Shakedown solutions for ballasted track structure under multiple uniform loads

Abstract

Abstract Shakedown analysis method is attractive in calculating the bearing capacity of structures under repeated loads with a large number of cycles. This paper firstly introduces an equivalent Finite Element (FE) model to simulate the ballasted track structure, whose results of elastic stress field were calibrated against those obtained by the full three-dimensional (3D) model, so as to reach an optimum balance between the accuracy and consumption of the numerical simulation. By representing the wheel loads as equivalent uniform loads acting on the ballast layer, an analytical lower-bound shakedown solution is developed to determine the capacity of a half-space subjected to multiple uniform loads, and is further extent to shakedown analysis of ballasted track structure. The required elastic stresses in shakedown analysis are derived analytically for homogenous half-space, while are acquired numerically based on the equivalent FE models. The parametric study on the basis of the proposed shakedown solution is finally performed by introducing the envelope diagrams of shakedown limit, to investigate how the properties and thickness of the materials affect the shakedown limit of ballasted track structure under multiple uniform loads, whose conclusion may provide reference for the optimized design of ballasted track structure subjected to repeated moving train loads.