Had a question about underground nuclear detonation.

[Aratech]

Sorry to bother everyone, but I'm wrapping up one of my stories over at SB.com, and the upcoming chapter has a pivotal scene involving the detonation of a trio of 30 megaton fusion bombs within a large, underground cavern, and I want to get the effects a close to being proper as I can. I've tried my best to seek out advice from individuals like Connor, and they helpfully suggested I ask here.

Context wise, the cavern that the bombs are being detonated in is about six kilometers long by 4-4.5 in width( overall, its roughly oblong, with the west/east being the longer part, and north/south being the shorter), and about 600 meters tall. The cavern is predominantly granite, located approximately 4 kilometers below the surface of the planet, and is surrounded by a large number of tunnels of varying sizes (they typically range around 2-20 meters in diameter) going off in just about every conceivable direction, including above and below the cavern itself. The three bombs are located in a rough line running from north to south, at about the rough center of the cavern east/west wise. The bombs are on timers to all detonate in tandem with one another.

I apologize if I'm not giving enough information, or am being confusing, but I suppose ultimately, my question is what is the most likely outcome for this event, and what type of damage would be conceivable from factors such as the overpressure, intense heat, and so on and so forth.

My sincerest thanks in advance to anyone who can help me out here.

[Simon_Jester]

Did anyone ever do stability calculations on that? You're talking about an unsupported ceiling several kilometers across; what keeps it from collapsing?

[Sea Skimmer]

4-4.5in in width?

[Aratech]

Did anyone ever do stability calculations on that? You're talking about an unsupported ceiling several kilometers across; what keeps it from collapsing?

No, I do not believe so. It was one of the reasons I was curious about the detonation effects of the bombs.

Sea Skimmer: my sincerest apologies, that should be 4-4.5 kilometers in width.

[Vehrec]

Did anyone ever do stability calculations on that? You're talking about an unsupported ceiling several kilometers across; what keeps it from collapsing?

As I recall, the cavern in question is a typical high fantasy cave used as a city by an underground dwelling race. Most of the construction would probably be hewn stone, labor and stone not being in short supply, and with a population of at least 100,000 individuals. In the case of the specific fantasy genre, questions of stability are not really the kinds of things authors want to think about-they want their mushroom forests and giant cave cities!

[Sea Skimmer]

4.5km is way too wide for rock to hold up, around 600 meters is IIRC the limit but only then in totally optimal conditions and buried shallower then 4km down, and the shape needs to be a sphere to control stress build up. An arch over flat floor wouldn't work.

But anyway ignoring that a nuke is going to damage the tunnels in two main ways. The first is the simple blast pressure; the second is acceleration which turns into vibrations. The surfaces directly exposed to the blast will also suffer a lot from heat and radiation. The end result of 30 megaton nukes going off like that would be total or near total destruction of the complex, and most likely a shattering effect that reaches the surface and causes a subsistence crater. The tunnel voids would serve to reduce the transmission of shock, but that's unlikely to matter with a 30 megatons contained so far underground.

[cosmicalstorm]

I think Stuart mentioned that bombs are likely to commit fratricide if initiated too close to each other unless the initiations are extremly precise.

[Ariphaos]

Well, these are bombs presumably being detonated on a timer, which don't have the same issues that timing missile reentry does. They probably are within each others fireballs in the cavern, however, which probably means only one will detonate.

[Simon_Jester]

4.5km is way too wide for rock to hold up, around 600 meters is IIRC the limit but only then in totally optimal conditions and buried shallower then 4km down, and the shape needs to be a sphere to control stress build up. An arch over flat floor wouldn't work.

Just out of curiousity, what happens if you have a large spherical cavern and just fill the bottom half with loose-fill material and build a flagstone "floor" over it or whatever? In effect you wind up with a big hemispherical dome, but I can't see why it wouldn't have the structural strength of a sphere.

Of course, I suspect from the way you said it that the real problem is the hemisphere being stronger than the half-cylinder, because the hemisphere has arch-like support distributing stress all across its surface, not just in one dimension along the curvature of the vaulted roof.

