> Also, what is the general mathematical relationship between depth, rock pressure / weight, and energy required to drill?

There isn't any. It completely depends on the local geology.

Liquids are easy because there are no lateral load transfers, and the structures have to bear the weight of the entire water column above them. But with soil you get lateral load transfer, so the pressure on the tunnel is not easily relatable to its depth.

That's also why you can have mines that are kilometers deep, yet with tunnels held by wooden beams.