New hut foundations will appear when you have researched the required levels of various technologies. For housing huts (which allow larger populations), new foundations will appear with each new level of Construction Technology. Foundations for other types of huts will appear as you research other technologies.
Note: The maximum population with all three housing huts built is approximately 90 villagers. You will need to complete other parts of the game to enable larger populations. For more information, see the entry on Trophies (Population).