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 KabirProfessor, Dept. of Civil Engineering

Bangladesh University of Engineering and Technology, Dhaka 1000, BangladeshMonjurul Hasan

Lecturer, Dept. of Civil EngineeringZ H Sikder University of Science & Technology, Shariatpur, Bangladesh

Dr. Md. Khasru MiahProfessor, 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 importantand useful properties of concrete.

The design strength of the concrete normallyrepresents its 28th day strength.

28 days is a considerable time to wait for the testresults of concrete strength, while it is mandatory torepresent the process of quality control.

Introduction

For every mix one has to wait a long time for theassurance 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 = 𝑎0𝐶𝑎1𝑊𝑎2𝐹𝐴𝑎3𝐶𝐴𝑎4𝜌𝑎5𝑤/𝑐𝑎6

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+qp (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. 𝟒𝟕𝟖𝒇𝒄.𝟕′ + 𝟎. 𝟎𝟗𝟗𝟒𝒒. 𝒇𝒄.𝟕

′ −𝟎. 𝟎𝟎𝟕𝟒{𝒇𝒄.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. 𝟑𝟕𝟑𝒇𝒄.𝟏𝟒′ + 𝟎. 𝟏𝟒𝟎𝟔𝒒. 𝒇𝒄.𝟏𝟒

′ − 𝟎. 𝟎𝟏𝟐𝟓 𝒇𝒄.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 − 𝐴𝑖2 (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 theConcrete laboratories of Bangladesh Universityof Engineering & Technology (BUET) and DhakaUniversity of Engineering and Technology(DUET). This work was supported by the CivilEngineering departments of the twouniversities.

Acknowledgement

Thank You