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Depends on the compressive strength of the material. Sooner or later the weight of the pyramid above the base exceeds the base's ability to support it. Considering that a mountain is basically a stone pyramid, Everest has to be in the neighbourhood of how tall you could go -- call it 10-12 kilometers high. Other materials would do better.
I'm not convinced Mt Everest represents the most weight normal earth can sustain but rather the most height gained by regular tectonic motion. However, I stead of asking how much weight can stony earth support before collapsing, it leads me to ask how much weight can the crust support before buckling? Perhaps this project has diminishing returns as more weight above causes the crust to bulge downward and compensate.
Imagining an aerogel pyramid 30 miles high getting blown around the world
This made me think "WHEEEE!" when I imagined riding along, and that made me think of the longest cocktail party from the hitchhiker guide to the galaxy. So thanks I guess.
With the way the bricks are laid, wouldn't it distribute the weight across the entire base?
Yes, but it doesn't matter enough. The square-cube law means that the mass being supported goes up faster than the area of the layer doing the supporting does. So each additional brick on the bottom still ends up carrying more weight as the pyramid gets taller.
That's not really the limiting factor for pyramids. If you were to build a shape of equal height, say a cube, then yes this would be the main issue.
What are the failure modes for a pyramid?
- A 45° pyramid can't tip over since it's center of mass is always sufficiently far enough from the bottom edge. So tipping isn't one.
- I'd say bending through cross winds is also not an issue for a pyramid unless you make it out of jello. So that's also not a failure mode.
- Crumbling of the bottom layers because of the weight of the top layers is definetly one.
- Uneven foundation strength can cause the supporting area to be weaker in some spots more than in others, so that's another failure mode.
I'd say the crumbling and Foundation issues are heavily mitigated by 2 main factors.
1st:
The outer edge is always of height zero. As the pyramid grows in height it also gets wider, but the only point that is at risk of imminent collapse is the very center of the pyramid, since it is the only point that will reach a critical supporting mass first.
Let's say the pyramid reaches a height and the furthes block at the bottom in the center crumbles (let's assume it actually turns into straight up dust). The clumbled block will still support some pressure but will also transfer it laterally into the adjacent blocks (essentialy like a liquid). Now the main question is "How many adjacent blocks does it need to support one crumbled block?". If the answer is ≤1, than you have no problem, because with each new block in height, the pyramid also gets 1 block wider at each side. Similar to water pressure, the lateral force the blocks exhibit will increase linearly with height therefore never outpassing the increase in pyramid width. If it's >1 than you will reach a point where the outer walls of the pyramid will start to collapse from inside pressure, and that will be your limiting factor for height.2nd:
The blocks can be cemeted together, so whatever forces are being transfered laterally will not only be supported by the adjacent blocks, but also blocks adjacent to them and so on, and so on...
Same thing goes for uneven foundation strength. The local decrease in support will be spread over a wider area because the blocks are merged together. Also Pyramids are usually not build block on block, but with a 50% offset, which will further aid to stabilize the structure.Usually, If you look at mathematical calculations for things like sky elevators the form to support the structure looks like a symmetric reciprocal function. This function actually requires way less material to support the weight of the center piece of the structure than a pyramid. So not only could a pyramid essentialy support itself until earths centrifugal forces take over, it would also be way too overkill in doing that.