Research ArticleEffect of Cylinder Size on the Modulus ofElasticity and Compressive Strength of Concrete fromStatic and Dynamic Tests

Byung Jae Lee1 Seong-Hoon Kee2 Taekeun Oh3 and Yun-Yong Kim4

1RampD Center JNTINC Co Ltd 9 Hyundaikia-ro 830 beon-Gil Bibong-Myeon Hwaseong Gyeonggi-do 18284 Republic of Korea2Department of Architectural Engineering Dong-A University 37 Nakdong-Daero 550 beon-Gil Saha-guBusan 49315 Republic of Korea3Department of Safety Engineering Incheon National University 119 Academy-ro Yeonsu-gu Incheon 22012 Republic of Korea4Department of Civil Engineering Chungnam National University 99 Daehak-ro Yuseong-gu Daejeon 34134 Republic of Korea

Correspondence should be addressed to Seong-Hoon Kee shkeedauackr

Received 1 June 2015 Revised 23 August 2015 Accepted 2 September 2015

Academic Editor Santiago Garcia-Granda

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

The primary objective of this study is to investigate the effects of cylinder size (150 by 300mm and 100 by 200mm) on empiricalequations that relate static elastic moduli and compressive strength and static and dynamic elastic moduli of concrete For thepurposes two sets of one hundred and twenty concrete cylinders 150 by 300mm and 100 by 200mm were prepared from threedifferent mixtures with target compressive strengths of 30 35 and 40MPa Static and dynamic tests were performed at 4 7 14and 28 days to evaluate compressive strength and static and dynamic moduli of cylinders The effects of the two different cylindersizes were investigated through experiments in this study and database collected from the literature For normal strength concrete(le40MPa) the two different cylinder sizes do not result in significant differences in test results including experimental variabilitycompressive strength and static and dynamic elastic moduli However it was observed that the size effect became substantial inhigh strength concrete greater than 40MPa Therefore special care is still needed to compare the static and dynamic properties ofhigh strength concrete from the two different cylinder sizes

1 Introduction

The elastic modulus of concrete 119864119888is of great interest for

design of new structures and condition assessment of exist-ing structures In structure design there are requirementsfor serviceability of concrete structures such as maximumpermissible deflections and allowable story drift for high-risebuildings in general building codes [1 2] 119864

119888is a fundamental

parameter for calculating the static and dynamic behavior ofstructural elements (eg deflection side sway of tall build-ings and vibration of concrete elements) Furthermore 119864

119888is

a good indicator of degree of concrete deterioration moredegradation results in lower 119864

119888 Therefore 119864

119888is popularly

used for condition assessment of concrete structures such asbuilding components pavements and bridge decks [3]

Elastic modulus of concrete 119864119888is directly measured by

the static uniaxial compressive test in accordance with ASTM

C469 [4] which is called static elastic modulus In practice119864119888is generally determined from compressive strength based

on design codes rather than on the direct measurement ACI318 committee [1] proposes an empirical equation that relates119864119888and 119865

119888

119864ACI 318 = 0043119908119888

15

radic119865119888(MPa) (1)

where 119865119888is compressive strength of concrete in MPa and

119908119888is a unit weight of concrete in kgm3 (for 1440 le 119908

119888le

2560 kgm3) for a value of 119865119888less than 38MPa [5] Further-

more ACI 363 committee [6] proposes a different equationfor linking 119864

119888and 119865

119888for a value of 119865

119888between 21MPa and

83Mpa

119864ACI 363 = (119908119888

2300)

15

(3320radic119865119888+ 6900) (MPa) (2)

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2015 Article ID 580638 12 pageshttpdxdoiorg1011552015580638

2 Advances in Materials Science and Engineering

For both normal strength and high strength concrete theComite-Euro-International du Beton and the FederationInternationale de la Precontrainte (CEB-FIP)Model code andEurocode 2 suggests an empirical equation relating 119864

119888and 119865119888

as follows

119864CEB-FIP = 220003radic

119865119888

10(MPa) (3)

However it has been reported that the simple code equationsmay not always produce accurate 119864

119888compared to the value

based on direct measurements [7 8] In fact there was nostandard test method for determining 119864

119888when the equation

adopted by ACI 318 [1] was developed consequently therewas a substantial variation according to the definition ofelastic modulus of concrete (ie initial tangent or secantmodulus) [5] Furthermore the code equations (see (1)ndash(4))do not take into account the critical parameters such as thetype of coarse aggregates mineral admixtures and size of testspecimens for compressive strength of concrete

Elastic modulus of concrete 119864119888can be determined by

dynamic test methods such as ultrasonic pulse velocity andresonance frequency tests [9] The resulting elastic modulusis commonly referred to as dynamic elastic modulus 119864

119889

which is larger than static elastic modulus 119864119888[10] There are

several empirical equations that relate 119864119889and 119864

119888 Lydon and

Balendran [11] proposed the following empirical relationshipbetween 119864

119889and 119864

119888

119864119888= 083119864

119889(GPa) (4)

The British testing standard BS8100 Part 2 [12] providesanother empirical equation for 119864

119888as follows

119864119888= 125119864

119889minus 19 (GPa) (5)

It is noteworthy that this equation does not apply to concretecontaining more than 500 kgm3 or to lightweight aggregateconcrete [10] A more general relationship was proposedby Popovics [13] for both lightweight and normal concretetaking into account the effect of a unit weight of concrete

119864119888=

44609119864119889

14

119908119888

(GPa) (6)

However119864119888values for a given concrete predicted by different

empirical equations do not agree with each other In fact it isknown that the value of 119864

119889may vary significantly according

to testmethods and size and type of test specimens [7]There-fore it is difficult to select a correct equation that produces theleast error for different dynamic tests and test specimens

Requirements for the cylinder size of concrete are descri-bed in ASTM C192 [14] and ASTM C31 [15] which are adop-ted by general building code [1] and other ASTM standardsfor measuring compressive strength static elastic modulusand dynamic elastic moduli of concrete Even though dimen-sions are not stipulated in a specification test method orpractice the concrete cylinder should have a diameter at leastthree times nominalmaximum aggregate size and the height-to-diameter ratio of 2 In practice maximum aggregate size

ranges between 125mm and 25mm therefore a size of 100by 200mm cylinder is accepted by the standard tests methodThe use of 100 by 200mm cylinders has many advantagesagainst using larger specimens (eg 150 by 300mmcylinders)because it facilitates handling in practice and needs smallerspace and reduces construction wastes For dynamic elasticmodulus the frequency equations in ASTM C215 [16] aresupposed to produce the same value of 119864

119889when test cylinder

has the same diameter-to-height ratio without regard tocylinder sizes however different size of cylindermay produceinelastic effect and dispersion and consequently affect avalue of 119864

119889 For static tests a number of researchers [17ndash24]

have observed that the size of cylinders affects compressivestrength and elastic modulus of concrete In summary thecylinder size may affect the accuracy of the empirical equa-tions that relate compressive strength and static elastic mod-ulus (see (1)ndash(3)) and dynamic and static elastic moduli (see(4)ndash(6)) However it is difficult to quantitatively say the sizeeffect due to scarcity of experimental data comparing variousempirical equations for estimating static elastic modulus ofconcrete119864

119888from compressive strength119865

119888and dynamic elastic

modulus of concrete 119864119889

The primary objective of this study is to investigate theeffect of cylinder size (100 by 200mm and 150 by 300mm)on empirical equations that relate static and dynamic elasticmoduli of concrete and static elastic modulus and compres-sive strength of concrete For the purposes a series of experi-mental studies was performed in the laboratory which is des-cribed in Section 2Main experimental variables in this studyinclude the cylinder size (100 by 200mm and 150 by 300mmcylinders) concrete ages at the test (4 7 14 and 28 days)and compressive strength (20 30 and 40MPa) The results(ie experimental variability compressive strength and staticand dynamic elastic moduli) from various static and dynamictest methods are compared in Section 3 For a comparisonthe experimental results in this study were compared withdatabase collected from the literature

2 Experimental Program

21 Preparation of Specimens For experimental studies twosets of one hundred and twenty concrete cylinderswith differ-ent sizes (100 by 200mm and 150 by 300mm cylinders) wereprepared in the laboratory Concrete used in this study has thesame mix proportions of Type I Portland cement river sandcrushed granite with maximum size of 25mm and mineraladmixtures (fly ash and granulate-furnace slag) except forthree different water-to-binder ratios (WB) 03 035 and045 Specific concrete mix proportions are summarized inTable 1 Concrete was cast in two standard plastic molds withdimensions of 100 by 200mm and 150 by 300mm and placedin a curing chamber within 30 minutes Plastic molds wereremoved after 24 h and specimens were cured in a waterpond A series of static and dynamic tests were conducted atdifferent ages 4 7 14 and 28 days One day before testingten 100 by 200mm and 150 by 300mm cylinders for eachtest series were taken out of a water pond and air-cured ina constant temperature-and-humidity room

Advances in Materials Science and Engineering 3

Table 1 Mix proportions of concrete design

ID Cement type WB SAUnit quantity (kgm3)

W C S G Mineral admixture Chemical admixtureFA GBFS AE (binder ) SP (binder )

Mix 1Type I

045 046 259 121 777 934 58 69 09 mdashMix 2 035 047 308 166 761 886 81 85 mdash 1Mix 3 03 046 357 165 714 868 94 99 mdash 1NoteW water C cement S sand G gravel FA fly ash GBFS granulated blast furnace slag AE air-entraining agent SP superplasticizer

Figure 1 Testing setup and instrumentation for the uniaxial com-pressive test of a concrete cylinder

22 Static Tests for Compressive Strength and Elastic ModulusThe cylinders were ground at both ends before testing toremove any surface irregularity as well as ensure the ends tobe perpendicular to the sides of the specimen Elastic modu-lus and compressive strength of the cylinders were measuredusing a Universal Testing Machine (UTM) with a capacity of1000 kN according to ASTM C469 [4] and ASTM C39 [25]respectively Tests were performed at a loading rate of approx-imately 028MPas Deformationsweremeasured using threesets of linear voltage differential transducers attached to twofixed rings (see Figure 1) The apparatus consisted of twoaluminum rings with screws for attachment to the specimenThe spacing between screws on the top and bottom rings was70mm and 150mm for 100 by 200mm and 150 by 300mmcylinders respectively which served as a gauge length forcalculating axial strain from the measured deformationsThe static elastic modulus of concrete is defined as a chordmodulus from the stress-strain curve with a first point atstrain level of 000005 (120576

1) and second point at 40 of the

maximum stress as follows

119864119888=

04119891119888minus 120590 (120576

1)

120576 (04119891119888) minus 1205761

(7)

23 Dynamic Tests for Estimating Dynamic Elastic ModulusDynamic elastic modulus of concrete was estimated by mea-suring fundamental longitudinal and transverse resonancefrequencies of cylinders in accordance with ASTMC215 [16]Shown in Figure 2(a) is the test setup and data acquisitionsystem for the transverse resonance frequency test For thelongitudinal resonance frequency test an accelerometer was

placed on the center of one concrete surface and an impactsource was hit on the center of the other concrete surface Asteel ball having a diameter of 10mm was used as an impactsource for generating incident stress waves in a concretespecimen the steel ball was effective for generating widebandfrequency signals from very low to 20 kHz which covers afrequency range of the resonance tests for the 100 by 200mmand 150 by 300mm cylinders in this study Dynamic responseof concrete cylinder was measured by an accelerometerattached to concrete specimen according to ASTM C215[16] Resulting time signals were converted to the frequencydomain using the FFT (Fast Fourier Transformation) algo-rithm The resonance frequencies of concrete are manifestedas dominant amplitude in the frequency domain The mostdominant frequency was regarded as fundamental resonancefrequencies of longitudinal (or transverse) mode Dynamicelastic moduli based on the fundamental longitudinal fre-quency (119864

119889119871119877) were estimated using the following equation

119864119889119871119877

= 120573119871119872119891119871

2

(Pa) (8)

where 120573119871is constant dependent on dimensions and Poissonrsquos

ratio of concrete specimen (= 5093(1198711198632

)) for a cylinder inNsdots2 (kgsdotm2) 119872 is mass of specimen in kg and 119891

119871is funda-

mental longitudinal resonance frequency in Hz In additiondynamic elasticmoduli of concrete based on the fundamentaltransverse frequency (119864

119889119879119877) were estimated using the follow-

ing equation

119864119889119879119877

= 120573119879119872119891119879

2

(Pa) (9)

where 120573119879is constant dependent on dimensions of concrete

cylinder (= 16067[1198713

1198791198634

] for a cylinder and 119879 is a correc-tion factor dependent on ratio of the radius of gyration 119870

to the height of specimen 119867 [for concrete cylinder 119870119867 =

1198634119867] and Poissonrsquos ratio) in Nsdots2 (kgsdotm2) and 119891119879is funda-

mental transverse resonance frequency in HzFor comparison purposes the 119875-wave velocity of con-

crete 119862119875 was measured according to ASTM C597 [26] using

a pair of 119875-wave transducers (see Figure 2(b)) each of whichgenerates and receives a longitudinal ultrasonic pulse of about52 kHz through a concrete cylinder Dynamic elasticmodulusbased on 119862

119875(119864119889119875

) is determined using the following equa-tion

119864119889119875

= 120572119875120588119862119875

2

(10)

where 120572119875is constant dependent on Poissonrsquos ratio 120592 that is

(1 + 120592)(1 minus 2120592)(1 minus 120592)

4 Advances in Materials Science and Engineering

(a) (b)

Figure 2 Test setups and data acquisition system for evaluating dynamic elastic moduli using two different nondestructive evaluation tests(a) resonance frequency test (transverse mode) and (b) ultrasonic pulse velocity test (longitudinal mode)

Table 2 Summary of test results measured from 100 by 200mm and 150 by 300mm cylinders

Cylinder size Mix Day 119865119888

119864119888

119862119901

119891119871

119891119879

120583 [MPa] COV [] 120583 [GPa] COV [] 120583 [ms] COV [] 120583 [Hz] COV [] 120583 [Hz] COV []

100 times 200

Mix 1

D4 776 096 96 350 3327 205 6845 132 4165 186D7 103 364 116 770 3511 118 7220 128 4455 238D14 144 244 154 1062 3855 082 7795 158 4810 129D28 189 505 157 541 4032 124 8420 066 5165 115

Mix 2

D4 256 350 166 254 3803 110 8360 095 5160 155D7 293 340 170 210 4108 083 8570 053 5215 074D14 367 225 191 244 4224 142 8995 132 5455 119D28 393 363 231 318 4375 125 9280 091 5690 141

Mix 3

D4 229 379 1654 460 3978 190 8365 117 5150 137D7 282 459 198 821 4122 092 8730 052 5335 132D14 340 575 204 323 4261 121 8995 101 5445 133D28 408 576 223 582 4361 104 9185 196 5555 305

150 times 300

Mix 1

D4 77 275 104 733 3223 216 4585 098 2800 080D7 101 363 122 656 3487 153 4870 131 3015 166D14 138 355 147 708 3723 139 5220 115 3215 121D28 193 434 157 523 3937 142 5600 138 3430 116

Mix 2

D4 249 302 166 567 3934 147 5630 132 3450 174D7 299 260 175 332 4067 159 5730 089 3485 158D14 369 437 209 226 4219 072 6010 073 3645 129D28 432 492 237 337 4296 099 6200 081 3800 102

Mix 3

D4 231 233 169 344 3922 123 5605 084 3435 093D7 290 150 187 222 4056 084 5825 110 3535 110D14 397 284 215 709 4192 097 6060 081 3675 091D28 444 447 213 721 4295 063 6260 117 3820 133

3 Result and Discussion

31 Experimental Variability In this study the coefficient ofvariation (COV the standard deviation 120590 divided by themean value120583 of a set of samples) was used as ameans of eval-uating the experimental variability of compressive strengthand static and dynamic properties of concrete Table 2 com-pares the statistical parameters (120583 and COV) of test results

(119865119888 119864119888 119862119901 119891119871 and 119891

119879) obtained from 100 by 200mm and

150 by 300mm cylindersThe average COVs of the compressive strength of con-

crete 119865119888from different mix proportions and testing ages are

441 and 365 for 100 by 200mm and 150 by 300mmcylinders respectively The 100 by 200mm cylinders haveabout 10 higher within-test variability than 150 by 300mmcylinders The result is consistent with the observation by

Advances in Materials Science and Engineering 5

previous researchers that 100 by 200mm cylinder tends tohave about 20 higher within-test variability than 150 by300mm cylinder [27] The COVs from the 150 by 300mmcylinder are between good (40 to 50) and excellent (lt20)categories according to ACI 214R [28] whereas for 100 by200mm cylinder the COVs are between fair (50 to 60) andexcellent categories

The average COVs of the static elastic modulus 119864119888from

100 by 200mm and 150 by 300mm cylinders are 632 and583 respectively A slightly higher COV of 119864

119888is mainly

due to imperfect concrete specimens and testing procedurethe opposite faces of the specimens were slightly skew andtheir deformations under compression were not uniformThis may also affect compressive strength of concrete butappears to be more influential to determination of elasticmodulus Table 2 shows that the COVs of both119865

119888and119864

119888from

the three differentmixes are reasonably consistent at differentages in 4 7 14 and 28 days

For the dynamic tests the 100 by 200mm cylinders pro-duce equivalent or slightly higher variability than the 150by 300mm cylinders however the differences appear to beinsignificant The average COVs of the fundamental longitu-dinal 119891

119871and transverse 119891

119879frequencies measured from 100 by

200mm and 150 by 300mm cylinders are 164 and 120and 162 and 117 respectively Furthermore the averageCOVs of the 119875-wave velocity (119862

119871) for 100 by 200mm and 150

by 300mm cylinders are 140 and 123 respectively bothof which are consistent with observations by ACI committee228 [29]

32 Compressive Strength Figure 3 compares compressivestrengths of concrete cylinders measured from 100 by200mm and 150 by 300mm cylinders (119865

119888100and 119865119888150

resp)The experimental data represented as open symbols showthat there is no significant difference between 119865

119888100and 119865

119888150

in the lower strength range of 8MPa to 30MPa with a meanabsolute error (MAE) less than 1MPa In this studyMAEwasdefined as follows

MAE =sum

1003816100381610038161003816119865119888150

minus 119865119888100

1003816100381610038161003816

119873 (11)

where 119873 is the number of the experimental data (ie in thisstudy 119873 = 120) The result for low compressive strength isconsistent with observations by prior researchers [22 24 30]

However it was noticed that scattering of experimentaldata in this study becomes greater as compressive strengthincreases in the higher strength range greater than 30MPa119865119888150

-to-119865119888100

ratio in this study gradually increases as 119865119888100

increases An approximated equation that relates 119865119888150

and119865119888100

was established by a linear regression analysis of theexperimental data set in this study as follows

119865119888150

= 111119865119888100

minus 156 [MPa] (1198772

= 096) (12)

The best-fit line presented as a red dash line in Figure 3 iscompatible with the equations proposed by prior researchers[19 20] However there is contradiction in the relationshipbetween 119865

119888150and 119865119888100

reported by different researchers (see

Com

pres

sive s

treng

thFc150

(MPa

)

10 20 30 40 50 60 70 80 90 1000Compressive strength Fc100 (MPa)

0

10

20

30

40

50

60

70

80

90

100

Test results mix 1Test results mix 2Test results mix 3Issa et al (2000) Malaikah (2005)Vandergrift and Schindler (2006)

P M Carrasquillo and R L Carrasquillo (1988)Carrasquillo et al (1981) Cook (1989)Line of equalityBest-fit line in the present study(Fc150 = 111Fc100 minus 156 R2

= 096)

Figure 3 Comparison of compressive strength of concrete mea-sured from 100 by 200mm and 150 by 300mm cylinders (119865

119888100and

119865119888150

resp)

Figure 2) [18ndash22 24 30] The inconsistency results in thehigher strength range are attributed to complexity in theinterfacial transition zone of concrete [10 24] It is knownthat considerable stresses are transferred at cement paste andaggregatesrsquo interface of high strength concrete due to lowerporosity of the interfacial transition zone (ITZ) In fact thereare a number of factors affecting the ITZ which includecoarse aggregates mineral admixtures and curing methodsand various factors affect compressive strength in differentways for different cylinder sizes [14] Therefore special careis still needed for selecting the cylinder size for measuringcompressive strength of relatively high strength concrete(gt40MPa)

33 Static Elastic Moduli Figure 4 compares static elasticmoduli of concrete measured from 100 by 200mm and 150by 300mm cylinders (119864

119888100and 119864

119888150 resp) in this study For

a comparison database collected from the literature [22 30]was shown in the same figure The experimental data set inthis study presented as open symbols shows that 119864

119888100is

closely correlated with 119864119888150

in the elastic modulus range of10GPa to 25GPa For the lower elastic modulus range of 10to 15GPa 119864

119888100values are comparable with 119864

119888150values with

6 Advances in Materials Science and EngineeringSt

atic

elas

tic m

odul

usEc150

(GPa

)

Test results mix 1Test results mix 2Test results mix 3Malaikah (2005)

Best-fit line of the experimental data in this study(Ec150 = 09Ec100 + 19 R2

= 084)

Issa et al (2000)95 confidence boundsLine of equality

0

5

10

15

20

25

30

35

40

45

50

55

4010 15 20 25 30 35 500 45 555Static elastic modulus Ec100 (GPa)

Figure 4 Comparison of static elastic moduli of concrete measuredfrom 100 by 200mm and 150 by 300mm cylinders (119864

119888100and 119864

119888150

resp)

MAE between 119864119888100

and 119864119888150

of about 045GPaTherefore itmay be acceptable to assume from a practical perspective thatstatic elastic moduli using 100 by 200mm and 150 by 300mmcylinders are equivalent

However the ratio of 119864119888150

to 119864119888100

appears to graduallyincrease as 119864

119888150increases to 25GPa The higher elasticity

in the smaller size is attributed to the fact that the quantityof mortar required to fill the space between the particles ofthe coarse aggregate and the wall of the mold is greater thanthat necessary in the interior of the mass (ie wall effect)[10] In general the elasticity of cementmortar is greater thanthat of concrete which consequently results in increasing theeffective elasticity of concrete in smaller size In this study thebest-fit line that approximates the relationship between 119864

119888150

and 119864119888100

was established by a linear regression analysis asfollows

119864119888150

= 09119864119888100

+ 19 [MPa] (1198772

= 084) (13)

The best-fit line and 95 confidence bounds of the best-fitline are presented as solid and dash lines respectively inFigure 3 Interestingly the best-fit line of the experimentaldata in this study (10GPa le 119864

119888100le 25GPa) appears to be

valid for predicting the data set in the higher elastic modulusrange of 25GPa to 55GPa reported by prior researchers [2230] However it is still difficult to attain general conclusionson the relationship between 119864

119888150and 119864

119888100 especially for

Test results mix 1Test results mix 2Test results mix 3

Best-fit line for experimental data in this study

95 confidence boundsLine of equality

5010 15 20 25 30 35 40 600 455 550

5

10

15

20

25

30

35

40

45

50

55

60

Dyn

amic

elas

tic m

odul

usEdP150

(GPa

)

Dynamic elastic modulus EdP100 (GPa)

(EdP150 = 097Ed + 0138 R2= 092)100P

Figure 5 Comparison of velocity moduli from 100 by 200mm and150 by 300mm cylinders

concrete in the higher strength range greater than 50MPabecause of scarcity of available experimental data

34 Dynamic Elastic Moduli Figure 5 compares dynamicelastic moduli measured using UPV tests (ie velocitymoduli) from 100 by 200mm and 150 by 300mm cylinders(119864119889119875100

and 119864119889119875150

resp) in accordance with ASTM C597[26] It was observed that 100 by 200mm cylinders consis-tently result in slightly higher dynamic elastic moduli than150 by 300mm cylinders Linear regression of 119864

119889119875100and

119864119889119875150

measured in this study shows that 119864119889119875100

is about3 greater than 119864

119889119875150in a range of 20GPa to 40GPa (see

Figure 5) The MAE from two different cylinders was about05 GPa which is only 25 of the MAE from static elasticmoduli in this study (ie 2 GPa)

In addition shown in Figures 6(a) and 6(b) is the compar-ison of dynamic elastic moduli measured from longitudinaland transverse resonance frequency tests (ie resonancemoduli) 119864

119889119871119877and 119864

119889119879119877 respectively from 100 by 200mm

and 150 by 300mm cylinders in accordance with ASTMC125[16] The use of 150 by 300mm cylinders tends to resultin slightly higher resonance moduli (both 119864

119889119871119877and 119864

119889119879119877)

than those from 100 by 200mm cylinders According to thelinear regression analysis it was found that the resonancemoduli measured using the 150 by 300mm cylinder (119864

119889119871119877150

or 119864119889119877119877150

) are 1 to 2 greater than those from the 100by 200mm cylinder (119864

119889119871119877100or 119864119889119877119877100

) Approximatedequations that relate the resonance moduli from the twodifferent cylinder sizes are shown in Figures 6(a) and 6(b)

Advances in Materials Science and Engineering 7

Test results mix 1Test results mix 2Test results mix 3

0

5

10

15

20

25

30

35

40

3510 15 20 25 30 400 5

(EdLR150 = 102EdLR100 + 0127 R2= 096)

Best-fit line for experimental data in this study

95 confidence boundsLine of equality

EdLR100 (GPa)Dynamic elastic modulus

EdLR150

(GPa

)D

ynam

ic el

astic

mod

ulus

(a)

Test results mix 1Test results mix 2Test results mix 395 confidence boundsLine of equalityBest-fit line for experimental data in this study(EdTR150 = 101EdTR100 + 0438 R2

= 093)

0

5

10

15

20

25

30

35

40

3510 15 20 25 30 400 5EdTR100 (GPa)Dynamic elastic modulus

EdTR150

(GPa

)D

ynam

ic el

astic

mod

ulus

(b)

Figure 6 Comparison of resonance moduli from 100 by 200mm and 150 by 300mm cylinders (a) 119864119889119871119877150

versus 119864119889119871119877100

and (b) 119864119889119879119877150

versus 119864119889119879119877100

Furthermore without regard to longitudinal or transversemodes the MAE between the resonance moduli from thedifferent cylinder is less than 03GPa Therefore the findingsin this study demonstrate that the dynamic elastic moduli(both velocity and resonance moduli) using the 100 by200mm and 150 by 300mm cylinders are regarded as beingequal from a practical standpoint

However it was observed that there is a precaution inmeasuring reliable and consistent resonance frequency usingthe 100 by 200mm cylinder The smaller cylinder has higherchance of mistakenly hitting an impact source (location andinclination to test surface) which may cause undesirableresonance modes such as torsional modes in the frequencydomain Consequently it was often difficult to select a rightfrequency peak corresponding to the fundamental longitudi-nal or transverse modes In this study preliminary numeri-cal simulations were conducted to calculate theoretical fre-quency peak values which was helpful to select a rightfrequency peak In addition to improve accuracy and con-sistency resonance tests were repeated until the COV of fivesuccessive testing procedures is less than 5 and average ofthe five test results was finally accepted in this study

35 Relationship between Static Elastic Modulus and Com-pressive Strength Figure 7 is a plot representing relationshipbetween static elastic modulus and compressive strengthmeasured in accordance with ASTM C469 [4] and ASTM

C39 [25] respectively The data points obtained from 100 by200mm and 150 by 300mm cylinders are presented as openand solid symbols in Figures 7(a) and 7(b) respectively For acomparison Figure 7 presents three code equations adoptedby ACI 318 and ACI 363 committees and CEB-FIP Modelcode and a practical equation proposed by Noguchi et al [8](see (14)) which was developed based on an extensive exper-imental database from normal to high strength concrete

119864119888= 1198961119896233500 (

119865119888

60)

13

(119908119888

2400)

2

(14)

where 1198961and 119896

2are correction factors for coarse aggregates

and mineral admixturesIt was found that the effect of cylinder size appears to be

insignificant on the relationship between static elastic modu-lus and compressive strength of concrete for normal strengthconcrete (lt40MPa) in this study Approximated equationsthat relate 119864

119888and 119865119888from 100 by 200mm and 150 by 300mm

cylinders were established by nonlinear regression analysesand shown in Figures 7(a) and 7(b) respectivelyTheMAE ofthe two best-fit curves is less than 01 GPa in the compressivestrength range of 10MPa to 40MPa In this studyMAE of thetwo continuous curves was defined as follows

MAEcon =

[int 1198921(119865119888) minus 1198922(119865119888) 119889119865119888]

int 119889119865119888

(15)

8 Advances in Materials Science and Engineering

Best-fit line for experimental data in this study(Ec150 = 456Fc150

0418 R2= 090)

Noguchi et al [2009] k1 = k2 = 1

Noguchi et al [2009] k1 = k2 = 095

Mix 1

Mix 3

ACI 318ACI 363CEB-FIP Model code and Eurocode 2

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

5010 15 20 25 30 35 40 45 55 6050Compressive strength Fc (MPa)

150 by 300mm cylindersMix 2

(a)

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

Best-fit line for experimental data in this study(Ec100 = 416Fc100

0446 R2= 084)

Noguchi et al [2009] k1 = k2 = 1

Noguchi et al [2009] k1 = k2 = 095

Mix 1

Mix 3

ACI 318ACI 363CEB-FIP Model code and Eurocode 2

50 15 20 25 30 35 40 45 50 55 6010Compressive strength Fc (MPa)

0

5

10

15

20

25

30

35

40

Mix 2 100 by 200mm cylinders

(b)

Figure 7 Comparison of compressive strength and static elastic modulus of concrete

where MAEcon is mean average error (MAE) of two contin-uous functions 119892

119894is a function presenting 119864

119888expressed as

119865119888 and the subscript 119894 indicates cylinder size (1 and 2 for the

100 by 200mm and 150 by 300mm cylinders resp) Further-more there is no significant difference in 119877

2 values of thetwo best-fit curves 1198772 values for the 100 by 200mm and150 by 300mm cylinders are 088 and 090 respectivelyTherefore the 100 by 200mm cylinders can be used insteadof 150 by 300mm cylinders to estimate static elastic modulusfrom compressive strength without reducing accuracy andconsistency However the three code equations tend tooverestimate static modulus of concrete compared to thosefrom direct measurement according to ASTM C469 [4] Assummarized in Table 3 mean average error (MAE) betweenmeasured and predicted 119864

119888from the three code equations is

in a range of 44 to 12GPa corresponding to about 10 to30 of the measured 119864

119888 In contrast the Noguchi equation

[8] predicts experimental results with far more improvedaccuracy (ie MAE less than 2GPa) by addressing correctionfactors for the effects of aggregates and mineral admixtures(ie 119896

1= 1198962= 095)

36 Relationship between Static and Dynamic Elastic ModuliFigure 8 presents the relationship between static and dynamicelastic moduli determined using different nondestructivetesting methods 119864

119889119875 119864119889119871119877

and 119864119889119879119877

respectively with

Table 3 Mean absolute error (MAE) of expressions relating staticelastic modulus and compressive strength measured using 100 by200mm and 150 by 300mm cylinders

Equation to convert 119864119889to

119864119888

MAE (GPa)150 by 300mm

cylinder100 by 200mm

cylinder119864119889119871119879

119864119889119871119879

Equation (1) 483 463Equation (2) 454 443Equation (3) 1221 1215Equation (14) with1198961= 1198962= 1

342 341

Equation (14) with1198961= 1198962= 095

156 188

Best-fit line 132 157

Poissonrsquos ratio of 02Theuse of Poissonrsquos ratio of 02 is reason-able for common concrete in practice [10] In Figure 8 119864

119889119875

119864119889119871119877

and 119864119889119879119877

measured from 100 by 200mm and 150 by300mm cylinders are shown as open and solid symbols in leftand right columns For comparison purposes several well-known empirical equations (see (3) (4) and (5)) proposedby prior researchers are shown in the figures

Advances in Materials Science and Engineering 9

Best-fit line for experimental data in this study(Ec150 = 044EdLR150

115 R2= 090)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equalityLydon and Balendran (1986)BS8100 Part 2Popovics (1975)

5 10 15 20 25 30 35 400Dynamic elastic modulus EdLR (GPa)

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

(a)

Best-fit line for experimental data in this study(Ec150 = 044EdTR100

115 R2= 090)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equality

BS8100 Part 2

5 10 15 20 25 30 35 400Dynamic elastic modulus EdTR (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

Popovics (1975)

Lydon and Balendran (1986)

(b)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equality

BS8100 Part 2

Best-fit line for experimental data in this study(Ec150 = 022EdP150

129 R2= 087)

Popovics (1975)

Lydon and Balendran (1986)

3510 15 20 25 30 400 5Dynamic elastic modulus EdP (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

(c)

Best-fit line for experimental data in this study(Ec100 = 040EdLR100

118 R2= 088)

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

3510 15 20 25 30 400 5Dynamic elastic modulus EdLR (GPa)

Lydon and Balendran (1986)

Popovics (1975)

(d)

Figure 8 Continued

10 Advances in Materials Science and Engineering

Best-fit line for experimental data in this study(Ec100 = 039EdTR100

120 R2= 087)

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

3510 15 20 25 30 400 5Dynamic elastic modulus EdTR (GPa)

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

Lydon and Balendran (1986)

Popovics (1975)

(e)

Best-fit line for experimental data in this study

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

3510 15 20 25 30 400 5Dynamic elastic modulus EdP (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

EdLR100135 R2

= 085)(Ec100 = 017

Popovics (1975)

Lydon and Balendran (1986)

(f)

Figure 8 Comparison of static and resonance elastic moduli of concrete (a) 119864119889119871119877150

versus 119864119888150

(b) 119864119889119879119877150

versus 119864119888150

(c) 119864119889119875150

versus119864119888150

(d) 119864119889119871119877100

versus 119864119888100

(e) 119864119889119879119877100

versus 119864119888100

and (f) 119864119889119875100

versus 119864119888100

Table 4 Mean absolute error (MAE) of expressions relating static and dynamic elastic modulus measured using 100 by 200mm and 150 by300mm cylinders

Equation to convert 119864119889to 119864119888

MAE (GPa)150 by 300mm cylinder 100 by 200mm cylinder

119864119889119871119879

119864119889119877119879

119864119889119875

119864119889119871119879

119864119889119877119879

119864119889119875

Equation (4) 302 282 754 283 254 846Equation (5) 559 591 277 607 649 335Equation (6) 125 111 658 113 107 780Best-fit line 090 095 126 109 110 117

It is observed that there is only slight difference in therelationship between119864

