I have followed the debate on storage of high level nuclear waste for some time. The discussions have been interminable — worse that the recently concluded US presidential campaign. The questions of safety for unimaginable terms were fascinating — especially how one would guarantee the isolation of the chosen site for many thousands of years. I think there are a number of problems with both the approach and indeed the whole concept:
1. The thesis that nuclear waste is a problem — the discarded components of nuclear fission will be releasing energy for a very long time. Somehow it seems that there is an opportunity here more than a problem. But it remains for some bright engineer to realize that this stuff could be a sustained power source and develop the technology to safely utilize it. I would not be the least surprised to find that in the future (probably long after I am with my ancestors) that our waste piles are being mined for resources.
2. That it is sensible to try and design structures that would outlast the entire history of human civilization. No civilization so far has lasted more than a few centuries before being replaced with a different way to organize society. Even China and Egypt changed over time. Nice idea but hugely expensive and no real way to prove one way or another — but I am sure that it was a nice cash stream for engineers and lawyers.
And of course, while the search for the ultimate answer was going on, the waste was simply accumulated at the generating nuclear plants — so there is a huge backlog to deal with.
My simple suggestion would be for folks to look at this stuff as an opportunity to be used rather than just a problem — it may free creative minds to a better solution. And to stop wasting money on predicting the future so far out that mankind may no longer exist.