Force of Freezing Water

Name: Clayton
Status: student
Grade: 9-12
Location: IA

Question: How much force can freezing water exert on its
surroundings? Water can flow into cracks into streets and rocks and
then break the rock or street when it freezes. What is its maximum
outward force? How could I calculate/test this?
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As you have guessed, freezing water can exert a LOT of force on its
surroundings.  And yes, you can determine the approximate force, but you will
need to go onto the Internet for some additional information.  I will explain
how to do it, but first I will give some information about ice.

There are at least 12 different forms of ice.  Each form has a different
arrangement  of atoms and can exist at different pressures and temperatures.
There are "phase  diagrams" easily available on the Internet.  These are
graphs that look like maps, and which show the stability of water, ice,
steam, and fluid for various pressures and temperatures.  Ordinary ice is
Ice 1 -  hexagonal.

Water stays liquid at temperatures below 0 C when subjected to high
pressures.   But there comes a limit to this, and this limit is about ­20C
and a pressure of  200 megapascals.  At higher pressures, the trend reverses
and the high pressures tend to make the water solid.  At really high
pressures, water is solid up to many hundreds of degrees.

Let us do a thought experiment.  You can put the ice in a perfectly rigid
container, freeze it, and then measure the pressure it is exerting on the
walls.  Or you can put the ice in a bowl, freeze it, and then measure how
much pressure it takes to squeeze the ice back down to the volume that the
water originally occupied.  Both methods ought to give the same result.

Suppose we have a bowl of water.  As the water is cooled, the water will
become more dense and the water will shrink a little bit.

At 0C and below, ice will start to form.  Water expands about 9% when it
freezes, and  so the water-ice mixture will start to expand in size as the
first bits of ice  form.  As more and more ice freezes, there will be more
and more expansion of the mixture.

The diagrams show that at -20C, solid ice is ALWAYS the stable phase of
water, so pressure or not, you are guaranteed to have solid ice at -20C.

The "bulk modulus" of ice is about 8.8E9 pascals.  You can find that number
on the Internet.  "Bulk modulus" is a term that describes how stiff a solid
is.  Styrofoam has a small bulk modulus.  Rocks have large bulk modulus.

If you completely freeze the ice it expands 9%.  If you try to SQUEEZE the
ice back down to the original size, you would need to  push with a pressure
of about 790 megapascals of force.  (8,800,000,000*0.09)  That is about
114,000 pounds per square inch, and is a simple estimate of the  pressure
that ice could exert when it freezes, under ideal conditions.

Now, this estimate is not actually correct because in the process of freezing
under pressure, these high pressures can transform the ice into type 3 or 5,
and it is difficult to know what will exactly happen.  One can find the bulk
modulus and expansion of ordinary ice, but probably only ice experts know
the bulk modulus and expansion of the other kinds of ice.  So I will leave a
perfectly correct calculation up to the ice experts.

In any case, water expands strongly when it freezes, and whether it is
114,000 psi, or 100,000 psi or even 50,000 psi, it can burst pipes and
disrupt foundations.

Robert Erck
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Clayton,

This is a really tough question. We all know the force is "big" -- but to
quantify how much is tough! And even tougher to design an experiment!

After more than an hour of pounding my head against the wall trying to find
where the liquid and solid specific gravity curves meet, Ahhh... I finally
found a better answer.

OK, you probably know that there are many different kinds of ice, depending
on how the water molecules are arranged. If you put ice under very high
pressure, the atoms rearrange into a tighter arrangement. It turns out that
around 200MPa (that is about 2000 times atmospheric pressure), the density of
ice becomes lower than the density of water. So we have found one upper
bound of the pressure ice can exert, but it might be lower than that.

At some pressure below where the ice goes from "normal ice" (called ice 1H)
to the first of several exotic ices (one transition is at 0C and around
200MPa), you will have a mix of liquid water, normal ice, and 1H ice, or
more probably an unstable transition mix of the two. So the real "maximum"
force is probably somewhat less that 200MPa, although still very, very
large.

I want to be clear: this is the "maximum" force the ice "could" exert. In a
real street, where it is not contained to a constant or near-constant volume,
the forces are much less. The water can expand, and only in specific areas
does it actually exert large forces. Moreover, those forces are only exerted
over a very small distance. A water structure site I really like
(http://www.lsbu.ac.uk/water/explan2.html) claims that up to 25MPa pressures
can be generated in pipes -- but this is what happens in pipes, and is not
necessarily the full maximum possible pressure for all situations.

Now, for your second question -- how to test this. Well, I am not sure how to
test it with common every day items. A diamond anvil cell is used to create
these massive pressures (up to 210 GPa, or 210,000 MPa) in laboratories. How
it would be done easily and cheaply at home? I am at a loss. Not only would
it be difficulty technically, but safety would be an equally enormous
concern. Hopefully someone else can make a good suggestion. I can think of
lots of complicated ideas, but not many simple ones.

Hope this helps,
Burr Zimmerman
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This is not so simple a question as it appears. You can get a feel for basic 
principles from the Newton archives:

www.newton.dep.anl.gov/askasci/eng99/eng99530.htm

www.newton.dep.anl.gov/askasci/eng99/eng99532.htm

In addition, the web site:

http://www.lsbu.ac.uk/water/phase.html

goes into the question of the equilibrium pressure (force / area) and temperature 
of the solid and liquid forms of water in detail.

To summarize the conclusions extracted from the sites above:
From the phase diagram of water you can see that the water -- ice equilibrium 
line is nearly vertical, which means that if you lower the temperature from the 
"normal" freezing point (=0 C.  = 273.15 K), ice starts to form and this ice 
wants to expand, really wants to expand! So to keep the volume constant you have 
to push very hard on the ice + water. In fact, to keep both phases (you can find 
the numbers in the reference http://www.lsbu.ac.uk/water/phase.html) you have to 
apply  about 10^8 Pascals (in more common units this is about 1000 atmospheres = 
14.5x10^3 psi).

This force of expansion exceeds the strength of all but specially designed 
laboratory equipment, so what happens is the pressure (force / area) causes 
the concrete, rocks, etc. and they crack or rupture to relieve this intense 
pressure.
   
Vince Calder
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