Rippled Roads - the granular physics of washboards

Leaving the tarmac, anywhere in the world, is liberating. For a geologist, a dirt road is often the highway to fieldwork and all its pleasures, satisfactions, frustrations, and challenges. You set out, going through in your mind the plan for the day, with the window down and a rapidly growing sense of isolation and freedom; the road is good and straight, and you speed up, the hills in which the day's challenges lie coming increasingly into focus, that one outcrop that will reveal all beckoning you on - and then, suddenly, there they are in front of you, corrugations, a washboard road, the strange behaviours of granular materials rearing their ugly heads. You slow down, and it's excruciating, both physically and mentally. To avoid this, there are two choices, the first to drive at a glacial pace, around four feet a fortnight or so it seems. This is, of course, intolerable, so you elect for the more thrilling approach - you accelerate to the point where the washboard only generates a sort of background massaging vibration as you fly over the corrugations with little or no traction at all, dry aquaplaning in the clouds of dust.

I did years of fieldwork in the glorious lonesome country of the northern Nevada basin and range; it was some of the most enjoyable time that I've spent in the field, but boy did I get to know washboard roads. Entire stretches of road across the broad valley floors would be smooth, only isolated stretches corrugated, or the whole journey would be over a washboard. Why does this happen, inevitably, to dirt roads (and train tracks and ski runs, for that matter)? The corrugations look like ripples in the sand, regularly spaced, asymmetric, and of a constant bone-shaking amplitude. Conventional wisdom for a long time decreed that it was all to do with driver behaviour, vehicle speed, characteristics of the suspension and tires, weight, wind, and the grain sizes of the gravel and sand used on the road. But then why are the corrugations so uniform? And why, despite many attempts, did the design of a non-washboarding road elude the best engineering minds? Well, it turns out that the phenomenon is quite simple, and like anything to do with granular materials, at the same time immensely complex. Back in 1993, Keith Mather, former director of the Geophysical Institute at the University of Alaska, Fairbanks, reported on a simple experiment that demonstrated that the corrugations build spontaneously in a bed of sand, however apparently smooth the starting surface, when a simple wheel rolls continuously over it (http://www.gi.alaska.edu/ScienceForum/ASF12/1291.html).

Then, a couple of years ago, a team from the Universities of Toronto and Cambridge published the results of an again simple experiment and quantitative numerical simulations of what is going on. In the experiment, they simply rolled a free-floating hard rubber wheel around and around a circular bed of smooth sand (photo, right). Above a critical velocity (around 1.5 meters per second, an intolerable 3.5 miles an hour), ripples developed spontaneously and spread around the circumference of the sand, migrating in the direction of the wheel's motion, but retaining a regular amplitude and frequency. They repeated the experiment with different materials, different ranges of grain sizes and demonstrated that these make no difference, and that compaction and segregation have nothing to do with the result. Using the mathematical modelling approach of the "soft-particle Discrete Element Method" (beyond my skills to explain further, but see the references below), they replicated the experimental results and were able to analyse the internal structures and evolution of the ripples (illustration below).

Washboard roads are the result of the spontaneous - and bizarre - behaviour of granular materials; if it's any consolation as you shake yourself and your vehicle to pieces, the physics involved is, once again, non-linear and driven by power laws (see the January 11 post, "Granular stuff, earthquakes, and power laws - again").

Of course, no awareness of non-linear granular physics would have changed what happened to me on a washboard road many years ago. It was dusk, after a good day's fieldwork, and I was heading back to my motel room in Battle Mountain, driving fast over the corrugations, a shower and a beer, and maybe a game of pool, all luring me on. In the gathering gloom, I saw too late the shallow ditch excavated across the road in front of me. I hit it full tilt, hammering my head into the roof, and the truck took to the air, coming down with a crash and two exploded tires. Fortunately, as was my quite sensible habit, I had two spare wheels with me. The beer was somewhat delayed. 

[Details of the research, including videos, see the website, from which the illustrations are taken,  http://perso.ens-lyon.fr/nicolas.taberlet/washboard/, and the complete pdf at http://www.physics.utoronto.ca/~nonlin/preprints/TMM07.pdf. There is also a good Science News summary: http://www.damtp.cam.ac.uk/user/jnm11/media/sciencenews-2007-08/www.sciencenews.org/articles/20070818/fob7.asp.]

Comments

[BrianR]

Great post ... once again, your writing style motivated me to read the entire post (not a trivial thing in this day and age); so, I am now going to have to pick up a copy of 'Sand'. After reading, I'll make sure to put together a review blog post.

This is fascinating stuff ... as a sed geologist, me and my cohorts have had countless conversations about the origin of this phenomenon while out in the field.

Regarding power laws, I guess I would say that these relationships are *described* by a power law rather than *driven* by them ... I just don't think we have a good handle yet on why the power-law relationship (when it is truly there) pops up again and again. I recommend Mark Buchanan's book 'Ubiquity' for a popular treatment of the subject.

[Sandglass]

Thanks for the comment and reading time devoted! You're absolutely right about power laws - they show up everywhere and yet we really don't know why (I was just watching a program that showed how the distribution of resonance frequencies of a glass sphere when struck by a steel ball parallels the distribution of prime numbers - these things are all so wondrously mysterious). So yes, "described" would be better - I guess I just had driving in my mind as I was writing. I've read the Ubiquity book - good stuff - I would highly recommend Per Bak's "How nature Works" in the same vein.

And a review of my book would be greatly appreciated!

[Steve Gough]

Wow--for many years I've wondered if gravel road washboard had anything in common with ripples in flowing water, and sure enough, at http://perso.ens-lyon.fr/nicolas.taberlet/washboard/, I see the Froude equation, which is exactly the same relationship that describes ripple and dune formation in riverbeds. Thanks.

[Sandglass]

Steve - I'm pleased this was of interest and that the Froude equation (which at some remote earlier stage of my life I knew more intimately than I seem to do today) continues to demonstrate its versatility!

I followed up and went to your website - the stream tables are great and I found myself totally absorbed with the videos.