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RE: Crack control for swimming pool.

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Title: Crack control for swimming pool.
I am probably writing more with questions than with answers.  First, let me "second" the excellent responses already provided by Gail Kelley, Daryl Richardson, Bill Cain, and Roger Turk.  I concur with all of their comments.  Here are my questions and concerns:
Since you mention grade beams, and recently wrote about piles, is the pool slab truly a slab-on-grade, or just initially placed on-grade?  If the latter, use some 1/4" plywood and a couple of sheets of plastic, or a mud slab, to avoid the 3" cover requirement.
If you have a geotech report indicating 12" settlement, it seems incomprehensible to me that you would have anything other than a structural slab supported on deep foundation elements (like piles).  From personal experience, I can attest that swimming pools don't tolerate ANY differential movement.  My first backyard pool eventually developed a 40' long crack right down the middle of the bottom.  Dirt would accumulate at the crack, so that it stood out like a big black stripe, even to the casual observer.  So far, after more than 10 years, my second backyard pool remains crack free (knock on wood).
I am assuming that your project is in Alaska.  If your pool is outside, how do you plan to handle frost heave?  Our equivalent in Texas is heaving clay, and the forces resulting therefrom mess up a lot of swimming pools every year.  If you plan to drain your pool during winter, be aware that buoyancy can be a real problem.  In Texas, we leave our pools full of water year-round, and use freeze switches to automatically turn on the pumps during those infrequent and brief periods that native Texans call "blue northers".  If a pool is ever drained, such as for renovation, holes are always drilled through the shell floor to alleviate any potential uplift pressures.
Finally, I should mention that concrete doesn't actually hold water.  That is why the inside surfaces of virtually all swimming pools are lined with plaster (or some modern petrochemical membrane).  As long as the plaster doesn't crack, the pool won't leak.  Of course, the bad news is that any cracks in the concrete shell will reflect through the plaster.  Consequently, in your situation with potential settlement, I recommend that you specify some sort of flexible membrane instead of plaster.
Perhaps if I knew more about your pool, I could offer more help.
Best Regards,
Stan R. Caldwell, P.E.
Dallas, Texas 
The French own France, a country which we have
always judged to be much too good for them.    
                                              ...Robert Morley