We (US Army) had a gizmo that relied on expansive foam and fabric to provide a structural basis for overhead cover for a fighting position - late cold-war stuff, oriented at the usual scenario. I've tried to recall if I ever actually saw one... maybe. Anyway, IIRC, imagine a giant arched air matress with the tubes filled with PU foam. Once in place over the hole, pile on dirt until a meter or so of earth is on it, etc.
I was not impressed with it - logistical headache, cost, questions in my mind about real effectiveness VS "looking good", etc.
You could take an ultra-light view of that sort of thing or the "foam dome" approach that I think you're after - externally applied foam over a fabric form. My guess is that it's going to take a lot more than one can to accomplish what you're after.
But I think that you are onto a cool idea - it's got me thinking about how improvisation with natural materials and expansive foam could help extend safety and comfort in some scenarios.
Take pictures! I want to see what you come up with.
Regards,
Tom