Corrugation of roads

We present a one dimensional model for the development of corrugations in r oads subjected to compressive forces from a flux of cars. The cars are mode led as damped harmonic oscillators translating with constant horizontal vel ocity across the surface, and the road surface is subject to diffusive rela xation. We derive dimensionless coupled equations of motion for the positio ns of the cars and the road surface H(x, t), which contain two phenomenolog ical variables: an effective diffusion constant Delta (H) that characterize s the relaxation of the road surface, and a function a(H) that characterize s the plasticity or erodibility of the road bed. Linear stability analysis shows that corrugations grow if the speed of the cars exceeds a critical va lue, which decreases if the flux of cars is increased. Modifying the model to enforce the simple fact that the normal force exerted by the road can ne ver be negative seems to lead to restabilized, quasi-steady road shapes, in which the corrugation amplitude and phase velocity remain fixed. (C) 2001 Published by Elsevier Science B.V.