Analytical Solution for Railway Transition Zones With Abrupt Changes in Elastic Stiffness

Abstract

Transition zones in railway systems, where properties of the track foundation change abruptly, are known to increase dynamic loads, track deterioration, and passenger discomfort. As such, it is of particular importance to study railway transition zones with abrupt changes in foundation properties to minimize these railway problems. This paper presents a closed-form solution for the long-term deformation of an Euler-Bernoulli beam on an elastic foundation with multiple abrupt changes in foundation stiffness and under multiple applied stationary point loads. The solutions are obtained by dividing the beam into segments and applying the method of undetermined coefficients. This exact analytical solution constitutes an improvement upon an approximate solution, which is presented in the literature as a recent method for modeling rail infrastructure at transition zones. A limitation of the approximate solution is its inability to account for the changed behavior of the beam close to a transition zone. The closed-form solution overcomes this limitation and can be used to assess the suitability of the approximate solution.