A plasma cutter will not make for clean cuts on your tin work. Shears or a circle saw are the typical go-to.
What you're describing and what is shown in the photo is typically considered a full foundation around here.
Information on the 3 types of concrete foundations: T-Shaped, Slab-on-grade foundation, Frost Protected
www.concretenetwork.com
Makes sense: full foundation it is. Thanks!
I’ll challenge the plasma cutter not making a good enough cut though. I worked for Hypertherm as an engineer. By hand, a good straight edge made from pieces of the same material and the right settings would make short work of it. Might have to strip the paint depending, but might get away with it on. I can even cheat as I have a table with torch height control. I haven’t tried programming z-height changes this drastic yet, but it can do it. A circular saw will probably still be easier to deal with, but I don’t think a plasma cutter would not work.
Just to get the terminology correct. You do NOT have an out-of-square slab. You have an out-of-square frost wall foundation. You haven't started on your slab on grade yet.
Maybe I missed the answer but I'm also curious what is actually causing the out of square condition. Were the ICF walls built this way from the footing up or did the foundation rack and is no longer plumb? Either is feasible given the lack of bracing but I suspect it's the former.
Regardless of the cause, I would correct the problem before proceeding with framing. A skilled framer could finesse it but unless you have one there is no way I'd fight this problem all the way through. Your diagonal measurement should be 51'-10 1/4" so you are out about 4" in either direction. It obviously depends on which way it's racked but you should theoretically have lips and overhangs of about 2". Not insignificant but probably manageable.
Put a plate down with square corners that is wide enough for bearing and attachment and then figure out how to deal with the lips and overhangs. You need to cover the exposed ICF foam anyway so you could remove foam where you have lips and furr it out where your structure overhangs. You could then cover it all with metal flashing, stucc, etc. to ground level on the outside. Likewise, remove foam on the inside as necessary so your slab on grade covers your sins on the inside.
Btw, Unless you want to see the top of the ICF wall where you drive in, I'd go ahead and cut out some "exits" so your slab can pour over the frost walls. It's the way it's generally done. Also, make sure your slab edge lines up with your corrected wall lines rather than the frost wall below.
The root cause is me being dumb. The last time I check square was to the pins laid in the footer base. It was out by 1” and I was supposed to correct when laying the forms. We were in a rush to finish the forms, and by the time I checked square, we’d already installed and tied rebar to a point that it would be several hours to fix if not days. To our credit, we had the forms installed in three days and had just barely poured the base 6 days prior. Lesson learned: we rushed and we laid for it. I canceled the slab pour until we get the mistakes sorted out.
The walls are plumb and straight, just not square; we used a lot more bracing than you can see, and more than the guy who sold it to us recommended. He said the diagonals are critical on one side, but the supports at the top of the wall are just for adjustment after the face. This is very short for an ICF wall. I actually called Amvic and asked if I could just backfill the forms for support, and they said go for it. I didn’t do it, and glad I didn’t, but it probably would have worked.