119888and119864

119889obtained from 100 by 200mm

and 150 by 300mm cylinders In this study approximatedequations that relate119864

119888and119864

119889(119864119889119875

119864119889119871119877

or119864119889119879119877

) from 100by 200mm and 150 by 300mm cylinders were established bynonlinear regression analyses and shown in Figures 8(a)ndash8(f)The MAEs of the two best-fit curves are less than 01MPa inthe dynamic elastic modulus range of 10GPa to 25GPa Fur-thermore there is no significant difference in 119877

2 values of thetwo best-fit curves (see Figure 8) However for both data setsfrom different cylinders the three dynamic moduli (119864

119889119871119877

119864119889119879119877

and 119864119889119875

) obtained from resonance tests and UPVmethod are greater than the static elastic modulus 119864

119888 with

different static-to-dynamic elastic modulus ratio 119864119888119864119889119875

ratio with an average of 056 and COV of 92 is too faraway from the line of equality as well as from the three well-known equations relating static and dynamic elastic modu-lus Therefore the use of 119864

119889119875appears to be inappropriate

to estimate static elastic modulus which is consistent withobservations from other researchers [7 10] In contrast119864119888119864119889119871119877

(or 119864119888119864119889119879119877

) ratio was closer to the line of equalitythan 119864

119888119864119889119875

with an average of 072 and COV of 715The equation proposed by Popovics [13] (see (6)) shows verygood agreement with the experimental results regardless ofcylinder size in this study (see Table 4) In addition priorresearcher [7] observed that the Popovics equation (see (6))can be extended to high strength concrete up to 60MPawith-out regard to cylinder size However it should be mentioned

Advances in Materials Science and Engineering 11

that additional experimental data should be accumulated tobetter understand the size effect on the relationship betweenstatic and dynamic elastic moduli of high strength concrete(gt60MPa) due to scarcity of experimental studies in such ahigh strength range

4 Conclusions

A series of experimental studies was conducted to explore theeffect of cylinder size (100 by 200mm and 150 by 300mmcylinders) on the relationship between static elastic modulusand compressive strength and static and dynamic elasticmoduli of concrete Conclusions based on experiments in thisstudy and database from the literature are drawn as follows

(1) Experimental results in this study show that theCOVsof test results from 100 by 200mm cylinders areabout 10 higher than those from 150 by 300mmcylinders however the differences are statisticallyinsignificantThe averageCOVs of static and dynamicelastic moduli using the UPV and longitudinal andtransverse resonance frequency tests from 100 by200mm cylinders are 632 140 162 and 117respectively while those values from 150 by 300mmcylinders are 583 123 162 and 117 respec-tively For compressive strength the average COVsfrom the 100 by 200mm and 150 by 300mm cylindersare 441 and 365 respectively

(2) According to the findings from similarity tests of best-fit curves and comparison of 1198772 based on regressionanalyses it has been demonstrated that the effect ofcylinder size (100 by 200mm and 150 by 300mmcylinders) is insignificant on compressive strengthand static elastic modulus and the relationship bet-ween the two parameters for normal strength con-crete up to 30MPa However in the higher strengthrange greater than 30MPa there is contradiction inthe relationship between 119865

119888150and 119865

119888100based on

experimental test in this study and database reportedby different researchers Therefore it is difficult toestablish a simple equation that relates 119865

119888100and 119865119888150

and 119864

119888100and 119864

119888150because of limited experimental

and theoretical studies

(3) The three code equations tend to overestimate staticmodulus of concrete compared to those from directmeasurement according to ASTM C469 with MAEin a range of 44GPa to 12GPa In contrast theNoguchi equation predicts experimental results withfar more improved accuracy (ie MAE less than2GPa) by addressing correction factors for the effectsof aggregates and mineral admixtures (ie 119896

1= 1198962=

095)

(4) There is only a slight difference in the relationshipbetween static and resonance moduli from 100 by200mm and 150 by 300mm cylinders for normalstrength concrete Test results from this study and theliterature show that the empirical equation suggested

by Popovics [13] ((6) in this study) is effective for pre-dicting static elastic moduli from resonance moduliof concrete with compressive strength up to 60MParegardless of the cylinder size with MAE of less than15 GPa

(5) However the velocity moduli are excessively greaterthan static elastic modulus The empirical equations(see (4) (5) and (6)) produce considerable errors(with MAE in a range of 277GPa to 846GPa) bet-ween measured and predicted elastic moduli There-fore the use of velocitymoduli appears to be inappro-priate to estimate static elastic modulus

Conflict of Interests

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

Acknowledgment

This research was supported by the Basic Science ResearchProgram through theNational Research Foundation of Korea(NRF) funded by the Ministry of Science ICT amp FuturePlanning (no 2015R1A5A1037548)

References

[1] ACI Committee 318 Building Code Requirements for StructuralConcrete (ACI 318-11) and Commentary American ConcreteInstitute Farmington Hills Mich USA 2014

[2] IBC Council International Building Code (IBC 2012) 2014[3] N Gucunski A Imani F Romero et al ldquoNondestructive testig

to identify concrete bridge deck deteriorationrdquo SHRP 2 ReportS2-R06A-RR-1 2013

[4] ACI Committee 469 Standard Test Method for Static Modulusof Elasticity and Poissonrsquos Ratio of Concrete in CompressionAmerican Concrete Institute Farmington Hills Mich USA2014

[5] A Pauw ldquoStatic modulus of elasticity of concrete as affected bydensityrdquo ACI Journal Proceedings vol 57 no 12 pp 679ndash6871960

[6] ACI Committee 363 ldquoState-of-the-art report on high-strengthconcreterdquo ACI Journal Proceedings vol 81 no 4 pp 364ndash4111984

[7] J S Popovics ldquoA study of static and dynamic modulus ofelasticity of concreterdquo ACI-CRC Final Report 2008

[8] T Noguchi F Tomosawa KM Nemati BM Chiaia and A RFantilli ldquoA practical equation for elastic modulus of concreterdquoACI Structural Journal vol 106 no 5 pp 690ndash696 2009

[9] R E Philleo ldquoComparison of results of threemethods for deter-mining Youngrsquos modulus of elasticity of concreterdquo InternationalConcrete Abstracts Portal vol 51 no 1 pp 461ndash469 1955

[10] A M Neville Properties of Concrete John Wiley amp Sons NewYork NY USA 4th edition 1997

[11] F D Lydon and R V Balendran ldquoSome observations on elasticproperties of plain concreterdquo Cement and Concrete Researchvol 16 no 3 pp 314ndash324 1986

[12] B S Institute ldquoStructural use of concretemdashpart 2 code ofpractice for special circumstancerdquo BS 8110-21995 BSI LondonUK 1995

12 Advances in Materials Science and Engineering

[13] S Popovics ldquoVerification of relationships between mechanicalproperties of concrete-like materialsrdquoMaterials and Structuresvol 8 no 3 pp 183ndash191 1975

[14] ASTM C191 Standard Practice for Making and Curing ConcreteTest Specimens in the Laboratory ASTM 2014

[15] ASTM ldquoStandard practice for making and curing concrete testspecimen in the fieldrdquo ASTM C31 ASTM International 2012

[16] ASTM International ldquoStandard test method for fundamentaltransverse longitudinal and torsional resonant frequencies ofconcrete specimensrdquo ASTM C215 ASTM International WestConshohocken Pa USA 2002

[17] P-C Aitcin and P K Mehta ldquoEffect of coarse-aggregate char-acteristics on mechanical properties of high-strength concreterdquoACI Materials Journal vol 87 no 2 pp 103ndash107 1990

[18] P-C Aitcin B Miao W D Cook and D Mitchell ldquoEffectsof size and curing on cylinder compressive strength of normaland high-strength concretesrdquo ACIMaterials Journal vol 91 pp349ndash354 1994

[19] P M Carrasquillo and R L Carrasquillo ldquoEvaluation of the useof current concrete practice in the production of high strengthconcreterdquo ACI Materials Journal vol 85 no 1 pp 49ndash54 1988

[20] R L Carrasquillo A H Nilson and F O Slate ldquoProperties ofhigh strength concrete subject to short-term loadsrdquo Journal ofthe American Concrete Institute vol 78 no 3 pp 171ndash178 1981

[21] J E Cook ldquo10000 psi concreterdquo Concrete International vol 11pp 67ndash75 1989

[22] A S Malaikah ldquoA proposed relationship for the modulus ofelasticity of high strength concrete using local materials inRiyadhrdquo Journal of King Saud UniversitymdashEngineering Sciencesvol 17 pp 1ndash11 2005

[23] A Mokhtarzadeh and C French ldquoMechanical properties ofhigh-strength concrete with consideration for precast applica-tionsrdquo ACI Materials Journal vol 97 no 2 pp 136ndash147 2000

[24] DVandergrift Jr andA K Schindler ldquoThe effect of test cylindersize on the compressive strength of sulfur capped concretespecimensrdquo Tech Rep IR-06-01 Highway Research Centerand Department of Civil Engineering at Auburn UniversityAuburn Ala USA 2006

[25] ASTM International ldquoStandard test method for compressivestrength of cylindrical concrete specimensrdquo ASTM C39 ASTMInternational West Conshohocken Pa USA 2014

[26] ASTM ldquoStandard test method for pulse velocity throughconcreterdquo ASTM C597 ASTM International 1997

[27] N J CarinoW F Guthrie E S Lagergren and G MMullingsldquoEffects of testing variables on the strength of high-strength(90MPa) concrete cylindersrdquo in High-Performance ConcreteV M Malhotra Ed SP-149 pp 589ndash632 American ConcreteInstitute Farmington Hills Mich USA 1994

[28] ACI ldquoGuide for evaluation of strength test results of concrete(ACI 214R-11)rdquo ASTM C214 American Concrete InstituteFarmington Hills Mich USA 2011

[29] ACI Committee 228 ldquoNondestructive test methods for evalua-tion of concrete in structuresrdquo ReportACI 2282R-98AmericanConcrete Institute Farmington Hills Mich USA 1998

[30] S A Issa M S Islam M A Issa A A Yousif and M A IssaldquoSpecimen and aggregate size effect on concrete compressivestrengthrdquo Cement Concrete and Aggregates vol 22 no 2 pp103ndash115 2000

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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International Journal of

Biomaterials

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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

For both normal strength and high strength concrete theComite-Euro-International du Beton and the FederationInternationale de la Precontrainte (CEB-FIP)Model code andEurocode 2 suggests an empirical equation relating 119864

119888and 119865119888

as follows

119864CEB-FIP = 220003radic

119865119888

10(MPa) (3)

However it has been reported that the simple code equationsmay not always produce accurate 119864

119888compared to the value

based on direct measurements [7 8] In fact there was nostandard test method for determining 119864

119888when the equation

adopted by ACI 318 [1] was developed consequently therewas a substantial variation according to the definition ofelastic modulus of concrete (ie initial tangent or secantmodulus) [5] Furthermore the code equations (see (1)ndash(4))do not take into account the critical parameters such as thetype of coarse aggregates mineral admixtures and size of testspecimens for compressive strength of concrete

Elastic modulus of concrete 119864119888can be determined by

dynamic test methods such as ultrasonic pulse velocity andresonance frequency tests [9] The resulting elastic modulusis commonly referred to as dynamic elastic modulus 119864

119889

which is larger than static elastic modulus 119864119888[10] There are

several empirical equations that relate 119864119889and 119864

119888 Lydon and

Balendran [11] proposed the following empirical relationshipbetween 119864

119889and 119864

119888

119864119888= 083119864

119889(GPa) (4)

The British testing standard BS8100 Part 2 [12] providesanother empirical equation for 119864

119888as follows

119864119888= 125119864

119889minus 19 (GPa) (5)

It is noteworthy that this equation does not apply to concretecontaining more than 500 kgm3 or to lightweight aggregateconcrete [10] A more general relationship was proposedby Popovics [13] for both lightweight and normal concretetaking into account the effect of a unit weight of concrete

119864119888=

44609119864119889

14

119908119888

(GPa) (6)

However119864119888values for a given concrete predicted by different

empirical equations do not agree with each other In fact it isknown that the value of 119864

119889may vary significantly according

to testmethods and size and type of test specimens [7]There-fore it is difficult to select a correct equation that produces theleast error for different dynamic tests and test specimens

Requirements for the cylinder size of concrete are descri-bed in ASTM C192 [14] and ASTM C31 [15] which are adop-ted by general building code [1] and other ASTM standardsfor measuring compressive strength static elastic modulusand dynamic elastic moduli of concrete Even though dimen-sions are not stipulated in a specification test method orpractice the concrete cylinder should have a diameter at leastthree times nominalmaximum aggregate size and the height-to-diameter ratio of 2 In practice maximum aggregate size

ranges between 125mm and 25mm therefore a size of 100by 200mm cylinder is accepted by the standard tests methodThe use of 100 by 200mm cylinders has many advantagesagainst using larger specimens (eg 150 by 300mmcylinders)because it facilitates handling in practice and needs smallerspace and reduces construction wastes For dynamic elasticmodulus the frequency equations in ASTM C215 [16] aresupposed to produce the same value of 119864

119889when test cylinder

has the same diameter-to-height ratio without regard tocylinder sizes however different size of cylindermay produceinelastic effect and dispersion and consequently affect avalue of 119864

119889 For static tests a number of researchers [17ndash24]

have observed that the size of cylinders affects compressivestrength and elastic modulus of concrete In summary thecylinder size may affect the accuracy of the empirical equa-tions that relate compressive strength and static elastic mod-ulus (see (1)ndash(3)) and dynamic and static elastic moduli (see(4)ndash(6)) However it is difficult to quantitatively say the sizeeffect due to scarcity of experimental data comparing variousempirical equations for estimating static elastic modulus ofconcrete119864

119888from compressive strength119865

119888and dynamic elastic

modulus of concrete 119864119889

The primary objective of this study is to investigate theeffect of cylinder size (100 by 200mm and 150 by 300mm)on empirical equations that relate static and dynamic elasticmoduli of concrete and static elastic modulus and compres-sive strength of concrete For the purposes a series of experi-mental studies was performed in the laboratory which is des-cribed in Section 2Main experimental variables in this studyinclude the cylinder size (100 by 200mm and 150 by 300mmcylinders) concrete ages at the test (4 7 14 and 28 days)and compressive strength (20 30 and 40MPa) The results(ie experimental variability compressive strength and staticand dynamic elastic moduli) from various static and dynamictest methods are compared in Section 3 For a comparisonthe experimental results in this study were compared withdatabase collected from the literature

2 Experimental Program

21 Preparation of Specimens For experimental studies twosets of one hundred and twenty concrete cylinderswith differ-ent sizes (100 by 200mm and 150 by 300mm cylinders) wereprepared in the laboratory Concrete used in this study has thesame mix proportions of Type I Portland cement river sandcrushed granite with maximum size of 25mm and mineraladmixtures (fly ash and granulate-furnace slag) except forthree different water-to-binder ratios (WB) 03 035 and045 Specific concrete mix proportions are summarized inTable 1 Concrete was cast in two standard plastic molds withdimensions of 100 by 200mm and 150 by 300mm and placedin a curing chamber within 30 minutes Plastic molds wereremoved after 24 h and specimens were cured in a waterpond A series of static and dynamic tests were conducted atdifferent ages 4 7 14 and 28 days One day before testingten 100 by 200mm and 150 by 300mm cylinders for eachtest series were taken out of a water pond and air-cured ina constant temperature-and-humidity room

Advances in Materials Science and Engineering 3

Table 1 Mix proportions of concrete design

ID Cement type WB SAUnit quantity (kgm3)

W C S G Mineral admixture Chemical admixtureFA GBFS AE (binder ) SP (binder )

Mix 1Type I

045 046 259 121 777 934 58 69 09 mdashMix 2 035 047 308 166 761 886 81 85 mdash 1Mix 3 03 046 357 165 714 868 94 99 mdash 1NoteW water C cement S sand G gravel FA fly ash GBFS granulated blast furnace slag AE air-entraining agent SP superplasticizer

Figure 1 Testing setup and instrumentation for the uniaxial com-pressive test of a concrete cylinder

22 Static Tests for Compressive Strength and Elastic ModulusThe cylinders were ground at both ends before testing toremove any surface irregularity as well as ensure the ends tobe perpendicular to the sides of the specimen Elastic modu-lus and compressive strength of the cylinders were measuredusing a Universal Testing Machine (UTM) with a capacity of1000 kN according to ASTM C469 [4] and ASTM C39 [25]respectively Tests were performed at a loading rate of approx-imately 028MPas Deformationsweremeasured using threesets of linear voltage differential transducers attached to twofixed rings (see Figure 1) The apparatus consisted of twoaluminum rings with screws for attachment to the specimenThe spacing between screws on the top and bottom rings was70mm and 150mm for 100 by 200mm and 150 by 300mmcylinders respectively which served as a gauge length forcalculating axial strain from the measured deformationsThe static elastic modulus of concrete is defined as a chordmodulus from the stress-strain curve with a first point atstrain level of 000005 (120576

1) and second point at 40 of the

maximum stress as follows

119864119888=

04119891119888minus 120590 (120576

1)

120576 (04119891119888) minus 1205761

(7)

23 Dynamic Tests for Estimating Dynamic Elastic ModulusDynamic elastic modulus of concrete was estimated by mea-suring fundamental longitudinal and transverse resonancefrequencies of cylinders in accordance with ASTMC215 [16]Shown in Figure 2(a) is the test setup and data acquisitionsystem for the transverse resonance frequency test For thelongitudinal resonance frequency test an accelerometer was

placed on the center of one concrete surface and an impactsource was hit on the center of the other concrete surface Asteel ball having a diameter of 10mm was used as an impactsource for generating incident stress waves in a concretespecimen the steel ball was effective for generating widebandfrequency signals from very low to 20 kHz which covers afrequency range of the resonance tests for the 100 by 200mmand 150 by 300mm cylinders in this study Dynamic responseof concrete cylinder was measured by an accelerometerattached to concrete specimen according to ASTM C215[16] Resulting time signals were converted to the frequencydomain using the FFT (Fast Fourier Transformation) algo-rithm The resonance frequencies of concrete are manifestedas dominant amplitude in the frequency domain The mostdominant frequency was regarded as fundamental resonancefrequencies of longitudinal (or transverse) mode Dynamicelastic moduli based on the fundamental longitudinal fre-quency (119864

119889119871119877) were estimated using the following equation

119864119889119871119877

= 120573119871119872119891119871

2

(Pa) (8)

where 120573119871is constant dependent on dimensions and Poissonrsquos

ratio of concrete specimen (= 5093(1198711198632

)) for a cylinder inNsdots2 (kgsdotm2) 119872 is mass of specimen in kg and 119891

119871is funda-

mental longitudinal resonance frequency in Hz In additiondynamic elasticmoduli of concrete based on the fundamentaltransverse frequency (119864

119889119879119877) were estimated using the follow-

ing equation

119864119889119879119877

= 120573119879119872119891119879

2

(Pa) (9)

where 120573119879is constant dependent on dimensions of concrete

cylinder (= 16067[1198713

1198791198634

] for a cylinder and 119879 is a correc-tion factor dependent on ratio of the radius of gyration 119870

to the height of specimen 119867 [for concrete cylinder 119870119867 =

1198634119867] and Poissonrsquos ratio) in Nsdots2 (kgsdotm2) and 119891119879is funda-

mental transverse resonance frequency in HzFor comparison purposes the 119875-wave velocity of con-

crete 119862119875 was measured according to ASTM C597 [26] using

a pair of 119875-wave transducers (see Figure 2(b)) each of whichgenerates and receives a longitudinal ultrasonic pulse of about52 kHz through a concrete cylinder Dynamic elasticmodulusbased on 119862

119875(119864119889119875

) is determined using the following equa-tion

119864119889119875

= 120572119875120588119862119875

2

(10)

where 120572119875is constant dependent on Poissonrsquos ratio 120592 that is

(1 + 120592)(1 minus 2120592)(1 minus 120592)

4 Advances in Materials Science and Engineering

(a) (b)

Figure 2 Test setups and data acquisition system for evaluating dynamic elastic moduli using two different nondestructive evaluation tests(a) resonance frequency test (transverse mode) and (b) ultrasonic pulse velocity test (longitudinal mode)

Table 2 Summary of test results measured from 100 by 200mm and 150 by 300mm cylinders

Cylinder size Mix Day 119865119888

119864119888

119862119901

119891119871

119891119879

120583 [MPa] COV [] 120583 [GPa] COV [] 120583 [ms] COV [] 120583 [Hz] COV [] 120583 [Hz] COV []

100 times 200

Mix 1

D4 776 096 96 350 3327 205 6845 132 4165 186D7 103 364 116 770 3511 118 7220 128 4455 238D14 144 244 154 1062 3855 082 7795 158 4810 129D28 189 505 157 541 4032 124 8420 066 5165 115

Mix 2

D4 256 350 166 254 3803 110 8360 095 5160 155D7 293 340 170 210 4108 083 8570 053 5215 074D14 367 225 191 244 4224 142 8995 132 5455 119D28 393 363 231 318 4375 125 9280 091 5690 141

Mix 3

D4 229 379 1654 460 3978 190 8365 117 5150 137D7 282 459 198 821 4122 092 8730 052 5335 132D14 340 575 204 323 4261 121 8995 101 5445 133D28 408 576 223 582 4361 104 9185 196 5555 305

150 times 300

Mix 1

D4 77 275 104 733 3223 216 4585 098 2800 080D7 101 363 122 656 3487 153 4870 131 3015 166D14 138 355 147 708 3723 139 5220 115 3215 121D28 193 434 157 523 3937 142 5600 138 3430 116

Mix 2

D4 249 302 166 567 3934 147 5630 132 3450 174D7 299 260 175 332 4067 159 5730 089 3485 158D14 369 437 209 226 4219 072 6010 073 3645 129D28 432 492 237 337 4296 099 6200 081 3800 102

Mix 3

D4 231 233 169 344 3922 123 5605 084 3435 093D7 290 150 187 222 4056 084 5825 110 3535 110D14 397 284 215 709 4192 097 6060 081 3675 091D28 444 447 213 721 4295 063 6260 117 3820 133

3 Result and Discussion

31 Experimental Variability In this study the coefficient ofvariation (COV the standard deviation 120590 divided by themean value120583 of a set of samples) was used as ameans of eval-uating the experimental variability of compressive strengthand static and dynamic properties of concrete Table 2 com-pares the statistical parameters (120583 and COV) of test results

(119865119888 119864119888 119862119901 119891119871 and 119891

119879) obtained from 100 by 200mm and

150 by 300mm cylindersThe average COVs of the compressive strength of con-

crete 119865119888from different mix proportions and testing ages are

441 and 365 for 100 by 200mm and 150 by 300mmcylinders respectively The 100 by 200mm cylinders haveabout 10 higher within-test variability than 150 by 300mmcylinders The result is consistent with the observation by

Advances in Materials Science and Engineering 5

previous researchers that 100 by 200mm cylinder tends tohave about 20 higher within-test variability than 150 by300mm cylinder [27] The COVs from the 150 by 300mmcylinder are between good (40 to 50) and excellent (lt20)categories according to ACI 214R [28] whereas for 100 by200mm cylinder the COVs are between fair (50 to 60) andexcellent categories

The average COVs of the static elastic modulus 119864119888from

100 by 200mm and 150 by 300mm cylinders are 632 and583 respectively A slightly higher COV of 119864

119888is mainly

due to imperfect concrete specimens and testing procedurethe opposite faces of the specimens were slightly skew andtheir deformations under compression were not uniformThis may also affect compressive strength of concrete butappears to be more influential to determination of elasticmodulus Table 2 shows that the COVs of both119865

119888and119864

119888from

the three differentmixes are reasonably consistent at differentages in 4 7 14 and 28 days

For the dynamic tests the 100 by 200mm cylinders pro-duce equivalent or slightly higher variability than the 150by 300mm cylinders however the differences appear to beinsignificant The average COVs of the fundamental longitu-dinal 119891

119871and transverse 119891

119879frequencies measured from 100 by

200mm and 150 by 300mm cylinders are 164 and 120and 162 and 117 respectively Furthermore the averageCOVs of the 119875-wave velocity (119862

119871) for 100 by 200mm and 150

by 300mm cylinders are 140 and 123 respectively bothof which are consistent with observations by ACI committee228 [29]

32 Compressive Strength Figure 3 compares compressivestrengths of concrete cylinders measured from 100 by200mm and 150 by 300mm cylinders (119865

119888100and 119865119888150

resp)The experimental data represented as open symbols showthat there is no significant difference between 119865

119888100and 119865

119888150

in the lower strength range of 8MPa to 30MPa with a meanabsolute error (MAE) less than 1MPa In this studyMAEwasdefined as follows

MAE =sum

1003816100381610038161003816119865119888150

minus 119865119888100

1003816100381610038161003816

119873 (11)

where 119873 is the number of the experimental data (ie in thisstudy 119873 = 120) The result for low compressive strength isconsistent with observations by prior researchers [22 24 30]

However it was noticed that scattering of experimentaldata in this study becomes greater as compressive strengthincreases in the higher strength range greater than 30MPa119865119888150

-to-119865119888100

ratio in this study gradually increases as 119865119888100

increases An approximated equation that relates 119865119888150

and119865119888100

was established by a linear regression analysis of theexperimental data set in this study as follows

119865119888150

= 111119865119888100

minus 156 [MPa] (1198772

= 096) (12)

The best-fit line presented as a red dash line in Figure 3 iscompatible with the equations proposed by prior researchers[19 20] However there is contradiction in the relationshipbetween 119865

119888150and 119865119888100

reported by different researchers (see

Com

pres

sive s

treng

thFc150

(MPa

)

10 20 30 40 50 60 70 80 90 1000Compressive strength Fc100 (MPa)

0

10

20

30

40

50

60

70

80

90

100

Test results mix 1Test results mix 2Test results mix 3Issa et al (2000) Malaikah (2005)Vandergrift and Schindler (2006)

P M Carrasquillo and R L Carrasquillo (1988)Carrasquillo et al (1981) Cook (1989)Line of equalityBest-fit line in the present study(Fc150 = 111Fc100 minus 156 R2

= 096)

Figure 3 Comparison of compressive strength of concrete mea-sured from 100 by 200mm and 150 by 300mm cylinders (119865

119888100and

119865119888150

resp)

Figure 2) [18ndash22 24 30] The inconsistency results in thehigher strength range are attributed to complexity in theinterfacial transition zone of concrete [10 24] It is knownthat considerable stresses are transferred at cement paste andaggregatesrsquo interface of high strength concrete due to lowerporosity of the interfacial transition zone (ITZ) In fact thereare a number of factors affecting the ITZ which includecoarse aggregates mineral admixtures and curing methodsand various factors affect compressive strength in differentways for different cylinder sizes [14] Therefore special careis still needed for selecting the cylinder size for measuringcompressive strength of relatively high strength concrete(gt40MPa)

33 Static Elastic Moduli Figure 4 compares static elasticmoduli of concrete measured from 100 by 200mm and 150by 300mm cylinders (119864

119888100and 119864

119888150 resp) in this study For

a comparison database collected from the literature [22 30]was shown in the same figure The experimental data set inthis study presented as open symbols shows that 119864

119888100is

closely correlated with 119864119888150

in the elastic modulus range of10GPa to 25GPa For the lower elastic modulus range of 10to 15GPa 119864

119888100values are comparable with 119864

119888150values with

6 Advances in Materials Science and EngineeringSt

atic

elas

tic m

odul

usEc150

(GPa

)

Test results mix 1Test results mix 2Test results mix 3Malaikah (2005)

Best-fit line of the experimental data in this study(Ec150 = 09Ec100 + 19 R2

= 084)

Issa et al (2000)95 confidence boundsLine of equality

0

5

10

15

20

25

30

35

40

45

50

55

4010 15 20 25 30 35 500 45 555Static elastic modulus Ec100 (GPa)

Figure 4 Comparison of static elastic moduli of concrete measuredfrom 100 by 200mm and 150 by 300mm cylinders (119864

119888100and 119864

119888150

resp)

MAE between 119864119888100

and 119864119888150

of about 045GPaTherefore itmay be acceptable to assume from a practical perspective thatstatic elastic moduli using 100 by 200mm and 150 by 300mmcylinders are equivalent

However the ratio of 119864119888150

to 119864119888100

appears to graduallyincrease as 119864

119888150increases to 25GPa The higher elasticity

in the smaller size is attributed to the fact that the quantityof mortar required to fill the space between the particles ofthe coarse aggregate and the wall of the mold is greater thanthat necessary in the interior of the mass (ie wall effect)[10] In general the elasticity of cementmortar is greater thanthat of concrete which consequently results in increasing theeffective elasticity of concrete in smaller size In this study thebest-fit line that approximates the relationship between 119864

119888150

and 119864119888100

was established by a linear regression analysis asfollows

119864119888150

= 09119864119888100

+ 19 [MPa] (1198772

= 084) (13)

The best-fit line and 95 confidence bounds of the best-fitline are presented as solid and dash lines respectively inFigure 3 Interestingly the best-fit line of the experimentaldata in this study (10GPa le 119864

119888100le 25GPa) appears to be

valid for predicting the data set in the higher elastic modulusrange of 25GPa to 55GPa reported by prior researchers [2230] However it is still difficult to attain general conclusionson the relationship between 119864

119888150and 119864

119888100 especially for

Test results mix 1Test results mix 2Test results mix 3

Best-fit line for experimental data in this study

95 confidence boundsLine of equality

5010 15 20 25 30 35 40 600 455 550

5

10

15

20

25

30

35

40

45

50

55

60

Dyn

amic

elas

tic m

odul

usEdP150

(GPa

)

Dynamic elastic modulus EdP100 (GPa)

(EdP150 = 097Ed + 0138 R2= 092)100P

Figure 5 Comparison of velocity moduli from 100 by 200mm and150 by 300mm cylinders

concrete in the higher strength range greater than 50MPabecause of scarcity of available experimental data

34 Dynamic Elastic Moduli Figure 5 compares dynamicelastic moduli measured using UPV tests (ie velocitymoduli) from 100 by 200mm and 150 by 300mm cylinders(119864119889119875100

and 119864119889119875150

resp) in accordance with ASTM C597[26] It was observed that 100 by 200mm cylinders consis-tently result in slightly higher dynamic elastic moduli than150 by 300mm cylinders Linear regression of 119864

119889119875100and

119864119889119875150

measured in this study shows that 119864119889119875100

is about3 greater than 119864

119889119875150in a range of 20GPa to 40GPa (see

Figure 5) The MAE from two different cylinders was about05 GPa which is only 25 of the MAE from static elasticmoduli in this study (ie 2 GPa)

In addition shown in Figures 6(a) and 6(b) is the compar-ison of dynamic elastic moduli measured from longitudinaland transverse resonance frequency tests (ie resonancemoduli) 119864

119889119871119877and 119864

119889119879119877 respectively from 100 by 200mm

and 150 by 300mm cylinders in accordance with ASTMC125[16] The use of 150 by 300mm cylinders tends to resultin slightly higher resonance moduli (both 119864

119889119871119877and 119864

119889119879119877)

than those from 100 by 200mm cylinders According to thelinear regression analysis it was found that the resonancemoduli measured using the 150 by 300mm cylinder (119864

119889119871119877150

or 119864119889119877119877150

) are 1 to 2 greater than those from the 100by 200mm cylinder (119864

119889119871119877100or 119864119889119877119877100

) Approximatedequations that relate the resonance moduli from the twodifferent cylinder sizes are shown in Figures 6(a) and 6(b)

Advances in Materials Science and Engineering 7

Test results mix 1Test results mix 2Test results mix 3

0

5

10

15

20

25

30

35

40

3510 15 20 25 30 400 5

(EdLR150 = 102EdLR100 + 0127 R2= 096)

Best-fit line for experimental data in this study

95 confidence boundsLine of equality

EdLR100 (GPa)Dynamic elastic modulus

EdLR150

(GPa

)D

ynam

ic el

astic

mod

ulus

(a)

Test results mix 1Test results mix 2Test results mix 395 confidence boundsLine of equalityBest-fit line for experimental data in this study(EdTR150 = 101EdTR100 + 0438 R2

= 093)

0

5

10

15

20

25

30

35

40

3510 15 20 25 30 400 5EdTR100 (GPa)Dynamic elastic modulus

EdTR150

(GPa

)D

ynam

ic el

astic

mod

ulus

(b)

Figure 6 Comparison of resonance moduli from 100 by 200mm and 150 by 300mm cylinders (a) 119864119889119871119877150

versus 119864119889119871119877100

and (b) 119864119889119879119877150

versus 119864119889119879119877100

Furthermore without regard to longitudinal or transversemodes the MAE between the resonance moduli from thedifferent cylinder is less than 03GPa Therefore the findingsin this study demonstrate that the dynamic elastic moduli(both velocity and resonance moduli) using the 100 by200mm and 150 by 300mm cylinders are regarded as beingequal from a practical standpoint

However it was observed that there is a precaution inmeasuring reliable and consistent resonance frequency usingthe 100 by 200mm cylinder The smaller cylinder has higherchance of mistakenly hitting an impact source (location andinclination to test surface) which may cause undesirableresonance modes such as torsional modes in the frequencydomain Consequently it was often difficult to select a rightfrequency peak corresponding to the fundamental longitudi-nal or transverse modes In this study preliminary numeri-cal simulations were conducted to calculate theoretical fre-quency peak values which was helpful to select a rightfrequency peak In addition to improve accuracy and con-sistency resonance tests were repeated until the COV of fivesuccessive testing procedures is less than 5 and average ofthe five test results was finally accepted in this study

35 Relationship between Static Elastic Modulus and Com-pressive Strength Figure 7 is a plot representing relationshipbetween static elastic modulus and compressive strengthmeasured in accordance with ASTM C469 [4] and ASTM

C39 [25] respectively The data points obtained from 100 by200mm and 150 by 300mm cylinders are presented as openand solid symbols in Figures 7(a) and 7(b) respectively For acomparison Figure 7 presents three code equations adoptedby ACI 318 and ACI 363 committees and CEB-FIP Modelcode and a practical equation proposed by Noguchi et al [8](see (14)) which was developed based on an extensive exper-imental database from normal to high strength concrete

119864119888= 1198961119896233500 (

119865119888

60)

13

(119908119888

2400)

2

(14)

where 1198961and 119896

2are correction factors for coarse aggregates

and mineral admixturesIt was found that the effect of cylinder size appears to be

insignificant on the relationship between static elastic modu-lus and compressive strength of concrete for normal strengthconcrete (lt40MPa) in this study Approximated equationsthat relate 119864

119888and 119865119888from 100 by 200mm and 150 by 300mm

cylinders were established by nonlinear regression analysesand shown in Figures 7(a) and 7(b) respectivelyTheMAE ofthe two best-fit curves is less than 01 GPa in the compressivestrength range of 10MPa to 40MPa In this studyMAE of thetwo continuous curves was defined as follows

