Mechanical Properties Of Hpc fc27

ACI STRUCTURAL JOURNAL

TECHNICAL PAPER

Title no. 101-S45

Mechanical Properties of High-Strength Concrete for Prestressed by Mary Beth D. Hueste, Praveen Chompreda, David Trejo, Daren B. H. Cline, and Peter B. Keating High-strength concrete (HSC) is widely used in prestressed concrete bridges. Current design provisions for prestressed concrete bridge structures, such as the AASHTO LRFD specifications, however, were developed based on mechanical properties of normalstrength concrete (NSC). As a first step toward evaluating the applicability of current AASHTO design provisions for HSC prestressed bridge , statistical parameters for the mechanical properties of plant-produced HSC were determined. In addition, prediction equations relating mechanical properties with the compressive strength were evaluated. HSC samples were collected in the field from precasters in Texas and tested in the laboratory at different ages for compressive strength, modulus of rupture, splitting tensile strength, and modulus of elasticity. Statistical analyses were conducted to determine the probability distribution, bias factors (actual mean-to-specified design ratios), and coefficients of variation for each mechanical property. It was found that for each mechanical property, the mean values are not significantly different among the considered factors (precaster, age, specified strength class) or a combination of these factors, regardless of the specified design compressive strength. Overall, the 28-day bias factors (mean-to-nominal ratios) decrease with an increase in specified design compressive strength due to the relative uniformity of mixture proportions provided for the specified strength range. Nevertheless, the 28-day bias factors for compressive strength are greater than those used for the calibration of the AASHTO LRFD specifications. With few exceptions, the coefficients of variation were uniform for each mechanical property. In addition, the coefficients of variation for the compressive strength and splitting tensile strength of HSC in this study are lower than those for NSC used in the development of the AASHTO LRFD specifications. Keywords: compressive strength; high-strength concrete; modulus of elasticity; prestressed concrete; splitting tensile strength.

INTRODUCTION Currently, high-strength concrete (HSC) is widely used in bridges, buildings, and other structures. In prestressed bridge structures, many studies have shown that using HSC can allow engineers to design bridges with longer spans for a given girder cross section and reduce the number of girders per span by increasing the girder spacings (Zia, Schemmel, and Tallman 1989; Durning and Rear 1993; Russell 1994). Increases in girder spacings and bridge spans using standard girder cross sections can lead to substantial costs savings for bridges. However, design provisions for prestressed concrete in current codes, such as the AASHTO standard specifications (1999) and AASHTO LRFD specifications (2000), are primarily based on empirical relationships for mechanical properties developed from testing normalstrength concrete (NSC) and the corresponding statistical parameters. This creates concern that the design may not be conservative when equations developed with NSC are applied to HSC member design. In contrast, the equations may be too conservative such that the advantages of using HSC are ACI Structural Journal/July-August 2004

not fully realized. Thus, research is needed to determine statistically significant relationships between the specified design compressive strength (specified design fc′ ) of HSC and the corresponding splitting tensile strength ft , modulus of rupture (MOR), and modulus of elasticity (MOE). In addition, statistical parameters for each mechanical property are needed to evaluate the structural reliability of HSC prestressed relative to NSC prestressed . The overall objective of the research is to evaluate potential modifications to the current AASHTO LRFD specifications for HSC prestressed beams. Potential refinements in ultimate load design would most likely be achieved through modification of the resistance factors, while refinements in service load design may be accomplished through the adjustment of the allowable stresses. The portion of the study reported in this paper focuses on determining representative mechanical property relationships and corresponding statistical parameters for HSC produced for prestressed bridge by precasters in Texas. RESEARCH SIGNIFICANCE Current design provisions for prestressed concrete bridge structures, such as the AASHTO LRFD specifications, were developed based on mechanical properties of NSC. The data and recommended prediction equations determined experimentally in this study may be used to refine specifications for HSC used for prestressed bridge in Texas and possibly in other states. Moreover, this information can be used in future developments of probability-based design provisions, such as the AASHTO LRFD specifications, for design of HSC prestressed for both ultimate and service load design limit states. EXPERIMENTAL PROGRAM, MATERIALS, AND TEST PROCEDURES HSC samples were collected from three selected precasters in Texas. These precasters are considered to be representative of the eight precasters in Texas that produce prestressed bridge at the time of this study. As much as possible, precasters were selected to cover different geographical locations in Texas, coarse aggregate types (crushed river gravel and crushed limestone), and precaster production capacities. For each precaster, concrete samples were categorized by specified design fc′ into three classes—41 ± 7 MPa (6000 ± 1000 psi), 55 ± 7 MPa (8000 ± 1000 psi), ACI Structural Journal, V. 101, No. 4, July-August 2004. MS No. 02-367 received October 3, 2002, and reviewed under Institute publication policies. Copyright © 2004, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published in the May-June 2005 ACI Structural Journal if the discussion is received by January 1, 2005.

