7
ACI Materials Journal/September-October 2009 1 A CI MATERIALS J OURNAL TECHNI CAL PAPER  ACI Materials Journal , V. 106, No. 5, September-October 2009. MS No. M-2008-005 received January 3, 2008, and reviewed under Institute publication policies . Copyright © 2009, American Concrete Institute. All rights reserved, includin g the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including authors’ closure, if any, will be published in the July-August 2010  ACI Materials Journal if the discussion is received by April 1, 2010.  A comprehensive experimental program was undertaken to determine the short-term mechanical properties of high-strength concrete (HSC). Modulus of rupture beams and two different sizes of concrete cylinders with three different target compressive strengths ranging from 10 to 18 ksi (69 to 124 MPa) were subjected to three different curing methods and durations. Test results were combined with data from the literature to improve predictive equations for the elastic modulus and modulus of rupture of HSC. Of the three different curing methods, cylinders moist-cured for 7 days exhibited the highest compressive strengths at ages of 28 and 56 days. In contrast, 1-day heat curing generally resulted in the lowest compressive strength. The study shows that a Poisson’s ratio of 0.2 can be adequately used for HSC. Keywords: compressive strength; elastic modulus; high-strength concrete; modulus of rupture; Poisson’s ratio. INTRODUCTION The development of high-strength concrete (HSC) has led to more efficient design of buildings and bridges, with shallower members and longer spans. Although some design specifications have addressed the use of HSC, many have implicitly or explicitly placed restrictions on its use, primarily because of limited research data. 1 For example, the American Association of Highway and Transportation Officials (AASHTO) LRFD Bridge Design Specifications 2 limits its applicability to concrete compressive strength of 10 ksi (69 MPa) unless physical tests are conducted. Furthermore, many design provisions in both ACI 318-05 3 and AASHTO-LRFD 2 are based on test data obtained from specimens with compressive strengths up to 6 ksi (41 MPa) and, therefore, do not accurately reflect the mechanical properties of HSC. In the late 1970s, Carrasquillo et al. 4 tested specimens from three concrete mixtures with 53-day compressive strengths ranging from 4.6 to 11.1 ksi (31.7 to 76.5 MPa). Some of the specimens were moist-cured for 7 days and were then allowed to dry until tested at an age of 28 days. Others were moist-cured for 28 days and then allowed to dry until tested at an age of 95 days. The control group was moist- cured until 2 hours prior to testing. The data suggested that drying of HSC cylinders resulted in a lower compressive strength and modulus of rupture, in contrast to the normal- strength concrete (NSC). The reduction in the modulus of rupture was more significant than that of the compressive strength. The study also revealed that the compressive strength of 6 x 12 in. (150 x 300 mm) cylinders was, on average, approximately 90% of that of the 4 x 8 in. (100 x 200 mm) cylinders, irrespective of the compressive strength or the age at testing. Carrasquillo et al. 4 then proposed equations for both modulus of elasticity and modulus of rupture of HSC, which were later included in the ACI 363R-92 report. 5 The Strategic Highway Research Program (SHRP) of the early 1990s also focused on the mechanical properties of high-performance concrete (HPC), with some specimens referred to as “very high strength,” with 28-day compressive strengths ranging from 8 to 13.4 ksi (55 to 92 MPa). 6 The study found that the ratio of the compressive strength of the 6 x 12 in. (150 x 300 mm) cylinders to that of the 4 x 8 in. (100 x 200 mm) cylinders ranged from 0.91 to 0.98, depending on the type of coarse aggregates used. 6 The study also determined that the proposed equation of Carrasquillo et al. 4 (and ACI 363R-92 5 ) underestimated the elastic modulus of HSC. With regards to the modulus of rupture, the study showed that at the design age, the ratio of the observed value to that predicted by ACI 318-05 3 was 1.06 for concrete made with fly ash and 1.15 for concrete made with silica fume. Comparing the measured values to those predicted by Carrasquillo et al. 4 (and ACI 363R-92 5 ), the ratio was as low as 0.686. Mokhtarzadeh and French 7 studied 142 concrete mixtures with 28-day compressive strengths ranging from 8 to 18.6 ksi (55 to 128 MPa). Their data showed the ACI 318-05 3 equation to overestimate the elastic modulus of HSC, whereas the ACI 363R-92 5 equation was found more favorable. Also, the ACI 363R-92 5 equation for the modulus of rupture was found acceptable for the moist-cured specimens, whereas the modulus of rupture of the heat-cured specimens fell in between the values predicted by the ACI 363R-92 5 and ACI 318-05 3 equations. The study proposed a new modulus of rupture equation with a coefficient of 9.3 to be used instead of the 7.5 in the ACI 318-05 3 equation. Légeron and Paultre 8 reported that curing conditions significantly affected the measured value of the modulus of rupture. They also compiled data from the literature and proposed predictive equations for the minimum, average, and maximum values of the modulus of rupture. They suggested that the minimum values be used for service limit states to control deflections and cracking, whereas the maximum values should be used for the ultimate limit state to ensure ductility of flexural members. Burg and Ost 9 found that the ratio of the moduli of rupture of moist-cured specimens to air-cured specimens ranged from 1.54 to 2.02. In the last few years, the AASHTO has addressed the need to expand the applicability of its LRFD Specifications 2 to HSC with a number of research projects conducted through the National Cooperative Highway Research Program (NCHRP). This paper reports on one of these projects (NCHRP 12-64), which focused on flexure and compression design provisions Title no. 106-M46 Short-T erm Mechanical Properties of High-Strength Concrete by Andrew Logan, Wonchang Choi, Amir Mirmiran, Sami Rizkalla, and Paul Zia

