Typically, the excavation starts with digging a 3' x 3' hole (by hand) on the exterior wall of the home to locate failed drain. This makes it large enough for any plumber (and helper if need be) get under the slab and make the necessary repairs.
The most important part of tunnel work is putting the dirt back the right way, and hand packing certainly does not qualify. After returning the excavated fill, we mud pump the remaining voids and any nearby voids that may have occurred due to settlement or erosion from the leak. The slurry is a mix of Portland Cement and sifted topsoil that is injected at approximately 400 PSI. It travels extremely well filling all the nooks, crannies, and crevices and hardens up like sandstone to keep everything nice and tight. Make sure drain lines are secured to bottom of the slab with appropriate pipe hangers as the slurry will weigh in at close to 90 lbs per cubic foot.
The biggest advantage: the mess stays on the exterior of the home and doesn't disturb any flooring, furniture or belongs.