Monday, December 29, 2008

The thrust belt in my driveway

It's snowed a lot in the past two weeks. Somewhere around two feet of snow fell between the last day of classes and December 26. Good for ski areas, but a lot of work to shovel. Fortunately, structural geology can make all kinds of difficult labor fascinating.

When you push a shovel through a relatively thin layer of snow, it piles up next to the shovel in a wedge shape. Push the shovel along, and the wedge gets longer and thicker, but it maintains the same shape: a triangular wedge, with a consistent angle at its front end.

Photo: a wedge of folded and faulted snow in my driveway, 12/22/08.

You see similar shapes in belts of thrust-faulted rocks from mountain belts all around the world, from the Himalayas to the Canadian Rockies to the Appalachians to Taiwan:

The cross-section above is from a classic paper by Davis, Suppe, and Dahlgren (1983) that explains what's going on mechanically in these wedges. The shape of the wedge is governed by a balance of horizontal forces: the push from behind the wedge; gravity, which would tend to flatten out the wedge (by moving material from the higher back part of the wedge to the front); and the frictional resistance to sliding, which tends to keep the front of the wedge from sliding along, causing the wedge to be steeper. The other big assumption is that the wedge is always just about to fail: its internal strength exactly balances the stresses that compress it. This means that the nature of the material also makes a difference - cohesive sheets of material behave differently from loose sand.

There's a lot of underlying math behind the explanation of wedge mechanics, but the cool thing about it is that it all boils down to a pretty simple concept. If the friction at the base of the wedge and the mechanical behavior of the rock (or snow) stays the same, the wedge should maintain the same shape. It can get bigger, but the front of the wedge should keep the same angle. That simple geometry has a lot of predictive power. It tells what should happen in a mountain belt that's eroded by a lot of rain or glaciers, compared to one that's in a rain shadow. It's been used as one explanation for the exhumation of high-pressure metamorphic rocks. And it solved a long-standing problem for structural geology: how could huge masses of rocks slide along a nearly flat plane for immense distances, as had been observed in places like the Canadian Rockies.

And it turns snow shoveling into an analog modeling experiment. Take a driveway made of smooth concrete. Drive a truck over it, and pack down snow in parallel ridges. Then let it snow another couple inches before shoveling the driveway. The results of the experiment look like this:

The wedge started out small. It's hard to see the exact structure forming - are there thrust faults beneath the folds on that surface? But it formed a nice taper, and slid along fairly easily. (Note the highly rigorous descriptions of basal friction from this experiment.)

I pushed the shovel a bit more, and the wedge got longer and thicker, but kept the same shape:

But then I reached the old tire track, and it suddenly got really hard to push that shovel. And the wedge looked like this:

The taper of the wedge suddenly got steeper, at least until I got past the tire track. But by that time I was experiencing significant edge effects, both from the top of the shovel and the snowbank beside the driveway, so the experiment ended.

The different snow storms led to somewhat different wedge shapes. Over Thanksgiving, we had a couple inches of wet snow. It formed a cohesive layer, and I could see the individual fault blocks. (I even had some tear faults separating thrust faults with different offset! Unfortunately, I didn't have the camera yet.) Before AGU, we had an inch or so of powder, which compacted somewhat when I shoveled it. And on Christmas night, we had about five inches of wet, heavy snow, and I stopped doing experiments because moving it was a lot of work, and besides, it kept falling over the top of my shovel.

My students still think that snow is for skiing, not for experimenting with structural geology. But if you've got to shovel, you might as well have geeky fun at the same time.

Reference: Davis, D., Suppe, J., and Dahlgren, F. A., 1983, Mechanics of fold-and-thrust belts and accretionary wedges: Journal of Geophysical Research, v. 88, n. B2, p. 1153-1172.

Photo note: I adjusted the levels on all the snow photos, because I haven't figured out how to take good photos of snow with my new camera yet.


Anonymous said...

What an incredibly nerdy post. I loved it!

Kim said...

And I didn't even post the image I made for the structural geology exam, with thrust fault map symbols drawn all over one of the photos. (I don't think the students appreciated the question, despite their general love of snow.)

Julian said...

Ahahaha, yesss! I was eagerly awaiting your post of these images as soon as you mentioned it at AGU!
As Brian said, this is delightfully nerdy. It makes me happy.

(Also, I think I still owe you a post of those fault character things I mentioned. Yeah.)

Eddie Willers said...

