I agreed with hokie. Yes, you can do the 10" mat slab with 2" thickened edge to cover 2" of sand between the slab and the visqueen. This practice is done in Northern California and Reno areas. Southern Cal does the 5" ribbed mostly.
I have not run the calcuation yet. From the numbers you listed, my estimate would be 5" ribbed slab with 12" wide x 18" deep (below the finished grade) exterior footing and 12" wide x15" deep interior footing spacing 12'-0"+/- both ways. 1/2" dia. Cables should be 4'-0" on center on the 30'...
I did the post tension design for tract homes in California, Nevada and Arizona. I use the PTI software to design and all the building departments from three states have accepted the design. Basically, you can design 5" slab with rib beams spacing about 12'-15' apart or you can design 10" mat...