590

(c) AIJs in RCC

Figure 1 The detailed joint treatments of AIJs for different mass concrete

cross section embeddedAIJs and so forth is themost key andimportant parameter in the study of AIJs in mass concreteThis is because only the right value of cracking strength can beexpected to avoid random cracks in other partssections andthereby to ldquojustrdquo and ldquoperfectlyrdquo release temperature stress inmass concrete If the value of cracking strength is too smallor large the cross section embedded AIJs cannot be crackedfirstly or cannot completely reduce the early stress of otherpartssections In this situation the setting of AIJs to inhibitthe growth of random early-age cracks will to some extentbe limited Therefore it is of great importance to accuratelypredict the cracking strength of AIJs in evaluating the effectof controlling the early stress in mass concrete structuresUp to now the accurately analytical solution of crackingstrength to ldquojustrdquo and ldquoperfectlyrdquo release temperature stressin mass concrete is still not yet available although someexperimental investigation theoretical model and numericalsimulation have been carried out [15ndash17] This is becausethere are so many complex factors such as boundary ofcross section different size shape of AIJs concrete strengthand construction schedule which affect the cracking strength[16 17] Therefore it is necessary and of great importanceto illustrate the highly precise model and accurate FEA forthe prediction of cracking strength of AIJs so as to be able toevaluate its effect on releasing the early stress [18ndash20]

In this paper an analytical model of the cracking strengthof AIJs in RCC is studied and improved after considering thevarious factors such as size and boundary of AIJsThen a kindof hyper-finite element method along with the experimental

2a

2w

middot middot middot

Figure 2 Model of penetrated crack in infinite plate

data is present The results from the present model andnumerical simulation are discussed and further verified Themodel presented in this study for the cracking strength is asimple and useful tool to accurately evaluate the reductionof early-age stress The theoretical solution and FEA resultscould also be contributed to find the ldquojustrdquo and ldquoperfectrdquorelease of the temperature stress and to improve the designlevel of AIJs in mass concrete structure

2 Analytical Model of CrackingStrength for AIJs

The analytical solution of cracking strength for AIJs inFigure 1(c) can be simplified as a problem of penetratedcrack in an infinite plate due to the fact that the lengthof arch direction is often hundreds of meters (Figure 2)The vertical distance between two adjacent embedded gapcentres in Figure 2 is 2119908 Similar to the development of

Advances in Materials Science and Engineering 3

Table 1 The indexes for cracking process of AIJ

Fracture energy parameters Cracking strength parameters Crack length parameters Phase of process119866 lt 119866

119904120590 lt 120590

119904119886 = 1198860

Before cracking initiation119866119904le 119866 le 119866

119906120590119904le 120590 le 120590max 119886

0⩽ 119886 ⩽ 119886

119888Stable growth

119866 gt 119866119906

120590 gt 120590max 119886 gt 119886119888

Unstable propagation

other cracks in concretes the AIJs also include crackinginitiation stable growth and unstable propagation processfor mass concrete As assumed 120590 is the tensile strength alongthe arch direction and 120590

119904and 120590max represent initial and

unstable cracking strength respectively The propagation ofAIJs occurredwhen thermal stress away from theAIJs is up to120590119904 thereby weakening the cross sections Similarly AIJs start

to be unstably fractured as thermal stress comes to unstablecracking strength 120590max Apparently one can find that there isa stable propagation stage of the cracking of AIJs between 120590

119904

and 120590maxAs mentioned above the values of 120590

119904and 120590max are

influenced by many factors [16 17] In the present study thecoupling effect of these factors such as boundary of crosssection different size and concrete strength on the crackingstrength of AIJs can be expressed as the following equations[16 17]

120590 = 119860 (1205720) 119891119905(1 + 119861 (120572

0)

119886

119886lowast

infin

)

minus12

(1)

119861 (1205720) = [

119860 (1205720)119884(1205720)

112]

2

(2)

119886lowast

infin=

119864119866119865

12551205871198912

119905

(3)

where1205720is the ratio of initiation crack length to depth and119866

119865

is the fracture energy of concretematerials119891119905and119864 represent

the tensile strength and elastic modulus of RCC respectively119860(1205720) and 119884(120572

0) are the functions of 120572

0and can be varied

from different types of structureAlthough the fracture energy 119866

119865in (3) can be generally

used to describe the average amount of energy consumedduring the breaking down process of AIJs in mass concreteit cannot effectively express the respective consumption ofenergy during two important stages of cracking expansionnamely the stable growth and unstable propagation pro-cess [21] To characterize the energy release ratio in theabove different crack expanding periods 119866

119865is divided into

two fracture parameters initiation fracture energy 119866119904and

unstable fracture energy 119866119906 119866119904is associated with cracking

initiation stress 120590119904and initial crack length 120572

0 while 119866

119906is

related to maximum stress 120590max and critical effective cracklength 119886

119888 More information about the parameters is shown

in Table 1The solution of 119866

119906can be determined by experimental

test of the three-point bending beams [21]

119866119906=

31198752

max1198782

4119861211986331198641198811015840

(120572) (4)

120590(120590ft)

ft(10)

O ws(c1) w0(10)

w(ww0)

120590s(c2)

Figure 3 Bilinear cohesive force model of mass concrete

where 119861 and 119878 are the specimen thickness and loading spanrespectively 120572 = 119886

119888119863 is the ratio of the critical effective crack

length to beam depth119863119875max is themaximum load and119881(120572)

is a coefficient related to 120572

1198811015840

(120572) =2120572

(1 minus 120572)3[558 minus 1957120572 + 3682120572

2

minus 34941205723

+ 12771205724

] + (120572

1 minus 120572)

2

(minus1957 + 7364120572

minus 104821205722

+ 51081205723

)

(5)

If the contribution of energy due to cohesive forces isdefined as 119866

119888 the initiation fracture energy 119866

119904can also be

given as

119866119904= 119866119906minus 119866119888 (6)

where 119866119888can be obtained by integration method of cohesive

forces on the crack surfaceAccording to fracture theory the softening models of

concrete [21] can be simplified into the bilinear cohesive forcemodel to describe the cracking behaviors of mass concrete asillustrated in Figure 3 The expression is

119886119888= 1198860+ Δ119886lowast

119888= 1198860+

41199030

1198881+ 1198882

minus 1199030 (7)

In (7) Δ119886lowast119888is the effective crack propagation length w is the

crack opening displacement and 1199080is the critical value of

119908 1199030can be regarded as crevice genesis zone which can be

evaluated by the following expression

1199030=

119864119866119906

21205871198912

119905

(8)

The stress distribution of the cross section where AIJsembedded will be more affected by the plasticity of concrete

4 Advances in Materials Science and Engineering

CrackCOD

y

x

120590(r)R2

R1

120579

r

o

Figure 4 Crack-singular-analytical element loaded by the linearcohesive force

materials with the lager values of the fracture energy ofRCC As a result the initiation cracking strength 120590

119904and the

unstable cracking strength 120590max of AIJs in mass concrete canbe determined by the above values of 119866

119904and 119866

119906in (4) and

(6) The initiation cracking strength 120590119904can be given as

120590119904= (

119864119866119904

2119882)

12

[tan(120587

2

119886

119882)]

minus12

(9)

After the stable growth and unstable propagation stage ofAIJs the critical value of unstable cracking strength 120590max canalso be written as

120590max = (119864119866119906

2119882)

12

[tan(120587

2

119886119888

119882)]

minus12

(10)

3 The Hyper-Finite Element Analysis for AIJs

Among the fracturemodels of concretematerials proposed byresearchers the fictitious crack model is famous and widelyused It is especially suitable for FEM analysis of AIJs in massconcrete However there still exist many difficulties to obtainaccurate stress distribution on the vicinity of the crack tipeven though a refined mesh is used [21] An effective way tosolve the problem in this study is to apply a hyperelement onthe vicinity of AIJs tip based on the Hamiltonian theory ofelasticity Thereafter the cracking strength of FEM analysisfor AIJs inmass concrete is described when the hyperelementis combined with general finite elements

For bilinear cohesive force distribution in fictitious crackmodel shown in Figure 4 the propagation process of AIJsin mass concrete can be considered as propagation of elasticcracks which is a function of a cohesive distribution closeforce 120590(119909) along the propagation length Δ119886 The regionof cross section embedded AIJs is dispersed with a ringhyperelement surrounding the crack tip and also ordinaryfinite elements around the hyperelement as is illustrated inFigure 4 The equation of variation in the form of Hamilto-nian for the crack-ring-singular element loaded by the linearcohesive force can be expressed as

120575int

120587

0

int

ln1198772

ln1198771119878119903

120597119906

120597120585+ 119878119903120579

120597V120597120585

+ ]119878119903(119906 +

120597V120597120579

) + 119878119903120579(120597119906

120597120579minus V) +

119864

2(119906 +

120597V120597120579

)

2

minus1

2119864[(1 minus ]2) 1198782

119903+ 2 (1 + ]) 1198782

119903120579] 119889120585 119889120579

minus int

ln1198772

ln1198771[1198963exp (2120585) + 119896

4exp (120585)] ∙ V

120579=120587119889120585 = 0

(11)

where 119906 and V are the radial and tangential displacementrespectively 119902 = 119906 V119879 is its displacement vector 119878

119903= 119903120590119903

119878119903120579

= 119903120591119903120579 and 119901 = 119878

119903 119878119903120579119879 is the dual vector

The parameters 120577 1198963 1198964are obtained by

120585 = ln 119903

1198963= minus

(120590119904minus 120590 (119908))

(1198772minus 1198771)

1198964=

(120590119904minus 120590 (119908) 119877

2)

(1198772minus 1198771)

(12)

where 1198771= Δ119886119888and 119877

2= 119886 minus 119886

0

Assuming that there are 119899119903nodes on the hyperelement

and the unknown variables of each node are displacements of119906 V except for the node at 120579 = 0 which has only one variable119906 so the hyperelement has 2119899

119903minus 1 degrees of freedom If 120583

119894

is Eigen value and 120595119894= 119902119894 119901119894119879 is Eigen-function vector the

complete state function vector expansion is expressed as

V (120585 120579) = 119902 119901119879

= 119906 V 119878119903 119878119903120579119879

= 119888120572119894

2119899119903minus1

sum

119894=1

119906120572119894 V120572119894 119878119903120572119894

119878119903120579120572119894

119879

+ 119888120573119894

2119899119903minus1

sum

119894=1

119906120573119894 V120573119894 119878119903120573119894

119878119903120579120573119894

119879

+ V (120585 120579)

= 1198881205721V01+

2119899119903minus2

sum

119894=1

119888120572119894+1

120595120572119894exp (120583

119894120585) + 1198881205731V02

+

2119899119903minus2

sum

119894=1

119888120573119894+1

120595120573119894exp (minus120583

119894120585) + V (120585 120579)

(13)

Advances in Materials Science and Engineering 5

where 119888120572119894 119888120573119894

(119894 = 1 2 119871 2119899119903minus 1) are unknown generalized

constants and V(120585 120579) is a special solution

V (120585 120579) = V 119878119903 119878119903120579119879

= 1198964exp (120585)

1 minus ]119864

0 1 0

119879

minus 1198963exp (2120585)

sdot 1 minus 3]6119864

cos 120579 5 + ]6119864

sin 1205791

3cos 120579 1

3sin 120579

119879

(14)

If 119888 and 119889 are the generalized constant vector andthe nodal displacement vector respectively the relationshipbetween 119888 and 119889 is

(119889 minus 119889) = 119879 ∙ 119888 119888 = 119879minus1

∙ (119889 minus 119889) (15)

where 119888 = 1198881205721 1198881205722 119888

1205722119899119903minus1 1198881205731 1198881205732 119888

1205732119899119903minus1119879 119889 =

11990611 11990612 V12 119906

1119899119903 V1119899119903

11990621 11990622 V22 119906

2119899119903 V2119899119903

119879 119889 =

1198891 1198892119879 =

11 12 V12

1119899119903 V1119899119903

21 22 V22

2119899119903

V2119899119903

119879 and 119889 is the value vector of special solution at the

nodesThe components of the inverse of matrix 119879 are

119879 = [

11987911

11987912

11987921

11987922

] (16)

where

(11987911)119895119894= 119906120572119894

1003816100381610038161003816

120585=ln1198771120579=1205791=0

119895 = 1 119894 = 1 2 2119899119903minus 1

(11987911)119895119894= 119906120572119894

1003816100381610038161003816

120585=ln1198771120579=120579119896

119895 = 2119896 minus 2 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987911)119895119894= V120572119894

1003816100381610038161003816

120585=ln1198771120579=120579119896

119895 = 2119896 minus 1 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987912)119895119894= 119906120573119894

10038161003816100381610038161003816

120585=ln1198771120579=1205791=0

119895 = 1 119894 = 1 2 2119899119903minus 1

(11987912)119895119894= 119906120573119894

10038161003816100381610038161003816

120585=ln1198771120579=120579119896

119895 = 2119896 minus 2 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987912)119895119894= V120573119894

10038161003816100381610038161003816

120585=ln1198771120579=120579119896

119895 = 2119896 minus 1 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987921)119895119894= 119906120572119894

1003816100381610038161003816

120585=ln1198772120579=1205791=0

119895 = 1 119894 = 1 2 2119899119903minus 1

(11987921)119895119894= 119906120572119894

1003816100381610038161003816

120585=ln1198772120579=120579119896

119895 = 2119896 minus 2 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987921)119895119894= V120572119894

