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Effect of Temperature-Time History on Concrete Strength in Mass Concrete 1
Structures 2
3
Tahsin Alper Yikici, M.Sc. 4
Research Assistant 5
Department of Civil and Environmental Engineering 6
College of Engineering and Mineral Resources 7
West Virginia University 8
PO Box 6103 9
Morgantown, WV 26506-6103 10
Ph: 304-293-4013 11
Fax: 304-293-7109 12
Email: [email protected] 13
14
Dr. Roger H.L. Chen (Corresponding Author) 15
Professor 16
Department of Civil and Environmental Engineering 17
College of Engineering and Mineral Resources 18
West Virginia University 19
PO Box 6103 20
Morgantown, WV 26506-6103 21
Ph: 304-293-9925 22
Fax: 304-293-7109 23
Email: [email protected] 24
25
26
Submission Date: November 15, 2012 27
Number of Words in Text: 3515 28
Number of Tables: 4 29
Number of Figures: 8 30
Total Equivalent Number of Words: 651531
TRB 2013 Annual Meeting Paper revised from original submittal.
Yikici and Chen
2
ABSTRACT
Concrete maturity method is a popular non-destructive testing method to estimate in-
place strength development of concrete structures. Many state highway agencies adopted
procedures for using maturity method to obtain better quality control while monitoring
in-place strength development in real time. In this study, maturity method was used to
estimate in-place strength of large concrete placements. Four 6-foot cube blocks were
constructed in four different locations and calibration curves for those concrete mixtures
were established using 6x12 inch cylinder specimens collected from the construction site.
Temperature sensors were embedded in specific locations throughout the depth of the
cubes, and the equivalent age of the in-place concrete was calculated. 4-inch diameter
core samples, with 6-foot in length, were taken from the cubes at four-day after
construction and the core strengths were compared with the predicted strengths using
maturity. In addition, activation energy values were determined in the laboratory and
used for equivalent age calculations as recommended in ASTM C 1074. According to
the test results, the concrete top surface strength prediction is always higher than the
actual core strength. For three cube constructions, core results from mid-section were
close to the predicted strengths and core results from the bottom section were higher than
the predicted values. Results show that in-place concrete strength is being influenced by
several factors other than temperature, including the location of the sample in the
structure, lack of compaction quality, higher air content and in-situ water-cement ratio,
so that establishing a reliable maturity and in-place strength relationship is rather difficult
within given circumstances. The results of this study provide useful information to
examine the accuracy of the maturity method used in the estimation of in-place concrete
strength in large structures.
TRB 2013 Annual Meeting Paper revised from original submittal.
Yikici and Chen
3
INTRODUCTION
The strength of properly batched, placed and vibrated concrete does not depend only on
the curing time, but also on the temperature-time history. This concept is known in the
concrete industry as maturity concept. According to the maturity concept, an empirical
relationship can be established between temperature-time history and strength
development of the concrete in order to predict strength of in-place concrete during the
curing period (1). ASTM C 1074 recommends maturity method as “a technique for
estimating concrete strength that is based on the assumption that samples of given
concrete mixture attains equal strength if they attain equal values of maturity index”(2).
The method assumes that the temperature-time history of concrete can be used to develop
a strength-maturity curve that is specific to each mix design. By preparing these
correlation curves, the strength development of in-place concrete can be estimated by
monitoring the concrete temperatures in real time. Consequently, this information can be
used to make decisions (e.g. time of formwork removal, or time of post-tensioning) that
save time and reduce the construction cost (1). Furthermore, monitoring concrete
temperatures, especially in mass concrete pours, can be used to prevent high internal
concrete temperatures and large temperature gradients that are specified by several state
agencies in order to reduce the possibility of thermal cracking.
Many state transportation agencies have already instituted procedures or are still
conducting research projects to implement the maturity method to predict in-place
concrete strength. According to the West Virginia Department of Highway (WVDOH)
survey results conducted in 2007, twenty-five out of thirty-six states used the maturity
concept mainly as a substitute for early cylinder compressive strength to allow formwork
to be removed or pavements to be opened to traffic (3). In 2008, Auburn University
employed maturity method on several precast, prestressed girders and a bridge deck.