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ACI Materials Journal/September-October 2009 1

ACI MATERIALS JOURNAL TECHNICAL PAPER

 ACI Materials Journal, V. 106, No. 5, September-October 2009.MS No. M-2008-005 received January 3, 2008, and reviewed under Institute publication

policies. Copyright © 2009, American Concrete Institute. All rights reserved, including themaking of copies unless permission is obtained from the copyright proprietors. Pertinentdiscussion including authors’ closure, if any, will be published in the July-August 2010

 ACI Materials Journal if the discussion is received by April 1, 2010.

 A comprehensive experimental program was undertaken to determinethe short-term mechanical properties of high-strength concrete(HSC). Modulus of rupture beams and two different sizes of concrete cylinders with three different target compressive strengthsranging from 10 to 18 ksi (69 to 124 MPa) were subjected to threedifferent curing methods and durations. Test results were combined with data from the literature to improve predictive equations for the elastic modulus and modulus of rupture of HSC. Of the threedifferent curing methods, cylinders moist-cured for 7 days exhibited the highest compressive strengths at ages of 28 and 56 days. Incontrast, 1-day heat curing generally resulted in the lowest compressive strength. The study shows that a Poisson’s ratio of 0.2can be adequately used for HSC.

Keywords: compressive strength; elastic modulus; high-strength concrete;modulus of rupture; Poisson’s ratio.

INTRODUCTIONThe development of high-strength concrete (HSC) has led

to more efficient design of buildings and bridges, with shallowermembers and longer spans. Although some design specificationshave addressed the use of HSC, many have implicitly orexplicitly placed restrictions on its use, primarily becauseof limited research data.1 For example, the American Associationof Highway and Transportation Officials (AASHTO) LRFDBridge Design Specifications2 limits its applicability toconcrete compressive strength of 10 ksi (69 MPa) unlessphysical tests are conducted. Furthermore, many designprovisions in both ACI 318-053 and AASHTO-LRFD2 arebased on test data obtained from specimens with compressivestrengths up to 6 ksi (41 MPa) and, therefore, do not accuratelyreflect the mechanical properties of HSC.