MAEcon =

[int 1198921(119865119888) minus 1198922(119865119888) 119889119865119888]

int 119889119865119888

(15)

8 Advances in Materials Science and Engineering

Best-fit line for experimental data in this study(Ec150 = 456Fc150

0418 R2= 090)

Noguchi et al [2009] k1 = k2 = 1

Noguchi et al [2009] k1 = k2 = 095

Mix 1

Mix 3

ACI 318ACI 363CEB-FIP Model code and Eurocode 2

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

5010 15 20 25 30 35 40 45 55 6050Compressive strength Fc (MPa)

150 by 300mm cylindersMix 2

(a)

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

Best-fit line for experimental data in this study(Ec100 = 416Fc100

0446 R2= 084)

Noguchi et al [2009] k1 = k2 = 1

Noguchi et al [2009] k1 = k2 = 095

Mix 1

Mix 3

ACI 318ACI 363CEB-FIP Model code and Eurocode 2

50 15 20 25 30 35 40 45 50 55 6010Compressive strength Fc (MPa)

0

5

10

15

20

25

30

35

40

Mix 2 100 by 200mm cylinders

(b)

Figure 7 Comparison of compressive strength and static elastic modulus of concrete

where MAEcon is mean average error (MAE) of two contin-uous functions 119892

119894is a function presenting 119864

119888expressed as

119865119888 and the subscript 119894 indicates cylinder size (1 and 2 for the

100 by 200mm and 150 by 300mm cylinders resp) Further-more there is no significant difference in 119877

2 values of thetwo best-fit curves 1198772 values for the 100 by 200mm and150 by 300mm cylinders are 088 and 090 respectivelyTherefore the 100 by 200mm cylinders can be used insteadof 150 by 300mm cylinders to estimate static elastic modulusfrom compressive strength without reducing accuracy andconsistency However the three code equations tend tooverestimate static modulus of concrete compared to thosefrom direct measurement according to ASTM C469 [4] Assummarized in Table 3 mean average error (MAE) betweenmeasured and predicted 119864

119888from the three code equations is

in a range of 44 to 12GPa corresponding to about 10 to30 of the measured 119864

119888 In contrast the Noguchi equation

[8] predicts experimental results with far more improvedaccuracy (ie MAE less than 2GPa) by addressing correctionfactors for the effects of aggregates and mineral admixtures(ie 119896

1= 1198962= 095)

36 Relationship between Static and Dynamic Elastic ModuliFigure 8 presents the relationship between static and dynamicelastic moduli determined using different nondestructivetesting methods 119864

119889119875 119864119889119871119877

and 119864119889119879119877

respectively with

Table 3 Mean absolute error (MAE) of expressions relating staticelastic modulus and compressive strength measured using 100 by200mm and 150 by 300mm cylinders

Equation to convert 119864119889to

119864119888

MAE (GPa)150 by 300mm

cylinder100 by 200mm

cylinder119864119889119871119879

119864119889119871119879

Equation (1) 483 463Equation (2) 454 443Equation (3) 1221 1215Equation (14) with1198961= 1198962= 1

342 341

Equation (14) with1198961= 1198962= 095

156 188

Best-fit line 132 157

Poissonrsquos ratio of 02Theuse of Poissonrsquos ratio of 02 is reason-able for common concrete in practice [10] In Figure 8 119864

119889119875

119864119889119871119877

and 119864119889119879119877

measured from 100 by 200mm and 150 by300mm cylinders are shown as open and solid symbols in leftand right columns For comparison purposes several well-known empirical equations (see (3) (4) and (5)) proposedby prior researchers are shown in the figures

Advances in Materials Science and Engineering 9

Best-fit line for experimental data in this study(Ec150 = 044EdLR150

115 R2= 090)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equalityLydon and Balendran (1986)BS8100 Part 2Popovics (1975)

5 10 15 20 25 30 35 400Dynamic elastic modulus EdLR (GPa)

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

(a)

Best-fit line for experimental data in this study(Ec150 = 044EdTR100

115 R2= 090)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equality

BS8100 Part 2

5 10 15 20 25 30 35 400Dynamic elastic modulus EdTR (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

Popovics (1975)

Lydon and Balendran (1986)

(b)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equality

BS8100 Part 2

Best-fit line for experimental data in this study(Ec150 = 022EdP150

129 R2= 087)

Popovics (1975)

Lydon and Balendran (1986)

3510 15 20 25 30 400 5Dynamic elastic modulus EdP (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

(c)

Best-fit line for experimental data in this study(Ec100 = 040EdLR100

118 R2= 088)

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

3510 15 20 25 30 400 5Dynamic elastic modulus EdLR (GPa)

Lydon and Balendran (1986)

Popovics (1975)

(d)

Figure 8 Continued

10 Advances in Materials Science and Engineering

Best-fit line for experimental data in this study(Ec100 = 039EdTR100

120 R2= 087)

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

3510 15 20 25 30 400 5Dynamic elastic modulus EdTR (GPa)

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

Lydon and Balendran (1986)

Popovics (1975)

(e)

Best-fit line for experimental data in this study

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

3510 15 20 25 30 400 5Dynamic elastic modulus EdP (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

EdLR100135 R2

= 085)(Ec100 = 017

Popovics (1975)

Lydon and Balendran (1986)

(f)

Figure 8 Comparison of static and resonance elastic moduli of concrete (a) 119864119889119871119877150

versus 119864119888150

(b) 119864119889119879119877150

versus 119864119888150

(c) 119864119889119875150

versus119864119888150

(d) 119864119889119871119877100

versus 119864119888100

(e) 119864119889119879119877100

versus 119864119888100

and (f) 119864119889119875100

versus 119864119888100

Table 4 Mean absolute error (MAE) of expressions relating static and dynamic elastic modulus measured using 100 by 200mm and 150 by300mm cylinders

Equation to convert 119864119889to 119864119888

MAE (GPa)150 by 300mm cylinder 100 by 200mm cylinder

119864119889119871119879

119864119889119877119879

119864119889119875

119864119889119871119879

119864119889119877119879

119864119889119875

Equation (4) 302 282 754 283 254 846Equation (5) 559 591 277 607 649 335Equation (6) 125 111 658 113 107 780Best-fit line 090 095 126 109 110 117

It is observed that there is only slight difference in therelationship between119864

119888and119864

119889obtained from 100 by 200mm

and 150 by 300mm cylinders In this study approximatedequations that relate119864

119888and119864

119889(119864119889119875

119864119889119871119877

or119864119889119879119877

) from 100by 200mm and 150 by 300mm cylinders were established bynonlinear regression analyses and shown in Figures 8(a)ndash8(f)The MAEs of the two best-fit curves are less than 01MPa inthe dynamic elastic modulus range of 10GPa to 25GPa Fur-thermore there is no significant difference in 119877

2 values of thetwo best-fit curves (see Figure 8) However for both data setsfrom different cylinders the three dynamic moduli (119864

119889119871119877

119864119889119879119877

and 119864119889119875

) obtained from resonance tests and UPVmethod are greater than the static elastic modulus 119864

119888 with

different static-to-dynamic elastic modulus ratio 119864119888119864119889119875

ratio with an average of 056 and COV of 92 is too faraway from the line of equality as well as from the three well-known equations relating static and dynamic elastic modu-lus Therefore the use of 119864

119889119875appears to be inappropriate

to estimate static elastic modulus which is consistent withobservations from other researchers [7 10] In contrast119864119888119864119889119871119877

(or 119864119888119864119889119879119877

) ratio was closer to the line of equalitythan 119864

119888119864119889119875

with an average of 072 and COV of 715The equation proposed by Popovics [13] (see (6)) shows verygood agreement with the experimental results regardless ofcylinder size in this study (see Table 4) In addition priorresearcher [7] observed that the Popovics equation (see (6))can be extended to high strength concrete up to 60MPawith-out regard to cylinder size However it should be mentioned

Advances in Materials Science and Engineering 11

that additional experimental data should be accumulated tobetter understand the size effect on the relationship betweenstatic and dynamic elastic moduli of high strength concrete(gt60MPa) due to scarcity of experimental studies in such ahigh strength range

4 Conclusions

A series of experimental studies was conducted to explore theeffect of cylinder size (100 by 200mm and 150 by 300mmcylinders) on the relationship between static elastic modulusand compressive strength and static and dynamic elasticmoduli of concrete Conclusions based on experiments in thisstudy and database from the literature are drawn as follows

(1) Experimental results in this study show that theCOVsof test results from 100 by 200mm cylinders areabout 10 higher than those from 150 by 300mmcylinders however the differences are statisticallyinsignificantThe averageCOVs of static and dynamicelastic moduli using the UPV and longitudinal andtransverse resonance frequency tests from 100 by200mm cylinders are 632 140 162 and 117respectively while those values from 150 by 300mmcylinders are 583 123 162 and 117 respec-tively For compressive strength the average COVsfrom the 100 by 200mm and 150 by 300mm cylindersare 441 and 365 respectively

(2) According to the findings from similarity tests of best-fit curves and comparison of 1198772 based on regressionanalyses it has been demonstrated that the effect ofcylinder size (100 by 200mm and 150 by 300mmcylinders) is insignificant on compressive strengthand static elastic modulus and the relationship bet-ween the two parameters for normal strength con-crete up to 30MPa However in the higher strengthrange greater than 30MPa there is contradiction inthe relationship between 119865

119888150and 119865

119888100based on

experimental test in this study and database reportedby different researchers Therefore it is difficult toestablish a simple equation that relates 119865

119888100and 119865119888150

and 119864

119888100and 119864

119888150because of limited experimental

and theoretical studies

(3) The three code equations tend to overestimate staticmodulus of concrete compared to those from directmeasurement according to ASTM C469 with MAEin a range of 44GPa to 12GPa In contrast theNoguchi equation predicts experimental results withfar more improved accuracy (ie MAE less than2GPa) by addressing correction factors for the effectsof aggregates and mineral admixtures (ie 119896

1= 1198962=

095)

(4) There is only a slight difference in the relationshipbetween static and resonance moduli from 100 by200mm and 150 by 300mm cylinders for normalstrength concrete Test results from this study and theliterature show that the empirical equation suggested

by Popovics [13] ((6) in this study) is effective for pre-dicting static elastic moduli from resonance moduliof concrete with compressive strength up to 60MParegardless of the cylinder size with MAE of less than15 GPa

(5) However the velocity moduli are excessively greaterthan static elastic modulus The empirical equations(see (4) (5) and (6)) produce considerable errors(with MAE in a range of 277GPa to 846GPa) bet-ween measured and predicted elastic moduli There-fore the use of velocitymoduli appears to be inappro-priate to estimate static elastic modulus

Conflict of Interests

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

Acknowledgment

This research was supported by the Basic Science ResearchProgram through theNational Research Foundation of Korea(NRF) funded by the Ministry of Science ICT amp FuturePlanning (no 2015R1A5A1037548)

References

[1] ACI Committee 318 Building Code Requirements for StructuralConcrete (ACI 318-11) and Commentary American ConcreteInstitute Farmington Hills Mich USA 2014

[2] IBC Council International Building Code (IBC 2012) 2014[3] N Gucunski A Imani F Romero et al ldquoNondestructive testig

to identify concrete bridge deck deteriorationrdquo SHRP 2 ReportS2-R06A-RR-1 2013

[4] ACI Committee 469 Standard Test Method for Static Modulusof Elasticity and Poissonrsquos Ratio of Concrete in CompressionAmerican Concrete Institute Farmington Hills Mich USA2014

[5] A Pauw ldquoStatic modulus of elasticity of concrete as affected bydensityrdquo ACI Journal Proceedings vol 57 no 12 pp 679ndash6871960

[6] ACI Committee 363 ldquoState-of-the-art report on high-strengthconcreterdquo ACI Journal Proceedings vol 81 no 4 pp 364ndash4111984

[7] J S Popovics ldquoA study of static and dynamic modulus ofelasticity of concreterdquo ACI-CRC Final Report 2008

[8] T Noguchi F Tomosawa KM Nemati BM Chiaia and A RFantilli ldquoA practical equation for elastic modulus of concreterdquoACI Structural Journal vol 106 no 5 pp 690ndash696 2009

[9] R E Philleo ldquoComparison of results of threemethods for deter-mining Youngrsquos modulus of elasticity of concreterdquo InternationalConcrete Abstracts Portal vol 51 no 1 pp 461ndash469 1955

[10] A M Neville Properties of Concrete John Wiley amp Sons NewYork NY USA 4th edition 1997

[11] F D Lydon and R V Balendran ldquoSome observations on elasticproperties of plain concreterdquo Cement and Concrete Researchvol 16 no 3 pp 314ndash324 1986

[12] B S Institute ldquoStructural use of concretemdashpart 2 code ofpractice for special circumstancerdquo BS 8110-21995 BSI LondonUK 1995

12 Advances in Materials Science and Engineering

[13] S Popovics ldquoVerification of relationships between mechanicalproperties of concrete-like materialsrdquoMaterials and Structuresvol 8 no 3 pp 183ndash191 1975

[14] ASTM C191 Standard Practice for Making and Curing ConcreteTest Specimens in the Laboratory ASTM 2014

[15] ASTM ldquoStandard practice for making and curing concrete testspecimen in the fieldrdquo ASTM C31 ASTM International 2012

[16] ASTM International ldquoStandard test method for fundamentaltransverse longitudinal and torsional resonant frequencies ofconcrete specimensrdquo ASTM C215 ASTM International WestConshohocken Pa USA 2002

[17] P-C Aitcin and P K Mehta ldquoEffect of coarse-aggregate char-acteristics on mechanical properties of high-strength concreterdquoACI Materials Journal vol 87 no 2 pp 103ndash107 1990

[18] P-C Aitcin B Miao W D Cook and D Mitchell ldquoEffectsof size and curing on cylinder compressive strength of normaland high-strength concretesrdquo ACIMaterials Journal vol 91 pp349ndash354 1994

[19] P M Carrasquillo and R L Carrasquillo ldquoEvaluation of the useof current concrete practice in the production of high strengthconcreterdquo ACI Materials Journal vol 85 no 1 pp 49ndash54 1988

[20] R L Carrasquillo A H Nilson and F O Slate ldquoProperties ofhigh strength concrete subject to short-term loadsrdquo Journal ofthe American Concrete Institute vol 78 no 3 pp 171ndash178 1981

[21] J E Cook ldquo10000 psi concreterdquo Concrete International vol 11pp 67ndash75 1989

[22] A S Malaikah ldquoA proposed relationship for the modulus ofelasticity of high strength concrete using local materials inRiyadhrdquo Journal of King Saud UniversitymdashEngineering Sciencesvol 17 pp 1ndash11 2005

[23] A Mokhtarzadeh and C French ldquoMechanical properties ofhigh-strength concrete with consideration for precast applica-tionsrdquo ACI Materials Journal vol 97 no 2 pp 136ndash147 2000

[24] DVandergrift Jr andA K Schindler ldquoThe effect of test cylindersize on the compressive strength of sulfur capped concretespecimensrdquo Tech Rep IR-06-01 Highway Research Centerand Department of Civil Engineering at Auburn UniversityAuburn Ala USA 2006

[25] ASTM International ldquoStandard test method for compressivestrength of cylindrical concrete specimensrdquo ASTM C39 ASTMInternational West Conshohocken Pa USA 2014

[26] ASTM ldquoStandard test method for pulse velocity throughconcreterdquo ASTM C597 ASTM International 1997

[27] N J CarinoW F Guthrie E S Lagergren and G MMullingsldquoEffects of testing variables on the strength of high-strength(90MPa) concrete cylindersrdquo in High-Performance ConcreteV M Malhotra Ed SP-149 pp 589ndash632 American ConcreteInstitute Farmington Hills Mich USA 1994

[28] ACI ldquoGuide for evaluation of strength test results of concrete(ACI 214R-11)rdquo ASTM C214 American Concrete InstituteFarmington Hills Mich USA 2011

[29] ACI Committee 228 ldquoNondestructive test methods for evalua-tion of concrete in structuresrdquo ReportACI 2282R-98AmericanConcrete Institute Farmington Hills Mich USA 1998

[30] S A Issa M S Islam M A Issa A A Yousif and M A IssaldquoSpecimen and aggregate size effect on concrete compressivestrengthrdquo Cement Concrete and Aggregates vol 22 no 2 pp103ndash115 2000

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

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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 Mix proportions of concrete design

ID Cement type WB SAUnit quantity (kgm3)

W C S G Mineral admixture Chemical admixtureFA GBFS AE (binder ) SP (binder )

Mix 1Type I

045 046 259 121 777 934 58 69 09 mdashMix 2 035 047 308 166 761 886 81 85 mdash 1Mix 3 03 046 357 165 714 868 94 99 mdash 1NoteW water C cement S sand G gravel FA fly ash GBFS granulated blast furnace slag AE air-entraining agent SP superplasticizer

Figure 1 Testing setup and instrumentation for the uniaxial com-pressive test of a concrete cylinder

22 Static Tests for Compressive Strength and Elastic ModulusThe cylinders were ground at both ends before testing toremove any surface irregularity as well as ensure the ends tobe perpendicular to the sides of the specimen Elastic modu-lus and compressive strength of the cylinders were measuredusing a Universal Testing Machine (UTM) with a capacity of1000 kN according to ASTM C469 [4] and ASTM C39 [25]respectively Tests were performed at a loading rate of approx-imately 028MPas Deformationsweremeasured using threesets of linear voltage differential transducers attached to twofixed rings (see Figure 1) The apparatus consisted of twoaluminum rings with screws for attachment to the specimenThe spacing between screws on the top and bottom rings was70mm and 150mm for 100 by 200mm and 150 by 300mmcylinders respectively which served as a gauge length forcalculating axial strain from the measured deformationsThe static elastic modulus of concrete is defined as a chordmodulus from the stress-strain curve with a first point atstrain level of 000005 (120576

1) and second point at 40 of the

maximum stress as follows

119864119888=

04119891119888minus 120590 (120576

1)

120576 (04119891119888) minus 1205761

(7)

23 Dynamic Tests for Estimating Dynamic Elastic ModulusDynamic elastic modulus of concrete was estimated by mea-suring fundamental longitudinal and transverse resonancefrequencies of cylinders in accordance with ASTMC215 [16]Shown in Figure 2(a) is the test setup and data acquisitionsystem for the transverse resonance frequency test For thelongitudinal resonance frequency test an accelerometer was

placed on the center of one concrete surface and an impactsource was hit on the center of the other concrete surface Asteel ball having a diameter of 10mm was used as an impactsource for generating incident stress waves in a concretespecimen the steel ball was effective for generating widebandfrequency signals from very low to 20 kHz which covers afrequency range of the resonance tests for the 100 by 200mmand 150 by 300mm cylinders in this study Dynamic responseof concrete cylinder was measured by an accelerometerattached to concrete specimen according to ASTM C215[16] Resulting time signals were converted to the frequencydomain using the FFT (Fast Fourier Transformation) algo-rithm The resonance frequencies of concrete are manifestedas dominant amplitude in the frequency domain The mostdominant frequency was regarded as fundamental resonancefrequencies of longitudinal (or transverse) mode Dynamicelastic moduli based on the fundamental longitudinal fre-quency (119864

119889119871119877) were estimated using the following equation

119864119889119871119877

= 120573119871119872119891119871

2

(Pa) (8)

where 120573119871is constant dependent on dimensions and Poissonrsquos

ratio of concrete specimen (= 5093(1198711198632

)) for a cylinder inNsdots2 (kgsdotm2) 119872 is mass of specimen in kg and 119891

119871is funda-

mental longitudinal resonance frequency in Hz In additiondynamic elasticmoduli of concrete based on the fundamentaltransverse frequency (119864

119889119879119877) were estimated using the follow-

ing equation

119864119889119879119877

= 120573119879119872119891119879

2

(Pa) (9)

where 120573119879is constant dependent on dimensions of concrete

cylinder (= 16067[1198713

1198791198634

] for a cylinder and 119879 is a correc-tion factor dependent on ratio of the radius of gyration 119870

to the height of specimen 119867 [for concrete cylinder 119870119867 =

1198634119867] and Poissonrsquos ratio) in Nsdots2 (kgsdotm2) and 119891119879is funda-

mental transverse resonance frequency in HzFor comparison purposes the 119875-wave velocity of con-

crete 119862119875 was measured according to ASTM C597 [26] using

a pair of 119875-wave transducers (see Figure 2(b)) each of whichgenerates and receives a longitudinal ultrasonic pulse of about52 kHz through a concrete cylinder Dynamic elasticmodulusbased on 119862

119875(119864119889119875

) is determined using the following equa-tion

119864119889119875

= 120572119875120588119862119875

2

(10)

where 120572119875is constant dependent on Poissonrsquos ratio 120592 that is

(1 + 120592)(1 minus 2120592)(1 minus 120592)

4 Advances in Materials Science and Engineering

(a) (b)

Figure 2 Test setups and data acquisition system for evaluating dynamic elastic moduli using two different nondestructive evaluation tests(a) resonance frequency test (transverse mode) and (b) ultrasonic pulse velocity test (longitudinal mode)

Table 2 Summary of test results measured from 100 by 200mm and 150 by 300mm cylinders

Cylinder size Mix Day 119865119888

119864119888

119862119901

119891119871

119891119879

120583 [MPa] COV [] 120583 [GPa] COV [] 120583 [ms] COV [] 120583 [Hz] COV [] 120583 [Hz] COV []

100 times 200

Mix 1

D4 776 096 96 350 3327 205 6845 132 4165 186D7 103 364 116 770 3511 118 7220 128 4455 238D14 144 244 154 1062 3855 082 7795 158 4810 129D28 189 505 157 541 4032 124 8420 066 5165 115

Mix 2

D4 256 350 166 254 3803 110 8360 095 5160 155D7 293 340 170 210 4108 083 8570 053 5215 074D14 367 225 191 244 4224 142 8995 132 5455 119D28 393 363 231 318 4375 125 9280 091 5690 141

Mix 3

D4 229 379 1654 460 3978 190 8365 117 5150 137D7 282 459 198 821 4122 092 8730 052 5335 132D14 340 575 204 323 4261 121 8995 101 5445 133D28 408 576 223 582 4361 104 9185 196 5555 305

150 times 300

Mix 1

D4 77 275 104 733 3223 216 4585 098 2800 080D7 101 363 122 656 3487 153 4870 131 3015 166D14 138 355 147 708 3723 139 5220 115 3215 121D28 193 434 157 523 3937 142 5600 138 3430 116

Mix 2

D4 249 302 166 567 3934 147 5630 132 3450 174D7 299 260 175 332 4067 159 5730 089 3485 158D14 369 437 209 226 4219 072 6010 073 3645 129D28 432 492 237 337 4296 099 6200 081 3800 102

Mix 3

D4 231 233 169 344 3922 123 5605 084 3435 093D7 290 150 187 222 4056 084 5825 110 3535 110D14 397 284 215 709 4192 097 6060 081 3675 091D28 444 447 213 721 4295 063 6260 117 3820 133

3 Result and Discussion

31 Experimental Variability In this study the coefficient ofvariation (COV the standard deviation 120590 divided by themean value120583 of a set of samples) was used as ameans of eval-uating the experimental variability of compressive strengthand static and dynamic properties of concrete Table 2 com-pares the statistical parameters (120583 and COV) of test results

(119865119888 119864119888 119862119901 119891119871 and 119891

119879) obtained from 100 by 200mm and

150 by 300mm cylindersThe average COVs of the compressive strength of con-

crete 119865119888from different mix proportions and testing ages are

441 and 365 for 100 by 200mm and 150 by 300mmcylinders respectively The 100 by 200mm cylinders haveabout 10 higher within-test variability than 150 by 300mmcylinders The result is consistent with the observation by

Advances in Materials Science and Engineering 5

previous researchers that 100 by 200mm cylinder tends tohave about 20 higher within-test variability than 150 by300mm cylinder [27] The COVs from the 150 by 300mmcylinder are between good (40 to 50) and excellent (lt20)categories according to ACI 214R [28] whereas for 100 by200mm cylinder the COVs are between fair (50 to 60) andexcellent categories

The average COVs of the static elastic modulus 119864119888from

100 by 200mm and 150 by 300mm cylinders are 632 and583 respectively A slightly higher COV of 119864

119888is mainly

due to imperfect concrete specimens and testing procedurethe opposite faces of the specimens were slightly skew andtheir deformations under compression were not uniformThis may also affect compressive strength of concrete butappears to be more influential to determination of elasticmodulus Table 2 shows that the COVs of both119865

119888and119864

119888from

the three differentmixes are reasonably consistent at differentages in 4 7 14 and 28 days

For the dynamic tests the 100 by 200mm cylinders pro-duce equivalent or slightly higher variability than the 150by 300mm cylinders however the differences appear to beinsignificant The average COVs of the fundamental longitu-dinal 119891

119871and transverse 119891

119879frequencies measured from 100 by

200mm and 150 by 300mm cylinders are 164 and 120and 162 and 117 respectively Furthermore the averageCOVs of the 119875-wave velocity (119862

119871) for 100 by 200mm and 150

by 300mm cylinders are 140 and 123 respectively bothof which are consistent with observations by ACI committee228 [29]

32 Compressive Strength Figure 3 compares compressivestrengths of concrete cylinders measured from 100 by200mm and 150 by 300mm cylinders (119865

119888100and 119865119888150

resp)The experimental data represented as open symbols showthat there is no significant difference between 119865

119888100and 119865

119888150

in the lower strength range of 8MPa to 30MPa with a meanabsolute error (MAE) less than 1MPa In this studyMAEwasdefined as follows

MAE =sum

1003816100381610038161003816119865119888150

minus 119865119888100

1003816100381610038161003816

119873 (11)

where 119873 is the number of the experimental data (ie in thisstudy 119873 = 120) The result for low compressive strength isconsistent with observations by prior researchers [22 24 30]

However it was noticed that scattering of experimentaldata in this study becomes greater as compressive strengthincreases in the higher strength range greater than 30MPa119865119888150

-to-119865119888100

ratio in this study gradually increases as 119865119888100

increases An approximated equation that relates 119865119888150

and119865119888100

was established by a linear regression analysis of theexperimental data set in this study as follows

119865119888150

= 111119865119888100

minus 156 [MPa] (1198772

= 096) (12)

The best-fit line presented as a red dash line in Figure 3 iscompatible with the equations proposed by prior researchers[19 20] However there is contradiction in the relationshipbetween 119865

119888150and 119865119888100

reported by different researchers (see

Com

pres

sive s

treng

thFc150

(MPa

)

10 20 30 40 50 60 70 80 90 1000Compressive strength Fc100 (MPa)

0

10

20

30

40

50

60

70

80

90

100

Test results mix 1Test results mix 2Test results mix 3Issa et al (2000) Malaikah (2005)Vandergrift and Schindler (2006)

P M Carrasquillo and R L Carrasquillo (1988)Carrasquillo et al (1981) Cook (1989)Line of equalityBest-fit line in the present study(Fc150 = 111Fc100 minus 156 R2

= 096)

Figure 3 Comparison of compressive strength of concrete mea-sured from 100 by 200mm and 150 by 300mm cylinders (119865

119888100and

119865119888150

resp)

Figure 2) [18ndash22 24 30] The inconsistency results in thehigher strength range are attributed to complexity in theinterfacial transition zone of concrete [10 24] It is knownthat considerable stresses are transferred at cement paste andaggregatesrsquo interface of high strength concrete due to lowerporosity of the interfacial transition zone (ITZ) In fact thereare a number of factors affecting the ITZ which includecoarse aggregates mineral admixtures and curing methodsand various factors affect compressive strength in differentways for different cylinder sizes [14] Therefore special careis still needed for selecting the cylinder size for measuringcompressive strength of relatively high strength concrete(gt40MPa)

33 Static Elastic Moduli Figure 4 compares static elasticmoduli of concrete measured from 100 by 200mm and 150by 300mm cylinders (119864

119888100and 119864

119888150 resp) in this study For

a comparison database collected from the literature [22 30]was shown in the same figure The experimental data set inthis study presented as open symbols shows that 119864

119888100is

closely correlated with 119864119888150

in the elastic modulus range of10GPa to 25GPa For the lower elastic modulus range of 10to 15GPa 119864

119888100values are comparable with 119864

119888150values with

6 Advances in Materials Science and EngineeringSt

atic

elas

tic m

odul

usEc150

(GPa

)

Test results mix 1Test results mix 2Test results mix 3Malaikah (2005)

Best-fit line of the experimental data in this study(Ec150 = 09Ec100 + 19 R2

= 084)

Issa et al (2000)95 confidence boundsLine of equality

0

5

10

15

20

25

30

35

40

45

50

55

4010 15 20 25 30 35 500 45 555Static elastic modulus Ec100 (GPa)

Figure 4 Comparison of static elastic moduli of concrete measuredfrom 100 by 200mm and 150 by 300mm cylinders (119864

119888100and 119864

119888150

resp)

MAE between 119864119888100

and 119864119888150

of about 045GPaTherefore itmay be acceptable to assume from a practical perspective thatstatic elastic moduli using 100 by 200mm and 150 by 300mmcylinders are equivalent

However the ratio of 119864119888150

to 119864119888100

appears to graduallyincrease as 119864

119888150increases to 25GPa The higher elasticity

in the smaller size is attributed to the fact that the quantityof mortar required to fill the space between the particles ofthe coarse aggregate and the wall of the mold is greater thanthat necessary in the interior of the mass (ie wall effect)[10] In general the elasticity of cementmortar is greater thanthat of concrete which consequently results in increasing theeffective elasticity of concrete in smaller size In this study thebest-fit line that approximates the relationship between 119864

119888150

and 119864119888100

was established by a linear regression analysis asfollows

119864119888150

= 09119864119888100

+ 19 [MPa] (1198772

= 084) (13)

The best-fit line and 95 confidence bounds of the best-fitline are presented as solid and dash lines respectively inFigure 3 Interestingly the best-fit line of the experimentaldata in this study (10GPa le 119864

119888100le 25GPa) appears to be

valid for predicting the data set in the higher elastic modulusrange of 25GPa to 55GPa reported by prior researchers [2230] However it is still difficult to attain general conclusionson the relationship between 119864

119888150and 119864

119888100 especially for

Test results mix 1Test results mix 2Test results mix 3

Best-fit line for experimental data in this study

95 confidence boundsLine of equality

5010 15 20 25 30 35 40 600 455 550

5

10

15

20

25

30

35

40

45

50

55

60

Dyn

amic

elas

tic m

odul

usEdP150

(GPa

)

Dynamic elastic modulus EdP100 (GPa)

(EdP150 = 097Ed + 0138 R2= 092)100P

Figure 5 Comparison of velocity moduli from 100 by 200mm and150 by 300mm cylinders

concrete in the higher strength range greater than 50MPabecause of scarcity of available experimental data

34 Dynamic Elastic Moduli Figure 5 compares dynamicelastic moduli measured using UPV tests (ie velocitymoduli) from 100 by 200mm and 150 by 300mm cylinders(119864119889119875100

and 119864119889119875150

resp) in accordance with ASTM C597[26] It was observed that 100 by 200mm cylinders consis-tently result in slightly higher dynamic elastic moduli than150 by 300mm cylinders Linear regression of 119864

119889119875100and

119864119889119875150

measured in this study shows that 119864119889119875100

is about3 greater than 119864

119889119875150in a range of 20GPa to 40GPa (see

Figure 5) The MAE from two different cylinders was about05 GPa which is only 25 of the MAE from static elasticmoduli in this study (ie 2 GPa)

In addition shown in Figures 6(a) and 6(b) is the compar-ison of dynamic elastic moduli measured from longitudinaland transverse resonance frequency tests (ie resonancemoduli) 119864

119889119871119877and 119864

119889119879119877 respectively from 100 by 200mm

and 150 by 300mm cylinders in accordance with ASTMC125[16] The use of 150 by 300mm cylinders tends to resultin slightly higher resonance moduli (both 119864

119889119871119877and 119864

119889119879119877)

than those from 100 by 200mm cylinders According to thelinear regression analysis it was found that the resonancemoduli measured using the 150 by 300mm cylinder (119864

119889119871119877150

or 119864119889119877119877150

) are 1 to 2 greater than those from the 100by 200mm cylinder (119864

119889119871119877100or 119864119889119877119877100

) Approximatedequations that relate the resonance moduli from the twodifferent cylinder sizes are shown in Figures 6(a) and 6(b)

Advances in Materials Science and Engineering 7

Test results mix 1Test results mix 2Test results mix 3

0

5

10

15

20

25

30

35

40

3510 15 20 25 30 400 5

(EdLR150 = 102EdLR100 + 0127 R2= 096)

Best-fit line for experimental data in this study

95 confidence boundsLine of equality

EdLR100 (GPa)Dynamic elastic modulus

EdLR150

(GPa

)D

ynam

ic el

astic

mod

ulus

(a)

Test results mix 1Test results mix 2Test results mix 395 confidence boundsLine of equalityBest-fit line for experimental data in this study(EdTR150 = 101EdTR100 + 0438 R2

= 093)

0

5

10

15

20

25

30

35

40

3510 15 20 25 30 400 5EdTR100 (GPa)Dynamic elastic modulus

EdTR150

(GPa

)D

ynam

ic el

astic

mod

ulus

(b)

Figure 6 Comparison of resonance moduli from 100 by 200mm and 150 by 300mm cylinders (a) 119864119889119871119877150

versus 119864119889119871119877100

and (b) 119864119889119879119877150

versus 119864119889119879119877100

Furthermore without regard to longitudinal or transversemodes the MAE between the resonance moduli from thedifferent cylinder is less than 03GPa Therefore the findingsin this study demonstrate that the dynamic elastic moduli(both velocity and resonance moduli) using the 100 by200mm and 150 by 300mm cylinders are regarded as beingequal from a practical standpoint

However it was observed that there is a precaution inmeasuring reliable and consistent resonance frequency usingthe 100 by 200mm cylinder The smaller cylinder has higherchance of mistakenly hitting an impact source (location andinclination to test surface) which may cause undesirableresonance modes such as torsional modes in the frequencydomain Consequently it was often difficult to select a rightfrequency peak corresponding to the fundamental longitudi-nal or transverse modes In this study preliminary numeri-cal simulations were conducted to calculate theoretical fre-quency peak values which was helpful to select a rightfrequency peak In addition to improve accuracy and con-sistency resonance tests were repeated until the COV of fivesuccessive testing procedures is less than 5 and average ofthe five test results was finally accepted in this study

