The formation of planets remains one of the most challenging problems of contemporary astrophysics. Starting with micron-sized dust grains, coagulation models predict growth up to centimeter (pebbles), but growth beyond this size is difficult because of fragmentation and drift. Ways to bypass this problem have focused on inhomogeneities in the flow, be that zonal flows, streaming instability, or vortices. Because vortices are in equilibrium between the Coriolis and the pressure force, the pressureless grains will orbit along a vortex streamline experiencing a drag force. This is a very effective mechanism to concentrate pebbles as also seen in numerical simulations and possibly in ALMA observations. Yet, a high pebble load is dangerous for the vortex, and we showed that in two-dimensional simulations the backreaction eventually leads to vortex disruption. We investigate whether the same happens in three dimensions. We perform 3D simulations with pebbles in a local box finding that, although the pebbles disturb the vortex around the midplane, the column does not get destroyed. This result is important because, based on the previous 2D result suggesting complete disruption, the vortex interpretation of ALMA observations has been called into question. We show instead that the vortex behaves like a Taylor column, and the pebbles as obstacles to the flow. Pebble accumulation in the center of the vortices proceeds to roughly the same concentration as in the control run without backreaction