research article calculation of constrained stress in...

Research ArticleCalculation of Constrained Stress in Expansive Mortar witha Composite Creep Model

Hyeonggil Choi1 and Bongsuk Cho2

1Graduate School of Engineering Muroran Institute of Technology 27-1 Mizumoto-cho Muroran Hokkaido 080-8585 Japan2Slag Utilization Research Team Research Institute of Industrial Science amp Technology 32 Hyoja-dong Nam-kuPohang 37673 Republic of Korea

Correspondence should be addressed to Bongsuk Cho chos8hanmailnet

Received 26 February 2016 Revised 11 May 2016 Accepted 29 May 2016

Academic Editor Antonio G de Lima

Copyright copy 2016 H Choi and B ChoThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The creep phenomenon of hardening cement paste mixed with an expansive additive was modeled by considering the creepperformance of hydration products of cement and expansive additive A new composite model that is appropriate for particleconditions is proposed by considering the balance of the hydration products of cement and expansive additive and the stressredistribution phenomenon of hydration products newly generated by the progress of hydrationThe creep of mortar and concretemixed with the expansive additive was evaluated using a composite model of the paste and aggregate Under the assumption thatthe modeled creep deformation is proportional to the stress and the gel volume of the hydration products which allows the law ofsuperposition to be applied the distribution stress was predicted by applying the step-by-step method at each time increment Bypredicting the maximum tensile stress applied to an inner steel ring through a creep analysis based on the measured deformationof the inner steel ring it is possible to predict the stress progression with age to some degree

1 Introduction

Stress occurs within concrete under various constraints Ifthis stress exceeds the allowable limit cracks may be gener-ated in the concrete Such cracks facilitate the penetration ofsalt or acid which leads to the corrosion of the internal rebarand in turn decreases the internal strength and durability ofthe structures [1 2] In particular cracks that form before thepublic use of the structuremay initiate functional or aestheticdegradation even below the allowable crack width of thedesignThus the demand to reduce shrinkage cracks in rein-forced concrete structures has increased in recent years [1ndash3]Concrete experiences strain under a certain stress conditioncalled creep this decreases the stress which must be takeninto account Hence identifying the creep performance iscrucial to calculating the stress in concrete and should notbe overlooked during the design process [4ndash6] Under thesecircumstances the use of expansive additives has increased asa countermeasure against cracking due to concrete shrinkageand the material characteristics of concrete mixed with

expansive additives have been widely studied [7ndash11] How-ever only a few studies have focused on creep Thus theavailable literature is insufficient for a quantitative evaluationof the creep performance

In this study the creep of hardening cement paste mixedwith an expansive additive was modeled to estimate theconstrained stress of expansive mortar and calculate changesin this stress

2 Composite Creep Modeling

21 Composite CreepModel of Hardening Cement Paste Mixedwith Expansive Additive The creep of hardening cementpaste mixed with an expansive additive [12 13] was modeledby following the creepmodel for normal concrete of Lokhorstand van Breugel [14] and Maruyama [15] Figure 1 shows thecomposite creep model of the hardening cement paste mixedwith expansive additive In this model the hydration productof the expansive additive inside the hardening paste providesresistance and balance against the hydration product of the

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2016 Article ID 2372835 10 pageshttpdxdoiorg10115520162372835

2 Advances in Materials Science and Engineering

Hydrationgel

Unhydratedcement

Unhydratedexpansive addWater + air Water + airNew

hydration gel

Aggregate(sand gravel)

Unhydratedexpansive add


Unhydratedcement

Unhydratedcement or

expansive add

Water

Air Hydrationgel

Water

Air

Unhydratedcement or

expansive add

Hydrationgel

t = 120572 t = 120572 + Δ120572

r0

ru

Rtr0

Figure 1 Composite creep model of the cement paste mixed with expansive additive

cement Only the cement and expansive additive hydrationproducts are assumed to exhibit creep and the creep proper-ties and conditions of these hydration products are assumedto be uniform temporally and spatially The model assumesthat the unhydrated cement and expansive additive are solidswith a uniform elastic modulus and that the moisture insidethe capillary does not share the burden of stress

The cement paste mixed with expansive additive con-sists of water hydration products unhydrated cement andunhydrated expansive additive as shown in Figure 1 Duringthe hydration process the radius of the original cement andexpansive additive particle 119903

0decreases to 119903

119906with a decreas-

ing amount of water At the same time the amount of hydra-tion products increases which increases the radius of the out-ermost hydration product 119877

119905 The figure shows the hydration

products generated during this process in the form of anelement of a bar based on the work of Lokhorst and vanBreugel [14] and Maruyama et al [15 16] The inserted ele-ments of hydration products are assumed to increase becauseof the increase in the outermost radius 119877

119905 and an element is

inserted every time the contact area 119860119888changes by 1 Here

119860119888was assumed to be a parameter for the formation of the

paste structuremixedwith expansive additive and it dependson the hydration rate The existing concept of the contactarea according to the Computational Cement Based Material(C-CBM) model [15] was proposed by Maruyama and isintroduced and modeled here As hydration progresses

the contact area between particles increases because of thecollision between particles 119860

119888depends on the radius of the

hydration products and can be expressed as follows [12 15]Case of 05 le 119877

119905lt radic22

119860119888= 120587 (119877

119905

2minus 052) (1)

Case ofradic22 le 119877119905lt radic32

119860119888= 8

[

[

[

1

2

(119877119905

2minus 052)

sdot (

120587

4

minus 119860cos ( 05

radic119877119905

2minus 052

))

+ 025radic119877119905

2minus 05

]

]

]

(2)

Similar to previous studies the outermost radius 119877119905can

be obtained as follows [13 15]

119877119905= (1 + (119881 minus 1) 120572)

13sdot 1199030 (3)

The volume increase rate119881 of cement has been defined as19ndash22 in previous studies [17] Based on this range119881was set

Advances in Materials Science and Engineering 3

Table 1 Mineral composition of cement and expansive additive [12]

