how to stabilize underground bunker

You better plan on earthquakes for pretty much any catastrophe that is going to require a serious underground shelter. At the very least your going to get shock waves that will pretty much do the same thing as an earthquake, and depending on the soil composition they can travel long distances and become amplified just like a tsunami.

The best shelters are made from formed concrete and rebar, because they will not rust out over time and are stronger then something like cinder block. If you look at most WWII military bunkers and pillboxes, thats how they were built. Water penetration and humidity are the biggest problems people tend to have with building shelters. Cement at least eliminates the problem of rust, but not of leaking or condensation. A dome is structurally probably the strongest shape.

If I ever had the money to build a shelter I would go with a Monolithic Dome:
Monolithic Domes

I also came across this, but I'd have to research into them more:
Concrete Canvas

I would also prefer to build it into a hill, or have enough dirt shipped in that I could bury it above ground level. The minute you start going below ground, your problems and costs start to exponentially increase as do your problems with water intrusion, shockwaves, etc...

As to your question about support, whats the point if your not expecting any earthquakes or shock waves? Just build a normal foundation/footer with rebar, and packed on the correct combination of soil, I would assume. If you're planning on building a shock absorber type of arrangement like the US government, then you obviously have enough money to hire a contractor to have a shelter professionally built. Personally, I wouldn't even worry about trying to provide a shock absorber under my slab, as to me, it would be a potential place for that slab to crack.

Besides...
If you're getting hit with something that is so severe that its going to damage the foundation, you have bigger problems to worry about like the roof and walls caving in, or you getting forcefully thrown/bounced around inside until you're nothing but a bloody pulp.