In the late 1970s, Carrasquillo et al.4 tested specimensfrom three concrete mixtures with 53-day compressivestrengths ranging from 4.6 to 11.1 ksi (31.7 to 76.5 MPa).Some of the specimens were moist-cured for 7 days and werethen allowed to dry until tested at an age of 28 days. Otherswere moist-cured for 28 days and then allowed to dry untiltested at an age of 95 days. The control group was moist-cured until 2 hours prior to testing. The data suggested thatdrying of HSC cylinders resulted in a lower compressivestrength and modulus of rupture, in contrast to the normal-strength concrete (NSC). The reduction in the modulus of rupture was more significant than that of the compressivestrength. The study also revealed that the compressivestrength of 6 x 12 in. (150 x 300 mm) cylinders was, onaverage, approximately 90% of that of the 4 x 8 in. (100 x200 mm) cylinders, irrespective of the compressive strengthor the age at testing. Carrasquillo et al.4 then proposed equationsfor both modulus of elasticity and modulus of rupture of HSC,which were later included in the ACI 363R-92 report.5

The Strategic Highway Research Program (SHRP) of theearly 1990s also focused on the mechanical properties of 

high-performance concrete (HPC), with some specimensreferred to as “very high strength,” with 28-day compressivestrengths ranging from 8 to 13.4 ksi (55 to 92 MPa).6 Thestudy found that the ratio of the compressive strength of the6 x 12 in. (150 x 300 mm) cylinders to that of the 4 x 8 in.(100 x 200 mm) cylinders ranged from 0.91 to 0.98,depending on the type of coarse aggregates used.6 The studyalso determined that the proposed equation of Carrasquillo etal.4 (and ACI 363R-925) underestimated the elastic modulusof HSC. With regards to the modulus of rupture, the studyshowed that at the design age, the ratio of the observed value

to that predicted by ACI 318-053

was 1.06 for concrete madewith fly ash and 1.15 for concrete made with silica fume.Comparing the measured values to those predicted byCarrasquillo et al.4 (and ACI 363R-925), the ratio was aslow as 0.686.

Mokhtarzadeh and French7 studied 142 concrete mixtureswith 28-day compressive strengths ranging from 8 to 18.6 ksi(55 to 128 MPa). Their data showed the ACI 318-053 equationto overestimate the elastic modulus of HSC, whereas theACI 363R-925 equation was found more favorable. Also, theACI 363R-925 equation for the modulus of rupture wasfound acceptable for the moist-cured specimens, whereas themodulus of rupture of the heat-cured specimens fell inbetween the values predicted by the ACI 363R-925 and

ACI 318-053 equations. The study proposed a new modulusof rupture equation with a coefficient of 9.3 to be usedinstead of the 7.5 in the ACI 318-053 equation.

Légeron and Paultre8 reported that curing conditionssignificantly affected the measured value of the modulus of rupture. They also compiled data from the literature andproposed predictive equations for the minimum, average,and maximum values of the modulus of rupture. Theysuggested that the minimum values be used for service limitstates to control deflections and cracking, whereas themaximum values should be used for the ultimate limit stateto ensure ductility of flexural members. Burg and Ost9 foundthat the ratio of the moduli of rupture of moist-cured specimens

to air-cured specimens ranged from 1.54 to 2.02.In the last few years, the AASHTO has addressed the needto expand the applicability of its LRFD Specifications2 to HSCwith a number of research projects conducted through theNational Cooperative Highway Research Program (NCHRP).This paper reports on one of these projects (NCHRP 12-64),which focused on flexure and compression design provisions

Title no. 106-M46

Short-Term Mechanical Properties of High-Strength

Concrete

by Andrew Logan, Wonchang Choi, Amir Mirmiran, Sami Rizkalla, and Paul Zia

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ACI Materials Journal/September-October 20092

the trial batches and the selected mixture proportions can befound elsewhere.11

Specimen preparation and curing proceduresConcrete was batched in a ready mixed concrete plant

using commercial production procedures. The 4 x 8 in.(100 x 200 mm) and 6 x 12 in. (150 x 300 mm) cylinderswere used for the compressive strength and elastic modulusof concrete, and 6 x 6 x 20 in. (150 x 150 x 510 mm) beamswere used for the modulus of rupture. Cylinders were cast inplastic molds, and the beams were cast in steel molds. The spec-imens were made according to AASHTO T23 (ASTM C31)(ACI 363.2R-9812). Table 2 shows the test matrix. Testing ageswere 1, 7, 14, 28, and 56 days. On each testing day, two of the4 x 8 in. (100 x 200 mm) cylinders were used to determine theelastic modulus before being tested to failure.