Type Mineral composition ()SiO2

Fe2O3

Al2O3

CaO SO3

MgO Total f-CaOOrdinary Portland cement 210 29 52 644 23 12 970 mdashExpansive additive 10 08 72 706 185 mdash 981 498

to 20 in this study by considering the time at which it con-verges to a certain value with regard to the hydration reactionrate and the adsorbed water present in the hydration productor the water in the gel pores that does not contribute to thehydration reaction [13] For the expansive additive 119881 wasset to 334 by considering a layer of hydration products andfollowing the reasoning of Yamamoto et al who describedthe expansion mechanism of expansive additives [18]

The time-dependent creep strain of the hydration productwas applied according to the following equation This is thesame type of equation as that proposed by Lokhorst and vanBreugel [14]

120576119888119890 (

119905) = 119886 sdot

(119905 minus 120591)119899

1199050

sdot 120590 (120591) (4)

where 120576119888119890(119905) is the creep strain at the age 119905 119905 minus 120591 is the time

under the load ℎ 1199050is 1 h 120590(120591) is the stress applied at the age

119905 119886 is the creep constant (mm2N) and 119899 is a constant (here119899 = 03 [14])

The creep constant 119886 of the hydration product of cementwas set to 15 times 10minus5 based on the existing literature [14 19]Although many studies have dealt with the material char-acteristics of hardening cement paste mixed with expansiveadditives only a few have examined creepThe creep constantof hydration products produced by the hydration of only theexpansive additive should be different from that of cementOwing to the lack of sufficient data however this value wasset to 21 times 10minus4 in this study based on previous experimentalresults [13] and other existing studies [12 13] which showedthat creep is slightly higher in expansive concrete than innormal concrete because the former expands through thegeneration of air gaps

The activation energy for the temperature-dependentcreep strain of the hydration products of cement and expan-sive additive was evaluated according to themodel of Lokhorstand van Breugel [14] and Maruyama [15] by using thefollowing equation

119881 (119879) = exp(119876119877

sdot

119879 minus 1198790

119879 sdot 1198790

) (5)

where 119881(119879) is a function describing the temperature effects119877 is the gas constant (831 Jmol K) 119879 is the temperature ofthe paste and 119879

0is the reference temperature (293K) When

119879 = 1198790 119881(119879) is 1 The activation energy 119876 for ordinary

Portland cement was assumed to be 20000 Jmol which is atypical value [14 15 20] In the case of the expansive additivethe activation energy was set to 43496 Jmol which wascalculated with the following equation by using the C

3SC2S

ratioThis value can be calculated by considering the mineral


Paste(cement

+expansive

add)1

1minus120582c

120582c

1 minus 120582c 120582c

Figure 2 Composite model of mortar and concrete

composition of the expansive additive as presented in Table 1Consider

119876 = minus4070 sdot (

C3S ()

C2S ()

) + 38010 (6)

where C3S and C

2S represent the ratio of C

3S and C

2S in

the expansive additive and are calculated according to thefollowing equation proposed by Bogue [21]

C3S = 40710 sdot CaO minus 76024 sdot SiO

2minus 14297 sdot Fe

2O3

minus 67187 sdot Al2O3

C2S = 28675 sdot SiO

2minus 07544 sdot C

3S

(7)

The strain of the newly created elements varies becauseeach element has a different stress history depending on theage however a uniform strainwas considered for all elementsowing to the redistribution of stress Thus the creep strain ofthe paste mixed with expansive additive can be expressed by(8) depending on the mixture rate of the expansive additiveaccording to the balance of the creep strain of the cement andexpansive additive parts

120576paste(119862+EX) = 120576119888(119862) sdot 119862119881() + 120576119888(EX) sdot EX119881() (8)

where 120576paste(119862+EX) is the creep strain of the cement pastemixedwith expansive additive 120576

119888(119862)is the creep strain of the cement

part 120576119888(EX) is the creep strain of the expansive additive part

119862119881() is the volume mixing rate of cement and EX

119881() is thevolume mixing rate of expansive additive

22 Composite Model for Mortar and Concrete In order toextend the creep phenomenon to mortar and concrete acomposite model of paste and aggregate (fine and courseaggregate) was used The model shown in Figure 2 is based


1 2 3 k k k1 2 3 k

120576 = 120576e + 120576c

middot middot middot middot middot middot

middot middot middot

◼d120576e1

dt+

d120576c1

dt=

d120576eb

dt+

d120576cb

dt◼

d120590r1

dt+

d120590r2

dt+

d120590r3

dt+ middot middot middot +

d120590rk

dt= 0

Δ1205901 Δ120590k

Figure 3 Strain and stress redistributions due to newly created elements

on the assumption that aggregates do not experience time-dependent strain With this composite model the stressload of the paste was considered to be redistributed to theaggregates because the aggregates should be under the sameamount of time-dependent strain experienced by the pasteThus the time-dependent strain of mortar and concretemixed with expansive additive can be calculated as followsby considering the strain attributed to the load shared by theaggregates as initiated by the paste strain

120576mortar or concrete(119862+EX)

= 120576paste(119862+EX)

sdot [(

(1 minus 120582119888) sdot 119864119901sdot 120582119888

120582119888sdot 119864agg + (1 minus 120582119888) sdot 119864119901

) + (1 minus 120582119888)]

(9)

where 120576mortar or concrete(119862+EX) is the creep strain of mortar orconcrete mixed with expansive additive 120576paste(119862+EX) is thecreep strain of the paste mixed with expansive additive 119864

119901

is the elastic modulus of the paste mixed with expansiveadditive and 119864agg is the elastic modulus of the aggregateIn addition 120582

119888is a constant related to the volume of the

aggregates119881agg relative to the unit volume it can be expressedas 120582119888= radic119881agg

23 Estimation of Stress Redistribution The stress redis-tribution was estimated by analyzing the modeled creepphenomenon The required redistributed stress can be deter-mined by solving 119896 linear equations when 119896 elements areconsidered as shown in Figure 3The sum of the creep strainand elastic strain over the time 119905 + Δ119905 is the same for allelements and the sumof the stresses does not change becauseof the generation of elements Furthermore if the creep strainfollows the law of superposition and is proportional to the gelvolume of the hydration products and the stress the creep

strain can be expressed as follows by applying the step-by-step method to each time increment

