Mudjacking or slabjacking can both raise the old cracked slab back to its original position and create a new foundation of cement mortar or sand mix by injecting the mortar under the slab through a hole, under pressure. The viscosity of the mortar will keep it from flowing back through the hole until it sets.
Accounts of raising large concrete slabs through the use of hydraulic pressure go back almost a century and it has been in common use for about 50 years.
Generally a portable pump is carried to the location of the block to be raised. A hole of up to 3 inches in diameter is drilled into the block. Varying combinations of soil, sand, cement, or other materials, are mixed and then injected under the sunken concrete block, causing it to rise.
Modern methods use smaller holes to avoid weakening the concrete slab, or raising the blocks too quickly. A highly dense crushed limestone is sometimes mixed with moderate amounts of cement, and can be pumped slowly and safely through hoses that are connected directly to the pumping truck, with little or no destruction of landscaping or surrounding structures. (Wikipedia)
At Wells Foundation Specialist, we use HMI concrete lifting equipment and processes.
Below is an example of mudjacking by HMI (Hydraulic Mudpumps, Inc.)