I am not sure yet. It's going to be a 20' circle essentially. I plan to go 3 feet or so. Deeper if needed. Though about using rocks to fill I the space of a tube if some sort. I am open to suggestions
Discussion
I am curious how you went about choosing these dimensions
I found ceiling joists for free.
The depth I am guessing. I just make stuff up really and it tends to work out. 
Are you using earth bags? Or tires? As your outer walls a la an earthship?
quality of life improvement for free..