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So I'm working on a planet for a Sci-fi RPG setting. The basic idea is 'an earth-sized planet, far from the sun, too cold to live on, but with very earth-like gravity, so people live in underground cities'. The planet probably has Mars-like levels of geologic activity, and was colonized for mining.

I'm assuming that they are more advanced than we are (for example, fusion power is cheap and easy), but not super advanced.

These cities are deep underground- like, more than a kilometer- to stay safe from pirates and invasions and orbital bombardment.

So what I want to know is: how deep could they plausibly dig their cities? How deep underground could they live? What are the deciding factors, and how could moderately more advanced technology deal with them?

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    $\begingroup$ What research have you done on how deep mines go on Earth and the reason for the limits? $\endgroup$ Mar 5, 2023 at 22:35
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    $\begingroup$ @KerrAvon2055, I'm not sure that mineshafts would be an appropriate comparison. The shape of the space inside of a mine isn't important, as long as it doesn't collapse and allows people to access whatever they're mining. Reinforcement is minimized for cost efficiency purposes. For an architected living space, they could purposely pick geologically stable areas. $\endgroup$ Mar 5, 2023 at 22:46
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    $\begingroup$ @RobertRapplean looking at the limits on mines and the reasons for those limits would hopefully let the OP answer the last part of their multi-part question themself "What are the deciding factors...?" That would let the OP ask a better-focused question than is currently articulated, especially given the very vague tech capabilities described. $\endgroup$ Mar 5, 2023 at 22:53
  • $\begingroup$ @KerrAvon2055 The primary question is "how deep?" Given better tech than we have it's not sensible to impose Earth's mining limitations. It would be sensible to use those limits as issues that would improve the final story by adding depth to the descriptions. Nevertheless, Atlan? Stack Exchange does expect you to do your due diligence with research. If you roll your mouse over the down vote arrow, you'll see that failure to perform research is a reason to down vote. $\endgroup$
    – JBH
    Mar 6, 2023 at 19:31
  • $\begingroup$ @Atlan. One more thing. We give latitude to new users, but asking more than one question (no matter how related) is a literal reason to close a question ("Needs More Focus"). For future reference, please restrict your posts to one and only one question. $\endgroup$
    – JBH
    Mar 6, 2023 at 19:32

6 Answers 6

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I was going to do this as comments, but there's enough here to warrant its own answer.

No more than 12 km.

At this point, the rock becomes plastic, with the other rock around it squeezing into the space. Have you ever studied banded gneiss? Those bands occur because the heavy layers of rock were squishing this rock like Play-doh. At 12 km, the rock will deform to squeeze you out of whatever space you carve for yourself. This isn't something you can just put a steel shell around you, expecting to keep it out. At 10km, the rock presses in at 18k atmospheres, about 17x the pressure at the bottom of the Marianas trench. Rock is heavy!

Heat wouldn't be an issue

If you can dig that deep, you could vent heat to the surface and use it for power generation.

This statement seems to have drawn some criticism, based on how much effort has to be put into ventilation in mining operations. This "effort" is the corporate owners wingeing at anything that erodes their profit margin. OSHA has to heavily regulate this due to the number of times mine owners have tried to cut corners in this area, resulting in poor health and fatality of the miners.

Comparing mining ventilation to the effort required to keep an underground population of a million alive is a little like comparing a rope bridge to the Governor Alfred E. Driscoll Bridge.

Here's how I would do it.

Quick physics: Warm air is less dense, and it rises. If you dig a hole straight down to an area of geological heat, then dig another upward at a diagonal, the mass of the air in the diagonal will be larger, so the warm air would naturally float up the vertical shaft. That motion would suck cool air down the diagonal.

Your habitation would have a layer of aerogel above and below it, a layer of rock outside the aerogel, and a network of wind tunnels above and below that. The effect would be like a solar updraft tower, with hurricane force winds pulling cold air across the surface and drawing it upward. You could even generate power off of it.

This is a civil engineer's concept of "not a problem" in that, mathematically, it's solved. This is not a capitalist's concept of "not a problem" in that the work doesn't do itself.