They concluded that the method can be used accurately for estimating in-place concrete
strength up to an equivalent age of seven days (4). University of Washington researchers
reported in 2009 that the maturity method was used in three different Portland cement
concrete pavement (PCCP) projects in order to open traffic faster. Only one out of the
three trials was successfully conducted (3). Similarly, University of Maryland evaluated
maturity method for use in pavements and they concluded that the procedure is very
sensitive to the constituent materials and concrete mixtures. They recommended taking
extreme pre-cautions in order to obtain maximum accuracy when using maturity method
for field applications (5). Furthermore, the cross over effect (1) due to high temperature
curing has been shown to limit the applicability of maturity method in predicting the
behavior of concrete that has high early temperature, such as mass concrete construction.
One of the objectives of this study is to investigate the applicability of maturity
method to estimate the in-place concrete strength of large bridge sub-structure elements,
such as piers, pier footers, pier caps or abutments, using WVDOH approved Class B
concrete mixtures that are currently used in bridge projects. Class B concrete, as
described in WVDOH Standard Specifications, has minimum 3,000 psi (20 MPa) 28-day
design strength with optimum 4-inches slump and 7% target air. Class B concrete may
be designed using supplementary cementitious materials such as fly-ash, ground
granulated blast furnace slag (GGBFS) or micro-silica with 564 pound per cubic yard
(330 kg/m3) target cement content and 0.49 maximum water-cementitious ratio. In
addition, this study outlines the effect of the strength development from the temperature
TRB 2013 Annual Meeting Paper revised from original submittal.
Yikici and Chen
4
variations in concrete throughout the depth of 6-ft concrete cubes. This paper presents
test results from four different 6-ft cube constructions and the predicted in-place concrete
strength using a maturity function based on concrete equivalent age.
RESEARCH METHODOLOGY
Six-ft concrete cube blocks were constructed at different locations in West Virginia,
using Class B concrete from local ready-mix plants. Temperature sensors were
instrumented, fresh concrete properties were determined and 6x12 inch cylinders were
taken for the maturity test. Core samples were taken from the hardened concrete cube
block and the measured compressive strengths from the core samples were compared to
the predicted strengths from equivalent age calculations. Activation energy values for the
concrete mixtures were determined in the laboratory following ASTM C 1074 (2).
SIX-FT CUBE CONSTRUCTION
Six-ft concrete cubes were constructed at four different WVDOH districts (D1, D5, D6
and D9), located in Charleston (D1), Lewisburg (D9), Martinsburg (D5), and Wheeling
(D6), pouring approximately nine cubic-yards of concrete in each cube provided by local
ready-mix concrete plants. The concrete mix design for each casting is given in Table 1.
The cube blocks were constructed two feet in the ground on a two inch layer of #57
limestone. Each cube was instrumented with temperature loggers attached on a rebar
cage (Figure 1). A schematic of the sensor locations is given in Figure 2. Concrete was
poured directly from the mixer truck without pumping and then was subjected to
vibration in order to get sufficient compaction. Ordinary surface finish using wood-float
rubbing was applied on the top surface. The concrete surface was maintained completely
and continuously moist during the seven-day curing period. After the concrete placement
the top of the block was covered with white polyethylene sheeting. If necessary, concrete
blankets were used on top surface as well as around the formwork on the side surfaces.
One of the purposes of the six-foot cube constructions was to investigate strength
development of in-place concrete by monitoring the temperature distribution in concrete
and investigate the applicability and the limitations of the maturity concept for large
concrete placements throughout West Virginia.
(a) Instrumentation of the rebar cage
(b) Sensors attached to the rebar
FIGURE 1 Mounting of the temperature loggers.
TRB 2013 Annual Meeting Paper revised from original submittal.
Yikici and Chen
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TABLE 1 One yd3 Theoretical Mix Design
Item
D1 D9 D5 D6
Class B
Fly-Ash Class B
Class B
GGBFS
Class B –
1 Extra
Cement (TYPE I/II), lbs 470 564 423 658
Fly-Ash (TYPE F). lbs 75 - - -
GGBFS (Grade 100), lbs - - 141 -
Water, lbs 245 262 276 260
Coarse Aggregate (#57), lbs 1775 1723 1815 1750
Fine Aggregate, lbs 1255 1299 1225 1111
Target Air Content, % 7.0 7.0 7.0 7.0
w/cm 0.45 0.45 0.49 0.40
NOTE: 1 lb = 0.454 kilograms (kg)
FIGURE 2 Schematic of the sensor locations.
