I've seen .38JHP's punch through 2" oak planking while .45 ball was stopped cold. I'd say a .357 would go a bit further than you think.
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So what exactly are you trying to Prove or Disprove? Are you planning for an attack and want a shelter .357mag Proof?
Nope. Trying to build a box for a loaded weapon that will contain the bullet if it goes off. Consider it a thought experiment.
Note also my original post specified a particular round as an example -- Speer Gold Dot 357 mag.
I found this which suggests six inches of sand might be sufficient, but I imagine the height of the sand is a factor in the density / difficulty of displacing it, and his sand boxes are taller than I want. I'd like to do it with less than six inches of something...
I've never seen or heard of a revolver spontaneously discharging. There's usually a mental lapse and a finger placed someplace where it shouldn't be that causes a negligent discharge. No box or any amount of good intentions will failsafe that.