The invention relates to improving the endurance of a bead of a radial tire for a heavy vehicle of construction plant type by reducing the compression to which the turn-up is subjected when the tire is driven on. According to the invention, for a tire for a heavy vehicle of construction plant type comprising two beads intended to come into contact with a rim having two rim flanges, a carcass reinforcement comprising at least one carcass reinforcement layer having a main part wrapped, within each bead, from the inside towards the outside of the tire, around a bead wire of substantially circular meridian section, to form a turn-up, a filling element extending the bead wire radially towards the outside and axially separating the main part and the turn-up, the distance (d) between a first segment of turn-up and the main part decreasing continuously, radially towards the outside, from the bead wire as far as a minimum distance (d1), the distance (d2) between a second segment of turn-up, extending the first segment of turn-up radially towards the outside, and the main part is substantially constant and equal to the minimum distance (d1) between the first segment of turn-up and the main part.