6’-0”
6’-0”
SIDE VIEW
3
3’-0”
3’-0”
11
2’-0”
1’-0”
10 9
5
1 13
12
4
2
1’-6”
1’-6”
1’-0”
6
7
8
14
TRB 2013 Annual Meeting Paper revised from original submittal.
Yikici and Chen
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Experimental Work
In order to establish the maturity-strength relationship of each mix, 6x12 inch cylinders
were cast during the cube constructions. Additionally, two 6x12 inch cylinders were
embedded with temperature loggers recording hourly temperature history. All cylinders
were placed inside insulated boxes to reduce the effect from the ambient conditions
overnight and then transported the next day to temperature controlled curing tanks at the
district material laboratory (Figure 3). Compressive strength of the concrete was
determined at 1, 3, 7, 14 and 28 days, testing at least two cylinders at each age.
In addition to that, at 4-days, 4-inch-diameter by 6-foot long core samples were
taken from the hardened concrete cube (Figure 5) and a total of six 4x8 inch cylinder
specimens were extracted from the core along the 6-ft length (Figure 6). The specimens
were prepared and tested immediately after coring to represent the in-place compressive
strength of the concrete cube at different depth. A schematic drawing that shows the cut
locations and specimen designations is presented in Figure 4.
(a) Concrete placement
(b) Maturity cylinders
(c) Cylinders on the field
FIGURE 3 D5-Cube construction and sampling.
FIGURE 4 Core specimen cut locations and designations.
8” 2” 4” 4” 8” 4” 8” 4” 8” 4” 8” 2” 8”
36” 36”
1C 2C 3C 4C 5C 6C 1R 2R 3R 4R 5R
1 foot Top of the core
(30.5 cm)
TRB 2013 Annual Meeting Paper revised from original submittal.
Yikici and Chen
7
(a) Coring machine
(b) 6-ft core
FIGURE 5 Six-ft cube coring.
FIGURE 6 Schematic of the coring locations.
X: Temperature sensors O: Coring positions
X X X X
O O
O
6’0”
X
2’0”
TOP VIEW
2’0”
1’0”
O
X
X
6’0”
28 days
56 days
4 days 28 days
TRB 2013 Annual Meeting Paper revised from original submittal.
Yikici and Chen
8
TEST RESULTS AND DISCUSSION
Determination of Activation Energy
The activation energy of concrete mixtures was determined experimentally following
ASTM C 1074-10 A1 procedure. It requires establishing the compressive strength versus
age relationship of 2-inch mortar cubes cured at three different temperatures (2). The
mortar was proportioned to have a fine-aggregate to cement- ratio equal to the coarse-
aggregate to cement ratio of the concrete mixture. Specimens were cured at three
different temperatures: high (104°F), low (50°F), and laboratory temperature (73°F).
Three cubes were tested at six different times in compression following the recommended
test schedule by Tank R. C. (6), based on equal temperature-time factors for different
curing temperatures.
Upon the completion of the compressive strength tests, hyperbolic equation
(1,2,7) was used to fit the set of data to determine the best fit regression parameters, such
as the limiting strength, Su, the rate constant of strength gain, k, and the dormant period
t0, for three different curing temperatures. After that, natural logarithm of the k-values
versus reciprocal curing temperature in Kelvin was plotted. From that, the negative slope
of the line is obtained which equals to the value of the activation energy divided by the
universal gas constant (R), also known as Q. This calculation is based on the Arrhenius
function that is being used to explain the temperature dependence of the rate constant, k
(1,7).
Apparent activation energy values for the Class B concrete containing fly ash and
GGBFS were determined according to ASTM C 1074 procedures. The calculation of this
value requires the determination of several parameters using the linear hyperbolic
equation:
)(1
)(
0
0
ttk
ttkSS u
where:
S= average strength of the cubes at age t
t= test age in hours
Su= limiting strength
t0= age when strength development assumed to begin
k=
rate constant.
It was found that the hyperbolic strength-age function can properly model the
strength development with the lowest goodness of fit R-square value 0.93 for each set of
experiment. The apparent activation energy values were calculated approximately 45,900
J/mol and 44,750 J/mol for Class B Fly-Ash and Class B GGBFS concrete mixtures,
respectively.
TRB 2013 Annual Meeting Paper revised from original submittal.
Yikici and Chen
9
Maturity Calculations
Equivalent age approach was used to establish maturity-strength relationship. The
actual age of the concrete was converted to its equivalent age at a specified temperature.
