Tire for a heavy goods vehicle comprising a tread of total thickness E and total volume V, having a tread surface intended to come into contact with a roadway, at least one cavity or groove that is continuous in a main direction, and delimited by side walls connected by a bottom, a cross section, the points furthest towards the inside of the bottom of each cavity defining a bottom line, wherein each cavity or groove comprises a plurality of open sections open onto the tread surface in the new state and a plurality of closed sections, connected to the open sections being arranged in alternation, each closed section being spaced away from the tread surface by a bridge of rubber, wherein the points on the bottom line of said cavity or groove lie at distances between a minimum distance Dm and a maximum distance DM with respect to the tread surface, the bottom line of each cavity or groove following a wavy geometry of positive amplitude equal to the difference (DM−Dm).