Hey there,
I for one am not a big fan of building anything in the northern part of this country (USA) on any sort of slab, unless it is a small stick framed garage that no one cares about.
One way to support the frame and still be below the frost line is to set the sill beams on top of buried treated posts which in turn rest on concrete footings called cookies. Treated posts are placed below grade, and the sill sits just above final grade.
The concrete floor can then be poured inside the building, between the sill beams. Expansion boards can be added to the inside sufaces before the floor is poured,... this way the floor can "float" without heaving the building.
A couple things to think about is that woodchucks and rats love slabs!....
and the sills could also be cut out of preasure treated SYP utility poles since they will be in contact with the ground and the concrete/ water.
Good Luck,
Rooster
