theoretical limits to tunnel strength

[tolworthy]

A materials science question: what's the theoretical limit for the strength of a tunnel wall? Advanced alien technology is assumed.

I'm working on a sci-fi story (actually a game) that involves aliens with tunnels deep underground. Obviously the pressure is a great problem (so is the heat and magma convection, but that's a different topic). I would love to include planets with honeycombs of tunnels right to the core, but I won't do it if that is theoretically impossible.

Would it be possible to create tunnels big enough to live in, perhaps tubes of 100 meter diameter, that would survive the pressure near the center of the earth? Would it be possible to create vast caverns (as in Jules Verne's Journey To The Center of the Earth) nearer to the surface? I realize that gravity would fall to zero at the center, but I also realize that the accumulated force from the rock and magma overhead will increase the deeper you go. I would like to think that alien technology - perhaps using ten-mile-thick walls built from the successors to carbon nanotubes - might be up to the task. Anyone care to guess?

[Boerseun]

Interesting question!

Material strengths and weaknesses not being my strong point, I can point a few issues, though. The physical make-up of your imaginary planet would probably dictate what structures could be built to the scale you propose.

A smallish Mars-like planet with a solidified centre should be able to house caverns of any size, as long the arch of your tunnel's roof is well-built and the walls thick enough. The absence of a magnetic field should indicate a solid centre. Earth-sized planets would present problems with molten rock weakening your structure. Cooling would present a problem, although access to the molten rock would probably solve all your society's energy needs!

Another fundamental problem would be that your honeycomb-structure will present huge issues as far as atmospheric pressure goes. If your tunnel is two thousand kilometres under the surface, pressure control is going to be a huge problem if you don't want your people to implode under several thousand bars' worth of pressure!

[tolworthy]

Originally Posted by Boerseun

A smallish Mars-like planet with a solidified centre should be able to house caverns of any size, as long the arch of your tunnel's roof is well-built and the walls thick enough.

That's a interesting point for me. Perhaps there is no limit to cavern size as long as the walls have the right thickness and design (each layer reduces the force on the layer below) and the roof has a well arched shape? That would be good - can anyone confirm this?

Originally Posted by Boerseun

your honeycomb-structure will present huge issues as far as atmospheric pressure goes.

Good point. I'd been ignoring that. I suppose the only practical solution (lol) would be for clearly defined tunnels, with clearly defined airlocks, unless the lower levels were reserved for the equivalent of ocean floor species.

[HydrogenBond]

When I was young during the winter we would make large piles of snow an then dig tunnels through them. What appeared to happen was that the pile was self supporting and could handle huge diameter tunnels. During snowball wars opponents would try to cave in the tunnels. Sometime it took a lot of jumping up and down to cave it in. This strength increased with smaller tunnel diameter. Build your alien tunnels within solid rock and they should be self supporting. Parabolic arch design will look nice and add a little extra security. Tunneling into non solid like sand or coal will need support.

Next line your tunnels with fast moving water channels. This will act as an insulator, i.e. heat of vaporization at 212F, and can be used to generate steam for electricity.

[tolworthy]

Originally Posted by HydrogenBond

Build your alien tunnels within solid rock and they should be self supporting.

This is really good news. It seems like there is no real limit for modest sized tunnels. I take it there are no dissenters?

Originally Posted by HydrogenBond

Next line your tunnels with fast moving water channels. This will act as an insulator, i.e. heat of vaporization at 212F, and can be used to generate steam for electricity.

That is an excellent idea, I'll definitely use that. On a related note (and this should probably be on the earth science forum), does anyone know how fast earth's mantle moves? I assume it moves not much faster than continental drift, since the continents float on top of it. So if the heat could be overcome, ti should be possible to build permanent tunnels through the magma, and just maintain them every few years to compensate for magma drift. Or does the mantle convect at a much higher speed?

[CraigD]

Since advanced technology is assumed, I conclude that structural strength is a surmountable problem. Since the huge heat differentials deep underground make available lots of energy, a tunnel wall’s lack of material strength could be addressed by making it a conductor, passing a strong current through it, and supporting it magnetically with a much larger inner structure. An “advanced technology” could likely deliver yet more exotic ways to convert energy into structural strength.

