# Is there a metric for how far underground a nuclear bomb needs to be to safely be tested?

I'm running a one-shot cold war campaign where the PCs are going to sabotage a prototype Soviet giga-ton bomb. Realistically, how far underground would a giga-ton bomb have to be buried to be safely tested?

• Just don't set it off near a fault line. Unless you want to. Feb 22 at 6:25
• Put the nuke on a rocket & test in space, preferably far from Earth's atmosphere. Have probes monitor the blast & send the result to Earth.
– Fred
Feb 24 at 12:23

Yes, there is a metric.

The Wikipedia page on underground nuclear tests contains a table listing the extension of the various zones with the nuke yield in kt, which I report below

One figure used in determining how deeply the device should be buried is the scaled depth of burial, or -burst (SDOB) This figure is calculated as the burial depth in metres divided by the cube root of the yield in kilotons. It is estimated that, in order to ensure containment, this figure should be greater than 100.

The radius r (in feet) of the cavity is proportional to the cube root of the yield y (in kilotons), $$r = 55 \sqrt[3]{y}$$ ; an 8 kiloton explosion will create a cavity with radius of 110 feet (34 m)

Melt cavity 4–12 $$m/kt^{1/3}$$
Crushed zone 30–40 $$m/kt^{1/3}$$
Cracked zone 80–120 $$m/kt^{1/3}$$
Zone of irreversible strain 800–1100 $$m/kt^{1/3}$$

Using the above table and the estimated yield of your nuke, you should be able to determine the minimum depth. For a 1 Gt nuke, the molten radius should be between 400 and 1200 m.

Using the table in @L.Dutch's answer, you need to look at more than the melt cavity. That's simply the diameter of the spherical hole that's created. In the crushed zone, the rock is basically pulverized into fragments and has no strength, which means it will collapse. Into the cracked zone, the rock is mostly intact but fractured, which means less structural strength. In the final zone, the rock is deformed, but remains intact.

So, in the event of an explosion close to the surface, the melt cavity will form but will fill with the collapse of the broken rock above it, which will form a larger void. Into that void, the rock in the cracked zone will sag, the lower parts breaking off, and cracks will form that could allow radioactive material to escape.

So if your explosion is too close to the surface, it will form a crater. If the crater is formed by slight slumping of the strain zone, you're okay and depending on the thickness of that zone, the surface may not even significantly move. If the cracked zone reaches the surface, you may or may not get a crater, but you have a likelihood of fractures that could release radioactive material over time. If the crushed zone gets too near the surface, you will form a crater and will almost certainly have the escape of fallout. Clearly, in order to conduct a safe test with everything contained, you need to be below the cracked zone depth. Which, for a 1 gigaton weapon, means a depth greater than 8-12 kilometers.

This creates some issues:

1. There are no mines anywhere near that deep. The deepest mine in the world is at around 4,000 meters below surface. So massive engineering issue. During the Cold War? Not happening.

2. Geothermal gradient. If we take 10km as a "safe" depth, the temperature Can be between 150 and 300 degrees C. That is less than optimum to be working in to set up a test.

3. Spheres are 3-dimensional.

What I mean: the force of the explosion propagates up and down. Now, granted as you go down the greater temperature of the rock gives it more ductility, thus greater flexibility to absorb sudden shocks without fracturing, but still, you are probably looking at several kilometers of rock below the explosion that suddenly forms a weakened zone that extends upward toward the surface. You really, really, really don't want a weakened zone of rock penetrating a good fraction of the way through the crust. That could be bad. It would be awkward to have your test facility turn into a volcano.

Long story short: there is no "safe" depth for a test of this nature. If you could even get there in the first place.