35 Relationship between Static Elastic Modulus and Com-pressive Strength Figure 7 is a plot representing relationshipbetween static elastic modulus and compressive strengthmeasured in accordance with ASTM C469 [4] and ASTM

C39 [25] respectively The data points obtained from 100 by200mm and 150 by 300mm cylinders are presented as openand solid symbols in Figures 7(a) and 7(b) respectively For acomparison Figure 7 presents three code equations adoptedby ACI 318 and ACI 363 committees and CEB-FIP Modelcode and a practical equation proposed by Noguchi et al [8](see (14)) which was developed based on an extensive exper-imental database from normal to high strength concrete

119864119888= 1198961119896233500 (

119865119888

60)

13

(119908119888

2400)

2

(14)

where 1198961and 119896

2are correction factors for coarse aggregates

and mineral admixturesIt was found that the effect of cylinder size appears to be

insignificant on the relationship between static elastic modu-lus and compressive strength of concrete for normal strengthconcrete (lt40MPa) in this study Approximated equationsthat relate 119864

119888and 119865119888from 100 by 200mm and 150 by 300mm

cylinders were established by nonlinear regression analysesand shown in Figures 7(a) and 7(b) respectivelyTheMAE ofthe two best-fit curves is less than 01 GPa in the compressivestrength range of 10MPa to 40MPa In this studyMAE of thetwo continuous curves was defined as follows

MAEcon =

[int 1198921(119865119888) minus 1198922(119865119888) 119889119865119888]

int 119889119865119888

(15)

8 Advances in Materials Science and Engineering

Best-fit line for experimental data in this study(Ec150 = 456Fc150

0418 R2= 090)

Noguchi et al [2009] k1 = k2 = 1

Noguchi et al [2009] k1 = k2 = 095

Mix 1

Mix 3

ACI 318ACI 363CEB-FIP Model code and Eurocode 2

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

5010 15 20 25 30 35 40 45 55 6050Compressive strength Fc (MPa)

150 by 300mm cylindersMix 2

(a)

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

Best-fit line for experimental data in this study(Ec100 = 416Fc100

0446 R2= 084)

Noguchi et al [2009] k1 = k2 = 1

Noguchi et al [2009] k1 = k2 = 095

Mix 1

Mix 3

ACI 318ACI 363CEB-FIP Model code and Eurocode 2

50 15 20 25 30 35 40 45 50 55 6010Compressive strength Fc (MPa)

0

5

10

15

20

25

30

35

40

Mix 2 100 by 200mm cylinders

(b)

Figure 7 Comparison of compressive strength and static elastic modulus of concrete

where MAEcon is mean average error (MAE) of two contin-uous functions 119892

119894is a function presenting 119864

119888expressed as

119865119888 and the subscript 119894 indicates cylinder size (1 and 2 for the

100 by 200mm and 150 by 300mm cylinders resp) Further-more there is no significant difference in 119877

2 values of thetwo best-fit curves 1198772 values for the 100 by 200mm and150 by 300mm cylinders are 088 and 090 respectivelyTherefore the 100 by 200mm cylinders can be used insteadof 150 by 300mm cylinders to estimate static elastic modulusfrom compressive strength without reducing accuracy andconsistency However the three code equations tend tooverestimate static modulus of concrete compared to thosefrom direct measurement according to ASTM C469 [4] Assummarized in Table 3 mean average error (MAE) betweenmeasured and predicted 119864

119888from the three code equations is

in a range of 44 to 12GPa corresponding to about 10 to30 of the measured 119864

119888 In contrast the Noguchi equation

[8] predicts experimental results with far more improvedaccuracy (ie MAE less than 2GPa) by addressing correctionfactors for the effects of aggregates and mineral admixtures(ie 119896

1= 1198962= 095)

36 Relationship between Static and Dynamic Elastic ModuliFigure 8 presents the relationship between static and dynamicelastic moduli determined using different nondestructivetesting methods 119864

119889119875 119864119889119871119877

and 119864119889119879119877

respectively with

Table 3 Mean absolute error (MAE) of expressions relating staticelastic modulus and compressive strength measured using 100 by200mm and 150 by 300mm cylinders

Equation to convert 119864119889to

119864119888

MAE (GPa)150 by 300mm

cylinder100 by 200mm

cylinder119864119889119871119879

119864119889119871119879

Equation (1) 483 463Equation (2) 454 443Equation (3) 1221 1215Equation (14) with1198961= 1198962= 1

342 341

Equation (14) with1198961= 1198962= 095

156 188

Best-fit line 132 157

Poissonrsquos ratio of 02Theuse of Poissonrsquos ratio of 02 is reason-able for common concrete in practice [10] In Figure 8 119864

119889119875

119864119889119871119877

and 119864119889119879119877

measured from 100 by 200mm and 150 by300mm cylinders are shown as open and solid symbols in leftand right columns For comparison purposes several well-known empirical equations (see (3) (4) and (5)) proposedby prior researchers are shown in the figures

Advances in Materials Science and Engineering 9

Best-fit line for experimental data in this study(Ec150 = 044EdLR150

115 R2= 090)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equalityLydon and Balendran (1986)BS8100 Part 2Popovics (1975)

5 10 15 20 25 30 35 400Dynamic elastic modulus EdLR (GPa)

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

(a)

Best-fit line for experimental data in this study(Ec150 = 044EdTR100

115 R2= 090)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equality

BS8100 Part 2

5 10 15 20 25 30 35 400Dynamic elastic modulus EdTR (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

Popovics (1975)

Lydon and Balendran (1986)

(b)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equality

BS8100 Part 2

Best-fit line for experimental data in this study(Ec150 = 022EdP150

129 R2= 087)

Popovics (1975)

Lydon and Balendran (1986)

3510 15 20 25 30 400 5Dynamic elastic modulus EdP (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

(c)

Best-fit line for experimental data in this study(Ec100 = 040EdLR100

118 R2= 088)

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

3510 15 20 25 30 400 5Dynamic elastic modulus EdLR (GPa)

Lydon and Balendran (1986)

Popovics (1975)

(d)

Figure 8 Continued

10 Advances in Materials Science and Engineering

Best-fit line for experimental data in this study(Ec100 = 039EdTR100

120 R2= 087)

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

3510 15 20 25 30 400 5Dynamic elastic modulus EdTR (GPa)

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

Lydon and Balendran (1986)

Popovics (1975)

(e)

Best-fit line for experimental data in this study

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

3510 15 20 25 30 400 5Dynamic elastic modulus EdP (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

EdLR100135 R2

= 085)(Ec100 = 017

Popovics (1975)

Lydon and Balendran (1986)

(f)

Figure 8 Comparison of static and resonance elastic moduli of concrete (a) 119864119889119871119877150

versus 119864119888150

(b) 119864119889119879119877150

versus 119864119888150

(c) 119864119889119875150

versus119864119888150

(d) 119864119889119871119877100

versus 119864119888100

(e) 119864119889119879119877100

versus 119864119888100

and (f) 119864119889119875100

versus 119864119888100

Table 4 Mean absolute error (MAE) of expressions relating static and dynamic elastic modulus measured using 100 by 200mm and 150 by300mm cylinders

Equation to convert 119864119889to 119864119888

MAE (GPa)150 by 300mm cylinder 100 by 200mm cylinder

119864119889119871119879

119864119889119877119879

119864119889119875

119864119889119871119879

119864119889119877119879

119864119889119875

Equation (4) 302 282 754 283 254 846Equation (5) 559 591 277 607 649 335Equation (6) 125 111 658 113 107 780Best-fit line 090 095 126 109 110 117

It is observed that there is only slight difference in therelationship between119864

119888and119864

119889obtained from 100 by 200mm

and 150 by 300mm cylinders In this study approximatedequations that relate119864

119888and119864

119889(119864119889119875

119864119889119871119877

or119864119889119879119877

) from 100by 200mm and 150 by 300mm cylinders were established bynonlinear regression analyses and shown in Figures 8(a)ndash8(f)The MAEs of the two best-fit curves are less than 01MPa inthe dynamic elastic modulus range of 10GPa to 25GPa Fur-thermore there is no significant difference in 119877

2 values of thetwo best-fit curves (see Figure 8) However for both data setsfrom different cylinders the three dynamic moduli (119864

119889119871119877

119864119889119879119877

and 119864119889119875

) obtained from resonance tests and UPVmethod are greater than the static elastic modulus 119864

119888 with

different static-to-dynamic elastic modulus ratio 119864119888119864119889119875

ratio with an average of 056 and COV of 92 is too faraway from the line of equality as well as from the three well-known equations relating static and dynamic elastic modu-lus Therefore the use of 119864

119889119875appears to be inappropriate

to estimate static elastic modulus which is consistent withobservations from other researchers [7 10] In contrast119864119888119864119889119871119877

(or 119864119888119864119889119879119877

) ratio was closer to the line of equalitythan 119864

119888119864119889119875

with an average of 072 and COV of 715The equation proposed by Popovics [13] (see (6)) shows verygood agreement with the experimental results regardless ofcylinder size in this study (see Table 4) In addition priorresearcher [7] observed that the Popovics equation (see (6))can be extended to high strength concrete up to 60MPawith-out regard to cylinder size However it should be mentioned

Advances in Materials Science and Engineering 11

that additional experimental data should be accumulated tobetter understand the size effect on the relationship betweenstatic and dynamic elastic moduli of high strength concrete(gt60MPa) due to scarcity of experimental studies in such ahigh strength range

4 Conclusions

A series of experimental studies was conducted to explore theeffect of cylinder size (100 by 200mm and 150 by 300mmcylinders) on the relationship between static elastic modulusand compressive strength and static and dynamic elasticmoduli of concrete Conclusions based on experiments in thisstudy and database from the literature are drawn as follows

(1) Experimental results in this study show that theCOVsof test results from 100 by 200mm cylinders areabout 10 higher than those from 150 by 300mmcylinders however the differences are statisticallyinsignificantThe averageCOVs of static and dynamicelastic moduli using the UPV and longitudinal andtransverse resonance frequency tests from 100 by200mm cylinders are 632 140 162 and 117respectively while those values from 150 by 300mmcylinders are 583 123 162 and 117 respec-tively For compressive strength the average COVsfrom the 100 by 200mm and 150 by 300mm cylindersare 441 and 365 respectively

(2) According to the findings from similarity tests of best-fit curves and comparison of 1198772 based on regressionanalyses it has been demonstrated that the effect ofcylinder size (100 by 200mm and 150 by 300mmcylinders) is insignificant on compressive strengthand static elastic modulus and the relationship bet-ween the two parameters for normal strength con-crete up to 30MPa However in the higher strengthrange greater than 30MPa there is contradiction inthe relationship between 119865

119888150and 119865

119888100based on

experimental test in this study and database reportedby different researchers Therefore it is difficult toestablish a simple equation that relates 119865

119888100and 119865119888150

and 119864

119888100and 119864

119888150because of limited experimental

and theoretical studies

(3) The three code equations tend to overestimate staticmodulus of concrete compared to those from directmeasurement according to ASTM C469 with MAEin a range of 44GPa to 12GPa In contrast theNoguchi equation predicts experimental results withfar more improved accuracy (ie MAE less than2GPa) by addressing correction factors for the effectsof aggregates and mineral admixtures (ie 119896

1= 1198962=

095)

(4) There is only a slight difference in the relationshipbetween static and resonance moduli from 100 by200mm and 150 by 300mm cylinders for normalstrength concrete Test results from this study and theliterature show that the empirical equation suggested

by Popovics [13] ((6) in this study) is effective for pre-dicting static elastic moduli from resonance moduliof concrete with compressive strength up to 60MParegardless of the cylinder size with MAE of less than15 GPa

(5) However the velocity moduli are excessively greaterthan static elastic modulus The empirical equations(see (4) (5) and (6)) produce considerable errors(with MAE in a range of 277GPa to 846GPa) bet-ween measured and predicted elastic moduli There-fore the use of velocitymoduli appears to be inappro-priate to estimate static elastic modulus

Conflict of Interests

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

Acknowledgment

This research was supported by the Basic Science ResearchProgram through theNational Research Foundation of Korea(NRF) funded by the Ministry of Science ICT amp FuturePlanning (no 2015R1A5A1037548)

References

[1] ACI Committee 318 Building Code Requirements for StructuralConcrete (ACI 318-11) and Commentary American ConcreteInstitute Farmington Hills Mich USA 2014

[2] IBC Council International Building Code (IBC 2012) 2014[3] N Gucunski A Imani F Romero et al ldquoNondestructive testig

to identify concrete bridge deck deteriorationrdquo SHRP 2 ReportS2-R06A-RR-1 2013

[4] ACI Committee 469 Standard Test Method for Static Modulusof Elasticity and Poissonrsquos Ratio of Concrete in CompressionAmerican Concrete Institute Farmington Hills Mich USA2014

[5] A Pauw ldquoStatic modulus of elasticity of concrete as affected bydensityrdquo ACI Journal Proceedings vol 57 no 12 pp 679ndash6871960

[6] ACI Committee 363 ldquoState-of-the-art report on high-strengthconcreterdquo ACI Journal Proceedings vol 81 no 4 pp 364ndash4111984

[7] J S Popovics ldquoA study of static and dynamic modulus ofelasticity of concreterdquo ACI-CRC Final Report 2008

[8] T Noguchi F Tomosawa KM Nemati BM Chiaia and A RFantilli ldquoA practical equation for elastic modulus of concreterdquoACI Structural Journal vol 106 no 5 pp 690ndash696 2009

[9] R E Philleo ldquoComparison of results of threemethods for deter-mining Youngrsquos modulus of elasticity of concreterdquo InternationalConcrete Abstracts Portal vol 51 no 1 pp 461ndash469 1955

[10] A M Neville Properties of Concrete John Wiley amp Sons NewYork NY USA 4th edition 1997

[11] F D Lydon and R V Balendran ldquoSome observations on elasticproperties of plain concreterdquo Cement and Concrete Researchvol 16 no 3 pp 314ndash324 1986

[12] B S Institute ldquoStructural use of concretemdashpart 2 code ofpractice for special circumstancerdquo BS 8110-21995 BSI LondonUK 1995

12 Advances in Materials Science and Engineering

[13] S Popovics ldquoVerification of relationships between mechanicalproperties of concrete-like materialsrdquoMaterials and Structuresvol 8 no 3 pp 183ndash191 1975

[14] ASTM C191 Standard Practice for Making and Curing ConcreteTest Specimens in the Laboratory ASTM 2014

[15] ASTM ldquoStandard practice for making and curing concrete testspecimen in the fieldrdquo ASTM C31 ASTM International 2012

[16] ASTM International ldquoStandard test method for fundamentaltransverse longitudinal and torsional resonant frequencies ofconcrete specimensrdquo ASTM C215 ASTM International WestConshohocken Pa USA 2002

[17] P-C Aitcin and P K Mehta ldquoEffect of coarse-aggregate char-acteristics on mechanical properties of high-strength concreterdquoACI Materials Journal vol 87 no 2 pp 103ndash107 1990

[18] P-C Aitcin B Miao W D Cook and D Mitchell ldquoEffectsof size and curing on cylinder compressive strength of normaland high-strength concretesrdquo ACIMaterials Journal vol 91 pp349ndash354 1994

[19] P M Carrasquillo and R L Carrasquillo ldquoEvaluation of the useof current concrete practice in the production of high strengthconcreterdquo ACI Materials Journal vol 85 no 1 pp 49ndash54 1988

[20] R L Carrasquillo A H Nilson and F O Slate ldquoProperties ofhigh strength concrete subject to short-term loadsrdquo Journal ofthe American Concrete Institute vol 78 no 3 pp 171ndash178 1981

[21] J E Cook ldquo10000 psi concreterdquo Concrete International vol 11pp 67ndash75 1989

[22] A S Malaikah ldquoA proposed relationship for the modulus ofelasticity of high strength concrete using local materials inRiyadhrdquo Journal of King Saud UniversitymdashEngineering Sciencesvol 17 pp 1ndash11 2005

[23] A Mokhtarzadeh and C French ldquoMechanical properties ofhigh-strength concrete with consideration for precast applica-tionsrdquo ACI Materials Journal vol 97 no 2 pp 136ndash147 2000

[24] DVandergrift Jr andA K Schindler ldquoThe effect of test cylindersize on the compressive strength of sulfur capped concretespecimensrdquo Tech Rep IR-06-01 Highway Research Centerand Department of Civil Engineering at Auburn UniversityAuburn Ala USA 2006

[25] ASTM International ldquoStandard test method for compressivestrength of cylindrical concrete specimensrdquo ASTM C39 ASTMInternational West Conshohocken Pa USA 2014

[26] ASTM ldquoStandard test method for pulse velocity throughconcreterdquo ASTM C597 ASTM International 1997

[27] N J CarinoW F Guthrie E S Lagergren and G MMullingsldquoEffects of testing variables on the strength of high-strength(90MPa) concrete cylindersrdquo in High-Performance ConcreteV M Malhotra Ed SP-149 pp 589ndash632 American ConcreteInstitute Farmington Hills Mich USA 1994

[28] ACI ldquoGuide for evaluation of strength test results of concrete(ACI 214R-11)rdquo ASTM C214 American Concrete InstituteFarmington Hills Mich USA 2011

[29] ACI Committee 228 ldquoNondestructive test methods for evalua-tion of concrete in structuresrdquo ReportACI 2282R-98AmericanConcrete Institute Farmington Hills Mich USA 1998

[30] S A Issa M S Islam M A Issa A A Yousif and M A IssaldquoSpecimen and aggregate size effect on concrete compressivestrengthrdquo Cement Concrete and Aggregates vol 22 no 2 pp103ndash115 2000

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

(a) (b)

Figure 2 Test setups and data acquisition system for evaluating dynamic elastic moduli using two different nondestructive evaluation tests(a) resonance frequency test (transverse mode) and (b) ultrasonic pulse velocity test (longitudinal mode)

Table 2 Summary of test results measured from 100 by 200mm and 150 by 300mm cylinders

Cylinder size Mix Day 119865119888

119864119888

119862119901

119891119871

119891119879

120583 [MPa] COV [] 120583 [GPa] COV [] 120583 [ms] COV [] 120583 [Hz] COV [] 120583 [Hz] COV []

100 times 200

Mix 1

D4 776 096 96 350 3327 205 6845 132 4165 186D7 103 364 116 770 3511 118 7220 128 4455 238D14 144 244 154 1062 3855 082 7795 158 4810 129D28 189 505 157 541 4032 124 8420 066 5165 115

Mix 2

D4 256 350 166 254 3803 110 8360 095 5160 155D7 293 340 170 210 4108 083 8570 053 5215 074D14 367 225 191 244 4224 142 8995 132 5455 119D28 393 363 231 318 4375 125 9280 091 5690 141

Mix 3

D4 229 379 1654 460 3978 190 8365 117 5150 137D7 282 459 198 821 4122 092 8730 052 5335 132D14 340 575 204 323 4261 121 8995 101 5445 133D28 408 576 223 582 4361 104 9185 196 5555 305

150 times 300

Mix 1

D4 77 275 104 733 3223 216 4585 098 2800 080D7 101 363 122 656 3487 153 4870 131 3015 166D14 138 355 147 708 3723 139 5220 115 3215 121D28 193 434 157 523 3937 142 5600 138 3430 116

Mix 2

D4 249 302 166 567 3934 147 5630 132 3450 174D7 299 260 175 332 4067 159 5730 089 3485 158D14 369 437 209 226 4219 072 6010 073 3645 129D28 432 492 237 337 4296 099 6200 081 3800 102

Mix 3

D4 231 233 169 344 3922 123 5605 084 3435 093D7 290 150 187 222 4056 084 5825 110 3535 110D14 397 284 215 709 4192 097 6060 081 3675 091D28 444 447 213 721 4295 063 6260 117 3820 133

3 Result and Discussion

31 Experimental Variability In this study the coefficient ofvariation (COV the standard deviation 120590 divided by themean value120583 of a set of samples) was used as ameans of eval-uating the experimental variability of compressive strengthand static and dynamic properties of concrete Table 2 com-pares the statistical parameters (120583 and COV) of test results

(119865119888 119864119888 119862119901 119891119871 and 119891

119879) obtained from 100 by 200mm and

150 by 300mm cylindersThe average COVs of the compressive strength of con-

crete 119865119888from different mix proportions and testing ages are

441 and 365 for 100 by 200mm and 150 by 300mmcylinders respectively The 100 by 200mm cylinders haveabout 10 higher within-test variability than 150 by 300mmcylinders The result is consistent with the observation by

Advances in Materials Science and Engineering 5

previous researchers that 100 by 200mm cylinder tends tohave about 20 higher within-test variability than 150 by300mm cylinder [27] The COVs from the 150 by 300mmcylinder are between good (40 to 50) and excellent (lt20)categories according to ACI 214R [28] whereas for 100 by200mm cylinder the COVs are between fair (50 to 60) andexcellent categories

The average COVs of the static elastic modulus 119864119888from

100 by 200mm and 150 by 300mm cylinders are 632 and583 respectively A slightly higher COV of 119864

119888is mainly

due to imperfect concrete specimens and testing procedurethe opposite faces of the specimens were slightly skew andtheir deformations under compression were not uniformThis may also affect compressive strength of concrete butappears to be more influential to determination of elasticmodulus Table 2 shows that the COVs of both119865

119888and119864

119888from

the three differentmixes are reasonably consistent at differentages in 4 7 14 and 28 days

For the dynamic tests the 100 by 200mm cylinders pro-duce equivalent or slightly higher variability than the 150by 300mm cylinders however the differences appear to beinsignificant The average COVs of the fundamental longitu-dinal 119891

119871and transverse 119891

119879frequencies measured from 100 by

200mm and 150 by 300mm cylinders are 164 and 120and 162 and 117 respectively Furthermore the averageCOVs of the 119875-wave velocity (119862

119871) for 100 by 200mm and 150

by 300mm cylinders are 140 and 123 respectively bothof which are consistent with observations by ACI committee228 [29]

32 Compressive Strength Figure 3 compares compressivestrengths of concrete cylinders measured from 100 by200mm and 150 by 300mm cylinders (119865

119888100and 119865119888150

resp)The experimental data represented as open symbols showthat there is no significant difference between 119865

119888100and 119865

119888150

in the lower strength range of 8MPa to 30MPa with a meanabsolute error (MAE) less than 1MPa In this studyMAEwasdefined as follows

MAE =sum

1003816100381610038161003816119865119888150

minus 119865119888100

1003816100381610038161003816

119873 (11)

where 119873 is the number of the experimental data (ie in thisstudy 119873 = 120) The result for low compressive strength isconsistent with observations by prior researchers [22 24 30]

However it was noticed that scattering of experimentaldata in this study becomes greater as compressive strengthincreases in the higher strength range greater than 30MPa119865119888150

-to-119865119888100

ratio in this study gradually increases as 119865119888100

increases An approximated equation that relates 119865119888150

and119865119888100

was established by a linear regression analysis of theexperimental data set in this study as follows

119865119888150

= 111119865119888100

minus 156 [MPa] (1198772

= 096) (12)

The best-fit line presented as a red dash line in Figure 3 iscompatible with the equations proposed by prior researchers[19 20] However there is contradiction in the relationshipbetween 119865

119888150and 119865119888100

reported by different researchers (see

Com

pres

sive s

treng

thFc150

(MPa

)

10 20 30 40 50 60 70 80 90 1000Compressive strength Fc100 (MPa)

0

10

20

30

40

50

60

70

80

90

100

Test results mix 1Test results mix 2Test results mix 3Issa et al (2000) Malaikah (2005)Vandergrift and Schindler (2006)

P M Carrasquillo and R L Carrasquillo (1988)Carrasquillo et al (1981) Cook (1989)Line of equalityBest-fit line in the present study(Fc150 = 111Fc100 minus 156 R2

= 096)

Figure 3 Comparison of compressive strength of concrete mea-sured from 100 by 200mm and 150 by 300mm cylinders (119865

119888100and

119865119888150

resp)

Figure 2) [18ndash22 24 30] The inconsistency results in thehigher strength range are attributed to complexity in theinterfacial transition zone of concrete [10 24] It is knownthat considerable stresses are transferred at cement paste andaggregatesrsquo interface of high strength concrete due to lowerporosity of the interfacial transition zone (ITZ) In fact thereare a number of factors affecting the ITZ which includecoarse aggregates mineral admixtures and curing methodsand various factors affect compressive strength in differentways for different cylinder sizes [14] Therefore special careis still needed for selecting the cylinder size for measuringcompressive strength of relatively high strength concrete(gt40MPa)

33 Static Elastic Moduli Figure 4 compares static elasticmoduli of concrete measured from 100 by 200mm and 150by 300mm cylinders (119864

119888100and 119864

119888150 resp) in this study For

a comparison database collected from the literature [22 30]was shown in the same figure The experimental data set inthis study presented as open symbols shows that 119864

119888100is

closely correlated with 119864119888150

in the elastic modulus range of10GPa to 25GPa For the lower elastic modulus range of 10to 15GPa 119864

119888100values are comparable with 119864

119888150values with

6 Advances in Materials Science and EngineeringSt

atic

elas

tic m

odul

usEc150

(GPa

)

Test results mix 1Test results mix 2Test results mix 3Malaikah (2005)

Best-fit line of the experimental data in this study(Ec150 = 09Ec100 + 19 R2

= 084)

Issa et al (2000)95 confidence boundsLine of equality

0

5

10

15

20

25

30

35

40

45

50

55

4010 15 20 25 30 35 500 45 555Static elastic modulus Ec100 (GPa)

Figure 4 Comparison of static elastic moduli of concrete measuredfrom 100 by 200mm and 150 by 300mm cylinders (119864

119888100and 119864

119888150

resp)

MAE between 119864119888100

and 119864119888150

of about 045GPaTherefore itmay be acceptable to assume from a practical perspective thatstatic elastic moduli using 100 by 200mm and 150 by 300mmcylinders are equivalent

However the ratio of 119864119888150

to 119864119888100

appears to graduallyincrease as 119864

119888150increases to 25GPa The higher elasticity

in the smaller size is attributed to the fact that the quantityof mortar required to fill the space between the particles ofthe coarse aggregate and the wall of the mold is greater thanthat necessary in the interior of the mass (ie wall effect)[10] In general the elasticity of cementmortar is greater thanthat of concrete which consequently results in increasing theeffective elasticity of concrete in smaller size In this study thebest-fit line that approximates the relationship between 119864

119888150

and 119864119888100

was established by a linear regression analysis asfollows

119864119888150

= 09119864119888100

+ 19 [MPa] (1198772

= 084) (13)

The best-fit line and 95 confidence bounds of the best-fitline are presented as solid and dash lines respectively inFigure 3 Interestingly the best-fit line of the experimentaldata in this study (10GPa le 119864

119888100le 25GPa) appears to be

valid for predicting the data set in the higher elastic modulusrange of 25GPa to 55GPa reported by prior researchers [2230] However it is still difficult to attain general conclusionson the relationship between 119864

119888150and 119864

119888100 especially for

Test results mix 1Test results mix 2Test results mix 3

Best-fit line for experimental data in this study

95 confidence boundsLine of equality

5010 15 20 25 30 35 40 600 455 550

5

10

15

20

25

30

35

40

45

50

55

60

Dyn

amic

elas

tic m

odul

usEdP150

(GPa

)

Dynamic elastic modulus EdP100 (GPa)

(EdP150 = 097Ed + 0138 R2= 092)100P

Figure 5 Comparison of velocity moduli from 100 by 200mm and150 by 300mm cylinders

concrete in the higher strength range greater than 50MPabecause of scarcity of available experimental data

34 Dynamic Elastic Moduli Figure 5 compares dynamicelastic moduli measured using UPV tests (ie velocitymoduli) from 100 by 200mm and 150 by 300mm cylinders(119864119889119875100

and 119864119889119875150

resp) in accordance with ASTM C597[26] It was observed that 100 by 200mm cylinders consis-tently result in slightly higher dynamic elastic moduli than150 by 300mm cylinders Linear regression of 119864

119889119875100and

119864119889119875150

measured in this study shows that 119864119889119875100

is about3 greater than 119864

119889119875150in a range of 20GPa to 40GPa (see

Figure 5) The MAE from two different cylinders was about05 GPa which is only 25 of the MAE from static elasticmoduli in this study (ie 2 GPa)

In addition shown in Figures 6(a) and 6(b) is the compar-ison of dynamic elastic moduli measured from longitudinaland transverse resonance frequency tests (ie resonancemoduli) 119864

119889119871119877and 119864

119889119879119877 respectively from 100 by 200mm

and 150 by 300mm cylinders in accordance with ASTMC125[16] The use of 150 by 300mm cylinders tends to resultin slightly higher resonance moduli (both 119864

119889119871119877and 119864

119889119879119877)

than those from 100 by 200mm cylinders According to thelinear regression analysis it was found that the resonancemoduli measured using the 150 by 300mm cylinder (119864

119889119871119877150

or 119864119889119877119877150

) are 1 to 2 greater than those from the 100by 200mm cylinder (119864

119889119871119877100or 119864119889119877119877100

) Approximatedequations that relate the resonance moduli from the twodifferent cylinder sizes are shown in Figures 6(a) and 6(b)

Advances in Materials Science and Engineering 7

Test results mix 1Test results mix 2Test results mix 3

0

5

10

15

20

25

30

35

40

3510 15 20 25 30 400 5

(EdLR150 = 102EdLR100 + 0127 R2= 096)

Best-fit line for experimental data in this study

95 confidence boundsLine of equality

EdLR100 (GPa)Dynamic elastic modulus

EdLR150

(GPa

)D

ynam

ic el

astic

mod

ulus

(a)

Test results mix 1Test results mix 2Test results mix 395 confidence boundsLine of equalityBest-fit line for experimental data in this study(EdTR150 = 101EdTR100 + 0438 R2

= 093)

0

5

10

15

20

25

30

35

40

3510 15 20 25 30 400 5EdTR100 (GPa)Dynamic elastic modulus

EdTR150

(GPa

)D

ynam

ic el

astic

mod

ulus

(b)

Figure 6 Comparison of resonance moduli from 100 by 200mm and 150 by 300mm cylinders (a) 119864119889119871119877150

versus 119864119889119871119877100

and (b) 119864119889119879119877150

versus 119864119889119879119877100

Furthermore without regard to longitudinal or transversemodes the MAE between the resonance moduli from thedifferent cylinder is less than 03GPa Therefore the findingsin this study demonstrate that the dynamic elastic moduli(both velocity and resonance moduli) using the 100 by200mm and 150 by 300mm cylinders are regarded as beingequal from a practical standpoint

However it was observed that there is a precaution inmeasuring reliable and consistent resonance frequency usingthe 100 by 200mm cylinder The smaller cylinder has higherchance of mistakenly hitting an impact source (location andinclination to test surface) which may cause undesirableresonance modes such as torsional modes in the frequencydomain Consequently it was often difficult to select a rightfrequency peak corresponding to the fundamental longitudi-nal or transverse modes In this study preliminary numeri-cal simulations were conducted to calculate theoretical fre-quency peak values which was helpful to select a rightfrequency peak In addition to improve accuracy and con-sistency resonance tests were repeated until the COV of fivesuccessive testing procedures is less than 5 and average ofthe five test results was finally accepted in this study

35 Relationship between Static Elastic Modulus and Com-pressive Strength Figure 7 is a plot representing relationshipbetween static elastic modulus and compressive strengthmeasured in accordance with ASTM C469 [4] and ASTM

C39 [25] respectively The data points obtained from 100 by200mm and 150 by 300mm cylinders are presented as openand solid symbols in Figures 7(a) and 7(b) respectively For acomparison Figure 7 presents three code equations adoptedby ACI 318 and ACI 363 committees and CEB-FIP Modelcode and a practical equation proposed by Noguchi et al [8](see (14)) which was developed based on an extensive exper-imental database from normal to high strength concrete

119864119888= 1198961119896233500 (

119865119888

60)

13

(119908119888

2400)

2

(14)

where 1198961and 119896

2are correction factors for coarse aggregates

and mineral admixturesIt was found that the effect of cylinder size appears to be

insignificant on the relationship between static elastic modu-lus and compressive strength of concrete for normal strengthconcrete (lt40MPa) in this study Approximated equationsthat relate 119864

119888and 119865119888from 100 by 200mm and 150 by 300mm

cylinders were established by nonlinear regression analysesand shown in Figures 7(a) and 7(b) respectivelyTheMAE ofthe two best-fit curves is less than 01 GPa in the compressivestrength range of 10MPa to 40MPa In this studyMAE of thetwo continuous curves was defined as follows

MAEcon =

[int 1198921(119865119888) minus 1198922(119865119888) 119889119865119888]

int 119889119865119888

(15)

8 Advances in Materials Science and Engineering

Best-fit line for experimental data in this study(Ec150 = 456Fc150

0418 R2= 090)

Noguchi et al [2009] k1 = k2 = 1

Noguchi et al [2009] k1 = k2 = 095

Mix 1

Mix 3

ACI 318ACI 363CEB-FIP Model code and Eurocode 2

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

5010 15 20 25 30 35 40 45 55 6050Compressive strength Fc (MPa)

150 by 300mm cylindersMix 2

(a)

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

Best-fit line for experimental data in this study(Ec100 = 416Fc100

0446 R2= 084)

Noguchi et al [2009] k1 = k2 = 1

Noguchi et al [2009] k1 = k2 = 095

Mix 1

Mix 3

ACI 318ACI 363CEB-FIP Model code and Eurocode 2

50 15 20 25 30 35 40 45 50 55 6010Compressive strength Fc (MPa)

0

5

10

15

20

25

30

35

40

Mix 2 100 by 200mm cylinders

(b)

Figure 7 Comparison of compressive strength and static elastic modulus of concrete

where MAEcon is mean average error (MAE) of two contin-uous functions 119892

119894is a function presenting 119864

119888expressed as

119865119888 and the subscript 119894 indicates cylinder size (1 and 2 for the

100 by 200mm and 150 by 300mm cylinders resp) Further-more there is no significant difference in 119877

2 values of thetwo best-fit curves 1198772 values for the 100 by 200mm and150 by 300mm cylinders are 088 and 090 respectivelyTherefore the 100 by 200mm cylinders can be used insteadof 150 by 300mm cylinders to estimate static elastic modulusfrom compressive strength without reducing accuracy andconsistency However the three code equations tend tooverestimate static modulus of concrete compared to thosefrom direct measurement according to ASTM C469 [4] Assummarized in Table 3 mean average error (MAE) betweenmeasured and predicted 119864

119888from the three code equations is

in a range of 44 to 12GPa corresponding to about 10 to30 of the measured 119864

119888 In contrast the Noguchi equation

[8] predicts experimental results with far more improvedaccuracy (ie MAE less than 2GPa) by addressing correctionfactors for the effects of aggregates and mineral admixtures(ie 119896