The specimens were subjected to one of the threefollowing curing conditions: 1) 7-day moist curing to representtypical curing procedures for reinforced concrete members;2) 1-day heat curing similar to that used in precast concreteplants for prestressed structural members; and 3) continualmoist curing until the day of testing according to the ASTMstandards used for the purposes of quality control and certifyingthe compressive strength of concrete in the industry.12 The heat-cured specimens were placed in a chamber with a heatingregime ramping up to a constant temperature of 150 to 160° F(66 to 71°C), and back to room temperature in 24 hours.

Testing procedures and instrumentationsThe cylinders were ground at both ends before testing to

remove any surface irregularity and to also ensure that theends would be perpendicular to the sides of the specimen.Compression tests were performed using a Universal testingmachine for both the 4 x 8 in. (100 x 200 mm) and the 6 x 12 in.(150 x 300 mm) cylinders. Tests followed ASHTO T22(ASTM C39) at a loading rate of approximately 0.04 ksi/s(0.28 MPa/s). The loading rate was selected at the higher endof the standard range to avoid prolonged loading, which couldpossibly cause extensive microcracking in concrete cylinders.

The elastic modulus was determined using the 4 x 8 in.(100 x 200 mm) concrete cylinders and in accordance withASTM C469. Deflections were measured using potentiometers

Andrew Logan works for a civil engineering firm in Leesburg, FL. He received his

 BS and MS in civil engineering from the University of Florida, Gainesville, FL, and 

  North Carolina State University, Raleigh, NC, respectively. His research interests

include short-term mechanical properties of high-strength concrete.

Wonchang Choi received his PhD from North Carolina State University, and his BS

and MS in civil engineering from Hongik University, Seoul, Korea. His research interests

include the flexural behavior of prestressed girders using high-strength concrete.

Amir Mirmiran , FACI, is Professor and Interim Dean of the College of Engineering

and Computing at Florida International University, Miami, FL. He is a member of 

 ACI Committees 440, Fiber Reinforced Polymer Reinforcement, and E803, Faculty

  Network Coordinating Committee, and Joint ACI-ASCE Committee 343, Concrete

 Bridge Design. His research interests include high-strength concrete and advanced composite materials for bridge applications.

Sami Rizkalla , FACI, is Distinguished Professor of Civil Engineering and Construction at 

 North Carolina State University. He serves as Director of the Constructed Facilities

 Laboratory as well as the NSF I/UCR Center on Repair of Structures and Bridges at 

 NC State. He is a member of ACI Committees 440, Fiber Reinforced Polymer Reinforcement,

and E803, Faculty Network Coordinating Committee, and Joint ASI-ASCE Committees

423, Prestressed Concrete, and 550, Precast Concrete Structures.

 ACI Honorary Member Paul Zia is a Distinguished University Professor Emeritus at 

 NC State University. He is an ACI Past President and is currently a member of the

Concrete Research Council, ACI Committee 363, High-Strength Concrete; Concrete

 Research Council; and Joint ACI-ASCE Committees 423, Prestressed Concrete; and 

445, Shear and Torsion.