Very good post actually. It is a good demonstration of thrust faluting. Now if you have a good snowpack all winter long on your lawn, and if your lawn slopes, you should have little eskers of grass clippings visible in the Spring.

Lockwood said...

Yet another terrific geo-analogy! I would love to see that structural diagram. If we get any more snow this winter, this sounds like a fun way to whle away some time. Thanks!

Andrew Alden, Oakland Geology blog said...

Next, you distribute marker beds between snowfalls (preferably NOT using birdseed) and cut cross-sections of your wedges. Darn, I wish I lived in a snowy area.

Kim said...

I'm not sure what to use for marker beds. It would need to be similar mechanically to snow, some color other than white, and not likely to dissolve in water. (I don't want to lower the melting point of the snow below the air temperature!)

Besides, for a nice controlled analog experiment, I really should just build a sandbox. (Michele Cooke has a great web page with instructions.)

Anonymous said...

So a thrust belt is a shock wave in solid materials. How interesting...

Kim said...

A shock wave would be elastic behavior, wouldn't it? A thrust belt involves permanent deformation.

Eddie Willers said...

Try spraying some food coloring on the surface. If it changes the melting point consider it a better experiment. That way your thrusting in not an a homogenous environment, more like the real thing. Or try some saw dust.

Silver Fox said...

I think this is way cool, though I'm hoping not to have to try it out any time soon!

Anonymous said...


The best description of a shock I've seen is basically that ring of water that forms when you turn on a faucet over an empty sink ( The ring (a termination shock) forms because the water outside the shock can't flow out of the way faster than water from the faucet reaches and travels through the shock. Similarly, the snow building up in front of the shovel is a termination shock because the snow just outside the pile can't get out of the way faster than the shovel and pile of snow comes at it. And this behavior is why mathematically you are right about the lack of elastic behavior.

For behavior to be elastic, it has to have two characteristics. The forces related to these stresses obey energy and momentum conservation in a way that is restorative. The medium tries to return to its undeformed state in order to minimize the overall potential energy density due to stresses in the medium. Elastic behavior would mean that when you remove the shovel, internal forces tend to lay the snow back down where it was before you started shoveling. This is the minus sign in Hooke's law.

Second, stresses and strains in a medium are linearly related each other. If it ain't linear, it ain't elastic. You'd have to push on the shovel twice as hard at 2 meters as you pushed on the shovel at 1 meter, just to keep everything from moving backward and undoing your efforts.

Shocks don't show this restorative linear relationship between stresses and strains across the shock, so you're right, they aren't elastic.

erwini said...

wow, so nerdy that i love it!

reminds me of Leslie Winkle on 'The Big Bang Theory'

Anonymous said...

I really liked the post, however.... If you look closely at the first photo it appears that the snow is piling up and over itself in the direction of the compressional force (snow shovel), in essence "reverse thrusting". Typical thrust sheets in the Canadian rockies and like the example diagram of Taiwan detatch at a decollement and the thrust rides forward away from the compression force and over itself in the opposite direction of the photo. Or so it appears to me from the photos.

Kim said...

Phil -

When the snow was more cohesive, the faults generally dipped towards the "hinterland" (in my case, the shovel), like they do in typical thrust belts. The first photo was of pretty dry, fluffy snow, and I have trouble recognizing faults (as opposed to what look like surface folds) in it. I think the lighting may make it look as though the shovel-facing limbs of the surface folds look steeper than they are - I think the folds were pretty symmetrical. (But I was juggling a shovel and a camera, so I'm not sure.)

Also, I couldn't take pictures and keep the shovel moving at the same time, so the photos all represent times when the motion stopped. (And I got some tensional features if I accidentally let the shovel fall. Probably not a good analog for extensional in compressional environments, though.)

Mike said...

Is this the same effect we see with google earth on the eastern shore of central and south america? Here South of Natal Brazil 6° 1' 59.86" S 35° 7' 31.99" W and Along the Nicaragua - Costa Rica border on the Atlantic 10° 51' 26.69" N 83° 37' 0.69" W

Anonymous said...

This is ABSOLUTELY PHENOMENAL! I OBSERVED THE VERY SAME THING when I shoveled after the recent VERY WET snow in Denver on March 24th. But I FAILED to take photos! Thank you Kim for verifying my observations! I have sent your site over to Ned Sterne who is our local "thrust fault" expert so he can see your photos and use them in his talks!!!