Experiments and simulations of the compaction force in a confined binary granular mixture column were conducted. We measured the resistance force encountered by a piston pushing a vertical granular mixture in this confined arrangement. Granular mixtures with two different particle sizes were considered; the size ratio and the size fraction were both varied. An important decrease of the compaction force was found for volumetric fractions between 15% and 40% and size ratios larger than 3. By conducting some supplementary discrete element simulations, we found that the force chain network is fractured and redistributed when small particles are present. Hence we argue that the reduction of compaction force results from the redistribution of force within the granular column.