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these calculations are based on the materials listed in the plans, as i haven't built my dome or hearth yet. note that the measurements for the hearth are based on a normal cement mix, as i don't have the weight measurements for the insulating concrete mix, and so it will be an overestimate. if anyone else wants to chip in with how much mortar is used in the dome etc., it will answer the question better, but i'd say most of the weight on the stand seems to be from the hearth and dome, unless you finish the walls with stone as well.
-hearth (69"x76")= 2265#
-floor and dome bricks=2240#
-bricks for doorway and decorative arches= 200# (depending on style and type of brick
-weight of the upper wall material would vary greatly, but could weigh upwards of another ton, so we'll say 2000# for walls, roof, chimney
this would put the weight on the stand between 6 and 7 tons.
The vermiculite concrete used in the insulating hearth layer or the outer covering for an igloo finish should weigh in at about 25 pcf.
One of the big benefits of the Pompeii design over Alan's breadbox style is the elimination of the cladding layer. The cladding on the standard Scott 32x36" rectangular oven weighs just shy of 2,000 pounds. That's why it takes 3 or 4 hours to reach cooking temps. This goes on regardless of the finish technique (gabled house type or igloo).
My house style finish probably weighed in at a total of 300 lbs for the Durock, metal studs, Ondura roofing tiles and winged gargoyle.