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arXiv · 0903.4586

Scaling and dynamics of washboard road

Anne-Florence Bitbol·Nicolas Taberlet·Stephen W. Morris·Jim N. McElwaine
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Abstract

Granular surfaces subjected to forces due to rolling wheels develop ripples above a critical speed. The resulting pattern, known as "washboard" or "corrugated" road, is common on dry, unpaved roads. We investigated this phenomenon theoretically and experimentally, using laboratory-scale apparatus and beds of dry sand. A thick layer of sand on a circular track was forced by a rolling wheel on an arm whose weight and moment of inertia could be varied. We compared the ripples made by the rolling wheel to those made using a simple inclined plow blade. We investigated the dependence of the critical speed on various parameters, and describe a scaling argument which leads to a dimensionless ratio, analogous to the hydrodynamic Froude number, which controls the instability. This represents the crossover between conservative, dynamic forces and dissipative, static forces. Above onset, wheel-driven ripples move in the direction of motion of the wheel, but plow-driven ripples move in the reverse direction for a narrow range of Froude numbers.

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Anne-Florence Bitbol, Nicolas Taberlet, Stephen W. Morris, Jim N. McElwaine. 2009-06-19. Scaling and dynamics of washboard road. https://doi.org/10.1103/physreve.96.062904

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