Tread (1) for a heavy-duty vehicle tire having, when new, a tread surface (10), with at least one evolving cut (2) comprising a part (22) hidden inside the tread which is delimited by opposing walls (221, 222) distant from one another by a maximum width Lc. The part (22) being extended towards the tread surface (10) by a sipe (21), opening into the hidden part (22) to be offset from one of the walls (221, 222) delimiting the hidden part to form a bridge situated radially over said hidden part (22). The tread having a plurality of grooves (4) open when new onto the tread surface (10), these grooves (4) opening into an evolving cut (2) to form a connecting region (41), the tread (1) further comprising, in at least 50% of the connecting regions (41, 42), a protuberance (5) extending over the entire height Hc of the hidden part (22) and over a maximum thickness Ep so as to act as a support for the bridge (211) situated radially over the hidden part (22) in the connecting region (41).