The analysis of plates on springs is by now maybe (other than outright footings) the more usual way to design foundations. Springs are used mainly as a substitute for the actual behaviour of the soil, and are derived from ballast factors taken from geotechnical reports.
Albert Fuentes gave 3 ballast factors
0.5 kgf/cm3 for bad soils like yours
4 kgf/cm3 for middle strength soils (working stress, service level 2 kgf/cm2)
12 kgf/cm3 for strong soils.
These surely were k30 ballast factors based on tests sinking 30x30 cm plates (the text as I had it in spanish didn't precise). These values would need be corrected by some formula to a lower value for practical foundations, depending on soil and dimensions. I have found in practice that just taking such values directly for the analysis produces more consistent correlation with the observed behaviour. This surely a fruit of the general conservative approach of the geotechnical sciences when talking values.
It might also be argued that when doing analysis in FEM and being the elements small, taking a ballast factor on the overall width of the foundation be incorrect, but I do NOT have seen this being stated nor practiced in programs, such CYPECAD. The theoretical correction of this may be ascertained from an exam of the literature that I have not time to do, yet I have above stated what is my experience. Each element with each spring reaction force, stiffness will tie everything together in the plate.
I ordinarily bracket the behaviour by taking more than one ballast factor (classes of soils) and examine how the foundation requirements vary. It uses not to be much.
Anyway, the usual approach is making a model of the foundation divided in elements within the program or in autocad or so and then putting foundation constraints and acting forces, or generate a complete 3D model, foundation AND structure. The spring constants you put are the ballast factor multiplied by the tributary area of elements. Then you analyze the model and have settlements and stresses for the plate. You can also derive (or the program directly gives) pressures in the soil at every node of the foundation by multiplying its settlement by the standing ballast factor.