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

nternational Conference on Advances in Design and Construction of
Structure - 2012
19-20 October 2012, Bangalore, India
(presentation slides)

1. 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. AhsanulKabir
Professor, Dept. of Civil Engineering
Bangladesh University of Engineering and Technology, Dhaka 1000, Bangladesh
MonjurulHasan
Lecturer,Dept. of Civil Engineering
Z H SikderUniversity of Science & Technology, Shariatpur, Bangladesh
Dr. Md. KhasruMiah
Professor, Dept. of Civil Engineering
Dhaka University of Engineering and Technology, Gazipur, Bangladesh

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

3. Concretehasversatileuseintheconstructionpractice.
Thecompressivestrengthisoneofthemostimportant
andusefulpropertiesofconcrete.
Thedesignstrengthoftheconcretenormally
representsits28
th
daystrength.
28daysisaconsiderabletimetowaitforthetest
resultsofconcretestrength,whileitismandatoryto
representtheprocessofqualitycontrol.
Introduction

4. Foreverymixonehastowaitalongtimeforthe
assuranceofitsquality.
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..)

5. 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

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

7. Liner regression equation ( Jeeet al., 2004)
�=�+�(
�
??????
)
Multi variable regression model ( Zainet al., 2010)
�
??????????????????=�
0�
??????1??????
??????2??????�
??????3��
??????4??????
??????5??????/�
??????6
Artificial neural network
Early Approach (cntd…)
Figure: Feed forward neural network

8. 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

9. 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

10. Concrete Data Ranges
(without Admixture, ordinary Portland cement)
Proposed Approach ( cont. …)
TABLE 1 : PROPERTY RANGES OF GROUP-1 AND GROUP-2 TESTS

11. First step : to understand the strength gaining pattern of
the concrete with age
Proposed Approach ( cont. …)
Figure a : Strength gaining curve for representative sets

12. Proposed Mathematical Model
f
c,D
′
=
D
D+q
p (3)
where, f
c,D
′
= Strength of the concrete at Dthday.(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.
(f
c
′
)
t=
t
a+b.t
.f
c
′
28d 4
Here, a and b are constants, (f
c
′
)
28d= 28-day strength and t is time. This
equation (Eq. 2) can be recast to similar form of Eq. 1.

13. 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

14. 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
f
c,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 f
c,D
′
[which represent a polynomial surface]. The equation of the
correlation is given below:
�=�+�.�+�.�
??????.??????
′
+�.�.�
??????.??????
′
+�.{�
??????.??????
′
}
2
(5)
Where, f
c,D
′
= Strength of the concrete at D
th
day; (D = 1, 2, 3 …) and
a, b, c, dand eare the coefficients of different terms.
Mathematical Model( Cont. ...)

15. As we build up the correlation for 7
th
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 = -0.0074from 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:
�=−�.��+�.�����+�.���??????
??????.�
′
+�.�����.??????
??????.�
′
−�.����{??????
??????.�
′
}
�
(6)
For 14
th
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:
�=−�.���−�.����+�.���??????
??????.��
′
+�.�����.??????
??????.��
′
−�.����??????
??????.��
′ �
(7)
Mathematical Model ( Cont. ...)

16. Mathematical Model ( Cont. ...)
Represented surface ….
Figure b : Polynomial Surface Representing Equation 6

17. 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
�=�(�
??????,??????
′
)
??????
(8)
Where, f
c,D
′
= Strength of the concrete at D
th
day and m and r are
the coefficients.
Mathematical Model( Cont. ...)

18. 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.
�=3.0(�
??????,7
′
)
0.8
(9)
Using 14 days concrete strength the general correlation
equation (Eq. 8) may be expressed as,
�=2.5(�
??????,14
′
)
0.8
(10)
Mathematical Model( Cont. ...)

19. Plots of Eq. 9 and Eq. 10 is shown in Fig. 4
Mathematical Model( Cont. ...)
Figure I: Variation of p with the strength of Concrete.

20. 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
�

??????=1
??????
(|??????
??????−�
??????|) (11)
RMSE=
1
�

??????=1
??????
??????
??????−�
??????
2
(12)
EF=1−
1
�

??????=1
??????
(????????????−�
??????)
�
??????
×100% (13)

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

22. Performance ( Cont. ...)
Test for Stone-Aggregate

23. Performance ( Cont. ...)
Test for Brick-Aggregate

24. Performance ( Cont. ...)

25. 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

26. Theauthorswishtothankthetechniciansofthe
ConcretelaboratoriesofBangladeshUniversity
ofEngineering&Technology(BUET)andDhaka
UniversityofEngineeringandTechnology
(DUET).ThisworkwassupportedbytheCivil
Engineeringdepartmentsofthetwo
universities.
Acknowledgement

27. Thank You