The document I used to use in Texas with expansive clays was:
"Design of Slab-on-Ground Foundations", August, 1981
Prepared for: Wire Reinforcement Institute, 7900 Westpark Drive, McLean, Virginia 22101 and for the Concrete Reinforcing Steel Institute, 180 North LaSalle Street, Chicago, Illinois 60601.
The method was developed by a Mr. Walter L. Snowden, PE in Austin, Texas. It is an empirical method. There may be an updated version out there somewhere. I would start with CRSI.