Full Paper Proc. of Int. Conf. on Advances in Design and Construction of Structures 2012
Predicting 28 Days Compressive Strength of Concrete from 7 Days Test Result Ahsanul Kabir1, Monjurul Hasan2 and Md. Khasro Miah3 1
Bangladesh University of Engg. & Tech. /Dept. of Civil Engineering, Dhaka, Bangladesh Email: firstname.lastname@example.org 2 Z H Sikder University of Science & Tech. /Dept. of Civil Engineering, Shariatpur, Bangladesh Email: email@example.com 3 Dhaka University of Engg. & Tech. /Dept. of Civil Engineering, Gazipur, Bangladesh Email: firstname.lastname@example.org process becomes mandatory, which can be costly and time consuming. For every failure, it is necessary to wait at least 28 days, thus the need for an easy and reliable method for estimating the final strength at an early age of concrete is a long felt necessity. Hence, a rapid and suitable concrete strength prediction would be of great significance . Many studies are being carried out to explore the behavior of concrete and to make a better prediction of its characteristic strength. In this paper a mathematical model to evaluate the concrete strength from early age test results is discussed which represents a relationship equation in between concrete strength and its age . A simplification of the model is also proposed. The model is established based on the experimental result of concrete cylinder tests made with stone aggregate  and then checked for stone aggregate concrete prepared and tested in a different laboratory of a different country . Finally, the same model is used to predict 28 days strength of concrete made with brick aggregates.
Abstractâ€”Concrete structures are designed on the basis of 28 days cylinder crushing strength. 28 days cylinder strength actually represents the characteristic strength of the concrete. It is mandatory to test the concrete cylinders at the age of 28 days as per almost all building code requirements. Though it is quite time consuming to wait 28 days for such tests, it is important to continue the construction work and ensure the quality control process. This paper presents a simple mathematical model to predict the compressive strength of concrete at 28 day from early age (say 7 days) results. The model is a simple equation (a rational polynomial) that consists of only two constants and one variable which is the age of concrete in days. It is found that the constants have the relation of a surface polynomial with the strength of a particular day (7 th day or 14 th day). This is further simplified with a direct correlation of one of the coefficient with concrete strength value. The mathematical model is developed based on the analysis of stone aggregate concrete data collected from a previous study and is validated with some experimental data of cylinder tests performed in the Concrete laboratory of Bangladesh University of Engineering and Technology (BUET), Dhaka. The proposed model has a good potential to predict concrete strength at different age with high accuracy. This has been finally employed to predict 28 days strength of concrete made with brick aggregates from their 7 days test results.
II. BACKGROUND Early prediction of concrete compressive strength enables to know quickly about the concrete and its probable weakness and decide to continue the construction or manage the destruction program. Therefore, prediction of the compressive strength of concrete has been an active area of research. Several methods for early estimation have been introduced in some previously published studies. These attempts were made to predict the 28 days concrete compressive strength from early days test results but those had some limitations . Many efforts are made on using different techniques as computational modeling, statistical techniques. A number of research efforts have concentrated on using multivariable regression model to improve the accuracy of prediction. In a recent study  multivariable power equation is chosen as an effective model for prediction of strength of different ages of concrete (Eq. 1). The general format of the equation is given below:
Index Termsâ€”concrete, compressive strength, brick aggregate concrete, strength prediction.