120576tot (119905119894+1) = 120576tot (119905119894) +Δ120590 (120591119894)

119864

+

119894

sum

119895=1

119886 sdot 119881 (119879119894) sdot Δ120590 (120591

119895)

sdot [(119905119894+1

minus 120591119895)

119899

minus (119905119894minus 120591119895)

119899

]

(10)

Thus the total strain can be calculated by summing thefollowing three sets of terms according to (10)

(i) Total strain at time 119905119894

(ii) Elastic strain Δ120576119890(119905119894) attributed to the new stress

increment Δ120590(120591119894)

(iii) Creep strain increment Δ120576119888(119905119894 120591119895 119879119894) generated by

the stress increment Δ120590(120591119895) in the next time interval

(119905119894 119905119894+1)

3 Experiment

31 Outline of the Experiment Two types of specimens witha waterbinder ratio of 050 were used an expansive mortarwith a 1 3 ratio of fine aggregate and binder towhich 5wtofan ettringite-gypsum type of expansive additives was mixedand a normal mortar Strength and shrinkage tests wereconducted in order to evaluate the basic and modified prop-erties of the mortars Air content and slump flow tests wereperformed to determine the properties of the mortars whenfresh The specimens for the strength test were demoldedon day 1 and cured in water (20 plusmn 2

∘C) after which thecompressive and splitting tensile strengths were measured

A 40mm times 40mm times 160mm mold was used in theshrinkage test to measure the drying shrinkage with anembedded strain gauge Drying shrinkage specimens weredemolded on day 1 and a portion of each specimen wascompletely sealed with aluminum tape in order to match thevolume-to-surface area ratio (VS) used in the ring test Theywere then left in a moist room to dry (temperature 20 plusmn 2∘Chumidity 60 plusmn 5)


(top and bottom)

A

Drying directionOutside steel 79mm

Inside steel 12mm

75mm

4572mm2985mm

Drying direction(top and bottom)

Inside steel 25mmOutside steel 79mm

75mm

4572mm2985mm

Drying direction(top and bottom) Outside steel 79mm

Inside steel 12mm

4572mm3650mm

75mmB C

Figure 4 Overview of the ring test

120575120579120575120574

120574im120574om

Pi

P998400i

120574os

120574is

Figure 5 Stress distribution in the ring test

In the ring-type constraint test to induce drying shrink-age across the cross sections of the mortar rings in an evenmanner as shown in Figure 4 the height of the ring-typeconstraint specimen was set to 75mm instead of 152mm asprescribed by AASHTO PP34-98 [22] Tests were conductedwith ring-type constraint specimens at three levels A B andC This was to assess the strain and stress under differentconstraints such as different inner ring thicknesses anddiameters The inner steel rings were left free of any surfacetreatment such as oil or other lubricants After the mortarwas deposited the surfaces of the mortar rings were sealedwith vinyl sheets in order to prevent fast drying caused bymoisture evaporation After 1 day the bottom forms wereremoved to allow only the top and bottom surfaces of themortar to dry Three strain gauges (ℎ = 375mm) wereinstalled on the inner steel rings and the constrained strainwas assessed with a datalogger while the rings remained inthe constant temperature and humidity room (temperature20 plusmn 2

∘C humidity 60 plusmn 5)

32 Calculation of the Constrained Stress in the Ring TestFigure 5 shows a conceptual picture of the stress distributionin the ring test The conversion of the steel strain to thetensile strength of the mortar is based on the assumption ofan arbitrary interface pressure119875 of the same size but oppositein direction This interface pressure 119875 was attributed to theshrinkage of the mortar and constraint of the steel rings Ifthe mortar shrinks evenly and linearly across the whole crosssection the circumferential stress 120590

120579of a specimen can be

defined as follows [23ndash25]

120590120579=

1199032

im sdot 119875

1199032

om minus 1199032

im[1 +

1199032

om1199032] (11)

where 119903im and 119903om are the inner and outer radii respectivelyof the mortar and 119903 is an arbitrary value in the direction ofthe axis In addition the maximum constrained stress in thecircumferential direction occurs at the border between theinner steel ring and mortar (119903 = 119903im) This can be calculatedby using the following equation

120590120579119894=

119875119894sdot (1199032

im + 1199032

om)

1199032

om minus 1199032

im 119903 = 119903im (12)

The pressure 119875119894on the inner steel ring acts as the external

pressure of the samemagnitude but in the opposite directionIt can be expressed by using the following equation for themeasured strain of the inner steel ring

119875119894=

(1199032

os minus 1199032

is)

21199032

ossdot 120590120579st =

(1199032

os minus 1199032

is)

21199032

ossdot 119864st sdot 120576st 119903 = 119903is (13)

where 120590120579st is the stress on the inner steel ring in the

circumferential direction 119864st and 120576st are the elastic modulusand constrained strain respectively and 119903is and 119903os are theinner and outer radii respectively of the inner steel ring

Therefore if (13) is substituted into (12) the maximumconstrained stress of the mortar can be obtained as follows

120590120579119894max =

(1199032

os minus 1199032

is)

21199032

ossdot

(1199032

im + 1199032

om)

(1199032

om minus 1199032

im)sdot 119864st sdot 120576st (14)

33 Test Results Table 2 lists the test results for the slumpflow air content and strength When the expansive additivewas mixed in the workability and air content did not changeconsiderably The expansive mortar had lower compressivestrength and splitting tensile strength than the normal mor-tar but these differences were negligible In other words theexpansive additive had minimal effect in terms of the freshand strength properties

Figure 6 shows the drying shrinkage results The dryingshrinkage of the normal mortar was 941 120583 at day 56 whilethat of the expansive mortar was 866 120583 The drying shrinkagedecreased in the expansivemortar However these results didnot consider the effect of expansion at an early age from theexpansive additive Thus a reduction of 100 120583 from dryingshrinkage due to the early expansion of the expansive additive[26 27] was considered along with the drying shrinkagestrain under unconstrained conditions Then using the


