Tests on concrete are generally limited to strength, not compaction, and that's usually tested after 28 days in the US. If air-entrained, then it's meant to be lightweight (actually lower density), and one may want to know what the density of the concrete is. If regular concrete, compaction is what it is. Over vibrating any concrete will cause aggregate to sink through cement binder and alter the characteristics of the slab, column or beam, but the compaction will be affected to a small degree.
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to measure the temperature of fresh concrete, you can use the the bimetallic thermometer
or infrared thermometer
with regards to compaction of concrete, maybe you are reffering to the compressive strength.
the expected compressive strength (on 28 days) of fresh concrete can be determined on the design mix you use (cement factor, water-cement ratio, types of aggregates, additives if there is any, etc).
the usual schedule of compressive test is 7 day old, 21 day old & 28 day old. on the 7 day old results, you have already the idea how much will be the compressive strength on the 28th day. 7th day strength = more or less 70% of 28th day strength.
there are some cases that compression test will be conducted on the 3rd day as to determine if the concrete is already capable for partial tensioning of tendons (precast concrete piles, precast concrete girders, etc). immediate tensioning is required in order to lift & transfer the concrete products and the forworks/molds will be free for the next preparation/casting.
ask the materials engineer for further details of conducting the tests.
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