Thinking outside your "original question" - you have indicated a soft clay with an Allowable bearing capacity of 50 kPa - this implies an undrained shear strength of about 25 kPa. It also implies that your clay is normally consolidated. What is the loading your mat is having on the clay? How thick, as someone asked, is the clay? You may have mat settlement issues - with 10,000 m2 of floor (say 50m x 200 m) - this is a huge slab area - two football pitches in length and one in width or if 100 m x 100 m, a football pitch in both directions. The variability that you would expect across a site this large might in the soil properties could be huge (say a portion of the site was a fill dump for a while where the area might have been preloaded - hence portions might undergo larger settlements than other areas).
The slab thickness is small which leads me to believe that it might be better to simply use spread footings for the columns (which I would assume would be at 20 to 40 ft spacings??) and then use a typical floor slab on a layer of sand and gravel bedding at least 500 mm thick. I do not think, personally, that I would look at your situation as a "unified" slab - either in theory or practice.
And I think you are incorrect in thinking about the suggested layer of granular in the concept of increasing the bearing capacity - it is there principally to offer a flexibility to the slab. But, again, I wouldn't be looking at this as a slab as you are.
In slab design, you might wish to look at the work of Poulos and others on raft stiffness and supporting deformation modulus (E) values. You can find numerous articles that discuss the design of rafts using the elastic approach which is, again, my personal view, a better way to approach than "k" values which are almost "pulled out of the air".