Air pressure would need to be regulated

This is a little dependent upon what kind of atmosphere was on the planet itself, but you would almost assuredly want to have an airlock system to keep the temperature and pressure inside your living spaces stable. You would also want to seal the rock around you, just to avoid issues with trapped underground gasses leaking in.

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    $\begingroup$ "Heat wouldn't be an issue..." I once lived in a mining town. That statement is factually (very, very, very factually) false. The Sunshine silver mine in northern Idaho is only 5,000 feet (1.5 km) deep and has ambient temperatures of 127F (53C). What they go through to vent that heat is enormously complex and expensive. Ignoring all the heat the city itself is generating and can't dissipate into the atmosphere, that's like living in Death Valley. $\endgroup$
    – JBH
    Mar 6, 2023 at 19:25
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    $\begingroup$ The planet is cold, so presumably they choose a depth for the sake of having some of that heat, and the surface being cold makes venting easier. $\endgroup$ Mar 7, 2023 at 1:01
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    $\begingroup$ 12 km is just barely doable: the pressure is right around the compressive yield strength for the strongest alloys we can make. $\endgroup$
    – Mark
    Mar 7, 2023 at 4:31
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    $\begingroup$ @JBH, As I said, you can't take mining as an example of how living spaces would be constructed. Mines just have to be cool enough that the workers don't die. If you built a city, it would be inhabited by the people who run things, so they would be sure to put in enough insulation and ventilation to the surface to keep their space at a comfortable temperature. Ventilation, even miles deep, is a solved problem. $\endgroup$ Mar 7, 2023 at 4:36
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    $\begingroup$ @RobertRapplean Did you miss my point about complex and expensive? And that only to provide working space for miners. You're entirely incorrect that mines shouldn't be an example - they're perfect examples of the problems to be solved and reflect the cost of doing the least amount necessary. I'm sorry, but I'm wondering why the OP selected your answer as the best answer when it's nothing more than the best-case condition due to ignoring everything else that will limit the depth - like the examples faced by much simpler mining. $\endgroup$
    – JBH
    Mar 7, 2023 at 16:07
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ROUGHLY 10 KM

You mention that your planet has geologic activity similar to that of Mars. According to the study "An Extensive Phase Space for the Potential Martian Biosphere", pressure and temperature conditions on Mars allows liquid water down to a depth of ~310 km. At this depth, however, the temperature is too high to be comfortable to humans - around 300 celsius (the pressure of the rocks above makes water liquid at this depth).

Looking at the diagram below, taken from the article, we can eyeball that at a depth at roughly 10 km, we have room temperature. Deeper than this, cooling becomes a serious issue. Note that this is an estimate, and the higher gravity and greater diameter of your planet may change the details. As a rule of thumb, temperature increases linearly with depth, so the depth where you find room temperature can be determined by the formula: temp = (core temp minus surface temp)/(planet radius) x depth plus surface temp.

enter image description here

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    $\begingroup$ It looks to me like the temperature increases logarithmically with depth in that plot, right? Since the lines look linear but the depth axis is logarithmic. Or am I reading it wrong? $\endgroup$
    – Drake P
    Mar 6, 2023 at 19:48
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    $\begingroup$ @DrakeP: Both axes are logarithmic:. Temperature is roughly constant until 1 km depth, then roughly linear with depth thereafter (since straigtht lines in a double-logarithmic chart would also be straight in a linear chart). The temperature increases with roughly 1 degree per km. $\endgroup$ Mar 6, 2023 at 20:23
  • $\begingroup$ Oh my bad, I somehow missed that the temperature axis was logarithmic as well. $\endgroup$
    – Drake P
    Mar 6, 2023 at 21:56
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    $\begingroup$ @ChrisH oh you're correct. I'll delete my mistake. But this graph says the average GROUND temperature is NEGATIVE? <edit> Oh, it's planet Mars, not Earth. $\endgroup$
    – Cœur
    Mar 8, 2023 at 17:47
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Klaus shows the Geothermal Gradient chart for Mars. That's a starting point, but it's listing the best-case solution.