1003816100381610038161003816

120585=ln1198772120579=120579119896

119895 = 2119896 minus 1 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987922)119895119894= 119906120573119894

10038161003816100381610038161003816

120585=ln1198772120579=1205791=0

119895 = 1 119894 = 1 2 2119899119903minus 1

(11987922)119895119894= 119906120573119894

10038161003816100381610038161003816

120585=ln1198772120579=120579119896

119895 = 2119896 minus 2 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987922)119895119894= V120573119894

10038161003816100381610038161003816

120585=ln1198772120579=120579119896

119895 = 2119896 minus 1 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(17)

where 120579119896(119896 = 1 2 119871119899

119903) are tangential coordinates of node 120579

The solution can be carried out by iterating over (13) and(11) 119877

0and load vector 119865

0can be obtained by the integration

of partial stiffness matrix of hyperelement

1198770= 119879minus119879

∙ 119877119888∙ 119879minus1

119877119888= [

11987711

11987712

11987721

11987722

]

1198770= 119879minus119879

∙ (119865119888+ 119877119888∙ 119879minus1

∙ 119889) 119865119888= [1198651 1198652]119879

(18)

where 1198770and 119865

0are

(11987711)119895119894= int

120587

0

[119878119903120572119894

(120585 120579) 119906120572119895(120585 120579)

+ 119878119903120579120572119894

(120585 120579) V120572119895(120585 120579)]

10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(11987712)119895119894= int

120587

0

[119878119903120573119894

(120585 120579) 119906120572119895(120585 120579)

+ 119878119903120579120573119894

(120585 120579) V120572119895(120585 120579)]

10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(11987721)119895119894= int

120587

0

[119878119903120572119894

(120585 120579) 119906120573119895(120585 120579)

+ 119878119903120579120572119894

(120585 120579) V120573119895(120585 120579)]

10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(11987722)119895119894= int

120587

0

[119878119903120573119894

(120585 120579) 119906120573119895(120585 120579)

+ 119878119903120579120573119894

(120585 120579) V120573119895(120585 120579)]

10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(1198651)119895= minusint

120587

0

[119878119903119906120572119895

+ 119878119903120579V120572119895]10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(1198652)119895= minusint

120587

0

[119878119903119906120573119895

+ 119878119903120579V120573119895]10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

119894 = 1 2 2119899119903minus 1 119895 = 1 2 2119899

119903minus 1

(19)

6 Advances in Materials Science and Engineering

Table 2 The FEM and experimental results of unstable fractureenergy 119866

119906(Nm)

Specimen designation Experimental value FEMA1 6495 6133A2 6205 6325A3 6208 6222B1 6844 6682B2 5767 6437B3 6606 6592

4 Efficiency and Accuracy ofthe Present Method

To obtain parameters of fracture energy (119866119904and 119866

119906) for AIJs

of mass concrete two types of beams with sizes of 800 times

200 times 100mm and 1600 times 400 times 200mm were prepared forthree-point bendingmeasurementThenumerical results andlaboratory measurement were then compared to verify theanalytical model developed in this study as well as investigatethe accuracy of FEM analysis for prediction According tothe experimental data of RCC and (4)-(5) the values for119866119904and 119866

119906are shown in Figure 5 It can be seen that the

evaluated values of 119866119904and 119866

119906are independent of both size

and boundaryThe average values of119866119904and119866

119906for both series

are 1532Nm and 6482Nm respectively And these valuesare applied to calculate the cracking strength for AIJs in thefollowing discussions

41 FEM Simulation of Three-Point Bending Beams For theFEM simulation of three-point bending beams the tangentialstress distribution near the crack tip is illustrated in Figure 6Here the critical crack length for stable propagation andunstable propagation is 30mm and 50mm respectively Thenumerical results of unstable fracture energy 119866

119906for three-

point bending beams as well as its experimental resultsare present in Table 2 It can be seen that the predictiongiven by the present FEM is in a good agreement with theexperimental data which demonstrates that the FEManalysisis efficient and accurate for 119866

119906prediction

42 Results of Cracking Strength for AIJs in Mass ConcreteWhether AIJs in the early period ofmass concrete will inducecrack or not is important because there is no longer effect ifsetting of AIJs on the cross section is carried out after thermalstress is released As a result the ldquojustrdquo and ldquoperfectlyrdquocracking strength of AIJs in depositing concrete constructionperiod is a key parameter alongwith the increase of altitude ofmass concrete like RCC Taking into account representativealtitude of RCC the cross section embedded AIJs of massconcrete can be considered as penetrated cracks in infiniteplate for the simplification of hyper-finite element analysis(Figure 2)The typical local mesh for artificial-induced jointsis shown in Figure 7

The cracking strength for AIJs in mass concrete predictedby the present model is listed in Table 3 It can be found fromTable 3 that the results fromFEAare in consistencewith those

1489151014961540

1342

1556

Series A of specimensSeries B of specimens

(a) Values for 119866119904(Nm)

649562056208

6844

5767

6606

Series A of specimensSeries B of specimens

(b) Values for 119866119906(Nm)

Figure 5 Experimental data for 119866119904and 119866

119906of RCC three-point

bending beams series A 800times200times100mm series B 1600times400times

200mm

from analytical models indicating that the proposed modelcan be used to accurately assess the effects of AIJs on releasingthe early stress in mass concrete One can also see when therelative cracking strength of AIJs (ie 120590

119904119891119905and 120590max119891119905 for

2119886 = 03m 2119887 = 06m to 09m) reaches about 30ndash36 and55ndash58 separately the AIJs will be initiated to propagateand to be in unstable propagation process respectivelyWhilefor 2119886 = 06m 2119887 = 12m to 15m the above two values ofrelative cracking strength slightly decrease to about 23ndash28

Advances in Materials Science and Engineering 7

Table 3 Cracking strength for AIJs in mass concrete

Analytical model FEM Analytical model FEM

Cracking strength 2119886 = 03m2119887 = 06m 2119887 = 09m

120590max 1294 1339 1374 1365120590max119891119905 0552 0571 0586 0582120590119904

0788 0693 0837 0851120590119904119891119905

0336 0296 0357 0363

Cracking strength 2119886 = 06m2119887 = 12m 2119887 = 15m

120590max 1102 1293 1113 1019120590max119891119905 0470 0551 0475 0435120590119904

0557 0612 0578 0658120590119904119891119905

0237 0261 0247 0281

3

2

1

0minus40 minus20 0 20 40

Coh

esiv

e for

ce (M

Pa)

Propagation length (mm)

(a)

3

2

1

00 10 20 30 40 50

Coh

esiv

e for

ce (M

Pa)

minus50 minus40 minus30 minus20 minus10

minus1Propagation length (mm)

(b)

Figure 6 Tangential stress distribution near the crack tip (a)the subcritical point under maximum load and (b) an unstablepropagation point

and 43ndash55 These results can be considered as the basicfindings to assess the reduction of early stress of AIJs in massconcrete structure

5 Conclusions

The effect of setting artificial-induced joints (AIJs) during theconstruction period of mass concrete structures to releasethe early-stage thermal stress is theoretically and numericallyassessed in this study An analytical model which is relatedto the cracking strength of AIJs on the setting section ofmass concrete along with its hyper-finite element analysisin simplified plane pate is also proposed based on theconsideration on coupling influence of various factors such

Figure 7 Local mesh of hyper-FEM for AIJs (number of hyperele-ment 41 radius 0175m nodes 4420 and elements 8138)

as size and boundary effect The numerical results togetherwith the experimental data prove that the analytical modelsuggested in this study is efficient and accurate in assessingthe cracking strength of AIJs The basic findings can also beused to describe the effects of AIJs on ldquojustrdquo and ldquoperfectrdquoreleasing the early-age stress as well as further improve thedesign level of AIJs in the mass concrete

Conflict of Interests

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

Acknowledgments

This research was supported by the National NaturalScience Foundation of China (51278304) the NationalBasic Research Program (973 Program) of China (2011-CB013604) and the Technology Research and Develop-ment Program (basic research project) of Shenzhen China(JCYJ20120613174456685 and JCYJ20130329143859418) Theauthors greatly appreciate these supports

8 Advances in Materials Science and Engineering

References

[1] X G Zhang Y P Song and Z M Wu ldquoCalculation modelof equivalent strength for induced crack based on double-Kfracture theory and its optimizing setting in RCC arch damrdquoTransactions of Tianjin University vol 1 pp 8ndash15 2005

[2] J-H Ha Y S Jung and Y-G Cho ldquoThermal crack controlin mass concrete structure using an automated curing systemrdquoAutomation in Construction vol 45 pp 16ndash24 2014

[3] K D Hansen ldquoRoller compacted concrete a civil engineeringinnovation concreterdquo International Design amp Construction vol18 no 3 pp 25ndash31 1996

[4] Y Yuan and Z L Wan ldquoPrediction of cracking within early-ageconcrete due to thermal drying and creep behaviorrdquo Cementand Concrete Research vol 32 no 7 pp 1053ndash1059 2002

[5] N Liu and G-T Liu ldquoTime-dependent reliability assessmentfor mass concrete structuresrdquo Structural Safety vol 21 no 1 pp23ndash43 1999

[6] S H Chen P F Su and I Shahrour ldquoComposite elementalgorithm for the thermal analysis of mass concrete simulationof lift jointrdquo Finite Elements in Analysis and Design vol 47 no5 pp 536ndash542 2011

[7] YWu and R Luna ldquoNumerical implementation of temperatureand creep in mass concreterdquo Finite Elements in Analysis andDesign vol 37 no 2 pp 97ndash106 2001

[8] Z Yunchuana B Liangb Y Shengyuana and C Gutinga ldquoSim-ulation analysis of mass concrete temperature fieldrdquo ProcediaEarth and Planetary Science vol 5 pp 5ndash12 2012

[9] J Yang YHu Z Zuo F Jin andQ Li ldquoThermal analysis ofmassconcrete embedded with double-layer staggered heterogeneouscooling water pipesrdquo Applied Thermal Engineering vol 35 no1 pp 145ndash156 2012

[10] B I Yoshitake H Wong T Ishida and A Y Nassif ldquoThermalstress of high volume fly-ash (HVFA) concrete made withlimestone aggregaterdquo Construction and Building Materials vol71 pp 216ndash225 2014

[11] O Kayali and M Sharfuddin Ahmed ldquoAssessment of highvolume replacement fly ash concrete-concept of performanceindexrdquo Construction and Building Materials vol 39 pp 71ndash762013

[12] D Jeon Y Jun Y Jeong and J E Oh ldquoMicrostructuraland strength improvements through the use of Na

2CO3in a

cementless Ca(OH)2-activated class F fly ash systemrdquo Cement

and Concrete Research vol 67 pp 215ndash225 2015[13] J Tikkanen A Cwirzen and V Penttala ldquoEffects of mineral

powders on hydration process and hydration products innormal strength concreterdquoConstruction and BuildingMaterialsvol 72 pp 7ndash14 2014

[14] F LoMonte and P G Gambarova ldquoThermo-mechanical behav-ior of baritic concrete exposed to high temperaturerdquo Cement ampConcrete Composites vol 53 pp 305ndash315 2014

[15] X-ZWang Y-P Song J-K Dong and Z-Q Huang ldquoStudy onequivalent strength for crack directors of RCC arch dam basedon size effect rulerdquo Journal of Harbin Institute of Technology vol16 no 2 pp 149ndash153 2009

[16] K Duan X Z Hu and F H Wittmann ldquoBoundary effect onconcrete fracture and non-constant fracture energy distribu-tionrdquo Engineering Fracture Mechanics vol 70 no 16 pp 2257ndash2268 2003

[17] K Duan X-Z Hu and F H Wittmann ldquoSize effect onfracture resistance and fracture energy of concreterdquo Materialsand Structures vol 36 no 256 pp 73ndash80 2003

[18] Y Ballim ldquoA numerical model and associated calorimeter forpredicting temperature profiles in mass concreterdquo Cement ampConcrete Composites vol 26 no 6 pp 695ndash703 2004

[19] Y Li L Nie and B Wang ldquoA numerical simulation of thetemperature cracking propagation process when pouring massconcreterdquo Automation in Construction vol 37 pp 203ndash2102014

[20] I Chu Y Lee M N Amin B-S Jang and J-K Kim ldquoApplica-tion of a thermal stress device for the prediction of stresses dueto hydration heat in mass concrete structurerdquo Construction andBuilding Materials vol 45 pp 192ndash198 2013

[21] H W Reinhardt and S L Xu ldquoCrack extension resistancebased on the cohesive force in concreterdquo Engineering FractureMechanics vol 64 no 5 pp 563ndash587 1999

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 3

Table 1 The indexes for cracking process of AIJ

Fracture energy parameters Cracking strength parameters Crack length parameters Phase of process119866 lt 119866

119904120590 lt 120590

119904119886 = 1198860

Before cracking initiation119866119904le 119866 le 119866

119906120590119904le 120590 le 120590max 119886

0⩽ 119886 ⩽ 119886

119888Stable growth

119866 gt 119866119906

120590 gt 120590max 119886 gt 119886119888

Unstable propagation

other cracks in concretes the AIJs also include crackinginitiation stable growth and unstable propagation processfor mass concrete As assumed 120590 is the tensile strength alongthe arch direction and 120590