I. INTRODUCTION Concrete has its benefits of strength, availability, durability, flexibility and economy. In case of designing a concrete structure, the compressive strength of concrete is an essential element. 28days compressive strength of concrete is usually considered as the design strength. To ensure this strength it is necessary to wait a considerable time i.e. 28 days. It becomes mandatory because it also represents the quality control process of concrete mixing, placing, compaction, curing etc. Concrete mix design is a process that uses code recommendation and blends with the experience of the concerned engineer. Due to some error in mix design or mix preparation at site the test results may fail to achieve the designed strength, then repetition of the entire Corresponding Author: Dr. Ahsanul kabir, Department of Civil Engineering, BUET, Dhaka 1000, Bangladesh
ÂŠ 2012 ACEE DOI: 02.ADCS.2012.1.505
Full Paper Proc. of Int. Conf. on Advances in Design and Construction of Structures 2012 In the above equation compressive strength of a particular day (fage) is considered as the dependent variable on the variables which has significant correlation with the strength like the water-cement ratio (w/c), cement (C), water (W), sand (FA), Aggregate (CA) content and density of concrete (ρ) and then the Eqn. 1 becomes: (2)
it is expected that the strength gain pattern of brick aggregate concrete would be quite similar to that of stone aggregate concrete, the effectiveness of the proposed mathematical model for strength prediction is also tested with these brick aggregate concrete test results. TABLE I. PROPERTY RANGES OF GROUP 1 AND GROUP 2 T EST DATA
The values of a0, a1, a2, a3, a4, a5 and a6 were determined from regression of statistical data and able to predict the strength of concrete for a particular age directly. To know about the strength history of the corresponding day it is required to identify the coefficients [a0, a1, a2…] of the model (Eq. 2) individually. Alternatively, soft computing models namely Neural Network, Fuzzy-Logic and Genetic Algorithm are used for strength prediction but in this case training computation is needed to form the model and to solve the problem [5, 7-8]. Some recent studies considered the early days strength result as an important index for the prediction of concrete strength [5, 8] and the aim of this study is also to predict the concrete compressive strength from early days strength result. Previously many parameters have been considered for prediction of concrete strength which influences its strength gaining characteristics. In this study, attempt is made to predict the concrete strength from an early days concrete strength test result. The model is developed by exploring the concrete strength gain pattern with age.
IV. MATHEMATICAL MODEL The mathematical model for predicting the compressive strength of the concrete focused on the determination of a general equation of strength gaining nature of concrete with its age . Investigation shows that all the concrete strength maintains a correlation with its age according to the following simple equation:
III. EXPERIMENTAL DATA Total 56 sets of available Data (called Group-1) have been used for developing the mathematical model which are taken from a previous study by Garg  and the validation of the model is done using the experimental data (called Group-2) obtained from tests carried out recently in the Concrete laboratory of BUET . Ranges of material properties and concrete strengths achieved for Group-1 and Group-2 data sets are summarized in Table I. No admixtures or additives are used in either case of study; only the general constituents of concrete [Cement(C), Coarse-Aggregate (CA), Fine-Aggregate (FA) and Water (W)] are used to evaluate the concrete compressive strength. Different mix proportions of the ingredients and different w/c ratio are used to study the variations. All the specimens were immersed in water until the day of testing and variation of temperature was negligible so, the effect of temperature variation is neglected. Group-1 and Group-2 experimental data are for stone aggregate normal concrete made with ordinary Portland cement. The experimental investigations are carried out in two different laboratories of two different countries. Later, some test results are made available for brick aggregate concrete  which is widely used in Bangladesh. These are also cast using ordinary Portland cement. Altogether 27 test results for different sizes of cylinder molds are available. As
© 2012 ACEE DOI: 02.ADCS.2012.1. 505
(3) where = 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. 3) is similar to the equation (Eq. 4) proposed by ACI committee ( ACI 209-71)  for predicting compressive strength at any day based on 28 days strength. (4) Here, a and b are constants, = 28-day strength and t is the time in days and this equation (Eq. 4) can be recast to similar form of Eq. 3. To utilize the derived equation (Eq. 3), just value of two constants (p and q) are to be determined. It may be mentioned that the constant q has the unit of day and p has the stress unit to be consistent with the expression.
Full Paper Proc. of Int. Conf. on Advances in Design and Construction of Structures 2012 The values of p and q can be determined by putting strength test results in Eq. 3 for any two days and solving it; but for this, test results for at least two different days are required. An attempt has been made to determine these values from only one day test result . It is observed that, all values of p, q and strength of a particular day for each set maintain a correlation of polynomial surface. In other words,
(10) Plots of Eq. 9 and Eq. 10 is shown in Fig. 1. Thus, the ccorresponding p values can be obtained by putting known 7 days or 14 days concrete strength values in the Eq. 9 or Eq. 10. Then, q is computed from Eq. 3 using 7 or 14 days strength value and the p-value just obtained in the last step. Finally, the q and p-value determined can be used to find the 28 days strength of concrete using Eq. 3
values of p can be expressed as the function of q and [which fits well with a second degree polynomial surface equation]. The equation of correlation is given below: (5) Where = Strength of the concrete at Dth day. (D = 1, 2, 3 …) and a, b, c, d and e are the coefficients. This general relation of p, q and is valid for any days test result of concrete strength. For different D days strength, just the coefficients [a, b, c, d, e] of Eq. 5 will be different. As the correlation is built up for 7th day test result of concrete [D=7], the values of the coefficients becomes, a = -6.26; b = 0.7898; c = 1.478; d = 0.0994; e = -0.0074. Putting these values in Eq. 5 the following equation is obtained:
Figure 1. Variation of p with the strength of Concrete.
