Scaling and dynamics of washboard roads.
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 described a scaling argument that 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.
Bitbol
Anne-Florence
AF
Université de Lyon, Laboratoire de Physique, Ecole Normale Supérieure de Lyon, 46 allée d'Italie, 69007 Lyon, France.
Taberlet
Nicolas
N
Morris
Stephen W
SW
McElwaine
Jim N
JN