Equivalent age can be calculated according to the following “Arrhenius Equation”:
where:
te = equivalent age
Q = activation energy divided by the gas constant (R),
Ta = average temperature of the concrete during time interval,
Ts = specified (reference) temperature (typically 23°C)
Δt = the time interval
A calibration curve was prepared from strengths of the laboratory cured specimens using
the recorded temperature-time history of the cylinders. The calibration curve can be used
to estimate the in-place concrete strength if temperature history of the structure is known
(1,2,8). The calibration curve that represents the strength gain of the concrete was
modeled using the linear hyperbolic model suggested by ASTM C 1074-10 (2). The age
when strength development assumed to begin (t0) was set equal to the final setting time of
the concrete. Figure 8 shows the compressive strength versus equivalent age
relationships based on the cylinder compressive strength results. The equivalent age of
the D1 and D5 concrete were calculated using the measured activation energy values of
45,900 J/mol and 44,750 J/mol, respectively. The equivalent age of the D9 and D6
concrete were calculated using an assumed activation energy value of 41,800 J/mol based
on the model proposed by Han S.H. (9).
FIGURE 7 Concrete mix design calibration curve, strength vs equivalent age.
TRB 2013 Annual Meeting Paper revised from original submittal.
Yikici and Chen
10
Core Strength
The compressive strength results from the concrete cores obtained at 4-day from each 6-ft
cube are listed in Table 2. The test results show that there is a significant strength
difference along the depth, between the top (1C) position and the bottom (6C) position.
1C position appears to be the weakest and 5C and 6C positions are the strongest. This
appears to coincide with observation by other researchers that cores usually have lower
strength near the top surface and the strength increases with depth (10).
The core test results clearly indicate the variations from the conditions occurred
during concrete placement. During D9 cube construction concrete was delivered in two
separate trucks and the air content measured on the field was 7.8% and 9.5%,
respectively. The unexpected difference in air content may be the reason that shows a
large variation in strength between the cores 3C and 4C positions. During D6 cube
construction the slump of the fresh concrete was only 1.75 inches and vibration was very
difficult. Hence, honeycombing was observed at the mid-height section from the
concrete surfaces. The effect of the segregation and honeycombing on the core strengths
was detected between core samples 3C and 4C. Furthermore, there is a possibility of
strength reduction due to drilling operations. The coefficient of variation of strength
estimation using 4-in diameter cores was presented 4 to 5.5%. (11) However, it is really
difficult to separate out the errors due to on-site quality control issues, such as concrete
placement, compaction, air-content, actual water to cement ratio, etc. (10).
TABLE 2 Concrete Compressive Strength from the 6-ft Core at 4-day
1C 2C 3C 4C 5C 6C
Depth from the surface, inch 2”-10" 14"-22" 26"-34" 38"-46" 50"-58" 62"-70"
D1 Cube 3,160 4,670 4,830 4,690 4,850 4,930
D5 Cube 3,880 4,790 4,790 4,870 4,790 5,300
D9 Cube 2,420 2,660 * 3,620 3,670 4,010
D6 Cube 4,460 5,710 4,100 3,310 5,250 5,250
Note: 1 inch = 2.54 cm, * the core was broken at 3C position
In-Place Concrete Strength Prediction
Even though the maturity method is more reliable in predicting the relative strength than
the absolute strength (1), in this study, it was assumed that the 28-day (equivalent-age)
cylinder strength and the in-place concrete strength are same, hence, the developed
maturity-strength relationship is used to predict the concrete strength in the cube. In
order to estimate the in-place concrete strength, temperature sensors were installed at
critical locations in the 6-ft cubes. The locations were selected to be representative of the
temperatures at the locations of coring due to symmetry. In-place concrete strengths
were estimated using strength-equivalent age calibration curves (Figure 7) for each
concrete mixture. The equivalent ages of the concrete at three locations were calculated
based on the temperature-time history of three specific locations in the 6-ft cubes,
corresponding to sensor #6 (top section), #7 (mid-section) and #8 (bottom section) and
TRB 2013 Annual Meeting Paper revised from original submittal.
Yikici and Chen
11
given in Table 3. These sensors #6, #7 and #8 were located at 2”, 36” and 70” from the
cube top surface, respectively. Figure 8 shows a typical temperature-time history of
those three locations up to 14 days (from the D5 Cube).
