OT (?): Lithostatic pressure ...

[Jethro_uk]

How can I get to the age of 50, and never heard of this before ?

(from

which led to

I love learning new stuff :)

[Syd Rumpo]

A long time ago, I was involved in in-situ rock stress measurements. Essentially, from a tunnel you drill a ~40mm hole a few metres into the rock and then grout in an array of strain gauges (a CSIRO cell). You then 'overcore' this with a ~150mm core bit to relieve the stress in this piece of rock, thus you know what the stress must have been. With lots of gauges, you can get a 3D interpretation of stress which is not just due to the overburden but also to tectonic plate pressure. Where I was, you could (ok the geologist could) clearly see the component of the sideways force which helped to create the Andes.

Cheers

[Robin]

Yerrbut "rock that reaches temperatures of 46?C without ventilation due to a high lithostatic pressure from rock above it" is not a good example.

[Chris Hogg]

AIUI it accounts for the high pressures in deep oil and gas wells that can cause blowouts(1), and why rock walls in deep mines can 'explode'(2). But what I don't understand is the phrase from your first link "rock that reaches temperatures of 46°C without ventilation due to a high lithostatic pressure from rock above it". I don't see why mere static pressure generates heat. AIUI the temperature in deep mines and presumably in this tunnel is simply due to the build-up of heat from radioactive decay in the surrounding rocks such as granites. Unless of course the rocks above the tunnel are on the move due to the lithostatic pressure, and it's friction that's generating the heat, in which case I'm not sure I'd want to drive through it.

[Jethro_uk]

No, indeed, as I read in the comments :)

[newshound]

Two points:

Lithostatic pressure: what do you think is keeping the rock, under the influence of gravity, from accelerating towards the centre of the earth? Answer, a pressure generated in the rock below it. In exactly the same way, the first course of bricks in your house are supporting the weight of all the bricks above it, plus the roof, floors, contents etc. It's not rocket science.

Secondly, as Chris says, this quote in the article is total nonsense.

"The completed tunnel travels up to 2.3km below the surface of the mountains above and through rock that reaches temperatures of 46?C without ventilation due to a high lithostatic pressure from rock above it ? which can measure up to 2,500m in some sections".

That's apart from the confusion that the *length* of the tunnel is 57 km, and its maximum depth cannot be both 2.3 and 2.5 km.

The temperature of 46 C is not so much because of radioactive decay in the surrounding rocks, it is because the centre of the earth is at around 6000 degrees C. Since the surface temperature is much lower, heat is convected (in the liquid parts) and conducted (in the solid parts up to the surface. Hence there is a temperature gradient in the crust, this is evident in deep mines as well as tunnels.

The heat from radioactive materials certainly contributes to maintaining the temperature. In the ninteenth century, Lord Kelvin famously estimated the age of the earth as 20 to 400 million years

not knowing about radioactivity, a timescale which seemed to Darwin to be too short to account for evolution.

Chris is right that there could be some movement in near surface rocks, indeed this is what happens at plate boundaries and the associated "frictional" heating explains how volcanoes work. Strictly, though, this would not be caused by lithostatic pressure: the term static implies that there is no shear stress. (That's me being a pedant).

[Brian Gaff]

You mean they never offered to create a very long particle accelerator as an add on while they were making this? Brian

[Vir Campestris]

It's not long enough to be useful.

CERN is 27kM around the ring. I'm sure they do a lot more than 2 orbits getting stuff up to speed.

Andy

[Robin]

A straight tunnel of 57km would offer great scope for a linear accelerator with enormous research potential - see e.g.

Whether people would like to travel alongside one is another matter

[newshound]

But I think it is unlikely to be straight.

[Tim+]

What would happen to gravity in the middle of a truly straight tunnel? Which way would a ball roll?

Tim

[Robin]

First, straight does not equal horizontal. The entry and exit points could be at different altitudes.

Second, the Earth is not a true sphere so it depends where the tunnel is

- including how the mass above the tunnel varies.

Third, the Earth is not of homogeneous density.

But if the Earth were a perfect, uniform sphere then the classic school problem in applied maths shows the ball would not move. See e.g.

[The Natural Philosopher]

To the middle obviously, assuming it was 'level' in the middle.

The train tracks on which the original radio telescopes at Cambridge run are 4" 'higher' at each end to allow for earth curvature..

[Tim Streater]

If it was truly straight, then the ball would roll towards the middle, from anywhere it was placed.

Note: particles accelerated along such a tunnel would be unaffected by the gravity question, gravity being some 10^40 times less powerful than the other fundamental forces.

[The Natural Philosopher]

I think you have got your applied maths wrong.

Consider a tunnel punched straight from your house to Australia. Its going down into the floor almost vertically. Do you really think a ball wouldn't , if let go , fall down it?

Or do a basic energy calculation on - say - a 3000 mile straight track between here and New York. Each end of the track is going to be above the ground by several hundred miles if the middle is dipping into the ocean.

You only have to consider the potential energy variations.

I think your mistake is in comparing it to a tunnel going deep inside the earth where gravity is actually less, due to being inside the solid earth.

[Tim Streater]

Only if the tunnel were curved to follow the curve of the Earth. But then it wooden be straight.

[newshound]

The question formulated was for a ball in the *middle* of the tunnel. So it won't move in your tunnel either.

[Tim Streater]

Maybe I missed an earlier post, but the question I saw (see above also) was:

which specifies nothing about where the ball is initially placed. If placed in the middle, it *obviously* won't move.

[The Natural Philosopher]

No, that was a *different* question.

There were two questions. Q1. What would happen to gravity in the middle of a truly straight tunnel?

A1. It would still exist.

Q2.Which way would a ball roll?

A2. Towards the middle of the tunnel, if the tunnel was tangential to the earth's curvature at the middle, and the ball wasn't at the middle.. If the ball was at the middle I suspect it would curl up and have a nap.

I mean this is barely O level applied maths and physics?

Or do you need a degree these days?

[The Natural Philosopher]

Well being pedantic tim, that only applies to tunnels whose middles are tangential to the curvature of the earth at that point.

The issue about gravity being perhaps less because there is a sodding big mountain on top, is interesting,. but of a vastly lower order of magnitude.