1= 1198962= 095)

36 Relationship between Static and Dynamic Elastic ModuliFigure 8 presents the relationship between static and dynamicelastic moduli determined using different nondestructivetesting methods 119864

119889119875 119864119889119871119877

and 119864119889119879119877

respectively with

Table 3 Mean absolute error (MAE) of expressions relating staticelastic modulus and compressive strength measured using 100 by200mm and 150 by 300mm cylinders

Equation to convert 119864119889to

119864119888

MAE (GPa)150 by 300mm

cylinder100 by 200mm

cylinder119864119889119871119879

119864119889119871119879

Equation (1) 483 463Equation (2) 454 443Equation (3) 1221 1215Equation (14) with1198961= 1198962= 1

342 341

Equation (14) with1198961= 1198962= 095

156 188

Best-fit line 132 157

Poissonrsquos ratio of 02Theuse of Poissonrsquos ratio of 02 is reason-able for common concrete in practice [10] In Figure 8 119864

119889119875

119864119889119871119877

and 119864119889119879119877

measured from 100 by 200mm and 150 by300mm cylinders are shown as open and solid symbols in leftand right columns For comparison purposes several well-known empirical equations (see (3) (4) and (5)) proposedby prior researchers are shown in the figures

Advances in Materials Science and Engineering 9

Best-fit line for experimental data in this study(Ec150 = 044EdLR150

115 R2= 090)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equalityLydon and Balendran (1986)BS8100 Part 2Popovics (1975)

5 10 15 20 25 30 35 400Dynamic elastic modulus EdLR (GPa)

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

(a)

Best-fit line for experimental data in this study(Ec150 = 044EdTR100

115 R2= 090)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equality

BS8100 Part 2

5 10 15 20 25 30 35 400Dynamic elastic modulus EdTR (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

Popovics (1975)

Lydon and Balendran (1986)

(b)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equality

BS8100 Part 2

Best-fit line for experimental data in this study(Ec150 = 022EdP150

129 R2= 087)

Popovics (1975)

Lydon and Balendran (1986)

3510 15 20 25 30 400 5Dynamic elastic modulus EdP (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

(c)

Best-fit line for experimental data in this study(Ec100 = 040EdLR100

118 R2= 088)

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

3510 15 20 25 30 400 5Dynamic elastic modulus EdLR (GPa)

Lydon and Balendran (1986)

Popovics (1975)

(d)

Figure 8 Continued

10 Advances in Materials Science and Engineering

Best-fit line for experimental data in this study(Ec100 = 039EdTR100

120 R2= 087)

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

3510 15 20 25 30 400 5Dynamic elastic modulus EdTR (GPa)

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

Lydon and Balendran (1986)

Popovics (1975)

(e)

Best-fit line for experimental data in this study

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

3510 15 20 25 30 400 5Dynamic elastic modulus EdP (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

EdLR100135 R2

= 085)(Ec100 = 017

Popovics (1975)

Lydon and Balendran (1986)

(f)

Figure 8 Comparison of static and resonance elastic moduli of concrete (a) 119864119889119871119877150

versus 119864119888150

(b) 119864119889119879119877150

versus 119864119888150

(c) 119864119889119875150

versus119864119888150

(d) 119864119889119871119877100

versus 119864119888100

(e) 119864119889119879119877100

versus 119864119888100

and (f) 119864119889119875100

versus 119864119888100

Table 4 Mean absolute error (MAE) of expressions relating static and dynamic elastic modulus measured using 100 by 200mm and 150 by300mm cylinders

Equation to convert 119864119889to 119864119888

MAE (GPa)150 by 300mm cylinder 100 by 200mm cylinder

119864119889119871119879

119864119889119877119879

119864119889119875

119864119889119871119879

119864119889119877119879

119864119889119875

Equation (4) 302 282 754 283 254 846Equation (5) 559 591 277 607 649 335Equation (6) 125 111 658 113 107 780Best-fit line 090 095 126 109 110 117

It is observed that there is only slight difference in therelationship between119864

119888and119864

119889obtained from 100 by 200mm

and 150 by 300mm cylinders In this study approximatedequations that relate119864

119888and119864

119889(119864119889119875

119864119889119871119877

or119864119889119879119877

) from 100by 200mm and 150 by 300mm cylinders were established bynonlinear regression analyses and shown in Figures 8(a)ndash8(f)The MAEs of the two best-fit curves are less than 01MPa inthe dynamic elastic modulus range of 10GPa to 25GPa Fur-thermore there is no significant difference in 119877

2 values of thetwo best-fit curves (see Figure 8) However for both data setsfrom different cylinders the three dynamic moduli (119864

119889119871119877

119864119889119879119877

and 119864119889119875

) obtained from resonance tests and UPVmethod are greater than the static elastic modulus 119864

119888 with

different static-to-dynamic elastic modulus ratio 119864119888119864119889119875

ratio with an average of 056 and COV of 92 is too faraway from the line of equality as well as from the three well-known equations relating static and dynamic elastic modu-lus Therefore the use of 119864

119889119875appears to be inappropriate

to estimate static elastic modulus which is consistent withobservations from other researchers [7 10] In contrast119864119888119864119889119871119877

(or 119864119888119864119889119879119877

) ratio was closer to the line of equalitythan 119864

119888119864119889119875

with an average of 072 and COV of 715The equation proposed by Popovics [13] (see (6)) shows verygood agreement with the experimental results regardless ofcylinder size in this study (see Table 4) In addition priorresearcher [7] observed that the Popovics equation (see (6))can be extended to high strength concrete up to 60MPawith-out regard to cylinder size However it should be mentioned

Advances in Materials Science and Engineering 11

that additional experimental data should be accumulated tobetter understand the size effect on the relationship betweenstatic and dynamic elastic moduli of high strength concrete(gt60MPa) due to scarcity of experimental studies in such ahigh strength range

4 Conclusions

A series of experimental studies was conducted to explore theeffect of cylinder size (100 by 200mm and 150 by 300mmcylinders) on the relationship between static elastic modulusand compressive strength and static and dynamic elasticmoduli of concrete Conclusions based on experiments in thisstudy and database from the literature are drawn as follows

(1) Experimental results in this study show that theCOVsof test results from 100 by 200mm cylinders areabout 10 higher than those from 150 by 300mmcylinders however the differences are statisticallyinsignificantThe averageCOVs of static and dynamicelastic moduli using the UPV and longitudinal andtransverse resonance frequency tests from 100 by200mm cylinders are 632 140 162 and 117respectively while those values from 150 by 300mmcylinders are 583 123 162 and 117 respec-tively For compressive strength the average COVsfrom the 100 by 200mm and 150 by 300mm cylindersare 441 and 365 respectively

(2) According to the findings from similarity tests of best-fit curves and comparison of 1198772 based on regressionanalyses it has been demonstrated that the effect ofcylinder size (100 by 200mm and 150 by 300mmcylinders) is insignificant on compressive strengthand static elastic modulus and the relationship bet-ween the two parameters for normal strength con-crete up to 30MPa However in the higher strengthrange greater than 30MPa there is contradiction inthe relationship between 119865

119888150and 119865

119888100based on

experimental test in this study and database reportedby different researchers Therefore it is difficult toestablish a simple equation that relates 119865

119888100and 119865119888150

and 119864

119888100and 119864

119888150because of limited experimental

and theoretical studies

(3) The three code equations tend to overestimate staticmodulus of concrete compared to those from directmeasurement according to ASTM C469 with MAEin a range of 44GPa to 12GPa In contrast theNoguchi equation predicts experimental results withfar more improved accuracy (ie MAE less than2GPa) by addressing correction factors for the effectsof aggregates and mineral admixtures (ie 119896

1= 1198962=

095)

(4) There is only a slight difference in the relationshipbetween static and resonance moduli from 100 by200mm and 150 by 300mm cylinders for normalstrength concrete Test results from this study and theliterature show that the empirical equation suggested

by Popovics [13] ((6) in this study) is effective for pre-dicting static elastic moduli from resonance moduliof concrete with compressive strength up to 60MParegardless of the cylinder size with MAE of less than15 GPa

(5) However the velocity moduli are excessively greaterthan static elastic modulus The empirical equations(see (4) (5) and (6)) produce considerable errors(with MAE in a range of 277GPa to 846GPa) bet-ween measured and predicted elastic moduli There-fore the use of velocitymoduli appears to be inappro-priate to estimate static elastic modulus

Conflict of Interests

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

Acknowledgment

This research was supported by the Basic Science ResearchProgram through theNational Research Foundation of Korea(NRF) funded by the Ministry of Science ICT amp FuturePlanning (no 2015R1A5A1037548)

References

[1] ACI Committee 318 Building Code Requirements for StructuralConcrete (ACI 318-11) and Commentary American ConcreteInstitute Farmington Hills Mich USA 2014

[2] IBC Council International Building Code (IBC 2012) 2014[3] N Gucunski A Imani F Romero et al ldquoNondestructive testig

to identify concrete bridge deck deteriorationrdquo SHRP 2 ReportS2-R06A-RR-1 2013

[4] ACI Committee 469 Standard Test Method for Static Modulusof Elasticity and Poissonrsquos Ratio of Concrete in CompressionAmerican Concrete Institute Farmington Hills Mich USA2014

[5] A Pauw ldquoStatic modulus of elasticity of concrete as affected bydensityrdquo ACI Journal Proceedings vol 57 no 12 pp 679ndash6871960

[6] ACI Committee 363 ldquoState-of-the-art report on high-strengthconcreterdquo ACI Journal Proceedings vol 81 no 4 pp 364ndash4111984

[7] J S Popovics ldquoA study of static and dynamic modulus ofelasticity of concreterdquo ACI-CRC Final Report 2008

[8] T Noguchi F Tomosawa KM Nemati BM Chiaia and A RFantilli ldquoA practical equation for elastic modulus of concreterdquoACI Structural Journal vol 106 no 5 pp 690ndash696 2009

[9] R E Philleo ldquoComparison of results of threemethods for deter-mining Youngrsquos modulus of elasticity of concreterdquo InternationalConcrete Abstracts Portal vol 51 no 1 pp 461ndash469 1955

[10] A M Neville Properties of Concrete John Wiley amp Sons NewYork NY USA 4th edition 1997

[11] F D Lydon and R V Balendran ldquoSome observations on elasticproperties of plain concreterdquo Cement and Concrete Researchvol 16 no 3 pp 314ndash324 1986

[12] B S Institute ldquoStructural use of concretemdashpart 2 code ofpractice for special circumstancerdquo BS 8110-21995 BSI LondonUK 1995

12 Advances in Materials Science and Engineering

[13] S Popovics ldquoVerification of relationships between mechanicalproperties of concrete-like materialsrdquoMaterials and Structuresvol 8 no 3 pp 183ndash191 1975

[14] ASTM C191 Standard Practice for Making and Curing ConcreteTest Specimens in the Laboratory ASTM 2014

[15] ASTM ldquoStandard practice for making and curing concrete testspecimen in the fieldrdquo ASTM C31 ASTM International 2012

[16] ASTM International ldquoStandard test method for fundamentaltransverse longitudinal and torsional resonant frequencies ofconcrete specimensrdquo ASTM C215 ASTM International WestConshohocken Pa USA 2002

[17] P-C Aitcin and P K Mehta ldquoEffect of coarse-aggregate char-acteristics on mechanical properties of high-strength concreterdquoACI Materials Journal vol 87 no 2 pp 103ndash107 1990

[18] P-C Aitcin B Miao W D Cook and D Mitchell ldquoEffectsof size and curing on cylinder compressive strength of normaland high-strength concretesrdquo ACIMaterials Journal vol 91 pp349ndash354 1994

[19] P M Carrasquillo and R L Carrasquillo ldquoEvaluation of the useof current concrete practice in the production of high strengthconcreterdquo ACI Materials Journal vol 85 no 1 pp 49ndash54 1988

[20] R L Carrasquillo A H Nilson and F O Slate ldquoProperties ofhigh strength concrete subject to short-term loadsrdquo Journal ofthe American Concrete Institute vol 78 no 3 pp 171ndash178 1981

[21] J E Cook ldquo10000 psi concreterdquo Concrete International vol 11pp 67ndash75 1989

[22] A S Malaikah ldquoA proposed relationship for the modulus ofelasticity of high strength concrete using local materials inRiyadhrdquo Journal of King Saud UniversitymdashEngineering Sciencesvol 17 pp 1ndash11 2005

[23] A Mokhtarzadeh and C French ldquoMechanical properties ofhigh-strength concrete with consideration for precast applica-tionsrdquo ACI Materials Journal vol 97 no 2 pp 136ndash147 2000

[24] DVandergrift Jr andA K Schindler ldquoThe effect of test cylindersize on the compressive strength of sulfur capped concretespecimensrdquo Tech Rep IR-06-01 Highway Research Centerand Department of Civil Engineering at Auburn UniversityAuburn Ala USA 2006

[25] ASTM International ldquoStandard test method for compressivestrength of cylindrical concrete specimensrdquo ASTM C39 ASTMInternational West Conshohocken Pa USA 2014

[26] ASTM ldquoStandard test method for pulse velocity throughconcreterdquo ASTM C597 ASTM International 1997

[27] N J CarinoW F Guthrie E S Lagergren and G MMullingsldquoEffects of testing variables on the strength of high-strength(90MPa) concrete cylindersrdquo in High-Performance ConcreteV M Malhotra Ed SP-149 pp 589ndash632 American ConcreteInstitute Farmington Hills Mich USA 1994

[28] ACI ldquoGuide for evaluation of strength test results of concrete(ACI 214R-11)rdquo ASTM C214 American Concrete InstituteFarmington Hills Mich USA 2011

[29] ACI Committee 228 ldquoNondestructive test methods for evalua-tion of concrete in structuresrdquo ReportACI 2282R-98AmericanConcrete Institute Farmington Hills Mich USA 1998

[30] S A Issa M S Islam M A Issa A A Yousif and M A IssaldquoSpecimen and aggregate size effect on concrete compressivestrengthrdquo Cement Concrete and Aggregates vol 22 no 2 pp103ndash115 2000

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

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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

previous researchers that 100 by 200mm cylinder tends tohave about 20 higher within-test variability than 150 by300mm cylinder [27] The COVs from the 150 by 300mmcylinder are between good (40 to 50) and excellent (lt20)categories according to ACI 214R [28] whereas for 100 by200mm cylinder the COVs are between fair (50 to 60) andexcellent categories

The average COVs of the static elastic modulus 119864119888from

100 by 200mm and 150 by 300mm cylinders are 632 and583 respectively A slightly higher COV of 119864

119888is mainly

due to imperfect concrete specimens and testing procedurethe opposite faces of the specimens were slightly skew andtheir deformations under compression were not uniformThis may also affect compressive strength of concrete butappears to be more influential to determination of elasticmodulus Table 2 shows that the COVs of both119865

119888and119864

119888from

the three differentmixes are reasonably consistent at differentages in 4 7 14 and 28 days

For the dynamic tests the 100 by 200mm cylinders pro-duce equivalent or slightly higher variability than the 150by 300mm cylinders however the differences appear to beinsignificant The average COVs of the fundamental longitu-dinal 119891

119871and transverse 119891

119879frequencies measured from 100 by

200mm and 150 by 300mm cylinders are 164 and 120and 162 and 117 respectively Furthermore the averageCOVs of the 119875-wave velocity (119862

119871) for 100 by 200mm and 150

by 300mm cylinders are 140 and 123 respectively bothof which are consistent with observations by ACI committee228 [29]

32 Compressive Strength Figure 3 compares compressivestrengths of concrete cylinders measured from 100 by200mm and 150 by 300mm cylinders (119865

119888100and 119865119888150

resp)The experimental data represented as open symbols showthat there is no significant difference between 119865

119888100and 119865

119888150

in the lower strength range of 8MPa to 30MPa with a meanabsolute error (MAE) less than 1MPa In this studyMAEwasdefined as follows

MAE =sum

1003816100381610038161003816119865119888150

minus 119865119888100

1003816100381610038161003816

119873 (11)

where 119873 is the number of the experimental data (ie in thisstudy 119873 = 120) The result for low compressive strength isconsistent with observations by prior researchers [22 24 30]

However it was noticed that scattering of experimentaldata in this study becomes greater as compressive strengthincreases in the higher strength range greater than 30MPa119865119888150

-to-119865119888100

ratio in this study gradually increases as 119865119888100

increases An approximated equation that relates 119865119888150

and119865119888100

was established by a linear regression analysis of theexperimental data set in this study as follows

119865119888150

= 111119865119888100

minus 156 [MPa] (1198772

= 096) (12)

The best-fit line presented as a red dash line in Figure 3 iscompatible with the equations proposed by prior researchers[19 20] However there is contradiction in the relationshipbetween 119865

119888150and 119865119888100

reported by different researchers (see

Com

pres

sive s

treng

thFc150

(MPa

)

10 20 30 40 50 60 70 80 90 1000Compressive strength Fc100 (MPa)

0

10

20

30

40

50

60

70

80

90

100

Test results mix 1Test results mix 2Test results mix 3Issa et al (2000) Malaikah (2005)Vandergrift and Schindler (2006)

P M Carrasquillo and R L Carrasquillo (1988)Carrasquillo et al (1981) Cook (1989)Line of equalityBest-fit line in the present study(Fc150 = 111Fc100 minus 156 R2

= 096)

Figure 3 Comparison of compressive strength of concrete mea-sured from 100 by 200mm and 150 by 300mm cylinders (119865

119888100and

119865119888150

resp)

Figure 2) [18ndash22 24 30] The inconsistency results in thehigher strength range are attributed to complexity in theinterfacial transition zone of concrete [10 24] It is knownthat considerable stresses are transferred at cement paste andaggregatesrsquo interface of high strength concrete due to lowerporosity of the interfacial transition zone (ITZ) In fact thereare a number of factors affecting the ITZ which includecoarse aggregates mineral admixtures and curing methodsand various factors affect compressive strength in differentways for different cylinder sizes [14] Therefore special careis still needed for selecting the cylinder size for measuringcompressive strength of relatively high strength concrete(gt40MPa)

33 Static Elastic Moduli Figure 4 compares static elasticmoduli of concrete measured from 100 by 200mm and 150by 300mm cylinders (119864

119888100and 119864

119888150 resp) in this study For

a comparison database collected from the literature [22 30]was shown in the same figure The experimental data set inthis study presented as open symbols shows that 119864

119888100is

closely correlated with 119864119888150

in the elastic modulus range of10GPa to 25GPa For the lower elastic modulus range of 10to 15GPa 119864

119888100values are comparable with 119864

119888150values with

6 Advances in Materials Science and EngineeringSt

atic

elas

tic m

odul

usEc150

(GPa

)

Test results mix 1Test results mix 2Test results mix 3Malaikah (2005)

Best-fit line of the experimental data in this study(Ec150 = 09Ec100 + 19 R2

= 084)

Issa et al (2000)95 confidence boundsLine of equality

0

5

10

15

20

25

30

35

40

45

50

55

4010 15 20 25 30 35 500 45 555Static elastic modulus Ec100 (GPa)

Figure 4 Comparison of static elastic moduli of concrete measuredfrom 100 by 200mm and 150 by 300mm cylinders (119864

119888100and 119864

119888150

resp)

MAE between 119864119888100

and 119864119888150

of about 045GPaTherefore itmay be acceptable to assume from a practical perspective thatstatic elastic moduli using 100 by 200mm and 150 by 300mmcylinders are equivalent

However the ratio of 119864119888150

to 119864119888100

appears to graduallyincrease as 119864

119888150increases to 25GPa The higher elasticity

in the smaller size is attributed to the fact that the quantityof mortar required to fill the space between the particles ofthe coarse aggregate and the wall of the mold is greater thanthat necessary in the interior of the mass (ie wall effect)[10] In general the elasticity of cementmortar is greater thanthat of concrete which consequently results in increasing theeffective elasticity of concrete in smaller size In this study thebest-fit line that approximates the relationship between 119864

119888150

and 119864119888100

was established by a linear regression analysis asfollows

119864119888150

= 09119864119888100

+ 19 [MPa] (1198772

= 084) (13)

The best-fit line and 95 confidence bounds of the best-fitline are presented as solid and dash lines respectively inFigure 3 Interestingly the best-fit line of the experimentaldata in this study (10GPa le 119864

119888100le 25GPa) appears to be

valid for predicting the data set in the higher elastic modulusrange of 25GPa to 55GPa reported by prior researchers [2230] However it is still difficult to attain general conclusionson the relationship between 119864

119888150and 119864

119888100 especially for

Test results mix 1Test results mix 2Test results mix 3

Best-fit line for experimental data in this study

95 confidence boundsLine of equality

5010 15 20 25 30 35 40 600 455 550

5

10

15

20

25

30

35

40

45

50

55

60

Dyn

amic

elas

tic m

odul

usEdP150

(GPa

)

Dynamic elastic modulus EdP100 (GPa)

(EdP150 = 097Ed + 0138 R2= 092)100P

Figure 5 Comparison of velocity moduli from 100 by 200mm and150 by 300mm cylinders

concrete in the higher strength range greater than 50MPabecause of scarcity of available experimental data

34 Dynamic Elastic Moduli Figure 5 compares dynamicelastic moduli measured using UPV tests (ie velocitymoduli) from 100 by 200mm and 150 by 300mm cylinders(119864119889119875100

and 119864119889119875150

resp) in accordance with ASTM C597[26] It was observed that 100 by 200mm cylinders consis-tently result in slightly higher dynamic elastic moduli than150 by 300mm cylinders Linear regression of 119864

119889119875100and

119864119889119875150

measured in this study shows that 119864119889119875100

is about3 greater than 119864

119889119875150in a range of 20GPa to 40GPa (see

Figure 5) The MAE from two different cylinders was about05 GPa which is only 25 of the MAE from static elasticmoduli in this study (ie 2 GPa)

In addition shown in Figures 6(a) and 6(b) is the compar-ison of dynamic elastic moduli measured from longitudinaland transverse resonance frequency tests (ie resonancemoduli) 119864

119889119871119877and 119864

119889119879119877 respectively from 100 by 200mm

and 150 by 300mm cylinders in accordance with ASTMC125[16] The use of 150 by 300mm cylinders tends to resultin slightly higher resonance moduli (both 119864

119889119871119877and 119864

119889119879119877)

than those from 100 by 200mm cylinders According to thelinear regression analysis it was found that the resonancemoduli measured using the 150 by 300mm cylinder (119864

119889119871119877150

or 119864119889119877119877150

) are 1 to 2 greater than those from the 100by 200mm cylinder (119864

119889119871119877100or 119864119889119877119877100

) Approximatedequations that relate the resonance moduli from the twodifferent cylinder sizes are shown in Figures 6(a) and 6(b)

Advances in Materials Science and Engineering 7

Test results mix 1Test results mix 2Test results mix 3

0

5

10

15

20

25

30

35

40

3510 15 20 25 30 400 5

(EdLR150 = 102EdLR100 + 0127 R2= 096)

Best-fit line for experimental data in this study

95 confidence boundsLine of equality

EdLR100 (GPa)Dynamic elastic modulus

EdLR150

(GPa

)D

ynam

ic el

astic

mod

ulus

(a)

Test results mix 1Test results mix 2Test results mix 395 confidence boundsLine of equalityBest-fit line for experimental data in this study(EdTR150 = 101EdTR100 + 0438 R2

= 093)

0

5

10

15

20

25

30

35

40

3510 15 20 25 30 400 5EdTR100 (GPa)Dynamic elastic modulus

EdTR150

(GPa

)D

ynam

ic el

astic

mod

ulus

(b)

Figure 6 Comparison of resonance moduli from 100 by 200mm and 150 by 300mm cylinders (a) 119864119889119871119877150

versus 119864119889119871119877100

and (b) 119864119889119879119877150

versus 119864119889119879119877100

Furthermore without regard to longitudinal or transversemodes the MAE between the resonance moduli from thedifferent cylinder is less than 03GPa Therefore the findingsin this study demonstrate that the dynamic elastic moduli(both velocity and resonance moduli) using the 100 by200mm and 150 by 300mm cylinders are regarded as beingequal from a practical standpoint

However it was observed that there is a precaution inmeasuring reliable and consistent resonance frequency usingthe 100 by 200mm cylinder The smaller cylinder has higherchance of mistakenly hitting an impact source (location andinclination to test surface) which may cause undesirableresonance modes such as torsional modes in the frequencydomain Consequently it was often difficult to select a rightfrequency peak corresponding to the fundamental longitudi-nal or transverse modes In this study preliminary numeri-cal simulations were conducted to calculate theoretical fre-quency peak values which was helpful to select a rightfrequency peak In addition to improve accuracy and con-sistency resonance tests were repeated until the COV of fivesuccessive testing procedures is less than 5 and average ofthe five test results was finally accepted in this study

35 Relationship between Static Elastic Modulus and Com-pressive Strength Figure 7 is a plot representing relationshipbetween static elastic modulus and compressive strengthmeasured in accordance with ASTM C469 [4] and ASTM

C39 [25] respectively The data points obtained from 100 by200mm and 150 by 300mm cylinders are presented as openand solid symbols in Figures 7(a) and 7(b) respectively For acomparison Figure 7 presents three code equations adoptedby ACI 318 and ACI 363 committees and CEB-FIP Modelcode and a practical equation proposed by Noguchi et al [8](see (14)) which was developed based on an extensive exper-imental database from normal to high strength concrete

119864119888= 1198961119896233500 (

119865119888

60)

13

(119908119888

2400)

2

(14)

where 1198961and 119896

2are correction factors for coarse aggregates

and mineral admixturesIt was found that the effect of cylinder size appears to be

insignificant on the relationship between static elastic modu-lus and compressive strength of concrete for normal strengthconcrete (lt40MPa) in this study Approximated equationsthat relate 119864

119888and 119865119888from 100 by 200mm and 150 by 300mm

cylinders were established by nonlinear regression analysesand shown in Figures 7(a) and 7(b) respectivelyTheMAE ofthe two best-fit curves is less than 01 GPa in the compressivestrength range of 10MPa to 40MPa In this studyMAE of thetwo continuous curves was defined as follows

MAEcon =

[int 1198921(119865119888) minus 1198922(119865119888) 119889119865119888]

int 119889119865119888

(15)

8 Advances in Materials Science and Engineering

Best-fit line for experimental data in this study(Ec150 = 456Fc150

0418 R2= 090)

Noguchi et al [2009] k1 = k2 = 1

Noguchi et al [2009] k1 = k2 = 095

Mix 1

Mix 3

ACI 318ACI 363CEB-FIP Model code and Eurocode 2

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

5010 15 20 25 30 35 40 45 55 6050Compressive strength Fc (MPa)

150 by 300mm cylindersMix 2

(a)

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

Best-fit line for experimental data in this study(Ec100 = 416Fc100

0446 R2= 084)

Noguchi et al [2009] k1 = k2 = 1

Noguchi et al [2009] k1 = k2 = 095

Mix 1

Mix 3

ACI 318ACI 363CEB-FIP Model code and Eurocode 2

50 15 20 25 30 35 40 45 50 55 6010Compressive strength Fc (MPa)

0

5

10

15

20

25

30

35

40

Mix 2 100 by 200mm cylinders

(b)

Figure 7 Comparison of compressive strength and static elastic modulus of concrete

where MAEcon is mean average error (MAE) of two contin-uous functions 119892

119894is a function presenting 119864

119888expressed as

119865119888 and the subscript 119894 indicates cylinder size (1 and 2 for the

100 by 200mm and 150 by 300mm cylinders resp) Further-more there is no significant difference in 119877

2 values of thetwo best-fit curves 1198772 values for the 100 by 200mm and150 by 300mm cylinders are 088 and 090 respectivelyTherefore the 100 by 200mm cylinders can be used insteadof 150 by 300mm cylinders to estimate static elastic modulusfrom compressive strength without reducing accuracy andconsistency However the three code equations tend tooverestimate static modulus of concrete compared to thosefrom direct measurement according to ASTM C469 [4] Assummarized in Table 3 mean average error (MAE) betweenmeasured and predicted 119864

119888from the three code equations is

in a range of 44 to 12GPa corresponding to about 10 to30 of the measured 119864

119888 In contrast the Noguchi equation

[8] predicts experimental results with far more improvedaccuracy (ie MAE less than 2GPa) by addressing correctionfactors for the effects of aggregates and mineral admixtures(ie 119896

1= 1198962= 095)

36 Relationship between Static and Dynamic Elastic ModuliFigure 8 presents the relationship between static and dynamicelastic moduli determined using different nondestructivetesting methods 119864

119889119875 119864119889119871119877

and 119864119889119879119877

respectively with

Table 3 Mean absolute error (MAE) of expressions relating staticelastic modulus and compressive strength measured using 100 by200mm and 150 by 300mm cylinders

Equation to convert 119864119889to

119864119888

MAE (GPa)150 by 300mm

cylinder100 by 200mm

cylinder119864119889119871119879

119864119889119871119879

Equation (1) 483 463Equation (2) 454 443Equation (3) 1221 1215Equation (14) with1198961= 1198962= 1

342 341

Equation (14) with1198961= 1198962= 095

156 188

Best-fit line 132 157

Poissonrsquos ratio of 02Theuse of Poissonrsquos ratio of 02 is reason-able for common concrete in practice [10] In Figure 8 119864

119889119875

119864119889119871119877

and 119864119889119879119877

measured from 100 by 200mm and 150 by300mm cylinders are shown as open and solid symbols in leftand right columns For comparison purposes several well-known empirical equations (see (3) (4) and (5)) proposedby prior researchers are shown in the figures

Advances in Materials Science and Engineering 9

Best-fit line for experimental data in this study(Ec150 = 044EdLR150

115 R2= 090)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equalityLydon and Balendran (1986)BS8100 Part 2Popovics (1975)

5 10 15 20 25 30 35 400Dynamic elastic modulus EdLR (GPa)

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

(a)

Best-fit line for experimental data in this study(Ec150 = 044EdTR100

115 R2= 090)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equality

BS8100 Part 2

5 10 15 20 25 30 35 400Dynamic elastic modulus EdTR (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

Popovics (1975)

Lydon and Balendran (1986)

(b)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equality

BS8100 Part 2

Best-fit line for experimental data in this study(Ec150 = 022EdP150

129 R2= 087)

Popovics (1975)

Lydon and Balendran (1986)

3510 15 20 25 30 400 5Dynamic elastic modulus EdP (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

(c)

Best-fit line for experimental data in this study(Ec100 = 040EdLR100

118 R2= 088)

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

3510 15 20 25 30 400 5Dynamic elastic modulus EdLR (GPa)

Lydon and Balendran (1986)

Popovics (1975)

(d)

Figure 8 Continued

10 Advances in Materials Science and Engineering

Best-fit line for experimental data in this study(Ec100 = 039EdTR100

120 R2= 087)

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

3510 15 20 25 30 400 5Dynamic elastic modulus EdTR (GPa)

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

Lydon and Balendran (1986)

Popovics (1975)

(e)

Best-fit line for experimental data in this study

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

3510 15 20 25 30 400 5Dynamic elastic modulus EdP (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

EdLR100135 R2

= 085)(Ec100 = 017

Popovics (1975)

Lydon and Balendran (1986)

(f)

Figure 8 Comparison of static and resonance elastic moduli of concrete (a) 119864119889119871119877150

versus 119864119888150

(b) 119864119889119879119877150

versus 119864119888150

(c) 119864119889119875150

versus119864119888150

(d) 119864119889119871119877100

versus 119864119888100

(e) 119864119889119879119877100

versus 119864119888100

and (f) 119864119889119875100

versus 119864119888100

Table 4 Mean absolute error (MAE) of expressions relating static and dynamic elastic modulus measured using 100 by 200mm and 150 by300mm cylinders

Equation to convert 119864119889to 119864119888

MAE (GPa)150 by 300mm cylinder 100 by 200mm cylinder

119864119889119871119879

119864119889119877119879

119864119889119875

119864119889119871119879

119864119889119877119879

119864119889119875

Equation (4) 302 282 754 283 254 846Equation (5) 559 591 277 607 649 335Equation (6) 125 111 658 113 107 780Best-fit line 090 095 126 109 110 117

It is observed that there is only slight difference in therelationship between119864

119888and119864

119889obtained from 100 by 200mm

and 150 by 300mm cylinders In this study approximatedequations that relate119864

119888and119864

119889(119864119889119875

119864119889119871119877

or119864119889119879119877

) from 100by 200mm and 150 by 300mm cylinders were established bynonlinear regression analyses and shown in Figures 8(a)ndash8(f)The MAEs of the two best-fit curves are less than 01MPa inthe dynamic elastic modulus range of 10GPa to 25GPa Fur-thermore there is no significant difference in 119877

2 values of thetwo best-fit curves (see Figure 8) However for both data setsfrom different cylinders the three dynamic moduli (119864

119889119871119877

119864119889119879119877

and 119864119889119875

) obtained from resonance tests and UPVmethod are greater than the static elastic modulus 119864

119888 with

different static-to-dynamic elastic modulus ratio 119864119888119864119889119875

ratio with an average of 056 and COV of 92 is too faraway from the line of equality as well as from the three well-known equations relating static and dynamic elastic modu-lus Therefore the use of 119864

119889119875appears to be inappropriate

to estimate static elastic modulus which is consistent withobservations from other researchers [7 10] In contrast119864119888119864119889119871119877

(or 119864119888119864119889119879119877

) ratio was closer to the line of equalitythan 119864

119888119864119889119875

with an average of 072 and COV of 715The equation proposed by Popovics [13] (see (6)) shows verygood agreement with the experimental results regardless ofcylinder size in this study (see Table 4) In addition priorresearcher [7] observed that the Popovics equation (see (6))can be extended to high strength concrete up to 60MPawith-out regard to cylinder size However it should be mentioned

Advances in Materials Science and Engineering 11

that additional experimental data should be accumulated tobetter understand the size effect on the relationship betweenstatic and dynamic elastic moduli of high strength concrete(gt60MPa) due to scarcity of experimental studies in such ahigh strength range

4 Conclusions

A series of experimental studies was conducted to explore theeffect of cylinder size (100 by 200mm and 150 by 300mmcylinders) on the relationship between static elastic modulusand compressive strength and static and dynamic elasticmoduli of concrete Conclusions based on experiments in thisstudy and database from the literature are drawn as follows

