You can greatly lower the depth by using foam insulation. Here in Maine, if you toss down a 2" piece of foam board on the ground, frost will not go underneath it. By burying foam on top of whatever it is you are trying to keep from freezing/moving with frost action, you can greatly reduce the burial depth.
For instance in my house I put 2" Styrofoam over the pipe going from my well into my house because I could not bury it as deeply as I wanted too. Even with a driveway going right over it (no snow cover to limit frost depth) it has never froze in the past 17 years. (Note minus sign in front of picture of outside temp making this statement impressive).
Styrofoam is expensive, but it can be cost effective depending upon what your project is.