Abstract: A method and weaving machine for weaving a thick reinforcing fabric comprising multiple noncleaving layers with a 2.5 D or 3 D type structure. The warp yarns successively move into a yarn joining comb, a calibrating comb and then into a dobby weaving unit, where the warp yarns on n superimposed laps are separated upstream of the calibrating comb, n being equal to (N- 1/2 ) and N being the number of layers of said reinforcement so as to have (N- 1/2 ) warp yarns moving into each tooth of the calibrating comb. Two adjacent yarns of a given tooth of the calibrating comb are threaded into the eyes of two heddles of the same row of two heddle frames of the dobby, so that the displacement planes of two adjacent yarns during formation of the shed form between them a sufficient angle so as to prevent the yarns from catching on one another.