A foundation resting on soil reinforced by floating stone or sand columns?
Please consider the below article
http://www.geosynthetica.net/Uploads/CollinHanHuang.pdf
You have several methods. One is the one Keller recommends for computing the equivalent overall mechanical parameters using Priebe's method. You can find it here: http://www.getec-ac.de/download/en/pdf/GT07-13E.pdf
Another way is to use any FEM analysis and consider the stone columns as such, with proper interaction with the adjacent soil.
A third method, if you intend to have a gradual change of mechanical parameters from the column axis to the soil, is to use the thermal dependence trick, namely consider a homogeonous medium with parameters variable with temperature so that a 0 degrees you have soil parameters and at 1 degree you have the stone column parameters. You control the linear variation in the zones with temperatures between 0 and 1, you have the columns in the zones with 1 degree and the rest of the soil remains at 0. If you want to pursue this path I can give you additional info.
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