Predicting 28 Days Compressive Strength of Concrete from 7 Days Test Result

International Conference on Advances in Design and Construction of
Structure - 2012
19-20 October 2012, Bangalore, India
Predicting 28 Days Compressive
Strength of Concrete from 7 Days
Test Result
Dr. Ahsanul Kabir
Professor, Dept. of Civil Engineering
Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh
Monjurul Hasan
Lecturer, Dept. of Civil Engineering
Z H Sikder University of Science & Technology, Shariatpur, Bangladesh
Dr. Md. Khasru Miah
Professor, Dept. of Civil Engineering
Dhaka University of Engineering and Technology, Gazipur, Bangladesh

 Introduction
 Objective
 Early Approaches
 Proposed Approach
 Mathematical Model
 Performance
 Conclusion
Outline

 Concrete has versatile use in the construction practice.
 The compressive strength is one of the most important
and useful properties of concrete.
 The design strength of the concrete normally
represents its 28th day strength.
 28 days is a considerable time to wait for the test
results of concrete strength, while it is mandatory to
represent the process of quality control.
Introduction

 For every mix one has to wait a long time for the
assurance of its quality.
 Hence, the need for an easy and suitable means for
estimating the strength at an early age of concrete
is being felt all the time.
Introduction (Contd..)

 To evaluate nature of concrete strength gain
pattern with time for a particular type of mix.
 To formulate a quick, handy & flexible
computational method to asses the nature of
concrete strength gain with time.
 To develop a simple relation which has the
potential to predict the compressive strength of
the concrete from early days strength.
Objective

 Traditional empirical formula
 Linear Regression model
 Multivariable Regression model
 Artificial neural network
 Genetic algorithm
 Support vector mechanism
Early Approaches

Liner regression equation ( Jee et al., 2004)
𝑓 = 𝐴 + 𝐵(
𝑐
𝑤
)
Multi variable regression model ( Zain et al., 2010)
𝑓𝑎𝑔𝑒 = 𝑎0 𝐶 𝑎1 𝑊 𝑎2 𝐹𝐴 𝑎3 𝐶𝐴 𝑎4 𝜌 𝑎5 𝑤/𝑐 𝑎6
Artificial neural network
Early Approach (cntd…)
Figure: Feed forward neural network

 Data used for this study (Group-1) was taken from previous study (Garg,
2003)
Proposed Approach
Experimental Data
TABLE A : CONCRETE MIX PROPORTION OF GROUP-1 SAMPLES

 Another completely a different sets of data(called Group-2)
are also used , which are from a recent work ( Hasan, 2012)
Proposed Approach ( cont. …)
TABLE B : CONCRETE MIX PROPORTION OF GROUP-2 SAMPLES

 Concrete Data Ranges
(without Admixture, ordinary Portland cement)
TABLE 1 : PROPERTY RANGES OF GROUP-1 AND GROUP-2 TESTS

 First step : to understand the strength gaining pattern of
the concrete with age
Figure a : Strength gaining curve for representative sets

Proposed Mathematical Model
fc,D
′
=
D
D+q
p (3)
where, fc,D
′
= Strength of the concrete at Dth day.(D = 1,2,3,…..); D= Number
of days; p and q are constants for each curve but different for different data
sets (curves). It may be mentioned that this equation (Eq. 1) is similar to the
equation (Eq. 2) proposed by ACI committee ( ACI 209-71) for predicting
compressive strength at any day based on 28 days strength.
(fc
′
)t =
t
a + b. t
. fc
′
28d 4
Here, a and b are constants, (fc
′)28d= 28-day strength and t is time. This
equation (Eq. 2) can be recast to similar form of Eq. 1.

 Table 4 shows the values of p and q for three arbitrary data
sets.
 These are obtained from the best fit curves for each set of
data.
 The values of p and q can also be determined by putting
strength test results in Equation 1 for any two days and
solving it
Mathematical Model ( Cont. ...)
TABLE C : REPRESENTATIVE SAMPLE SETS CORRELATION

 In this study, an attempt has been made to determine these values
from only one day test result.
 An empirical relation is developed for this particular case (particular
type of ingredients of concrete) to solve the problem.
 It is observed that, all values of p, q and strength of a particular day
fc,D
′
for each set maintain a correlation of polynomial surface.
 In other words, values of p can be expressed as the function of q
and fc,D
′
[which represent a polynomial surface]. The equation of the
correlation is given below:
𝑝 = 𝑎 + 𝑏. 𝑞 + 𝑐. 𝑓𝑐.𝐷
′
+ 𝑑. 𝑞. 𝑓𝑐.𝐷
′
+ 𝑒. {𝑓𝑐.𝐷
′
}2 (5)
Where, fc,D
′
= Strength of the concrete at Dth day; (D = 1, 2, 3 …) and
a, b, c, d and e are the coefficients of different terms.

