Let's say, hypothetically, that I wanted to build a giant pyramid. Let's also say that I want to build it out of ordinary dirt.

If the base was in the shape of an equlateral triangle, and the 3 sides had 45 degree angles at the base and 90 degree angles at the top (to make the tip of the pyramid)...

How tall could it be before its base liquified under the pressure?

(If your answer could also include the math behind the reason, that would be very helpful).

I don't think it's possible to answre, not enough information given. What do you have holding the dirt together? What is the composition of the dirt? Is it sandy or black dirt rich in basalt?

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Originally posted by mahal:
I don't think it's possible to answre, not enough information given. What do you have holding the dirt together? What is the composition of the dirt? Is it sandy or black dirt rich in basalt?

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Let's assume the dirt is just moist enough (with water) to hold its shape but not so moist that it is wet to the touch. Let's also assume a composition of all the types of dirt in the world combined with the same ratio between each in the pyramid and each on earth.

Is that enough, or do I need to give more info?

Shaggy

From http://www.vacets.org/tc/tc51.html:

"...Actually, there is a limit to the maximum height of mountains, based on the strength of materials from which mountains are formed. The rock underneath a mountain is subject to tremendous pressure from the weight of the overlying rock, which would be enough to crush or liquefy the base if the mountain was tall enough. The maximum height possible for mountains on earth is probably not much more than 10 km, as indicated by Mount Everest or Mauna Kea and by the fact that the earth's near liquid mantle is as little as about 10 km below the surface..."

First, I have to debunk the myth expressed in the question (and some replies and/or references) that solid material "liquefy" under pressure.  For most materials, the exact opposite is true: liquids solidify under pressure (the reason being that most materials have a greater density in the solid form compared to the liquid form, so they tend to become or remain solid when squezzed).  There are very few exceptions to this rule: water/ice is the best known example [ice floats!], bismuth is another.

The reason why rocks are liquid at a certain depth beneath the Earth crust (and upper mantle) is that the temperature is higher there.  With depth, there's an increase in both the pressure (which tends to solidify things) and the temperature (which tends to liquefy them).  Sometimes the temperature wins, sometimes the pressure does:  That's why we have a solid crust and upper mantle, a liquid mantle and outer core, and a solid inner core.  (BTW, rock is not normally liquid at a depth as shallow as 10 km, unless there's a volcano or a potential volcano around!)

It turns out that a heap of loose particles of virtually any reasonable shape or size (sandlike) will have a maximum slope of about 34°.  This applies to dry stuff only with negligible stickiness of any kind between grains that are roughly spherical.  This is strictly due to the behavior of the grains at the surface of the slope; if the slope is too steep the grains roll down... (Wet stuff is more complicated.)

I am not sure I understand the exact geometry of your desired pyramid (if you're talking about the corner of a cube, the 45° slope is wrong, if you're talking about a 45° slope, I fail to see the meaning of your 90° angle "at the top") but it seems clear that you have in mind is a slope well over 34°.  In that case, there will be a residual lateral force at the base of the pyramid (pushing the grains outward horizontally) which is proportional to its height.  The maximum height of the pyramid thus depends on the ability of the grains (with a stickiness due to wetness, glue, cement, etc.) to resist this pulling force.  If, however, you are pleased with a slope less than 34° or so, there is no theoretical upper limit to the height of the pyramid, even if the grains of dirt/sand are dry and do not stick together at all (the grains themselves may actually get squezzed into a solid mass or crushed into finer grains, but that's largely irrelevant since this would only make the structure more stable)...

Hope this helps.

I have to agree with DrGerard. Pressure forces substances towards their most dense form. For virtually all substances that can become solids, this is the solid form.
We don't always think of it that way because the liquid we are most commonly exposed to (water) is one of the very, very few exceptions to the rule. The reaons that the earth is liquid below the crust is not pressure, but high temperature, which favors liquids over solids. If you keep going deeper into the earth, the pressure continues to increase and at some point the pressure is actually great enough to overwhelm the temperature effect. This is why the center of the earth is solid, not liquid.

I always enjoy Dr Gerards posts. Even a scientific neandrethal like me can understand the forces involved. Just don't confuse me with the mathmatics.

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Originally posted by DrGerard:
I am not sure I understand the exact geometry of your desired pyramid (if you're talking about the corner of a cube, the 45° slope is wrong, if you're talking about a 45° slope, I fail to see the meaning of your 90° angle "at the top")

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If you were looking at a side of my hypothetical pyramid, it would be a triangle with 45 degree angles at the bottom and a 90 degree angle at the top. Take three of these triangles and put them together on a base in the shape of an equilateral triangle, and you have my hypothetical pyramid. I wasn't talking about the slope of the pyramid, I was talking about the shape of the triangles. Sorry for the confusion.

Shaggy

i have a similar idea to build such a pyramid out of metal and other strong materials, with the stronger stuff on the bottom, and the lightest stuff on top. my goal is 5 miles. hahaha im serious