119904and 120590max represent initial and

unstable cracking strength respectively The propagation ofAIJs occurredwhen thermal stress away from theAIJs is up to120590119904 thereby weakening the cross sections Similarly AIJs start

to be unstably fractured as thermal stress comes to unstablecracking strength 120590max Apparently one can find that there isa stable propagation stage of the cracking of AIJs between 120590

119904

and 120590maxAs mentioned above the values of 120590

119904and 120590max are

influenced by many factors [16 17] In the present study thecoupling effect of these factors such as boundary of crosssection different size and concrete strength on the crackingstrength of AIJs can be expressed as the following equations[16 17]

120590 = 119860 (1205720) 119891119905(1 + 119861 (120572

0)

119886

119886lowast

infin

)

minus12

(1)

119861 (1205720) = [

119860 (1205720)119884(1205720)

112]

2

(2)

119886lowast

infin=

119864119866119865

12551205871198912

119905

(3)

where1205720is the ratio of initiation crack length to depth and119866

119865

is the fracture energy of concretematerials119891119905and119864 represent

the tensile strength and elastic modulus of RCC respectively119860(1205720) and 119884(120572

0) are the functions of 120572

0and can be varied

from different types of structureAlthough the fracture energy 119866

119865in (3) can be generally

used to describe the average amount of energy consumedduring the breaking down process of AIJs in mass concreteit cannot effectively express the respective consumption ofenergy during two important stages of cracking expansionnamely the stable growth and unstable propagation pro-cess [21] To characterize the energy release ratio in theabove different crack expanding periods 119866

119865is divided into

two fracture parameters initiation fracture energy 119866119904and

unstable fracture energy 119866119906 119866119904is associated with cracking

initiation stress 120590119904and initial crack length 120572

0 while 119866

119906is

related to maximum stress 120590max and critical effective cracklength 119886

119888 More information about the parameters is shown

in Table 1The solution of 119866

119906can be determined by experimental

test of the three-point bending beams [21]

119866119906=

31198752

max1198782

4119861211986331198641198811015840

(120572) (4)

120590(120590ft)

ft(10)

O ws(c1) w0(10)

w(ww0)

120590s(c2)

Figure 3 Bilinear cohesive force model of mass concrete

where 119861 and 119878 are the specimen thickness and loading spanrespectively 120572 = 119886

119888119863 is the ratio of the critical effective crack

length to beam depth119863119875max is themaximum load and119881(120572)

is a coefficient related to 120572

1198811015840

(120572) =2120572

(1 minus 120572)3[558 minus 1957120572 + 3682120572

2

minus 34941205723

+ 12771205724

] + (120572

1 minus 120572)

2

(minus1957 + 7364120572

minus 104821205722

+ 51081205723

)

(5)

If the contribution of energy due to cohesive forces isdefined as 119866

119888 the initiation fracture energy 119866

119904can also be

given as

119866119904= 119866119906minus 119866119888 (6)

where 119866119888can be obtained by integration method of cohesive

forces on the crack surfaceAccording to fracture theory the softening models of

concrete [21] can be simplified into the bilinear cohesive forcemodel to describe the cracking behaviors of mass concrete asillustrated in Figure 3 The expression is

119886119888= 1198860+ Δ119886lowast

119888= 1198860+

41199030

1198881+ 1198882

minus 1199030 (7)

In (7) Δ119886lowast119888is the effective crack propagation length w is the

crack opening displacement and 1199080is the critical value of

119908 1199030can be regarded as crevice genesis zone which can be

evaluated by the following expression

1199030=

119864119866119906

21205871198912

119905

(8)

The stress distribution of the cross section where AIJsembedded will be more affected by the plasticity of concrete

4 Advances in Materials Science and Engineering

CrackCOD

y

x

120590(r)R2

R1

120579

r

o

Figure 4 Crack-singular-analytical element loaded by the linearcohesive force

materials with the lager values of the fracture energy ofRCC As a result the initiation cracking strength 120590

119904and the

unstable cracking strength 120590max of AIJs in mass concrete canbe determined by the above values of 119866

119904and 119866

119906in (4) and

(6) The initiation cracking strength 120590119904can be given as

120590119904= (

119864119866119904

2119882)

12

[tan(120587

2

119886

119882)]

minus12

(9)

After the stable growth and unstable propagation stage ofAIJs the critical value of unstable cracking strength 120590max canalso be written as

120590max = (119864119866119906

2119882)

12

[tan(120587

2

119886119888

119882)]

minus12

(10)

3 The Hyper-Finite Element Analysis for AIJs

Among the fracturemodels of concretematerials proposed byresearchers the fictitious crack model is famous and widelyused It is especially suitable for FEM analysis of AIJs in massconcrete However there still exist many difficulties to obtainaccurate stress distribution on the vicinity of the crack tipeven though a refined mesh is used [21] An effective way tosolve the problem in this study is to apply a hyperelement onthe vicinity of AIJs tip based on the Hamiltonian theory ofelasticity Thereafter the cracking strength of FEM analysisfor AIJs inmass concrete is described when the hyperelementis combined with general finite elements

For bilinear cohesive force distribution in fictitious crackmodel shown in Figure 4 the propagation process of AIJsin mass concrete can be considered as propagation of elasticcracks which is a function of a cohesive distribution closeforce 120590(119909) along the propagation length Δ119886 The regionof cross section embedded AIJs is dispersed with a ringhyperelement surrounding the crack tip and also ordinaryfinite elements around the hyperelement as is illustrated inFigure 4 The equation of variation in the form of Hamilto-nian for the crack-ring-singular element loaded by the linearcohesive force can be expressed as

120575int

120587

0

int

ln1198772

ln1198771119878119903

120597119906

120597120585+ 119878119903120579

120597V120597120585

+ ]119878119903(119906 +

120597V120597120579

) + 119878119903120579(120597119906

120597120579minus V) +

119864

2(119906 +

120597V120597120579

)

2

minus1

2119864[(1 minus ]2) 1198782

119903+ 2 (1 + ]) 1198782

119903120579] 119889120585 119889120579

minus int

ln1198772

ln1198771[1198963exp (2120585) + 119896

4exp (120585)] ∙ V

120579=120587119889120585 = 0

(11)

where 119906 and V are the radial and tangential displacementrespectively 119902 = 119906 V119879 is its displacement vector 119878

119903= 119903120590119903

119878119903120579

= 119903120591119903120579 and 119901 = 119878

119903 119878119903120579119879 is the dual vector

The parameters 120577 1198963 1198964are obtained by

120585 = ln 119903

1198963= minus

(120590119904minus 120590 (119908))

(1198772minus 1198771)

1198964=

(120590119904minus 120590 (119908) 119877

2)

(1198772minus 1198771)

(12)

where 1198771= Δ119886119888and 119877

2= 119886 minus 119886

0

Assuming that there are 119899119903nodes on the hyperelement

and the unknown variables of each node are displacements of119906 V except for the node at 120579 = 0 which has only one variable119906 so the hyperelement has 2119899

119903minus 1 degrees of freedom If 120583

119894

is Eigen value and 120595119894= 119902119894 119901119894119879 is Eigen-function vector the

complete state function vector expansion is expressed as

V (120585 120579) = 119902 119901119879

= 119906 V 119878119903 119878119903120579119879

= 119888120572119894

2119899119903minus1

sum

119894=1

119906120572119894 V120572119894 119878119903120572119894

119878119903120579120572119894

119879

+ 119888120573119894

2119899119903minus1

sum

119894=1

119906120573119894 V120573119894 119878119903120573119894

119878119903120579120573119894

119879

+ V (120585 120579)

= 1198881205721V01+

2119899119903minus2

sum

119894=1

119888120572119894+1

120595120572119894exp (120583

119894120585) + 1198881205731V02

+

2119899119903minus2

sum

119894=1

119888120573119894+1

120595120573119894exp (minus120583

119894120585) + V (120585 120579)

(13)

Advances in Materials Science and Engineering 5

where 119888120572119894 119888120573119894

(119894 = 1 2 119871 2119899119903minus 1) are unknown generalized

constants and V(120585 120579) is a special solution

V (120585 120579) = V 119878119903 119878119903120579119879

= 1198964exp (120585)

1 minus ]119864

0 1 0

119879

minus 1198963exp (2120585)

sdot 1 minus 3]6119864

cos 120579 5 + ]6119864

sin 1205791

3cos 120579 1

3sin 120579

119879

(14)

If 119888 and 119889 are the generalized constant vector andthe nodal displacement vector respectively the relationshipbetween 119888 and 119889 is

(119889 minus 119889) = 119879 ∙ 119888 119888 = 119879minus1

∙ (119889 minus 119889) (15)

where 119888 = 1198881205721 1198881205722 119888

1205722119899119903minus1 1198881205731 1198881205732 119888

1205732119899119903minus1119879 119889 =

11990611 11990612 V12 119906

1119899119903 V1119899119903

11990621 11990622 V22 119906

2119899119903 V2119899119903

119879 119889 =

1198891 1198892119879 =

11 12 V12

1119899119903 V1119899119903

21 22 V22

2119899119903

V2119899119903

119879 and 119889 is the value vector of special solution at the

nodesThe components of the inverse of matrix 119879 are

119879 = [

11987911

11987912

11987921

11987922

] (16)

where

(11987911)119895119894= 119906120572119894

1003816100381610038161003816

120585=ln1198771120579=1205791=0

119895 = 1 119894 = 1 2 2119899119903minus 1

(11987911)119895119894= 119906120572119894

1003816100381610038161003816

120585=ln1198771120579=120579119896

119895 = 2119896 minus 2 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987911)119895119894= V120572119894

1003816100381610038161003816

120585=ln1198771120579=120579119896

119895 = 2119896 minus 1 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987912)119895119894= 119906120573119894

10038161003816100381610038161003816

120585=ln1198771120579=1205791=0

119895 = 1 119894 = 1 2 2119899119903minus 1

(11987912)119895119894= 119906120573119894

10038161003816100381610038161003816

120585=ln1198771120579=120579119896

119895 = 2119896 minus 2 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987912)119895119894= V120573119894

10038161003816100381610038161003816

120585=ln1198771120579=120579119896

119895 = 2119896 minus 1 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987921)119895119894= 119906120572119894

1003816100381610038161003816

120585=ln1198772120579=1205791=0

119895 = 1 119894 = 1 2 2119899119903minus 1

(11987921)119895119894= 119906120572119894

1003816100381610038161003816

120585=ln1198772120579=120579119896

119895 = 2119896 minus 2 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987921)119895119894= V120572119894

1003816100381610038161003816

120585=ln1198772120579=120579119896

119895 = 2119896 minus 1 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987922)119895119894= 119906120573119894

10038161003816100381610038161003816

120585=ln1198772120579=1205791=0

119895 = 1 119894 = 1 2 2119899119903minus 1

(11987922)119895119894= 119906120573119894

10038161003816100381610038161003816

120585=ln1198772120579=120579119896

119895 = 2119896 minus 2 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987922)119895119894= V120573119894

10038161003816100381610038161003816

120585=ln1198772120579=120579119896

119895 = 2119896 minus 1 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(17)

where 120579119896(119896 = 1 2 119871119899

119903) are tangential coordinates of node 120579

The solution can be carried out by iterating over (13) and(11) 119877

0and load vector 119865

0can be obtained by the integration

of partial stiffness matrix of hyperelement

1198770= 119879minus119879

∙ 119877119888∙ 119879minus1

119877119888= [

11987711

11987712

11987721

11987722

]

1198770= 119879minus119879

∙ (119865119888+ 119877119888∙ 119879minus1

∙ 119889) 119865119888= [1198651 1198652]119879

(18)

where 1198770and 119865

0are

(11987711)119895119894= int

120587

0

[119878119903120572119894

(120585 120579) 119906120572119895(120585 120579)

+ 119878119903120579120572119894

(120585 120579) V120572119895(120585 120579)]

10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(11987712)119895119894= int

120587

0

[119878119903120573119894

(120585 120579) 119906120572119895(120585 120579)

+ 119878119903120579120573119894

(120585 120579) V120572119895(120585 120579)]

10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(11987721)119895119894= int

120587

0

[119878119903120572119894

(120585 120579) 119906120573119895(120585 120579)

+ 119878119903120579120572119894

(120585 120579) V120573119895(120585 120579)]

10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(11987722)119895119894= int

120587

0

[119878119903120573119894

(120585 120579) 119906120573119895(120585 120579)

+ 119878119903120579120573119894

(120585 120579) V120573119895(120585 120579)]

10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(1198651)119895= minusint

120587

0

[119878119903119906120572119895

+ 119878119903120579V120572119895]10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(1198652)119895= minusint

120587

0

[119878119903119906120573119895

+ 119878119903120579V120573119895]10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

119894 = 1 2 2119899119903minus 1 119895 = 1 2 2119899

119903minus 1

(19)

6 Advances in Materials Science and Engineering

Table 2 The FEM and experimental results of unstable fractureenergy 119866

119906(Nm)

Specimen designation Experimental value FEMA1 6495 6133A2 6205 6325A3 6208 6222B1 6844 6682B2 5767 6437B3 6606 6592

