Does nuclear waste dissolve?

Nuclear waste is a mixture of various substances but held within the fuel rods which are encased in zircaloy, and these are not soluble in water.  In fact the spent fuel is stored under water to both keep it cool and prevent radiation to power plant staff.  This is safe for the short to medium term, but for long term storage something more permanent is required.  Over thousands of years the fuel cladding could deteriorate and allow radioactive substances to leak out, and there could be some contamination if water was to flow through the storage area.  So the long term store needs to be underground but in a geological formation which is known not to have had water present in the past.