Turbine assemblies for a turbine of a gas turbine engine are disclosed herein. The turbine assembly includes a turbine wheel assembly and a turbine shroud. The turbine wheel assembly includes a disk and a plurality of blades that extend outwardly from the disk in a radial direction away from an axis. The turbine shroud extends around the blades of the turbine wheel assembly to block gasses from passing over the blades during operation of the turbine assembly. The turbine shroud includes a plurality of blade track segments arranged circumferentially adjacent to one another about the axis to form a ring. Each blade track segment has a runner that forms a primary track surface facing the axis and spaced from the axis in the radial direction.