If you go deeper you get sicker, and you find there is an intensity indicator with the next level filled in.
Like if the structure itself will be there in 10,000 years, then making part of that structure protrude to the surface with some sort of intensity indicator that changes along its depth, as graduated exposure to radiation increases, should be pretty clear.
Recovery from Mild Symptoms
At a dose of 0.5–1 Sv, symptoms such as nausea, fatigue, and possibly mild skin reddening may appear within a few hours to a day after exposure.
Recovery is likely within days to weeks as long as there is no further radiation exposure and the total dose does not exceed the body's capacity to repair cellular damage.
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But then it's just a machine so obviously one should consult a nuclear physicist before actually implementing this in a multi-millenia nuclear waste containment site