Bit chilly down here & believe it or not, I have two enquiries for putting in new fence posts.
I know concrete doesn't like cold temperatures & it occurs to me that the concrete at the bottom of a 2' deep hole will be colder than ambient air temperature.
Warmer! Why are water pipes buried at a minimum of 18"? Well, that used to be the guidelines. Might have changed since I was actively involved in these things.
I'd suggest that it is the other way around in cold weather. My money would be on the very bottom of a 2' deep hole, filled with concrete/post, staying above freezing even if the air temperature goes below. I mean, what would be making it colder than the current 0.0 C?
it will be warmer at the bottom of the hole than at the top
for fence posts, you don't have any worries WRT frost - you may get a small amount of spalling at the uppermost surface of the concrete, but it's not on show, nor is it a finish - it's just bulk,[1] so it's irrelevant.
[1] almost all the fencing contractors I know don't even mix the concrete - it's just ballast, with a small amount of cement here and there in pockets, some don't use cement at all and just stamp down the ballast, or wedge the post tight with bricks, rocks, whatever and then fill the hole around with soil - they never move.
as a footnote, I'd like to add that last week I mixed 6 cubic feet of MOT (50kg) with half a shovelful of cement (1kg) and water to fill in behind a retaining wall and a fence...two days later I couldn't make a mark in it swinging a pick axe at it, although to be fair, MOT mixed with water and laid like concrete sets like it without cement.
Cold air sinks. If the hole is left open the top of the concrete will be affected by sub zero temperatures. The rest will be kept warm by the ground around it so overall no worries. In the UK frost does not penetrate very far. If you are really worried add a few beers. That keeps me warm.
And, since it drains so well, the posts don't rot so quickly either. A solid lump of concrete is a post-shaped sump for water to sit in.
In the deep mines the temperature is often very hot, the gold mines (deepest, several kilometres down) it can be at 50C+. This is not, however, why it stays warm 30cm down - that's just insulation.
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