Well, these are bombs presumably being detonated on a timer, which don't have the same issues that timing missile reentry does. They probably are within each others fireballs in the cavern, however, which probably means only one will detonate.

If the timing is truly good you can avoid this: nuclear devices spaced a kilometer apart can't possibly affect each other for the first thirty microseconds or so after initiation, because they're outside each other's light cones until that happens. If you get the synchronization that tight, all the devices will go off as normally.

And with the right equipment it is at least theoretically possible to get that level of precision timing, though unless a lot of care was taken in the setup it won't work. For a more simplistic "dump nukes and light off" approach, yes, fratricide on the part of one of the charges will probably destroy the other two.

[Purple]

On the subject of stability, would it not be far more logical to build a number of smaller hemispheres and connect them through tunels?

Also, when the OP said:

The bombs are on timers to all detonate in tandem with one another.

I assumed he mean that the timers are set that way to avoid a fratricide scenario.

Edit: SJ beat me to it.

[Atlan]

If we simply assume that the people setting off the nukes are sufficiently advanced that timing isn't a problem, and all three initiate: In air, the fireballs would rise, and cool off.
In the cave complex there is no space for that. Would it be wrong to say that before the whole shebang collapses, the whole cave will reach some insane temperature?

I mean, the three fireballs are likely large enough to fill most of the cave. Even though the whole thing will start collapsing rapidly, for a few moments the whole cave should reach a temperature of tens of thousands of degrees.

[Simon_Jester]

If we simply assume that the people setting off the nukes are sufficiently advanced that timing isn't a problem...

It's not so much advancement; we could do it today. It's a question of taking the trouble to set it up right.

It's like the difference between demolition experts wiring a building for controlled demo, and random guys strapping TNT to whatever looks important inside. It's not so much about the equipment as it is about the level of professionalism and control that are being applied. A bunch of amateurs could blow down a building, but they'll probably waste a lot of explosives doing so, and the results won't be as neat.

Of course, in this case, more than one nuke is almost certainly overkill anyway.

[Atlan]

If we simply assume that the people setting off the nukes are sufficiently advanced that timing isn't a problem...

It's not so much advancement; we could do it today. It's a question of taking the trouble to set it up right.

It's like the difference between demolition experts wiring a building for controlled demo, and random guys strapping TNT to whatever looks important inside. It's not so much about the equipment as it is about the level of professionalism and control that are being applied. A bunch of amateurs could blow down a building, but they'll probably waste a lot of explosives doing so, and the results won't be as neat.

Of course, in this case, more than one nuke is almost certainly overkill anyway.

I know what Aratech is after: The placement of the nukes is not random, and was decided on beforehand. An error margin of a few dozen meters at most per placement. It is acknowledged that each nuke on it's own can do the job. Using three simultaneous initiations was chosen in case one or even two devices were discovered before initiation, and each nuke is on/near a high-value target, although the spacing is not equal in distance. If left undisturbed the three WILL initiate simultaneous. It's more the aftereffects he's interested in.

[Simon_Jester]

In that case there's no point in the microsecond-precision timing it would take to prevent fratricide, if all you want is systems redundancy. Any one of the nukes will heat the cavern to incredibly high temperatures and then cave in the roof; it's just a question of how incredible.

[Purple]

What kind of temperatures are we talking about?
Are we in the "will scorch the wall and make it black like coal" area or the "will melt the rock volcano style" area?

[Sea Skimmer]

What kind of temperatures are we talking about?
Are we in the "will scorch the wall and make it black like coal" area or the "will melt the rock volcano style" area?

A nuclear fireball is hotter then the surface of the sun, and a 30 megaton nuclear blast would cause third degree burns at 45km, IIRC this is around 160 degrees F required for the time frame of a nuclear thermal pulse. Shorter the time frame the hotter you have to get for third degree burns. At 13km the heat intensity will be 12 times higher according to Shep's calculator, and that’s if it went off in the open with an optimal height of burst. That's already past the blacken the walls range.

