How far down could you go?

The basic question is about how dynamic is hydrostatic equilibrium.

In reading about TNOs and KBOs, one of the parameters for them is that they have relaxed into hydrostatic equilibrium, or that gravity has forced them into a predominantly spherical shape. Then, of course, one sees a depiction of Haumea, which is thought to be ellipsiod but spinning so fast that it stays that way. So that got me to wondering.

Go to Mars, which is thought to be all solid, taking one of those tunnel borers and a really, really long auger for clearing the “dirt”. Assume that this is an exceptionally good borer that can make short work of solid rock. Digging a twenty foot wide hole straight down, can you make it to the center of the planet before the hole gets squeezed shut?

How fast would you have to go, could you pull the borer all the way back in time? If you could dig a widening hole (larger deeper), would that work? In a smaller, round body, might it be possible, and if so, is there a size limit?

I mean, I just want rocks and stuff.

I wouldn’t expect it to be possible to reach the center in any solid object massive enough to be formed into a sphere by gravity. It’s a sphere in the first place because its gravity is strong enough to overwhelm its structural strength.

No, it isn’t. It doesn’t have plate tectonics hence mantle convection, but that’s not the same as “all solid”

Nope. In fact, you’re going to get no more than a few score kilometres before your hole is going to act as a pressure release, leading to mantle melting, never mind solid flow.

And of course it depends on what you’re digging through.
A nice glacial sand deposit (For instance, Long Island)? It’s going to collapse nearly instantly, until the sides are 30 degrees or whatever the angle of repose is.
Nice solid unstressed granite? I’d guess a hole would go until you reached some kind of fracture or boundary in the rock that allowed pieces to splinter off the wall into the hole.

First up IANA engineer or space geek. But I think I recall that the pressure on the walls of a vertical shaft is roughly gravity(G) by depth(H) by rock density§ by the local stress field coefficient (K).
The local lateral stress has both magnitude and orientation, as shown here, so its maybe a value of 1.2 east-west then 2.5 north-south.

For example the roughly expected peak rock pressure at 100 metres in typical rock (3000 kg/m3) from the surface of the earth (9.8 m/s2) with 2.0 lateral would be 10030009.8*2= 5.88 MPa, or 852 PSI.

I have no idea how this might apply to your mars digging plans but your going to run up against material limits by the time your get down further then a few thousand metres.

ISTR that in the deepest gold mines in South Africa, spontaneous mechanical explosion of exposed rock faces is a problem.

Yep, here it is. The deepest mines are only about 2.5 miles deep. The deeper you go with your borehole, the more frequently you would expect these events to occur. At some point, they would happen with such regularity that you wouldn’t be able to bore your hole any deeper because you’d be too busy removing the debris from the self-widening hole. The only way to go deeper would be to allow the hole to form its own naturally stable angle of repose. IOW, if you want a really deep hole, it needs to be a conical.

Yes, yes they are a problem. I speak from experience - being underground when there’s a rockburst in the same level is very, very scary - luckily I’ve never been at the face when one happens. A mate of mine was, and he lucky to come away with concussion and bruises.