The basic problem of maintaining a civilization, according to Tainter, is maintaining a positive energy balance; spending less energy than it consumes. With a negative energy balance, gradually the entire population starves to death. For this reason, all historical human populations have lived on the surface of the Earth, not inside it, because on the surface there is lots of readily available sun energy, and even inefficient ways of harvesting it (such as plants) suffice to support humans. Also, the conditions are relatively mild. The worst problem is that parts of the surface do not have salt water covering them, which is a problem we learned to cope with some hundreds of millions of years ago, with means duch as lungs, eggs, and amniotic sacs. Inside the Earth, all of our necessities must be provided by clever contrivances; not just food, but light, oxygen, low pressure, cool, dry (we have become accustomed to it in the last few hundred million years) , and sanitation.
These things can all be provided with some expenditure of energy, but until the 20th century, this required access to sunlight or oxygen, both of which are scarce inside the Earth. But in the last few decades, it has become possible for the first time to generate useful energy from materials found within. Today a fleet of nuclear submarines silently stalking the oceans of the Earth runs on these materials, originally uranium and later plutonium, supplying the needs of the canned humans within raping one another with grease guns. They typically bring food and the like with them to begin with, and of course the refined nuclear fuel.
A civilization of mole people, however, could supply their own energy needs by mining and refining fuel, and using the resulting nuclear energy to supply all their other needs: illuminating crops (or direc synthesis of carbohydrates and peoteins from mineral feedstock) .for food, illuminating people, refrigerative cooling of the dwelling -caverns, repairing and building machinery, and further mining.
Vinay Gupta's Simple Critical Infrastructure Maps may be a good fraamewko for anakyzing this civilization's needs. But this is not the place to do that.
To calculate the energy balance of just the mining, refining, and reacting cycle, it is necessary to know the energy density of thorium or other less favorable fissionable, its concentration in the rock, and the energy costs of mining operations. I don't know the numbers but I'm pretty confident that it will work out well.
The big problem, though, us cooling. As has been observed about hypothetical battles between spaceships with directed energy weapons, cooling ability is the crucial figure of merit. Most of the Earth's crust us far too hot for human habitation, and so active cooling will be needed for the dwelling caverns. It would be easy, in fact, for the mole people to spend most of their energy refrigerating their refrigeration systems, much as a rocket spends most of its fuel on lifting fuel ti near orbit.
To ameliorate this problem, ideally most if the civilization 's machinery can run at temperatures above the ambient temperature at their depth in tge crust, separated from the city proper by many meters of rock. Thus it can be cooled passively by coolant fkows between it and the rock that sinks its heat. These.can.either be passively powered by the heat itself,as in heat pipes,or with some kind of active pumping. But the society must continuously seek not just more fuel but more rick that is cool enough to passively cool their machinery.
As an example, typical lighting technologies, including halogen lamps, gas discharge lamps, LEDs, and fluorescent tubes, are in the 10% efficiency range. For every joule of heat produced by the absorption of the light they produce, they themselves produce about another nine. If they can be contained in a cavern far from the city, connected to it by quartz lightpipes, they can avoid heating the people by more than the light they send, and the lighting cavern itself can be maintained at a much higher, hellish temperature. Perhaps under such circumstances, incandescent lighting might be more efficient: if the entire lighting cavern is yellow -hot, and the only way it can lose heat is either by radiating through the lightpipes or very slowly conducting into the surrounding rock, eventually most of its heat will be turned into light. This, of course,requires that the cavern itself not be melted into lava by the heat.
Earth's crust has billions of years of heat built up in it, mostly from its own radioactive decay, not from the heat from the mantle below. This heat itself is an energy resource that can be harvested, at least if you are good at tunneling and laying pipe. It diffuses out at about a kilometer per billion years, or a meter per million years, because the gradient is so mild. A few hundred meters of rock should suffice over human timescales to insulate against even some hundreds of degrees of temperature difference.
Refrigerative cooling with a heat sink at a temperature of hundreds of degrees may require nontraditional refrigerants, since the common ones are developed for use at.surface temperatures. The first stage of air conditioning for a troglodyte city could perhaps use one of the traditional HCFC refrigerants, with an exhaust of heat.in another cavern at perhaps 50°, but the subsequent stage pumping heat from there into coolant at 70° or 100° may need to use a different coolant, something that boils above 70° at a reasonable pressure.
Speaking of which, pressure itself is one of.the novel issues here. If the mole people have no shaft to the surface, the tendency will be for water or other fluids permeating the rock's pores to leak into the dwelling -chambers, compressing the air already present, until the pressure is equal to that in the surrounding rock. This would be quickly fatal at any substantial depth, even leaving aside the issues of poisonous gases and liquids like oil. So in addition to actively pumping heat out of the subterranean Xanadu, it is also necessary to actively pump liquid out, and to seal the interface with the rock as well as possible - a sort of stationary submarine hull. This is also necessary to shut out radon that would otherwise appear.
This also suggests that there will be a minimum efficient size for particular dwelling-caverns, since a larger contained volume will reduce the amount of hull needed per unit volume. The expense can be divided over a larger space; also, any failure of pumping will thus have more