As everyone else has said here already, modulus of subgrade reaction will vary depending on many things.....including the definition. For instance, I recall one standard method that used modulus values within the upper 10 feet of soils at a site (might be good for pavements, but not mats). However, if you are using a mat analysis for a large area, the upper 10 feet will definitely not represent what will actually occur at the site, as you depth of influence will be much greater than 10 feet.
On large mat projects, I use an iterative analysis to come up with spring constants(modulus of subgrade reaction), which I in turn supply to the structural engineer to formulate a pressure distribution. I then re-analyze the situation with the new pressure distribution to come up with revised spring constants. This continues until the spring constants reach agreement with calculated settlements. In the first step, I start out with a pressure distribution supplied by the structurual engineer which is based on an assumed spring constant. I split out the pressure distribution into representatively loaded individual elements, calculating settlements due to each of these elements, which then allows me to calculate modulus values. I provide the structural engineer the moduli across the mat, and the structural re-analyzes this data, and supplies me with another pressure distribution. Usually this only requires 1-2 iterations until reasonable agreement is made.
I have used this approach on a few projects, and my company has been doing this for a while. However, you will need very detailed subsurface information. On jobs like this, we do extensive CPT work, supplemented with consolidation testing and vane shear testing if we are in clays. Settlement monitoring of the structures indicates that our estimates are pretty reliable.
We don't have a lot of structures on mats in this area, but we do have a few. Mat settlements are usually high, which is one of our main reasons for providing this type of analyses. Obviously, there is a lot of work involved in this type of analysis, although we use computer programs and spreadsheets for most of the computations.