My foam under pool liner has held up for 8 years now and will not be without it.
The foam protects the bottom, makes it feel nicer, more visually appealing and easier to vacuum and insulates the pool from the cold ground.
Just make sure you tape the seams together with a good quality tape such as Gorilla tape (BUY ON AMAZON) and place a good quality taro over the top too.
The only drawback of a pool foam is the costs.
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Should I place the foam in the entire bottom, including under the supports? If not, does the foam cause the liner to be a little slack on the sides?
Simply place the supports on the foam or just cut the foam where the supports are and add concrete or brick pavers. I didn’t use pavers under mine and have the legs and the pool sitting right on the foam. The one under the legs are a bit pressed in.
I imagine the regular styrofoam wouldn’t be stiff enough for that, but the stuff I got posted above is.
I advising avoiding polyisocyanurate foams since they absorb water. I recommend staying with the extruded polystyrene foams instead since they handle wet applications better. Plus, you would avoid the expanded polystyrene since that foam dents easily.
I have had great success with the extruded polystyrene for my agp.