4 Efficiency and Accuracy ofthe Present Method

To obtain parameters of fracture energy (119866119904and 119866

119906) for AIJs

of mass concrete two types of beams with sizes of 800 times

200 times 100mm and 1600 times 400 times 200mm were prepared forthree-point bendingmeasurementThenumerical results andlaboratory measurement were then compared to verify theanalytical model developed in this study as well as investigatethe accuracy of FEM analysis for prediction According tothe experimental data of RCC and (4)-(5) the values for119866119904and 119866

119906are shown in Figure 5 It can be seen that the

evaluated values of 119866119904and 119866

119906are independent of both size

and boundaryThe average values of119866119904and119866

119906for both series

are 1532Nm and 6482Nm respectively And these valuesare applied to calculate the cracking strength for AIJs in thefollowing discussions

41 FEM Simulation of Three-Point Bending Beams For theFEM simulation of three-point bending beams the tangentialstress distribution near the crack tip is illustrated in Figure 6Here the critical crack length for stable propagation andunstable propagation is 30mm and 50mm respectively Thenumerical results of unstable fracture energy 119866

119906for three-

point bending beams as well as its experimental resultsare present in Table 2 It can be seen that the predictiongiven by the present FEM is in a good agreement with theexperimental data which demonstrates that the FEManalysisis efficient and accurate for 119866

119906prediction

42 Results of Cracking Strength for AIJs in Mass ConcreteWhether AIJs in the early period ofmass concrete will inducecrack or not is important because there is no longer effect ifsetting of AIJs on the cross section is carried out after thermalstress is released As a result the ldquojustrdquo and ldquoperfectlyrdquocracking strength of AIJs in depositing concrete constructionperiod is a key parameter alongwith the increase of altitude ofmass concrete like RCC Taking into account representativealtitude of RCC the cross section embedded AIJs of massconcrete can be considered as penetrated cracks in infiniteplate for the simplification of hyper-finite element analysis(Figure 2)The typical local mesh for artificial-induced jointsis shown in Figure 7

The cracking strength for AIJs in mass concrete predictedby the present model is listed in Table 3 It can be found fromTable 3 that the results fromFEAare in consistencewith those

1489151014961540

1342

1556

Series A of specimensSeries B of specimens

(a) Values for 119866119904(Nm)

649562056208

6844

5767

6606

Series A of specimensSeries B of specimens

(b) Values for 119866119906(Nm)

Figure 5 Experimental data for 119866119904and 119866

119906of RCC three-point

bending beams series A 800times200times100mm series B 1600times400times

200mm

from analytical models indicating that the proposed modelcan be used to accurately assess the effects of AIJs on releasingthe early stress in mass concrete One can also see when therelative cracking strength of AIJs (ie 120590

119904119891119905and 120590max119891119905 for

2119886 = 03m 2119887 = 06m to 09m) reaches about 30ndash36 and55ndash58 separately the AIJs will be initiated to propagateand to be in unstable propagation process respectivelyWhilefor 2119886 = 06m 2119887 = 12m to 15m the above two values ofrelative cracking strength slightly decrease to about 23ndash28

Advances in Materials Science and Engineering 7

Table 3 Cracking strength for AIJs in mass concrete

Analytical model FEM Analytical model FEM

Cracking strength 2119886 = 03m2119887 = 06m 2119887 = 09m

120590max 1294 1339 1374 1365120590max119891119905 0552 0571 0586 0582120590119904

0788 0693 0837 0851120590119904119891119905

0336 0296 0357 0363

Cracking strength 2119886 = 06m2119887 = 12m 2119887 = 15m

120590max 1102 1293 1113 1019120590max119891119905 0470 0551 0475 0435120590119904

0557 0612 0578 0658120590119904119891119905

0237 0261 0247 0281

3

2

1

0minus40 minus20 0 20 40

Coh

esiv

e for

ce (M

Pa)

Propagation length (mm)

(a)

3

2

1

00 10 20 30 40 50

Coh

esiv

e for

ce (M

Pa)

minus50 minus40 minus30 minus20 minus10

minus1Propagation length (mm)

(b)

Figure 6 Tangential stress distribution near the crack tip (a)the subcritical point under maximum load and (b) an unstablepropagation point

and 43ndash55 These results can be considered as the basicfindings to assess the reduction of early stress of AIJs in massconcrete structure

5 Conclusions

The effect of setting artificial-induced joints (AIJs) during theconstruction period of mass concrete structures to releasethe early-stage thermal stress is theoretically and numericallyassessed in this study An analytical model which is relatedto the cracking strength of AIJs on the setting section ofmass concrete along with its hyper-finite element analysisin simplified plane pate is also proposed based on theconsideration on coupling influence of various factors such

Figure 7 Local mesh of hyper-FEM for AIJs (number of hyperele-ment 41 radius 0175m nodes 4420 and elements 8138)

as size and boundary effect The numerical results togetherwith the experimental data prove that the analytical modelsuggested in this study is efficient and accurate in assessingthe cracking strength of AIJs The basic findings can also beused to describe the effects of AIJs on ldquojustrdquo and ldquoperfectrdquoreleasing the early-age stress as well as further improve thedesign level of AIJs in the mass concrete

Conflict of Interests

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

Acknowledgments

This research was supported by the National NaturalScience Foundation of China (51278304) the NationalBasic Research Program (973 Program) of China (2011-CB013604) and the Technology Research and Develop-ment Program (basic research project) of Shenzhen China(JCYJ20120613174456685 and JCYJ20130329143859418) Theauthors greatly appreciate these supports

8 Advances in Materials Science and Engineering

References

[1] X G Zhang Y P Song and Z M Wu ldquoCalculation modelof equivalent strength for induced crack based on double-Kfracture theory and its optimizing setting in RCC arch damrdquoTransactions of Tianjin University vol 1 pp 8ndash15 2005

[2] J-H Ha Y S Jung and Y-G Cho ldquoThermal crack controlin mass concrete structure using an automated curing systemrdquoAutomation in Construction vol 45 pp 16ndash24 2014

[3] K D Hansen ldquoRoller compacted concrete a civil engineeringinnovation concreterdquo International Design amp Construction vol18 no 3 pp 25ndash31 1996

[4] Y Yuan and Z L Wan ldquoPrediction of cracking within early-ageconcrete due to thermal drying and creep behaviorrdquo Cementand Concrete Research vol 32 no 7 pp 1053ndash1059 2002

[5] N Liu and G-T Liu ldquoTime-dependent reliability assessmentfor mass concrete structuresrdquo Structural Safety vol 21 no 1 pp23ndash43 1999

[6] S H Chen P F Su and I Shahrour ldquoComposite elementalgorithm for the thermal analysis of mass concrete simulationof lift jointrdquo Finite Elements in Analysis and Design vol 47 no5 pp 536ndash542 2011

[7] YWu and R Luna ldquoNumerical implementation of temperatureand creep in mass concreterdquo Finite Elements in Analysis andDesign vol 37 no 2 pp 97ndash106 2001

[8] Z Yunchuana B Liangb Y Shengyuana and C Gutinga ldquoSim-ulation analysis of mass concrete temperature fieldrdquo ProcediaEarth and Planetary Science vol 5 pp 5ndash12 2012

[9] J Yang YHu Z Zuo F Jin andQ Li ldquoThermal analysis ofmassconcrete embedded with double-layer staggered heterogeneouscooling water pipesrdquo Applied Thermal Engineering vol 35 no1 pp 145ndash156 2012

[10] B I Yoshitake H Wong T Ishida and A Y Nassif ldquoThermalstress of high volume fly-ash (HVFA) concrete made withlimestone aggregaterdquo Construction and Building Materials vol71 pp 216ndash225 2014

[11] O Kayali and M Sharfuddin Ahmed ldquoAssessment of highvolume replacement fly ash concrete-concept of performanceindexrdquo Construction and Building Materials vol 39 pp 71ndash762013

[12] D Jeon Y Jun Y Jeong and J E Oh ldquoMicrostructuraland strength improvements through the use of Na

2CO3in a

cementless Ca(OH)2-activated class F fly ash systemrdquo Cement

and Concrete Research vol 67 pp 215ndash225 2015[13] J Tikkanen A Cwirzen and V Penttala ldquoEffects of mineral

powders on hydration process and hydration products innormal strength concreterdquoConstruction and BuildingMaterialsvol 72 pp 7ndash14 2014

[14] F LoMonte and P G Gambarova ldquoThermo-mechanical behav-ior of baritic concrete exposed to high temperaturerdquo Cement ampConcrete Composites vol 53 pp 305ndash315 2014

[15] X-ZWang Y-P Song J-K Dong and Z-Q Huang ldquoStudy onequivalent strength for crack directors of RCC arch dam basedon size effect rulerdquo Journal of Harbin Institute of Technology vol16 no 2 pp 149ndash153 2009

[16] K Duan X Z Hu and F H Wittmann ldquoBoundary effect onconcrete fracture and non-constant fracture energy distribu-tionrdquo Engineering Fracture Mechanics vol 70 no 16 pp 2257ndash2268 2003

[17] K Duan X-Z Hu and F H Wittmann ldquoSize effect onfracture resistance and fracture energy of concreterdquo Materialsand Structures vol 36 no 256 pp 73ndash80 2003

[18] Y Ballim ldquoA numerical model and associated calorimeter forpredicting temperature profiles in mass concreterdquo Cement ampConcrete Composites vol 26 no 6 pp 695ndash703 2004

[19] Y Li L Nie and B Wang ldquoA numerical simulation of thetemperature cracking propagation process when pouring massconcreterdquo Automation in Construction vol 37 pp 203ndash2102014

[20] I Chu Y Lee M N Amin B-S Jang and J-K Kim ldquoApplica-tion of a thermal stress device for the prediction of stresses dueto hydration heat in mass concrete structurerdquo Construction andBuilding Materials vol 45 pp 192ndash198 2013

[21] H W Reinhardt and S L Xu ldquoCrack extension resistancebased on the cohesive force in concreterdquo Engineering FractureMechanics vol 64 no 5 pp 563ndash587 1999

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

4 Advances in Materials Science and Engineering

CrackCOD

y

x

120590(r)R2

R1

120579

r

o

Figure 4 Crack-singular-analytical element loaded by the linearcohesive force

materials with the lager values of the fracture energy ofRCC As a result the initiation cracking strength 120590

119904and the

unstable cracking strength 120590max of AIJs in mass concrete canbe determined by the above values of 119866

119904and 119866

119906in (4) and

(6) The initiation cracking strength 120590119904can be given as

120590119904= (

119864119866119904

2119882)

12

[tan(120587

2

119886

119882)]

minus12

(9)

After the stable growth and unstable propagation stage ofAIJs the critical value of unstable cracking strength 120590max canalso be written as

120590max = (119864119866119906

2119882)

12

[tan(120587

2

119886119888

119882)]

minus12

(10)

3 The Hyper-Finite Element Analysis for AIJs

Among the fracturemodels of concretematerials proposed byresearchers the fictitious crack model is famous and widelyused It is especially suitable for FEM analysis of AIJs in massconcrete However there still exist many difficulties to obtainaccurate stress distribution on the vicinity of the crack tipeven though a refined mesh is used [21] An effective way tosolve the problem in this study is to apply a hyperelement onthe vicinity of AIJs tip based on the Hamiltonian theory ofelasticity Thereafter the cracking strength of FEM analysisfor AIJs inmass concrete is described when the hyperelementis combined with general finite elements

For bilinear cohesive force distribution in fictitious crackmodel shown in Figure 4 the propagation process of AIJsin mass concrete can be considered as propagation of elasticcracks which is a function of a cohesive distribution closeforce 120590(119909) along the propagation length Δ119886 The regionof cross section embedded AIJs is dispersed with a ringhyperelement surrounding the crack tip and also ordinaryfinite elements around the hyperelement as is illustrated inFigure 4 The equation of variation in the form of Hamilto-nian for the crack-ring-singular element loaded by the linearcohesive force can be expressed as

120575int

120587

0

int

ln1198772

ln1198771119878119903

120597119906

120597120585+ 119878119903120579

120597V120597120585

+ ]119878119903(119906 +

120597V120597120579

) + 119878119903120579(120597119906

120597120579minus V) +

119864

2(119906 +

120597V120597120579

)

2

minus1

2119864[(1 minus ]2) 1198782

119903+ 2 (1 + ]) 1198782

119903120579] 119889120585 119889120579

minus int

ln1198772

ln1198771[1198963exp (2120585) + 119896

4exp (120585)] ∙ V

120579=120587119889120585 = 0

(11)

where 119906 and V are the radial and tangential displacementrespectively 119902 = 119906 V119879 is its displacement vector 119878

119903= 119903120590119903

119878119903120579

= 119903120591119903120579 and 119901 = 119878

119903 119878119903120579119879 is the dual vector

The parameters 120577 1198963 1198964are obtained by

120585 = ln 119903

1198963= minus

(120590119904minus 120590 (119908))

(1198772minus 1198771)

1198964=

(120590119904minus 120590 (119908) 119877

2)

(1198772minus 1198771)

(12)

where 1198771= Δ119886119888and 119877

2= 119886 minus 119886

0

Assuming that there are 119899119903nodes on the hyperelement

and the unknown variables of each node are displacements of119906 V except for the node at 120579 = 0 which has only one variable119906 so the hyperelement has 2119899