457

ACI member Mary Beth D. Hueste is an assistant professor in the Department of Civil Engineering at Texas A&M University, College Station, Tex., and a researcher with the Texas Transportation Institute. She is a member of ACI Committees 374, Performance-Based Seismic Design of Concrete Buildings, and 375, PerformanceBased Design of Concrete Buildings for Wind Loads. Her research interests include studying the behavior of reinforced and prestressed concrete structures using experimental and analytical techniques, with a focus on the design of earthquake-resistant structures. Praveen Chompreda is a PhD student at the University of Michigan, Ann Arbor, Mich. He received his MS from Texas A&M University. His research interests include high-strength concrete and behavior of prestressed concrete . ACI member David Trejo is an assistant professor in the Department of Civil Engineering at Texas A&M University and is a researcher with the Texas Transportation Institute. He is a member of ACI Committees 222, Corrosion of Metals in Concrete; 229, Controlled Low Strength Materials; 236, Materials Science of Concrete; and 365, Service Life Prediction. His research interests include studying the mechanical and physical characteristics and deterioration of reinforced concrete structures. Daren B. H. Cline is a professor in the Department of Statistics at Texas A&M University. His research interests include stochastic processes and time series. Peter B. Keating is an associate professor in the Department of Civil Engineering at Texas A&M University and is a researcher with the Texas Transportation Institute. His research interests include fatigue and fracture of steel structures and the material behavior of concrete.

Table 1—Summary of plant-produced concrete sample collections

Precaster ID A

B

41 MPa (6000 psi)

55 MPa (8000 psi)

69 MPa (10,000 psi)

Collection no. 1

Specified fc′, MPa (psi) 40.7 (5909)

Specified fc′, MPa (psi) 52.0 (7540)

Specified fc′, MPa (psi) 63.4 (9196)

2

43.1 (6250)

1

45.0 (6525) 45.5 and 45.0 (6598 and 6525) 42.6 (6178)

2 1

C

2

44.8 (6500)

59.1 and 58.5 (8573 and 8484) 61.8 (8963) 55.1 (8000)

61.9 (8983)

55.1 (8000)

61.9 (8983)

55.8 (8102)

63.1 (9152)

48.9 and 51.5 62.0 (9000) (7099 and 7469)

Note: 18 collections × two batches per collection × three test ages = 108 data points per mechanical property tested. Test results from three specimens are used to calculate mean and standard deviation for fc′ , ft , and MOR; two specimens are used for MOE.

and 69 ± 7 MPa (10,000 ± 1000 psi)—so that effects of the specified design fc′ on other concrete properties could be observed. For each strength class, two collections were made from each precaster on different days to capture variability within mixtures used by a precaster for the same specified design fc′ . Two sets of concrete samples were made during each collection, sampling from two different batches of the same mixture on the same collection date, to for variability in the mixing and batching procedures. In the majority of cases, the concrete evaluated in the research program was obtained directly from the precast plants during casting of prestressed bridge . For three collections, however, the concrete was specifically produced for the research study because these particular specified design strengths were not available from the precasters during the time frame of this program. In these cases, the precaster produced their standard concrete mixtures for the given specified design fc′ . Type III high-early-strength portland cement was used for all concrete mixtures sampled in this study. Table 1 provides a summary of the specified design fc′ of the bridge girders for which concrete was being produced during each sample collection. Several collections have two specified fc′ values listed, indicating that samples for the full set had to be collected at two different times. In these cases, fc′ 458

was tested for both collections to ensure that appropriate fc′ data were available when evaluating the prediction relationships. Specimens were made in the field using 150 x 150 x 500 mm (6 x 6 x 20 in.) steel prism molds for the MOR and 100 x 200 mm (4 x 8 in.) plastic cylindrical molds for fc′, ft , and MOE. All samples were collected following the procedure outlined in ASTM C 31-98 (ASTM 1998a) with the exception that the temperature was not controlled until the samples were transported to the laboratory. After casting, all cylinders in plastic molds were covered with plastic lids. All other specimens were covered with plastic sheets to prevent moisture loss from evaporation. In addition, they were covered with wet burlap and plastic tarp to supply the moisture during the first 24 h. Approximately 24 h after casting, the specimens were transported back to the laboratory for final curing and testing. During transportation, moisture loss was prevented by means of wet burlap covers and plastic tarps. Immediately on arrival at the laboratory, specimens were removed from the molds, labeled, and stored in a moist room for final curing. The temperature and humidity in the moist room were controlled at 23 ± 2 °C (73 ± 3 °F) and greater than 98%, respectively. All mechanical properties relevant to prestressed concrete design were determined experimentally in the laboratory with the exception of the 1-day fc′, which was obtained from the precasters who typically tested samples within 24 h of casting to that the required release strength was achieved. In the laboratory, compressive strength testing followed ASTM C 39-99 procedures (ASTM 1999), MOR testing followed ASTM C 78-94 procedures (ASTM 1994a), ft testing followed ASTM C 496-96 procedures (ASTM 1996), and MOE testing followed ASTM C 469-94 procedures (ASTM 1994b). Laboratory tests were performed at the age of 7, 28, and 56 days for each of these four mechanical properties. Creep and shrinkage are also being monitored for three sample collections from each precaster (one set from each strength class) and these long-term properties will be reported when the tests are completed. ANALYSIS OF DATA Statistical analysis Statistical parameters including mean values, coefficients of variation, and bias factors were determined for each mechanical property. This section discusses the determination of the probability distribution functions, the analysis of variance, and each statistical parameter. Probability distribution function—The probability distribution function for each mechanical property was determined using a normal quantile plot. For this analysis, no specific test of hypothesis (with significance level) was conducted—rather, the purpose was to the use of standard assumptions of normal or lognormal for the distribution functions. Analysis of variance—The analysis of variance was used to determine the effect of several factors on the measured response. The three factors of interest were precasters, specified design fc′, and ages of concrete at testing, along with combinations of these factors. The measured responses that were investigated include the mean and coefficient of variation (CV) within a batch, the CV within a mixture, and the mean of the logarithm of batch averages. The significance level p-value used in this study is 0.05; therefore, a p-value less than 0.05 is considered an indication of a significant effect from a particular factor or group of factors. Details of this procedure can be found in many statistics textbooks (Milton ACI Structural Journal/July-August 2004

