I can give some advice from my experience;- others can complete the rest of the requested field.
Depends, always depends. The size of the tank and the size of the voids are important. A large tank with significant static pressure will exert a significant bending stress on the floor designed to take no bending stresses. Remember, the API 650 specifically stipulates the full support of the flat bottom. There is a good chance the fillet weld will give in and the floor plate will break. As always, depending on the size, you might dig under the empty tank and use some pressure filling which hardens to similar strength or consistency like the rest of soil. Lift the tank or cut the plate if your calculations show the risk of excessive deformation and weld overstress. Can you afford a leaking tank? if yes, then ignore the leak.
If you need specific help, then you might want to share with us some secrets of your tank like size, content, design standard and conditions, estimated size of voids and some explanation of the origin of those voids that were not supposed be there.
Cheers,
gr2vessels