Contained inside a deep underground cave, even one some kilometers in length and span is going to greatly intensify the thermal effects since the heat can't vent into the sky with a 50,000+ foot tall mushroom cloud. The fireball itself would be 2.7km in radius for an open air ground burst. But since the cave in question is only 600 meters high that means… the roof of the cave gets vaporized in the fireball just as it digs a crater out of the floor… and well this squishing effect is likely to result in more or less the entire 4.5x4km cavity being nuclear fireball until it collapses which should occur almost instantly.

The result would be a lot of vaporized rock, and a massive thermal shock that shatters the rock behind the vaporized mass, which in turn its then shattered even more by the blast which then turns into those wonderful vibrations and a pressure wave that wreck everything else. This place is going to be utterly utterly obliterated. Some melting will be mixed into that but this is a weird situation so it’s hard to say much in detail. Just the shock of the roof and 4km of rock above it falling down ought to create a fair strength earthquake.

[Simon_Jester]

Basically, nothing made out of atoms in the cave is going to be in very good shape afterwards; most realistic structures or creatures are going to be totally destroyed.

[Vehrec]

Which only begs the question-how unrealistic would structures and creatures have to be in order to live through this?

[ShadowDragon8685]

Which only begs the question-how unrealistic would structures and creatures have to be in order to live through this?

About the only way I can see would be some kind of AI with reaction times measured in nanoseconds, with some kind of instantaneous teleport evacuation system to isolate and evacuate everyone in the unimaginably small time-frame between initiation and expansion. You'd be in the middle of the conversation and not even notice you were nuked until you finished your sentence and hey, why are you on the surface?

That, or they'd have to have some kind of really, truly ridiculous, Schlockian-style gravitic unified shields capable of containing the blasts and channeling it up and out through those tunnels. If you're talking about "Survive on it's own," I don't think anything would survive without some kind of ridiculously sci-fi unified shield or a magical "Immunity to Nukes" charm.

[Sea Skimmer]

Which only begs the question-how unrealistic would structures and creatures have to be in order to live through this?

Well lets see the roof load for 4km thick rock at 2,500kg per cubic meter would be roughly 10,000 metric tons per square meter of roof, which is about 1 ton per square centimeter or a modest 14,219psi. Multiplied over a 6 x 4 km rectangle that gives a total roof weight of 24 billion tons! In contrast the Hoover dam weighs under 7 million tons.

That much weight is going to fall 600 meters, and create a damn bit of heat when it impacts. I dare say that nothing even remotely plausible will ever survive that. Surviving deep inside a 30 megaton nuclear fireball isn't gonna happen easily either unless you are already buried under the cavern floor in some kind of superbunker.

You need I think about Star Wars level magic to even think about surviving in inside that situation or building a structure which can hold up. But Even for Star Wars you might have to build something like that cut and cover, not tunneled if you wanted physical roof supports, as opposed to magic anti gravity plates that simply push the roof up and let you dig out under it.

[Kuroneko]

Even individually, a 30MT airburst would have a fireball volume that's greater than the cavity, and reflection from the ground is the reason that ground-contact bursts are larger. Actually, they tend to be even larger than equal-volume comparison would predict, so one can expect that the fireball to easily fill the entire cavern, as Sea Skimmer predicts.

What you may want to do is to do a scaled depth calculation: (4.0km)/[Yield/1kT]1/3, which is 130, 100m, and 90 m for one, two, and three of your 30MT bombs, respectively, and look up some of underground tests at similar scaled depths, especially at hard rock sites. Unfortunately, I don't know of any easily-available resource that compiles such data, but some dramatic explosions on the site of the largest US underground test are:
Milrow, 1MT @ 120m sc. depth. Surface oscillated 13ft*, up then down[25:00]; 6.5 Richter.
Cannikin, 5MT @ 105m sc.depth. Surface oscillated 15ft; 7.0 Richter.
*Note that it looks less in the close-up video because the camera is also moving with the ground.