and Arnold 1995; Triola 1986). SAS statistical analysis software was used for this analysis (SAS Institute Inc. 1999). Mean—Three types of sample mean, or average, values were calculated: batch average, mixture average, and average of mixture averages. • The batch average is the average of the test results from the specimens within the same batch. Test results from three specimens are used to calculate the batch average for fc′, ft , and MOR; and two specimens are used for the MOE. The batch average is considered to be the primary response variable because the material properties are usually obtained or verified from tests of samples within the same concrete batch. Batch averages are used in the calculation of the CV within a mixture; • The mixture average is calculated by averaging two batch averages from the same collection day. The two batches that are averaged have the same mixture proportion and specified design fc′. This mixture average value can be taken as an average strength of a prestressed beam because several batches are required to cast a beam; and • The average value of mixture averages was found across various categories such as precaster, age of concrete, or strength categories (based on specified fc′ ). It represents the strength characteristic in a particular group; for instance, compressive strength for Precaster A at the age of 28 days. Coefficient of variation—The CV is defined as the ratio of the standard deviation to the mean. It measures the relative variability of the data with respect to the mean. Four types of coefficients of variation are calculated: • The CV within a batch CVBatch is calculated from the test values of specimens in the same batch at the same age. Test results from three specimens are used to calculate the mean and standard deviation for fc′, ft , and MOR; and two specimens are used for the MOE. This CV captures the variation within a batch and any variation in test procedures; • The CV within a mixture CVMix is calculated from two batch average values from the same mixture collected on the same day. This CV indicates the consistency of the proportioning and mixing processes by measuring the variation between two batches; • The CV of mixture averages CVMixAvg is calculated from several mixture average values for a particular material property. This CV captures the variation of a mechanical property within a group, such as the variation among precasters; and • The CV of batch averages CVBatchAvg provides a measure of the relative variation in batch average values. Because the batch average value is considered to be the primary response variable of the analysis, this CV is the value that should be used in the determination of resistance parameters or other reliability studies. The statistical analysis, however, was performed for the mixture average values because the two batches within a mixture are not independent. Because the variation of the batch average is a combination of the variation of mixture average values and the variation within a mixture, the CVBatchAvg is calculated from the CVMix and CVMixAvg as CV BatchAve =

2

2

CV Mix + CV MixAvg

ACI Structural Journal/July-August 2004

(1)

Bias factor—The bias factor λ provides a measure of the difference between the actual and the expected strength or stiffness of the concrete. For each mechanical property, the bias factor is defined as the ratio of the mean to the nominal value as follows µ λ = -----RRn

(2)

where µR is the mean value of resistance that can be approximated from the sample mean X, and Rn is the specified design value of resistance. Rn is taken as the specified design fc′ when computing the bias factors for fc′. For other mechanical properties, Rn is the design value based on the relationship in the AASHTO LRFD specifications and the specified design fc′. Prediction equations The goodness of fit of various prediction equations that relate mechanical properties to the corresponding fc′ was evaluated. Evaluations were made based on the actual fc′ from tests and the corresponding specified design fc′ using a relative prediction error (RPE) as follows 1 RPE = --n

n

f′

∑  --f- – 1

2

(3)

i=1

where f is the experimental value of a mechanical property (MOR, ft, or MOE) from the test, and f ′ is the predicted value based on the corresponding fc′ (either actual or specified). RESULTS AND DISCUSSION Statistical analysis Probability distribution function—The normal quantile plot for the lognormal distribution of fc′ data followed a reasonably linear relationship (R = 0.99587). This relationship was slightly more linear than when the normal distribution is assumed. A constant CV is a frequent assumption for lognormally distributed data, whereas it is often assumed that normally distributed data has a constant standard deviation or variance. The use of CV in this analysis is convenient because it provides more information about the relative variation of the data than the use of standard deviation or variance. The constant CV assumption was evaluated in the analysis of variance. This analysis was also performed for MOE, ft, and MOR. The results are similar to the fc′ in that either a normal or a lognormal distribution may be reasonably used. All properties are assumed to follow lognormal distribution due to the convenience of using CV in the analysis. Analysis of variance—Table 2 summarizes the analyses of variance for fc′ , MOE, ft, and MOR. This table lists the p-values for each factor or group of factors, both for the means and for the coefficients of variation. The assumption of constant coefficients of variation was checked. As can be observed in Table 2, the CVBatch for the fc′ and the MOR are not significantly different at a 0.05 level for all ages, precasters and specified design fc′ classes. No interactions of these factors were significant. The CVBatch for the MOE and ft are significantly different among ages and precasters, respectively. The CVMix for all properties, except the MOE, is not significantly different at a 0.05 level for all factors and 459