(6) Similar equation is developed for 14th day strength results [D=14] and can be expressed as follows:
V. PERFORMANCE The performance of the proposed equations was evaluated by three statistical parameters, mean absolute error (MAE), root mean square error (RMSE) and normal efficiency (EF); their expressions are given below.
(7) Now, if the 7 days strength value is put in Eq. 6, it becomes a linear equation in p and q. Thus, solving two linear equations (Eq. 3 and Eq. 6), values of p and q are obtained for each case. Finally, after finding the values of p and q the complete equation for the particular case can be formed which can effectively predict the compressive strength of 28th days. Eq. 5 contains five constants which need to be determined, before solving the prediction problem. These constants can be evaluated by regression with sufficient data of test results of a particular day. From the study, 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 (Eq. 8). It simplifies the problem of prediction significantly (8)
(13) Here, Ai = Actual value; Pi = Predicted value; n = number of data (1, 2, 3 …). A. Test for Stone AggregateConcrete The model is basically developed using Group-1 test data made available by the study of Garg  where crushed stone are used as coarse aggregates. The test results of Hasan  (Group-2 data) for stone aggregate concrete is used to validate the prediction capability of the proposed model. Some twenty three data (each average of 3 sets) are employed and from there arbitrary seven results are tabulated here in Table II.
Where = Strength of the concrete at D 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. Thus the Eq. 8 becomes: (9) Using 14 days concrete strength the general correlation equation (Eq. 8) may be expressed as, © 2012 ACEE DOI: 02.ADCS.2012.1.505
Full Paper Proc. of Int. Conf. on Advances in Design and Construction of Structures 2012 TABLE V. PREDICTION O F C OMPRESSIVE STRENGTH OF B RICK AGGREGATE CONCRETE
TABLE II. PREDICTION OF CONCRETE STRENGTH (GROUP -2 DATA)
The overall effectiveness of the proposed model considering all the 56 test data of Group-1 and 23 test data of Group-2 is summarized below in Table III. TABLE III. EFFECTIVENESS OF THE PROPOSED MODEL FOR G ROUP-1 & GROUP -2 DATA
C. Discussion on Results This study is carried out for normal weight concrete having no admixture and the ordinary Portland cement (OPC) used as binder for concrete mixing. The model is developed for the strength results of concrete made with stone aggregate (Group-1) and the efficiency is found to be 90%. Observed RMSE, MAE and avg. Pi/Ai are 3.23, 2.68 and 1.03 respectively, which may be considered as quite satisfactory. Next the developed model is validated for the data sets of concrete strength which are cast in a different country with local ingredients (Group-2) and for these concrete specimens made with locally available crushed stone chips, the same good performance is observed. Table III shows the prediction efficiency for both Group-1 & Group-2 data. The comparison demonstrates that the RMSE (3.23, 2.53), MAE (2.68, 2.12) and avg. Pi/Ai (1.03, 1.04) are very close to each other. Finally, the proposed model was further checked for concrete made with brick aggregates. In some countries like Bangladesh use of brick chips as the coarse aggregate is a common practice. The nature of strength gain of brick aggregate concrete with age follows similar trend like that of stone aggregate concrete if ordinary Portland cement is used as a binder in either case. So, the proposed model is expected to perform well. As expected, the results of prediction for brick aggregate concrete shows equal accuracy as that of the concrete made with stone aggregate. The efficiency of prediction is about 92% and the average Pi/Ai is very close to unity. The RMSE [2.26] and MAE [1.92] are within acceptable range considering the level of scatter usually exhibited by concrete strength.
