I posted this link on another Forum Post but it definitely applies here.
It's common details pertaining to straw bale construction and rammed earth tires are included.
http://www.ecohabitar.org/PDF/strawbalebuildinguide.pdf The only problem with the pdf is that it uses rammed earth tires to make a raised building, which generally isn't what you want in a barn.
The biggest problem with rammed earth tires by themselves is guaranteeing that they're level and stable over long periods of time. If you draw a beam between two rammed earth walls for a floor then only frost heave and landslides could possibly move it.
If on the other hand if you just put up a regular wall above a rammed earth foundation, any instability will come through as a moment at the support 10-15 feet above it's base, almost guaranteeing problems.
If you're still sure you want to used a rammed earth tire foundation, your moment connections will have to be seriously strong on both top and bottom of the wall. Beyond just the hazel stub to hold the bales in place, you would probably need at least one wall pin per tire, I'd personally probably try two, connected through the tire just below the top row. At the top of the pin you'd want to screw them in instead of nailing them. This would probably bring your spacing down from the common 20" to 5-15" O.C. for the hazel pins depending on the tire size.
I'm saying this from an architectural perspective that's what would feel safe. I haven't seen the detail for something similar, and an engineer might be able to calculate the needed support and formulate a structural detail.