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Geodesic roof for earthbag house?

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Can't find a forum that would specifically address this, so...

I'm envisioning a little earthbag roundhouse cabin and would like to make a domed, monolithic roof. I don't like the conventional earthbag "conehead" domes, I'd like something with a shallow spherical curve that I can gutter to harvest rainwater or maybe do a living roof on. I know geodesic domes have awesome free-supporting strength, but I don't want an observatory or grain silo... maybe a small arc-section of a much larger dome would give the desired shallow curve... like a wok, not a hemisphere.

But I'm no physicist (I don't even play one on TV), and I fear a shallow arc from a geodesic wouldn't have the sort of stability and strength a full hemisphere dome would have. Maybe it would need trusses like a regular roof. I don't know. I just thought the geodesic would be a good strong framework to skin with ferrocrete for a solid, monolithic roof that had a gradual enough slope to do rain collection or a green roof on. I know it would be easier to just get a metal silo roof but I'd rather go monolithic than metal; less noise and more tornado-resistant.

Anybody know much about the physics of geodesic domes? Would this "lens" design have enough strength to be self-supporting?
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For supporting the weight of anything above it, including a living roof, a parabolic or catenary curve are ideal for the strongest shape. I believe a catenary is best for self-supporting structures, while a parabola is best if there is a vertical load atop it. A "pointy" ogive arch (or dome, if done in 3 dimensions) is close to both of those shapes.

The next best "ideal" shape is a semi-circle or hemi-sphere-- like a Roman arch-- but that is still a bit weaker for bearing a load.

A flatter dome provides a little strength with the shape, but due to the curves, I would think that one might just as well over-engineer it and span the distance with straight beams, or go for a triangular/conical roof using straight-beam trusses. The complexities of curved surfaces might not be worth the small gains you would make.
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Location: Colorado Springs, CO zone 5A / Canon City, CO zone 5B
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Here is an excellent article addressing the very issue of shallow domes - http://www.monolithic.org/stories/the-dangers-of-low-profile-monolithic-domes My husband and I are also considering putting a geodesic topper on our scoria bag well/tank house. It seems like a logical marriage.
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