B. Test for Brick-AggregateConcrete The proposed model was developed on the basis of compressive strength of concrete cylinder made with stone aggregates. However, it is also validated here with test results of compressive strength of concrete cylinders made with brick aggregates . TABLE IV. PREDICTION EFFECTIVENESS FOR B RICK AGGREGATE CONCRETE
Table IV shows the summary of the prediction effectiveness with all the 27 concrete test results of brick aggregate concrete made in different size concrete molds and Table V represents the predicted values of compressive strength for sixteen concrete cylinders (150x300mm size) made with brick aggregates. The predicted 28 days compressive strength for concrete made with brick aggregate from 7 days test result is quite satisfactory. ÂŠ 2012 ACEE DOI: 02.ADCS.2012.1. 505
Full Paper Proc. of Int. Conf. on Advances in Design and Construction of Structures 2012 CONCLUSIONS
 Hasan M.M. and Kabir A., “Prediction of Compressive Strength of Concrete from Early Age Test Result”. Proceedings of 4th Annual Paper Meet and 1st Civil Engineering Congress, Dhaka, Bangladesh, December 22-24, 2011, pp. 1-7.  Garg R., “Artificial Neural Network for Concrete Mix Design”. Masters of Engineering thesis, Department of Civil Engineering, Thapar Institute of Engineering and Technology, Patiala, 2003.  Hasan M., “Concrete mix design using artificial neural network”. Bachelor of Engineering thesis, Department of Civil Engineering, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh 2012.  Hamid-Zadeh N., Jamli A., Nariman-Zadeh N. and Akbarzadeh H., “A Polynomial Model for Concrete Compressive Strength Prediction using GMDH-type Neural Networks and Genetic Algorithm”. Proceedings of the 5th WSEAS International Conference on System Science and Simulation in Engineering, Canary Islands, Spain, December 16-18, 2006, pp. 13-18.  Zain M.F.M., Suhad M. Abd, Hamid R. and Jamil M., “Potential for Utilizing Concrete Mix Properties to Predict Strength at Different Ages”. Journal of Applied Sciences, Vol. 10(22), 2010, pp. 2831-2838.  Neshat M., Adeli A., Sepidnam G., Sargolzaei M., “Comparative Study on Fuzzy Interference System for Prediction of Concrete Compressive Strength”, International Journal of the Physical Sciences, Vol. 7(3), 2012, pp. 440-455.  Alilou V.K., Teshnehlab M., “Prediction of 28-day compressive strength of concrete on the third day using neural networks”, International Journal of Engineering, Vol. 3(6), 2010, pp. 565575.  Islam Md. M., Islam Md. Z. and Shahabuddin, B. M, “Effect of Specimen Sizes on the compressive strength of Brick Aggregate Concrete”, Undergraduate thesis, Department of Civil Engineering, Dhaka University of Engineering & Technology (DUET), Gazipur, Bangladesh, 2008.  ACI COMMITTEE 209, “Creep Shrinkage Temperature in Concrete Structures” (ACI 209-71), American concrete Institute, Detroit, Michigan, 1971, sp. 27-13, pp. 258-269.
This paper simplifies the mathematical model to estimate the 28 days compressive strength of concrete from just only one parameter, 7 days test results without considering the other index properties of concrete [e.g. water, cement, w/c ratio, FA, CA, density (ρ)] and gives an initial idea of the 28 days strength with reasonable accuracy. In this study, modeled concrete strength gain characteristic with age is simplified and a simple mathematical (power) equation is introduced which replaces the polynomial surface equation. The proposed equations predicts well the 28 days strength for concrete made with stone aggregate and has potential to predict the strength of concrete made with brick aggregates. The proposed technique can be used as a reliable tool for assessing the design strength of concrete from quite early age test results. Besides predicting 28 days strength for ordinary Portland cement concrete, expected concrete strength at any age (say 21, 60 or 360 days) can be determined from the proposed model. ACKNOWLEDGMENT 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. REFERENCES  Kheder G.F., Al-Gabban A.M. and Suhad M.A., “Mathematical model for the prediction of cement compressive strength at the ages of 7 and 28 days within 24 hours”. Materials and Structure. Vol. 36, 2003, pp. 693-701.
© 2012 ACEE DOI: 02.ADCS.2012.1. 505