More simply, this means that one can produce a concrete mixture more economical using the knowledges and methodology or resources accessible and attain the needs desired for a concrete structure. For this purpose one can use a lot of methods that follow a logical based in the optimization to indicate us one mixture that will be capable to attend all desired concrete properties.

Thank you very much Luiz for letting in your thoughts on the subject. I appreciate.

Just complementing the excellent definition provided by Luiz Antonio: traditionally, the concept of rational mix design of concrete is also linked to the experimental methodologies, involving the actual materials that will be applied in the concrete production, in opposite with the idea of use pre-conceived proportions based on empirical information.

The idea of rational design in brief would be:-

Rational design = Densest possible packing of available aggregate fractions (for economy and better stability) + Sufficient paste to produce work-ability with a w/c which would provide the desired strength (invariably with a plasticizing admixture)

it is a method to calculate the best percentage of each material to achieve your target characteristics. it is kind of optimization  

I agree with the nice submission of Luiz Antonio, particularly with the very KEY idea brought in by Antonio D. Figueiredo. In furtherance of their thoughts on this matter, I like to make it more open than others have explained it. With this, I hope the questioner will get a better picture, and I will also expose my own ignorance to learn more from others.

The term "rational" itself, linguistically speaking, is an adjective that means "in accordance with reason". In engineering theory and practice, technically speaking, we use it to mean "justifiable", mostly, in mathematical senses. Just like the nice contribution of Antonio D. Figueiredo, a rational design of anything - mixtures, structures, etc - should stand on clear mathematical basis, "in opposite with the idea of use pre-conceived proportions based on empirical information", such that any desired objective behavior of the system (such as the concrete mixture in the present matter) can be tuned by playing with mathematical parameters, rather than simply by empirical treatment.

It is worth mentioning that rational design does not have to be strictly based on mathematics: in an actual sense, it needs empirical complements, such as calibrating mathematical parameters by experimentation, derivation of correction factors, and a host of other things. Finally, a rational design method will allow optimization of certain desired properties, such as concrete workability, strength, density, etc.

thanks Luiz for your valuable answer

Good mr Kaustav Sarkar for your brief answer.