potatoes are usually mounded to provide gradualt covering to their "haulm". They are a solinaceous plant , and like all plants in that family, will send out roots (and hopefully tubers) from covered sections of stem.
I just grow them in shallow soil and mound them with straw. The potatoes are cleaner and i pick them smaller for boiling. They get really flavorful. Ive seen some magazine articles on growing them in wooden kegs but I never tried them as a patio plant).
Good luck and gradually covering them in the barrel seems right.