I drive about 30,000 miles per year on “Improved Roads” in the Nevada desert for work. I cant speak to the science behind it, but from my anecdotal 10 years of experience it has a lot to do with wheel slippage.
The roads I drive on are mostly just the natural dirt hit with a grader blade to defoliate and level them out. The more problematic areas of caliche and dry lake beds where it floods are improved with gravel taken from the surrounding area.
Every time someone driving on these roads accelerates or stops quickly, their tires slip a little. It may not even be perceptible but all it takes is a little bit of material thrown or pushed either way to create a high spot. You see this mostly in and out of turns where most braking and accelerating occurs. Now every time another tire hits that high spot, it bounces a little and when it hits the ground again, it moves more material. This happens over and over until its a big rutted nasty washboard of a road.
Like someone else said in another comment, washboard roads are uncomfortable so people will move to either side to avoid it and create more washboards.
Another thought I had was that the majority of the traffic on our roads are from solid axle vehicles so a bump on one side of the road can affect the opposing side tire as well
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