Prediction of Compressive Strength of In-Situ Concrete
Based on Mixture Proportions
Jee Namyong*1, Yoon Sangchun2 and Cho Hongbum3
1
2
Assistant Professor, Department of Architectural Engineering, Hanyang University, Korea
Assistant Professor, Department of Architectural Engineering, Kyeongju University, Korea
3
Ph. D. Candidate, Department of Architectural Engineering, Hanyang University, Korea
Abstract
This paper presents the regression equation for predicting compressive strength of in-situ concrete. For this
purpose, this study used the data of mixture proportions of ready-mixed concrete and test results of compressive
strength at construction sites.
This study used 1442 compressive strength test results obtained from the specimens having 59 different
kinds of mixtures with specified compressive strength of 18~27MPa, water-cement ratio of 0.39~0.62, maximum
aggregate size of 25mm, and slump of 12~15cm.
Principal factors that influence compressive strength of concrete are selected by a correlation analysis, and
then the multiple linear regression analysis is carried out for predicting compressive strength according to
water-cement ratio or cement-water ratio, cement contents and cement-aggregate ratio.
Keywords: mix proportions; correlation analysis; multiple linear regression analysis; prediction of compressive strength
1. Introduction
1.1 Background and Significance
Ready-mixed concrete (RMC) was first produced
through RMC plant constructed by J. H. Magen in
Germany in 1903, but was not settled at that time because
of segregation on carrying. Together with development
of agitator equipments in 1926, RMC had grown steadily.
In case of RMC industry in Korea, since 1965,
production capacity and consumption of RMC have
reached 355million cubic meter and 137million cubic
meter in 2002, respectively. However, several quality
problems of RMC remained.
Only a few tests have been done to ensure concrete
quality before placing; the slump test for workability,
tests of air contents and chloride contents for durability.
The compressive strength that is the one of influential
factors on concrete quality has been tested at 7 and 28
days. Several methods for early estimation of concrete
strength have been introduced for concrete quality
control, but they are expensive and time-consuming, and
need experienced skill as well.
Therefore, these strength tests are not practical to
predict. In addition, available documents offered from
RMC plants were not applied to strength control of
concrete at construction sites.
*Contact Author: Jee, Namyong, Assistant Professor, Department
of Architectural Engineering, Hanyang University, Haengdang1Dong Seongdong-Gu, Seoul, Korea
Tel: +82-02-2290-0302 Fax: +82-02-2293-3119
E-mail: [email protected]
(Received November 12, 2003 ; accepted April 6, 2004 )
This study aims to make the regression equation and
review applicability of prediction equation as a means
of strength control of concrete, which enables to predict
compressive strength by a multiple linear regression
analysis with respect to mixture proportions from RMC
plants and corresponding field test results of compressive
strength.
1.2 Procedure and Scope
Data, mixture proportions of RMC plants and quality
test results of fresh concrete and hardened concrete at
the construction sites, were attained from 8-apartment
construction sites located in the district of In-cheon and
Kyeong-gi between April 1999 and July 2001 for this
study. Mixtures using a binder except normal portland
cement were excluded. Data of this study are 1442
compressive strength test results based on 59 different
kinds of mixtures with specified compressive strength
of 18~27MPa, water-cement ratio of 0.39~0.62,
maximum aggregate size of 25mm, and slump of
12~15cm.
Sampling concrete was carried out just before placing
in structures. Compressive strength test specimens were
cast and cured according to KS F 2403, that is, stored in
water at the laboratory of construction site until the
moment of strength test in accordance with KS F 2405.
Table1 represents physical characteristics of concrete
constituents.
The flow diagram for predicting compressive strength
of in-situ concrete is shown in Fig.1.
Commercial software(SPSS) is used for statistical
analysis.
Journal of Asian Architecture and Building Engineering/May 2004/16
9
Fig.1. Flow diagram for predicting concrete strength
2. Variability of concrete strength
Variation in concrete strength of the test specimens
depends on how well the materials, concrete
manufacture, and testing is controlled. Especially
construction practices may cause variation in strength
of in-situ concrete due to inadequate mixing, poor
compaction, delay, and improper curing.
Table 2 shows mixture proportions on 59 kinds of insitu concretes and corresponding compressive strength.
Water-cement ratio for specified compressive strength
of 18, 24, and 27MPa are 0.57~0.62 (average: 0.60),
0.44~0.52 (average: 0.47), and 0.39~0.48 (average:
0.43), and cement contents are 289~315kg/m3 (average
: 305), 328~401kg/m3 (average : 374), and 390~420kg/
m3 (average: 420), respectively.
Table 1. Physical characteristics of constituents of concrete
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Jee, Namyong
Table 2. Mixture proportions of in-situ concrete and comcrete and compressive strength
JAABE vol.3 no.1 May. 2004
Jee, Namyong
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Table 3. Compressive strength and standard deviation of RMC
plants by strength(MPa)-slump(cm) at 28 days
1997) is “Excellent”. Standard deviation is bellow
2.8MPa as shown in Fig. 2 and Fig. 3. However,
compressive strength of specimens cured in water on
construction site is over 14~29% as compared with
specified compressive strength. It is estimated that
mixture proportions are not economical in case of some
RMC plants. Standard deviations of compressive
strength at 7 days are bigger than those of compressive
strength at 28 days, which means that the magnitude of
variation in strength is big at early ages.