Table 2—Summary of p-values fc′

ft

Modulus of elasticity

Factor

(1)

(2)

(3)

(1)

(2)

(3)

(1)

(2)

(3)

Modulus of rupture (1) (2) (3)

Precaster Age

0.28 0.15

0.62 0.73

0.45 0.65

0.12 0.05

0.30 0.72

0.54 0.00

0.01 0.43

0.13 0.35

0.81 0.63

0.56 0.30

0.05 0.28

0.77 0.12

Precaster age Class

0.90 0.18

0.98 0.39

0.79 0.97

0.17 0.51

0.02 0.04

0.22 0.99

0.17 0.55

0.58 0.65

0.95 0.93

0.22 0.12

0.26 0.46

0.40 0.90

Precaster class Age class

0.13 0.69

0.45 0.55

0.49 0.80

0.92 0.16

0.03 0.03

0.10 0.40

0.82 0.50

0.74 0.93

0.86 0.96

0.79 0.98

0.60 0.05

0.33 0.67

Precaster age class

0.57

0.69

0.98

0.21

0.05

0.99

0.51

0.72

0.90

0.11

0.27

0.96

Notes: (1) = CVBatch; (2) = CVMix; and (3) = mean of logarithm of batch average. Values shown in bold indicate significant effect at 0.05 level.

Table 3—Summary of mean and coefficient of variation values Modulus ft of elasticity Coefficient of variation, %

Modulus of rupture

Property

fc′

Average CVBatch

2.4

3.6

8.3

4.6

Average CVMix

2.4

3.3

5.7

3.1

Average CVMixAvg

6.4

4.3

7.5

9.5

Maximum CVMixAvg

8.8

5.2

10.8

11.8

Average CVBatchAvg

6.9

5.4

9.4

10.0

Maximum CVBatchAvg

9.1

6.1

12.2

12.2

Minimum 28-day mean

63.7 MPa (9240 psi)

Mean at 28 days (unlogged data)

Average 68.9 MPa 28-day mean (10,000 psi)

39,000 MPa (5,660,000 psi)

4.21 MPa (610 psi)

6.91 MPa (1000 psi)

43,900 MPa (6,360,000 psi)

4.65 MPa (674 psi)

7.31 MPa (1060 psi)

groups. For MOE, the CVMix appears to be significantly different in many groups. This is due to the fact that there are two high coefficients of variation from the first and the second set of the 8000 psi category samples from Precaster C. Because the mixture proportions of the samples collected from Precaster C are nearly the same, however, the high coefficients of variation in both sets may only be a coincidence. If these two values are excluded from the analysis, it was found that the CVMix values are not significantly different in any groups. Therefore, the CVMix for the MOE may be assumed to be not significantly different for the factors considered. From Table 2, the mean of the logarithm of batch averages (equivalent of the batch average if the data is normally distributed) does not appear to be significantly different for any factors for all mechanical properties, except when considering the effect of age for the MOE. However, a difference due to age is expected as the concrete gains strength over time. The variations between mixture proportions and testing procedures are likely the major causes of less significant differences observed in the mean of the logarithm of batch averages for other properties. The results from the analysis of variance indicate that the target mean for each mechanical property is constant for the data in this study. In other words, the mean values for the actual fc′, MOE, ft , and MOE are not dependent on the considered factors or combination of these factors regardless of the specified design fc′. Constant mean values were not anticipated in the beginning of this 460

