Tomlinson discusses a method of analysing foundations on a stiff soil overlying a soft layer, which is similar to what you are talking about, although reversed. (6th edition, page 132, figure 4.2 with associated equations).
He states that for square or circular foundations, the bearing pressure on the soft (lower layer), (q1) is equal to:
q1 = qn (B/(B + d))^2
or for strip footings:
q1 = qn (B / (B + d))
where B is the breadth of the foundation, qn is the bearing pressure from the foundations and d is the thickness of stiff soil(upper layer) below the base of the foundaiton above the soft layer (lower layer). This is based upon a 1:2 or 30º. I have also seen the french method of calculating working paltforms, where they use the angle of internal friction for granular layers to calcuate the corresponding 'footprint' of a loaded area on underlying layers of soil.
This does all seem to be based around a global poissons ratio of 0.5, although accroding to Tomlinson (trying to keep to the same reference here), only undrained clays have a v of 0.5, stiff undrained clays are in the order of 0.1 to 0.2, silt = 0.3, sands = 0.1 to 0.3 and rocks are around 0.2.
On the point of assessing the settlement to a layer which can be deemed to be 'relatively incompressible' Tomlinson also suggests limiting the effect of settlemnt analysis to where the applied vertical pressure reduces to less than 205 of the overburden pressure.
