I am an officially certified Fallout Shelter Manager. I took the course, and everything. Back in the days of the Civil Defense Authority, I was even on the list that would give me civil authority should a whole lot of people die.
Fallout is not some mysterious gas that seeps into your shelter. Fallout is debris from the bomb, and stuff near the center of blast at the original detonation. It doesn’t grow. Fallout will not make other stuff become radioactive. It’s just plain old ordinary atoms, usually in fairly large (well, multiple micron sized at least) dust motes, and larger pieces of uranium, and fission byproducts, like strontium, and such. A certain amount of ordinary stuff is close to the blast, if it was a ground burst, and could be bombarded with neutrons enough to become radioactive. Mostly not, though.
The convection system, the famous mushroom cloud draws up a lot of stuff, and scatters it into the atmosphere. Most of it is not radioactive, but the fallout is mixed up enough to make that an unimportant fact. It generally takes about an hour for the heaviest particles to settle to the ground, and predictions are that one hour after the blast will be the peak radiation rate. If the bomb was not enhanced to increase fallout, it will begin to reduce fairly rapidly. Each sevenfold increase in time will produce a tenfold decrease in dose rate in any one place. (If it was fallout enhanced, forget it, those numbers are too dismal to even consider. Centuries would mean nothing.)
The worst part of the fallout will form an oval shaped zone, downwind of the blast center. For eight hours after the blast it is most likely that unprotected persons in the area will get a fatal dose of radiation in times of less than an hour, although they might well continue to function normally for days, or even weeks afterwards. Forty eight hours after the blast, the radiation rate will be one percent of the peak rate over most of the oval. Unprotected persons would be fatally exposed in times of less than a day.
In the most benign of circumstances, you can expect rescue efforts to begin after two days. You have to convince everyone not to leave until transportation out of the irradiated area is available. This advice assumes your shelter is adequate. That is a whole other long explanation.
The next significant time stamp is two weeks after time zero. The rate at that time will be varied greatly by drainage patterns. The total will be one tenth of one percent of the peak. Rain and runoff will move the fallout, which is just dust, and grit, really, into the path of normal drainage. Sewers, and drainage streams, especially deltas will be “hot”. Good fallout shelter design includes sprinklers to wash off the roof and flush the nearest drains of fallout.
Good managers will send the little old ladies out after the two week measure, to forage for canned goods, and such. A few of the little old men (the oldest) will be sent along to guard, and assist. The two weeks gives you enough time to explain to everyone that half of you are likely to die, and those with less to offer the survivors, in terms of knowledge, skills, and reproductive capacity will have to decide how much they want to use of the resources that will keep the children alive.
Should the bombing have been part of a general war, you will have to maintain the fallout shelter as a base of operations for the working half of the survivors, and the innermost portions as a haven for the youngest. That need will continue for at least another ninety days. Depending on the time of year your crew of old folks will have to find protected stocks of seed, perhaps animals, and certainly whatever long term storage equipment you can scavenge.
The euphemism “civil disorder” was used in my training to describe what could be expected in the aftermath of widespread nuclear bombing. I considered that optimistic.
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