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A guess at how the SpaceX Starship's ground pad's destruction may have occurred:
Imagine you have supersonic, relatively low density gases coming out of a rocket and impacting on a flat surface below. As the gases "pile up" against the ground or just push the air, they could form a shock front separating the fast and lower density flow from the rocket nozzles from a denser, slow mass of compressed* gas near the ground. This shock front would be unstable due to Rayleigh-Taylor instability, and my guess is that maybe it was so unstable that it made contact with the pad and shattered it due to the large uneven forces, allowing the now extremely turbulent dense mass of compressed gases to pick up the pieces and throw them around.
If that's true, implications?
I imagine something similar could happen on the moon and doubt that, say, a pad made from sintered moon dust could withstand it.
Also, paradoxically, it might be the case that the pad could be protected by building a wall around it to prevent the gases from escaping to the side, as this would move the shock front upwards away from the pad (but risking damaging the rocket with the exhaust gases directly instead of with pad pieces).
It's also possible that I'm wrong about the instabilities reaching the pad, and the hot, turbulent flow of the denser gases alone was enough to damage the concrete, or that my mental model here is just completely wrong.
* ignoring air entrainment, the entire thrust of the rocket at liftoff needs to be balanced by forces on the pad (Newton's third law), so this compression could be to perhaps ~7 atmospheres of pressure or so (depending on air entrainment, actual thrust with engines failing, and actual area of the plume when it hits the ground).