Table 1—Concrete mixture proportions

Materials

Target compressive strengths

10 ksi(69 MPa)

14 ksi(97 MPa)

18 ksi(124 MPa)

Cement (Type I/II), lb/yd3 (kg/m3) 703 (417) 703 (417) 935 (555)

Densified microsilica fume, lb/yd3 (kg/m3) 75 (44) 75 (44) 75 (44)

Fly ash, lb/yd3 (kg/m3) 192 (114) 192 (114) 50 (30)

Sand, lb/yd3 (kg/m3) 1055 (625) 1315 (780) 1240 (736)

Rock (diabase 78M), lb/yd3 (kg/m3)1830

(1085)1830

(1085)1830

(1085)

Water, lb/yd3 (kg/m3) 292 (173) 250 (148) 267 (158)

High-range water-reducing admixture

(HRWRA), oz/100 lb (mL/100 kg)* 17 (1110) 24 (1565) 36 (2345)

Retarding agent, oz/100 lb (mL/100 kg)* 3 (195) 3 (195) 3 (195)

w / cm 0.30 0.26 0.25

Average 28-day compressive strength of laboratory batch, ksi (MPa)

11.45(78.9)

14.37(99.1)

17.09(117.8)

*Ounces per 100 lb of cementitious materials (mL per 100 kg cementitious materials).

for HSC.10 As part of this project, an effort was made tocharacterize the short-term mechanical properties of HSC.

RESEARCH SIGNIFICANCE AND OBJECTIVESThe main objective of this study was to improve predictive

equations for short-term mechanical properties of HSC,including its elastic modulus, modulus of rupture, andPoisson’s ratio. The significance of this research is not onlyto improve the predictive equations, but also to enhance thetest database for HSC with three different target compressivestrengths, different specimen sizes, and different curingconditions. The database is especially significant because itis based on ready mixed concrete delivered from batchplants, and not laboratory-scale mixtures. Although notdirectly the focus of this paper, it is also important to notethat the specimens for short-term mechanical propertieswere made and tested side-by-side and as part of a larger testmatrix, which included reinforced concrete columns andbeams and prestressed girders.

EXPERIMENTAL PROGRAMMaterials and mixture design

Three different concrete mixtures with target compressivestrengths of 10, 14, and 18 ksi (69, 97, and 124 MPa) wereprepared using ready mixed concrete delivered from a batchplant. The mixture proportions were selected from a largenumber of trial laboratory batches and are shown in Table 1.The mixtures for the 10 and 14 ksi (69 and 97 MPa)compressive strengths were proportioned to exceed theirtarget values by 10 to 20%, assuming that there would be astrength reduction due to the large batch size and theincreased difficulty in maintaining quality control in truck-mixed batches. In both cases, however, as will be discussedlater, the compressive strengths of the truck-mixed batches wereapproximately the same as those of the laboratory batches.

The coarse aggregates were crushed stone quarried inButner, NC, with a nominal maximum size of 3/8 in. (9.5 mm).Manufactured sand made from the same type of rock was usedas fine aggregates because the lab mixtures had clearlyshown that it would increase the compressive strength of concrete. The cement was Type I/II. Additional details on

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ACI Materials Journal/September-October 2009 3

attached to two fixed rings (Fig. 1). Four vertical potentiometers

measured axial deflections, while two horizontal potentiometers

attached at midheight measured lateral dilation of concrete.

The apparatus consisted of two aluminum rings with screws

for attachment to the specimen. Prior to attaching the apparatus

to the specimen, the rings were joined by three aluminum bars.The spacing between the screws on the top ring and the

screws on the bottom ring when the aluminum bars were

attached was 5 in. (127 mm), which served as a gauge length

for calculating axial strains from the measured deformations.

The modulus of rupture beams were placed in the testing

frame, oriented in such a way that the specimen was turned

on its side with respect to its molded position, as specified in

ASTM C78 (Fig. 2). The load was applied using a hand

pump. The loading rate was controlled such that the stress at

the extreme bottom fiber of the beam would increase at a rate

of 0.15 ksi/s (1.03 MPa/s).

TEST RESULTS AND DISCUSSIONSCompressive strength

The compressive strengths for the first two concrete

mixtures exceeded their target values, whereas the thirdbatch failed to reach its target value (Table 1). The tests,however, still provided useful information for expanding andadding to the knowledge base on mechanical properties of HSC.

