How deep would a bunker have to be to prevent significant radiation seep?

Thousands of years after a nuclear war that killed all life on the surface of earth, the descendants of the humans who fled to bunkers emerge...

How deep would these bunkers have to be to prevent radiation seep (radiation radiating down) from significantly harming the people in these bunkers? The radiation levels are just high enough to kill all life on the surface (except possibly cockroaches) fairly rapidly (1-2 hours). The bunker doesn't get a nuke dropped on it, and you don't need to worry about food or power. If lead or some other material would drastically help, feel free to include reasonable amounts of it covering the base (but not more than say, a few meters of it).

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How deep would a bunker have to be to prevent significant radiation seep?

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