Rock is a great insulator

Thus the heat generated by the city (even the heat generated by your inhabitants' bodies and breathing) make this much worse. At almost any depth the excess heat of the city must be removed — and that's a question of both technology and economics. Assuming water as your heat conductor, the hydrostatic pressure on your Earth-sized planet will be a difficult to manage 969 atm (remember, sea-level pressure is 1 atm).

Most mines in operation on Earth are forced to remove water in stages due to the enormous pressure. Unless the tech allows for unbreakable pipes, the city will be forced to do the same. Every stage will have its own pump and storage tank, meaning power distribution and maintenance. Every stage is also a potential failure point.

Granted, I don't know enough about Martial geography to know what the water temperatures will be at various depths below the surface. Here on Earth, underground water gets pretty hot pretty fast. What that means is you can't use the water sourced from the city's surroundings to cool the city. You need to import water from the surface. Now you have two staging systems — one for import and one for export.

And you'll need a lot of water. It'll depend on city size, but off the top of my head we're talking about moving at least a 6-7 meter pipe worth of water up and down.

And the hot water radiators or discharge on the surface will be a target for pirates. You sure you want to do this? General George Patton is famous for saying that fixed fortifications are monuments to the stupidity of Man. An underground city is kinda the ultimate fixed fortification. Plug the hole to the surface and everybody dies. But, I'm getting ahead of myself.

Oxygen isn't the problem. CO2 is

And so is every other non-breathable gas that now has nowhere to go. The underlying basis of Climate Change is that humanity isn't paying attention to how we're using our atmosphere. We take it for granted, and in no way do we do so more than ignoring all the little things we pump into it that aren't obvious. Anyway... It's true that, technology could be believably used to solve this problem, but your story can't ignore it. Theoretically, an atmosphere is 100% recyclable. But any good scientist will tell you that 100% is really, really, really hard to achieve. There's always inefficiencies. That means some method of bringing good air in (probably not too hard...) and getting bad air out (a bit more complex...).

But this brings up an even bigger problem... sewage.

Yes, once again, theoretically 100% recyclable. However, that's unrealistic. That means disposal and gasses (see above) that come with it.

Managing air pressure

Have you ever entered a cave and noticed air rushing into the cave? Or out of it? It can do both depending on what the barometric pressure on the surface is doing. That in-rush and out-rush of air is no small thing in mining where the changes can do everything from popping ears to pulling gas out of rock.

I'm going to go out on a limb and suggest that it's not solvable by putting an airlock on the passage down to the city. It's not just the outside pressure that's the problem. Fluctuation in heat from the core (your core isn't completely cold, is it?) and the city itself can also cause pressure shifts that need to be managed, not blocked.

Finally... I'm assuming the surface isn't worthless...

Just as a lot of waste must be exported, a great amount of resources must likely be imported. The amount of farm land needed to support a city has been asked a number of times on this Stack. The simple truth is, it's hard to replace the sun when you consider everything it does — from naturally cleaning/sanitizing the surface to promoting growth to providing heat, etc. You can replace some of that with fusion generators, but (at least economically) not all of it. It takes a lot of food to feed a city, and the assumption that you can move all that food production (and its dependent effects, like solar purifying of vast amounts of water...) underground.

And we won't even talk about the psychological effect of living permanently underground or the potential need to create a diurnal habitation with a wide enough spectrum of light to not drive people stark raving mad....

What's my point?

Knowing what your maximum depth is, isn't enough unless your story depends on the result to so small a degree that it wasn't really worth asking about here. Even a partial consideration of the difficulties of an underground city (giant cavern? How are you holding it up? Massive warren of tunnels? What about the psychology of the inhabitants?) for the sake of adding depth to the description suggests that from a practical standpoint, your cities won't be anywhere near that maximum 10km depth.

A practical limit might be 0.5km.

But that brings us to the real economic driver... what can pirates do from space? There isn't a reason to be any further underground than is necessary. If the most thorough and destructive orbital bombardment can affect (including seismic effects such as concussion waves) down to 2km, then the minimum depth is 2.5-3.0 km.