Table 2 Fresh and strength properties

TypeSlump flow

(cm)Air content

()Compressive strength (Nmm2) Splitting tensile strength

(Nmm2)7 days 14 days 28 days 7 days 14 days 28 days

N 185 56 2175 3439 4561 281 319 364EX 175 51 2106 3312 4713 280 327 359

minus1000

minus800

minus600

minus400

minus200

0

200

0 10 20 30 40Age (days)

Normal mortarExpansive mortar

Stra

in(120583

)

Figure 6 Results of drying shrinkage

expansive additive was found to reduce the drying shrinkageby approximately 186

Figures 7 and 8 show the constrained strains and stressesof the inner steel rings The strains decreased because of thecompressive force due to the early expansion of the expansiveadditive However the strains of the normal mortar abruptlyincreased with the increase in nonconstrained shrinkagecracking occurred immediately after themaximum strainwasattained In addition the admixture of expansive additivedecreased the maximum pressure on the inner steel ringwhich in turn decreased the constrained stress and delayedthe cracking time of the mortar

The maximum constrained stress tended to decrease asthe thickness and diameter of the inner ring were increasedThiswas probably because evenwhen the constrained load onthe interface remained constant the thickness and diameterof the inner steel ring increased with the degree of constraintThat is as the inner steel ring became thicker it was notstrained and the amount of relaxing shrinkage increasedfrom an early age

Overall the admixture with expansive additive delayedcracking by 17ndash28 days Thus the use of the expansiveadditive was confirmed to reduce the tensile stress and crackresistance

minus150

minus120

minus90

minus60

minus30

0

30

60

0 10 20 30 40Age (days)

N-AN-BN-C

EX-AEX-BEX-C

Stee

l str

ain (120583

)

Figure 7 Constrained strains of the inner rings

4 Estimation of the Constrained Stress byCreep Analysis

41 Hydration Reaction Rate For the analysis of the creepmodel the hydration rate 120572 is the parameter required toobtain the outermost radius of the cement and expansiveadditive particles according to (3) Here the hydration reac-tion rate was defined as the amounts of cement and expansiveadditive that underwent reactions compared to their cor-responding total amounts In order to determine this ratea value calculated from using the net calorific value wasapplied The calorific value was obtained by measuring thecalories generated during the hydration process with a multi-micro calorimeter (MMC-511 SV) When the watercementand waterexpansive additive ratios were 050 the netcalorific values were 43753 and 88712 Jg for the cement andexpansive additive respectively Figure 9 shows an examplecalculation for the rate of heat liberation and degree of hydra-tion The figure confirms that the hydration reaction rate forthe expansive additive was higher than that for cement at allages owing to the increased exothermic peak from the rapidreaction of the expansive additive at an early age The experi-mental data were used in the creep analysis

42 Elastic Modulus The elastic modulus for creep analysiswas obtained by using (15) based on previous modeling


minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)

N-AN-BN-C

EX-AEX-BEX-C

Figure 8 Constrained stresses of the inner rings

0

02

04

06

08

1

0

10

20

30

40

50

0 12 24 36 48 60 72

Deg

ree o

f hyd

ratio

n

Time (hr)

CementExpansive add

05

Rate

of h

eat l

iber

atio

n (J

ghr

)

WC

Figure 9 Rate of heat liberation and degree of hydration of thecement and expansive additives

work [12 28] based on Maruyamarsquos C-CBM model [15] Thisequation indicates that the outer product has a lower densitythan the inner product as shown in Figure 10 Howeverthe phenomenon of densification with age was consideredthrough the large expansion in terms of space based on theeffective contact area 119860ceff

119864paste(119862EX)

=

1

120582119901 (120582119901sdot 119864gel(119862EX) + (1 minus 120582119901) sdot 119864119862EX) + (1 minus 120582119901) 119864gel(119862EX)

sdot 119860ceff

(15)

where 119864paste(119862EX) is the elastic modulus of the cement pasteor expansive paste 119864

119862EX is the elastic modulus of theunhydrated cement or expansive additive 119864gel(119862EX) is theelastic modulus of the hydration product and 119860ceff is theeffective contact area In addition 120582

119901is a constant related to

the volume of the unhydrated cement or expansive additive119881119862EX relative to the unit volume and can be expressed as120582119901= radic119881119862EXWith the model 119864

119862EX and 119864gel(119862EX) had values of 50 and25GPa respectivelyThese values were taken from the resultsof Maruyama [15] who determined these values by referringto the values of 40 and 20GPa suggested byHua et al [29] and60 and 30GPa suggested by Lokhorst and van Breugel [14] Inthe case of the expansive additive the value for cement wasapplied because sufficient data could not be found

The elasticmodulus of the pastemixedwith the expansiveadditive can be expressed by (16) It depends on the mixtureratio of the expansive additive by balancing the elasticmodulus of the required cement part and elastic modulus ofthe expansive additive part

119864paste(119862+EX) = 119864paste(119862) sdot 119862119881() + 119864paste(EX) sdot EX119881() (16)

where 119864paste(119862+EX) is the elastic modulus of the cement pastemixed with the expansive additive 119864paste(119862) is the elasticmodulus of the cement part119864paste(EX) is the elasticmodulus ofthe expansive additive part 119862

119881() is the volume mixing rateof the cement and EX

119881() is the volume mixing rate of theexpansive additive

In order to extend this equation to the elastic moduliof mortar and concrete a composite model of the pasteand aggregate was used as a creep model The aggregatewas assumed to exhibit no creep behavior Hence the pastedominates the behavior of the mortar or concrete Thereforethe aggregate has a resistor function without affecting thebehavior of the paste If a composite model for the aggregateand paste is assumed the elastic modulus of the mortar orconcrete can be expressed by


=

1

120582119888 (120582119888sdot 119864paste(119862+EX) + (1 minus 120582119888) sdot 119864agg) + (1 minus 120582119888) 119864paste(119862+EX)

(17)

where 119864mortar or concrete(119862+EX) is the elastic modulus of theconcrete mixed with the expansive additive 119864paste(119862+EX) isthe elastic modulus of the cement paste mixed with theexpansive additive and 119864agg is the elastic modulus of theaggregate In addition 120582

