You are right - based on the numbers given at the start of the article, and a density of clay around 1700 Kg/M3, if one kept within the footprint of the tower,

You are right - based on the numbers given at the start of the article, and a density of clay around 1700 Kg/M3, if one kept within the footprint of the tower, it seems one would have to excavate ~100 feet down to create a sufficient volume (less, of course, if you can broaden the chamber beyond that footprint, but I guess the scope for that is limited - and, on the other hand, the landfill layer may be less dense than clay.)