Detailed Synopsis: I started writing a story wherein advanced technology slowly stop working (starting from most advanced, and progressing until only handmade items function), while the global climate simultaneously cools.
In response, governments (and other wealthy/powerful organizations) begin to build massive underground cities/shelters so people can survive the cold. The problem I'm running into is that the degradation of technology must be slow enough for humanity to react...so I need to know how fast that reaction can reasonably be.
Question: Roughly how much time would it take for a government (such as the US) to build a single, self-sustaining, underground shelter capable of supporting 10,000 people?
The shelter can be designed and constructed using all modern capabilities (such as using a computer for engineering simulations, automated construction vehicles, and 3D printing), but the shelter itself must be relatively low-tech: no electronics or complex moving parts, no steam power, etc. Essentially, tech no more advanced that ancient Egypt.
The shelter must be self-sustaining for 10,000 people. This includes being able to grow food which can survive without direct sunlight (such as mushrooms and insects, most likely). It can use things like coal or natural gas to provide heat (those substances will still burn), but any attempt to use those substances as fuel for an engine will fail (the engine will, at best, simply not function).
The shelter may be built in an extreme hurry: everyone involved is aware that these shelters may be humanity's last hope for survival. Existing subterranean infrastructure (such as subway tunnels) may be used to expedite the process.
I'm mainly concerned about the rough construction time, ((Would it take months? Years? Decades?), but any suggestions regarding food and heat (or other logistics) would also be welcome.