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For compression test of concrete specimen, mainly2 types of concrete specimen are used, Cubes and Cylinders.
Cube sizes of150mm are more common in Asia and European countries while Cylinders of150mm in diameter and300mm height are common in Australia and USA.
The most common age of testing is7 &28 days, but tests can be carried-out at1,3 and14 days as well.
It has been observed that the probability of weak spots in a specimen is greater when the volume of concrete is larger for a given compression level. This seems true to some extent because smaller specimen can be better compacted, therefore smaller specimen show smaller amount of bleeding hence the concrete would be of better quality and exhibit better strength.
Depending on aggregate size, size of mould (Cylindrical/ Cube) are specified... Also the other factor is proper tamping of concrete inside mould...
I am not quoting it from any specs.. If anyone have diffrent view/better answer.. Kindly share