I don’t think we even need to store it. Nuclear waste has been sitting in regular storage for over 50 years now, seems to be perfectly safe. We should just keep doing what we’re doing.
Why do we even need to bother putting it underground except for some unlikely what if scenarios 1000 years in the future.
1. Expecting current political and economic structures etc to remain for thousands of years is silly, so we do need a more permanent solution to a long-term problem.
2. Keeping lots of nuclear waste in spent fuel pools just increases the risk picture unnecessarily.
If there's a regional instability for a year or two and spent fuel pools boil off and then waste melts through, possibly poisoning the groundwater for that region, that's a big problem.
Mostly corrosion. The half lives involved, combined with the great expense of safely adjusting these things after they're put to rest, means that you would really like something really dry and remote. Fear of contaminating ground water is incredibly sensible to me, at least. It'd be a hell of a thing to get Yucca Mountain un-cancelled...
