I think you would have settling issues that would mess up the tile work. My earthen floor seems alive. It seems to rise and fall, living and breathing. So if you really wanted to install tile, I would make sure that your floor is really stable before you tile it. I know that for my earthen floor, it would definitely be problematic.
good luck, let us know how it goes
I laid ceramic tile on the floor of the first small cabin I built in GA. I filled in the floor to almost the desired level, then laid down a sheet of plastic as a moisture barrier, and then about two inches of sand. I raked this as level as I could and dampened it slightly and then laid the tiles directly onto it, butting one another as much as possible. A little sand worked its way up between them for the first few weeks but after that they locked into place and it didn't seem to be any dirtier than any other kind of floor. And another beauty of the system was that if I cracked a tile by dropping something heavy on it, I simply pried it up and replaced it with another one from my scrounge pile.....
The out of print earthen floor pamphlet from Canelo Project mentions installing tile and carpet over earthen floor. I have no personal knowledge of doing this other than hearing it has been done before.
Saltillo tiles are a terra cotta tile popular in the Southwest and warm climates. Natural grout goes nicely with Saltillo. Not good with freeze-thaw situations because they crack. Some methods involve sealants and glazes, but not necessary. Probably not a good choice for radiant heat tubing below the tiles, I imagine the temp. fluctuation would cause them to crack as well.
I remember when I had the marvelous opportunity to visit the indigenous Tarahumara people in Chihuahua, Mexico. They had natural earth floors, rammed earth I believe. I wiped my feet before I entered the house, which caused a bit of an uproar of laughter. The dirt on my shoes was what the floors were made of! Ah, cultural diversity. Gotta love it! ((Keeping my fingers crossed for the Keyline ticket! This would be such a game-changer in my career and impact on the world!! Best of luck to everyone!))
My experience living in a daylight basement dug out by my father. The ground was sand and well drained. The up hill side of the house was dry because of the attached carport so even though we live in a high rain area there was no problem with dampness. He had dug down to the level of the foundation blocks then laid down plastic then covered the plastic with sand. Then another layer of plastic and plywood with battens under the seems. This was covered with indoor/outdoor carpet.
This floor was relatively temperature stable because of the layer of dry sand. It had a comfortable give to it when walking.
From my experience laying engineered flooring that snaps together and has a foam underlay, I think it would hold up to shifting with the plywood underneath.
You may want to consider using cork underlay, its relatively cheap, renewable, water proof, soundproof, insects hate it and it chars, but is not easily burned. It does work well under tile. I used some under tile before on an earthen floor, it worked great. Good luck withthe project.