It can be seen that the frequency distribution of
strength test results by specified compressive strength
follows normal distribution curve as shown in Fig. 4.
Fig.2. Standard deviation by specified compressive strength
on RMC plants at 28 days
Fig.3. Standard deviation by specified compressive strength
on construction sites at 28 days.
The class of strength control for in-situ concrete can
be evaluated by standard deviation.
Mean and standard deviation of compressive
strength(MPa) at the RMC plants are given on Table 3.
Based on the analysis of standard deviation of strength
obtained by RMC plants and construction sites, the class
of strength control given in ACI 214-77 (Reapproved
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JAABE vol.3 no.1 May. 2004
Fig.4. Frequency distribution of strength data and
corresponding normal distribution curve
Jee, Namyong
3. Prediction of compressive strength of concrete
According to the formula by Abrams, an increase in
the water-cement ratio decreases the concrete strength,
whereas a decrease in the water-cement ratio increases
the strength.
The formula of Abrams is;
..................................................... Eq. (1)
Eq. (1) can be rewritten in the following form;
long as their w/c and c/w remain the same regardless of
the details of the compositions. The quantity of the
cement or aggregate was not accounted for predicting
concrete strength.
However quite a few investigators have reported that
the higher the cement contents, the lower the strength of
concrete in identical water-cement ratio. Therefore, effort
should be made to analyze the role of constituents of
concrete.
It is worthwhile to analyze effects of cement, water,
and aggregate contents including water-cement ratio as
well as those of water-cement ratio for the increase of
reliability on the concrete strength prediction.
Log f = logA - w/c logB = b0 + b1 w/c ............. Eq.(2)
where,
f
w/c
A, B
b 0, b 1
: compressive strength of concrete
: water-cement ratio
: empirical constants
: correlation coefficient
Another model for the strength versus concrete
constituents relationship is based on the cement-water
ratio, that is, the reciprocal value of w/c. Lyse made the
formula, wherein concrete strength and cement-water
ratio are linearly related. This formula becomes very
popular because of its arithmetic simplicity.
The general form of linear c/w model is shown as
following;
f = A + B c/ w
where,
.........................................Eq.(3)
f = compressive strength
c/w = cement-water ratio
A, B = empirical constants
By the numerical form of the Abrams and Lyse,
strength values are identical with various concretes as
3.1 Analysis of influential factors on compressive strength
Table 4 shows correlation coefficients between
compositions of mixture based on documented data from
RMC plants and field test results of compressive
strength.
Correlation coefficients between compressive strength
and factors for mixture such as water-cement ratio,
cement-water ratio, cement contents, and cementaggregate ratio are above 0.6. These are considered as
the principal influential factors that determine
compressive strength of concrete.
The strength of concrete increases with increasing
cement-water ratio, cement contents, coarse aggregate
contents, and cement-aggregate ratio, and with
decreasing water-cement ratio, water contents, fine
aggregate contents, total aggregate contents and fine
aggregate-total aggregate ratio.
Thus compressive strength of in-situ concrete is found
to be closer correlation with cement contents than water
contents. In case of aggregates, it was analyzed that
correlation of fine aggregate with strength is higher than
that of coarse aggregate with compressive strength of
in-situ concrete.
Table 4. Correlation coefficients between compositions of mixture on the basis of documented data and compressive strength
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Jee, Namyong
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3.2 Prediction of compressive strength
Influential factors that determine compressive strength
of concrete are analyzed by correlation analysis. Then,
a multiple linear regression analysis is carried out with
respect to compressive strength and principal influencing
factors of mixture such as water-cement ratio, cementwater ratio, cement contents, and cement-aggregate ratio.
Prediction equations are augmented on the basis of
Eq.(1) and Eq.(3).
Table 5 represents variables of multiple regression
analysis and compressive strength prediction model.
Table 8. Best-fit coefficient for various augmentations of the Lyse
formula. fp = b0 + b1(c/w) + b2c + b3(c/(s+g)) – at 28 days
Table 5. A variable of multiple linear regression analysis and
compressive strength prediction model
Table 9. Best-fit coefficient for various augmentations of the Abrams
formula. log fp = b0 + b1(w/c) + b2c + b3(c/(s+g))–at 28 days
Tables 6~9 show best-fit coefficient for various
augmentations of the Abrams and Lyse at 7 and 28 days.
Table 6. Best-fit coefficient for various augmentations of the Lyse
formula. fp = b0 + b1(c/w) + b2c + b3(c/(s+g)) – at 7 days
Prediction equations of No. 14 in Table 7 and 9 have
best-fit coefficient among various augmentations of
equations. Therefore, prediction equations of concrete
strength at 7 and 28 days are expressed as Eq.(4) and
(5). These are augmented from Abrams formula with
cement contents and cement-aggregate ratio.
