Siege of Athens and Piraeus (87–86 BC) - Wikipedia
en.m.wikipedia.org
He encircled the city and the port. This would involve constructing a defensible palisade out of local timber, stone, brick, and whatever else was at hand.
Caesar's seige of Alesia is a well-attested example--there he used a double-encirclement, with the inner palisade protecting against sallies from the city itself and the outer palisade protecting against sympathetic armies that might try to lift the seige.
So Sulla's destruction of the Academy may have been incidental to his larger engineering project; he needed the trees and the rubble. I don't know one way or the other.