study. The practice of each precaster using fairly consistent mixture proportions, however, helps to substantiate that constant mean values are possible. Mean and coefficient of variation— Current study—Table 3 provides a summary of the means and coefficients of variation for fc′, MOE, ft , and MOR obtained from the statistical analysis of the data from this study. The CVBatch and CVMix values in Table 3 are average values from all samples because these statistical parameters were determined to not be significantly different for various factors or combinations of factors. Both average and maximum values for CVMixAvg are reported. For this analysis, the average CVMixAvg is defined as the average of the 28-day data for all samples for a given mechanical property. For the maximum CVMixAvg , the 28-day average value was found for each of the three precasters and the maximum of these three values is given as an upper-bound CV. The CVBatchAvg values were calculated using Eq. (1) for both the average and maximum cases of the CVMixAvg. Although the precasters for this study were selected to be representative of precasters in Texas, it was not possible to choose precasters in a completely random way. Therefore, the maximum CVBatchAvg is considered to be more conservative for representing the overall practice in Texas. Because the batch average is considered to be the primary response variable of the analysis, CVBatchAvg should be used for reliability studies. Similar to the CV, 28-day mean values are reported for each mechanical property in Table 3, with both average and minimum values provided. The average 28-day mean is representative of all samples tested at 28 days of age, while the minimum 28-day mean value is the minimum value found for the three precasters. Again, this minimum value among precasters was computed to provide a more conservative mean value for representing the practice in Texas. The reported 28-day mean values in Table 3 were computed using the unlogged batch average values. It should be noted again that for the analysis of variance, a logarithmic distribution was assumed, which is equivalent to making comparisons of the median values for the unlogged data. There is not a great deal of distinction for these data when using a normal or lognormal distribution. When using the statistical information from this study to model a mechanical property with a lognormal distribution, the mean of the logarithm of batch average values should be used. If not readily available, this can be determined mathematically based on the appropriate CV and the mean of the unlogged data given in Table 3. Comparison of CV with other studies—Table 4 and 5 provide a comparison of the coefficients of variation for fc′ and ft, respectively, between the data obtained in this study and values reported by Ellingwood et al. (1980) and Tabsh ACI Structural Journal/July-August 2004

Table 4—Comparison of coefficients of variation for compressive strength Source

Specified compressive strength level, MPa (psi)

Coefficient of variation, %

This study

40.7 to 63.4 (5900 to 9200)

9.1 (6.9*)

20.7 (3000)

15.5 (18†)

27.6 (4000)

15.5 (18†)

34.5 (5000) < 41.4 (6000)

11.9 (15†) 12.5

41.4 to 48.3 (6000 to 7000) > 48.3 (7000)

7.6 6.5

Ellingwood et al. (1980)

Tabsh and Aswad (1997) *Value †

Fig. 1—Bias factor (mean-to-nominal ratio) versus specified design strength. and Aswad (1997). Ellingwood et al.’s bias factors and coefficients of variation were derived from relationships proposed by Mirza, Hatzinikolas, and MacGregor (1979) based on a large collection of test data for NSC from various researchers. These statistical parameters were then used to develop the AASHTO LRFD specifications for prestressed concrete design (Nowak 1999). For comparison, these values have been adjusted (number given outside the parentheses) to provide the value that is obtained for the non-in-place case using the same relationship given by Mirza, Hatzinikolas, and MacGregor (1979). It can be seen that the CV from this study, even for the conservative case, is smaller than values reported by Ellingwood et al. (1980) for NSC. The coefficients of variation from this study are also within the range of coefficients of variation reported by Tabsh and Aswad (1997) for HSC produced by precasters in Pennsylvania. The study by Tabsh and Aswad did not include the variation of concrete between batches. Therefore, the coefficients of variation from their analyses would be larger had the batch variation been ed for. This comparison is important because a smaller CV indicates less relative variation in the concrete strength, and, when combined with larger bias factors, can lead to a smaller probability of failure for limit states where the concrete strength is critical. Bias factor— Compressive strength—The bias factors for the 1and 28-day fc′ versus the corresponding specified design fc′ values are shown in Fig. 1. Note that the precasters provided the 1-day strength data. The 1-day bias factor shows less reduction with respect to increasing specified design strengths than the 28-day bias factor. It was observed that for the inproduction concrete samples collected in this study, the precasters tended to proportion their mixtures more for the 1-day release strength than for the 28-day specified design strength. The decrease in the 28-day bias factor as a function of increasing specified fc′ may be explained by the production practices of the precasters. Two precasters use relatively similar mixture proportions for all specified fc′ values in this study. As a result, the bias factors at lower specified design fc′ values would be expected to be higher than the bias factors at higher specified design fc′ values. The third precaster in this study had more variety in the mixture proportions used for the samples collected at that plant. The selection of the mixture proportions ACI Structural Journal/July-August 2004

based on mean values of all precasters. Values for in-place condition (originally reported).

Table 5—Comparison of coefficients of variation for splitting tensile strength Source

Specified compressive strength level, MPa (psi)

Coefficient of variation, %

This study

40.7 to 63.4 (5900 to 9200)

12.2 (9.4*)

20.7 (3000)

18†

27.6 (4000)

18†

34.5 (5000)

18†

Ellingwood et al. (1980)

* †

Value based on average values for all precasters. Values assumed for in-place condition.

