A gravity-type offshore structure, useful as an offshore drilling platform, e.g., is provided for use in ice-covered waters such as offshore of the Alaskan and Canadian North Slope. The structure is composed of a plurality of floatable and controllably ballastable modules, each of which can be fully submerged. The modules are stackable by selective ballasting and deballasting operations in a suitable sequence to define a mobile offshore structure. The structure is assemblable adjacent a site of use and is floatable after assembly to, from and between successive sites of use. At each site of use the assembled structure is ballasted by sea water to be supported by the sea floor and to have sufficient deadweight, in combination with its support by the sea floor, to stand against ice loads urging the structure laterally of the site. Major ones of the modules preferably are constructed of reinforced concrete arranged within the modules in a honeycomb cellular fashion. A reinforced concrete armor belt is removably installed around the structure at its on-site load waterline. The structure is useful in a range of water depths. The armor belt is mountable to the structure at a number of different elevations on the structure to suit differing on-site load waterline locations. Individual modules can be used with other modules of the same or different size in a series of offshore structures individually useful in a characteristic range of water depths.