As we build up the correlation for 7th day test result of concrete [D=7], the
values of the coefficients were derived as, a = -6.26 ; b = 0.7898 ;
c = 1.478; d = 0.0994; e = - 0.0074 from regression analysis of the available data
for concrete with stone chips as course aggregate
Putting these values in Equation 3 the following equation was obtained:
𝒑 = −𝟔. 𝟐𝟔 + 𝟎. 𝟕𝟖𝟗𝟖𝒒 + 𝟏. 𝟒𝟕𝟖𝒇 𝒄.𝟕
′
+ 𝟎. 𝟎𝟗𝟗𝟒𝒒. 𝒇 𝒄.𝟕
′
−𝟎. 𝟎𝟎𝟕𝟒{𝒇 𝒄.𝟕
′
} 𝟐 (6)
For 14th day strength results [D=14] the coefficients are, a = -4.527; b = -
1.041; c = 1.373; d = 0.1406; e = -0.0125. Putting these values into Equation 3 the
following equation was obtained:
𝒑 = −𝟒. 𝟓𝟐𝟕 − 𝟏. 𝟎𝟒𝟏𝒒 + 𝟏. 𝟑𝟕𝟑𝒇 𝒄.𝟏𝟒
′
+ 𝟎. 𝟏𝟒𝟎𝟔𝒒. 𝒇 𝒄.𝟏𝟒
′
− 𝟎. 𝟎𝟏𝟐𝟓 𝒇 𝒄.𝟏𝟒
′ 𝟐
(7)

Represented surface ….
Figure b : Polynomial Surface Representing Equation 6

 Eq. 5 contains five constants which need to be determined,
before solving the prediction problem
 It is observed that the p value which is obtained by solving Eq.
3 and Eq. 6 for 7 days strengths maintains a systematic
correlation
 This correlation can be expressed in a general form as given
by the following equation
𝑝 = 𝑚(𝑓𝑐,𝐷
′
) 𝑟
(8)
Where, fc,D
′
= Strength of the concrete at Dth day and m and r are
the coefficients.

Using the available 56 test data, these coefficients are
determined from best fit equation. With slight rounding off it is
found that, m = 3.0; r = 0.80, goes quite well with the 7 days
strength results.
𝑝 = 3.0(𝑓𝑐,7
′
)0.8 (9)
Using 14 days concrete strength the general correlation
equation (Eq. 8) may be expressed as,
𝑝 = 2.5(𝑓𝑐,14
′
)0.8 (10)

Plots of Eq. 9 and Eq. 10 is shown in Fig. 4
Figure I : Variation of p with the strength of Concrete.

Performance
The performance of the proposed equations are evaluated by
three statistical parameters, mean absolute error (MAE), root
mean square error (RMSE) and normal efficiency (EF); their
expressions are given below.
MAE =
1
𝑛
𝑖=1
𝑛
(|𝑃𝑖 − 𝐴𝑖|) (11)
RMSE =
1
𝑛
𝑖=1
𝑛
𝑃𝑖 − 𝐴𝑖
2 (12)
EF = 1 −
1
𝑛
𝑖=1
𝑛
( 𝑃𝑖 − 𝐴𝑖 )
𝐴𝑖
× 100 % (13)

Performance ( Cont. ...)
Test for Stone-Aggregate
TABLE D : PREDICTION OF COMPRESSIVE STRENGTH (GROUP-1 DATA)

Test for Stone-Aggregate

Test for Brick-Aggregate

 This paper represents a simple mathematical model fro predicting
concrete strength from 7 days test result
 This model shows independency regarding aggregate types
 In this study, the concrete strength gain characteristic with age is
modeled by a simple mathematical equation (rational polynomial) and a
polynomial surface equation
 The polynomial surface equation is further simplified with a power
equation containing only two constants
( Reduced number of constants and so number of unknowns)
 The proposed equations have the potential to predict strength data for
every age.
 This will help in making quick decision for accidental poor concreting at
site and reduce delay.
Conclusion

The authors wish to thank the technicians of the
Concrete laboratories of Bangladesh University
of Engineering & Technology (BUET) and Dhaka
University of Engineering and Technology
(DUET). This work was supported by the Civil
Engineering departments of the two
universities.
Acknowledgement

Predicting 28 Days Compressive Strength of Concrete from 7 Days Test Result

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