for this precaster, however, depended not only on the specified fc′ for service loads, but also on the specified fc′i . In addition, the time of day and ambient temperature when a beam was cast impacted the selection of mixture proportions because releasing the strands as early as possible on the following day allowed greater productivity for the plant. Because the specified design fc′ is not the main factor in selecting the mixture proportions, no clear trend was observed when comparing the actual fc′ and the specified design fc′ . It should be noted that the 1-day fc′ values obtained from the precasters are not necessarily at 24 h, nor does all 1-day data reflect the same curing time. Precasters usually conduct fc′ testing to the release strength the morning after casting. If the required f ci ' is not met, then additional tests are conducted later in the day until the strength requirement is met. The prestressing strands are released only after the required release strength is achieved. The 1-day fc′ data used herein is the last 1-day fc′ tested before the release. Therefore, a bias factor close to 1.0 is expected for the 1-day data. The bias factors for the 28-day data within a batch (without any adjustments) range from 0.99 to 1.89. The 28-day bias factors for fc′ within a mixture (two batches with the same mixture proportions collected on the same day) range from 1.01 to 1.89. Average 28-day bias factors were computed for each of the three specified design strength ranges and compared to previously published data from Ellingwood et al. (1980) and Tabsh and Aswad (1995, 1997), as shown in Table 6. The bias factors in this study are higher than those from Ellingwood et al. (1980) for NSC, but in the same range as the values reported by Tabsh and Aswad (1995, 1997) for HSC produced by precasters in Pennsylvania. All of the data show decreases in the bias factor with an increase in the actual fc′ regardless of the specified design fc′ considered. Mirza, Hatzinikolas, and MacGregor (1979) suggested a reduction in the fc′ from the test values because loading in an 461

Table 6—Bias factors for compressive strength Source

Specified compressive strength, MPa (psi)

This study

Ellingwood et al. (1980)

Tabsh and Aswad (1997)

Bias factor

41 ± 7 (6000 ± 1000)

1.01 to 1.89* 1.59

55 ± 7 (8000 ± 1000) 69 ± 7 (10,000 ± 1000)

1.24 1.10

20.7 (3000)

0.92†

27.6 (400)

0.85†

34.5 (5000) < 41.4 (6000)

0.81† 1.4

41.4 to 48.3 (6000 to 7000)

1.2

> 48.3 (7000)

1.1

41 to 63 (5900 to 9200)

*Bias factor decreases with increase in compressive strength. † Values estimated for in-place (field) condition.

Table 7—Summary of 28-day bias factors Bias factor ft

Specified fc′ class, MPa (psi)

fc′

MOE

41 ± 7 (6000 ± 1000) 55 ± 7 (8000 ± 1000)

1.59 1.24

1.31 1.13

1.14 1.00

1.77 1.54

69 ± 7 (10,000 ± 1000)

1.10

1.09

0.98

1.54

MOR

Note: MOE = modulus of elasticity; and MOR = modulus of rupture.

actual structure is expected to be at a much slower rate than the standard rate of loading used in compression tests of cylindrical specimens. Ellingwood et al. (1980) used this relationship in developing statistical data for NSC. The use of this relationship may not be appropriate for prestressed bridge structures because the load that would likely cause failure in a bridge is dynamic and closer to an impact load than a static load. Limited data are available to quantify the difference between the actual fc′ in a structure (in-place strength) and the fc′ of the companion test specimens for HSC related to differences in curing conditions as well as size effect and geometry. For NSC, Mirza, Hatzinikolas, and MacGregor (1979) suggested that the fc′ of the concrete in a structure could be taken as 90% of the fc′ from the test cylinders. Assuming that this is applicable to HSC, the modified bias factors for this study would range from 0.91 to 1.70, still greater than those for NSC reported by Ellingwood et al. (1980). Additional mechanical properties—A comparison of the 28-day bias factors for each mechanical property is provided in Table 7. The bias factors for MOE, ft, and MOR were determined by dividing the mean value at 28 days by the nominal value determined from the appropriate code relationship found in the AASHTO LRFD specifications. In each case, the specified fc′ value was used in the code relationship to find the appropriate nominal value for a mechanical property. For each mechanical property, the 28-day bias factors decrease more substantially as the strength classification increases from 41 to 55 MPa, with a difference in bias factors ranging from 14 to 28% for each property. As the strength classification increases from 55 to 69 MPa, the difference in the 28-day bias factors for each property decreases from 0 to 13%, with the largest reduction occurring for the fc′. Overall, the largest 28-day bias factors correspond to the fc′ and MOR. The only 28-day bias factor less than 1.0 was for the ft for the 69 MPa strength class. 462

A bias factor for the fc′ that is greater than 1.0 is beneficial in of the moment capacity of a prestressed girder because the actual flexural strength should then be equal to or greater than the expected design value. The flexural strength of a reinforced or prestressed concrete member, however, tends to be relatively insensitive to the fc′ compared with the impact of increasing the tensile strength provided by the flexural reinforcement. On the other hand, a bias factor substantially different from 1.0 can lead to inaccurate predictions of mechanical properties that are estimated based on empirical relationships using the specified design fc′. This may result in serviceability problems in a bridge, such as inaccurate estimates of camber. Prediction equations Prediction equations are important for prestressed concrete design because many material properties required for design are not tested in practice, but rather calculated from expressions containing the specified design fc′. This section presents an evaluation of prediction formulas for the MOE, ft, and the MOR based on the test data for plant-produced HSC from this study. The focus is on the equations used by national codes such as the AASHTO LRFD specifications and the ACI 318 Building Code (ACI Committee 318 1999). In addition, prediction equations reported in current literature are included in the comparisons. Each mechanical property is plotted as a function of both the actual tested fc′ and the corresponding specified design fc′ . In the equations provided in the figures, all values have been converted to MPa units. Modulus of elasticity—Relationships between the MOE and the actual and specified design fc′ are shown in Fig. 2, along with the test data and best-fit equation determined from this study. The MOE is well-predicted using the actual fc′ with the equation from the AASHTO LRFD specifications (2000) (also used by ACI Committee 318 [1999]). The ACI 363 equation (ACI Committee 363 1997) for HSC, also used by the Canadian Code (CSA 1994), underestimates the MOE of concrete in this study. The relationship of the MOE with the actual fc′ was found to be highly dependent on the type of the aggregate used in the production. Concrete made with crushed river gravel in this study tends on have higher MOE values than those made using crushed limestone aggregates for the same fc′. Based on all the data obtained in this study (that is, containing different aggregates), the following prediction formula was determined to provide the best prediction of the MOE E c = 5230 f c ′ (40 MPa < f c ′ < 90 MPa )

