Aircrete (from my research) appears to be pretty good for insulation. However, the 'fluffier' (more insulative)you make it, the more fragile it is. The cement can absorb some
water as well. If it has to be mechanically strong as well, to contain the soil, or other Mass, it may not do very well.
And you can only pour about a foot to a foot and a half deep at one time. Over that depth the weight of the uncured aircrete has a habit of causing the cavitated bubbles to break down. Many of the people doing aircrete domes make blocks of aircrete that are then mortared together after curing to form the domes. I think this is how DomeGaia does it?
My guess is that Airecrete would work for insulating a dirt thermal Mass, but you might also consider papercrete or styro aircrete or dustcrete (sawdust). Both have good insulating properties as well. According to one
video, papercrete is mechanically very strong as well. Dustcrete is also reported to be strong and insulative.
The above mentioned variations all have some similarities to aircrete. Aircrete is air captured inside the cement in the form of micro bubbles. Tiny convection chambers, heat has to convect to the other side or 'soak' around the border of each bubble.
Think of the inclusions as a 'thermal void' aggregate
(Or at least voids of slower thermal transfer)
All of those tiny little 'empty' spaces slows down the transfer of thermal
energy. Styro aircrete uses the micro air bubbles as well as larger thermal voids formed by the styrofoam beads. Paper and Dust have the cellulose (
wood) fibers giving both structural strength as well as low thermal conductivity.
I think chunking up aircrete to use as aggregate would also work, but I don't know how crumbly it would be or if that would cause any problems in a stronger cement mix.
I guess one of the variables will also be what's available to you as well as costs.
I am answering this on my phone, but I've got some links I would like to add. It will be easier to add those on the computer. If I can I will add them to this message but I may have to add them as a separate reply.
One of the links is to a video of this gentleman's styro aircrete testing. He's changed the name of his channel to Abundance Building Concepts. He's got some great information. And I like his styro Shredder design. A couple of the other ones I might have actually gotten to off of other posts here on permies. I can't remember at the moment: it's that whole 'click a link then follow another link' thing. The guy who is doing the sawdust showed a clip of a dozer dumping sawdust into the back of a pickup truck and I think $20 was mentioned. Cheap if there's a sawmill nearby, possibly even free if you ask the right people.
I wonder if that would work with wood chips from a tree service? They wouldn't be aged or dry and there could possibly be leaves mixed in, but that might not be a problem? A lot larger and more irregular in shape than something like Styrofoam or sawdust
https://www.youtube.com/watch?v=6U4JAop0dTY
https://youtu.be/pBX1MJsJ0tY
https://www.youtube.com/watch?v=-RiWlwO5irE&t=39s
https://youtu.be/XyirHL9TvGE
https://youtu.be/4TPFgJC1xx8
I just found this. My Little Homestead has done a bunch of earthbag and some other stuff, I was not aware that they did some aircrete, too!
https://www.youtube.com/watch?v=VKyPVV-daqk