There’s me, an infinitely high wall, and a nuke on the other side. Since I’m in Aberdeen, the Granite City, let’s assume the wall is made of granite. The nuke is detonated. How thick would the wall have to be to protect me from a Hiroshima-sized nuke? How about a Tsar Bomba? What if the wall were honeycombed like tank armour?
Assume there’s no spalling.
Probably a good place to look at to get good numbers is Underground nuclear weapons testing - Wikipedia. Which gives the following distances.
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)
Clearly being in the melt cavity is bad, but you might be significantly safer than suggested by the number on the crushed zone, since unlike a underground explosion your weapon will be able to expend some of its energy ouside on the other side of the wall and the shock wave won’t couple to the wall. So lets say 25m/kt^-(1/3)
Which would be about 63m thick for a Hiroshima, and 920m for the Tsar.
Is this a bad time to point out that an infinitely high wall made out of any material would eventually collapse under its own weight? 
More seriously, you might want to look up the idea of overpressure, and blast from nukes specifically. This is the pressure per area exerted by the bomb’s blast force. Your material will have to be thick enough to stand up to this amount of pressure, and it can really be quite substantial. Most of the time, 10 psi is the goal for weapons designers, since this is about what’s needed for concrete buildings.
I’m not clear on how far you and the wall are from the bomb, though. PSI is probably more useful if you’re outside the fireball and Buck Godot’s comparison to an underground test might be better if you’re right next to it.
You also need to be able to breathe, right? That fireball wants your oxygen…
Concussive force is also a consideration - it will penetrate any solid and find it’s way to your innards.
And granite will assume and transmit radiation, giving off, ummm… radiation (more than it already does, according to the EPA).
Just a random fact I read that I thought was interesting about the Tsar Bomba: It said on the wiki article anyhow if you were 62 miles from the epicenter you would receive 3rd degree burns, that is truly horrifying power.
And we’ll also need to take into consideration the heat generated by the bomb. Off the top oh my head, I’m pretty sure that granite melts at around 2,200 degrees (F). The bomb dropped on Hiroshima generated a fireball with a temperature of over 10,000 degrees (F) with a diameter of roughly 370 metres. So the distance between the explosion and the wall would seem to be an important factor in deciding how thick of a wall you’ll need.
Between the blast, the heat and the radiation, if a Hiroshima-sized bomb went off directly on the other side… I’d go with a minimum thickness of one mile of granite.
Need answer fa …
(Too late.)
Inside of building up, better to dig down. Or find a cave.
So you’d need a wall over 370 metres thick if the bomb were to detonate right next to the wall.
I wouldn’t read it that way. While the fireball is hot enough to melt granite it’s very short-lived. You’d vaporize a little material off the outside and that’s about it, from the perspective of heat alone.
Of course, the fireball is ultimately the result of gamma ray released in such intensity that the atmosphere absorbs them. The gamma rays scale down in energy and that energy goes into the air as heat. Gamma rays can also penetrate stone to a substantial degree, and so you would be vaporizing some amount of rock within a few meters of the bomb. (Pretty much like the underground weapons testing results show).
How thick was the proposed blast shield on Project Orion?
Closest Hiroshima survivor was 300m from ground zero (inside a bank, not a bunker) so one mile thick wall would be some serious over-engineering.
Pretty sure this has probability to kill charts for different surface bursts. Since an infinitely tall wall is kinda like the ground surface stood upright that should give a decent estimate.
Keep in mind that the bomb was detonated 600 m above the ground. That makes the triangulated distance a total of 670 m for that survivor.
But, yes, clearly much less than a mile.
How far down under the ground does our wall go? I’ve read of a joke among Minuteman LCC crew is that while the rugged, multiple-feet thick concrete launch capsule might survive an ICBM detonation, they won’t survive the 200-300 foot drop to the bottom of the resulting crater.