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Game of Thrones: Engineering The Wall

Game of Thrones: Engineering The Wall

Today sees the end of Game of Thrones for another year. If you don’t watch it- start now; aside from being a fantastic slide-show of the Irish countryside, and tour de force of British actors, it’s also an epic fantasy that makes Lord of the Rings look like a cure for insomniac children.

To commiserate I thought I’d take a look at one of the most impressive structures in the whole of the Seven Kingdoms (spoiler free, of course). Forget the gilded fortifications of Kings Landing, or the castle of Winterfell- I’m talking about The Wall.

Our wall is going through the ‘giant-ice-structure’ equivalent of fatigue. Tiny cracks are forming each time the wind blows, which could, over numerous cycles, form a failure plane.

For those of you who don’t know, The Wall is, well, a wall (-obviously), 300 miles (482 km) long, 700-800 feet (213-244 m) tall and made entirely of ice. Although not specified explicitly, it is known that the wall is wide enough at its peak to fit “a dozen mounted knights to ride abreast” (isn’t the Internet amazing…). As a dozen horses are the width of six British railway gauges, we’re looking at a top width in the region of 8-10m.

For once, we’ve got at a structure within the realms of probability: the Bur Al Arab is 322m tall, the Wall of China was 13,171 miles long, and there are man-made structures of ice. The concern, however, is the combination of all these aspects…

Ice is actually a little less dense than water (which is weird), but for the sake of the maths let’s leave the bulk unit weight at the famous 10kN/m3, which makes the total stress (from self-weight) at the bottom of the structure somewhere in the region of 2.2 MN/m2. From a surprisingly interesting paper (discussing the use of ice to create a giant ‘berg-ship‘) it turns out that the ice at the foundation should be perfectly fine with this (~25% utilization).

The bigger concern, however, is wind. Unfortunately Westeros has been omitted from the Eurocodes, which is just as well given how much of a pain the backside EC Wind loads are to calculate. Making the massive assumption that blizzard and snow-storm winds are comparable, this slightly dubious source (comment if you’ve got a better one,) puts the wind pressure in the region of 0.622 kN/m2.

Taken over a unit meter the wall is safe from over-turning by a factor of ten, which is reassuring- and it’s probably alright to assume that it won’t go sliding away anytime soon. The stresses created by the wall bending cause the maximum compression (our wall doesn’t go into tension, it seems) to reach 3.4 MN/m2. While this is still within the working range of ice (~40% usage), it does move the material well within the brittle/ductile behaviour zone.

So what does that mean? It means that our wall is going through the ‘giant-ice-structure’ equivalent of fatigue. Tiny cracks are forming each time the wind blows, which could, over numerous cycles, form a failure plane. There is a saving grace, however; exposed ice is self-healing if it is given a chance to anneal. Luckily the cycle of day and night provides a chance for water to fill and heal these cracks and the ice to release the stresses caused by the wind.

Before I declare The Wall structurally sound (a first, since I started looking at fantastical structures) it is worth noting that the ultimate destruction of the wall will come from slump. Given the Wall’s erosion through sun and wind, the plastic flow of the fatigue and annealment cycle, and how thin it is; it seems safe to assume a fairly fast glacial flow. Given that Greenland’s Jakobshavn Isbræ is moving at 20-30m per day, even assuming a slow ’1 m/day’ flow doesn’t give our Wall a life-time longer than a year.

Let’s hope whatever’s on the other side isn’t very patient…

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  1. Yonadav Shavit

    Does the glacial flow take into account the fact that it’s getting colder, approaching winter?

    • No, it looks like he’s just eyeballed it. Glacial flow is the wrong method though – since the glacier is driven by the miles of ice +snow packed in above it along the flow path.

      Better off looking directly at creep, that would give you a steady bulging flow at the base, kinda like a wall made out of jelly scaled up. Check out: goo.gl/QjSJU and goo.gl/yIWQ9

      (Ed. Shortened links.)

  2. Andrew

    Glacial flow is not an issue here I think. It’s not a glacier. It’s a built structure. If you were to build this the obvious method would require a water source (non salt) and a constantly sub zero temprature. Not sure if it would need forms to hold the water – presumably if it’s cold enough you could do without.

