Tyre for a heavy goods vehicle intended to travel on aggressive grounds comprising: - two sidewalls linking a crown, intended to enter into contact with a ground, respectively with two beads intended to be mounted on a rim, - a carcass reinforcement extending from one bead to the other through the sidewalls and the crown, and radially inside a crown reinforcement extending axially in the crown, - at least one sidewall comprising, on an outer sidewall face, at least two circumferential projections radially positioned outside of a point B of the outer face of the sidewall axially aligned with respect to an axially outermost point M of the carcass reinforcement, the axial distance between the points B and M being called sidewall thickness E, - each circumferential projection having, in a meridian plane containing the axis of rotation of the tyre, a meridian section delimited by a contour, - said meridian section having a maximum height H, measured at right angles from the outer side wall face, at least equal to E and at most equal to 3*E, and an average width L, measured parallel to the outer sidewall face at mid height H/2 of the meridian section, - each circumferential projection consisting of a rubbery composition C1 having an elastic modulus in extension at 10% elongation M1 at least equal to 1.5 MPa and at most equal to 6 MPa, characterized in that the average width L of the meridian section of each circumferential projection is at least equal to a minimum width Lmin and at most equal to a maximum width Lmax, the minimum width Lmin being the width beyond which at least two distinct points of the contour of the meridian section enter into contact with one another, when the hemispherical end of an indenter, of radius R equal to 15 mm, enters into contact with the circumferential projection, the indenter having an axis D forming, in the meridian plane and with the radial direction (ZZ'), an angle A equal to 15°, measured on the tyre mounted on a nominal rim, inflated to a nominal pressure but not flattened, and being displaced radially inwards, that is to say the width below which there is a self-contact of the circumferential projection due to its folding back on itself, and the maximum width Lmax being the width beyond which the hemispherical end of the indenter, being displaced radially inwards, cannot move past the circumferential projection, that is to say the width beyond which there is a blocking of the hemispherical end of the indenter at the level of the circumferential protuberance. - two sidewalls linking a crown, intended to enter into contact with a ground, respectively with two beads intended to be mounted on a rim, - a carcass reinforcement extending from one bead to the other through the sidewalls and the crown, and radially inside a crown reinforcement extending axially in the crown, - at least one sidewall comprising, on an outer sidewall face, at least two circumferential projections radially positioned outside of a point B of the outer face of the sidewall axially aligned with respect to an axially outermost point M of the carcass reinforcement, the axial distance between the points B and M being called sidewall thickness E, - each circumferential projection having, in a meridian plane containing the axis of rotation of the tyre, a meridian section delimited by a contour, - said meridian section having a maximum height H, measured at right angles from the outer side wall face, at least equal to E and at most equal to 3*E, and an average width L, measured parallel to the outer sidewall face at mid height H/2 of the meridian section, - each circumferential projection consisting of a rubbery composition C1 having an elastic modulus in extension at 10% elongation M1 at least equal to 1.5 MPa and at most equal to 6 MPa, characterized in that the average width L of the meridian section of each circumferential projection is at least equal to a minimum width Lmin and at most equal to a maximum width Lmax, the minimum width Lmin being the width beyond which at least two distinct points of the contour of the meridian section enter into contact with one another, when the hemispherical end of an indenter, of radius R equal to 15 mm, enters into contact with the circumferential projection, the indenter having an axis D forming, in the meridian plane and with the radial direction (ZZ'), an angle A equal to 15°, measured on the tyre mounted on a nominal rim, inflated to a nominal pressure but not flattened, and being displaced radially inwards, that is to say the width below which there is a self-contact of the circumferential projection due to its folding back on itself, and the maximum width Lmax being the width beyond which the hemispherical end of the indenter, being displaced radially inwards, cannot move past the circumferential projection, that is to say the width beyond which there is a blocking of the hemispherical end of the indenter at the level of the circumferential protuberance.