How to safely construct deep underground harbors on a Snowball Earth?

Question

A radical shift in the Earth's orbit has made the Earth much colder, with all the oceans freezing over, and the atmosphere liquifying and falling as rain. Humans live deep underground in areas of high geothermal potential, such as the Ring of Fire around the Pacific.

Apart from tunnels, they also want to use submarines in the deep ocean to transport people and goods around the world. Assume that the depth of freeze is currently at around 1 km.

Physics Question

First, with 1 km worth of ice pressing down on the liquid oceans, that's around 100 atm. In reality, I assume it would be somewhat less. First, water expands when it freezes, so it will be more like 90 atm of pressure. Second, I assume there will also be a "bridge" effect, with some of the weight of the ice mass being held in place by adjoining ice as opposed to "floating" on the water.

I have no idea how big this "bridge effect" will be. I assume it's not going to be big, considering that the oceans are thousands of kilometers across, but that's just a guess. Are there any better estimates? And approximately how much pressure will the water be under where the ice meets the sea floor at e.g. the California coast?

In other words, if you were to drill a hole down to the liquid ocean, how high would the waters rise - halfway to the level of the old sea level; almost all of the way; won't rise at all? (I'm guessing to perhaps 80-90% of the old sea level?).

Engineering Question

Second, am I correct to assume that harbor construction/operation will be potentially very dangerous for an underground civilization? As I see it, there are three potential harbor designs:

• Docking system (as in space): Submarine sidles up to a hatch, screws itself on, goods/passengers are exchanged. Failure mode: Hatch breaks/is breached.
• Lock gates (as in canals): submarine enters a chamber, gate behind it is locked in place, water level is reduced, submarine cruises to the next chamber. Failure mode: gates break.
• Compression chamber: in which there are no gates/barriers at all, but air is kept at a very pressurized state e.g. 80 atm to keep the water in place (this may be just about doable, as humans can work in up to 70 atm environments with the right gas mix). Failure mode: Decompression.

Of course, failures in any of these systems - assuming that the water is highly pressurized - will have an absolutely catastrophic outcome, as the pressurized water roars upwards and floods all the tunnels in the system... unless they are collapsed or otherwise blocked in time.

Is this correct? If so, what kind of safety measures will be required to operate harbors? I can think of just two obvious ones:

• Constructing the tunnels leading to the harbors in such a way that the lowest point at which they connect with the main network is above the old sea line (e.g., via a large elevator or funicular). So, even if worst comes to worst, only the harbors themselves will be flooded, not the entire tunnel system.
• Having many more redundant gates that can be slammed shut in an emergency on detection of flooding, explosive charges, etc.

Are there any other good, practical, not too costly (submarine travel would still need to remain competitive with tunnel transport to be of any use) safety features?

Or will this civilization deem harbors too risky and completely forego deep oceanic submarine travel?

Thanks in advance for your feedback.

Answer 1

Physics question Converting the sea/atmosphere to different states of matter will not affect their mass or the pressure they exert. So the pressure at 1km below the surface would remain roughly the same.

Engineering question I suggest that the best option would be via an underwater tunnel cut from the bottom of the ice sheet (or a bit further down to allow for additional freezing over time). The tunnel should extend horizontally into the continental land mass until it is below a mountain range for insulation purposes. At that point the horizontal tunnel would meet a vertical shaft also filled with water which would rise to a point roughly level with the top of the ice sheet or a bit below.

Water pressure from the liquid ocean would force the water into the tunnel and up the shaft until the point where the column of water in the shaft matched a similar depth of ocean/ice/frozen atmosphere outside. The top of the shaft inside the mountain would be protected from freezing by several km of rock and would also be heated from the interior of the Earth in the same way that deep mines are.

At the top of this water shaft a floating harbour could be constructed with maintenance facilities for the submarines. The floating harbour could be linked to the main habitat by a lift of arbitrary length depending on the safety margin required. The level of floating harbour would change due to tidal influences assuming that the Moon was still in orbit around the Earth at this point and might also change over time in the thickness of the ice changed due to volcanic activity or additional freezing.

In summary no lock gates, no high pressure airlock (if the sea level rose or fell would compress or decompress the air above the shaft a little but the change would be small and easily accommodated) and no pressurised environment.

A high pressure air lock would be the next most suitable solution although as you state it would be subject to failure. Least optimal would be a high pressure environment. In fact a 100 atm pressure habitat would kill the inhabitants by nitrogen narcosis and oxygen toxicity

Answer 2

Physics Question: I do not think the pressure underwater changes when the surface freezes. Pressure is created by weight, and freezing does not change weight. You could say that liquid gases of former atmosphere add to weight, but again, turning atmosphere into liquid does not change its weight, or the pressure it creates.

For engineering problem, Compression chamber is the answer. If everybody is living at 1km depth, then everybody stays at the same pressure as water. It works fine as you said, saturation divers live in pressurized state for weeks. Decompression is only a risk if you go to the surface, but you have a nice solid sheet of ice preventing that.

Now I have a concern for you: food. There is very little light that gets to 1km underwater, so most of life there relies on food coming from the surface. now the surface is frozen, so no life and no more food. Your people will have to grow food in artificially lighted greenhouses, or breed extremophile bacteria that feed on underground chemicals.