119888is a constant related to the volume

of the aggregates 119881agg relative to the unit volume and can beexpressed as 120582

119888= radic119881agg

43 Estimation of the Constrained Stress The stress changein the expansive mortar under the constrained condition wasestimated by considering the modeled creep phenomenondescribed in Section 2 The estimated stress was comparedwith the experimental results of the ring test described in


① Unhydrated cement and expansive additives ② Inner product③ Outer product

Figure 10 Density changes in the hydration product during hydration [6]

minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)

Calculation (N-A) Experimental (ring test N-A)Calculation (EX-A) Experimental (ring test EX-A)

Figure 11 Calculation of the constrained stress by the creep model(Specimen A)

Section 3 to validate the stress prediction technique using themodel

If the mortar poured into the ring object is assumedto show linear elastic behavior under various constraintsthe pressure applied by the constraint of the steel and thatapplied to the mortar become identical Thus by calculatingthe pressure applied to the interface of the inner steel ringand mortar with the creep model by using the deformationmeasured from the inner steel ring the maximum tensilestress applied in the direction of the circumference of themortar can be calculated Figures 11ndash13 show the maximumtensile stress according to the ring test and calculated withthe creep model under various constraints The results ofthe ring test were predicted under the assumption that themortar poured to the ring exhibits linear elastic behaviorand the actual behavior of mortar differed from the stressapplied to the ring object Thus the maximum tensile stresspredicted for objects including object B differed slightlyfrom the maximum tensile stress according to the ring test

minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)

Calculation (N-B) Experimental (ring test N-B)Calculation (EX-B) Experimental (ring test EX-B)

Figure 12 Calculation of the constrained stress by the creep model(Specimen B)

However the results confirmed that the progression of stressin ordinary mortar and expansive mortar with age can bepredicted to some degree

5 Conclusions

A model was developed for the creep of hardening cementpaste mixed with expansive additive to control cracking Theconstrained stress of expansivemortarwas estimated by usingthemodeled creep to calculate the changes in the stress underconstraints The results of the study can be summarized asfollows

(1) The hydration products of the expansive additive andcement were considered under the assumption thatthese products cause creep The creep of hardeningcement paste mixed with expansive additive wasmodeled by considering the redistribution of stressbetween the newly generated hydration productsand the already existing hydration product that was


minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)

Calculation (N-C) Experimental (ring test N-C)Calculation (EX-C) Experimental (ring test EX-C)

Figure 13 Calculation of the constrained stress by the creep model(Specimen C)

bearing the stress as well as the balance between theexpansive additive and hydration products of cement

(2) If the creep deformation is proportional to the stressand the gel volume of the hydration products thelaw of superposition can be applied This was used topredict the stress development by applying the step-by-step method for each time increment

(3) For the ring test the maximum tensile stress appliedto the inner steel ring was predicted through a creepanalysis based on the measured deformation of theinner steel ring and under the assumption that themortar in the ring exhibits linear elastic behaviorTheresults confirmed that the progression with age ofstress in ordinary mortar and expansive mortar canbe predicted to some degree

Competing Interests

The authors declare that they have no competing interests

References

[1] AIJ (Architectural Institute of Japan) Recommendations forPractice of Crack Control in Reinforced Concrete Buildings(Design and Construction) AIJ 2006

[2] ACI ldquoStandard practice for the use of shrinkage compensatingconcreterdquo ACIManual of Concrete Practice ACI 223R-98 1993

[3] JCIC77Proceedings of JCI Symposium onEvaluation of ConcreteShrinkage and Its Effect Japan Concrete Institute Tokyo Japan2010

[4] ACI Committe Guide for Modeling and Calculating Shrinkageand Creep in Hardened Concrete ACI Committe 209 2008

[5] R I Gilbert Time-Effects in Concrete Structures Elsevier Sci-ence Amsterdam The Netherlands 1988

[6] A M Neville Creep of Concrete Plain Reinforced and Pre-Stressed North Holland Publishing Company AmsterdamNetherlands 1970

[7] M Morioka Hydration and material design of cement-basedexpansive additive [PhD thesis] Tokyo Institute of TechnologyTokyo Japan 1999

[8] P Carballosa J L Garcıa Calvo D Revuelta J J Sanchez andJ P Gutierrez ldquoInfluence of cement and expansive additivetypes in the performance of self-stressing and self-compactingconcretes for structural elementsrdquo Construction and BuildingMaterials vol 93 pp 223ndash229 2015

[9] T Higuchi M Eguchi M Morioka and E Sakai ldquoHydrationand properties of expansive additive treated high temperaturecarbonationrdquo Cement and Concrete Research vol 64 pp 11ndash162014

[10] R Sahamitmongkol and T Kishi ldquoTensile behavior ofrestrained expansive mortar and concreterdquo Cement andConcrete Composites vol 33 no 1 pp 131ndash141 2011

[11] H G Choi M Tsujino T Noguchi and R Kitagaki ldquoAppli-cation to buildings and cracking control effects of expansionconcreterdquo Cement Science and Concrete Technology vol 67 pp583ndash596 2014

[12] H G Choi A study on the macro prediction of shrinkage-reduction behavior in concrete using expansive additives [PhDthesis] The University of Tokyo Tokyo Japan 2013

[13] H G Choi M K Lim H S Choi T Noguchi and RKitagaki ldquoModelling of creep of concrete mixed with expansiveadditivesrdquoMagazine of Concrete Research vol 67 no 7 pp 335ndash348 2015

[14] S J Lokhorst and K van Breugel ldquoSimulation of the effectof geometrical changes of the microstructure on the deforma-tional behaviour of hardening concreterdquo Cement and ConcreteResearch vol 27 no 10 pp 1465ndash1479 1997

[15] I Maruyama Time dependent property of cement based materi-als on the basis of micro-mechanics [PhD thesis]TheUniversityof Tokyo Tokyo Japan 2003

[16] I Maruyama T Noguchi P Lura and K van Breugel ldquoCalcu-lation of self-induced stress in early-age concrete using creepand relaxation modelrdquo in Proceedings 1st FIB Congress Concretestructures in the 21st Century vol 1 Session 9 pp 215ndash221Osaka Japan 2002