(1) Experimental results in this study show that theCOVsof test results from 100 by 200mm cylinders areabout 10 higher than those from 150 by 300mmcylinders however the differences are statisticallyinsignificantThe averageCOVs of static and dynamicelastic moduli using the UPV and longitudinal andtransverse resonance frequency tests from 100 by200mm cylinders are 632 140 162 and 117respectively while those values from 150 by 300mmcylinders are 583 123 162 and 117 respec-tively For compressive strength the average COVsfrom the 100 by 200mm and 150 by 300mm cylindersare 441 and 365 respectively

(2) According to the findings from similarity tests of best-fit curves and comparison of 1198772 based on regressionanalyses it has been demonstrated that the effect ofcylinder size (100 by 200mm and 150 by 300mmcylinders) is insignificant on compressive strengthand static elastic modulus and the relationship bet-ween the two parameters for normal strength con-crete up to 30MPa However in the higher strengthrange greater than 30MPa there is contradiction inthe relationship between 119865

119888150and 119865

119888100based on

experimental test in this study and database reportedby different researchers Therefore it is difficult toestablish a simple equation that relates 119865

119888100and 119865119888150

and 119864

119888100and 119864

119888150because of limited experimental

and theoretical studies

(3) The three code equations tend to overestimate staticmodulus of concrete compared to those from directmeasurement according to ASTM C469 with MAEin a range of 44GPa to 12GPa In contrast theNoguchi equation predicts experimental results withfar more improved accuracy (ie MAE less than2GPa) by addressing correction factors for the effectsof aggregates and mineral admixtures (ie 119896

1= 1198962=

095)

(4) There is only a slight difference in the relationshipbetween static and resonance moduli from 100 by200mm and 150 by 300mm cylinders for normalstrength concrete Test results from this study and theliterature show that the empirical equation suggested

by Popovics [13] ((6) in this study) is effective for pre-dicting static elastic moduli from resonance moduliof concrete with compressive strength up to 60MParegardless of the cylinder size with MAE of less than15 GPa

(5) However the velocity moduli are excessively greaterthan static elastic modulus The empirical equations(see (4) (5) and (6)) produce considerable errors(with MAE in a range of 277GPa to 846GPa) bet-ween measured and predicted elastic moduli There-fore the use of velocitymoduli appears to be inappro-priate to estimate static elastic modulus

Conflict of Interests

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

Acknowledgment

This research was supported by the Basic Science ResearchProgram through theNational Research Foundation of Korea(NRF) funded by the Ministry of Science ICT amp FuturePlanning (no 2015R1A5A1037548)

References

[1] ACI Committee 318 Building Code Requirements for StructuralConcrete (ACI 318-11) and Commentary American ConcreteInstitute Farmington Hills Mich USA 2014

[2] IBC Council International Building Code (IBC 2012) 2014[3] N Gucunski A Imani F Romero et al ldquoNondestructive testig

to identify concrete bridge deck deteriorationrdquo SHRP 2 ReportS2-R06A-RR-1 2013

[4] ACI Committee 469 Standard Test Method for Static Modulusof Elasticity and Poissonrsquos Ratio of Concrete in CompressionAmerican Concrete Institute Farmington Hills Mich USA2014

[5] A Pauw ldquoStatic modulus of elasticity of concrete as affected bydensityrdquo ACI Journal Proceedings vol 57 no 12 pp 679ndash6871960

[6] ACI Committee 363 ldquoState-of-the-art report on high-strengthconcreterdquo ACI Journal Proceedings vol 81 no 4 pp 364ndash4111984

[7] J S Popovics ldquoA study of static and dynamic modulus ofelasticity of concreterdquo ACI-CRC Final Report 2008

[8] T Noguchi F Tomosawa KM Nemati BM Chiaia and A RFantilli ldquoA practical equation for elastic modulus of concreterdquoACI Structural Journal vol 106 no 5 pp 690ndash696 2009

[9] R E Philleo ldquoComparison of results of threemethods for deter-mining Youngrsquos modulus of elasticity of concreterdquo InternationalConcrete Abstracts Portal vol 51 no 1 pp 461ndash469 1955

[10] A M Neville Properties of Concrete John Wiley amp Sons NewYork NY USA 4th edition 1997

[11] F D Lydon and R V Balendran ldquoSome observations on elasticproperties of plain concreterdquo Cement and Concrete Researchvol 16 no 3 pp 314ndash324 1986

[12] B S Institute ldquoStructural use of concretemdashpart 2 code ofpractice for special circumstancerdquo BS 8110-21995 BSI LondonUK 1995

12 Advances in Materials Science and Engineering

[13] S Popovics ldquoVerification of relationships between mechanicalproperties of concrete-like materialsrdquoMaterials and Structuresvol 8 no 3 pp 183ndash191 1975

[14] ASTM C191 Standard Practice for Making and Curing ConcreteTest Specimens in the Laboratory ASTM 2014

[15] ASTM ldquoStandard practice for making and curing concrete testspecimen in the fieldrdquo ASTM C31 ASTM International 2012

[16] ASTM International ldquoStandard test method for fundamentaltransverse longitudinal and torsional resonant frequencies ofconcrete specimensrdquo ASTM C215 ASTM International WestConshohocken Pa USA 2002

[17] P-C Aitcin and P K Mehta ldquoEffect of coarse-aggregate char-acteristics on mechanical properties of high-strength concreterdquoACI Materials Journal vol 87 no 2 pp 103ndash107 1990

[18] P-C Aitcin B Miao W D Cook and D Mitchell ldquoEffectsof size and curing on cylinder compressive strength of normaland high-strength concretesrdquo ACIMaterials Journal vol 91 pp349ndash354 1994

[19] P M Carrasquillo and R L Carrasquillo ldquoEvaluation of the useof current concrete practice in the production of high strengthconcreterdquo ACI Materials Journal vol 85 no 1 pp 49ndash54 1988

[20] R L Carrasquillo A H Nilson and F O Slate ldquoProperties ofhigh strength concrete subject to short-term loadsrdquo Journal ofthe American Concrete Institute vol 78 no 3 pp 171ndash178 1981

[21] J E Cook ldquo10000 psi concreterdquo Concrete International vol 11pp 67ndash75 1989

[22] A S Malaikah ldquoA proposed relationship for the modulus ofelasticity of high strength concrete using local materials inRiyadhrdquo Journal of King Saud UniversitymdashEngineering Sciencesvol 17 pp 1ndash11 2005

[23] A Mokhtarzadeh and C French ldquoMechanical properties ofhigh-strength concrete with consideration for precast applica-tionsrdquo ACI Materials Journal vol 97 no 2 pp 136ndash147 2000

[24] DVandergrift Jr andA K Schindler ldquoThe effect of test cylindersize on the compressive strength of sulfur capped concretespecimensrdquo Tech Rep IR-06-01 Highway Research Centerand Department of Civil Engineering at Auburn UniversityAuburn Ala USA 2006

[25] ASTM International ldquoStandard test method for compressivestrength of cylindrical concrete specimensrdquo ASTM C39 ASTMInternational West Conshohocken Pa USA 2014

[26] ASTM ldquoStandard test method for pulse velocity throughconcreterdquo ASTM C597 ASTM International 1997

[27] N J CarinoW F Guthrie E S Lagergren and G MMullingsldquoEffects of testing variables on the strength of high-strength(90MPa) concrete cylindersrdquo in High-Performance ConcreteV M Malhotra Ed SP-149 pp 589ndash632 American ConcreteInstitute Farmington Hills Mich USA 1994

[28] ACI ldquoGuide for evaluation of strength test results of concrete(ACI 214R-11)rdquo ASTM C214 American Concrete InstituteFarmington Hills Mich USA 2011

[29] ACI Committee 228 ldquoNondestructive test methods for evalua-tion of concrete in structuresrdquo ReportACI 2282R-98AmericanConcrete Institute Farmington Hills Mich USA 1998

[30] S A Issa M S Islam M A Issa A A Yousif and M A IssaldquoSpecimen and aggregate size effect on concrete compressivestrengthrdquo Cement Concrete and Aggregates vol 22 no 2 pp103ndash115 2000

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

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CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

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TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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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 EngineeringSt

atic

elas

tic m

odul

usEc150

(GPa

)

Test results mix 1Test results mix 2Test results mix 3Malaikah (2005)

Best-fit line of the experimental data in this study(Ec150 = 09Ec100 + 19 R2

= 084)

Issa et al (2000)95 confidence boundsLine of equality

0

5

10

15

20

25

30

35

40

45

50

55

4010 15 20 25 30 35 500 45 555Static elastic modulus Ec100 (GPa)

Figure 4 Comparison of static elastic moduli of concrete measuredfrom 100 by 200mm and 150 by 300mm cylinders (119864

119888100and 119864

119888150

resp)

MAE between 119864119888100

and 119864119888150

of about 045GPaTherefore itmay be acceptable to assume from a practical perspective thatstatic elastic moduli using 100 by 200mm and 150 by 300mmcylinders are equivalent

However the ratio of 119864119888150

to 119864119888100

appears to graduallyincrease as 119864

119888150increases to 25GPa The higher elasticity

in the smaller size is attributed to the fact that the quantityof mortar required to fill the space between the particles ofthe coarse aggregate and the wall of the mold is greater thanthat necessary in the interior of the mass (ie wall effect)[10] In general the elasticity of cementmortar is greater thanthat of concrete which consequently results in increasing theeffective elasticity of concrete in smaller size In this study thebest-fit line that approximates the relationship between 119864

119888150

and 119864119888100

was established by a linear regression analysis asfollows

119864119888150

= 09119864119888100

+ 19 [MPa] (1198772

= 084) (13)

The best-fit line and 95 confidence bounds of the best-fitline are presented as solid and dash lines respectively inFigure 3 Interestingly the best-fit line of the experimentaldata in this study (10GPa le 119864

119888100le 25GPa) appears to be

valid for predicting the data set in the higher elastic modulusrange of 25GPa to 55GPa reported by prior researchers [2230] However it is still difficult to attain general conclusionson the relationship between 119864

119888150and 119864

119888100 especially for

Test results mix 1Test results mix 2Test results mix 3

Best-fit line for experimental data in this study

95 confidence boundsLine of equality

5010 15 20 25 30 35 40 600 455 550

5

10

15

20

25

30

35

40

45

50

55

60

Dyn

amic

elas

tic m

odul

usEdP150

(GPa

)

Dynamic elastic modulus EdP100 (GPa)

(EdP150 = 097Ed + 0138 R2= 092)100P

Figure 5 Comparison of velocity moduli from 100 by 200mm and150 by 300mm cylinders

concrete in the higher strength range greater than 50MPabecause of scarcity of available experimental data

34 Dynamic Elastic Moduli Figure 5 compares dynamicelastic moduli measured using UPV tests (ie velocitymoduli) from 100 by 200mm and 150 by 300mm cylinders(119864119889119875100

and 119864119889119875150

resp) in accordance with ASTM C597[26] It was observed that 100 by 200mm cylinders consis-tently result in slightly higher dynamic elastic moduli than150 by 300mm cylinders Linear regression of 119864

119889119875100and

119864119889119875150

measured in this study shows that 119864119889119875100

is about3 greater than 119864

119889119875150in a range of 20GPa to 40GPa (see

Figure 5) The MAE from two different cylinders was about05 GPa which is only 25 of the MAE from static elasticmoduli in this study (ie 2 GPa)

In addition shown in Figures 6(a) and 6(b) is the compar-ison of dynamic elastic moduli measured from longitudinaland transverse resonance frequency tests (ie resonancemoduli) 119864

119889119871119877and 119864

119889119879119877 respectively from 100 by 200mm

and 150 by 300mm cylinders in accordance with ASTMC125[16] The use of 150 by 300mm cylinders tends to resultin slightly higher resonance moduli (both 119864

119889119871119877and 119864

119889119879119877)

than those from 100 by 200mm cylinders According to thelinear regression analysis it was found that the resonancemoduli measured using the 150 by 300mm cylinder (119864

119889119871119877150

or 119864119889119877119877150

) are 1 to 2 greater than those from the 100by 200mm cylinder (119864

119889119871119877100or 119864119889119877119877100

) Approximatedequations that relate the resonance moduli from the twodifferent cylinder sizes are shown in Figures 6(a) and 6(b)

Advances in Materials Science and Engineering 7

Test results mix 1Test results mix 2Test results mix 3

0

5

10

15

20

25

30

35

40

3510 15 20 25 30 400 5

(EdLR150 = 102EdLR100 + 0127 R2= 096)

Best-fit line for experimental data in this study

95 confidence boundsLine of equality

EdLR100 (GPa)Dynamic elastic modulus

EdLR150

(GPa

)D

ynam

ic el

astic

mod

ulus

(a)

Test results mix 1Test results mix 2Test results mix 395 confidence boundsLine of equalityBest-fit line for experimental data in this study(EdTR150 = 101EdTR100 + 0438 R2

= 093)

0

5

10

15

20

25

30

35

40

3510 15 20 25 30 400 5EdTR100 (GPa)Dynamic elastic modulus

EdTR150

(GPa

)D

ynam

ic el

astic

mod

ulus

(b)

Figure 6 Comparison of resonance moduli from 100 by 200mm and 150 by 300mm cylinders (a) 119864119889119871119877150

versus 119864119889119871119877100

and (b) 119864119889119879119877150

versus 119864119889119879119877100

Furthermore without regard to longitudinal or transversemodes the MAE between the resonance moduli from thedifferent cylinder is less than 03GPa Therefore the findingsin this study demonstrate that the dynamic elastic moduli(both velocity and resonance moduli) using the 100 by200mm and 150 by 300mm cylinders are regarded as beingequal from a practical standpoint

However it was observed that there is a precaution inmeasuring reliable and consistent resonance frequency usingthe 100 by 200mm cylinder The smaller cylinder has higherchance of mistakenly hitting an impact source (location andinclination to test surface) which may cause undesirableresonance modes such as torsional modes in the frequencydomain Consequently it was often difficult to select a rightfrequency peak corresponding to the fundamental longitudi-nal or transverse modes In this study preliminary numeri-cal simulations were conducted to calculate theoretical fre-quency peak values which was helpful to select a rightfrequency peak In addition to improve accuracy and con-sistency resonance tests were repeated until the COV of fivesuccessive testing procedures is less than 5 and average ofthe five test results was finally accepted in this study

35 Relationship between Static Elastic Modulus and Com-pressive Strength Figure 7 is a plot representing relationshipbetween static elastic modulus and compressive strengthmeasured in accordance with ASTM C469 [4] and ASTM

C39 [25] respectively The data points obtained from 100 by200mm and 150 by 300mm cylinders are presented as openand solid symbols in Figures 7(a) and 7(b) respectively For acomparison Figure 7 presents three code equations adoptedby ACI 318 and ACI 363 committees and CEB-FIP Modelcode and a practical equation proposed by Noguchi et al [8](see (14)) which was developed based on an extensive exper-imental database from normal to high strength concrete

119864119888= 1198961119896233500 (

119865119888

60)

13

(119908119888

2400)

2

(14)

where 1198961and 119896

2are correction factors for coarse aggregates

and mineral admixturesIt was found that the effect of cylinder size appears to be

insignificant on the relationship between static elastic modu-lus and compressive strength of concrete for normal strengthconcrete (lt40MPa) in this study Approximated equationsthat relate 119864

119888and 119865119888from 100 by 200mm and 150 by 300mm

cylinders were established by nonlinear regression analysesand shown in Figures 7(a) and 7(b) respectivelyTheMAE ofthe two best-fit curves is less than 01 GPa in the compressivestrength range of 10MPa to 40MPa In this studyMAE of thetwo continuous curves was defined as follows

MAEcon =

[int 1198921(119865119888) minus 1198922(119865119888) 119889119865119888]

int 119889119865119888

(15)

8 Advances in Materials Science and Engineering

Best-fit line for experimental data in this study(Ec150 = 456Fc150

0418 R2= 090)

Noguchi et al [2009] k1 = k2 = 1

Noguchi et al [2009] k1 = k2 = 095

Mix 1

Mix 3

ACI 318ACI 363CEB-FIP Model code and Eurocode 2

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

5010 15 20 25 30 35 40 45 55 6050Compressive strength Fc (MPa)

150 by 300mm cylindersMix 2

(a)

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

Best-fit line for experimental data in this study(Ec100 = 416Fc100

0446 R2= 084)

Noguchi et al [2009] k1 = k2 = 1

Noguchi et al [2009] k1 = k2 = 095

Mix 1

Mix 3

ACI 318ACI 363CEB-FIP Model code and Eurocode 2

50 15 20 25 30 35 40 45 50 55 6010Compressive strength Fc (MPa)

0

5

10

15

20

25

30

35

40

Mix 2 100 by 200mm cylinders

(b)

Figure 7 Comparison of compressive strength and static elastic modulus of concrete

where MAEcon is mean average error (MAE) of two contin-uous functions 119892

119894is a function presenting 119864

119888expressed as

119865119888 and the subscript 119894 indicates cylinder size (1 and 2 for the

100 by 200mm and 150 by 300mm cylinders resp) Further-more there is no significant difference in 119877

2 values of thetwo best-fit curves 1198772 values for the 100 by 200mm and150 by 300mm cylinders are 088 and 090 respectivelyTherefore the 100 by 200mm cylinders can be used insteadof 150 by 300mm cylinders to estimate static elastic modulusfrom compressive strength without reducing accuracy andconsistency However the three code equations tend tooverestimate static modulus of concrete compared to thosefrom direct measurement according to ASTM C469 [4] Assummarized in Table 3 mean average error (MAE) betweenmeasured and predicted 119864

119888from the three code equations is

in a range of 44 to 12GPa corresponding to about 10 to30 of the measured 119864

119888 In contrast the Noguchi equation

[8] predicts experimental results with far more improvedaccuracy (ie MAE less than 2GPa) by addressing correctionfactors for the effects of aggregates and mineral admixtures(ie 119896

1= 1198962= 095)

36 Relationship between Static and Dynamic Elastic ModuliFigure 8 presents the relationship between static and dynamicelastic moduli determined using different nondestructivetesting methods 119864

119889119875 119864119889119871119877

and 119864119889119879119877

respectively with

Table 3 Mean absolute error (MAE) of expressions relating staticelastic modulus and compressive strength measured using 100 by200mm and 150 by 300mm cylinders

Equation to convert 119864119889to

119864119888

MAE (GPa)150 by 300mm

cylinder100 by 200mm

cylinder119864119889119871119879

119864119889119871119879

Equation (1) 483 463Equation (2) 454 443Equation (3) 1221 1215Equation (14) with1198961= 1198962= 1

342 341

Equation (14) with1198961= 1198962= 095

156 188

Best-fit line 132 157

Poissonrsquos ratio of 02Theuse of Poissonrsquos ratio of 02 is reason-able for common concrete in practice [10] In Figure 8 119864

119889119875

119864119889119871119877

and 119864119889119879119877

measured from 100 by 200mm and 150 by300mm cylinders are shown as open and solid symbols in leftand right columns For comparison purposes several well-known empirical equations (see (3) (4) and (5)) proposedby prior researchers are shown in the figures

Advances in Materials Science and Engineering 9

Best-fit line for experimental data in this study(Ec150 = 044EdLR150

115 R2= 090)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equalityLydon and Balendran (1986)BS8100 Part 2Popovics (1975)

5 10 15 20 25 30 35 400Dynamic elastic modulus EdLR (GPa)

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

(a)

Best-fit line for experimental data in this study(Ec150 = 044EdTR100

115 R2= 090)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equality

BS8100 Part 2

5 10 15 20 25 30 35 400Dynamic elastic modulus EdTR (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

Popovics (1975)

Lydon and Balendran (1986)

(b)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equality

BS8100 Part 2

Best-fit line for experimental data in this study(Ec150 = 022EdP150

129 R2= 087)

Popovics (1975)

Lydon and Balendran (1986)

3510 15 20 25 30 400 5Dynamic elastic modulus EdP (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

(c)

Best-fit line for experimental data in this study(Ec100 = 040EdLR100

118 R2= 088)

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

3510 15 20 25 30 400 5Dynamic elastic modulus EdLR (GPa)

Lydon and Balendran (1986)

Popovics (1975)

(d)

Figure 8 Continued

10 Advances in Materials Science and Engineering

Best-fit line for experimental data in this study(Ec100 = 039EdTR100

120 R2= 087)

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

3510 15 20 25 30 400 5Dynamic elastic modulus EdTR (GPa)

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

Lydon and Balendran (1986)

Popovics (1975)

(e)

Best-fit line for experimental data in this study

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

3510 15 20 25 30 400 5Dynamic elastic modulus EdP (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

EdLR100135 R2

= 085)(Ec100 = 017

Popovics (1975)

Lydon and Balendran (1986)

(f)

Figure 8 Comparison of static and resonance elastic moduli of concrete (a) 119864119889119871119877150

versus 119864119888150

(b) 119864119889119879119877150

versus 119864119888150

(c) 119864119889119875150

versus119864119888150

(d) 119864119889119871119877100

versus 119864119888100

(e) 119864119889119879119877100

versus 119864119888100

and (f) 119864119889119875100

versus 119864119888100

Table 4 Mean absolute error (MAE) of expressions relating static and dynamic elastic modulus measured using 100 by 200mm and 150 by300mm cylinders

Equation to convert 119864119889to 119864119888

MAE (GPa)150 by 300mm cylinder 100 by 200mm cylinder

119864119889119871119879

119864119889119877119879

119864119889119875

119864119889119871119879

119864119889119877119879

119864119889119875

Equation (4) 302 282 754 283 254 846Equation (5) 559 591 277 607 649 335Equation (6) 125 111 658 113 107 780Best-fit line 090 095 126 109 110 117

It is observed that there is only slight difference in therelationship between119864

119888and119864

119889obtained from 100 by 200mm

and 150 by 300mm cylinders In this study approximatedequations that relate119864

119888and119864

119889(119864119889119875

119864119889119871119877

or119864119889119879119877

) from 100by 200mm and 150 by 300mm cylinders were established bynonlinear regression analyses and shown in Figures 8(a)ndash8(f)The MAEs of the two best-fit curves are less than 01MPa inthe dynamic elastic modulus range of 10GPa to 25GPa Fur-thermore there is no significant difference in 119877

2 values of thetwo best-fit curves (see Figure 8) However for both data setsfrom different cylinders the three dynamic moduli (119864

119889119871119877

119864119889119879119877

and 119864119889119875

) obtained from resonance tests and UPVmethod are greater than the static elastic modulus 119864

119888 with

different static-to-dynamic elastic modulus ratio 119864119888119864119889119875

ratio with an average of 056 and COV of 92 is too faraway from the line of equality as well as from the three well-known equations relating static and dynamic elastic modu-lus Therefore the use of 119864

119889119875appears to be inappropriate

to estimate static elastic modulus which is consistent withobservations from other researchers [7 10] In contrast119864119888119864119889119871119877

(or 119864119888119864119889119879119877

) ratio was closer to the line of equalitythan 119864

119888119864119889119875

with an average of 072 and COV of 715The equation proposed by Popovics [13] (see (6)) shows verygood agreement with the experimental results regardless ofcylinder size in this study (see Table 4) In addition priorresearcher [7] observed that the Popovics equation (see (6))can be extended to high strength concrete up to 60MPawith-out regard to cylinder size However it should be mentioned

Advances in Materials Science and Engineering 11

that additional experimental data should be accumulated tobetter understand the size effect on the relationship betweenstatic and dynamic elastic moduli of high strength concrete(gt60MPa) due to scarcity of experimental studies in such ahigh strength range

4 Conclusions

A series of experimental studies was conducted to explore theeffect of cylinder size (100 by 200mm and 150 by 300mmcylinders) on the relationship between static elastic modulusand compressive strength and static and dynamic elasticmoduli of concrete Conclusions based on experiments in thisstudy and database from the literature are drawn as follows

(1) Experimental results in this study show that theCOVsof test results from 100 by 200mm cylinders areabout 10 higher than those from 150 by 300mmcylinders however the differences are statisticallyinsignificantThe averageCOVs of static and dynamicelastic moduli using the UPV and longitudinal andtransverse resonance frequency tests from 100 by200mm cylinders are 632 140 162 and 117respectively while those values from 150 by 300mmcylinders are 583 123 162 and 117 respec-tively For compressive strength the average COVsfrom the 100 by 200mm and 150 by 300mm cylindersare 441 and 365 respectively

(2) According to the findings from similarity tests of best-fit curves and comparison of 1198772 based on regressionanalyses it has been demonstrated that the effect ofcylinder size (100 by 200mm and 150 by 300mmcylinders) is insignificant on compressive strengthand static elastic modulus and the relationship bet-ween the two parameters for normal strength con-crete up to 30MPa However in the higher strengthrange greater than 30MPa there is contradiction inthe relationship between 119865

119888150and 119865

119888100based on

experimental test in this study and database reportedby different researchers Therefore it is difficult toestablish a simple equation that relates 119865

119888100and 119865119888150

and 119864

119888100and 119864

119888150because of limited experimental

and theoretical studies

(3) The three code equations tend to overestimate staticmodulus of concrete compared to those from directmeasurement according to ASTM C469 with MAEin a range of 44GPa to 12GPa In contrast theNoguchi equation predicts experimental results withfar more improved accuracy (ie MAE less than2GPa) by addressing correction factors for the effectsof aggregates and mineral admixtures (ie 119896

1= 1198962=

095)

(4) There is only a slight difference in the relationshipbetween static and resonance moduli from 100 by200mm and 150 by 300mm cylinders for normalstrength concrete Test results from this study and theliterature show that the empirical equation suggested

by Popovics [13] ((6) in this study) is effective for pre-dicting static elastic moduli from resonance moduliof concrete with compressive strength up to 60MParegardless of the cylinder size with MAE of less than15 GPa

(5) However the velocity moduli are excessively greaterthan static elastic modulus The empirical equations(see (4) (5) and (6)) produce considerable errors(with MAE in a range of 277GPa to 846GPa) bet-ween measured and predicted elastic moduli There-fore the use of velocitymoduli appears to be inappro-priate to estimate static elastic modulus

Conflict of Interests

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

Acknowledgment

This research was supported by the Basic Science ResearchProgram through theNational Research Foundation of Korea(NRF) funded by the Ministry of Science ICT amp FuturePlanning (no 2015R1A5A1037548)

References

[1] ACI Committee 318 Building Code Requirements for StructuralConcrete (ACI 318-11) and Commentary American ConcreteInstitute Farmington Hills Mich USA 2014

[2] IBC Council International Building Code (IBC 2012) 2014[3] N Gucunski A Imani F Romero et al ldquoNondestructive testig

to identify concrete bridge deck deteriorationrdquo SHRP 2 ReportS2-R06A-RR-1 2013

[4] ACI Committee 469 Standard Test Method for Static Modulusof Elasticity and Poissonrsquos Ratio of Concrete in CompressionAmerican Concrete Institute Farmington Hills Mich USA2014

[5] A Pauw ldquoStatic modulus of elasticity of concrete as affected bydensityrdquo ACI Journal Proceedings vol 57 no 12 pp 679ndash6871960

[6] ACI Committee 363 ldquoState-of-the-art report on high-strengthconcreterdquo ACI Journal Proceedings vol 81 no 4 pp 364ndash4111984

[7] J S Popovics ldquoA study of static and dynamic modulus ofelasticity of concreterdquo ACI-CRC Final Report 2008

[8] T Noguchi F Tomosawa KM Nemati BM Chiaia and A RFantilli ldquoA practical equation for elastic modulus of concreterdquoACI Structural Journal vol 106 no 5 pp 690ndash696 2009

[9] R E Philleo ldquoComparison of results of threemethods for deter-mining Youngrsquos modulus of elasticity of concreterdquo InternationalConcrete Abstracts Portal vol 51 no 1 pp 461ndash469 1955

[10] A M Neville Properties of Concrete John Wiley amp Sons NewYork NY USA 4th edition 1997

[11] F D Lydon and R V Balendran ldquoSome observations on elasticproperties of plain concreterdquo Cement and Concrete Researchvol 16 no 3 pp 314ndash324 1986

[12] B S Institute ldquoStructural use of concretemdashpart 2 code ofpractice for special circumstancerdquo BS 8110-21995 BSI LondonUK 1995

12 Advances in Materials Science and Engineering

[13] S Popovics ldquoVerification of relationships between mechanicalproperties of concrete-like materialsrdquoMaterials and Structuresvol 8 no 3 pp 183ndash191 1975

[14] ASTM C191 Standard Practice for Making and Curing ConcreteTest Specimens in the Laboratory ASTM 2014

[15] ASTM ldquoStandard practice for making and curing concrete testspecimen in the fieldrdquo ASTM C31 ASTM International 2012

[16] ASTM International ldquoStandard test method for fundamentaltransverse longitudinal and torsional resonant frequencies ofconcrete specimensrdquo ASTM C215 ASTM International WestConshohocken Pa USA 2002

[17] P-C Aitcin and P K Mehta ldquoEffect of coarse-aggregate char-acteristics on mechanical properties of high-strength concreterdquoACI Materials Journal vol 87 no 2 pp 103ndash107 1990

[18] P-C Aitcin B Miao W D Cook and D Mitchell ldquoEffectsof size and curing on cylinder compressive strength of normaland high-strength concretesrdquo ACIMaterials Journal vol 91 pp349ndash354 1994

[19] P M Carrasquillo and R L Carrasquillo ldquoEvaluation of the useof current concrete practice in the production of high strengthconcreterdquo ACI Materials Journal vol 85 no 1 pp 49ndash54 1988

[20] R L Carrasquillo A H Nilson and F O Slate ldquoProperties ofhigh strength concrete subject to short-term loadsrdquo Journal ofthe American Concrete Institute vol 78 no 3 pp 171ndash178 1981

[21] J E Cook ldquo10000 psi concreterdquo Concrete International vol 11pp 67ndash75 1989

[22] A S Malaikah ldquoA proposed relationship for the modulus ofelasticity of high strength concrete using local materials inRiyadhrdquo Journal of King Saud UniversitymdashEngineering Sciencesvol 17 pp 1ndash11 2005

[23] A Mokhtarzadeh and C French ldquoMechanical properties ofhigh-strength concrete with consideration for precast applica-tionsrdquo ACI Materials Journal vol 97 no 2 pp 136ndash147 2000

[24] DVandergrift Jr andA K Schindler ldquoThe effect of test cylindersize on the compressive strength of sulfur capped concretespecimensrdquo Tech Rep IR-06-01 Highway Research Centerand Department of Civil Engineering at Auburn UniversityAuburn Ala USA 2006

[25] ASTM International ldquoStandard test method for compressivestrength of cylindrical concrete specimensrdquo ASTM C39 ASTMInternational West Conshohocken Pa USA 2014

[26] ASTM ldquoStandard test method for pulse velocity throughconcreterdquo ASTM C597 ASTM International 1997

[27] N J CarinoW F Guthrie E S Lagergren and G MMullingsldquoEffects of testing variables on the strength of high-strength(90MPa) concrete cylindersrdquo in High-Performance ConcreteV M Malhotra Ed SP-149 pp 589ndash632 American ConcreteInstitute Farmington Hills Mich USA 1994

[28] ACI ldquoGuide for evaluation of strength test results of concrete(ACI 214R-11)rdquo ASTM C214 American Concrete InstituteFarmington Hills Mich USA 2011

[29] ACI Committee 228 ldquoNondestructive test methods for evalua-tion of concrete in structuresrdquo ReportACI 2282R-98AmericanConcrete Institute Farmington Hills Mich USA 1998

[30] S A Issa M S Islam M A Issa A A Yousif and M A IssaldquoSpecimen and aggregate size effect on concrete compressivestrengthrdquo Cement Concrete and Aggregates vol 22 no 2 pp103ndash115 2000

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

Test results mix 1Test results mix 2Test results mix 3

0

5

10

15

20

25

30

35

40

3510 15 20 25 30 400 5

(EdLR150 = 102EdLR100 + 0127 R2= 096)

Best-fit line for experimental data in this study

95 confidence boundsLine of equality

EdLR100 (GPa)Dynamic elastic modulus

EdLR150

(GPa

)D

ynam

ic el

astic

mod

ulus

(a)

Test results mix 1Test results mix 2Test results mix 395 confidence boundsLine of equalityBest-fit line for experimental data in this study(EdTR150 = 101EdTR100 + 0438 R2

= 093)

0

5

10

15

20

25

30

35

40

3510 15 20 25 30 400 5EdTR100 (GPa)Dynamic elastic modulus

EdTR150

(GPa

)D

ynam

ic el

astic

mod

ulus

(b)

Figure 6 Comparison of resonance moduli from 100 by 200mm and 150 by 300mm cylinders (a) 119864119889119871119877150

versus 119864119889119871119877100

and (b) 119864119889119879119877150

versus 119864119889119879119877100

Furthermore without regard to longitudinal or transversemodes the MAE between the resonance moduli from thedifferent cylinder is less than 03GPa Therefore the findingsin this study demonstrate that the dynamic elastic moduli(both velocity and resonance moduli) using the 100 by200mm and 150 by 300mm cylinders are regarded as beingequal from a practical standpoint

However it was observed that there is a precaution inmeasuring reliable and consistent resonance frequency usingthe 100 by 200mm cylinder The smaller cylinder has higherchance of mistakenly hitting an impact source (location andinclination to test surface) which may cause undesirableresonance modes such as torsional modes in the frequencydomain Consequently it was often difficult to select a rightfrequency peak corresponding to the fundamental longitudi-nal or transverse modes In this study preliminary numeri-cal simulations were conducted to calculate theoretical fre-quency peak values which was helpful to select a rightfrequency peak In addition to improve accuracy and con-sistency resonance tests were repeated until the COV of fivesuccessive testing procedures is less than 5 and average ofthe five test results was finally accepted in this study

35 Relationship between Static Elastic Modulus and Com-pressive Strength Figure 7 is a plot representing relationshipbetween static elastic modulus and compressive strengthmeasured in accordance with ASTM C469 [4] and ASTM

C39 [25] respectively The data points obtained from 100 by200mm and 150 by 300mm cylinders are presented as openand solid symbols in Figures 7(a) and 7(b) respectively For acomparison Figure 7 presents three code equations adoptedby ACI 318 and ACI 363 committees and CEB-FIP Modelcode and a practical equation proposed by Noguchi et al [8](see (14)) which was developed based on an extensive exper-imental database from normal to high strength concrete

119864119888= 1198961119896233500 (

119865119888

60)

13

(119908119888

2400)

2

(14)

where 1198961and 119896

2are correction factors for coarse aggregates

and mineral admixturesIt was found that the effect of cylinder size appears to be

insignificant on the relationship between static elastic modu-lus and compressive strength of concrete for normal strengthconcrete (lt40MPa) in this study Approximated equationsthat relate 119864

