If the Earth's interior was not hot and liquid, how deep could we dig before the tunnels collapsed by the pressure or the air became too pressurized to be breathable? In other words: how deep can underground tunnels be and still be scientifically plausible?

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    $\begingroup$ This might be useful: Kola Superdeep Borehole $\endgroup$ – Dan Pichelman Mar 18 '15 at 22:26
  • $\begingroup$ Tunnels are horizontal; holes are vertical. You want a horizontal opening? $\endgroup$ – HDE 226868 Mar 18 '15 at 22:54
  • $\begingroup$ American version of the Kola Borehole is the Bertha Rogers project...it was abandoned at 9.5 km deep after striking molten sulphur...I think your answer here will be entirely theoretical as any example from Earth sees it get far too hot long before pressure gets us. $\endgroup$ – Twelfth Mar 18 '15 at 23:39
  • $\begingroup$ what-if.xkcd.com/46 $\endgroup$ – Mithoron Mar 19 '15 at 1:06
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    $\begingroup$ @HDE226868 What I mean is system of horizontal tunnels that goes many, many floors down to the underground. But I guess the hole directly down will have similar limits, right? $\endgroup$ – Irigi Mar 19 '15 at 6:48

Problems for humans

The deepest tunnel-like structure created so far is the TauTona Mine in South Africa. The bottom of it is 2.4 miles below the surface. Temperatures there can reach 131°F, which has proven deadly many times in the past. The temperature can be lowered to more pleasant levels, but conditions are still very dangerous. Mponeg reaches similar, if not higher, temperatures (without cooling).

As Monty Wild mentioned in an answer to a different question, ventilation will be an issue for any underground structure. If you want people to survive this far underground, either they'll have to carry oxygen with them, sealed regions will have to be made, or many ventilation shafts will have to be dug, which will severely complicate the process.

Pressure is also a problem. We can use the barometric formulato calculate pressure (valid, I believe as per the derivation, e.g. here). It is $$P=P_b \times \left[ \frac{T_b}{T_b + L_b(h-h_b)} \right]^{\frac{g_0M}{RL_b}}$$ At, say, -15,000 meters (the missed goal of the Kola Borehole), this is $$P=101325 \times \left[ \frac{T_b}{T_b + L_b(-15,000-0)} \right]^{\frac{9.81 \times 0.0289644 }{8.31432 L_b}}$$ $L_b$ (the lapse rate) is calculated by $$L_b = \frac{dP}{dh} = - \frac{mg}{kT}P$$ You can plug this in, figure out $T_b$ from empirical data) and then solve for $P$ (after a bit of algebra). You won't like what you find.

Problems in general

Rocks are also under pressure. This is not good for excavating nor keeping what you've excavated intact. The tables can give you a good idea of what you're dealing with. A Powerpoint presentation downloadable here explains the pressure on tunnels and other structures.

The thing is, there's no good answer here. All of the really deep borehole were created for scientific drilling - experimental holes to see what's really down there. I can give you figures and equations and estimates aplenty, but I'd be lying if I claimed that I could give you an actual figure. We don't know what's down there. I gave you some necessary information to show you what you're up against.

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    $\begingroup$ +1 "We don't know what's down there." You're right, this is mostly speculative. We come across many "technical" problems as we move downwards, but nothing that can't be solved with enough time and money. Like any situation which depends on many factors turning out well, it just takes one of these factors to kill everyone in the tunnels, making it a risky endeavour. However, there has yet been anything that would keep us from continuing downwards even further. Just lack of resources or unacceptable risks preventing us from trying. $\endgroup$ – Neil Mar 19 '15 at 8:39
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    $\begingroup$ The combination of temperature and pressure is the final barrier. At one point you cease drilling, you just push new segments into molten magma. While we might develop materials that would withstand the pressure, and materials that might withstand the temperature, we have none that would withstand both - diamond walls will burn, and tungsten walls will buckle. $\endgroup$ – SF. Mar 19 '15 at 10:35
  • $\begingroup$ xkcd.com/1330 $\endgroup$ – apaul May 18 '15 at 22:04
  • $\begingroup$ OP specifically states that the proposed core is not hot. $\endgroup$ – WhatRoughBeast Jul 26 '17 at 10:16
  • $\begingroup$ @WhatRoughBeast The core's not hot, sure, but the air itself is. $\endgroup$ – HDE 226868 Jul 26 '17 at 14:43

Breathing regular air on Earth, humans can deal with about 8 times sea level pressure before taking harm, which would be at a depth of about 20 km. The damage comes from chemical reactions of the gases in the lungs, but with different gases to breath, it seems humans could even handle pressure ten times higher if the body is given time to slowly adjust to the changes. That would be at a depth of about 55 km. Since nobody has yet tried to crush a living human or big to death with air pressure the true maximum is unknown, but 70 times sea level pressure is the number you usually find.

It would even be possible to dig 20km deep on Earth, though it would probably get very hot. A depth of 50km would be all the way through the Earths crust but should be possible on other planets with a similar mass and gravity that don't have tectonic activity.

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If the earth was solid and the same low temperature as the surface regions of the current crust, the whole way through, a hole could theoretically be bored completely from one side of the world to the other. Air pressure could be an issue for unprotected humans, but suits like deep-sea rigid exoskeletons could be used to protect workers from the air pressure, or else the project could be carried out in a vacuum (which would be even more useful) with the workers carrying their own air supply. The machinery involved, if electrically powered, could easily be made to function in whatever atmosphere that was allowed to exist.

The advantage of an atmosphere-evacuated hole through earth would be that a sealed capsule carrying a payload could be dropped into it, and with minimal air resistance, would require very little net energy to reach the other side of the world if it relied on gravitic acceleration alone. Compared with airliners, it could well be worth the investment.

The main issue would be that the pressure of the overlying strata on deeper strata would tend to make solid stone and metal flow into the hole at sufficient depths. The question then becomes, "At what rate does this occur, can it be retarded, and what rate of collapse is acceptable?".

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    $\begingroup$ Interesting note, dropping through an evacuated hole in the Earth takes 42 minutes to get from end to end. $\endgroup$ – Samuel Mar 19 '15 at 0:40
  • $\begingroup$ @Samuel At a free fall drop? That can't be right. $\endgroup$ – Neil Mar 19 '15 at 8:42
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    $\begingroup$ @Neil At freefall in a vacuum, yes, it's right. It would take 42.2 minutes. The same period that a frictionless satellite, orbiting just above the surface of the Earth, takes to get halfway through a complete orbit. $\endgroup$ – Samuel Mar 19 '15 at 14:22
  • $\begingroup$ @Samuel Impressive. Did not know. $\endgroup$ – Neil Mar 19 '15 at 14:28
  • $\begingroup$ @Neil: Even more "interesting" is this figure is independent of the boring angle; I mean: if you drill a straight tunnel between any two points on Earth and you have a frictionless carriage (no air resistance and no friction on "wheels" or whatever you use to keep it along the tunnel) then the travel time under gravity pull alone will always be ~42 minutes (kudos to Douglas Adams!). $\endgroup$ – ZioByte Jul 26 '17 at 11:39

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