With ample energy, other problems become tractable. Breathing gases can be reprocessed, and losses replaced by a variety of “make a plasma and take the atoms you want” methods. Making more tunnels … etc.

The big problem, as I imaging it, would be cooling. The inside of the tunnels would have to be a temperature comfortable for their alien biochemistries, while the outside is flesh-vaporizing hot. No matter how well insulated, or how exotically (refrigerating water in the walls, etc) heat will intrude into the tunnel, and have to be sent somewhere cool.
A major feature of these tunnels would necessarily be system to exhaust heat.

• A low-tech solution is to run strong, insulated, heat conductive cables to cooler regions, such as surface oceans (Idea taken from the existing practice of enhancing commercial and residential building heat pumps via submerging or burying their heat exchange coils)
• A high-tech solution is to pump lasers with the heat, and beam the resulting energy as far away as possible (handy for making more tunnels, too). Optical cables could transmit the energy to the surface. (Idea taken from David Brin’s novel, Sundiver)
• A fantastically high-tech solution would be to somehow convert the heat into radiation to which the planet’s transparent, radiating trans-X rays into space. (My idea, or I’ve forgotten where I heard it)

PS: Thanks, tolworthy, for the Sludge link. I’ve often felt a craving to write a game like yours, and am always on the lookout for tools to do so, if I ever find the time and ambition. I’d love to hear more about your efforts in the Computers and Technology or Book, movies, games forums.

[tolworthy]

Originally Posted by CraigD

a tunnel wall’s lack of material strength could be addressed by making it a conductor, passing a strong current through it, and supporting it magnetically with a much larger inner structure. An “advanced technology” could likely deliver yet more exotic ways to convert energy into structural strength.

That's brilliant! Why don't I think of stuff like that? I suppose I could push my luck and say that earth's magnetism is a direct result of vast numbers of these tunnels; the ever increasing tunnel numbers are the cause of the earth's expansion (seriously: http://www.science-frontiers.com/sf037/sf037p11.htm) and the reason they don't show up in seismic testing is down to good design...

Originally Posted by CraigD

A high-tech solution is to pump lasers with the heat, and beam the resulting energy as far away as possible (handy for making more tunnels, too). Optical cables could transmit the energy to the surface. (Idea taken from David Brin’s novel, Sundiver)[*]A fantastically high-tech solution would be to somehow convert the heat into radiation to which the planet’s transparent, radiating trans-X rays into space. (My idea, or I’ve forgotten where I heard it)

That is like gold for what I want. Thanks!

Originally Posted by CraigD

PS: Thanks, tolworthy, for the Sludge link. I’ve often felt a craving to write a game like yours, and am always on the lookout for tools to do so, if I ever find the time and ambition. I’d love to hear more about your efforts in the Computers and Technology or Book, movies, games forums.

Consider it done... I can rave about Sludge for hours

[HydrogenBond]

Good ones. Now that is brain storming.

[UncleAl]

Would it be possible to create tunnels big enough to live in, perhaps tubes of 100 meter diameter, that would survive the pressure near the center of the earth?

No. Your material limit is the compressive strength of diamond. Nothing is stiffer. That limits you to about 100 miles depth of rock. Go much deeper and the stuff oozes like taffy under an asymmetric load. If you want to keep things inflated with Lorentz force (that tears apart solenoids), work out the amps you'll need - and the associated magnetic field. Biochemistry is loaded with unpaired spins - metabolism, transition metals, oxygen. Neutron star-like magnetic fields are a serious pookie-pookie.

Nuclear matter (neutronium) is stiffer (more incompressible) than ordinary matter. Alas, it is not stable to beta decay unless gravitationally bound. 10^11 to 10^13 gees would be inconvenient in all ways.

Cosmium and relux, Invaders from the Infinite by John W. Campbell, have been done.

OTOH, all you have to do is spin the walls and let centripetal force keep things inflated. That leads to minor problems of achieving relativistic velocities, and lubrication where the rubber meets the road. Little things like rotational instabilities of a hollow cylinder of fluid should be addressed.

[tolworthy]

Amazing stuff! Very useful. Thanks.