Some have asked me about the building foundation for a megastructure, as in: “wouldn’t the foundation need to me massive to support the weight?”
My first reaction was, no, but it spurred me to make some calculations to make sure. This is the initial result.
For the 1 Km dome, I postulated a simple foundation consisting of a ring footer, or series of posts, or just the dome structure sitting on the ground. I reviewed some foundation design from some civil engineering texts. The worst case appears to be clay soil.
Clay soil will support about 15 tons per square foot (sorry, but it was an American text … it works out to 147,000 Kg per square meter). So, if the load on the foundation is less than that, it’s stable.
A one kilometer diameter dome has a circumference of 3,140 meters. So, I calculated the area of different foundation widths using that numbers.
I assumed that the weight of the dome is a function of the external area of the dome (that there is no supporting inner structure — its structural integrity is only dependent upon the shell of the dome). I then calculated the ground pressure for a series of areal densities.
Areal density is how much the shell of the dome weighs per unit area. A really, really lightweight structure might weigh ten kilos per square meter, a heavier one might weigh one hundred kilos per square meter, and so on. If you multiply this areal density times the surface area of the dome, you get how much the dome weighs (for each different areal density). I went from 1.0 Kg/m2 to 1,024 Kg/m2, and this is what I got:
Turns out the foundation on clay soil only needs to be 1 meter wide at an areal density of about 350 Kg/m2 (assuming the foundation is a concrete ring on the ground). This is quite reasonable. At an areal density of 1024 Kg/m2 the foundation width is still only 3.6 meters.
So, no, the foundation is not unreasonably large and massive for a 1 Km dome.