Unless the thing is monstrous and deserving of hoop/arch type behavioral analysis, I'd probably just look at the walls as cantilevers rather than trying to justify horizontal spanning action.
I did something similar a few years back; had to design a circular precast concrete ring to serve as a tree pit. I can't find the calculation but I think I treated the soil as a fluid and calculated the hoop stress.
If you can reinforce it continuous around the perimeter, no need to design it as a cantilever. Load it as a straight retaining wall and design for the hoop stress. It doesn't even need to be connected to the foundation.