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In a scenario I'm thinking of, the Earth has been nuked bare and a few remnants of humanity are surviving in their underground bunkers. Let's say there is one in North America, one in Central American, and one in South America, then one or two in Europe, four in Africa, I could go on, but I think this is not so important.

Could the bunkers be somehow connected in order for their residents to communicate across the globe? And is there a way the bunkers could exchange (even if only within one continent) power harvested from solar panels in case one of them loses them?

Already Exists

Behold, the Submarine Cable Map! A wide network of underwater cable that connects the major coastal population centers. In fact, I believe you may be using it to view this page, or even if not you, someone else.

(By the way, don't use solar power. A nuke-fest that destroys the Earth and forces everyone to live in bunkers will cause a nuclear winter and shroud the world in darkness. Use nuclear generators instead. And that can be sent through subterranean power lines.)

I think it depends on the level of technology your world possessed before the Great Nuking.

If the world was already connected via deep underground tunnels burrowed miles beneath the surface then sure. But creating them after the Great Shellacking that presumably killed lots and lots of people would be a big challenge since they would require a power source to drive the tunnel boring machines that Solar power is not likely to be able to generate.

If robots were well developed in the world before the Great Burn, then robots could walk power cables to nearby settlements to share power and communicate with each other.

• The robots would be powered by the cable and even guided by the cable by operators in the originating settlement.


• The originating settlement would be fabricating the power cables as they were deployed unless they had hundreds of miles of power cable hanging around on spools.


• Since a robot can only carry so much weight, there would be multiple robots each supporting a length of the cable.


• The originating settlement would be fabricating the robots too unless they had the 10,000s required to carry heavy cables the 1000s of miles just parked in an underground garage


• The chain of cable carrying robots would look like a line of army ants moving forage to their nests from tens of mile away.


• It might not be possible for there to be enough robots to carry the cable all the way across the globe, so the robots might carry it so far and coil it up, then go back for more. The pattern would repeat until they'd moved one end of the cable the entire distance.


• RObots would break down so Wrecker Robots would be needed to pull the break downs back to somewhere they can be repaired or recycled.

It is possible. More so for bunkers in Eurpoe to be connected with one another or with those in Asia, or North to South America. You just lay cables as we do now. or you could just lay them on the surface, if there is no-one left to steal them. If you are thinking of potentially laying thousands of miles of tunnels then this is not a trivial task, but threading cables down them once constructed is simple.

The less relatively easy bit may come when havig to traverse oceanic treaches, subdution zones or mid ocean ridges. But, with current technologies we run cabels between continents to supply the internet to the world.

So communtication would be fine, but shifting power over long distances leads to large percentage losses, so it is possible but expensive. And rather than DC transmission which requires lage conductors, you would want high voltage AC which requires large distances between cables to prevent arcing... this is why pylons hold the cabels so far apart.

You could also use short wave radio to communicate between bunkers bouncing signals of the ionosphere. Then they would not have to be physically connected to be able to exchange information. But bandwidth is low. If there were still satalites these could potentially be used to communicate.

No.

Why not?

Physically: Earthquakes would sheer them off. Landslides would fill them up. Tree roots would pierce them. Lakes and rivers and rain would flood them. Not everywhere all at once, but once or twice in two thousand miles is enough to ruin the whole thing. And everything you do to shore up against those environmental factors is going to increase the cost.

How will the air pressure within the tunnel be regulated?

Economically: Who would maintain them? Who would pay for them? You're considering building the largest network of infrastructure inhuman history. That's going to cost quite a lot. If you have that much coordination and cooperation you've reduced the chances of all out war.

It is very important where you put your bunkers. The distance between them will determine their costs. At the moment tunnels are about $1 Billion a mile:

https://www.boringcompany.com/faq/

Keep in mind that current infrastructure is difficult to upkeep with everything running at full steam. Drastically reduce that population and everything is going to go to pot real fast.