119903minus 1 degrees of freedom If 120583

119894

is Eigen value and 120595119894= 119902119894 119901119894119879 is Eigen-function vector the

complete state function vector expansion is expressed as

V (120585 120579) = 119902 119901119879

= 119906 V 119878119903 119878119903120579119879

= 119888120572119894

2119899119903minus1

sum

119894=1

119906120572119894 V120572119894 119878119903120572119894

119878119903120579120572119894

119879

+ 119888120573119894

2119899119903minus1

sum

119894=1

119906120573119894 V120573119894 119878119903120573119894

119878119903120579120573119894

119879

+ V (120585 120579)

= 1198881205721V01+

2119899119903minus2

sum

119894=1

119888120572119894+1

120595120572119894exp (120583

119894120585) + 1198881205731V02

+

2119899119903minus2

sum

119894=1

119888120573119894+1

120595120573119894exp (minus120583

119894120585) + V (120585 120579)

(13)

Advances in Materials Science and Engineering 5

where 119888120572119894 119888120573119894

(119894 = 1 2 119871 2119899119903minus 1) are unknown generalized

constants and V(120585 120579) is a special solution

V (120585 120579) = V 119878119903 119878119903120579119879

= 1198964exp (120585)

1 minus ]119864

0 1 0

119879

minus 1198963exp (2120585)

sdot 1 minus 3]6119864

cos 120579 5 + ]6119864

sin 1205791

3cos 120579 1

3sin 120579

119879

(14)

If 119888 and 119889 are the generalized constant vector andthe nodal displacement vector respectively the relationshipbetween 119888 and 119889 is

(119889 minus 119889) = 119879 ∙ 119888 119888 = 119879minus1

∙ (119889 minus 119889) (15)

where 119888 = 1198881205721 1198881205722 119888

1205722119899119903minus1 1198881205731 1198881205732 119888

1205732119899119903minus1119879 119889 =

11990611 11990612 V12 119906

1119899119903 V1119899119903

11990621 11990622 V22 119906

2119899119903 V2119899119903

119879 119889 =

1198891 1198892119879 =

11 12 V12

1119899119903 V1119899119903

21 22 V22

2119899119903

V2119899119903

119879 and 119889 is the value vector of special solution at the

nodesThe components of the inverse of matrix 119879 are

119879 = [

11987911

11987912

11987921

11987922

] (16)

where

(11987911)119895119894= 119906120572119894

1003816100381610038161003816

120585=ln1198771120579=1205791=0

119895 = 1 119894 = 1 2 2119899119903minus 1

(11987911)119895119894= 119906120572119894

1003816100381610038161003816

120585=ln1198771120579=120579119896

119895 = 2119896 minus 2 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987911)119895119894= V120572119894

1003816100381610038161003816

120585=ln1198771120579=120579119896

119895 = 2119896 minus 1 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987912)119895119894= 119906120573119894

10038161003816100381610038161003816

120585=ln1198771120579=1205791=0

119895 = 1 119894 = 1 2 2119899119903minus 1

(11987912)119895119894= 119906120573119894

10038161003816100381610038161003816

120585=ln1198771120579=120579119896

119895 = 2119896 minus 2 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987912)119895119894= V120573119894

10038161003816100381610038161003816

120585=ln1198771120579=120579119896

119895 = 2119896 minus 1 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987921)119895119894= 119906120572119894

1003816100381610038161003816

120585=ln1198772120579=1205791=0

119895 = 1 119894 = 1 2 2119899119903minus 1

(11987921)119895119894= 119906120572119894

1003816100381610038161003816

120585=ln1198772120579=120579119896

119895 = 2119896 minus 2 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987921)119895119894= V120572119894

1003816100381610038161003816

120585=ln1198772120579=120579119896

119895 = 2119896 minus 1 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987922)119895119894= 119906120573119894

10038161003816100381610038161003816

120585=ln1198772120579=1205791=0

119895 = 1 119894 = 1 2 2119899119903minus 1

(11987922)119895119894= 119906120573119894

10038161003816100381610038161003816

120585=ln1198772120579=120579119896

119895 = 2119896 minus 2 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987922)119895119894= V120573119894

10038161003816100381610038161003816

120585=ln1198772120579=120579119896

119895 = 2119896 minus 1 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(17)

where 120579119896(119896 = 1 2 119871119899

119903) are tangential coordinates of node 120579

The solution can be carried out by iterating over (13) and(11) 119877

0and load vector 119865

0can be obtained by the integration

of partial stiffness matrix of hyperelement

1198770= 119879minus119879

∙ 119877119888∙ 119879minus1

119877119888= [

11987711

11987712

11987721

11987722

]

1198770= 119879minus119879

∙ (119865119888+ 119877119888∙ 119879minus1

∙ 119889) 119865119888= [1198651 1198652]119879

(18)

where 1198770and 119865

0are

(11987711)119895119894= int

120587

0

[119878119903120572119894

(120585 120579) 119906120572119895(120585 120579)

+ 119878119903120579120572119894

(120585 120579) V120572119895(120585 120579)]

10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(11987712)119895119894= int

120587

0

[119878119903120573119894

(120585 120579) 119906120572119895(120585 120579)

+ 119878119903120579120573119894

(120585 120579) V120572119895(120585 120579)]

10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(11987721)119895119894= int

120587

0

[119878119903120572119894

(120585 120579) 119906120573119895(120585 120579)

+ 119878119903120579120572119894

(120585 120579) V120573119895(120585 120579)]

10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(11987722)119895119894= int

120587

0

[119878119903120573119894

(120585 120579) 119906120573119895(120585 120579)

+ 119878119903120579120573119894

(120585 120579) V120573119895(120585 120579)]

10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(1198651)119895= minusint

120587

0

[119878119903119906120572119895

+ 119878119903120579V120572119895]10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(1198652)119895= minusint

120587

0

[119878119903119906120573119895

+ 119878119903120579V120573119895]10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

119894 = 1 2 2119899119903minus 1 119895 = 1 2 2119899

119903minus 1

(19)

6 Advances in Materials Science and Engineering

Table 2 The FEM and experimental results of unstable fractureenergy 119866

119906(Nm)

Specimen designation Experimental value FEMA1 6495 6133A2 6205 6325A3 6208 6222B1 6844 6682B2 5767 6437B3 6606 6592

4 Efficiency and Accuracy ofthe Present Method

To obtain parameters of fracture energy (119866119904and 119866

119906) for AIJs

of mass concrete two types of beams with sizes of 800 times

200 times 100mm and 1600 times 400 times 200mm were prepared forthree-point bendingmeasurementThenumerical results andlaboratory measurement were then compared to verify theanalytical model developed in this study as well as investigatethe accuracy of FEM analysis for prediction According tothe experimental data of RCC and (4)-(5) the values for119866119904and 119866

119906are shown in Figure 5 It can be seen that the

evaluated values of 119866119904and 119866

119906are independent of both size

and boundaryThe average values of119866119904and119866

119906for both series

are 1532Nm and 6482Nm respectively And these valuesare applied to calculate the cracking strength for AIJs in thefollowing discussions

41 FEM Simulation of Three-Point Bending Beams For theFEM simulation of three-point bending beams the tangentialstress distribution near the crack tip is illustrated in Figure 6Here the critical crack length for stable propagation andunstable propagation is 30mm and 50mm respectively Thenumerical results of unstable fracture energy 119866

119906for three-

point bending beams as well as its experimental resultsare present in Table 2 It can be seen that the predictiongiven by the present FEM is in a good agreement with theexperimental data which demonstrates that the FEManalysisis efficient and accurate for 119866

119906prediction

42 Results of Cracking Strength for AIJs in Mass ConcreteWhether AIJs in the early period ofmass concrete will inducecrack or not is important because there is no longer effect ifsetting of AIJs on the cross section is carried out after thermalstress is released As a result the ldquojustrdquo and ldquoperfectlyrdquocracking strength of AIJs in depositing concrete constructionperiod is a key parameter alongwith the increase of altitude ofmass concrete like RCC Taking into account representativealtitude of RCC the cross section embedded AIJs of massconcrete can be considered as penetrated cracks in infiniteplate for the simplification of hyper-finite element analysis(Figure 2)The typical local mesh for artificial-induced jointsis shown in Figure 7

The cracking strength for AIJs in mass concrete predictedby the present model is listed in Table 3 It can be found fromTable 3 that the results fromFEAare in consistencewith those

1489151014961540

1342

1556

Series A of specimensSeries B of specimens

(a) Values for 119866119904(Nm)

649562056208

6844

5767

6606

Series A of specimensSeries B of specimens

(b) Values for 119866119906(Nm)

Figure 5 Experimental data for 119866119904and 119866

119906of RCC three-point

bending beams series A 800times200times100mm series B 1600times400times

200mm

from analytical models indicating that the proposed modelcan be used to accurately assess the effects of AIJs on releasingthe early stress in mass concrete One can also see when therelative cracking strength of AIJs (ie 120590

119904119891119905and 120590max119891119905 for

2119886 = 03m 2119887 = 06m to 09m) reaches about 30ndash36 and55ndash58 separately the AIJs will be initiated to propagateand to be in unstable propagation process respectivelyWhilefor 2119886 = 06m 2119887 = 12m to 15m the above two values ofrelative cracking strength slightly decrease to about 23ndash28

Advances in Materials Science and Engineering 7

Table 3 Cracking strength for AIJs in mass concrete

Analytical model FEM Analytical model FEM

Cracking strength 2119886 = 03m2119887 = 06m 2119887 = 09m

120590max 1294 1339 1374 1365120590max119891119905 0552 0571 0586 0582120590119904

0788 0693 0837 0851120590119904119891119905

0336 0296 0357 0363

Cracking strength 2119886 = 06m2119887 = 12m 2119887 = 15m

120590max 1102 1293 1113 1019120590max119891119905 0470 0551 0475 0435120590119904

0557 0612 0578 0658120590119904119891119905

0237 0261 0247 0281

3

2

1

0minus40 minus20 0 20 40

Coh

esiv

e for

ce (M

Pa)

Propagation length (mm)

(a)

3

2

1

00 10 20 30 40 50

Coh

esiv

e for

ce (M

Pa)

minus50 minus40 minus30 minus20 minus10

minus1Propagation length (mm)

(b)

Figure 6 Tangential stress distribution near the crack tip (a)the subcritical point under maximum load and (b) an unstablepropagation point

and 43ndash55 These results can be considered as the basicfindings to assess the reduction of early stress of AIJs in massconcrete structure

5 Conclusions

The effect of setting artificial-induced joints (AIJs) during theconstruction period of mass concrete structures to releasethe early-stage thermal stress is theoretically and numericallyassessed in this study An analytical model which is relatedto the cracking strength of AIJs on the setting section ofmass concrete along with its hyper-finite element analysisin simplified plane pate is also proposed based on theconsideration on coupling influence of various factors such

Figure 7 Local mesh of hyper-FEM for AIJs (number of hyperele-ment 41 radius 0175m nodes 4420 and elements 8138)

as size and boundary effect The numerical results togetherwith the experimental data prove that the analytical modelsuggested in this study is efficient and accurate in assessingthe cracking strength of AIJs The basic findings can also beused to describe the effects of AIJs on ldquojustrdquo and ldquoperfectrdquoreleasing the early-age stress as well as further improve thedesign level of AIJs in the mass concrete

Conflict of Interests

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

Acknowledgments

This research was supported by the National NaturalScience Foundation of China (51278304) the NationalBasic Research Program (973 Program) of China (2011-CB013604) and the Technology Research and Develop-ment Program (basic research project) of Shenzhen China(JCYJ20120613174456685 and JCYJ20130329143859418) Theauthors greatly appreciate these supports

8 Advances in Materials Science and Engineering

References

[1] X G Zhang Y P Song and Z M Wu ldquoCalculation modelof equivalent strength for induced crack based on double-Kfracture theory and its optimizing setting in RCC arch damrdquoTransactions of Tianjin University vol 1 pp 8ndash15 2005

[2] J-H Ha Y S Jung and Y-G Cho ldquoThermal crack controlin mass concrete structure using an automated curing systemrdquoAutomation in Construction vol 45 pp 16ndash24 2014

[3] K D Hansen ldquoRoller compacted concrete a civil engineeringinnovation concreterdquo International Design amp Construction vol18 no 3 pp 25ndash31 1996

[4] Y Yuan and Z L Wan ldquoPrediction of cracking within early-ageconcrete due to thermal drying and creep behaviorrdquo Cementand Concrete Research vol 32 no 7 pp 1053ndash1059 2002

[5] N Liu and G-T Liu ldquoTime-dependent reliability assessmentfor mass concrete structuresrdquo Structural Safety vol 21 no 1 pp23ndash43 1999

[6] S H Chen P F Su and I Shahrour ldquoComposite elementalgorithm for the thermal analysis of mass concrete simulationof lift jointrdquo Finite Elements in Analysis and Design vol 47 no5 pp 536ndash542 2011

[7] YWu and R Luna ldquoNumerical implementation of temperatureand creep in mass concreterdquo Finite Elements in Analysis andDesign vol 37 no 2 pp 97ndash106 2001

[8] Z Yunchuana B Liangb Y Shengyuana and C Gutinga ldquoSim-ulation analysis of mass concrete temperature fieldrdquo ProcediaEarth and Planetary Science vol 5 pp 5ndash12 2012

[9] J Yang YHu Z Zuo F Jin andQ Li ldquoThermal analysis ofmassconcrete embedded with double-layer staggered heterogeneouscooling water pipesrdquo Applied Thermal Engineering vol 35 no1 pp 145ndash156 2012

