Dik
Here are some basics for purpose of judgement,and I am reading from some distant memory with apologies. You probably are familiar but allow me to punch a bit.
In a bin, you have downward pressure, lateral pressure and with this lateral pressure you have friction. some weight do not distribute directly to the base, it is instead resisted by the walls. These pressures surely varies with type of material and depth.
As far as silo supporting system is concerned, only the weight matters, unless the unloading OR unloading is not geometrically symmetric.
As far as wall design is concerned, variation of all these with depth becomes an issue. You then apply to Rankine or Janssen's formulas. They report exponential distributions, if I remember correctly.
In addition to that, the pressures change between static, loading and unloading conditions. They adjust that with some coefficients for use for vertical, lateral and friction.
I dont know how walls(slosh-like) take up seismic pressure, but design of support sytem for seismic load is usually based on a force applied at the centre of mass of the loaded silo or bin.
One other good reference is the old Fintels handbook of reinforced concrete. Unfortunately concrete walls rarely "slosh" and there is no such discussion there.
respects
ijr