Scaling and dynamics of washboard road

TL;DR

This study combines theoretical and experimental approaches to analyze the formation and behavior of washboard road ripples, revealing how a dimensionless ratio influences the instability and ripple dynamics.

Contribution

It introduces a scaling argument and a Froude number-like parameter to predict washboard ripple onset and movement direction in granular surfaces.

Findings

Critical speed depends on system parameters.

Ripple movement direction varies with Froude number.

A dimensionless ratio controls the instability onset.

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.