A fiber structure includes a plurality of weft layers and a plurality of warp layers interlinked with three-dimensional or multilayer weaving, the fiber structure including at least first and second portions that are adjacent in the warp direction, the first portion presenting thickness in a direction perpendicular to the warp and weft directions that is greater than the thickness of the second portion. The weft layers situated in the core of the first portion of the fiber structure include braids. The weft layers extending on either side of the weft layers including the braids and going as far as the skin of the first portion include yarns or strands, the braids presenting a section greater than the section of the yarns or strands.