There is a nuclear war between the Soviet Union and the USA in 2068. The war lasts about 4 hours but destroys most of the northern hemisphere and parts of Australia. But, the Soviet military relocated 250 people, mostly high military leaders, and their families, into an abandoned mineshaft that was converted into a bunker. My question is, what modifications would be needed for the population to be able to stay there for 30 years while being totally self-sufficient.
What modifications would be needed for the population to be able to stay their for 30 years, while being totally self sufficient?
You have already stated that they are in a mine shaft converted into a bunker, so I will assume the habitat is sealed off. They would need air and water filters and some way to grow/produce uncontaminated food. They would need a system to recycle human waste. A power supply that can run for 30 years, with fuel and spare parts (and people to operate them). There are probably more to this than what I have answered, but I would look into this first. 30 years is perhaps a short time, when considering that "most of the northern hemisphere is destroyed".
There is also this, from Wikipedia:
Biosphere 2 is an American Earth system science research facility located in Oracle, Arizona. It has been owned by the University of Arizona since 2011. Its mission is to serve as a center for research, outreach, teaching, and lifelong learning about Earth, its living systems, and its place in the universe. It is a 3.14-acre (1.27-hectare) structure originally built to be an artificial, materially closed ecological system, or vivarium. It remains the largest closed system ever created.
Biosphere 2 was originally meant to demonstrate the viability of closed ecological systems to support and maintain human life in outer space. Biosphere 2 was only used twice for its original intended purposes as a closed-system experiment: once from 1991 to 1993, and the second time from March to September 1994. Both attempts, though heavily publicized, ran into problems including low amounts of food and oxygen, die-offs of many animals and plants included in the experiment (though this was anticipated since the project used a strategy of deliberately "species-packing" anticipating losses as the biomes developed), group dynamic tensions among the resident crew, outside politics and a power struggle over management and direction of the project. Nevertheless, the closure experiments set world records in closed ecological systems, agricultural production, health improvements with the high nutrient/low caloric diet the crew followed, and insights into the self-organization of complex biomic systems and atmospheric dynamics. The second closure experiment achieved total food sufficiency and did not require injection of oxygen.
There are some novellas out there that also tackle this head on, like "Wool", and of course the "Fallout"-series of computer games. While probably not scientifically sound, it could help you make a somewhat credible survival setting.
People generally over-estimate the effects of nuclear fallout. When a nuke detonates there is a very powerful burst of neutron, gamma, X-ray, UV, IR, Beta and Alpha radiation. You can block most of these with just the regular walls of your house. The real killer is the gamma radiation. dependent on blast size the initial pulse of radiation is so powerful at ground zero that there is pretty much nothing that can shield you from it feasibly. Blast energy and thermal energy render just about any form of defense utterly useless at this range anyways.
Then there's fallout, which is irradiated dirt, dust, and ashes tossed into the atmosphere. Fallout is actually pretty short lived. it emits beta, alpha and gamma particles. you can block beta and alpha radiation with basically just very heavy clothing and wearing some kind of air filter. Fallout still emits gamma radiation however. Gamma radiation travels in straight lines, kind of like light. so imagine if you shined a really big spotlight into a tunnel. it would go all the way to the back, or until it hit a corner right? So fallout shelters need to have enough of a corner on the entrance that the gamma radiation cant "shine" in.
Fallout also doesn't last long unless the nuke was specifically "salted" with cobalt to produce long lived radioactive isotopes. It is dangerous for about 3 to 6 weeks, then the radiation dies down enough that you could walk around outside without any negative effects. It would basically be totally gone within a few months. as long as you didn't eat or inhale too much of of the radioactive dust before the 3 to 5 week mark you would pretty much be fine. Filtering for fallout is easy too, its just radioactive dust. Anything that can remove as close to 100% of the dust from the air is an adequate filter. You only need about 4 feet of soil to shield from the gamma radiation levels of fallout, or 2 feet of concrete. The average basement is already a fairly decent gamma radiation shield (as long as you aren't at ground zero and can keep the airborne radioactive dust out obviously.)
The biggest issue with a Mine shaft based fallout shelter is that that is a LOT of volume to provide clean air, power, and heat to while not protecting you any more than a buried concrete or metal structure closer to the surface would. Mine shafts also tend to build up toxic or even explosive gases, and would need to be very very well ventilated to be safe. You would need an Industrial air filtration and ventilation set up, a power source for that (also VERY big) and you would need to have a way to heat and light it. The entrance would either need to be curved or around a corner, or be built thick and heavy enough to shield from the gamma radiation of fallout (2 feet of concrete, 8 inches of lead, or 12 inches of steel.) If you are thinking "ground zero survival" forget it. Even ignoring the blast and heat you'd need about 20 feet of steel to pull it off, and thats ONLY for the radiation, not the heat, and over pressure (which would liquefy your organs and brain anyways).
So long answer short: Fallout shelters are pretty easy to build without using a mine-shaft, and pretty much nothing is going to survive a direct strike by a modern thermo-nuclear weapon. (which often carry anywhere from 3 to 12 warheads which they deploy against a target like a heavy bunker in a cluster-bomb style attack).
Here is a link to a modular bunker builder company that build fallout shelters big enough to hold a few hundred people if need be: