Another option I have used to determine the modulus of sub-grade reaction is to perform a CPT test with shear wave velocity testing. From the shear and compression wave velocity the in-situ modulus can be determined. There is also a nice method of determining the soil OCR from the electronic cone data. In the past I have used this approach for designing a RCC parking area and for a monolithic (raft slab) overlying soft clay.
You can perform Falling Weight Deflectometer testing to obtain the dynamic modulus of subgrade reaction (k). The dynamic k is usually reduced by 1/2 to obtain the static k. The FWD is a good choice especially if you are looking at a large area (parking lot) or long stretches (pavements). This is also much faster than the plate load test. A good reference (and easy to find) for calculating k is the AASHTO design guide. It gives an outline of how to use the FWD data.
Unless you have lots of testing to do or the FWD is being used nearby or on the same project, this method is typically cost prohibitive for single point determination of (k).
Great method for lots of testing, but not necessarily cheap.
Modulus of subgrade reaction for soil cement will be quite high. Check Yoder and Witczak for reference. Likely greater than 500 pci.
I would not design based on k for soil cement, since the layer is semi-rigid. Consider a three-layer approach with the soil cement as layer 2, with shear and bending controlling in the layer.
