'Mud jacking' is a grout injection technique that, as VG says, is mainly use to raise settled items. If you inject the grout to fill a void/ stabilize it is not mud jacking. However the contractors who do the grout injection work are generally listed as 'mud-jacking' contractors.
With the sand idea above keep adding as the sand settles (vibration will cause it to consolidate). But sand is quite porous so until/ unless it gets clogged with fines the river will still run through it