    We could do this today with technology as simple as pumps in the right location. Of course with magic anything is possible, but this structure at leasts looks plausible.

  3. It’s pretty interesting to see a bit of a discussion on this- especially because (as you can imagine) most of this article is based on a ‘back of a fag-packet’ calculation!

    Glacial flow was (strangely!) absent from my engineering education, but as I understand it the ‘flow’ is actually relatively fast creep. If you check this out: http://www.wired.com/wiredscience/2013/03/game-of-thrones-ice-wall-science/ you’ll see that I’m not the only person to be concerned about the wall simply flowing away!

  4. Chen

    One of the biggest things I think that got left out is the wall is not made entirely of ice. The rangers use gravel and ice at the top of the wall. I don’t think anything was said about when they stared this but that would ad a lot of weight and possibly strength. And another thing I was thinking was the cracks that form, assuming the bulk of the wind comes from the north would lead to an eventual leaning of the wall from the cracking, filling, freezing cycles. But in the end, this is all hypothetical but very interesting none-the-less.

    • I was wondering if your you think having stone in there would actually make it any better?

      I’m guessing this means it’s almost a masonry-like structure, with the ice acting as mortar; if so the additional weight (say stone is 2.5x the density of water) would be enough to cause the ice to fail at the base. I also had the impression that under additional weight the creep/flow will actually increase, especially as the sheet width will be smaller and cracks will be able to propagate quicker…

      If, instead, it’s a gravel fill; the vertical face means that the ice will essentially be retaining a 700ft gravel structure, and at a guess I’d expect this to be unfeasible.

      Obviously- there’s always magic!

      Thanks for the comments, as well; it’s fun writing these- but it’s been even more interesting reading the discussions (both on here, and reddit).

      • Andy Taylor

        No, not a masonry like structure, more of a mass concrete structure, where the cement is replaced by ice.

        I’ve only really read the books, not seen much of the TV series, and I’m not sure about the straight verticality of the wall. I’ve always assumed it to have inclined faces, which would at least reduce the pressure at the base somewhat. I’d have expected it to have counterforts on the southern side too.

        But anyway, many thanks for the article, great fun to read.

  5. Evan Thomas

    Personally, I don’t the “slump” would limit the life’s wall. Pretty sure I remember there being descriptions of a northerly wind. If cold wind is perpetually delivering moisture in the form of snow/sleet, the wall is essentially continually growing as long as the volumetric moisture deposition rate > melt rate.

    What about the ground beneath the ice? On a particularly warm summer day, the amount of melt would turn the ground beneath the wall into absolute slush.

    • Although with slump it’s not the volumetric loss; but the flow as the structure yields and heals at a micro-crack level. I suspect the Wall would smooth, like (relatively) quick mountain falling.
      I didn’t think too much about the ground- I’m not sure if the ground heat / ice wall would reach an equilibrium, especially if the snow protects it… It’s an interesting problem.

  6. Dave

    Read the book again.
    The wall is not made if ice, it’s covered in a layer of thick ice after standing for 1000s of years in the wintery, stormy north.

    • I haven’t actually read the books (I’m waiting for the TV series to finish, as the books are _always_ better than the film!), so I had to rely on anything I could find online; which seems to suggest the wall is made of ice.

      For example:
      - http://www.thejournal.co.uk/news/north-east-news/game-thrones-writer-inspired-hadrians-7214397
      - http://gameofthrones.wikia.com/wiki/The_Wall

      You should go correct them!

    • Andy Taylor

      I don’t recall reading that in the book. So I’ve gone and done a search for “wall” on my kindle.

      The earliest quote which gives any sort of definition of the wall is 22% of the way into the book (despite being about the 20th mention of The Wall) and says: “When they finally spied Castle Black, its timbered keeps and stone towers looked like nothing more than a handful of toy blocks scattered on the snow, beneath the vast wall of ice.”

      Added to that, the Builders in the Nightwatch add to the wall by chucking gravel (and water?) on it.

      So, I think it is a wall of ice, rather than a masonry wall which has become coated in ice.

  7. Ward Davis

    But when the winter comes, and there is a year without sun, the ice will not anneal, and the wall will shatter as the north wind blows, and the white walkers will tread over your folly of not considering local geological conditions, and the Starks (like Canada) will require one year of cold weather design experience before certification henceforth.

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