A Computational Approach to Smoothen the Abrupt Stiffness Variation along Railway Transitions

Abstract

This paper presents a novel approach to smoothen the abrupt stiffness variation along railway transitions and provides a step-by-step design of a multistep transition zone comprising adjoining segments with changing stiffness values. The influence of stiffness on track dynamic response applied to transition zones is investigated analytically, considering a beam on an elastic foundation. Vertical track displacements for varying stiffness values under different combinations of axle loads and speeds are calculated analytically and numerically, and they are found to be in good agreement. The results indicate that stiffer tracks undergo less settlement compared to those having a smaller stiffness. The effect of abrupt stiffness variation at transition sections is analyzed under four-carriage loading that causes considerable differential settlement, which is further exacerbated by increased train speeds. A mathematical process is introduced to determine the optimum stiffness of each segment to ensure a gradual change in stiffness while minimizing the corresponding differential settlement. The proposed methodology is further validated through the finite element modelling approach and worked-out examples epitomizing the effects of stiffness variation along the number of transition steps. From a practical perspective, this study provides a significant extension for design rejuvenation of transition zones by minimizing the differential settlement at any two consecutive transition segments.