I'm not sure how granite composition would alter the above visually between having different density and strength, but between the lower scaled depth and the already-existing cavity (less rock to move), there's some fudge factor that I think most people would allow for story purposes.

But since the cave in question is only 600 meters high that means… the roof of the cave gets vaporized in the fireball just as it digs a crater out of the floor… and well this squishing effect is likely to result in more or less the entire 4.5x4km cavity being nuclear fireball until it collapses which should occur almost instantly.

The first part seems very reasonable (even with the larger cavern dimensions in the OP), but I'm not so sure about the latter. The shock wave will fracture much of the rock above the cavern, so it will be much less able to support its weight, but for a while, the entire cavern will be superheated with a very strong shock wave traveling outward. That means that while there will be fiery death in the tunnels, there's also a chance that portions will collapse and be sealed with crushed or molten rock.

If that happens, the superheated conditions inside the cavern will provide a lot of additional pressure on the cavern walls, including the ceiling. That will persist until either the cavern cools or, much more likely, the once-sealed tunnels will eventually provide leaks. Depending on the size of the tunnels, a delay of anything between "almost instant" to "several minutes" may be reasonable. (There are tests in which subsidence took much longer, but they didn't have such tunnels to the main cavity.)

But here's a final thought: dropping 3.4km of granite 600m down is in itself a 300-350MT event. If I get my scaling right, in seismic terms that's an 8.9 Richter earthquake. That's bound to mess up the countryside much more than a huge crater would.

[Sea Skimmer]

The first part seems very reasonable (even with the larger cavern dimensions in the OP), but I'm not so sure about the latter. The shock wave will fracture much of the rock above the cavern, so it will be much less able to support its weight, but for a while, the entire cavern will be superheated with a very strong shock wave traveling outward. That means that while there will be fiery death in the tunnels, there's also a chance that portions will collapse and be sealed with crushed or molten rock.

I never said anything that specific about the tunnels. Right angle turns and dead ends do a lot to block the passage of high intensity blast so I would not expect the fireball to progress deeply into the system except in the vertical direction which is presumably vented to the outside air and thus lower pressure. The shock is going to be what kills most of the radial tunnels. A realistic underground city-cavern would also need lots hoards of air locks to ensure a reliable air circulation and those would collectively slightly impede fireball passage as well.

If that happens, the superheated conditions inside the cavern will provide a lot of additional pressure on the cavern walls, including the ceiling. That will persist until either the cavern cools or, much more likely, the once-sealed tunnels will eventually provide leaks. Depending on the size of the tunnels, a delay of anything between "almost instant" to "several minutes" may be reasonable. (There are tests in which subsidence took much longer, but they didn't have such tunnels to the main cavity.)

I really can't see how over 14,000psi of pressure could persisting evenly over such a wide squished area for any length of time, all the more so since I would expect a vent path to the surface being blasted wide open. Nuclear tests involve the nuke at the bottom of a simple shaft, and its more or less evenly contained from all directions. That's vastly more suitable situation for maintaining pressure and yet you still the roof often did fall in at once. So yeah, a delay is possible, but its unlikely particularly at the outer edges. But then on the other hand if all three 30 megaton nukes went off together, spread a 1km apart or so behind rock they don't destroy each other, then we'd have strong odds that the blasts would massively breach the surface.

But here's a final thought: dropping 3.4km of granite 600m down is in itself a 300-350MT event. If I get my scaling right, in seismic terms that's an 8.9 Richter earthquake. That's bound to mess up the countryside much more than a huge crater would.

Yeah the ground is going to crack up way beyond the edge of the crater. You'd get that from a nuke on the surface anyway, but it tends to be concealed by all the debris raining back down from the blast and limited in scope owing to lower yields. Tidal waves, landslides and similar results would depend on what the local surface topography is like.

