The corner of the slab in my garage was removed to bring in plumbing. It's been backfilled with ~3 feet of dirt (slab was 2ft thick). What is the best way to repair this? I'm thinking I'll dig out approx. 1 ft., compact as best I can, and fill with cement, only applying adhesive to slab sides (not the stem wall) and maybe chisel out an undercut on the slab. Anything I should do differently/think about? I've never worked with cement before. Thanks.
Pour in concrete after the base is known to have been fully compacted and settled. But do not make it a foot thick. If you ever have to work on this plumbing later you would highly regret having to break apart that block.
There should be no reason to have the patch portion be any thicker than the original slab. Also it appears that the original slab was not tied into the main foundation under the walls so you should maintain that with the patch. I see no special reason to chisel out an undercut of the slab. Just make sure that the edges of the slab are clean and free of loose particulate so that the new cement has the ability make somewhat of a bond to the existing slab. Adhesive on the slab edges would be a waste of time/money because the wet cement you pour into there would not stick to it.
If you want to work at it you could bore some holes into the edges of the existing slab and bond some short pieces of small diameter rebar that sticks out into the patch region. That would do more good to keep the patch edges lined up with the slab over time. If you so this however do it carefully so you don't end up just crumbling more of the existing slab in the process.