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A popular simplified mix design method is that from BRE.
Compressive strength is, in general, related to durability. The greater the strength the more durable the concrete.
To satisfy the required compressive strength, a value for water/cement (w/c) ratio is estimated for an appropriate test age (generally 28 days) and cement type. Tables in the BRE mix design handbook are consulted relating aggregate:cement (a/c) ratio, workability and water:cement (w/c) ratio for the different aggregate particle shapes and maximum size.
From these tables the a/c ratio can be selected. A desired level of workability is chosen. The ratio of sand to coarse aggregate is chosen to produce a satisfactory plastic concrete. Generally there is a minimum amount of sand necessary to fill the voids between the course aggregate particles. Increasing the percentage of sand makes for a less harsh and more easily placed mix.
While this is an over simplification, it does allow an assessment of the effects that changes to any of these controlling parameters have.
Other methods include: ACI (1991) and Basic Mix Method (P L Owens, C&CA 1973)
Acknowledgement: The Concrete Society
Other references:Owens PL, Basic mix design method, selection of proportions for medium strength concretes, C&CA, London, 1973.
ACI Standard practice for selecting proportions for normal, heavyweight and mass concrete, ACI 211.1-91
BRE Mix design for normal concrete