A fiber structure includes a plurality of weft layers and of warp layers interlinked by multilayer three-dimensional weaving, the fiber structure having at least first and second portions that are adjacent in the warp direction, the first portion presenting, in a direction perpendicular to the warp and weft directions, a thickness that is greater than the thickness of the second portion, wherein the first portion has at its core at least one fiber fabric obtained by three-dimensional weaving of warp yarns and weft yarns in the form of a Mock Leno weave grid, the at least one fabric being present between two skins present at the surface of the first portion and being linked to the skins by warp yarns belonging to the skins that are locally deflected into the fabric.