The effects of curing procedures on the compressivestrength measured from the 4 x 8 in. (100 x 200 mm) cylindersat 28 days are illustrated in Fig. 3. The 7-day moist-curedspecimens showed the highest compressive strengths at 28 daysin each of the three batches. The 1-day heat curing increasedstrength gain at an early age, but weakened it at later ages. Thisbehavior was attributed to rapid hydration, which causes the

structure of the cement paste to be more porous than whencement paste hydrates slowly. The higher porosity, in turn,leads to decreased strength. Although the majority of thestrength gain in heat-cured specimens occurred within thefirst few days, their strength continued to increase until 56 days,albeit at a slow rate. The average 28-day strength of the 7-daymoist-cured specimens were 1.17, 1.10, and 1.16 times those

of the heat-cured specimens for the 10, 14, and 18 ksi(69, 97, and 124 MPa) target strengths, respectively. Thecontinually moist-cured specimens exhibited a slightlylower strength, with failure closer to the surface, primarilybecause of the remaining moisture in the capillary pores.

Table 2—Description of test specimens for each target strength

Specimen Test type Curing method

Testing age (days)

Total1 7 14 28 56

4 x 8 in. (100 x 200 mm) cylinders Axial compression

7-day moist curing 3 3 3 3 3 15

1-day heat curing 3 3 3 3 3 15

Continual moist curing 3 3 6

Total number of 4 x 8 in. (100 x 200 mm) cylinders 36

6 x 12 in. (150 x 300 mm) cylinders Axial compression

7-day moist curing 3 3 6

1-day heat curing 3 3 6

Continual moist curing 3 3 6Total number of 6 x 12 in. (150 x 300 mm) cylinders 18

6 x 6 x 20 in. (150 x 150 x 510 mm) beams Modulus of rupture

7-day moist curing 3 3 3 3 3 15

1-day heat curing 3 3 3 3 3 15

Continual moist curing 3 3

Total number of 6 x 6 x 12 in. (150 x 150 x 510 mm) beams 33

Fig. 1—Fully instrumented 4 x 8 in. (100 x 200 mm)cylindrical specimen.

Fig. 2—Modulus of rupture test setup.

Fig. 3—Compressive strength of 4 x 8 in. (100 x 200 mm)cylinders at 28 days.

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4 ACI Materials Journal/September-October 2009

The strength gain of concrete over time is depicted in Fig. 4.

For the 10 and 14 ksi (69 and 97 MPa) target strengths, the heat-cured specimens reached approximately 90% of their 28-daystrength during the first day of curing. The specimens madefrom the 18 ksi (124 MPa) target strength concrete alsogained the majority of their 28-day strength in the first day,but at a lower rate. This was attributed to: 1) higher heat of hydration resulting from the larger cement content in themixture; and 2) the larger dose of high-range water-reducingadmixture in the mixture.

Elastic modulusThe current code equation in ACI 318-053 and the

AASHTO-LRFD2 for estimating the elastic modulus of concrete is as follows

(1)

where w is the unit weight of concrete, and  f c is the 28-daycompressive strength. ACI 363R-925 suggests the followingalternative equation

 E c = (40,000( f c )0.5 + 106)(wc /145)1.5 (psi)

 E c = (3320( f c )0.5 + 6900)(wc /2320)1.5 (MPa) (2)

 E c 33wc

1.5 f c psi =

 E c 0.043wc

1.5 f c MPa =

Figure 5 shows test results from this research project ascompared to the ACI 318-053 (AASHTO-LRFD2) and the

ACI 363R-925 equations. In the same figure, data byothers4,13-18 are also shown for comparison. The measuredvalues are generally in agreement with the predicted valuescalculated using the ACI 363R-925 equation, regardless of the curing method. The data also support the statement inACI 363R-925 that the ACI 318-053 (AASHTO-LRFD2) equa-tion consistently overestimates the elastic modulus for HSC.