(4)

where Ec is the MOE, in MPa, and fc′ is the compressive strength, in MPa (or E c = 63,000 f c′ when Ec and fc′ are in psi units). Because the data in this study cover a relatively small range of compressive strengths and there are considerable variations in the data, the square root model used by the AASHTO LRFD specifications (2000) and ACI Committee 318 (1999) was chosen for consistency with currently accepted relationships. No substantial improvement in the prediction error was achieved with a more complex equation. The coefficient in Eq. (4) was determined by finding a value that minimizes the relative prediction error value, using the actual fc′ values rather than the corresponding specified fc′ values. ACI Structural Journal/July-August 2004

Fig. 2—Relationships between MOE and fc′. When using the specified design fc′, all the prediction formulas evaluated in Fig. 2(b) underestimate the actual MOE values from the tests. This trend was more pronounced than when actual fc′ values are used. This is expected because the actual 28-day fc′ values from the tests are typically greater than the specified design 28-day fc′ values. Underestimation of the MOE for long-term conditions is conservative because the actual deflection of the member will be less than the predicted value. However, underestimation of the MOE at release will result in a smaller prestress loss than predicted, which can cause excessive stresses and camber immediately after transfer. The issue of underestimating camber is typically not a major concern for release conditions because there is only a small difference between the actual fc′ at release and the specified release strength. When applying the MOE prediction formula for long-term conditions, a conservative (low) long-term value of the MOE will be expected when using the specified design fc′ because the long-term deflection will be overestimated. Splitting tensile strength—Relationships between the ft and the actual and specified design fc′ values, in addition to the data and best-fit equation determined from this study, are shown in Fig. 3. The ft is well predicted using the actual fc′ with the ACI 318 equation and the Ahmad and Shah (1985) equation. The equation recommended by AASHTO (and ACI Committee 363) for HSC was found to overestimate the ft when the actual fc′ is used. The best-fit equation (using a square root of fc′ expression) for the data in this study is ACI Structural Journal/July-August 2004

Fig. 3—Relationships between ft and fc′ . f t = 0.55 f c ′ (40 MPa < f c ′ < 90 MPa)

(5)

where ft is in MPa (or f t = 6.6 f c′ when ft and fc′ are in psi units). This equation is almost the same as the ACI 318 equation (ACI 318 uses 0.56 as a coefficient for MPa units, or 6.7 for psi units). Therefore, the ACI 318 equation may be used to estimate ft with sufficient accuracy. When the specified design fc′ is used in the prediction, all of the equations tend to underestimate ft. The underestimation of ft, however, is conservative because the actual shear capacity will be greater than predicted. Therefore, the ACI 318 equation can be used to estimate a lower bound value of ft based on the specified design fc′ for the data in this study. Modulus of rupture—Expressions describing the relationship between the MOR and the fc′ of concrete, along with the test data and the best-fit relationship determined from this study, are shown in Fig. 4 for the actual and specified design fc′ values. The MOR based on the actual fc′ values was significantly underestimated by the AASHTO LRFD equation, which is the same as the ACI 318 equation. The equation recommended by ACI Committee 363 for HSC does not provide a good prediction for the data obtained in this study, as it overestimates the majority of the test data. The best-fit equation based on the data obtained in this study and using the square root form is f r = 0.83 f c ′ (40 MPa < f c ′ < 90 MPa)

(6) 463

to three strength classes, based on the specified design fc′, with these values ranging from 41 to 63 MPa (5900 to 9200 psi). The samples were tested in the laboratory at 7, 28, and 56 days of age for fc′, MOR, ft , and MOE. One-day fc′ data were obtained from the precasters.

