If you know the lateral load on the member and it's location, you can
calculate the bending moment at the top of the caisson. Then you have to
calculate the bearing pressure on the concrete from total shear load at the
top of the caisson and the bearing due to the bending moment in the column
assuming it is fixed at a trial depth. The bearing stress due to the moment
is the bending moment / the section modulus of the flange contact area on
the concrete (a rectangle) with a depth = to the depth of embedment. The
total bearing stress must be less than the allowable for the strength of
concrete specified. This is a trial and error method until yopu get a depth
Some one like Dennis may have a clever spread sheet program that simplifies
this procedure but normally it does not require more than a few trial runs
to a solution.
The vertical loads can be transmitted by a bearing plate.
I hope this helps.