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At 10 km depth, we have roughly 3000 bar pressure.
If the hole is empty (air), the pressure difference is 3000 bar. If it is full of water, it’s 2000 bar.
This is far above the unconfined elastic strength of most rocks, so the hole will collapse.
That’s why they use these high density drilling muds to support the walls of the hole. The problem is that we do not have muds with such high densities (3000 kg/m3), at least not easily available.
Of course what makes the hole collapse is not pressure, but the stress tensor.
If I remember correctly, the stress distribution around a circular inclusion (or hole) looks like a 4-leaved clover. And the intensity of these differential stresses does not scale linearly with the radius of the hole.
So that’s why larger holes can support less pressure/stresses than small holes.
Certain Geopolymers has the strength of 20 mpa,
We need to build a vertcal shaft 5 meter wide and 10000 meter deep
As supporting walls to prevent collaps of the rock, we need to make a supporting circular pipe wall inside the shaft.
How thick must the walls of circular pipes be to withtand the pressure of 3000 bar.
Make some good calculations.
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