It's difficult to imagine an advanced society that would dig a deeper hole than they require — if only to avoid the cost. Nothing is free, even in a society that magically doesn't use money. There is always an expenditure of resources and workforce that could be used to do other things... like feed your people.

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  • $\begingroup$ If they have fusion power and advanced technology they can probably solve those problems. For heat you could use heat pumps to bring it up to temperatures where it’s shed much quicker. Imagine lots of pipes containing molten salt (800°C melting point at ambient pressure) close to the surface. CO2 can be solved with plants (underground aquaponics farms?) which the inhabitants will need anyway. $\endgroup$
    – Michael
    Mar 7, 2023 at 8:54
  • $\begingroup$ @Michael That's an assumption I can't make. The OP said, "I'm assuming that they are more advanced than we are (for example, fusion power is cheap and easy), but not super advanced." Humanity isn't that far off of fusion power today, but we still couldn't solve most of these problems (if it heat was so simply solved, why isn't it solved today?). Fusion power only gives you a lot of electricity, which we can produce today. And plants need the sun unless you're using a lot of that electricity for lights - and you need a lot of them. I'm afraid the problem isn't nearly as easy as you suppose. $\endgroup$
    – JBH
    Mar 7, 2023 at 16:02
  • $\begingroup$ The "air pressure issue* (stack effect pressure) has been solved, on a smaller scale, already. The stack effect pressure in high-rise buildings ("skyscrapers") is nowadays managed with special, ingenious devices: "revolving doors". $\endgroup$
    – Klaws
    Mar 9, 2023 at 15:48
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With the technology you describe, tens or even hundreds of kilometers, but limited by the geology of the planet.

Earth consists of various layers, from crust to core. The thickness of the crust varies from half a dozen kilometers to several dozen kilometers. As one goes down, temperature goes up significantly. Your "Mars-like geologic activity" and lower overall temperature could go with a much thicker, cooler crust.

  • The tunneling of access shafts and ramps should not be a problem, compared to the excavation of the living caverns and mining galleries.
  • I'm assuming that they are going for a fully enclosed environment, like the Biosphere 2 but bigger and hence more stable.
  • Even with cheap fusion power, I would expect that they won't go below the depth where the temperature reaches 20 to 30°C (70-80°F, 270-280°K). Above that, they will need active cooling, which creates even more heat nearby. (If you open the fridge in the kitchen, on the long run you heat the kitchen.)
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  • $\begingroup$ What about air preasure? I tried looking this up for myself earlier, and I kept finding references to air preasure increasing as you dug down. How difficult would that be to manage? $\endgroup$
    – Atlan
    Mar 6, 2023 at 12:02
  • $\begingroup$ @Atlan hyperbaric conditions are fairly easily survivable for the average person though it may need adjusting the gas mix. IT's when people want to return the the surface does the journey turn into several hours to days of slowly letting their blood offgas in a pressure controlled environment. $\endgroup$ Mar 6, 2023 at 15:41
  • $\begingroup$ @Atlan, it should be no problem at all to regulate the pressure if the underground city also has to regulate the gas mix. Besides, a "tower" of several dozen miles of air does not add all that much, compared to a much smaller "tower" of water. $\endgroup$
    – o.m.
    Mar 6, 2023 at 16:56
  • $\begingroup$ @Atlan The fact that your planet has Mars-like levels of geologic activity means no magnetosphere to protect your atmosphere; so, there is a good chance surface level atmospheric pressure is much less than Earth to begin with. It is more likely that the atmosphere is artificially created so it will be whatever pressure you need it to be. $\endgroup$
    – Nosajimiki
    Mar 6, 2023 at 17:45
  • $\begingroup$ @Nosajimiki Assumptions can only be approved by the OP. It's an Earth-sized planet, so we have a colder core but Earth's gravity. Maybe it's thinner, maybe it's not (OP's choice). However, O.M.'s top depth is hundreds of km. Even with Mars-thin atmosphere, at that depth pressure control will be a big deal unless a series of airlocks are involved. $\endgroup$
    – JBH
    Mar 6, 2023 at 19:19
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I'd like to contest the following argument:

These cities are deep underground- like, more than a kilometer- to stay safe from pirates and invasions and orbital bombardment.