[10] B I Yoshitake H Wong T Ishida and A Y Nassif ldquoThermalstress of high volume fly-ash (HVFA) concrete made withlimestone aggregaterdquo Construction and Building Materials vol71 pp 216ndash225 2014

[11] O Kayali and M Sharfuddin Ahmed ldquoAssessment of highvolume replacement fly ash concrete-concept of performanceindexrdquo Construction and Building Materials vol 39 pp 71ndash762013

[12] D Jeon Y Jun Y Jeong and J E Oh ldquoMicrostructuraland strength improvements through the use of Na

2CO3in a

cementless Ca(OH)2-activated class F fly ash systemrdquo Cement

and Concrete Research vol 67 pp 215ndash225 2015[13] J Tikkanen A Cwirzen and V Penttala ldquoEffects of mineral

powders on hydration process and hydration products innormal strength concreterdquoConstruction and BuildingMaterialsvol 72 pp 7ndash14 2014

[14] F LoMonte and P G Gambarova ldquoThermo-mechanical behav-ior of baritic concrete exposed to high temperaturerdquo Cement ampConcrete Composites vol 53 pp 305ndash315 2014

[15] X-ZWang Y-P Song J-K Dong and Z-Q Huang ldquoStudy onequivalent strength for crack directors of RCC arch dam basedon size effect rulerdquo Journal of Harbin Institute of Technology vol16 no 2 pp 149ndash153 2009

[16] K Duan X Z Hu and F H Wittmann ldquoBoundary effect onconcrete fracture and non-constant fracture energy distribu-tionrdquo Engineering Fracture Mechanics vol 70 no 16 pp 2257ndash2268 2003

[17] K Duan X-Z Hu and F H Wittmann ldquoSize effect onfracture resistance and fracture energy of concreterdquo Materialsand Structures vol 36 no 256 pp 73ndash80 2003

[18] Y Ballim ldquoA numerical model and associated calorimeter forpredicting temperature profiles in mass concreterdquo Cement ampConcrete Composites vol 26 no 6 pp 695ndash703 2004

[19] Y Li L Nie and B Wang ldquoA numerical simulation of thetemperature cracking propagation process when pouring massconcreterdquo Automation in Construction vol 37 pp 203ndash2102014

[20] I Chu Y Lee M N Amin B-S Jang and J-K Kim ldquoApplica-tion of a thermal stress device for the prediction of stresses dueto hydration heat in mass concrete structurerdquo Construction andBuilding Materials vol 45 pp 192ndash198 2013

[21] H W Reinhardt and S L Xu ldquoCrack extension resistancebased on the cohesive force in concreterdquo Engineering FractureMechanics vol 64 no 5 pp 563ndash587 1999

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 5

where 119888120572119894 119888120573119894

(119894 = 1 2 119871 2119899119903minus 1) are unknown generalized

constants and V(120585 120579) is a special solution

V (120585 120579) = V 119878119903 119878119903120579119879

= 1198964exp (120585)

1 minus ]119864

0 1 0

119879

minus 1198963exp (2120585)

sdot 1 minus 3]6119864

cos 120579 5 + ]6119864

sin 1205791

3cos 120579 1

3sin 120579

119879

(14)

If 119888 and 119889 are the generalized constant vector andthe nodal displacement vector respectively the relationshipbetween 119888 and 119889 is

(119889 minus 119889) = 119879 ∙ 119888 119888 = 119879minus1

∙ (119889 minus 119889) (15)

where 119888 = 1198881205721 1198881205722 119888

1205722119899119903minus1 1198881205731 1198881205732 119888

1205732119899119903minus1119879 119889 =

11990611 11990612 V12 119906

1119899119903 V1119899119903

11990621 11990622 V22 119906

2119899119903 V2119899119903

119879 119889 =

1198891 1198892119879 =

11 12 V12

1119899119903 V1119899119903

21 22 V22

2119899119903

V2119899119903

119879 and 119889 is the value vector of special solution at the

nodesThe components of the inverse of matrix 119879 are

119879 = [

11987911

11987912

11987921

11987922

] (16)

where

(11987911)119895119894= 119906120572119894

1003816100381610038161003816

120585=ln1198771120579=1205791=0

119895 = 1 119894 = 1 2 2119899119903minus 1

(11987911)119895119894= 119906120572119894

1003816100381610038161003816

120585=ln1198771120579=120579119896

119895 = 2119896 minus 2 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987911)119895119894= V120572119894

1003816100381610038161003816

120585=ln1198771120579=120579119896

119895 = 2119896 minus 1 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987912)119895119894= 119906120573119894

10038161003816100381610038161003816

120585=ln1198771120579=1205791=0

119895 = 1 119894 = 1 2 2119899119903minus 1

(11987912)119895119894= 119906120573119894

10038161003816100381610038161003816

120585=ln1198771120579=120579119896

119895 = 2119896 minus 2 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987912)119895119894= V120573119894

10038161003816100381610038161003816

120585=ln1198771120579=120579119896

119895 = 2119896 minus 1 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987921)119895119894= 119906120572119894

1003816100381610038161003816

120585=ln1198772120579=1205791=0

119895 = 1 119894 = 1 2 2119899119903minus 1

(11987921)119895119894= 119906120572119894

1003816100381610038161003816

120585=ln1198772120579=120579119896

119895 = 2119896 minus 2 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987921)119895119894= V120572119894

1003816100381610038161003816

120585=ln1198772120579=120579119896

119895 = 2119896 minus 1 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987922)119895119894= 119906120573119894

10038161003816100381610038161003816

120585=ln1198772120579=1205791=0

119895 = 1 119894 = 1 2 2119899119903minus 1

(11987922)119895119894= 119906120573119894

10038161003816100381610038161003816

120585=ln1198772120579=120579119896

119895 = 2119896 minus 2 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(11987922)119895119894= V120573119894

10038161003816100381610038161003816

120585=ln1198772120579=120579119896

119895 = 2119896 minus 1 119896 = 2 3 119899119903 119894 = 1 2 2119899

119903minus 1

(17)

where 120579119896(119896 = 1 2 119871119899

119903) are tangential coordinates of node 120579

The solution can be carried out by iterating over (13) and(11) 119877

0and load vector 119865

0can be obtained by the integration

of partial stiffness matrix of hyperelement

1198770= 119879minus119879

∙ 119877119888∙ 119879minus1

119877119888= [

11987711

11987712

11987721

11987722

]

1198770= 119879minus119879

∙ (119865119888+ 119877119888∙ 119879minus1

∙ 119889) 119865119888= [1198651 1198652]119879

(18)

where 1198770and 119865

0are

(11987711)119895119894= int

120587

0

[119878119903120572119894

(120585 120579) 119906120572119895(120585 120579)

+ 119878119903120579120572119894

(120585 120579) V120572119895(120585 120579)]

10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(11987712)119895119894= int

120587

0

[119878119903120573119894

(120585 120579) 119906120572119895(120585 120579)

+ 119878119903120579120573119894

(120585 120579) V120572119895(120585 120579)]

10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(11987721)119895119894= int

120587

0

[119878119903120572119894

(120585 120579) 119906120573119895(120585 120579)

+ 119878119903120579120572119894

(120585 120579) V120573119895(120585 120579)]

10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(11987722)119895119894= int

120587

0

[119878119903120573119894

(120585 120579) 119906120573119895(120585 120579)

+ 119878119903120579120573119894

(120585 120579) V120573119895(120585 120579)]

10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(1198651)119895= minusint

120587

0

[119878119903119906120572119895

+ 119878119903120579V120572119895]10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

(1198652)119895= minusint

120587

0

[119878119903119906120573119895

+ 119878119903120579V120573119895]10038161003816100381610038161003816

120585=ln1198772120585=ln1198771

119889120579

119894 = 1 2 2119899119903minus 1 119895 = 1 2 2119899

119903minus 1

(19)

6 Advances in Materials Science and Engineering

Table 2 The FEM and experimental results of unstable fractureenergy 119866

119906(Nm)

Specimen designation Experimental value FEMA1 6495 6133A2 6205 6325A3 6208 6222B1 6844 6682B2 5767 6437B3 6606 6592

4 Efficiency and Accuracy ofthe Present Method

To obtain parameters of fracture energy (119866119904and 119866

119906) for AIJs

of mass concrete two types of beams with sizes of 800 times

200 times 100mm and 1600 times 400 times 200mm were prepared forthree-point bendingmeasurementThenumerical results andlaboratory measurement were then compared to verify theanalytical model developed in this study as well as investigatethe accuracy of FEM analysis for prediction According tothe experimental data of RCC and (4)-(5) the values for119866119904and 119866

119906are shown in Figure 5 It can be seen that the

evaluated values of 119866119904and 119866

119906are independent of both size

and boundaryThe average values of119866119904and119866

119906for both series

are 1532Nm and 6482Nm respectively And these valuesare applied to calculate the cracking strength for AIJs in thefollowing discussions

41 FEM Simulation of Three-Point Bending Beams For theFEM simulation of three-point bending beams the tangentialstress distribution near the crack tip is illustrated in Figure 6Here the critical crack length for stable propagation andunstable propagation is 30mm and 50mm respectively Thenumerical results of unstable fracture energy 119866

119906for three-

point bending beams as well as its experimental resultsare present in Table 2 It can be seen that the predictiongiven by the present FEM is in a good agreement with theexperimental data which demonstrates that the FEManalysisis efficient and accurate for 119866

119906prediction

42 Results of Cracking Strength for AIJs in Mass ConcreteWhether AIJs in the early period ofmass concrete will inducecrack or not is important because there is no longer effect ifsetting of AIJs on the cross section is carried out after thermalstress is released As a result the ldquojustrdquo and ldquoperfectlyrdquocracking strength of AIJs in depositing concrete constructionperiod is a key parameter alongwith the increase of altitude ofmass concrete like RCC Taking into account representativealtitude of RCC the cross section embedded AIJs of massconcrete can be considered as penetrated cracks in infiniteplate for the simplification of hyper-finite element analysis(Figure 2)The typical local mesh for artificial-induced jointsis shown in Figure 7

The cracking strength for AIJs in mass concrete predictedby the present model is listed in Table 3 It can be found fromTable 3 that the results fromFEAare in consistencewith those

1489151014961540

1342

1556

Series A of specimensSeries B of specimens

(a) Values for 119866119904(Nm)

649562056208

6844

5767

6606

Series A of specimensSeries B of specimens

(b) Values for 119866119906(Nm)

Figure 5 Experimental data for 119866119904and 119866

119906of RCC three-point

bending beams series A 800times200times100mm series B 1600times400times

200mm

from analytical models indicating that the proposed modelcan be used to accurately assess the effects of AIJs on releasingthe early stress in mass concrete One can also see when therelative cracking strength of AIJs (ie 120590

119904119891119905and 120590max119891119905 for

2119886 = 03m 2119887 = 06m to 09m) reaches about 30ndash36 and55ndash58 separately the AIJs will be initiated to propagateand to be in unstable propagation process respectivelyWhilefor 2119886 = 06m 2119887 = 12m to 15m the above two values ofrelative cracking strength slightly decrease to about 23ndash28

Advances in Materials Science and Engineering 7

Table 3 Cracking strength for AIJs in mass concrete

Analytical model FEM Analytical model FEM

Cracking strength 2119886 = 03m2119887 = 06m 2119887 = 09m

120590max 1294 1339 1374 1365120590max119891119905 0552 0571 0586 0582120590119904

0788 0693 0837 0851120590119904119891119905

0336 0296 0357 0363

Cracking strength 2119886 = 06m2119887 = 12m 2119887 = 15m

120590max 1102 1293 1113 1019120590max119891119905 0470 0551 0475 0435120590119904

0557 0612 0578 0658120590119904119891119905

0237 0261 0247 0281

3

2

1

0minus40 minus20 0 20 40

Coh

esiv

e for

ce (M

Pa)

Propagation length (mm)

(a)

3

2

1

00 10 20 30 40 50

Coh

esiv

e for

ce (M

Pa)

minus50 minus40 minus30 minus20 minus10

minus1Propagation length (mm)

(b)

Figure 6 Tangential stress distribution near the crack tip (a)the subcritical point under maximum load and (b) an unstablepropagation point

and 43ndash55 These results can be considered as the basicfindings to assess the reduction of early stress of AIJs in massconcrete structure

5 Conclusions

The effect of setting artificial-induced joints (AIJs) during theconstruction period of mass concrete structures to releasethe early-stage thermal stress is theoretically and numericallyassessed in this study An analytical model which is relatedto the cracking strength of AIJs on the setting section ofmass concrete along with its hyper-finite element analysisin simplified plane pate is also proposed based on theconsideration on coupling influence of various factors such

Figure 7 Local mesh of hyper-FEM for AIJs (number of hyperele-ment 41 radius 0175m nodes 4420 and elements 8138)

as size and boundary effect The numerical results togetherwith the experimental data prove that the analytical modelsuggested in this study is efficient and accurate in assessingthe cracking strength of AIJs The basic findings can also beused to describe the effects of AIJs on ldquojustrdquo and ldquoperfectrdquoreleasing the early-age stress as well as further improve thedesign level of AIJs in the mass concrete