In addition, the predicted strengths are compared to the 4-day core strength
results; “1C” representing the top position, “3C” and “4C” representing the center
position, and 6C representing the bottom position of the cubes. The results show that the
top surface predicted strength (#6) is always higher than the actual core strength at all
four cubes. For D1, D5 and D9 cubes, concrete strength at the mid-section (#7) were
close to the predicted strength, however the core strength results are higher than the
predicted values at the bottom section (#8). Essentially due to on-site quality issues
mentioned earlier, it is noticed that in D6 case the core strengths are lower than the
predicted strengths at each position.
TABLE 3 In-place Concrete Strength Prediction Compared with the Core
Strength Results
D1 D5 D9 D6
Sen
sor
Equ
ival
ent
age,
day
s
Pre
dic
ted
Str
eng
th, p
si
Co
re
Str
eng
th, p
si
Equ
ival
ent
age,
day
s
Pre
dic
ted
Str
eng
th,
psi
Co
re
Str
eng
th, p
si
Equ
ival
ent
age,
day
s
Pre
dic
ted
Str
eng
th,
psi
Co
re
Str
eng
th, p
si
Equ
ival
ent
age,
day
s
Pre
dic
ted
Str
eng
th,
psi
Co
re
Str
eng
th, p
si
#6 14.1 3,920 3,160 11.7 4,310 3,880 17.3 3,370 2,420 20.3 6,330 4,460
#7 21.2 4,060 4,760 18.2 4,970 4,830 31.1 3,500 3,620 24.5 6,400 3,710
#8 13.9 3,920 4,930 10.5 4,130 5,300 19.0 3,400 4,010 10.0 5,970 5,250
Note: 1 psi = 6.89 kPa
FIGURE 8 Measured concrete temperature-time history from D5 Cube.
TRB 2013 Annual Meeting Paper revised from original submittal.
Yikici and Chen
12
In addition to the 4-day core, there are 28-day and 56-day cores (Figure 6)
extracted from the cubes, and the compressive test results from these core specimens are
shown in Table 4. As expected, the long-term strength of the concrete from these core
specimens can not be predicted by the linear hyperbolic strength-maturity model (1,4).
Modification of the maturity method is needed for the prediction of long-term concrete
strength development, especially considering high-early temperature effects, such as
those seen in mass concrete.
TABLE 4 Compressive Strength from the 6-ft Core at 28-day and 56 day
1C 2C 3C 4C 5C 6C
Depth from the surface, inches 2"-10" 14"-22" 26"-34" 38"-46" 50"-58" 62"-70"
D1 CUBE
28 Days (center) 4,750 5,640 5,600 4,950 6,460 6,540
29 Days (corner) 4,370 5,600 5,640 5,490 6,070 5,900
56 Days 4,690 6,130 5,920 5,820 6,370 6,410
D5 CUBE
28 Days (center) 4,460 6,080 5,820 5,570 5,630 6,960
28 Days (corner) 4,510 4,800 5,150 6,040 5,700 6,590
76 Days* 4,180 5,750 5,580 5,310 6,090 7,430
D9 CUBE
28 Days (center) 2,960 2,670 2,520 3,710 3,630 4,120
28 Days (corner) 3,150 2,630 2,510 3,790 3,740 4,210
56 Days 3,350 2,730 2,640 4,000 3,840 4,330
D6 CUBE
28 Days (center) 6,010 6,440 5,150 6,490 6,210 6,230
28 Days (corner) 5,730 6,160 5,450 5,980 6,090 6,400
56 Days 5,390 6,530 6,160 6,590 6,630 6,440
Note: 1 inch = 2.54 cm
* Coring was delayed due to drilling equipment malfunction
SUMMARY AND CONCLUSIONS
Many states, including West Virginia are interested in using ASTM C 1074 Maturity
Method for the benefits of increasing quality control, accelerating construction time, or
reducing number and cost of sampling and testing standard cylinders. On the other hand,
accuracy, effectiveness, and reliability of the test method to estimate in-place concrete
strength have been a concern, especially for the concrete under high temperature
differential curing such as in the case of mass concrete. The purpose of this study is to
investigate the applicability of the maturity method on large concrete pours using regular
Class B Concrete in West Virginia. Four different concrete mix designs were
investigated in four 6-ft cube constructions in different districts. Maturity-strength
calibration curves for these mixes were established and concrete temperatures inside the
cubes were monitored in order to calculate equivalent concrete age using the measured
activation energy values. The in-place concrete strength was determined by testing core
samples extracted from cubes and results were compared with the predicted values.
