Drill holes in the concrete slab to allow access for the pump nozzle that will put the product beneath the slab that will lift it. Use a hammer drill and drill holes from 1 inch to 2 inches in diameter. A size of 1 5/8 inches is common because it fits the typical pump hose nozzle, however check your equipment for the correct size.
Space the holes on the slab based on the location of the sunken area. Don't place holes with 1 foot of the edge of the slab. Using one or two holes is adequate for a standard sidewalk slab that is 4 feet by 4 feet. Based on the orientation of the sunken area, you can drill one center hole to lift the entire slab, one hole placed where the sinking occurs, or two, one at each end. Drill all the way through the concrete.
Set the nozzle from the grout pumping machine hose into the hole at the lowest point of the slab. Begin pumping grout with the machine. Operation instructions for mud or grout pumping machines varies depending on the manufacturer, so follow the instructions for your machine.
Pump the grout until the slab rises and inch, then transfer to the next closest hole if there is one. Repeat the process of pumping until the slab raises another inch, then move to the next hole, and repeat this process alternating holes. If you are using only one hole continue with the same hole. Pump until the slab reaches the level that is even with the rest of the concrete.
Mix a stiff mortar or concrete mix to patch the hole or holes from the pump nozzle. Fill the holes with the mix and smooth with the trowel and allow to dry.