Conflict of Interests

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

Acknowledgments

This research was supported by the National NaturalScience Foundation of China (51278304) the NationalBasic Research Program (973 Program) of China (2011-CB013604) and the Technology Research and Develop-ment Program (basic research project) of Shenzhen China(JCYJ20120613174456685 and JCYJ20130329143859418) Theauthors greatly appreciate these supports

8 Advances in Materials Science and Engineering

References

[1] X G Zhang Y P Song and Z M Wu ldquoCalculation modelof equivalent strength for induced crack based on double-Kfracture theory and its optimizing setting in RCC arch damrdquoTransactions of Tianjin University vol 1 pp 8ndash15 2005

[2] J-H Ha Y S Jung and Y-G Cho ldquoThermal crack controlin mass concrete structure using an automated curing systemrdquoAutomation in Construction vol 45 pp 16ndash24 2014

[3] K D Hansen ldquoRoller compacted concrete a civil engineeringinnovation concreterdquo International Design amp Construction vol18 no 3 pp 25ndash31 1996

[4] Y Yuan and Z L Wan ldquoPrediction of cracking within early-ageconcrete due to thermal drying and creep behaviorrdquo Cementand Concrete Research vol 32 no 7 pp 1053ndash1059 2002

[5] N Liu and G-T Liu ldquoTime-dependent reliability assessmentfor mass concrete structuresrdquo Structural Safety vol 21 no 1 pp23ndash43 1999

[6] S H Chen P F Su and I Shahrour ldquoComposite elementalgorithm for the thermal analysis of mass concrete simulationof lift jointrdquo Finite Elements in Analysis and Design vol 47 no5 pp 536ndash542 2011

[7] YWu and R Luna ldquoNumerical implementation of temperatureand creep in mass concreterdquo Finite Elements in Analysis andDesign vol 37 no 2 pp 97ndash106 2001

[8] Z Yunchuana B Liangb Y Shengyuana and C Gutinga ldquoSim-ulation analysis of mass concrete temperature fieldrdquo ProcediaEarth and Planetary Science vol 5 pp 5ndash12 2012

[9] J Yang YHu Z Zuo F Jin andQ Li ldquoThermal analysis ofmassconcrete embedded with double-layer staggered heterogeneouscooling water pipesrdquo Applied Thermal Engineering vol 35 no1 pp 145ndash156 2012

[10] B I Yoshitake H Wong T Ishida and A Y Nassif ldquoThermalstress of high volume fly-ash (HVFA) concrete made withlimestone aggregaterdquo Construction and Building Materials vol71 pp 216ndash225 2014

[11] O Kayali and M Sharfuddin Ahmed ldquoAssessment of highvolume replacement fly ash concrete-concept of performanceindexrdquo Construction and Building Materials vol 39 pp 71ndash762013

[12] D Jeon Y Jun Y Jeong and J E Oh ldquoMicrostructuraland strength improvements through the use of Na

2CO3in a

cementless Ca(OH)2-activated class F fly ash systemrdquo Cement

and Concrete Research vol 67 pp 215ndash225 2015[13] J Tikkanen A Cwirzen and V Penttala ldquoEffects of mineral

powders on hydration process and hydration products innormal strength concreterdquoConstruction and BuildingMaterialsvol 72 pp 7ndash14 2014

[14] F LoMonte and P G Gambarova ldquoThermo-mechanical behav-ior of baritic concrete exposed to high temperaturerdquo Cement ampConcrete Composites vol 53 pp 305ndash315 2014

[15] X-ZWang Y-P Song J-K Dong and Z-Q Huang ldquoStudy onequivalent strength for crack directors of RCC arch dam basedon size effect rulerdquo Journal of Harbin Institute of Technology vol16 no 2 pp 149ndash153 2009

[16] K Duan X Z Hu and F H Wittmann ldquoBoundary effect onconcrete fracture and non-constant fracture energy distribu-tionrdquo Engineering Fracture Mechanics vol 70 no 16 pp 2257ndash2268 2003

[17] K Duan X-Z Hu and F H Wittmann ldquoSize effect onfracture resistance and fracture energy of concreterdquo Materialsand Structures vol 36 no 256 pp 73ndash80 2003

[18] Y Ballim ldquoA numerical model and associated calorimeter forpredicting temperature profiles in mass concreterdquo Cement ampConcrete Composites vol 26 no 6 pp 695ndash703 2004

[19] Y Li L Nie and B Wang ldquoA numerical simulation of thetemperature cracking propagation process when pouring massconcreterdquo Automation in Construction vol 37 pp 203ndash2102014

[20] I Chu Y Lee M N Amin B-S Jang and J-K Kim ldquoApplica-tion of a thermal stress device for the prediction of stresses dueto hydration heat in mass concrete structurerdquo Construction andBuilding Materials vol 45 pp 192ndash198 2013

[21] H W Reinhardt and S L Xu ldquoCrack extension resistancebased on the cohesive force in concreterdquo Engineering FractureMechanics vol 64 no 5 pp 563ndash587 1999

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

6 Advances in Materials Science and Engineering

Table 2 The FEM and experimental results of unstable fractureenergy 119866

119906(Nm)

Specimen designation Experimental value FEMA1 6495 6133A2 6205 6325A3 6208 6222B1 6844 6682B2 5767 6437B3 6606 6592

4 Efficiency and Accuracy ofthe Present Method

To obtain parameters of fracture energy (119866119904and 119866

119906) for AIJs

of mass concrete two types of beams with sizes of 800 times

200 times 100mm and 1600 times 400 times 200mm were prepared forthree-point bendingmeasurementThenumerical results andlaboratory measurement were then compared to verify theanalytical model developed in this study as well as investigatethe accuracy of FEM analysis for prediction According tothe experimental data of RCC and (4)-(5) the values for119866119904and 119866

119906are shown in Figure 5 It can be seen that the

evaluated values of 119866119904and 119866

119906are independent of both size

and boundaryThe average values of119866119904and119866

119906for both series

are 1532Nm and 6482Nm respectively And these valuesare applied to calculate the cracking strength for AIJs in thefollowing discussions

41 FEM Simulation of Three-Point Bending Beams For theFEM simulation of three-point bending beams the tangentialstress distribution near the crack tip is illustrated in Figure 6Here the critical crack length for stable propagation andunstable propagation is 30mm and 50mm respectively Thenumerical results of unstable fracture energy 119866

119906for three-

point bending beams as well as its experimental resultsare present in Table 2 It can be seen that the predictiongiven by the present FEM is in a good agreement with theexperimental data which demonstrates that the FEManalysisis efficient and accurate for 119866

119906prediction

42 Results of Cracking Strength for AIJs in Mass ConcreteWhether AIJs in the early period ofmass concrete will inducecrack or not is important because there is no longer effect ifsetting of AIJs on the cross section is carried out after thermalstress is released As a result the ldquojustrdquo and ldquoperfectlyrdquocracking strength of AIJs in depositing concrete constructionperiod is a key parameter alongwith the increase of altitude ofmass concrete like RCC Taking into account representativealtitude of RCC the cross section embedded AIJs of massconcrete can be considered as penetrated cracks in infiniteplate for the simplification of hyper-finite element analysis(Figure 2)The typical local mesh for artificial-induced jointsis shown in Figure 7

The cracking strength for AIJs in mass concrete predictedby the present model is listed in Table 3 It can be found fromTable 3 that the results fromFEAare in consistencewith those

1489151014961540

1342

1556

Series A of specimensSeries B of specimens

(a) Values for 119866119904(Nm)

649562056208

6844

5767

6606

Series A of specimensSeries B of specimens

(b) Values for 119866119906(Nm)

Figure 5 Experimental data for 119866119904and 119866

119906of RCC three-point

bending beams series A 800times200times100mm series B 1600times400times

200mm

from analytical models indicating that the proposed modelcan be used to accurately assess the effects of AIJs on releasingthe early stress in mass concrete One can also see when therelative cracking strength of AIJs (ie 120590

119904119891119905and 120590max119891119905 for

2119886 = 03m 2119887 = 06m to 09m) reaches about 30ndash36 and55ndash58 separately the AIJs will be initiated to propagateand to be in unstable propagation process respectivelyWhilefor 2119886 = 06m 2119887 = 12m to 15m the above two values ofrelative cracking strength slightly decrease to about 23ndash28

Advances in Materials Science and Engineering 7

Table 3 Cracking strength for AIJs in mass concrete

Analytical model FEM Analytical model FEM

Cracking strength 2119886 = 03m2119887 = 06m 2119887 = 09m

120590max 1294 1339 1374 1365120590max119891119905 0552 0571 0586 0582120590119904

0788 0693 0837 0851120590119904119891119905

0336 0296 0357 0363

Cracking strength 2119886 = 06m2119887 = 12m 2119887 = 15m

120590max 1102 1293 1113 1019120590max119891119905 0470 0551 0475 0435120590119904

0557 0612 0578 0658120590119904119891119905

0237 0261 0247 0281

3

2

1

0minus40 minus20 0 20 40

Coh

esiv

e for

ce (M

Pa)

Propagation length (mm)

(a)

3

2

1

00 10 20 30 40 50

Coh

esiv

e for

ce (M

Pa)

minus50 minus40 minus30 minus20 minus10

minus1Propagation length (mm)

(b)

Figure 6 Tangential stress distribution near the crack tip (a)the subcritical point under maximum load and (b) an unstablepropagation point

and 43ndash55 These results can be considered as the basicfindings to assess the reduction of early stress of AIJs in massconcrete structure

5 Conclusions

The effect of setting artificial-induced joints (AIJs) during theconstruction period of mass concrete structures to releasethe early-stage thermal stress is theoretically and numericallyassessed in this study An analytical model which is relatedto the cracking strength of AIJs on the setting section ofmass concrete along with its hyper-finite element analysisin simplified plane pate is also proposed based on theconsideration on coupling influence of various factors such

Figure 7 Local mesh of hyper-FEM for AIJs (number of hyperele-ment 41 radius 0175m nodes 4420 and elements 8138)

as size and boundary effect The numerical results togetherwith the experimental data prove that the analytical modelsuggested in this study is efficient and accurate in assessingthe cracking strength of AIJs The basic findings can also beused to describe the effects of AIJs on ldquojustrdquo and ldquoperfectrdquoreleasing the early-age stress as well as further improve thedesign level of AIJs in the mass concrete

Conflict of Interests

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

Acknowledgments

This research was supported by the National NaturalScience Foundation of China (51278304) the NationalBasic Research Program (973 Program) of China (2011-CB013604) and the Technology Research and Develop-ment Program (basic research project) of Shenzhen China(JCYJ20120613174456685 and JCYJ20130329143859418) Theauthors greatly appreciate these supports

8 Advances in Materials Science and Engineering

References

[1] X G Zhang Y P Song and Z M Wu ldquoCalculation modelof equivalent strength for induced crack based on double-Kfracture theory and its optimizing setting in RCC arch damrdquoTransactions of Tianjin University vol 1 pp 8ndash15 2005

[2] J-H Ha Y S Jung and Y-G Cho ldquoThermal crack controlin mass concrete structure using an automated curing systemrdquoAutomation in Construction vol 45 pp 16ndash24 2014

[3] K D Hansen ldquoRoller compacted concrete a civil engineeringinnovation concreterdquo International Design amp Construction vol18 no 3 pp 25ndash31 1996

[4] Y Yuan and Z L Wan ldquoPrediction of cracking within early-ageconcrete due to thermal drying and creep behaviorrdquo Cementand Concrete Research vol 32 no 7 pp 1053ndash1059 2002

[5] N Liu and G-T Liu ldquoTime-dependent reliability assessmentfor mass concrete structuresrdquo Structural Safety vol 21 no 1 pp23ndash43 1999

[6] S H Chen P F Su and I Shahrour ldquoComposite elementalgorithm for the thermal analysis of mass concrete simulationof lift jointrdquo Finite Elements in Analysis and Design vol 47 no5 pp 536ndash542 2011

[7] YWu and R Luna ldquoNumerical implementation of temperatureand creep in mass concreterdquo Finite Elements in Analysis andDesign vol 37 no 2 pp 97ndash106 2001

[8] Z Yunchuana B Liangb Y Shengyuana and C Gutinga ldquoSim-ulation analysis of mass concrete temperature fieldrdquo ProcediaEarth and Planetary Science vol 5 pp 5ndash12 2012

[9] J Yang YHu Z Zuo F Jin andQ Li ldquoThermal analysis ofmassconcrete embedded with double-layer staggered heterogeneouscooling water pipesrdquo Applied Thermal Engineering vol 35 no1 pp 145ndash156 2012

[10] B I Yoshitake H Wong T Ishida and A Y Nassif ldquoThermalstress of high volume fly-ash (HVFA) concrete made withlimestone aggregaterdquo Construction and Building Materials vol71 pp 216ndash225 2014

[11] O Kayali and M Sharfuddin Ahmed ldquoAssessment of highvolume replacement fly ash concrete-concept of performanceindexrdquo Construction and Building Materials vol 39 pp 71ndash762013

[12] D Jeon Y Jun Y Jeong and J E Oh ldquoMicrostructuraland strength improvements through the use of Na

2CO3in a

cementless Ca(OH)2-activated class F fly ash systemrdquo Cement

and Concrete Research vol 67 pp 215ndash225 2015[13] J Tikkanen A Cwirzen and V Penttala ldquoEffects of mineral

powders on hydration process and hydration products innormal strength concreterdquoConstruction and BuildingMaterialsvol 72 pp 7ndash14 2014