119888and 119865119888from 100 by 200mm and 150 by 300mm

cylinders were established by nonlinear regression analysesand shown in Figures 7(a) and 7(b) respectivelyTheMAE ofthe two best-fit curves is less than 01 GPa in the compressivestrength range of 10MPa to 40MPa In this studyMAE of thetwo continuous curves was defined as follows

MAEcon =

[int 1198921(119865119888) minus 1198922(119865119888) 119889119865119888]

int 119889119865119888

(15)

8 Advances in Materials Science and Engineering

Best-fit line for experimental data in this study(Ec150 = 456Fc150

0418 R2= 090)

Noguchi et al [2009] k1 = k2 = 1

Noguchi et al [2009] k1 = k2 = 095

Mix 1

Mix 3

ACI 318ACI 363CEB-FIP Model code and Eurocode 2

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

5010 15 20 25 30 35 40 45 55 6050Compressive strength Fc (MPa)

150 by 300mm cylindersMix 2

(a)

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

Best-fit line for experimental data in this study(Ec100 = 416Fc100

0446 R2= 084)

Noguchi et al [2009] k1 = k2 = 1

Noguchi et al [2009] k1 = k2 = 095

Mix 1

Mix 3

ACI 318ACI 363CEB-FIP Model code and Eurocode 2

50 15 20 25 30 35 40 45 50 55 6010Compressive strength Fc (MPa)

0

5

10

15

20

25

30

35

40

Mix 2 100 by 200mm cylinders

(b)

Figure 7 Comparison of compressive strength and static elastic modulus of concrete

where MAEcon is mean average error (MAE) of two contin-uous functions 119892

119894is a function presenting 119864

119888expressed as

119865119888 and the subscript 119894 indicates cylinder size (1 and 2 for the

100 by 200mm and 150 by 300mm cylinders resp) Further-more there is no significant difference in 119877

2 values of thetwo best-fit curves 1198772 values for the 100 by 200mm and150 by 300mm cylinders are 088 and 090 respectivelyTherefore the 100 by 200mm cylinders can be used insteadof 150 by 300mm cylinders to estimate static elastic modulusfrom compressive strength without reducing accuracy andconsistency However the three code equations tend tooverestimate static modulus of concrete compared to thosefrom direct measurement according to ASTM C469 [4] Assummarized in Table 3 mean average error (MAE) betweenmeasured and predicted 119864

119888from the three code equations is

in a range of 44 to 12GPa corresponding to about 10 to30 of the measured 119864

119888 In contrast the Noguchi equation

[8] predicts experimental results with far more improvedaccuracy (ie MAE less than 2GPa) by addressing correctionfactors for the effects of aggregates and mineral admixtures(ie 119896

1= 1198962= 095)

36 Relationship between Static and Dynamic Elastic ModuliFigure 8 presents the relationship between static and dynamicelastic moduli determined using different nondestructivetesting methods 119864

119889119875 119864119889119871119877

and 119864119889119879119877

respectively with

Table 3 Mean absolute error (MAE) of expressions relating staticelastic modulus and compressive strength measured using 100 by200mm and 150 by 300mm cylinders

Equation to convert 119864119889to

119864119888

MAE (GPa)150 by 300mm

cylinder100 by 200mm

cylinder119864119889119871119879

119864119889119871119879

Equation (1) 483 463Equation (2) 454 443Equation (3) 1221 1215Equation (14) with1198961= 1198962= 1

342 341

Equation (14) with1198961= 1198962= 095

156 188

Best-fit line 132 157

Poissonrsquos ratio of 02Theuse of Poissonrsquos ratio of 02 is reason-able for common concrete in practice [10] In Figure 8 119864

119889119875

119864119889119871119877

and 119864119889119879119877

measured from 100 by 200mm and 150 by300mm cylinders are shown as open and solid symbols in leftand right columns For comparison purposes several well-known empirical equations (see (3) (4) and (5)) proposedby prior researchers are shown in the figures

Advances in Materials Science and Engineering 9

Best-fit line for experimental data in this study(Ec150 = 044EdLR150

115 R2= 090)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equalityLydon and Balendran (1986)BS8100 Part 2Popovics (1975)

5 10 15 20 25 30 35 400Dynamic elastic modulus EdLR (GPa)

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

(a)

Best-fit line for experimental data in this study(Ec150 = 044EdTR100

115 R2= 090)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equality

BS8100 Part 2

5 10 15 20 25 30 35 400Dynamic elastic modulus EdTR (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

Popovics (1975)

Lydon and Balendran (1986)

(b)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equality

BS8100 Part 2

Best-fit line for experimental data in this study(Ec150 = 022EdP150

129 R2= 087)

Popovics (1975)

Lydon and Balendran (1986)

3510 15 20 25 30 400 5Dynamic elastic modulus EdP (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

(c)

Best-fit line for experimental data in this study(Ec100 = 040EdLR100

118 R2= 088)

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

3510 15 20 25 30 400 5Dynamic elastic modulus EdLR (GPa)

Lydon and Balendran (1986)

Popovics (1975)

(d)

Figure 8 Continued

10 Advances in Materials Science and Engineering

Best-fit line for experimental data in this study(Ec100 = 039EdTR100

120 R2= 087)

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

3510 15 20 25 30 400 5Dynamic elastic modulus EdTR (GPa)

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

Lydon and Balendran (1986)

Popovics (1975)

(e)

Best-fit line for experimental data in this study

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

3510 15 20 25 30 400 5Dynamic elastic modulus EdP (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

EdLR100135 R2

= 085)(Ec100 = 017

Popovics (1975)

Lydon and Balendran (1986)

(f)

Figure 8 Comparison of static and resonance elastic moduli of concrete (a) 119864119889119871119877150

versus 119864119888150

(b) 119864119889119879119877150

versus 119864119888150

(c) 119864119889119875150

versus119864119888150

(d) 119864119889119871119877100

versus 119864119888100

(e) 119864119889119879119877100

versus 119864119888100

and (f) 119864119889119875100

versus 119864119888100

Table 4 Mean absolute error (MAE) of expressions relating static and dynamic elastic modulus measured using 100 by 200mm and 150 by300mm cylinders

Equation to convert 119864119889to 119864119888

MAE (GPa)150 by 300mm cylinder 100 by 200mm cylinder

119864119889119871119879

119864119889119877119879

119864119889119875

119864119889119871119879

119864119889119877119879

119864119889119875

Equation (4) 302 282 754 283 254 846Equation (5) 559 591 277 607 649 335Equation (6) 125 111 658 113 107 780Best-fit line 090 095 126 109 110 117

It is observed that there is only slight difference in therelationship between119864

119888and119864

119889obtained from 100 by 200mm

and 150 by 300mm cylinders In this study approximatedequations that relate119864

119888and119864

119889(119864119889119875

119864119889119871119877

or119864119889119879119877

) from 100by 200mm and 150 by 300mm cylinders were established bynonlinear regression analyses and shown in Figures 8(a)ndash8(f)The MAEs of the two best-fit curves are less than 01MPa inthe dynamic elastic modulus range of 10GPa to 25GPa Fur-thermore there is no significant difference in 119877

2 values of thetwo best-fit curves (see Figure 8) However for both data setsfrom different cylinders the three dynamic moduli (119864

119889119871119877

119864119889119879119877

and 119864119889119875

) obtained from resonance tests and UPVmethod are greater than the static elastic modulus 119864

119888 with

different static-to-dynamic elastic modulus ratio 119864119888119864119889119875

ratio with an average of 056 and COV of 92 is too faraway from the line of equality as well as from the three well-known equations relating static and dynamic elastic modu-lus Therefore the use of 119864

119889119875appears to be inappropriate

to estimate static elastic modulus which is consistent withobservations from other researchers [7 10] In contrast119864119888119864119889119871119877

(or 119864119888119864119889119879119877

) ratio was closer to the line of equalitythan 119864

119888119864119889119875

with an average of 072 and COV of 715The equation proposed by Popovics [13] (see (6)) shows verygood agreement with the experimental results regardless ofcylinder size in this study (see Table 4) In addition priorresearcher [7] observed that the Popovics equation (see (6))can be extended to high strength concrete up to 60MPawith-out regard to cylinder size However it should be mentioned

Advances in Materials Science and Engineering 11

that additional experimental data should be accumulated tobetter understand the size effect on the relationship betweenstatic and dynamic elastic moduli of high strength concrete(gt60MPa) due to scarcity of experimental studies in such ahigh strength range

4 Conclusions

A series of experimental studies was conducted to explore theeffect of cylinder size (100 by 200mm and 150 by 300mmcylinders) on the relationship between static elastic modulusand compressive strength and static and dynamic elasticmoduli of concrete Conclusions based on experiments in thisstudy and database from the literature are drawn as follows

(1) Experimental results in this study show that theCOVsof test results from 100 by 200mm cylinders areabout 10 higher than those from 150 by 300mmcylinders however the differences are statisticallyinsignificantThe averageCOVs of static and dynamicelastic moduli using the UPV and longitudinal andtransverse resonance frequency tests from 100 by200mm cylinders are 632 140 162 and 117respectively while those values from 150 by 300mmcylinders are 583 123 162 and 117 respec-tively For compressive strength the average COVsfrom the 100 by 200mm and 150 by 300mm cylindersare 441 and 365 respectively

(2) According to the findings from similarity tests of best-fit curves and comparison of 1198772 based on regressionanalyses it has been demonstrated that the effect ofcylinder size (100 by 200mm and 150 by 300mmcylinders) is insignificant on compressive strengthand static elastic modulus and the relationship bet-ween the two parameters for normal strength con-crete up to 30MPa However in the higher strengthrange greater than 30MPa there is contradiction inthe relationship between 119865

119888150and 119865

119888100based on

experimental test in this study and database reportedby different researchers Therefore it is difficult toestablish a simple equation that relates 119865

119888100and 119865119888150

and 119864

119888100and 119864

119888150because of limited experimental

and theoretical studies

(3) The three code equations tend to overestimate staticmodulus of concrete compared to those from directmeasurement according to ASTM C469 with MAEin a range of 44GPa to 12GPa In contrast theNoguchi equation predicts experimental results withfar more improved accuracy (ie MAE less than2GPa) by addressing correction factors for the effectsof aggregates and mineral admixtures (ie 119896

1= 1198962=

095)

(4) There is only a slight difference in the relationshipbetween static and resonance moduli from 100 by200mm and 150 by 300mm cylinders for normalstrength concrete Test results from this study and theliterature show that the empirical equation suggested

by Popovics [13] ((6) in this study) is effective for pre-dicting static elastic moduli from resonance moduliof concrete with compressive strength up to 60MParegardless of the cylinder size with MAE of less than15 GPa

(5) However the velocity moduli are excessively greaterthan static elastic modulus The empirical equations(see (4) (5) and (6)) produce considerable errors(with MAE in a range of 277GPa to 846GPa) bet-ween measured and predicted elastic moduli There-fore the use of velocitymoduli appears to be inappro-priate to estimate static elastic modulus

Conflict of Interests

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

Acknowledgment

This research was supported by the Basic Science ResearchProgram through theNational Research Foundation of Korea(NRF) funded by the Ministry of Science ICT amp FuturePlanning (no 2015R1A5A1037548)

References

[1] ACI Committee 318 Building Code Requirements for StructuralConcrete (ACI 318-11) and Commentary American ConcreteInstitute Farmington Hills Mich USA 2014

[2] IBC Council International Building Code (IBC 2012) 2014[3] N Gucunski A Imani F Romero et al ldquoNondestructive testig

to identify concrete bridge deck deteriorationrdquo SHRP 2 ReportS2-R06A-RR-1 2013

[4] ACI Committee 469 Standard Test Method for Static Modulusof Elasticity and Poissonrsquos Ratio of Concrete in CompressionAmerican Concrete Institute Farmington Hills Mich USA2014

[5] A Pauw ldquoStatic modulus of elasticity of concrete as affected bydensityrdquo ACI Journal Proceedings vol 57 no 12 pp 679ndash6871960

[6] ACI Committee 363 ldquoState-of-the-art report on high-strengthconcreterdquo ACI Journal Proceedings vol 81 no 4 pp 364ndash4111984

[7] J S Popovics ldquoA study of static and dynamic modulus ofelasticity of concreterdquo ACI-CRC Final Report 2008

[8] T Noguchi F Tomosawa KM Nemati BM Chiaia and A RFantilli ldquoA practical equation for elastic modulus of concreterdquoACI Structural Journal vol 106 no 5 pp 690ndash696 2009

[9] R E Philleo ldquoComparison of results of threemethods for deter-mining Youngrsquos modulus of elasticity of concreterdquo InternationalConcrete Abstracts Portal vol 51 no 1 pp 461ndash469 1955

[10] A M Neville Properties of Concrete John Wiley amp Sons NewYork NY USA 4th edition 1997

[11] F D Lydon and R V Balendran ldquoSome observations on elasticproperties of plain concreterdquo Cement and Concrete Researchvol 16 no 3 pp 314ndash324 1986

[12] B S Institute ldquoStructural use of concretemdashpart 2 code ofpractice for special circumstancerdquo BS 8110-21995 BSI LondonUK 1995

12 Advances in Materials Science and Engineering

[13] S Popovics ldquoVerification of relationships between mechanicalproperties of concrete-like materialsrdquoMaterials and Structuresvol 8 no 3 pp 183ndash191 1975

[14] ASTM C191 Standard Practice for Making and Curing ConcreteTest Specimens in the Laboratory ASTM 2014

[15] ASTM ldquoStandard practice for making and curing concrete testspecimen in the fieldrdquo ASTM C31 ASTM International 2012

[16] ASTM International ldquoStandard test method for fundamentaltransverse longitudinal and torsional resonant frequencies ofconcrete specimensrdquo ASTM C215 ASTM International WestConshohocken Pa USA 2002

[17] P-C Aitcin and P K Mehta ldquoEffect of coarse-aggregate char-acteristics on mechanical properties of high-strength concreterdquoACI Materials Journal vol 87 no 2 pp 103ndash107 1990

[18] P-C Aitcin B Miao W D Cook and D Mitchell ldquoEffectsof size and curing on cylinder compressive strength of normaland high-strength concretesrdquo ACIMaterials Journal vol 91 pp349ndash354 1994

[19] P M Carrasquillo and R L Carrasquillo ldquoEvaluation of the useof current concrete practice in the production of high strengthconcreterdquo ACI Materials Journal vol 85 no 1 pp 49ndash54 1988

[20] R L Carrasquillo A H Nilson and F O Slate ldquoProperties ofhigh strength concrete subject to short-term loadsrdquo Journal ofthe American Concrete Institute vol 78 no 3 pp 171ndash178 1981

[21] J E Cook ldquo10000 psi concreterdquo Concrete International vol 11pp 67ndash75 1989

[22] A S Malaikah ldquoA proposed relationship for the modulus ofelasticity of high strength concrete using local materials inRiyadhrdquo Journal of King Saud UniversitymdashEngineering Sciencesvol 17 pp 1ndash11 2005

[23] A Mokhtarzadeh and C French ldquoMechanical properties ofhigh-strength concrete with consideration for precast applica-tionsrdquo ACI Materials Journal vol 97 no 2 pp 136ndash147 2000

[24] DVandergrift Jr andA K Schindler ldquoThe effect of test cylindersize on the compressive strength of sulfur capped concretespecimensrdquo Tech Rep IR-06-01 Highway Research Centerand Department of Civil Engineering at Auburn UniversityAuburn Ala USA 2006

[25] ASTM International ldquoStandard test method for compressivestrength of cylindrical concrete specimensrdquo ASTM C39 ASTMInternational West Conshohocken Pa USA 2014

[26] ASTM ldquoStandard test method for pulse velocity throughconcreterdquo ASTM C597 ASTM International 1997

[27] N J CarinoW F Guthrie E S Lagergren and G MMullingsldquoEffects of testing variables on the strength of high-strength(90MPa) concrete cylindersrdquo in High-Performance ConcreteV M Malhotra Ed SP-149 pp 589ndash632 American ConcreteInstitute Farmington Hills Mich USA 1994

[28] ACI ldquoGuide for evaluation of strength test results of concrete(ACI 214R-11)rdquo ASTM C214 American Concrete InstituteFarmington Hills Mich USA 2011

[29] ACI Committee 228 ldquoNondestructive test methods for evalua-tion of concrete in structuresrdquo ReportACI 2282R-98AmericanConcrete Institute Farmington Hills Mich USA 1998

[30] S A Issa M S Islam M A Issa A A Yousif and M A IssaldquoSpecimen and aggregate size effect on concrete compressivestrengthrdquo Cement Concrete and Aggregates vol 22 no 2 pp103ndash115 2000

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

Best-fit line for experimental data in this study(Ec150 = 456Fc150

0418 R2= 090)

Noguchi et al [2009] k1 = k2 = 1

Noguchi et al [2009] k1 = k2 = 095

Mix 1

Mix 3

ACI 318ACI 363CEB-FIP Model code and Eurocode 2

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

5010 15 20 25 30 35 40 45 55 6050Compressive strength Fc (MPa)

150 by 300mm cylindersMix 2

(a)

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

Best-fit line for experimental data in this study(Ec100 = 416Fc100

0446 R2= 084)

Noguchi et al [2009] k1 = k2 = 1

Noguchi et al [2009] k1 = k2 = 095

Mix 1

Mix 3

ACI 318ACI 363CEB-FIP Model code and Eurocode 2

50 15 20 25 30 35 40 45 50 55 6010Compressive strength Fc (MPa)

0

5

10

15

20

25

30

35

40

Mix 2 100 by 200mm cylinders

(b)

Figure 7 Comparison of compressive strength and static elastic modulus of concrete

where MAEcon is mean average error (MAE) of two contin-uous functions 119892

119894is a function presenting 119864

119888expressed as

119865119888 and the subscript 119894 indicates cylinder size (1 and 2 for the

100 by 200mm and 150 by 300mm cylinders resp) Further-more there is no significant difference in 119877

2 values of thetwo best-fit curves 1198772 values for the 100 by 200mm and150 by 300mm cylinders are 088 and 090 respectivelyTherefore the 100 by 200mm cylinders can be used insteadof 150 by 300mm cylinders to estimate static elastic modulusfrom compressive strength without reducing accuracy andconsistency However the three code equations tend tooverestimate static modulus of concrete compared to thosefrom direct measurement according to ASTM C469 [4] Assummarized in Table 3 mean average error (MAE) betweenmeasured and predicted 119864

119888from the three code equations is

in a range of 44 to 12GPa corresponding to about 10 to30 of the measured 119864

119888 In contrast the Noguchi equation

[8] predicts experimental results with far more improvedaccuracy (ie MAE less than 2GPa) by addressing correctionfactors for the effects of aggregates and mineral admixtures(ie 119896

1= 1198962= 095)

36 Relationship between Static and Dynamic Elastic ModuliFigure 8 presents the relationship between static and dynamicelastic moduli determined using different nondestructivetesting methods 119864

119889119875 119864119889119871119877

and 119864119889119879119877

respectively with

Table 3 Mean absolute error (MAE) of expressions relating staticelastic modulus and compressive strength measured using 100 by200mm and 150 by 300mm cylinders

Equation to convert 119864119889to

119864119888

MAE (GPa)150 by 300mm

cylinder100 by 200mm

cylinder119864119889119871119879

119864119889119871119879

Equation (1) 483 463Equation (2) 454 443Equation (3) 1221 1215Equation (14) with1198961= 1198962= 1

342 341

Equation (14) with1198961= 1198962= 095

156 188

Best-fit line 132 157

Poissonrsquos ratio of 02Theuse of Poissonrsquos ratio of 02 is reason-able for common concrete in practice [10] In Figure 8 119864

119889119875

119864119889119871119877

and 119864119889119879119877

measured from 100 by 200mm and 150 by300mm cylinders are shown as open and solid symbols in leftand right columns For comparison purposes several well-known empirical equations (see (3) (4) and (5)) proposedby prior researchers are shown in the figures

Advances in Materials Science and Engineering 9

Best-fit line for experimental data in this study(Ec150 = 044EdLR150

115 R2= 090)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equalityLydon and Balendran (1986)BS8100 Part 2Popovics (1975)

5 10 15 20 25 30 35 400Dynamic elastic modulus EdLR (GPa)

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

(a)

Best-fit line for experimental data in this study(Ec150 = 044EdTR100

115 R2= 090)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equality

BS8100 Part 2

5 10 15 20 25 30 35 400Dynamic elastic modulus EdTR (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

Popovics (1975)

Lydon and Balendran (1986)

(b)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equality

BS8100 Part 2

Best-fit line for experimental data in this study(Ec150 = 022EdP150

129 R2= 087)

Popovics (1975)

Lydon and Balendran (1986)

3510 15 20 25 30 400 5Dynamic elastic modulus EdP (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

(c)

Best-fit line for experimental data in this study(Ec100 = 040EdLR100

118 R2= 088)

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

3510 15 20 25 30 400 5Dynamic elastic modulus EdLR (GPa)

Lydon and Balendran (1986)

Popovics (1975)

(d)

Figure 8 Continued

10 Advances in Materials Science and Engineering

Best-fit line for experimental data in this study(Ec100 = 039EdTR100

120 R2= 087)

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

3510 15 20 25 30 400 5Dynamic elastic modulus EdTR (GPa)

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

Lydon and Balendran (1986)

Popovics (1975)

(e)

Best-fit line for experimental data in this study

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

3510 15 20 25 30 400 5Dynamic elastic modulus EdP (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

EdLR100135 R2

= 085)(Ec100 = 017

Popovics (1975)

Lydon and Balendran (1986)

(f)

Figure 8 Comparison of static and resonance elastic moduli of concrete (a) 119864119889119871119877150

versus 119864119888150

(b) 119864119889119879119877150

versus 119864119888150

(c) 119864119889119875150

versus119864119888150

(d) 119864119889119871119877100

versus 119864119888100

(e) 119864119889119879119877100

versus 119864119888100

and (f) 119864119889119875100

versus 119864119888100

Table 4 Mean absolute error (MAE) of expressions relating static and dynamic elastic modulus measured using 100 by 200mm and 150 by300mm cylinders

Equation to convert 119864119889to 119864119888

MAE (GPa)150 by 300mm cylinder 100 by 200mm cylinder

119864119889119871119879

119864119889119877119879

119864119889119875

119864119889119871119879

119864119889119877119879

119864119889119875

Equation (4) 302 282 754 283 254 846Equation (5) 559 591 277 607 649 335Equation (6) 125 111 658 113 107 780Best-fit line 090 095 126 109 110 117

It is observed that there is only slight difference in therelationship between119864

119888and119864

119889obtained from 100 by 200mm

and 150 by 300mm cylinders In this study approximatedequations that relate119864

119888and119864

119889(119864119889119875

119864119889119871119877

or119864119889119879119877

) from 100by 200mm and 150 by 300mm cylinders were established bynonlinear regression analyses and shown in Figures 8(a)ndash8(f)The MAEs of the two best-fit curves are less than 01MPa inthe dynamic elastic modulus range of 10GPa to 25GPa Fur-thermore there is no significant difference in 119877

2 values of thetwo best-fit curves (see Figure 8) However for both data setsfrom different cylinders the three dynamic moduli (119864

119889119871119877

119864119889119879119877

and 119864119889119875

) obtained from resonance tests and UPVmethod are greater than the static elastic modulus 119864

119888 with

different static-to-dynamic elastic modulus ratio 119864119888119864119889119875

ratio with an average of 056 and COV of 92 is too faraway from the line of equality as well as from the three well-known equations relating static and dynamic elastic modu-lus Therefore the use of 119864

119889119875appears to be inappropriate

to estimate static elastic modulus which is consistent withobservations from other researchers [7 10] In contrast119864119888119864119889119871119877

(or 119864119888119864119889119879119877

) ratio was closer to the line of equalitythan 119864

119888119864119889119875

with an average of 072 and COV of 715The equation proposed by Popovics [13] (see (6)) shows verygood agreement with the experimental results regardless ofcylinder size in this study (see Table 4) In addition priorresearcher [7] observed that the Popovics equation (see (6))can be extended to high strength concrete up to 60MPawith-out regard to cylinder size However it should be mentioned

Advances in Materials Science and Engineering 11

that additional experimental data should be accumulated tobetter understand the size effect on the relationship betweenstatic and dynamic elastic moduli of high strength concrete(gt60MPa) due to scarcity of experimental studies in such ahigh strength range

4 Conclusions

A series of experimental studies was conducted to explore theeffect of cylinder size (100 by 200mm and 150 by 300mmcylinders) on the relationship between static elastic modulusand compressive strength and static and dynamic elasticmoduli of concrete Conclusions based on experiments in thisstudy and database from the literature are drawn as follows

(1) Experimental results in this study show that theCOVsof test results from 100 by 200mm cylinders areabout 10 higher than those from 150 by 300mmcylinders however the differences are statisticallyinsignificantThe averageCOVs of static and dynamicelastic moduli using the UPV and longitudinal andtransverse resonance frequency tests from 100 by200mm cylinders are 632 140 162 and 117respectively while those values from 150 by 300mmcylinders are 583 123 162 and 117 respec-tively For compressive strength the average COVsfrom the 100 by 200mm and 150 by 300mm cylindersare 441 and 365 respectively

(2) According to the findings from similarity tests of best-fit curves and comparison of 1198772 based on regressionanalyses it has been demonstrated that the effect ofcylinder size (100 by 200mm and 150 by 300mmcylinders) is insignificant on compressive strengthand static elastic modulus and the relationship bet-ween the two parameters for normal strength con-crete up to 30MPa However in the higher strengthrange greater than 30MPa there is contradiction inthe relationship between 119865

119888150and 119865

119888100based on

experimental test in this study and database reportedby different researchers Therefore it is difficult toestablish a simple equation that relates 119865

119888100and 119865119888150

and 119864

119888100and 119864

119888150because of limited experimental

and theoretical studies

(3) The three code equations tend to overestimate staticmodulus of concrete compared to those from directmeasurement according to ASTM C469 with MAEin a range of 44GPa to 12GPa In contrast theNoguchi equation predicts experimental results withfar more improved accuracy (ie MAE less than2GPa) by addressing correction factors for the effectsof aggregates and mineral admixtures (ie 119896

1= 1198962=

095)

(4) There is only a slight difference in the relationshipbetween static and resonance moduli from 100 by200mm and 150 by 300mm cylinders for normalstrength concrete Test results from this study and theliterature show that the empirical equation suggested

by Popovics [13] ((6) in this study) is effective for pre-dicting static elastic moduli from resonance moduliof concrete with compressive strength up to 60MParegardless of the cylinder size with MAE of less than15 GPa

(5) However the velocity moduli are excessively greaterthan static elastic modulus The empirical equations(see (4) (5) and (6)) produce considerable errors(with MAE in a range of 277GPa to 846GPa) bet-ween measured and predicted elastic moduli There-fore the use of velocitymoduli appears to be inappro-priate to estimate static elastic modulus

Conflict of Interests

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

Acknowledgment

This research was supported by the Basic Science ResearchProgram through theNational Research Foundation of Korea(NRF) funded by the Ministry of Science ICT amp FuturePlanning (no 2015R1A5A1037548)

References

[1] ACI Committee 318 Building Code Requirements for StructuralConcrete (ACI 318-11) and Commentary American ConcreteInstitute Farmington Hills Mich USA 2014

[2] IBC Council International Building Code (IBC 2012) 2014[3] N Gucunski A Imani F Romero et al ldquoNondestructive testig

to identify concrete bridge deck deteriorationrdquo SHRP 2 ReportS2-R06A-RR-1 2013

[4] ACI Committee 469 Standard Test Method for Static Modulusof Elasticity and Poissonrsquos Ratio of Concrete in CompressionAmerican Concrete Institute Farmington Hills Mich USA2014

[5] A Pauw ldquoStatic modulus of elasticity of concrete as affected bydensityrdquo ACI Journal Proceedings vol 57 no 12 pp 679ndash6871960

[6] ACI Committee 363 ldquoState-of-the-art report on high-strengthconcreterdquo ACI Journal Proceedings vol 81 no 4 pp 364ndash4111984

[7] J S Popovics ldquoA study of static and dynamic modulus ofelasticity of concreterdquo ACI-CRC Final Report 2008

[8] T Noguchi F Tomosawa KM Nemati BM Chiaia and A RFantilli ldquoA practical equation for elastic modulus of concreterdquoACI Structural Journal vol 106 no 5 pp 690ndash696 2009

[9] R E Philleo ldquoComparison of results of threemethods for deter-mining Youngrsquos modulus of elasticity of concreterdquo InternationalConcrete Abstracts Portal vol 51 no 1 pp 461ndash469 1955

[10] A M Neville Properties of Concrete John Wiley amp Sons NewYork NY USA 4th edition 1997

[11] F D Lydon and R V Balendran ldquoSome observations on elasticproperties of plain concreterdquo Cement and Concrete Researchvol 16 no 3 pp 314ndash324 1986

[12] B S Institute ldquoStructural use of concretemdashpart 2 code ofpractice for special circumstancerdquo BS 8110-21995 BSI LondonUK 1995

12 Advances in Materials Science and Engineering

[13] S Popovics ldquoVerification of relationships between mechanicalproperties of concrete-like materialsrdquoMaterials and Structuresvol 8 no 3 pp 183ndash191 1975

[14] ASTM C191 Standard Practice for Making and Curing ConcreteTest Specimens in the Laboratory ASTM 2014

[15] ASTM ldquoStandard practice for making and curing concrete testspecimen in the fieldrdquo ASTM C31 ASTM International 2012

[16] ASTM International ldquoStandard test method for fundamentaltransverse longitudinal and torsional resonant frequencies ofconcrete specimensrdquo ASTM C215 ASTM International WestConshohocken Pa USA 2002

[17] P-C Aitcin and P K Mehta ldquoEffect of coarse-aggregate char-acteristics on mechanical properties of high-strength concreterdquoACI Materials Journal vol 87 no 2 pp 103ndash107 1990

[18] P-C Aitcin B Miao W D Cook and D Mitchell ldquoEffectsof size and curing on cylinder compressive strength of normaland high-strength concretesrdquo ACIMaterials Journal vol 91 pp349ndash354 1994

[19] P M Carrasquillo and R L Carrasquillo ldquoEvaluation of the useof current concrete practice in the production of high strengthconcreterdquo ACI Materials Journal vol 85 no 1 pp 49ndash54 1988

[20] R L Carrasquillo A H Nilson and F O Slate ldquoProperties ofhigh strength concrete subject to short-term loadsrdquo Journal ofthe American Concrete Institute vol 78 no 3 pp 171ndash178 1981

[21] J E Cook ldquo10000 psi concreterdquo Concrete International vol 11pp 67ndash75 1989

[22] A S Malaikah ldquoA proposed relationship for the modulus ofelasticity of high strength concrete using local materials inRiyadhrdquo Journal of King Saud UniversitymdashEngineering Sciencesvol 17 pp 1ndash11 2005

[23] A Mokhtarzadeh and C French ldquoMechanical properties ofhigh-strength concrete with consideration for precast applica-tionsrdquo ACI Materials Journal vol 97 no 2 pp 136ndash147 2000

[24] DVandergrift Jr andA K Schindler ldquoThe effect of test cylindersize on the compressive strength of sulfur capped concretespecimensrdquo Tech Rep IR-06-01 Highway Research Centerand Department of Civil Engineering at Auburn UniversityAuburn Ala USA 2006

[25] ASTM International ldquoStandard test method for compressivestrength of cylindrical concrete specimensrdquo ASTM C39 ASTMInternational West Conshohocken Pa USA 2014

[26] ASTM ldquoStandard test method for pulse velocity throughconcreterdquo ASTM C597 ASTM International 1997

[27] N J CarinoW F Guthrie E S Lagergren and G MMullingsldquoEffects of testing variables on the strength of high-strength(90MPa) concrete cylindersrdquo in High-Performance ConcreteV M Malhotra Ed SP-149 pp 589ndash632 American ConcreteInstitute Farmington Hills Mich USA 1994

[28] ACI ldquoGuide for evaluation of strength test results of concrete(ACI 214R-11)rdquo ASTM C214 American Concrete InstituteFarmington Hills Mich USA 2011

[29] ACI Committee 228 ldquoNondestructive test methods for evalua-tion of concrete in structuresrdquo ReportACI 2282R-98AmericanConcrete Institute Farmington Hills Mich USA 1998

[30] S A Issa M S Islam M A Issa A A Yousif and M A IssaldquoSpecimen and aggregate size effect on concrete compressivestrengthrdquo Cement Concrete and Aggregates vol 22 no 2 pp103ndash115 2000

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 9

Best-fit line for experimental data in this study(Ec150 = 044EdLR150

115 R2= 090)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equalityLydon and Balendran (1986)BS8100 Part 2Popovics (1975)

5 10 15 20 25 30 35 400Dynamic elastic modulus EdLR (GPa)

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

(a)

Best-fit line for experimental data in this study(Ec150 = 044EdTR100

115 R2= 090)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equality

BS8100 Part 2

5 10 15 20 25 30 35 400Dynamic elastic modulus EdTR (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

Popovics (1975)

Lydon and Balendran (1986)

(b)

Mix 1 (150 times 300mm)Mix 2 (150 times 300mm)Mix 3 (150 times 300mm)Line of equality

BS8100 Part 2

Best-fit line for experimental data in this study(Ec150 = 022EdP150

129 R2= 087)

Popovics (1975)

Lydon and Balendran (1986)

3510 15 20 25 30 400 5Dynamic elastic modulus EdP (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

(c)

Best-fit line for experimental data in this study(Ec100 = 040EdLR100

118 R2= 088)

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

3510 15 20 25 30 400 5Dynamic elastic modulus EdLR (GPa)

Lydon and Balendran (1986)

Popovics (1975)

(d)

Figure 8 Continued

10 Advances in Materials Science and Engineering

Best-fit line for experimental data in this study(Ec100 = 039EdTR100

120 R2= 087)

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

3510 15 20 25 30 400 5Dynamic elastic modulus EdTR (GPa)

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

Lydon and Balendran (1986)

Popovics (1975)

(e)

Best-fit line for experimental data in this study

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

3510 15 20 25 30 400 5Dynamic elastic modulus EdP (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

EdLR100135 R2

= 085)(Ec100 = 017

Popovics (1975)

Lydon and Balendran (1986)

(f)

Figure 8 Comparison of static and resonance elastic moduli of concrete (a) 119864119889119871119877150

versus 119864119888150

(b) 119864119889119879119877150

versus 119864119888150

(c) 119864119889119875150

versus119864119888150

(d) 119864119889119871119877100

versus 119864119888100

(e) 119864119889119879119877100

versus 119864119888100

and (f) 119864119889119875100

versus 119864119888100

Table 4 Mean absolute error (MAE) of expressions relating static and dynamic elastic modulus measured using 100 by 200mm and 150 by300mm cylinders