To predict the compressive strength at 7 days the
following equation is obtained. The standard prediction
error of Eq.(4) is 1.1MPa.
Table 7. Best-fit coefficient for various augmentations of the
Abrams formula. log fp = b0 + b1(w/c) + b2c + b3(c/(s+g))– at 7 days
fP = exp[2.393 - 1.217(w/c) - 0.0048c + 6.16{c/(s + g)}]
...................... Eq.(4)
To predict the compressive strength at 28 days the
following equation is obtained. The standard prediction
error of Eq.(5) is 1.1MPa.
fP = exp[2.98 - 1.588(w/c) - 0.00642c +7.6888{c/(s + g)}]
...................... Eq.(5)
fp
w/c
c
w
c/(s+g)
where,
: prediction compressive strength, MPa
: water-cement ratio
: cement contents, kg/m3
: water contents, kg/m3
: cement-aggregate ratio
In Fig. 5, the experimental strength are compared to
corresponding values calculated by Eq.(4), whereas in
Fig. 6 the experimental values are compared to the
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Jee, Namyong
Table10. Experimental compressive strength and corresponding
values calculated by Eq.(4) & (5)
Fig.5. Comparison of experimental compressive strength with
corresponding values calculated by Eq.(4) at 7 days
Fig.6. Comparison of experimental compressive strength with
corresponding values calculated by Eq.(5) at 28 days
calculated values of Eq. (5).
Table 10 shows experimental compressive strength,
calculated compressive strength by Eq.(4) and (5), and
prediction error with respect to each mixture.
In case of mix No. 8 and 15 of Table 10, the prediction
error of compressive strength at 28 days is above 3MPa,
due to the high standard deviation of compressive
strength on RMC plant of K. When standard deviation
is high at the RMC plants, it can be recognized that
prediction error is high. Therefore, superior quality
management is demanded at the RMC plants in order to
be more applicable prediction by mixture proportions.
Fig. 7 shows the relation of experimental compressive
strength at 7 and 28 days.
JAABE vol.3 no.1 May. 2004
Jee, Namyong
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formula of Abrams with respect to cement contents and
cement-aggregate ratio. Standard prediction error of
prediction equation is 1.1MPa.
To predict the compressive strength at 7 days the
following equation is obtained.
fP = exp[2.393 - 1.217(w/c) - 0.0048c + 6.16{c/(s + g)}]
To predict the compressive strength at 28 days the
following equation is obtained.
fP = exp[2.98 - 1.588(w/c) - 0.00642c +7.6888{c/(s + g)}]
Fig.7. Relationship between in-situ compressive strength at 7
days and In-situ compressive strength at 28 days
4. Conclusions
From this study the following conclusions are
deduced.
1) In this study, standard deviation of compressive
strength of in-situ concrete is almost ‘Excellent’ level
according to ACI 214. However, compressive strength
of specimens cured in water at the laboratory
construction sites is over 14~29% as compared with
specified compressive strength.
2) Based on the results of correlation analysis
influential factors are water-cement ratio, cement-water
ratio, cement contents, cement-aggregate ratio in order.
The w/c is most influential.
It is efficient to consider the effects of these influential
factors for reliability of prediction of compressive
strength.
3) Compressive strength prediction equations were
provided for in-situ concrete with water-cement ratio of
0.39~0.62 and specified compressive strength of
18~27MPa at 7 and 28 days, which are modified from
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JAABE vol.3 no.1 May. 2004
fp
w/c
c
w
c/(s+g)
where,
: prediction compressive strength, MPa
: water-cement ratio
: cement contents, kg/m3
: water contents, kg/m3
: cement-aggregate ratio
References
1) Architectural Institute of Korea, “Korean Architectural Standard
Specification”, 1999
2) Korea Concrete Institute,“Concrete Standard Specification”, 2003
3) ACI Committee 214 (Reapproved 1997), “Recommended Practice
for Evaluation of Strength Test Results of Concrete”
4) ACI Committee 211.1-91, “Standard practice for selecting
proportion for Normal, Heavyweight, and Mass concrete”
5) ASTM C94-96,“Standard Specification for Ready Mixed Concrete”
6) Snador Popovics, “Analysis of Concrete Strength versus WaterCement Ratio Relationship”, ACI Material Journal, V.87, No.5,
September-October 1990, pp.517 529
7) Sandor Popovics and John S. Popovics, “Computerization of the
Strength Versus w/c relationship”, Concrete International, April
1995, pp.37-40
8) Sandor Popovics and John S. Popovics,“Novel Aspects in
Computerization of Concrete Proportioning”, Concrete
International, December 1996, pp.54-58
9) Ken Hover,“Graphical Approach to Mixture Proportioning by ACI
211.1-91”, Concrete International, September 1995, pp.49-53
10) Architectural Institute of Japan, “Japanese Architectural Standard
Specification (JASS 5 Reinforced Concrete Work)”, 1997, pp.200223
Jee, Namyong