If it’s anything like the solution planned in Finland, the waste is placed in copper containers, transported in pretty much bomb-proof vessels, and the facility is kilometres deep underground split into multiple separated chambers that get filled with concrete (or bentonite to be more precise) once they are full.
The result is a solid block that will survive basically forever and the only thing you need to do is not go dig it back up.
If it’s anything like the solution planned in Finland, the waste is placed in copper containers, transported in pretty much bomb-proof vessels, and the facility is kilometres deep underground split into multiple separated chambers that get filled with concrete (or bentonite to be more precise) once they are full. The result is a solid block that will survive basically forever and the only thing you need to do is not go dig it back up.