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The issue with that is the slurry doesn't flow very well. It will go a ways with prodding, or with a vibrating compactor to help it flow.
I supported a (much thinner) slab that had the under-fill recede away by drilling 4" core holes every 6 feet or so and pouring concrete into the holes, it flows out as a pad about 2 feet in diameter under the slab as a "foot", and the rest is just floating.

With your 8" pour and rebar, you have more structure than many concrete parking garages. How wide an area is unsupported (on poorly done fill)? Is the front edge on the same fill, or does it bridge the "ditch" onto more native soil?

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Planning a Duratec powered, Miata suspended 442

The shop is 20 feet deep by 35 feet wide. The front 8-ish feet is unsupported to within a foot of the edge. When I removed the deck on the right side, I found I could see under the slab.

A couple of people have suggested just ignoring it, given the thickness of the slab... but if I move any heavy machinery to the front wall, I'm worried that the whole slab might tip slightly.

I considered digging a trench around the outside edge and pouring a footing. It would take more cement than filling underneath the slab, but I could mix the cement with aggregate and save a few bucks. No pumping needed, and I could do it in sections. But it's a lot of shovel work, and I'm not sure I can do that any more.

How about... Rent a mini-excavator with a narrow bucket for a day, practice up a bit somewhere AWAY from the shop walls/slab and then dig your footer trench. (Plan B- Ask around, maybe you know somebody that can operate one that will work for beer and pizza.) Might take some form boards around the outside so there's enough "head" on the concrete for it to get pushed into the void, but it should work.


JDK

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JD, father of Quinn, Son of a... Build Log
Quinn the Slotus:Ford 302 Powered, Mallock-Inspired, Tube Frame, Hillclimb Special
"Gonzo and friends: Last night must have been quite a night. Camelot moments, mechanical marvels, Rustoleum launches, flying squirrels, fru-fru tea cuppers, V8 envy, Ensure catch cans -- and it wasn't even a full moon." -- SeattleTom

Looks like... $425 per day, plus I'd have to rent a truck to move it.

Figuring time... I *might* be able to get the excavator rented and home and off the trailer, and that would be a full working day for me. One to two days using it, depending on how inept I turn out to be, and another day to get it loaded up and hauled back. And that all assumes I don't overdo things and lose a day or two in the middle of that.

I see your dilemma. It does seem the idea of pumping slurry under it is probably the best bet, as long as the grade doesn't recede any more later. As you said, a perimeter footing would also work, but takes more work. Ugh.

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Planning a Duratec powered, Miata suspended 442

Hey TRX-
What did you do, or what have you decided to do about that slab? Enquiring minds... Hope you get it fixed.

JDK

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JD, father of Quinn, Son of a... Build Log
Quinn the Slotus:Ford 302 Powered, Mallock-Inspired, Tube Frame, Hillclimb Special
"Gonzo and friends: Last night must have been quite a night. Camelot moments, mechanical marvels, Rustoleum launches, flying squirrels, fru-fru tea cuppers, V8 envy, Ensure catch cans -- and it wasn't even a full moon." -- SeattleTom

I am doing a mortgage for a guy right now who does that concrete lifting stuff. We were talking yesterday about the different options. They do both the concrete pumping and the foam and they recommend the foam. It gets into more cracks and does a better, cleaner job of filling the voids. I was concerned about the foam deteriorating and he said they have maybe 1/3 the call backs on the foam lift than the concrete lift.

It's also cheaper

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mobilito ergo sum
I drive therefore I am

I can explain it to you,
but I can't understand it for you.

It's not urgent and it's too flippin' hot to deal with it right now. I still need to get some more quotes, but I'm seriously considering the Gonzo Pump System and DIY.

Even if I do it in half a dozen sessions and wind up with voids here and there, all I need is enough area to keep the slab from tilting any more; it's plenty thick and reinforced and doesn't need a full full.

Plan B is to dig around the outside perimeter and pour pilings deep enough to reach through the fill into dirt. A real footer would take more digging and concrete than I can manage. Upsides: I wouldn't need a pump, and it's guaranteed to work. Downside: it's a lot more work.