1. The geotechnical engineer - the soil specialist - should provide you the modulus of subgrade / elastic spring stiffness in his SI Report. Get in contact with him - this is the best and safest option. He is best placed to offer advice.
2. I have found that the geotechnical engineers often provide subgrade modulus to structural engineers by undertaking a CBR test, and then correlate the subgrade modulus to CBR value. They use a (0.6m x 0.6m, or) 1m x 1m plate for the test. The reason they don't do it that they would need to bring in heavy weights to do the test, hence they don't bother! I am sceptical of the CBR test as it only gives the strength of the soil in the near surface - In my view it does not give much of an information at depth.
3. In the absence of any information consult Bowles book on Foundation Analysis and Design I know has a table - which gives the different ranges of subgrade modulus based on various soil types. I don't have the book handy but recall it from distant past. If someone has the Bowles book handy, then they can help.