Usually the tank constructor will have their own method.
In short, what normally happens is
1) Weld a bunch of columns to the floor plate and make an internal structure
2) Weld a bunch of supports to the tank wall
3) Install hydraulic rams between the two and lift
There is obviously a bunch of design that must be done, but this is the basic process
The only other way to do it is replace is small sections, including some of the bottom strake, e.g do 3-5 metres at a time, cut our the bottom strake, replace ring + bottom strake, move to next section and repeat.
Andrew O'Neill
Specialist Mechanical Engineer
Rio Tinto
Australia