I am curious about your diagnosis of the reason the shale is swelling. Stress relief after excavation? Expansion of montmorillonite due to water intrusion? Pyrite alteration? We have seen some heaving of shale in Alabama and am interested in what folks are experiencing in other parts of the country.
11 % swell is extrememly high, we would typically recommend drilled piers and structural floors on a site with that high of a swell. Deep overexcavations of 8 to 10 feet have also been used. The zone of overexcavation needs to extend one to one form the perimeter of the building.
Shales here (Ottawa, Ontario Canada) are expansive from pyritic alteration of limestone to gypsum. Greatest uplift pressure I have seen reported is 50 or 70 kPa, but this is only from recollection, and is typically only a problem under slabs on grade, or walls cast directly against it.
The conditions needs to be "right" for this bio-chemical reaction to occur. It can be mitigated by keeping the shale away from air, permanent submergence works if you can deal with the other issues associated with it. Sealing with bitumens has been tried but seems to be less than permanent. The reaction is worse under warm areas, like boiler rooms.
Drilled piles and a structural basement slab, with an expansion buffer is another successful strategy.
Another is to build a raft stiff enough to carry the swell load back to the columns, sort of an upside down uniform load on a two way column supported slab.
