On permanent long-wave distortions of a railway track due to the moving vehicle load

Summary

 The paper presents a simple mathematical model which describes the evolution of the vertical profile of a railway track caused by the load arising from moving vehicles. Owing to the fact that the track ballast is not perfectly elastic, each passage of a train is accompanied by a residual deformation of the ballast. Being very small, these deformations, however, accumulate with time. It is shown that an initial imperfection in the vertical profile of the track will either grow or diminish after each passage. For given track and vehicle, the rate of growth is determined by the characteristic length of the imperfection and by the velocity of the vehicle.