[17] T C Powers and T L Brownyard ldquoStudies of the physicalproperties of hardened Portland cement pasterdquo Journal of theAmerican Concrete Institute (Proceedings) vol 43 no 9 pp469ndash504 1974

[18] K Yamamoto M Morioka E Sakai and M Daimon ldquoExpan-sion mechanism of cement added with expansive additiverdquoConcrete Research and Technology vol 14 no 3 pp 23ndash31 2003

[19] K van Breugel and S J Lokhorst ldquoThe role of microstructuraldevelopment on creep and relaxation of hardening concreterdquoin Proceedings of the International RILEM Conference on EarlyAge Cracking in Cementitious Systems pp 3ndash10 RILEM Publi-cations 2003

[20] M Taniguchi O Katsura and Y Hama ldquoInfluence of type ofcement on temperature dependency of the strength develop-ment of mortarrdquo Proceedings of the Japan Concrete Institute vol31 no 1 pp 415ndash420 2009

[21] R H BogueTheChemistry of Portland Cement Reinhold NewYork NY USA 1955


[22] AASHTO (American Association of State Highway and Trans-portation Officials) Standard Practice for Estimating the CrackTendency of Concrete AASHTO 1998

[23] A C Ugural and S K Fenster Advanced Strength and AppliedElasticity Prentice Hall PTR Upper Saddle River NJ USA 3rdedition 1995

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

[25] W J Weiss and S Fergeson ldquoRestrained shrinkage testingThe impact of specimen geometry on quality control testingfor material performance assessmentrdquo in Concreep 6 CreepShrinkage and Durability Mechanic of Concrete and OtherQuasi-Brittle Materials F J Ulm Z P Bazant and F HWittman Eds pp 645ndash651 Elsevier Cambridge Mass USA2001

[26] H Hashida T Kikuchi M Tsujino and H Tanaka ldquoLowshrinkage concrete with both expansive additive and limestoneaggregates (part3 initial expansion force and shrinkage reduc-ing effectrdquo in Proceedings of the Summaries of Technical Papersof AnnualMeeting pp 927ndash928 Architectural Institute of Japan2010

[27] H Momose and T Kanda ldquoQuantitative estimation of dryingshrinkage reduction effects due to an expansive additiverdquoJournal of Structural and Construction Engineering vol 76 no666 pp 1367ndash1373 2011

[28] H G Choi and T Noguchi ldquoModeling of mechanical proper-ties of concrete mixed with expansive additiverdquo InternationalJournal of Concrete Structures and Materials vol 9 no 4 pp391ndash399 2015

[29] C Hua A Ehrlacher and P Acker ldquoAnalyses and models of theautogenous shrinkage of hardening cement paste II Modellingat scale of hydrating grainsrdquoCement and Concrete Research vol27 no 2 pp 245ndash258 1997

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


Hydrationgel

Unhydratedcement

Unhydratedexpansive addWater + air Water + airNew

hydration gel


Unhydratedexpansive add


Unhydratedcement

Unhydratedcement or

expansive add

Water

Air Hydrationgel

Water

Air

Unhydratedcement or

expansive add

Hydrationgel

t = 120572 t = 120572 + Δ120572

r0

ru

Rtr0

Figure 1 Composite creep model of the cement paste mixed with expansive additive

cement Only the cement and expansive additive hydrationproducts are assumed to exhibit creep and the creep proper-ties and conditions of these hydration products are assumedto be uniform temporally and spatially The model assumesthat the unhydrated cement and expansive additive are solidswith a uniform elastic modulus and that the moisture insidethe capillary does not share the burden of stress

The cement paste mixed with expansive additive con-sists of water hydration products unhydrated cement andunhydrated expansive additive as shown in Figure 1 Duringthe hydration process the radius of the original cement andexpansive additive particle 119903

0decreases to 119903

119906with a decreas-

ing amount of water At the same time the amount of hydra-tion products increases which increases the radius of the out-ermost hydration product 119877

119905 The figure shows the hydration

products generated during this process in the form of anelement of a bar based on the work of Lokhorst and vanBreugel [14] and Maruyama et al [15 16] The inserted ele-ments of hydration products are assumed to increase becauseof the increase in the outermost radius 119877

119905 and an element is

inserted every time the contact area 119860119888changes by 1 Here

119860119888was assumed to be a parameter for the formation of the

paste structuremixedwith expansive additive and it dependson the hydration rate The existing concept of the contactarea according to the Computational Cement Based Material(C-CBM) model [15] was proposed by Maruyama and isintroduced and modeled here As hydration progresses

the contact area between particles increases because of thecollision between particles 119860

119888depends on the radius of the

hydration products and can be expressed as follows [12 15]Case of 05 le 119877

119905lt radic22

119860119888= 120587 (119877

119905

2minus 052) (1)

Case ofradic22 le 119877119905lt radic32

119860119888= 8

[

[

[

1

2

(119877119905

2minus 052)

sdot (

120587

4

minus 119860cos ( 05

radic119877119905

2minus 052

))

+ 025radic119877119905

2minus 05

]

]

]

(2)

Similar to previous studies the outermost radius 119877119905can

be obtained as follows [13 15]

119877119905= (1 + (119881 minus 1) 120572)

13sdot 1199030 (3)

The volume increase rate119881 of cement has been defined as19ndash22 in previous studies [17] Based on this range119881was set




Fe2O3

Al2O3

CaO SO3




120576119888119890 (

119905) = 119886 sdot

(119905 minus 120591)119899

1199050

sdot 120590 (120591) (4)






119881 (119879) = exp(119876119877

sdot

119879 minus 1198790

119879 sdot 1198790

) (5)





3SC2S



Paste(cement

+expansive

add)1

1minus120582c

120582c

1 minus 120582c 120582c



119876 = minus4070 sdot (

C3S ()

C2S ()

) + 38010 (6)

where C3S and C


3S and C

2S in




2O3



2minus 07544 sdot C

3S

(7)










