Not fully sure of your question. However, if the site is such that an undercut of poor material is required, to be replaced by compacted gravel, be aware of the influence that the load of the tank has out beyond the tank wall.
I once investigated a grain bin of about 80 feet diameter and pretty high which failed due to the edge settling.
The preparation of the site, with removal of the poor material and replacement with good compacted fill stopped at the outside diameter limit of the bin. There even was a sizable thickened edge of the slab.
You can imagine the mess when the bin full of corn ripped open. It even knocked a railroad train off the tracks.
The moral, do the fixing out to a goodly distance outside the tank. I'd not stop until beyond equal to depth of the fix, measured at the base of the hole.