How about looking to the highway engineering handbook(s)? A thought.
I know I have had trouble with 2 yd LHDs sinking in or tearing up backfill under about 300psi compressive strength. At 500psi, no problem. Now, this was not a cap but a full 8ft deep pastefill.
This is a subject which depends on many variables. Resource size and geometry, depth, desired production rate, power and fuel costs, and dozens of other factors. A great application for simulation. One author - Northcote and Barnes (1973) gave the depth as 350 meters. Western Australian...