In this paper we discuss results relevant to 3D Double-Side Double Type Column (3D-DDTC) pixel sensors fabricated at FBK (Trento, Italy) and oriented to the ATLAS upgrade. Some assemblies of these sensors featuring different columnar electrode configurations (2, 3, or 4 columns per pixel) and coupled to the ATLAS FEI3 read-out chip were irradiated up to large proton fluences and tested in laboratory with radioactive sources. In spite of the non optimized columnar electrode overlap, sensors exhibit reasonably good charge collection properties up to an irradiation fluence of 2 x 10**15 neq/cm2, while requiring bias voltages in the order of 100 V. Sensor operation is further investigated by means of TCAD simulations which can effectively explain the basic mechanisms responsible for charge loss after irradiation.