I need to level a concrete carport slab that is attached to the house's main foundation and is 5 1/2" below it. The 20' x 24' slab is 4" thick with perimeter footing under it and drops 1.375" over the 24'. The carport was never added and the existing slab has been used as a patio area. I hope to level out the 1.375" drop with some type of concrete leveling compound and use a good portion of slab area to build a storage and shop area. The slab is at grade level and I was thinking of using treated 2x6 floor joists to raise the floor level up to that of the main house. However, sealing off water seepage between the slab and perimeter joists might be difficult. Maybe a 4" thick concrete perimeter wall 5 1/2" high with venting would be better. Anyone have any thoughts on the best way to accomplish this level flooring problem ? I've also read that some of the leveling compounds are not recommended for a thickness greater than 1". Trying to shim all the joists to level to doesn't seem practical either.