Identify the center of the sunken area in the concrete driveway. Use chalk to mark two spots about a foot apart.
Drill a hole 12 inches deep using a core drill with a diamond tip.
Mix concrete in a concrete mixer with small portions of water until it is thick like toothpaste.
Pump the mix through the drilled hole to fill the open cavity beneath the sunken section. Continue pumping until the slab rises to its original level.
Fill the drilled holes with concrete and smooth the top with a trowel. Wait a day for the new concrete to harden.
Remove edging from the sunken side of the driveway to slabjack it. Dig out the side with a shovel until you can see where the gravel base begins and the slab ends.
Wedge a pry bar between the base and the slab. Push the other end of the bar down with your hands until you're able to lift the side of the slab.
Fill the base back up with small gravel and stone dust and press it down with a flat shovel. Add rocks until the sunken base is the same height as the rest of the gravel.
Lower the slab back down. Fill in the removed dirt, grass and edging.