You might get more information looking up Ferro-Cement. There is a version of it that can be made with styrofoam popcorn stirred into the cement mixture. The ratio of styrofoam to cement matters so it will be structurally sound. Most often it's used in boat construction and floating dock construction. I don't know the engineering strength of it, if it is not floating.
Sometimes that really matters, because a floating platform can often support more weight than if it is on the ground trying to support weight. That is the case with dock floats, and we are warned not to let them be in a location where the
water will not be under them for part of the year if they are supporting the weight of a dock/roof/several people/furniture, etc. because they aren't capable of supporting weight when there is only soil under them.
Because cement with foam or styrofoam in it is lighter it's not going to be as much help holding a structure in place as heavy cement.
This is just my old guy, curmugeonly opinion, since I've had 100 feet of greenhouses for 20 years. A lot of the posts about greenhouses here are so into the architecture, the amazing structures, as if these buildings were for humans, not plants.
1. First and foremost, a
greenhouse is about the soil in it. Pots up above ground are just as subject to freezing as the air inside a
greenhouse. When the soil in a
greenhouse is improved with
hugel trenches, shin-high
compost layers covering the entire floorspace, and maintained at that level, active
composting layers provide the heat that keeps the air inside just above freezing. It's only a matter of keeping it a few degrees above freezing, not making it 75 degrees all year 'round.
2. Hot air rises, so if the point is to keep plants from freezing, the ceiling needs to be just high enough to walk into comfortably with a hat on. We all know how difficult it is to heat a house in winter, yet some of these greenhouses have ceilings in them we wouldn't even consider for a house, even when we have some kind of fuel heating system. If all the hot air is up at the ceiling, where is the protection for the plants in the ground?
A few barrels or troughs of water aren't even going to come close to keeping the temps up.
Sepp Holzer in the Alps has lakes a couple hundred feet across and deep enough to keep from freezing that provides protection for his plants.
3. Plants need serious airflow, even if it's freezing outside. Sealing up a
greenhouse in order to keep heat in is a recipe for plant diseases and
pests inside that will make you crazy. Which means when the air is freezing it needs to be moving, slowly, with fans, in addition to heat from
compost, which probably means an electrical connection, since batteries won't last long on a fan.
4. Greenhouses need to be able to withstand very high MPH wind gusts. The foundation needs to be below ground low enough where it won't freeze or heave. It needs to be wide enough and deep enough to support the entire weight of the
greenhouse. Does anyone know what their greenhouse weighs? Are there proper tie-downs built into the foundation? Any building that is tall catches the wind at the top, sends it straight down the wall and back the way it came. That kind of force, at high MPH, even a couple times a winter, is enough to move the structure if it is not tied down, and cause an inadequate wall to fail.
5. Light: Because they make most greenhouse coverings with some kind of sun protection, that lowers the amount of light inside the greenhouse. The average is 80% of the light. The best I've found is 90% of the light. In fall, winter, early spring that missing 10%-20% is a big deal to a plant. So that's why both walls and ceiling should be transparent and let in as much light as possible.
Short days in winter are going to limit plant growth, so even if the temps are above freezing inside a greenhouse plants are still getting the message there's not enough sun hours.
