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At the start of WWII the allies were looking at other non-traditional materials for the construction of ships, aircraft and other machinery. Specifically in regard to your question concrete was considered and several prototype ships were constructed. In the US starting in 1942 the McCloskey class of freighters were launched http://concreteships.org/ships/ww2/.
Meanwhile in the UK Geoffrey Pyke (https://en.wikipedia.org/wiki/Geoffrey_Pyke) developed a substance called pykrete made from frozen ice alloy (https://en.wikipedia.org/wiki/Pykrete#cite_note-1) ,originally made of approximately 14 percent or some other form of wood pulp (such as paper) and 86 percent ice. It was to be made into an aircraft carrier called the Habakkuk. A demonstration boat was successfully sailed but the project was cancelled when steel production was able to keep up demand. The construction methods were too unorthodox for the war production offices to implement.