[Kuroneko]

Extremely handwavy calculation: the number of air particles in the cavern is about N = V/(23L/mol) = 4.2E35. The thermal energy is then on the about (3/2)NkT = 2.6E15J, or almost five orders of magnitude from the total blast energy. If a reasonable fraction of it goes into here, a pressure increase of a thousand-fold that we're looking for is very plausible (unfortunately, at high temperatures, the cavern air will have a many more degrees of freedom, so we can't say it is guaranteed, however, this is somewhat offset by an increase in molar density, which would increase pressure despite a lower temperature than one might otherwise expect).

I really can't see how over 14,000psi of pressure could persisting evenly over such a wide squished area for any length of time, all the more so since I would expect a vent path to the surface being blasted wide open.

Why not? A kilobar of pressure is not particularly unusual in geological terms. The primary difference between that and, say, a volcanic magma chamber is that this cavity's pressure will last only as long as its temperature does, assuming it's sealed in the first place. This fireball would already last a full half-minute by itself, and all that heat is not going to go away in a hurry afterward.

That's vastly more suitable situation for maintaining pressure and yet you still the roof often did fall in at once.

I don't disagree with the tunnels being thus temporarily sealed being unlikely, but not singnificantly implausible.

But I have a related question: if we get rid of low-yield underground tests, then does the delay to the start of the collapse significantly increase? In a the low-yield case, the cavity formed is small and hence so is the time to rough thermal equilibrium as well as cooling time. I can't find a source for the molar mass of granite, but a weighted harmonic mean of wiki's composition stats give m = 64.6 g/mol. Hence the explosion produces a cavity filled with gas with molar density n = m/ρ = 42 mol/m³. If modeled as an ideal gas at thermal equilibrium with the molten granite in the same cavity (1400K), the pressure should then be P = nRT = 71 psi, and dropping further when the liquid solidifies. Thus, it's easy to see why a cavity from a low yield wouldn't support much.

On the other hand, a large-yield explosion provides a larger cavity, both taking more time for heat transfer within it and (as per the cube-square law) longer time to cool, maintaining it for a longer time.

But then on the other hand if all three 30 megaton nukes went off together, spread a 1km apart or so behind rock they don't destroy each other, then we'd have strong odds that the blasts would massively breach the surface.

Since that's a scaled depth of between 250 and 300 ft (3.4km-4.0km), a massive breach of the surface is very unlikely if the canopy is primarily granite. Hard rock is a tougher nut to crack, at least according to Glasstone. Given that, even at full blast, the surface will experience a violent oscillation followed by chimney collapse.

Yeah the ground is going to crack up way beyond the edge of the crater. You'd get that from a nuke on the surface anyway, but it tends to be concealed by all the debris raining back down from the blast and limited in scope owing to lower yields.

I know, but it's more significant here because the collapse itself is actually far more violent than the original explosion. In this case, it's violent enough to make a lot of surrounding people very unhappy even if the area is geologically stable.

[Connor MacLeod]

Well, I'm glad I told Aratech to ask here rather than just rely on my word. (Important lesson for those of you following this: when you do amateur analysis it never pays to assume or think you know everything. asking, then asking again, and getting multiple opinions is the ideal way to go. Because there's always a chance someone like me can either be wrong or incomplete. Case in point: I never once bothered to contemplate the "what is holding the ceiling up" angle.)

Which brings me to an interesting question. Assuming some sort of "magical" means of sustaining the ceiling (which is possible) would that influence the detonations any? (ranging from super durability or some magical reinforcement of the ceiling, to some sort of magical structural supports/braces or levitation of some kind perhaps)

I'm also still wondering (something I suggested to Aratech) that perhaps 30 megatons is more than a bit of overkill for what he wants. Sea Skimmer's mention of a subsistence crater and tremors is a not so minor concern (not to mention that there are other races belowground who aren't total dicks who might get fucked over) Whta about (Say) a couple one megaton devices? Or would less be better (kiloton?)

[Simon_Jester]

The problem is that any explosion sufficient to really demolish the interior of the cavern will probably cause a cave-in unless there is a LOT of magic holding it up. At that point, a massive earthquake is inevitable, just from all the stuff falling from above.