A total of 4388 test data for elastic modulus, with concretestrengths between 3.7 to 24 ksi and unit weight between90 to 176 lbf, were collected from the literature19 (seeReference 20 for details). Based on the collected data, thefollowing equation for the elastic modulus of concrete withcompressive strength up to 18 ksi (124 MPa) is proposed20

 E c (ksi) = 310,000K 1[wc(kip/ft3)]2.5 × [ f c (ksi)]0.33

 E c (MPa) = 0.000035K 1[wc(kg/m3)]2.5 × [ f c (MPa)]0.33 (3)

where K 1 is the correction factor to account for the source of aggregates, which may be taken as 1.0 unless determined byphysical tests. The collected data, including results from thisstudy, are compared with the proposed equation in Fig. 6.The figure indicates that the collected data are still scattered,however, with an improved  R2 = 0.76. Figure 7 shows theprobability distribution of the modulus of elasticity data as afunction of the predicted over the measured value for the

Fig. 4—Strength gain over time expressed as percentageof 28-day strength.

Fig. 5—Elastic modulus versus compressive strength. (Data from References 4 and 13 to 18).

Fig. 6—Predictions of over 4400 data points using proposed equation.

Fig. 7—Statistical comparisons for modulus of elasticity.

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ACI Materials Journal/September-October 2009 5

three different equations using statistical analysis. Thefigure shows that the ACI 318-053 (AASHTO-LRFD2)equation overestimates the elastic modulus. Althoughthe ACI 363R-925 equation has the lowest standard deviationamong the three predictions, its predictions are slightlyconservative. The proposed equation, on the other hand,has the best normal distribution, although its standard deviationis slightly higher than that of the ACI 363R-925 equation.

Poisson’s ratioFollowing ASTM C469,12 Poisson’s ratio was determined

using the measured lateral and axial strains of the cylinderstested in compression, based on two points on the stress-strain curve. The lower point was defined by an axial strainvalue of 0.00005, while the upper point was defined by anaxial stress value of 40% of the peak stress. The measuredPoisson’s ratios for concrete had large variations, as shownin Fig. 8. Test results do not show an apparent correlationbetween the Poisson’s ratio and the measured compressive

strength. In addition, it was observed that curing proceduresand age of concrete had little or no effect on the Poisson’sratio. The average Poisson’s ratio for all tested cylinders is0.17 with a standard deviation of 0.07. The generallyaccepted range for the Poisson’s ratio of NSC is between0.15 and 0.25, while it is generally assumed to be 0.2 foranalysis.21 Test data from this project suggest that it isreasonable to use 0.2 as Poisson’s ratio for HSC up tocompressive strength of 18 ksi (124 MPa).

Modulus of ruptureEffect of curing methods on the modulus of rupture for the

three different target strengths are shown in Fig. 9. Testresults suggest that the modulus of rupture is significantlyaffected by curing conditions for all target strengths. Thetrend indicates that removal of the beam specimen after 7 daysfrom the curing tank causes a significant reduction of themodulus of rupture. Similarly, the 1-day heat-cured beamsshowed low values of the modulus of rupture due to thedryness after removal from the molds, which had preventedmoisture loss during the first day of curing. In both cases, thereduced modulus of rupture is attributed to the microcracksinitiated by drying shrinkage. The low permeability of theHSC is expected to cause differential shrinkage strainsacross the depth of the specimen due to the fact that themoisture trapped in the interior part of the specimens

cannot evaporate as quickly as the surface moisture. This

relative shrinkage difference causes microcracking of 

concrete. Therefore, the specimens that were moist-cured up

to the day of testing showed much higher modulus of rupture

than those cured differently.

Figure 10 shows test data from material study tested in

this program along with the data collected from the litera-

Fig. 8—Poisson’s ratio for various concrete strengths.

Fig. 9—Effect of curing process on modulus of rupture for concrete compressive strength: modulus of rupture versustime for (a) 19 ksi (69 MPa) target strength; (b) 14 ksi (97 MPatarget strength; and (c) 18 ksi (124 MPa) target strength.