[14] F LoMonte and P G Gambarova ldquoThermo-mechanical behav-ior of baritic concrete exposed to high temperaturerdquo Cement ampConcrete Composites vol 53 pp 305ndash315 2014

[15] X-ZWang Y-P Song J-K Dong and Z-Q Huang ldquoStudy onequivalent strength for crack directors of RCC arch dam basedon size effect rulerdquo Journal of Harbin Institute of Technology vol16 no 2 pp 149ndash153 2009

[16] K Duan X Z Hu and F H Wittmann ldquoBoundary effect onconcrete fracture and non-constant fracture energy distribu-tionrdquo Engineering Fracture Mechanics vol 70 no 16 pp 2257ndash2268 2003

[17] K Duan X-Z Hu and F H Wittmann ldquoSize effect onfracture resistance and fracture energy of concreterdquo Materialsand Structures vol 36 no 256 pp 73ndash80 2003

[18] Y Ballim ldquoA numerical model and associated calorimeter forpredicting temperature profiles in mass concreterdquo Cement ampConcrete Composites vol 26 no 6 pp 695ndash703 2004

[19] Y Li L Nie and B Wang ldquoA numerical simulation of thetemperature cracking propagation process when pouring massconcreterdquo Automation in Construction vol 37 pp 203ndash2102014

[20] I Chu Y Lee M N Amin B-S Jang and J-K Kim ldquoApplica-tion of a thermal stress device for the prediction of stresses dueto hydration heat in mass concrete structurerdquo Construction andBuilding Materials vol 45 pp 192ndash198 2013

[21] H W Reinhardt and S L Xu ldquoCrack extension resistancebased on the cohesive force in concreterdquo Engineering FractureMechanics vol 64 no 5 pp 563ndash587 1999

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 7

Table 3 Cracking strength for AIJs in mass concrete

Analytical model FEM Analytical model FEM

Cracking strength 2119886 = 03m2119887 = 06m 2119887 = 09m

120590max 1294 1339 1374 1365120590max119891119905 0552 0571 0586 0582120590119904

0788 0693 0837 0851120590119904119891119905

0336 0296 0357 0363

Cracking strength 2119886 = 06m2119887 = 12m 2119887 = 15m

120590max 1102 1293 1113 1019120590max119891119905 0470 0551 0475 0435120590119904

0557 0612 0578 0658120590119904119891119905

0237 0261 0247 0281

3

2

1

0minus40 minus20 0 20 40

Coh

esiv

e for

ce (M

Pa)

Propagation length (mm)

(a)

3

2

1

00 10 20 30 40 50

Coh

esiv

e for

ce (M

Pa)

minus50 minus40 minus30 minus20 minus10

minus1Propagation length (mm)

(b)

Figure 6 Tangential stress distribution near the crack tip (a)the subcritical point under maximum load and (b) an unstablepropagation point

and 43ndash55 These results can be considered as the basicfindings to assess the reduction of early stress of AIJs in massconcrete structure

5 Conclusions

The effect of setting artificial-induced joints (AIJs) during theconstruction period of mass concrete structures to releasethe early-stage thermal stress is theoretically and numericallyassessed in this study An analytical model which is relatedto the cracking strength of AIJs on the setting section ofmass concrete along with its hyper-finite element analysisin simplified plane pate is also proposed based on theconsideration on coupling influence of various factors such

Figure 7 Local mesh of hyper-FEM for AIJs (number of hyperele-ment 41 radius 0175m nodes 4420 and elements 8138)

as size and boundary effect The numerical results togetherwith the experimental data prove that the analytical modelsuggested in this study is efficient and accurate in assessingthe cracking strength of AIJs The basic findings can also beused to describe the effects of AIJs on ldquojustrdquo and ldquoperfectrdquoreleasing the early-age stress as well as further improve thedesign level of AIJs in the mass concrete

Conflict of Interests

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

Acknowledgments

This research was supported by the National NaturalScience Foundation of China (51278304) the NationalBasic Research Program (973 Program) of China (2011-CB013604) and the Technology Research and Develop-ment Program (basic research project) of Shenzhen China(JCYJ20120613174456685 and JCYJ20130329143859418) Theauthors greatly appreciate these supports

8 Advances in Materials Science and Engineering

References

[1] X G Zhang Y P Song and Z M Wu ldquoCalculation modelof equivalent strength for induced crack based on double-Kfracture theory and its optimizing setting in RCC arch damrdquoTransactions of Tianjin University vol 1 pp 8ndash15 2005

[2] J-H Ha Y S Jung and Y-G Cho ldquoThermal crack controlin mass concrete structure using an automated curing systemrdquoAutomation in Construction vol 45 pp 16ndash24 2014

[3] K D Hansen ldquoRoller compacted concrete a civil engineeringinnovation concreterdquo International Design amp Construction vol18 no 3 pp 25ndash31 1996

[4] Y Yuan and Z L Wan ldquoPrediction of cracking within early-ageconcrete due to thermal drying and creep behaviorrdquo Cementand Concrete Research vol 32 no 7 pp 1053ndash1059 2002

[5] N Liu and G-T Liu ldquoTime-dependent reliability assessmentfor mass concrete structuresrdquo Structural Safety vol 21 no 1 pp23ndash43 1999

[6] S H Chen P F Su and I Shahrour ldquoComposite elementalgorithm for the thermal analysis of mass concrete simulationof lift jointrdquo Finite Elements in Analysis and Design vol 47 no5 pp 536ndash542 2011

[7] YWu and R Luna ldquoNumerical implementation of temperatureand creep in mass concreterdquo Finite Elements in Analysis andDesign vol 37 no 2 pp 97ndash106 2001

[8] Z Yunchuana B Liangb Y Shengyuana and C Gutinga ldquoSim-ulation analysis of mass concrete temperature fieldrdquo ProcediaEarth and Planetary Science vol 5 pp 5ndash12 2012

[9] J Yang YHu Z Zuo F Jin andQ Li ldquoThermal analysis ofmassconcrete embedded with double-layer staggered heterogeneouscooling water pipesrdquo Applied Thermal Engineering vol 35 no1 pp 145ndash156 2012

[10] B I Yoshitake H Wong T Ishida and A Y Nassif ldquoThermalstress of high volume fly-ash (HVFA) concrete made withlimestone aggregaterdquo Construction and Building Materials vol71 pp 216ndash225 2014

[11] O Kayali and M Sharfuddin Ahmed ldquoAssessment of highvolume replacement fly ash concrete-concept of performanceindexrdquo Construction and Building Materials vol 39 pp 71ndash762013

[12] D Jeon Y Jun Y Jeong and J E Oh ldquoMicrostructuraland strength improvements through the use of Na

2CO3in a

cementless Ca(OH)2-activated class F fly ash systemrdquo Cement

and Concrete Research vol 67 pp 215ndash225 2015[13] J Tikkanen A Cwirzen and V Penttala ldquoEffects of mineral

powders on hydration process and hydration products innormal strength concreterdquoConstruction and BuildingMaterialsvol 72 pp 7ndash14 2014

[14] F LoMonte and P G Gambarova ldquoThermo-mechanical behav-ior of baritic concrete exposed to high temperaturerdquo Cement ampConcrete Composites vol 53 pp 305ndash315 2014

[15] X-ZWang Y-P Song J-K Dong and Z-Q Huang ldquoStudy onequivalent strength for crack directors of RCC arch dam basedon size effect rulerdquo Journal of Harbin Institute of Technology vol16 no 2 pp 149ndash153 2009

[16] K Duan X Z Hu and F H Wittmann ldquoBoundary effect onconcrete fracture and non-constant fracture energy distribu-tionrdquo Engineering Fracture Mechanics vol 70 no 16 pp 2257ndash2268 2003

[17] K Duan X-Z Hu and F H Wittmann ldquoSize effect onfracture resistance and fracture energy of concreterdquo Materialsand Structures vol 36 no 256 pp 73ndash80 2003

[18] Y Ballim ldquoA numerical model and associated calorimeter forpredicting temperature profiles in mass concreterdquo Cement ampConcrete Composites vol 26 no 6 pp 695ndash703 2004

[19] Y Li L Nie and B Wang ldquoA numerical simulation of thetemperature cracking propagation process when pouring massconcreterdquo Automation in Construction vol 37 pp 203ndash2102014

[20] I Chu Y Lee M N Amin B-S Jang and J-K Kim ldquoApplica-tion of a thermal stress device for the prediction of stresses dueto hydration heat in mass concrete structurerdquo Construction andBuilding Materials vol 45 pp 192ndash198 2013

[21] H W Reinhardt and S L Xu ldquoCrack extension resistancebased on the cohesive force in concreterdquo Engineering FractureMechanics vol 64 no 5 pp 563ndash587 1999

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

8 Advances in Materials Science and Engineering

References

[1] X G Zhang Y P Song and Z M Wu ldquoCalculation modelof equivalent strength for induced crack based on double-Kfracture theory and its optimizing setting in RCC arch damrdquoTransactions of Tianjin University vol 1 pp 8ndash15 2005

[2] J-H Ha Y S Jung and Y-G Cho ldquoThermal crack controlin mass concrete structure using an automated curing systemrdquoAutomation in Construction vol 45 pp 16ndash24 2014

[3] K D Hansen ldquoRoller compacted concrete a civil engineeringinnovation concreterdquo International Design amp Construction vol18 no 3 pp 25ndash31 1996

[4] Y Yuan and Z L Wan ldquoPrediction of cracking within early-ageconcrete due to thermal drying and creep behaviorrdquo Cementand Concrete Research vol 32 no 7 pp 1053ndash1059 2002

[5] N Liu and G-T Liu ldquoTime-dependent reliability assessmentfor mass concrete structuresrdquo Structural Safety vol 21 no 1 pp23ndash43 1999

[6] S H Chen P F Su and I Shahrour ldquoComposite elementalgorithm for the thermal analysis of mass concrete simulationof lift jointrdquo Finite Elements in Analysis and Design vol 47 no5 pp 536ndash542 2011

[7] YWu and R Luna ldquoNumerical implementation of temperatureand creep in mass concreterdquo Finite Elements in Analysis andDesign vol 37 no 2 pp 97ndash106 2001

[8] Z Yunchuana B Liangb Y Shengyuana and C Gutinga ldquoSim-ulation analysis of mass concrete temperature fieldrdquo ProcediaEarth and Planetary Science vol 5 pp 5ndash12 2012

[9] J Yang YHu Z Zuo F Jin andQ Li ldquoThermal analysis ofmassconcrete embedded with double-layer staggered heterogeneouscooling water pipesrdquo Applied Thermal Engineering vol 35 no1 pp 145ndash156 2012

[10] B I Yoshitake H Wong T Ishida and A Y Nassif ldquoThermalstress of high volume fly-ash (HVFA) concrete made withlimestone aggregaterdquo Construction and Building Materials vol71 pp 216ndash225 2014

[11] O Kayali and M Sharfuddin Ahmed ldquoAssessment of highvolume replacement fly ash concrete-concept of performanceindexrdquo Construction and Building Materials vol 39 pp 71ndash762013

[12] D Jeon Y Jun Y Jeong and J E Oh ldquoMicrostructuraland strength improvements through the use of Na

2CO3in a

cementless Ca(OH)2-activated class F fly ash systemrdquo Cement

and Concrete Research vol 67 pp 215ndash225 2015[13] J Tikkanen A Cwirzen and V Penttala ldquoEffects of mineral

powders on hydration process and hydration products innormal strength concreterdquoConstruction and BuildingMaterialsvol 72 pp 7ndash14 2014

[14] F LoMonte and P G Gambarova ldquoThermo-mechanical behav-ior of baritic concrete exposed to high temperaturerdquo Cement ampConcrete Composites vol 53 pp 305ndash315 2014

[15] X-ZWang Y-P Song J-K Dong and Z-Q Huang ldquoStudy onequivalent strength for crack directors of RCC arch dam basedon size effect rulerdquo Journal of Harbin Institute of Technology vol16 no 2 pp 149ndash153 2009

[16] K Duan X Z Hu and F H Wittmann ldquoBoundary effect onconcrete fracture and non-constant fracture energy distribu-tionrdquo Engineering Fracture Mechanics vol 70 no 16 pp 2257ndash2268 2003

[17] K Duan X-Z Hu and F H Wittmann ldquoSize effect onfracture resistance and fracture energy of concreterdquo Materialsand Structures vol 36 no 256 pp 73ndash80 2003

[18] Y Ballim ldquoA numerical model and associated calorimeter forpredicting temperature profiles in mass concreterdquo Cement ampConcrete Composites vol 26 no 6 pp 695ndash703 2004

[19] Y Li L Nie and B Wang ldquoA numerical simulation of thetemperature cracking propagation process when pouring massconcreterdquo Automation in Construction vol 37 pp 203ndash2102014

[20] I Chu Y Lee M N Amin B-S Jang and J-K Kim ldquoApplica-tion of a thermal stress device for the prediction of stresses dueto hydration heat in mass concrete structurerdquo Construction andBuilding Materials vol 45 pp 192ndash198 2013

[21] H W Reinhardt and S L Xu ldquoCrack extension resistancebased on the cohesive force in concreterdquo Engineering FractureMechanics vol 64 no 5 pp 563ndash587 1999

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials