Building on the successful experience in operating the DarkSide-50 detector, the DarkSide Collaboration is going to construct DarkSide-20k, a direct WIMP search detector using a two-phase Liquid Argon Time Projection Chamber (LAr TPC) with an active (fiducial) mass of 23 t (20 t). This paper describes a preliminary design for the experiment, in which the DarkSide-20k LAr TPC is deployed within a shield/veto with a spherical Liquid Scintillator Veto (LSV) inside a cylindrical Water Cherenkov Veto (WCV). This preliminary design provides a baseline for the experiment to achieve its physics goals, while further development work will lead to the final optimization of the detector parameters and an eventual technical design. Operation of DarkSide-50 demonstrated a major reduction in the dominant 39Ar background when using argon extracted from an underground source, before applying pulse shape analysis. Data from DarkSide-50, in combination with MC simulation and analytical modeling, shows that a rejection factor for discrimination between electron and nuclear recoils of > 3 X 109 is achievable. This, along with the use of the veto system and utilizing silicon photomultipliers in the LAr TPC, are the keys to unlocking the path to large LAr TPC detector masses, while maintaining an experiment in which less than < 0.1 events (other than γ-induced nuclear recoils) is expected to occur within the WIMP search region during the planned exposure. DarkSide-20k will have ultra-low backgrounds than can be measured in situ, giving sensitivity to WIMP-nucleon cross sections of 1.2x10 -47 cm2 (1.1x10 -46 cm2) for WIMPs of 1TeV/c2 (10TeV/c2) mass, to be achieved during a 5 yr run producing an exposure of 100 t yr free from any instrumental background.