What kind of security do you to have? Essentially you cannot hide a city underground because you have to transfer generated heat to the planet's surface. The space pirates surely have infrared cameras to detect any interesting activity on the planet and will easily find your heat outlets. Those heat outlets are also a vulnerable critical infrastructure, just threatening to destroy them will force capitulation of the underground city.

So there is no specific reason to go deeper than absolutely necessary (e.g., using some amount of rock as protection against cosmic radiation). Going deeper will be mostly a consequence of population growth: Just like skyskrapers in modern cities, the colonists will dig deep houses for their cities to use the space on the planet effectively.

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    $\begingroup$ Excellent point, since all the answers so far require critical infrastructure on the surface, there may not much benefit to going underground in the first place. That said, I wonder if you could hide by dissipating heat in a large body of water - it might be harder to pinpoint an elevated heat signature at the bottom of a shallow ocean, rather than an obvious exhaust port at the surface. $\endgroup$ Mar 7, 2023 at 19:03
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    $\begingroup$ I don't think that they're actually trying to hide the city so much as armor it. Yes, you could put the whole thing underwater. The crust is a lot thinner under the oceans, though. Only 6-7km compared to the 35-40km of continental crust. That, however, would be a different question. $\endgroup$ Mar 7, 2023 at 21:07
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    $\begingroup$ It's mostly about armor- though hiding WAS at one point a factor. The backstory- though its not especially important- is that the planet began as a simple mining outpost. An explorer ship saw a planet far out from a sun (roughly pluto-like distance from a Sol-like sun) and dropped by to do a quick survey. The survey turned out to be rich in valuable minerals, so a mining company set out to exploit this planet. The valuable ore turned out to be mostly underground, so following the ore deposits with tunnel boreing machines ended up deep underground in man-made caverns. (1/2) $\endgroup$
    – Atlan
    Mar 7, 2023 at 21:45
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    $\begingroup$ As more workers moved in, and people moved in to support the workers, a colony grew- at first by accident, then on purpose. (valuable ore meant that they could afford imports of things they needed to set up the colony). As things in the wider galaxy got rough (rise of war and pirates), digging further down became a matter of safety as well as profit. The surface is basically unused- a few spaceports, tunnel entrances, that sort of thing. While people live in arcology-cities, fed by aquaponics, in an ever-growing tunnel warren which looks like an aluminum cast of an ant hive. (2/2) $\endgroup$
    – Atlan
    Mar 7, 2023 at 21:52
  • $\begingroup$ @Atlan Seems like the planet recruited mainly miners to expand their mining economy. Miners, like dwarves in fantasy literature, apparently spend a lot of their lifetime underground, on their own free will (YMMV). Maybe that's a genetic disposition which stuck to the population. Yep. Agoraphobia. -- The planet's surface is only visited by pirates and patrolled by robots which will approach, greet and welcome the pirate guests before blowing up their fusion power cores. It's never "talk like a pirate day" on that planet. $\endgroup$
    – Klaws
    Mar 9, 2023 at 16:10
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Many nice answers explaining difficulty of transportation and water exchange with the outer world. Also heat dissipation.

I would like to propose a city that is deep underground but is also reasonably close to the ocean.

If you connect lower part of the city and upper part of the city to the ocean, that will create a natural flow of water because city will use it for cooling. The heated water will be lighter than the cold ocean water so it will flow up replaced by new cold water from deep in the ocean.

Also if city generates enough heat and/or has access to geothermal sources, it could vaporize part of the water, which can be used to produce electricity as well use the desalinated water for agricultural and household needs. Although most likely fresh underground water sources will also be available to the city.

A water channel can be used to transport goods between city and surface. Attaching a float to a heavy object will lift it up in the water and attaching a weight to light object will bring it down.

The heated water of the city can help build algae and fish farms closer to the surface of the ocean as food sources.

In general such city will have its fate connected to the water a lot.

So to answer the question, if we assume that temperature raises with 25–30 °C/km, for the above concept to be credible, it has to be around 5km deep on an earth-like planet. But local factors can apply.

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