I have to wonder whether you are asking the right question. ponder
This question was cross-posted on two other forums. My response on one of them is shown below. I'm not sure what I was thinking when I wrote "5 kPa" instead of 10 kPa, but 10 kPa ~ 210 psf is still a pretty small number. One of you others might sound off on whether Young's modulus and elastic response is a good way to look at the problem of immediate settlement on that material.
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If the strength is only 5 kPa ~ 105 psf, it wouldn't take much of a fill on it to cause slope instability, mud waves, intrusion of individual rocks into the clay, etc. Initial settlement is probably governed much more by shear strain than by vertical compression.
If it really was just vertical compression, the initial settlement (before there is any consolidation due to dissipation of pore pressure) would be quite close to zero, since, if the material is saturated clear through, the compressibility is governed by the bulk modulus of water. There would be some consolidation taking place during the course of fill placement, however.
Can't say much more without knowing details.