1 2 3 k k k1 2 3 k

120576 = 120576e + 120576c



◼d120576e1

dt+

d120576c1

dt=

d120576eb

dt+

d120576cb

dt◼

d120590r1

dt+

d120590r2

dt+

d120590r3


d120590rk

dt= 0

Δ1205901 Δ120590k




= 120576paste(119862+EX)

sdot [(

(1 minus 120582119888) sdot 119864119901sdot 120582119888


) + (1 minus 120582119888)]

(9)


119901






120576tot (119905119894+1) = 120576tot (119905119894) +Δ120590 (120591119894)

119864

+

119894

sum

119895=1

119886 sdot 119881 (119879119894) sdot Δ120590 (120591

119895)

sdot [(119905119894+1

minus 120591119895)

119899

minus (119905119894minus 120591119895)

119899

]

(10)




increment Δ120590(120591119894)



(119905119894 119905119894+1)

3 Experiment





(top and bottom)

A


Inside steel 12mm

75mm

4572mm2985mm



75mm

4572mm2985mm


Inside steel 12mm

4572mm3650mm

75mmB C


120575120579120575120574

120574im120574om

Pi

P998400i

120574os

120574is







120590120579=

1199032

im sdot 119875

1199032

om minus 1199032

im[1 +

1199032

om1199032] (11)


120590120579119894=

119875119894sdot (1199032

im + 1199032

om)

1199032

om minus 1199032

im 119903 = 119903im (12)



119875119894=

(1199032

os minus 1199032

is)

21199032

ossdot 120590120579st =

(1199032

os minus 1199032

is)

21199032





120590120579119894max =

(1199032

os minus 1199032

is)

21199032

ossdot

(1199032

im + 1199032

om)

(1199032

om minus 1199032






TypeSlump flow

(cm)Air content



N 185 56 2175 3439 4561 281 319 364EX 175 51 2106 3312 4713 280 327 359

minus1000

minus800

minus600

minus400

minus200

0

200

0 10 20 30 40Age (days)


Stra

in(120583

)






minus150

minus120

minus90

minus60

minus30

0

30

60

0 10 20 30 40Age (days)

N-AN-BN-C

EX-AEX-BEX-C

Stee

l str

ain (120583

)






minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)

N-AN-BN-C

EX-AEX-BEX-C


0

02

04

06

08

1

0

10

20

30

40

50

0 12 24 36 48 60 72

Deg

ree o

f hyd

ratio

n

Time (hr)

CementExpansive add

05

Rate

of h

eat l

iber

atio

n (J

ghr

)

WC



119864paste(119862EX)

=

1


sdot 119860ceff

(15)













=

1


(17)




119888= radic119881agg





minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)





minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)




5 Conclusions




minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)






Competing Interests


References






































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






Fe2O3

Al2O3

CaO SO3




120576119888119890 (

119905) = 119886 sdot

(119905 minus 120591)119899

1199050

sdot 120590 (120591) (4)






119881 (119879) = exp(119876119877

sdot

119879 minus 1198790

119879 sdot 1198790

) (5)





3SC2S



Paste(cement

+expansive

add)1

1minus120582c

120582c

1 minus 120582c 120582c



119876 = minus4070 sdot (

C3S ()

C2S ()

) + 38010 (6)

where C3S and C


3S and C

2S in




2O3



2minus 07544 sdot C

3S

(7)










1 2 3 k k k1 2 3 k

120576 = 120576e + 120576c



◼d120576e1

dt+

d120576c1

dt=

d120576eb

dt+

d120576cb

dt◼

d120590r1

dt+

d120590r2

dt+

d120590r3


d120590rk

dt= 0

Δ1205901 Δ120590k




= 120576paste(119862+EX)

sdot [(

(1 minus 120582119888) sdot 119864119901sdot 120582119888


) + (1 minus 120582119888)]

(9)


119901






120576tot (119905119894+1) = 120576tot (119905119894) +Δ120590 (120591119894)

119864

+

119894

sum

119895=1

119886 sdot 119881 (119879119894) sdot Δ120590 (120591

119895)

sdot [(119905119894+1

minus 120591119895)

119899

minus (119905119894minus 120591119895)

119899

]

(10)




increment Δ120590(120591119894)



(119905119894 119905119894+1)

3 Experiment





(top and bottom)

A


Inside steel 12mm

75mm

4572mm2985mm



75mm

4572mm2985mm


Inside steel 12mm

4572mm3650mm

75mmB C


120575120579120575120574

120574im120574om

Pi

P998400i

120574os

120574is







120590120579=

1199032

im sdot 119875

1199032

om minus 1199032

im[1 +

1199032

om1199032] (11)


120590120579119894=

119875119894sdot (1199032

im + 1199032

om)

1199032

om minus 1199032

im 119903 = 119903im (12)



119875119894=

(1199032

os minus 1199032

is)

21199032

ossdot 120590120579st =

(1199032

os minus 1199032

is)

21199032





120590120579119894max =

(1199032

os minus 1199032

is)

21199032

ossdot

(1199032

im + 1199032

om)

(1199032

om minus 1199032






TypeSlump flow

(cm)Air content



N 185 56 2175 3439 4561 281 319 364EX 175 51 2106 3312 4713 280 327 359

minus1000

minus800

minus600

minus400

minus200

0

200

0 10 20 30 40Age (days)


Stra

in(120583

)






minus150

minus120

minus90

minus60

minus30

0

30

60

0 10 20 30 40Age (days)

N-AN-BN-C

EX-AEX-BEX-C

Stee

l str

ain (120583

)






minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)

N-AN-BN-C

EX-AEX-BEX-C


0

02

04

06

08

1

0

10

20

30

40

50

0 12 24 36 48 60 72

Deg

ree o

f hyd

ratio

n

Time (hr)

CementExpansive add

05

Rate

of h

eat l

iber

atio

n (J

ghr

)

WC



119864paste(119862EX)

=

1


sdot 119860ceff

(15)













=

1


(17)




119888= radic119881agg





minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)





minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)




5 Conclusions




minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)






