Your question is to estimate f'c after 28 days, not at 28 days based on earlier data. If this is true, then each mix design differs. For example if you have high volume fly ash mix, it will gain substantial strength after 28 days. On the other hand if you have a mix with high early strength cement it will not gain much strength after 28 days. So a single prediction equation or tool for all kinds of mixtures will not work. The best way is to do a maturity study on your particular mix design.

Dear Najla,

Many a time it may be necessary to estimate the strength of concrete not only at an early age but also at later ages. Many research workers have attempted to estimate the strength of concrete at 1, 3 or 7 days and correlate to 28-day strength. Numerous research works have provided certain relationships. For instance;

In Germany, the relation between 28-day strength fc28 and the 7-day strength, fc7 is taken to lie between,

equation(1)

Turn MathJaxon

Another formula was proposed as follows:equation(2)

fc28=K2(fc7)K1 Turn MathJaxon

where, fc7 and fc28 are the strengths at 7 and 28 days, respectively. K1 and K2 are the coefficients which are varied for different cements and curing conditions. The value ofK1 ranges from 0.3 to 0.8 and that of K2 from 3 to 6. 

Earlier ECP [3] considered compressive strength gain as a parameter of age through the coefficients for ordinary Portland cement concrete strength as 0.4, 0.75, 1.0, 1.176 and 1.33 for 3, 7, 28, 90 and 360 days age, respectively. Whereas, for rapid strength Portland cement concrete those values were given as 0.556, 0.8363, 1, 1.111 and 1.176 for 3, 7, 28, 90 and 360 days, respectively. But with issuing the last version of ECP , the coefficients considering the variation of compressive strength with age had been omitted.

In the history of concrete technology, Abrams’ formula was the first one describing the dependence of concrete strength on water cement ratio. Abrams suggested a mathematical relationship between concrete strength and water/cement ratio as:

equation(3)

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where (fc) is the compressive strength of concrete; A and B are experimental parameters for a given age, material and curing conditions; and (x) is water/cement ratio by mass. 

For an average Portland cement concrete cured under normal temperature and moisture, Abrams gave the relationship between compressive strength and water/cement ratio as;

equation(4)

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where, fc7 and fc28 are the strengths in MPa at 7 and 28 days, respectively. Moreover (x) is the water/cement ratio. 

To consider the use of mineral admixtures in concrete, many studies have shown that when the water/binder ratio is used instead of water/cement ratio as basis for mix design; strength prediction becomes more accurate.

The water binder ratio takes the following shape;

equation(5)

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where x is water/binder ratio; w is water content; c is cement content; f is fly ash content; s is granulated blast furnace slag (GBFS) content and k is an efficiency factor. 

Beside Abrams’ formula, the power formula is considered as one of the most useful formulae in the field of concrete technology. It takes the following form:

equation(6)

fc=Ax-BTurn MathJaxon

where (fc) is the compressive strength; A and B are experimental parameters for a given age and x is the water/cement ratio. 

Implementation of either Abrams’ formula or power formula to predict the concrete strength at any age requires collecting a lot of data at that age, then build a specific formula, and using a time factor (a function of age) multiplied by specific age strength (usually 28 – day strength) to estimate the strength at a given age.

Yeh proposed two novel methodologies, parameter – trend – regression and four – parameter – optimization methodology to extend Abrams’ formula and the power formula to any given age without collecting data at that age. The proposed model is a generalization of Abram, formula and the power formula, respectively, to be;

Turn MathJaxon

equation(7)

fc,t=Atx-BtTurn MathJaxon

where (fc,t) is the concrete compressive strength at age t days; (At) and (Bt) are experimental parameters depending on age and (x) is the water/binder ratio . 

Early age strength prediction in concrete is very useful in reducing construction cost and ensuring safety. Furthermore, early age strength prediction has several practical applications. It can be used to determine safe stripping time, prestressing application or post – tensioning time, to monitor strength development, particularly when concreting in cold weather, to check serviceability conditions or compliance criteria, to ensure construction safety and, generally to estimate the quality of construction and potential durability.

Moreover prediction of concrete strength at late ages is being significant from both technical and economical points of view. For instance, when considering the actual strength values at which the structure is being subjected to full load, materials safe could be achieved as considered by BS in the track of minimizing the pollution.

Concrete compressive strength is influenced by many factors including, water/cement ratio, cement content and properties, aggregate type and its properties, etc. This paper introduces a simple mathematical model that can help predicting the compressive strength for a specified concrete mix at any age with the help of two fixed constants indicating the mix. Those constants could be estimated by two different methods; the first method is based on solving two simultaneous equations at two different ages whereas, the second depends on compressive strength at 28-day age.

To view equations 1-7 and other models, please use the following link:

http://www.sciencedirect.com/science/article/pii/S1687404813000783

Hoping this will be helpful,

Rafik

Thank you very much

Your question is to estimate f'c after 28 days, not at 28 days based on earlier data. If this is true, then each mix design differs. For example if you have high volume fly ash mix, it will gain substantial strength after 28 days. On the other hand if you have a mix with high early strength cement it will not gain much strength after 28 days. So a single prediction equation or tool for all kinds of mixtures will not work. The best way is to do a maturity study on your particular mix design.

FC' depends on many parameters and especially on the porosity of concrete

FC' depends on many parameters and especially on the porosity of concrete irrespective of its constituents and mix

The compressive strength depends on several parameters, namely, the type of cement, type of aggregates and their size, the W / C ratio, the method of mixing and curing conditions.  For each composition and manufacturing method,  a relationship between the compressive strength and age of the concrete can be established. You can consult the attached files.