Equation to convert 119864119889to 119864119888

MAE (GPa)150 by 300mm cylinder 100 by 200mm cylinder

119864119889119871119879

119864119889119877119879

119864119889119875

119864119889119871119879

119864119889119877119879

119864119889119875

Equation (4) 302 282 754 283 254 846Equation (5) 559 591 277 607 649 335Equation (6) 125 111 658 113 107 780Best-fit line 090 095 126 109 110 117

It is observed that there is only slight difference in therelationship between119864

119888and119864

119889obtained from 100 by 200mm

and 150 by 300mm cylinders In this study approximatedequations that relate119864

119888and119864

119889(119864119889119875

119864119889119871119877

or119864119889119879119877

) from 100by 200mm and 150 by 300mm cylinders were established bynonlinear regression analyses and shown in Figures 8(a)ndash8(f)The MAEs of the two best-fit curves are less than 01MPa inthe dynamic elastic modulus range of 10GPa to 25GPa Fur-thermore there is no significant difference in 119877

2 values of thetwo best-fit curves (see Figure 8) However for both data setsfrom different cylinders the three dynamic moduli (119864

119889119871119877

119864119889119879119877

and 119864119889119875

) obtained from resonance tests and UPVmethod are greater than the static elastic modulus 119864

119888 with

different static-to-dynamic elastic modulus ratio 119864119888119864119889119875

ratio with an average of 056 and COV of 92 is too faraway from the line of equality as well as from the three well-known equations relating static and dynamic elastic modu-lus Therefore the use of 119864

119889119875appears to be inappropriate

to estimate static elastic modulus which is consistent withobservations from other researchers [7 10] In contrast119864119888119864119889119871119877

(or 119864119888119864119889119879119877

) ratio was closer to the line of equalitythan 119864

119888119864119889119875

with an average of 072 and COV of 715The equation proposed by Popovics [13] (see (6)) shows verygood agreement with the experimental results regardless ofcylinder size in this study (see Table 4) In addition priorresearcher [7] observed that the Popovics equation (see (6))can be extended to high strength concrete up to 60MPawith-out regard to cylinder size However it should be mentioned

Advances in Materials Science and Engineering 11

that additional experimental data should be accumulated tobetter understand the size effect on the relationship betweenstatic and dynamic elastic moduli of high strength concrete(gt60MPa) due to scarcity of experimental studies in such ahigh strength range

4 Conclusions

A series of experimental studies was conducted to explore theeffect of cylinder size (100 by 200mm and 150 by 300mmcylinders) on the relationship between static elastic modulusand compressive strength and static and dynamic elasticmoduli of concrete Conclusions based on experiments in thisstudy and database from the literature are drawn as follows

(1) Experimental results in this study show that theCOVsof test results from 100 by 200mm cylinders areabout 10 higher than those from 150 by 300mmcylinders however the differences are statisticallyinsignificantThe averageCOVs of static and dynamicelastic moduli using the UPV and longitudinal andtransverse resonance frequency tests from 100 by200mm cylinders are 632 140 162 and 117respectively while those values from 150 by 300mmcylinders are 583 123 162 and 117 respec-tively For compressive strength the average COVsfrom the 100 by 200mm and 150 by 300mm cylindersare 441 and 365 respectively

(2) According to the findings from similarity tests of best-fit curves and comparison of 1198772 based on regressionanalyses it has been demonstrated that the effect ofcylinder size (100 by 200mm and 150 by 300mmcylinders) is insignificant on compressive strengthand static elastic modulus and the relationship bet-ween the two parameters for normal strength con-crete up to 30MPa However in the higher strengthrange greater than 30MPa there is contradiction inthe relationship between 119865

119888150and 119865

119888100based on

experimental test in this study and database reportedby different researchers Therefore it is difficult toestablish a simple equation that relates 119865

119888100and 119865119888150

and 119864

119888100and 119864

119888150because of limited experimental

and theoretical studies

(3) The three code equations tend to overestimate staticmodulus of concrete compared to those from directmeasurement according to ASTM C469 with MAEin a range of 44GPa to 12GPa In contrast theNoguchi equation predicts experimental results withfar more improved accuracy (ie MAE less than2GPa) by addressing correction factors for the effectsof aggregates and mineral admixtures (ie 119896

1= 1198962=

095)

(4) There is only a slight difference in the relationshipbetween static and resonance moduli from 100 by200mm and 150 by 300mm cylinders for normalstrength concrete Test results from this study and theliterature show that the empirical equation suggested

by Popovics [13] ((6) in this study) is effective for pre-dicting static elastic moduli from resonance moduliof concrete with compressive strength up to 60MParegardless of the cylinder size with MAE of less than15 GPa

(5) However the velocity moduli are excessively greaterthan static elastic modulus The empirical equations(see (4) (5) and (6)) produce considerable errors(with MAE in a range of 277GPa to 846GPa) bet-ween measured and predicted elastic moduli There-fore the use of velocitymoduli appears to be inappro-priate to estimate static elastic modulus

Conflict of Interests

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

Acknowledgment

This research was supported by the Basic Science ResearchProgram through theNational Research Foundation of Korea(NRF) funded by the Ministry of Science ICT amp FuturePlanning (no 2015R1A5A1037548)

References

[1] ACI Committee 318 Building Code Requirements for StructuralConcrete (ACI 318-11) and Commentary American ConcreteInstitute Farmington Hills Mich USA 2014

[2] IBC Council International Building Code (IBC 2012) 2014[3] N Gucunski A Imani F Romero et al ldquoNondestructive testig

to identify concrete bridge deck deteriorationrdquo SHRP 2 ReportS2-R06A-RR-1 2013

[4] ACI Committee 469 Standard Test Method for Static Modulusof Elasticity and Poissonrsquos Ratio of Concrete in CompressionAmerican Concrete Institute Farmington Hills Mich USA2014

[5] A Pauw ldquoStatic modulus of elasticity of concrete as affected bydensityrdquo ACI Journal Proceedings vol 57 no 12 pp 679ndash6871960

[6] ACI Committee 363 ldquoState-of-the-art report on high-strengthconcreterdquo ACI Journal Proceedings vol 81 no 4 pp 364ndash4111984

[7] J S Popovics ldquoA study of static and dynamic modulus ofelasticity of concreterdquo ACI-CRC Final Report 2008

[8] T Noguchi F Tomosawa KM Nemati BM Chiaia and A RFantilli ldquoA practical equation for elastic modulus of concreterdquoACI Structural Journal vol 106 no 5 pp 690ndash696 2009

[9] R E Philleo ldquoComparison of results of threemethods for deter-mining Youngrsquos modulus of elasticity of concreterdquo InternationalConcrete Abstracts Portal vol 51 no 1 pp 461ndash469 1955

[10] A M Neville Properties of Concrete John Wiley amp Sons NewYork NY USA 4th edition 1997

[11] F D Lydon and R V Balendran ldquoSome observations on elasticproperties of plain concreterdquo Cement and Concrete Researchvol 16 no 3 pp 314ndash324 1986

[12] B S Institute ldquoStructural use of concretemdashpart 2 code ofpractice for special circumstancerdquo BS 8110-21995 BSI LondonUK 1995

12 Advances in Materials Science and Engineering

[13] S Popovics ldquoVerification of relationships between mechanicalproperties of concrete-like materialsrdquoMaterials and Structuresvol 8 no 3 pp 183ndash191 1975

[14] ASTM C191 Standard Practice for Making and Curing ConcreteTest Specimens in the Laboratory ASTM 2014

[15] ASTM ldquoStandard practice for making and curing concrete testspecimen in the fieldrdquo ASTM C31 ASTM International 2012

[16] ASTM International ldquoStandard test method for fundamentaltransverse longitudinal and torsional resonant frequencies ofconcrete specimensrdquo ASTM C215 ASTM International WestConshohocken Pa USA 2002

[17] P-C Aitcin and P K Mehta ldquoEffect of coarse-aggregate char-acteristics on mechanical properties of high-strength concreterdquoACI Materials Journal vol 87 no 2 pp 103ndash107 1990

[18] P-C Aitcin B Miao W D Cook and D Mitchell ldquoEffectsof size and curing on cylinder compressive strength of normaland high-strength concretesrdquo ACIMaterials Journal vol 91 pp349ndash354 1994

[19] P M Carrasquillo and R L Carrasquillo ldquoEvaluation of the useof current concrete practice in the production of high strengthconcreterdquo ACI Materials Journal vol 85 no 1 pp 49ndash54 1988

[20] R L Carrasquillo A H Nilson and F O Slate ldquoProperties ofhigh strength concrete subject to short-term loadsrdquo Journal ofthe American Concrete Institute vol 78 no 3 pp 171ndash178 1981

[21] J E Cook ldquo10000 psi concreterdquo Concrete International vol 11pp 67ndash75 1989

[22] A S Malaikah ldquoA proposed relationship for the modulus ofelasticity of high strength concrete using local materials inRiyadhrdquo Journal of King Saud UniversitymdashEngineering Sciencesvol 17 pp 1ndash11 2005

[23] A Mokhtarzadeh and C French ldquoMechanical properties ofhigh-strength concrete with consideration for precast applica-tionsrdquo ACI Materials Journal vol 97 no 2 pp 136ndash147 2000

[24] DVandergrift Jr andA K Schindler ldquoThe effect of test cylindersize on the compressive strength of sulfur capped concretespecimensrdquo Tech Rep IR-06-01 Highway Research Centerand Department of Civil Engineering at Auburn UniversityAuburn Ala USA 2006

[25] ASTM International ldquoStandard test method for compressivestrength of cylindrical concrete specimensrdquo ASTM C39 ASTMInternational West Conshohocken Pa USA 2014

[26] ASTM ldquoStandard test method for pulse velocity throughconcreterdquo ASTM C597 ASTM International 1997

[27] N J CarinoW F Guthrie E S Lagergren and G MMullingsldquoEffects of testing variables on the strength of high-strength(90MPa) concrete cylindersrdquo in High-Performance ConcreteV M Malhotra Ed SP-149 pp 589ndash632 American ConcreteInstitute Farmington Hills Mich USA 1994

[28] ACI ldquoGuide for evaluation of strength test results of concrete(ACI 214R-11)rdquo ASTM C214 American Concrete InstituteFarmington Hills Mich USA 2011

[29] ACI Committee 228 ldquoNondestructive test methods for evalua-tion of concrete in structuresrdquo ReportACI 2282R-98AmericanConcrete Institute Farmington Hills Mich USA 1998

[30] S A Issa M S Islam M A Issa A A Yousif and M A IssaldquoSpecimen and aggregate size effect on concrete compressivestrengthrdquo Cement Concrete and Aggregates vol 22 no 2 pp103ndash115 2000

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

10 Advances in Materials Science and Engineering

Best-fit line for experimental data in this study(Ec100 = 039EdTR100

120 R2= 087)

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

3510 15 20 25 30 400 5Dynamic elastic modulus EdTR (GPa)

0

5

10

15

20

25

30

35

40St

atic

elas

tic m

odul

usEc

(GPa

)

Lydon and Balendran (1986)

Popovics (1975)

(e)

Best-fit line for experimental data in this study

Mix 1 (100 times 200mm)Mix 2 (100 times 200mm)Mix 3 (100 times 200mm)Line of equality

BS8100 Part 2

3510 15 20 25 30 400 5Dynamic elastic modulus EdP (GPa)

0

5

10

15

20

25

30

35

40

Stat

ic el

astic

mod

ulus

Ec

(GPa

)

EdLR100135 R2

= 085)(Ec100 = 017

Popovics (1975)

Lydon and Balendran (1986)

(f)

Figure 8 Comparison of static and resonance elastic moduli of concrete (a) 119864119889119871119877150

versus 119864119888150

(b) 119864119889119879119877150

versus 119864119888150

(c) 119864119889119875150

versus119864119888150

(d) 119864119889119871119877100

versus 119864119888100

(e) 119864119889119879119877100

versus 119864119888100

and (f) 119864119889119875100

versus 119864119888100

Table 4 Mean absolute error (MAE) of expressions relating static and dynamic elastic modulus measured using 100 by 200mm and 150 by300mm cylinders

Equation to convert 119864119889to 119864119888

MAE (GPa)150 by 300mm cylinder 100 by 200mm cylinder

119864119889119871119879

119864119889119877119879

119864119889119875

119864119889119871119879

119864119889119877119879

119864119889119875

Equation (4) 302 282 754 283 254 846Equation (5) 559 591 277 607 649 335Equation (6) 125 111 658 113 107 780Best-fit line 090 095 126 109 110 117

It is observed that there is only slight difference in therelationship between119864

119888and119864

119889obtained from 100 by 200mm

and 150 by 300mm cylinders In this study approximatedequations that relate119864

119888and119864

119889(119864119889119875

119864119889119871119877

or119864119889119879119877

) from 100by 200mm and 150 by 300mm cylinders were established bynonlinear regression analyses and shown in Figures 8(a)ndash8(f)The MAEs of the two best-fit curves are less than 01MPa inthe dynamic elastic modulus range of 10GPa to 25GPa Fur-thermore there is no significant difference in 119877

2 values of thetwo best-fit curves (see Figure 8) However for both data setsfrom different cylinders the three dynamic moduli (119864

119889119871119877

119864119889119879119877

and 119864119889119875

) obtained from resonance tests and UPVmethod are greater than the static elastic modulus 119864

119888 with

different static-to-dynamic elastic modulus ratio 119864119888119864119889119875

ratio with an average of 056 and COV of 92 is too faraway from the line of equality as well as from the three well-known equations relating static and dynamic elastic modu-lus Therefore the use of 119864

119889119875appears to be inappropriate

to estimate static elastic modulus which is consistent withobservations from other researchers [7 10] In contrast119864119888119864119889119871119877

(or 119864119888119864119889119879119877

) ratio was closer to the line of equalitythan 119864

119888119864119889119875

with an average of 072 and COV of 715The equation proposed by Popovics [13] (see (6)) shows verygood agreement with the experimental results regardless ofcylinder size in this study (see Table 4) In addition priorresearcher [7] observed that the Popovics equation (see (6))can be extended to high strength concrete up to 60MPawith-out regard to cylinder size However it should be mentioned

Advances in Materials Science and Engineering 11

that additional experimental data should be accumulated tobetter understand the size effect on the relationship betweenstatic and dynamic elastic moduli of high strength concrete(gt60MPa) due to scarcity of experimental studies in such ahigh strength range

4 Conclusions

A series of experimental studies was conducted to explore theeffect of cylinder size (100 by 200mm and 150 by 300mmcylinders) on the relationship between static elastic modulusand compressive strength and static and dynamic elasticmoduli of concrete Conclusions based on experiments in thisstudy and database from the literature are drawn as follows

(1) Experimental results in this study show that theCOVsof test results from 100 by 200mm cylinders areabout 10 higher than those from 150 by 300mmcylinders however the differences are statisticallyinsignificantThe averageCOVs of static and dynamicelastic moduli using the UPV and longitudinal andtransverse resonance frequency tests from 100 by200mm cylinders are 632 140 162 and 117respectively while those values from 150 by 300mmcylinders are 583 123 162 and 117 respec-tively For compressive strength the average COVsfrom the 100 by 200mm and 150 by 300mm cylindersare 441 and 365 respectively

(2) According to the findings from similarity tests of best-fit curves and comparison of 1198772 based on regressionanalyses it has been demonstrated that the effect ofcylinder size (100 by 200mm and 150 by 300mmcylinders) is insignificant on compressive strengthand static elastic modulus and the relationship bet-ween the two parameters for normal strength con-crete up to 30MPa However in the higher strengthrange greater than 30MPa there is contradiction inthe relationship between 119865

119888150and 119865

119888100based on

experimental test in this study and database reportedby different researchers Therefore it is difficult toestablish a simple equation that relates 119865

119888100and 119865119888150

and 119864

119888100and 119864

119888150because of limited experimental

and theoretical studies

(3) The three code equations tend to overestimate staticmodulus of concrete compared to those from directmeasurement according to ASTM C469 with MAEin a range of 44GPa to 12GPa In contrast theNoguchi equation predicts experimental results withfar more improved accuracy (ie MAE less than2GPa) by addressing correction factors for the effectsof aggregates and mineral admixtures (ie 119896

1= 1198962=

095)

(4) There is only a slight difference in the relationshipbetween static and resonance moduli from 100 by200mm and 150 by 300mm cylinders for normalstrength concrete Test results from this study and theliterature show that the empirical equation suggested

by Popovics [13] ((6) in this study) is effective for pre-dicting static elastic moduli from resonance moduliof concrete with compressive strength up to 60MParegardless of the cylinder size with MAE of less than15 GPa

(5) However the velocity moduli are excessively greaterthan static elastic modulus The empirical equations(see (4) (5) and (6)) produce considerable errors(with MAE in a range of 277GPa to 846GPa) bet-ween measured and predicted elastic moduli There-fore the use of velocitymoduli appears to be inappro-priate to estimate static elastic modulus

Conflict of Interests

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

Acknowledgment

This research was supported by the Basic Science ResearchProgram through theNational Research Foundation of Korea(NRF) funded by the Ministry of Science ICT amp FuturePlanning (no 2015R1A5A1037548)

References

[1] ACI Committee 318 Building Code Requirements for StructuralConcrete (ACI 318-11) and Commentary American ConcreteInstitute Farmington Hills Mich USA 2014

[2] IBC Council International Building Code (IBC 2012) 2014[3] N Gucunski A Imani F Romero et al ldquoNondestructive testig

to identify concrete bridge deck deteriorationrdquo SHRP 2 ReportS2-R06A-RR-1 2013

[4] ACI Committee 469 Standard Test Method for Static Modulusof Elasticity and Poissonrsquos Ratio of Concrete in CompressionAmerican Concrete Institute Farmington Hills Mich USA2014

[5] A Pauw ldquoStatic modulus of elasticity of concrete as affected bydensityrdquo ACI Journal Proceedings vol 57 no 12 pp 679ndash6871960

[6] ACI Committee 363 ldquoState-of-the-art report on high-strengthconcreterdquo ACI Journal Proceedings vol 81 no 4 pp 364ndash4111984

[7] J S Popovics ldquoA study of static and dynamic modulus ofelasticity of concreterdquo ACI-CRC Final Report 2008

[8] T Noguchi F Tomosawa KM Nemati BM Chiaia and A RFantilli ldquoA practical equation for elastic modulus of concreterdquoACI Structural Journal vol 106 no 5 pp 690ndash696 2009

[9] R E Philleo ldquoComparison of results of threemethods for deter-mining Youngrsquos modulus of elasticity of concreterdquo InternationalConcrete Abstracts Portal vol 51 no 1 pp 461ndash469 1955

[10] A M Neville Properties of Concrete John Wiley amp Sons NewYork NY USA 4th edition 1997

[11] F D Lydon and R V Balendran ldquoSome observations on elasticproperties of plain concreterdquo Cement and Concrete Researchvol 16 no 3 pp 314ndash324 1986

[12] B S Institute ldquoStructural use of concretemdashpart 2 code ofpractice for special circumstancerdquo BS 8110-21995 BSI LondonUK 1995

12 Advances in Materials Science and Engineering

[13] S Popovics ldquoVerification of relationships between mechanicalproperties of concrete-like materialsrdquoMaterials and Structuresvol 8 no 3 pp 183ndash191 1975

[14] ASTM C191 Standard Practice for Making and Curing ConcreteTest Specimens in the Laboratory ASTM 2014

[15] ASTM ldquoStandard practice for making and curing concrete testspecimen in the fieldrdquo ASTM C31 ASTM International 2012

[16] ASTM International ldquoStandard test method for fundamentaltransverse longitudinal and torsional resonant frequencies ofconcrete specimensrdquo ASTM C215 ASTM International WestConshohocken Pa USA 2002

[17] P-C Aitcin and P K Mehta ldquoEffect of coarse-aggregate char-acteristics on mechanical properties of high-strength concreterdquoACI Materials Journal vol 87 no 2 pp 103ndash107 1990

[18] P-C Aitcin B Miao W D Cook and D Mitchell ldquoEffectsof size and curing on cylinder compressive strength of normaland high-strength concretesrdquo ACIMaterials Journal vol 91 pp349ndash354 1994

[19] P M Carrasquillo and R L Carrasquillo ldquoEvaluation of the useof current concrete practice in the production of high strengthconcreterdquo ACI Materials Journal vol 85 no 1 pp 49ndash54 1988

[20] R L Carrasquillo A H Nilson and F O Slate ldquoProperties ofhigh strength concrete subject to short-term loadsrdquo Journal ofthe American Concrete Institute vol 78 no 3 pp 171ndash178 1981

[21] J E Cook ldquo10000 psi concreterdquo Concrete International vol 11pp 67ndash75 1989

[22] A S Malaikah ldquoA proposed relationship for the modulus ofelasticity of high strength concrete using local materials inRiyadhrdquo Journal of King Saud UniversitymdashEngineering Sciencesvol 17 pp 1ndash11 2005

[23] A Mokhtarzadeh and C French ldquoMechanical properties ofhigh-strength concrete with consideration for precast applica-tionsrdquo ACI Materials Journal vol 97 no 2 pp 136ndash147 2000

[24] DVandergrift Jr andA K Schindler ldquoThe effect of test cylindersize on the compressive strength of sulfur capped concretespecimensrdquo Tech Rep IR-06-01 Highway Research Centerand Department of Civil Engineering at Auburn UniversityAuburn Ala USA 2006

[25] ASTM International ldquoStandard test method for compressivestrength of cylindrical concrete specimensrdquo ASTM C39 ASTMInternational West Conshohocken Pa USA 2014

[26] ASTM ldquoStandard test method for pulse velocity throughconcreterdquo ASTM C597 ASTM International 1997

[27] N J CarinoW F Guthrie E S Lagergren and G MMullingsldquoEffects of testing variables on the strength of high-strength(90MPa) concrete cylindersrdquo in High-Performance ConcreteV M Malhotra Ed SP-149 pp 589ndash632 American ConcreteInstitute Farmington Hills Mich USA 1994

[28] ACI ldquoGuide for evaluation of strength test results of concrete(ACI 214R-11)rdquo ASTM C214 American Concrete InstituteFarmington Hills Mich USA 2011

[29] ACI Committee 228 ldquoNondestructive test methods for evalua-tion of concrete in structuresrdquo ReportACI 2282R-98AmericanConcrete Institute Farmington Hills Mich USA 1998

[30] S A Issa M S Islam M A Issa A A Yousif and M A IssaldquoSpecimen and aggregate size effect on concrete compressivestrengthrdquo Cement Concrete and Aggregates vol 22 no 2 pp103ndash115 2000

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 11

that additional experimental data should be accumulated tobetter understand the size effect on the relationship betweenstatic and dynamic elastic moduli of high strength concrete(gt60MPa) due to scarcity of experimental studies in such ahigh strength range

4 Conclusions

A series of experimental studies was conducted to explore theeffect of cylinder size (100 by 200mm and 150 by 300mmcylinders) on the relationship between static elastic modulusand compressive strength and static and dynamic elasticmoduli of concrete Conclusions based on experiments in thisstudy and database from the literature are drawn as follows

(1) Experimental results in this study show that theCOVsof test results from 100 by 200mm cylinders areabout 10 higher than those from 150 by 300mmcylinders however the differences are statisticallyinsignificantThe averageCOVs of static and dynamicelastic moduli using the UPV and longitudinal andtransverse resonance frequency tests from 100 by200mm cylinders are 632 140 162 and 117respectively while those values from 150 by 300mmcylinders are 583 123 162 and 117 respec-tively For compressive strength the average COVsfrom the 100 by 200mm and 150 by 300mm cylindersare 441 and 365 respectively

(2) According to the findings from similarity tests of best-fit curves and comparison of 1198772 based on regressionanalyses it has been demonstrated that the effect ofcylinder size (100 by 200mm and 150 by 300mmcylinders) is insignificant on compressive strengthand static elastic modulus and the relationship bet-ween the two parameters for normal strength con-crete up to 30MPa However in the higher strengthrange greater than 30MPa there is contradiction inthe relationship between 119865

119888150and 119865

119888100based on

experimental test in this study and database reportedby different researchers Therefore it is difficult toestablish a simple equation that relates 119865

119888100and 119865119888150

and 119864

119888100and 119864

119888150because of limited experimental

and theoretical studies

(3) The three code equations tend to overestimate staticmodulus of concrete compared to those from directmeasurement according to ASTM C469 with MAEin a range of 44GPa to 12GPa In contrast theNoguchi equation predicts experimental results withfar more improved accuracy (ie MAE less than2GPa) by addressing correction factors for the effectsof aggregates and mineral admixtures (ie 119896

1= 1198962=

095)

(4) There is only a slight difference in the relationshipbetween static and resonance moduli from 100 by200mm and 150 by 300mm cylinders for normalstrength concrete Test results from this study and theliterature show that the empirical equation suggested

by Popovics [13] ((6) in this study) is effective for pre-dicting static elastic moduli from resonance moduliof concrete with compressive strength up to 60MParegardless of the cylinder size with MAE of less than15 GPa

(5) However the velocity moduli are excessively greaterthan static elastic modulus The empirical equations(see (4) (5) and (6)) produce considerable errors(with MAE in a range of 277GPa to 846GPa) bet-ween measured and predicted elastic moduli There-fore the use of velocitymoduli appears to be inappro-priate to estimate static elastic modulus

Conflict of Interests

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

Acknowledgment

This research was supported by the Basic Science ResearchProgram through theNational Research Foundation of Korea(NRF) funded by the Ministry of Science ICT amp FuturePlanning (no 2015R1A5A1037548)

References

[1] ACI Committee 318 Building Code Requirements for StructuralConcrete (ACI 318-11) and Commentary American ConcreteInstitute Farmington Hills Mich USA 2014

[2] IBC Council International Building Code (IBC 2012) 2014[3] N Gucunski A Imani F Romero et al ldquoNondestructive testig

to identify concrete bridge deck deteriorationrdquo SHRP 2 ReportS2-R06A-RR-1 2013

[4] ACI Committee 469 Standard Test Method for Static Modulusof Elasticity and Poissonrsquos Ratio of Concrete in CompressionAmerican Concrete Institute Farmington Hills Mich USA2014

[5] A Pauw ldquoStatic modulus of elasticity of concrete as affected bydensityrdquo ACI Journal Proceedings vol 57 no 12 pp 679ndash6871960

[6] ACI Committee 363 ldquoState-of-the-art report on high-strengthconcreterdquo ACI Journal Proceedings vol 81 no 4 pp 364ndash4111984

[7] J S Popovics ldquoA study of static and dynamic modulus ofelasticity of concreterdquo ACI-CRC Final Report 2008

[8] T Noguchi F Tomosawa KM Nemati BM Chiaia and A RFantilli ldquoA practical equation for elastic modulus of concreterdquoACI Structural Journal vol 106 no 5 pp 690ndash696 2009

[9] R E Philleo ldquoComparison of results of threemethods for deter-mining Youngrsquos modulus of elasticity of concreterdquo InternationalConcrete Abstracts Portal vol 51 no 1 pp 461ndash469 1955

[10] A M Neville Properties of Concrete John Wiley amp Sons NewYork NY USA 4th edition 1997

[11] F D Lydon and R V Balendran ldquoSome observations on elasticproperties of plain concreterdquo Cement and Concrete Researchvol 16 no 3 pp 314ndash324 1986

[12] B S Institute ldquoStructural use of concretemdashpart 2 code ofpractice for special circumstancerdquo BS 8110-21995 BSI LondonUK 1995

12 Advances in Materials Science and Engineering

[13] S Popovics ldquoVerification of relationships between mechanicalproperties of concrete-like materialsrdquoMaterials and Structuresvol 8 no 3 pp 183ndash191 1975

[14] ASTM C191 Standard Practice for Making and Curing ConcreteTest Specimens in the Laboratory ASTM 2014

[15] ASTM ldquoStandard practice for making and curing concrete testspecimen in the fieldrdquo ASTM C31 ASTM International 2012

[16] ASTM International ldquoStandard test method for fundamentaltransverse longitudinal and torsional resonant frequencies ofconcrete specimensrdquo ASTM C215 ASTM International WestConshohocken Pa USA 2002

[17] P-C Aitcin and P K Mehta ldquoEffect of coarse-aggregate char-acteristics on mechanical properties of high-strength concreterdquoACI Materials Journal vol 87 no 2 pp 103ndash107 1990

[18] P-C Aitcin B Miao W D Cook and D Mitchell ldquoEffectsof size and curing on cylinder compressive strength of normaland high-strength concretesrdquo ACIMaterials Journal vol 91 pp349ndash354 1994

[19] P M Carrasquillo and R L Carrasquillo ldquoEvaluation of the useof current concrete practice in the production of high strengthconcreterdquo ACI Materials Journal vol 85 no 1 pp 49ndash54 1988

[20] R L Carrasquillo A H Nilson and F O Slate ldquoProperties ofhigh strength concrete subject to short-term loadsrdquo Journal ofthe American Concrete Institute vol 78 no 3 pp 171ndash178 1981

[21] J E Cook ldquo10000 psi concreterdquo Concrete International vol 11pp 67ndash75 1989

[22] A S Malaikah ldquoA proposed relationship for the modulus ofelasticity of high strength concrete using local materials inRiyadhrdquo Journal of King Saud UniversitymdashEngineering Sciencesvol 17 pp 1ndash11 2005

[23] A Mokhtarzadeh and C French ldquoMechanical properties ofhigh-strength concrete with consideration for precast applica-tionsrdquo ACI Materials Journal vol 97 no 2 pp 136ndash147 2000

[24] DVandergrift Jr andA K Schindler ldquoThe effect of test cylindersize on the compressive strength of sulfur capped concretespecimensrdquo Tech Rep IR-06-01 Highway Research Centerand Department of Civil Engineering at Auburn UniversityAuburn Ala USA 2006

[25] ASTM International ldquoStandard test method for compressivestrength of cylindrical concrete specimensrdquo ASTM C39 ASTMInternational West Conshohocken Pa USA 2014

[26] ASTM ldquoStandard test method for pulse velocity throughconcreterdquo ASTM C597 ASTM International 1997

[27] N J CarinoW F Guthrie E S Lagergren and G MMullingsldquoEffects of testing variables on the strength of high-strength(90MPa) concrete cylindersrdquo in High-Performance ConcreteV M Malhotra Ed SP-149 pp 589ndash632 American ConcreteInstitute Farmington Hills Mich USA 1994

[28] ACI ldquoGuide for evaluation of strength test results of concrete(ACI 214R-11)rdquo ASTM C214 American Concrete InstituteFarmington Hills Mich USA 2011

[29] ACI Committee 228 ldquoNondestructive test methods for evalua-tion of concrete in structuresrdquo ReportACI 2282R-98AmericanConcrete Institute Farmington Hills Mich USA 1998

[30] S A Issa M S Islam M A Issa A A Yousif and M A IssaldquoSpecimen and aggregate size effect on concrete compressivestrengthrdquo Cement Concrete and Aggregates vol 22 no 2 pp103ndash115 2000

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

12 Advances in Materials Science and Engineering

[13] S Popovics ldquoVerification of relationships between mechanicalproperties of concrete-like materialsrdquoMaterials and Structuresvol 8 no 3 pp 183ndash191 1975

[14] ASTM C191 Standard Practice for Making and Curing ConcreteTest Specimens in the Laboratory ASTM 2014

[15] ASTM ldquoStandard practice for making and curing concrete testspecimen in the fieldrdquo ASTM C31 ASTM International 2012

[16] ASTM International ldquoStandard test method for fundamentaltransverse longitudinal and torsional resonant frequencies ofconcrete specimensrdquo ASTM C215 ASTM International WestConshohocken Pa USA 2002

[17] P-C Aitcin and P K Mehta ldquoEffect of coarse-aggregate char-acteristics on mechanical properties of high-strength concreterdquoACI Materials Journal vol 87 no 2 pp 103ndash107 1990

[18] P-C Aitcin B Miao W D Cook and D Mitchell ldquoEffectsof size and curing on cylinder compressive strength of normaland high-strength concretesrdquo ACIMaterials Journal vol 91 pp349ndash354 1994

[19] P M Carrasquillo and R L Carrasquillo ldquoEvaluation of the useof current concrete practice in the production of high strengthconcreterdquo ACI Materials Journal vol 85 no 1 pp 49ndash54 1988

[20] R L Carrasquillo A H Nilson and F O Slate ldquoProperties ofhigh strength concrete subject to short-term loadsrdquo Journal ofthe American Concrete Institute vol 78 no 3 pp 171ndash178 1981

[21] J E Cook ldquo10000 psi concreterdquo Concrete International vol 11pp 67ndash75 1989

[22] A S Malaikah ldquoA proposed relationship for the modulus ofelasticity of high strength concrete using local materials inRiyadhrdquo Journal of King Saud UniversitymdashEngineering Sciencesvol 17 pp 1ndash11 2005

[23] A Mokhtarzadeh and C French ldquoMechanical properties ofhigh-strength concrete with consideration for precast applica-tionsrdquo ACI Materials Journal vol 97 no 2 pp 136ndash147 2000

[24] DVandergrift Jr andA K Schindler ldquoThe effect of test cylindersize on the compressive strength of sulfur capped concretespecimensrdquo Tech Rep IR-06-01 Highway Research Centerand Department of Civil Engineering at Auburn UniversityAuburn Ala USA 2006

[25] ASTM International ldquoStandard test method for compressivestrength of cylindrical concrete specimensrdquo ASTM C39 ASTMInternational West Conshohocken Pa USA 2014

[26] ASTM ldquoStandard test method for pulse velocity throughconcreterdquo ASTM C597 ASTM International 1997

[27] N J CarinoW F Guthrie E S Lagergren and G MMullingsldquoEffects of testing variables on the strength of high-strength(90MPa) concrete cylindersrdquo in High-Performance ConcreteV M Malhotra Ed SP-149 pp 589ndash632 American ConcreteInstitute Farmington Hills Mich USA 1994

[28] ACI ldquoGuide for evaluation of strength test results of concrete(ACI 214R-11)rdquo ASTM C214 American Concrete InstituteFarmington Hills Mich USA 2011

[29] ACI Committee 228 ldquoNondestructive test methods for evalua-tion of concrete in structuresrdquo ReportACI 2282R-98AmericanConcrete Institute Farmington Hills Mich USA 1998

[30] S A Issa M S Islam M A Issa A A Yousif and M A IssaldquoSpecimen and aggregate size effect on concrete compressivestrengthrdquo Cement Concrete and Aggregates vol 22 no 2 pp103ndash115 2000

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