Have you excavated under one of your slabs middle of winter?
I bet you will find frost under your FPSF in northern Minnesota end of February if you did..
I think your slabs manage frost in hard freeze areas, not prevents it which is ok unless you have unequal heave.
I want to eliminate ALL concrete, by replacing soil with washed gravel 4' deep under my permacolumn Pole barn house walls. Rubble foundation. I would use FPSF insulation methods with rockwool, but build wooden floors over drained gravel, rockwool, and vapor barrier. But I'm reluctant, because I think the chance of heave is still high and I won't have a rebar slab to ride it out up here in Iowa. The site sits on top of a hill with great drainage, is why I'm considering this method.
Thanks!
There is no reason to excavate under a slab, and no, you would not find frost under a slab we built. We engineer them and build them to meet the conditions of our climate. Our last demo house is in Quebec, Canada, which is about the same climate conditions as yours in Minnesota.
By factoring the heat loss of a slab (meaning - how much insulation, and whether or not it is heated, and factoring that with regional climate data, it is very easy to design a slab so it will not freeze. You just need the right amount of skirting. You can read more here about frost heave -
All About Frost Heave Prevention in Cold Climates
Our last slab was built on a Legalett frost protected slab on grade, and Legalett has installed them all across North America and into the far north and after decades in business they have never had a single structural failure. And if you are asking for an opinion, what you are describing sounds pretty risky, you'd be better off with a slab and the right amount of skirting and you'll never have a problem. Skirting on a slab on grade replaces the dirt of a foundation, and you can put as much as you need to prevent heaving. Easy peasy.