Fig. 4—Relationships between MOR and fc′ . where fr is the MOR, in MPa (or f r = 10 f c′ when fr and fc′ are in psi units). The equation proposed by CEB-FIP (Comité Euro-International du Béton [CEB] 1993) also gives a good prediction for the data in this study. Based on the test data of the MOR, the current AASHTO allowable tensile stress in service for prestressed concrete design of 0.5 f c′ (in MPa) (or 6 f c′ in psi units) may be too conservative. This relationship is only approximately 60% of the MOR values predicted by the best-fit equation. Therefore, the data indicate that the allowable tensile stress has the potential to be increased. However, Nilson (1985) pointed out that the cracking stress of an actual structural member could be less than the MOR of laboratory samples due to the difference in curing conditions in the laboratory and in the field. Further study is planned to address this concern. SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS Summary As a first step toward evaluating the applicability of current AASHTO design provisions for HSC prestressed bridge , statistical parameters for the mechanical properties of plant-produced HSC were determined. In addition, prediction equations relating mechanical properties with fc′ were evaluated. Six sets of plant-produced HSC samples were collected in the field from three different precasters in Texas (a total of 18 collections with two batches sampled and tested for each collection). The sample collections corresponded 464

Conclusions 1. The following conclusions were drawn from the statistical analysis: • Due to precaster production practices in this study, very little or no increase in the average fc′, MOE, ft , and MOR is found with an increase in the specified design fc′. For all mechanical properties tested, the mean values are not significantly different at the 0.05 level among the considered factors (precaster, age, specified strength class) or combinations of these factors, regardless of the specified design fc′; • Overall, the 28-day bias factors (mean-to-nominal ratios) decrease with an increase in design fc′ due to the relative uniformity of mixture proportions provided for the specified strength range. Nevertheless, the 28-day bias factors are greater than or equal to 1.00, except for the bias factor for ft for the 69 MPa (10,000 psi) strength class; • The CV within a batch and the CV within a mixture for each mechanical property are not significantly different at the 0.05 level among specified strength classes or when considering any combination of precaster and age with the specified strength class. However, these coefficients of variation may be significantly different for the MOE and ft when considering the effect of different ages and precasters, respectively; and • The coefficients of variation for the fc′ and ft of HSC in this study are lower than those previously used in the development of the AASHTO LRFD specifications. 2. The code equations that gave the best prediction of the mechanical properties of the HSC tested in this study are as follows: • MOE: AASHTO LRFD specifications (2000)/ACI 318 (1999); • ft: ACI 318 (1999); • MOR: CEB-FIP (CEB 1993); and • Best-fit equations were also developed to give the lowest relative prediction error while maintaining a relatively simple expression. 3. Based on the MOR data, the allowable tensile stress in the AASHTO LRFD specifications are conservative. Curing effects, however, should also be considered. Recommendations and discussion The conclusions from the testing of plant-produced HSC from precasters in Texas point to possible advantages for HSC prestressed member design. A smaller CV, when combined with a larger bias factor (as observed for the fc′), can lead to a smaller probability of failure. Therefore, there is a potential for an increase in the resistance factors developed specifically for HSC in flexure and shear versus those developed for NSC. However, several issues must be considered. First, the lower coefficients of variation are likely a result of the relatively consistent mixture proportions used by each of the three precasters selected for this study. The coefficients of variation may be larger if one were to randomly select from a very large group of precasters across the country. Second, the differences in the behavior of HSC versus NSC must be considered in any future code changes. Third, the greatest ACI Structural Journal/July-August 2004

potential for increasing the economy of prestressed girders lies in increasing the allowable stresses for release and service conditions, and the ultimate flexural limit state does not typically control the maximum spans that can be achieved with standard prestressed girder cross sections. Therefore, further attention should be given to the allowable stress values. Based on the MOR data, the allowable tensile stress in the AASHTO LRFD specifications may be too conservative. Curing conditions, however, can affect the MOR. For this reason, additional work is planned for this study to compare the MOR for lab-cured and field-cured HSC specimens. ACKNOWLEDGMENTS The authors acknowledge and funding by the Texas Department of Transportation (TxDOT) through the Texas Transportation Institute (TTI) at Texas A&M University (TAMU). The input of K. Ozuna (TxDOT, Research Project Director), J. Vogel (TxDOT), and D. Mertz (University of Delaware) is appreciated. The authors also wish to thank A. Fawcett, J. Perry, and G. Harrison of the Texas Engineering Experiment Station Machining, Testing and Repair Facility at TAMU; D. Zimmer of TTI; S. Cronauer of the Department of Civil Engineering at TAMU; and all the students who assisted with the project including E. Bristowe, A. McCall, F. Moutassem, D. Pfingsten, J. Richards, G. Sharpe, and J. Sneed. Also appreciated are the three precasters who participated in this study.

NOTATION CV CVBatch CVBatchAvg CVMix CVMixAvg f f′ f c′ fci′ ft HSC MOE MOR NSC Rn RPE λ

= = = = = = = = = = = = = = = = =

µR

=

coefficient of variation coefficient of variation within batch coefficient of variation of batch averages coefficient of variation within mixture collected on same day coefficient of variation of mixture averages experimental value of mechanical property predicted value of mechanical property compressive strength of concrete specified design compressive strength of concrete at release splitting tensile strength of concrete high-strength concrete modulus of elasticity of concrete (also Ec) modulus of rupture of concrete (also fr) normal-strength concrete specified design value of resistance relative prediction error bias factor (ratio of mean to nominal value) for mechanical property mean value of resistance

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