Competing Interests


References






































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




1 2 3 k k k1 2 3 k

120576 = 120576e + 120576c



◼d120576e1

dt+

d120576c1

dt=

d120576eb

dt+

d120576cb

dt◼

d120590r1

dt+

d120590r2

dt+

d120590r3


d120590rk

dt= 0

Δ1205901 Δ120590k




= 120576paste(119862+EX)

sdot [(

(1 minus 120582119888) sdot 119864119901sdot 120582119888


) + (1 minus 120582119888)]

(9)


119901






120576tot (119905119894+1) = 120576tot (119905119894) +Δ120590 (120591119894)

119864

+

119894

sum

119895=1

119886 sdot 119881 (119879119894) sdot Δ120590 (120591

119895)

sdot [(119905119894+1

minus 120591119895)

119899

minus (119905119894minus 120591119895)

119899

]

(10)




increment Δ120590(120591119894)



(119905119894 119905119894+1)

3 Experiment





(top and bottom)

A


Inside steel 12mm

75mm

4572mm2985mm



75mm

4572mm2985mm


Inside steel 12mm

4572mm3650mm

75mmB C


120575120579120575120574

120574im120574om

Pi

P998400i

120574os

120574is







120590120579=

1199032

im sdot 119875

1199032

om minus 1199032

im[1 +

1199032

om1199032] (11)


120590120579119894=

119875119894sdot (1199032

im + 1199032

om)

1199032

om minus 1199032

im 119903 = 119903im (12)



119875119894=

(1199032

os minus 1199032

is)

21199032

ossdot 120590120579st =

(1199032

os minus 1199032

is)

21199032





120590120579119894max =

(1199032

os minus 1199032

is)

21199032

ossdot

(1199032

im + 1199032

om)

(1199032

om minus 1199032






TypeSlump flow

(cm)Air content



N 185 56 2175 3439 4561 281 319 364EX 175 51 2106 3312 4713 280 327 359

minus1000

minus800

minus600

minus400

minus200

0

200

0 10 20 30 40Age (days)


Stra

in(120583

)






minus150

minus120

minus90

minus60

minus30

0

30

60

0 10 20 30 40Age (days)

N-AN-BN-C

EX-AEX-BEX-C

Stee

l str

ain (120583

)






minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)

N-AN-BN-C

EX-AEX-BEX-C


0

02

04

06

08

1

0

10

20

30

40

50

0 12 24 36 48 60 72

Deg

ree o

f hyd

ratio

n

Time (hr)

CementExpansive add

05

Rate

of h

eat l

iber

atio

n (J

ghr

)

WC



119864paste(119862EX)

=

1


sdot 119860ceff

(15)













=

1


(17)




119888= radic119881agg





minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)





minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)




5 Conclusions




minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)






Competing Interests


References






































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




(top and bottom)

A


Inside steel 12mm

75mm

4572mm2985mm



75mm

4572mm2985mm


Inside steel 12mm

4572mm3650mm

75mmB C


120575120579120575120574

120574im120574om

Pi

P998400i

120574os

120574is







120590120579=

1199032

im sdot 119875

1199032

om minus 1199032

im[1 +

1199032

om1199032] (11)


120590120579119894=

119875119894sdot (1199032

im + 1199032

om)

1199032

om minus 1199032

im 119903 = 119903im (12)



119875119894=

(1199032

os minus 1199032

is)

21199032

ossdot 120590120579st =

(1199032

os minus 1199032

is)

21199032





120590120579119894max =

(1199032

os minus 1199032

is)

21199032

ossdot

(1199032

im + 1199032

om)

(1199032

om minus 1199032






TypeSlump flow

(cm)Air content



N 185 56 2175 3439 4561 281 319 364EX 175 51 2106 3312 4713 280 327 359

minus1000

minus800

minus600

minus400

minus200

0

200

0 10 20 30 40Age (days)


Stra

in(120583

)






minus150

minus120

minus90

minus60

minus30

0

30

60

0 10 20 30 40Age (days)

N-AN-BN-C

EX-AEX-BEX-C

Stee

l str

ain (120583

)






minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)

N-AN-BN-C

EX-AEX-BEX-C


0

02

04

06

08

1

0

10

20

30

40

50

0 12 24 36 48 60 72

Deg

ree o

f hyd

ratio

n

Time (hr)

CementExpansive add

05

Rate

of h

eat l

iber

atio

n (J

ghr

)

WC



119864paste(119862EX)

=

1


sdot 119860ceff

(15)













=

1


(17)




119888= radic119881agg





minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)





minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)




5 Conclusions




minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)






Competing Interests


References






































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





TypeSlump flow

(cm)Air content



N 185 56 2175 3439 4561 281 319 364EX 175 51 2106 3312 4713 280 327 359

minus1000

minus800

minus600

minus400

minus200

0

200

0 10 20 30 40Age (days)


Stra

in(120583

)






minus150

minus120

minus90

minus60

minus30

0

30

60

0 10 20 30 40Age (days)

N-AN-BN-C

EX-AEX-BEX-C

Stee

l str

ain (120583

)






minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)

N-AN-BN-C

EX-AEX-BEX-C


0

02

04

06

08

1

0

10

20

30

40

50

0 12 24 36 48 60 72

Deg

ree o

f hyd

ratio

n

Time (hr)

CementExpansive add

05

Rate

of h

eat l

iber

atio

n (J

ghr

)

WC



119864paste(119862EX)

=

1


sdot 119860ceff

(15)













=

1


(17)




119888= radic119881agg





minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)





minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)




5 Conclusions




minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)






Competing Interests


References






































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)

N-AN-BN-C

EX-AEX-BEX-C


0

02

04

06

08

1

0

10

20

30

40

50

0 12 24 36 48 60 72

Deg

ree o

f hyd

ratio

n

Time (hr)

CementExpansive add

05

Rate

of h

eat l

iber

atio

n (J

ghr

)

WC



119864paste(119862EX)

=

1


sdot 119860ceff

(15)













=

1


(17)




119888= radic119881agg





minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)





minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)




5 Conclusions




minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)






Competing Interests


References






































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)





minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)




5 Conclusions




minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)






Competing Interests


References






































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




minus15

0

15

3

45

6

75

0 10 20 30 40

Con

strai

ned

stres

s (M

Pa)

Age (days)






Competing Interests


References






































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



















CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



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