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6 ACI Materials Journal/September-October 2009

ture.1,7,13,16,19 Two equations for modulus of rupture givenin Section 5.4.2.6 of the current AASHTO-LRFD2 are alsoshown in the figure. Some of the tests results correspondbetter to the current upper bound of the AASHTO-LRFD.2

This is mainly due to the curing condition and moisturecontent of the specimens. Test results suggest that the

current lower bound of the AASHTO-LRFD

2

overestimatesthe modulus of rupture for HSC. A better predictive equation,which is the lower bound of the test data, f r = 0.19 ( f r = 0.5 ), is proposed for HSC up to 18 ksi (124 MPa).

CONCLUSIONS AND RECOMMENDATIONSA total of thirty-six 4 x 8 in. (100 x 200 mm) cylinders,

eighteen 6 x 12 in. (150 x 300 mm) cylinders, and thirty-three 6 x 6 x 20 in. (150 x 150 x 510 mm) beams wereprepared with three different target compressive strengths of 10, 14, and 18 ksi (69, 97, and 124 MPa) using ready mixedconcrete delivered from a batch plant. Three different curingregimes were used; 1-day heat curing, 7-day moist curing,and continuous moist curing until the day of testing. The

specimens were tested to determine short-term mechanicalproperties of HSC. Based on the test data from this researchcombined with those from the literature, the followingconclusions can be drawn:

• Of the three different curing methods, cylinders with 7-daymoist curing exhibited the highest compressive strengths atages of 28 and 56 days. In contrast, 1-day heat curinggenerally resulted in the lowest strength. Cylindersmoist-cured up to the day of testing resulted in strengthsslightly lower strengths than their counterparts with 7-daymoist-curing. The reduction in the strength may beattributed to the differences in the internal moistureconditions of the concrete at the time of testing.

• Comparisons of the strength gain under various curing

regimes showed that moist curing of HSC beyond 7 dayswould not result in any significant increase in strength.This is believed to be due to the low permeability of HSCand the short time required for the capillary pores of HSCto be blocked.

• The equation specified by the AASHTO-LRFD2 overesti-mated the elastic modulus for all specimens. Based on thetests’ results and the collected data in the literature, a newequation for the elastic modulus of concrete with compres-sive strength up to 18 ksi (124 MPa) was proposed.

• A Poisson’s ratio of 0.2 specified by the AASHTO-LRFD2 can adequately be used for HSC up to 18 ksi

 f c ksi   f c MPa  

(124 MPa).

• The modulus of rupture was reduced significantly forspecimens removed from their sealed or moist environmentsand allowed to dry. The continuously moist-curedspecimens developed modulus of rupture values, insome cases twice as much as those obtained from the7-day moist-cured specimens.

• The upper bound equation specified by the AASHTO-LRFD2 provided a good estimate of the modulus of rupture for the continuously moist-cured specimens,

but overestimated the modulus of rupture for the 1-dayheat-cured and 7-day moist-cured specimens. Thelower bound equation specified by the AASHTO-LRFD2 overestimated the measured modulus of rupturefor 1-day heat-cured and 7-day moist-cured specimens.Based on the test results, a better predictive equation,lower bound of the test data, was proposed for HSC upto 18 ksi (124 MPa).

ACKNOWLEDGMENTSThis study was sponsored by the American Association of State Highway

and Transportation Officials in cooperation with the Federal Highway

Administration, and was conducted as part of the National CooperativeHighway Research Program Project 12-64, which is administered by theTransportation Research Board of the National Research Council, Senior

Program Officer D. Beal. The experiments were carried out at theConstructed Facilities Laboratory at North Carolina State University. Thecontributions of consultants—H. Russell of Henry Russell, Inc. and R. Mast

of Berger/ABAM Engineers, Inc.—are greatly acknowledged. The assistance of Ready Mixed Concrete, Boral Material Technologies, Degussa Admixtures,Roanoke Cement, Carolina SunRock , and Elkem are also greatly appreciated.

Z. Wu, S. Kim, and H. C. Mertol provided significant assistance during allaspects of this research program. The findings and opinions expressed inthis paper, however, are those of the authors alone and not necessarily theviews of the sponsoring agency.

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