There is usualy steel reinforcement (rebar) in the concrete. Isn't introducing electrical current gonna cause galvanic corrosion of the rebar? Might even affect concrete structures around the capacitor, not just the capacitor itself.

Also if i understood correctly, this capacitor would need to be kept wet (with water) to remain operational right? Wet basement is extremely annoying thing with many unpleasant consequences to say the least. So this might require some efforts to maintain the moisture while keeping it contained.

How do you replace this thing? Eg. once cracks inevitably form in concrete, or when the carbon structure get damaged by accidental overvoltage/overcurrent, or when the insulation layers deteriorate. You cannot simply replace foundation of a building. Therefore it would make sense to keep the capacitor at least partialy separated from the structural parts of the building.

Anyway this seems as an interresting idea and i wonder if plastic bucket full of concrete would be enough to power something like UPS to provide 100W to keep PC running for 15 minutes. Might as well stop replacing lead acid batteries every other year if this is at least remotely viable.