Mudjacking is where bore holes are cut into a concrete item that isn't footed, under pressure a slurry of mostly CLAY and lots of water and sometimes some binders (rare and usually minimal)are pumped under pressure with the idea of lifting the concrete. It is NOT a thing that can be successful on foundations long-term. If the area is footed the actions just serve to sever the footing or crack or bust up what was a good concrete bond, and if there is any cracking, the slurry under pressure will go to that area of least resistance, fill it, and further damage the area. The clay will eventually rinse away...and then you end up with a worse situation in the first place.
Mud Jacking is best left to free standing sidewalks, patios that are NOT tied in or too close to foundations...that you are having to replace anyway to correct the problem but willing to throw some money at it to 'gamble' on it might working and saving the hassle of digging it out and completely replacing for a few more years, knowing that if the system fails, or during jacking or the first few years after, it makes the situation worse (heaving/cracking, twisiting, putting pressure on other areas not currently with problems causing problems in those other areas)then you'll be replacing anyway. Its a gamble always, and I've only had lasting success after 2-3 frost freeze heave, thaw cycles about 35 percent of the time. The other problem is that the epoxy plug filler often pops out like pop-corn after the first or second freeze/thaw cycle, so I usually patch myself when this occurs with hydralic cement (looks ugly though). success is only when you fully relief the jacked area, and then have much larger than normal expansion isolation and do surface drainage correction, as that clay will wash out very easily underground. any thing such as foundation/footings etc. which are tied in with re-bar and grids and the like will usually crack at application, or down the road when any part of that slurry dries out too much, and washes away with the next water exposure. The slurry will also travel the path, (when applied or later when "re-constituted" by ground water/drainage)and later plug up and choke things like drainage fields for septic and/or your drain tiles for your foundation then you end up with more hydrostatic pressure on your foundation walls and more trouble. I don't know of a single "structural engineer" (not architect sorry can't spell today) that would put his license/reputation on the line and ever recommend this as a permanent solution, but might use the process to temporarily lift something to later remove/replace a suspended/supported structure to create a pier footing tie-in down to bedrock or something.
Usually these mud-jackers are fly-by night type companies, changing names every few years, and moving on. You encounter about the same reliability and risks as those "black top coaters", lots of bad ones, a few good ones, but the process itself has limited useful application.
The resulting slurry under the concrete is not rated or stable or strong enough to be supportive long-term for foundation elements.
I only get areas jacked that are "free standing" so, like in a sidewalk, I rent the wet saw equipment and completely isolate the section to be jacked with double the normal width for expansion joint, excavate and put in a steel plate to isolate the "foundation" of the areas not to be jacked. If it shares any common grid or re-bar, it will end up heaving or cracking the shared area, or the area will settle, heave or behave differently after a few years of freeze, heave/thaw cycles and/or a few years of rainfall. If the issues that caused the failure (drainage etc.) aren't corrected, the same process will wash away the clay that much faster.
mud=jack only areas that you would have to replace anyway as a 1/3 chance that you can post-pone that eventuality for a few years if successful, and a 1/3 chance that you will end up in those few years replacing a greater area if when the mudjacking fails it damages more of your concrete.