Based on the test results the following conclusions can be made:
TRB 2013 Annual Meeting Paper revised from original submittal.
Yikici and Chen
13
1. Compressive strength-age development of concrete can be represented by testing
the corresponding mortar mixture following ASTM C 1074-A1. The hyperbolic
strength-age relationship can be used to model strength development at different
temperatures. Activation energy values for concrete mixtures including
supplementary cementitious materials were determined testing mortar cubes
prepared in the laboratory.
2. Test results show that the in-place concrete core strengths of the 6-ft cube close to
the concrete top surface were overly estimated using ASTM C1074 maturity
method. Effect of variable temperature curing in large structures cannot be
accurately predicted using the current maturity calculation with linear hyperbolic
equation. Further study is needed to modify the maturity calculation for its
application in mass concrete with high early-age temperature.
3. The error in estimating in-place concrete strength using equivalent age method is
unpredictable partly because the concrete in-place strength is highly dependent on
the quality control on-site. The variables include in-situ water-cementitious ratio,
air content, vibration/consolidation, and finishing.
ACKNOWLEDGEMENT
The authors acknowledge the support provided by the FHWA and West Virginia
Transportation Division of Highways for the project RP#257-Pre-liminary Analysis of
Use of Mass Concrete in West Virginia. Special thanks are extended to our project
monitors Michael A. Mance, Donald Williams and Ryan Arnold of WVDOH. The
assistance received from the Materials Control and Soils Testing Division (WVDOH
MC&ST), and WVDOH District 1, District 5, District 9 and District 6 Bridge and
Materials divisions are especially acknowledged.
REFERENCES
1. Carino N. J. “The Maturity Method,” Chapter 5 in Handbook on Nondestructive
Testing of Concrete, 2nd
Edition, Malhotra V. M. and Carino N. J., Eds., CRC
Press, Boca Raton, Fl, 2004.
2. ASTM C 1074-10. Standard Practice for Estimating Concrete Strength by the
Maturity Method. ASTM Standards, ASTM International, West Conshohocken,
PA.
3. Muench S., Pierce L.M., Kinne C., Uhlmeyer J.S. and Anderson K. W. Use of
Maturity Method In Accelerated PCCP Construction. WSDOT Research Report,
WA-RD 698.1. Washington State Department of Transportation, 2009.
4. Wade, S.A., Barnes R.W., Schindler, A.K. and Nixon J.M. Evaluation of the
Maturity Method to Estimate Concrete Strength in Field Applications. ALDOT
Research Report, Highway Research Center and Department of Civil Engineering
at Auburn University, 2008.
5. Hosten M. A., Johnson R. Implementation of the Concrete Maturity Meter for
Maryland. State Highway Administration Research Report, Report No. MD-11-
SP708B4K. Morgan State University, 2011.
6. Tank, R. C. The Rate Constant Model for Strength Development of Concrete.
Ph.D. Dissertation submitted at Polytechnic University of New York, June 1988,
209 pp.
TRB 2013 Annual Meeting Paper revised from original submittal.
Yikici and Chen
14
7. Brooks A. G., Schindler A. K. and Barnes R. W. Maturity Method Evaluated for
Various Cementitious Materials. Journal of Materials in Civil Engineering.
ASCE, December 2007, pp. 1017-1025
8. Poole, T.S. and Harrington P.J. An Evaluation of the Maturity Method (ASTM C
1074) for Use in Mass Concrete. Technical Report SL-96-16. U.S Army Corps of
Engineers, Vicksburg, MS, 1996.
9. Han S.H., Kim J.K., Park Y.D. Prediction of Compressive Strength of Fly Ash
Concrete by New Apparent Activation Energy Function. Cement and Concrete
Research, Vol. 33, 2003, pp. 965–971.
10. Neville, A. M. Properties of Concrete. Pearson Education Ltd, England, 2002.
11. Bartlett F. M., Precision of in-place concrete strengths predicted using core
strength correction factors obtained by weighted regression analysis, Structural
Safety, Vol. 19, Issue 4, 1997, pp. 397-410.
TRB 2013 Annual Meeting Paper revised from original submittal.