I the first reply mapj1  talks about the British Nuclear testing on the Pacific Islands.

I can still remember my uncle Dennis Ganderton who was a British Nuclear Testing veteran, he was told that he had developed leukaemia and died six weeks later aged twenty seven.

Coal mines tend to be very wet, with water permeating through the rocks.  So if you chuck nuclear waste in them, there's a high risk that the radioactivity is going to show up in someone's water supply a few years layer.

only really if you are talking about soluble materials in porous packing, you are imagining this is like sugar in  a paper bag.

The usual method these days is not that at all but rather as some kind of glass or ceramic block where the chemical mobility of the radioactive atoms is then essentially nil. (you may pack the blocks in a steel drum to allow them to be moved by forklift, but that is not the main containment and can safely rot out in the first 50 years or so)
Mike

Sorry to hear about your uncle.  He must have been very close to the explosion and received a massive dose of burning rays.

We are discussing minute quantities of radiation and infinitesimally small risks.   

The BBC reported on the Theddlethorpe proposal this morning. 

www.bbc.co.uk/.../cy4d3y33y3go.amp